1987 - virginia tech · 2020. 9. 28. · photovoltaic output expected to occur at certain lead...

IRRADIANCE FORECASTING AND DISPATCHING CENTRAL STATION PHOTOVOLTAIC

POWER PLANTS

by

Badrul Hasan Chowdhury

Dissertation submitted to the Faculty of the

Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

1 )(r~n7G. Phadke

Subhash C. Sarin

in

Electrical Engineering

APPROVED:

tSaifur Rahman, Chairman

August, 1987

Blacksburg, Virginia

loannis. M. Besieris

Charles E. Nunnally

IRRADIANCE FORECASTING AND DISPATCHING CENTRAL STATION PHOTOVOLTAIC

POWER PLANTS

by

Badrul Hasan Chowdhury

Saifur Rahman, Chairman

Electrical Engineering

(ABSTRACT)

This dissertation introduces a new operational tool for integrating a photovoltaic (PV) system

into the utility's generation mix. It is recognized at the outset, that much of the existing

research concentrated on the central PV system and its operations have concluded that

technical problems in PV operation will override any value or credit that can be earned by a

PV system, and that penetration of a PV plant in the utility will be severely limited. These are

real problems and their solutions are sought in this dissertation. Judging from the drawbacks

of the static approach, it is felt that a new approach or methodology needs to be developed

which would give a central station PV plant its due share of credit. This dissertation deals

mainly, with the development and implementation of this new approach -- a dynamic

rule-based dispatch algorithm which takes into account the problems faced by the dispatch

operator during a dispatch interval and channels those into a knowledge base.

The new dynamic dispatch requires forecasts of photovoltaic generations at the beginning of

each dispatch interval. A Box-Jenkins time-series method is used to model the sub-hourly

solar irradiance. The irradiance data at any specific site is stripped of its periodicities using

a pre-whitening process which involves parameterization of certain known atmospheric

phenomena. The pre-whitened data series is considered stationary, although some

non-stationarity might be introduced by the discontinuities in the data collection during night

hours. This model is extended to yield forecast equations which are then used to predict the

photovoltaic output expected to occur at certain lead times coinciding with the economic

dispatch intervals.

An rule-based (RB) dispatch algorithm is developed in this dissertation. The RB is introduced

to operate as a substitute for the dispatch operator. Some of the dispatcher's functions are

routine jobs, while some require specialized knowledge or experience. The RB is given these

two qualities through a number of rules. This algorithm works in tandem with a conventional

economic dispatch algorithm. The functions of the two are coordinated by another algorithm

which oversees the now of information and records them.

The RB gives one of 16 possible solutions as and when required. These solutions are written

as rules which manipulate the non-committable generation to achieve an optimal solution. The

RB system during its operation supervises the fact that the PV generation are kept at the

maximum level possible under all constraints. The case study revealed that the thermal

generating units which are scheduled by the unit commitment are able to absorb most of the

small to medium variations present in the PV generations. In cases of large variations during

a single interval, the thermal generators reach their response limits before they can reach

their maximum or minimum generation, thus causing mismatches in the load and generation.

The mismatches are then picked up by the non-committable sources of generation, comprised

of pumped storage units, hydro generation plant, or by interconnection tie-lines. If none of

these are sufficient, changes are made in the PV generation schedule.

It is concluded that results depend on the time of the year and the specific utility. The time of

the year information is reflected in the load demand profile. Most utilities in the U.S. have

single peaks in summer and double peaks in winter. Also, the time of the peak load

occurrence, varies with season. The utility generating capacity mix influences the results

greatly.

Acknowledgements

It gives me great pleasure to write this piece mainly because it does not contain any equations

or any technical jargon. Writing this small section also means that the job I had set out to do

some years ago, is now almost complete. I can actually see a streak of sunshine at the end

of the tunnel.

It has been my privilege and honor to have been associated with Dr. Saifur Rahman at Virginia

Tech. He has been my advisor, mentor, guide and friend for the past few years. My research

was initiated under his kind supervision, some six years ago. His persistence, insight and

devotion to research has helped me build my character. I am grateful to him for the support

he has shown me and the independence he has allowed me in structuring my research. Now,

that I move along into my own career, his ideals will always serve as a guiding light.

I would like to thank Dr. Arun Phadke, Dr. Charles Nunnally, Dr. loannis Besieris and Dr.

Subhash Sarin for serving on my committee. Their constant encouragement and interest in

my work has helped me a great deal. I have pestered them on so many occasions, the

runaway winner being the scheduling of my defense on a weekend. But everyone had

accommodated me without the slightest hint of objection.

Acknowledgements Iv

This dissertation is the product of years of struggle. Struggle with the research, with the mind

and body and in certain ways, the amazingly capricious phenomenon called the computer. A

lot has been said and done about the computer and I shall leave it at that. I will only remark

that it is a wonderful feeling, now that I have the final product in my hands.

It would be remiss, if I did not mention my fruitful association with the department. When I look

back to the days when I had my first days of classes, everything seemed distant and

unfriendly. Over the years, the relationship has grown. After my offices had moved from

temporary cubicles in various buildings on campus, I finally got a nice little room in an

expanded Whittemore hall. Now that I am getting ready to part from this relationship, I have

only fond memories.

I have been involved with the Energy Systems Research Laboratory in this department, since

its infancy. I have therefore developed a special feeling toward it. I extend my thanks to all the

people associated with the laboratory.

Finally, I would like to take this opportunity to express my deep gratitude to my wonderful

parents who have stood by me through thick and thin. They have been a constant source of

strength and motivation for me. I also thank the other members of my family, all of whom have

shown me great support and love.

Acknowledgements v

Table of Contents

Introduction • • • • • • . . • • • • . . • . • • • . . . • • • . . . • . • • . • • . . • • • . • . • . • • • . • . . • • • . . . . • 1

1.1 Historical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Present PV Status & Future Trends ...................................... 3

1.3 Central Station Photovoltaics ........................................... 4

1.3.1 Utility Point of View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3.2 Economics ...................................................... 6

1.3.3 Operating Characteristics .......................................... 7

1.4 PV Dispatchability ................................................... 9

1.5 Resource Forecast .................................................. 11

Recent Advances In Utility Integration . • . . . . • • • • . • • . . • • • • . . • • • • . • • . . • . . • . . . • . 12

2.1 Systems Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2 Operational Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3 Planning and Reliability Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.4 Economic Dispatch With PV Plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Table of Contents vi

Optimizing PV Output in the Utility • . . . . . . . • • . . . . • • • • • • . . • . . . • • • • • . • • • • . . • . . . 39

3.1 Array Orientation Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.1.1 South-facing array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.1.2 Optimal-Surface-Azimuth Oriented Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.1.3 Two-axis Tracking Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.2 PV Performance Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.2.1 Translation of Horizontal lrradiance on the Plane of Array . . . . . . . . . . . . . . . . . 52

3.2.1.1 Liu and Jordan Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.2.1.2 Duffie and Beckman Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.2.1.3 Klucher Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.2.1.4 Perez Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.2.1.5 Results of the Comparative Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.3 Energy Storage With Central Station PV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.3.1 Potential For A Combined Photovoltaic/Battery System . . . . . . . . . . . . . . . . . . . 64

3.3.2 Battery Plant Consideration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.3.3 PV/Battery Operating Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.3.4 Comparative Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

3.3.5 Relative Performance of Array Orientation Strategies . . . . . . . . . . . . . . . . . . . . 76

Resource Forecast . . . . . • . • . • . . . . . • . . . • . . • . • • . • • • . • • • • • • • . . • • . . . • . . . • . • • . 82

4.1 Background Information .............................................. 83

4.2 Time Series Modeling in lrradiance Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.2.1 Choosing the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.2.2 The Pre-whitening Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.2.2.1 Parameterization for the Prewhitening Process . . . . . . . . . . . . . . . . . . . . . . 88

4.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

4.3.1 Predicting the Output from a Photovoltaic System . . . . . . . . . . . . . . . . . . . . . . . 93

4.3.2 Programming Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

Table of Contents vii

4.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

4.4.1 Identification of the ARIMA Model (p,d,q) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

4.5 Conclusions on the Forecast Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Unit Commitment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

5.1 Solving the Unit Commitment problem .................................. 119

5.2 EPRl's Unit Commitment Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

5.2.1 Input Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.2.2 Priority List Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.2.3 Hourly Generation Maximum Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

5.2.4 Reserve capacity From Non-committable Sources . . . . . . . . . . . . . . . . . . . . . . 122

5.2.5 Precommitment of Peaking Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

5.2.6 Hourly Regulation Requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

5.2.7 Committable Unit Commitment Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

Economic Dispatch .•••••.••.•••.••.••.••••••••••••••••••••••••...•..•. 126

6.1 AGC and Economic Dispatch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

6.1.1 Load Frequency Control .......................................... 131

6.2 Formulating the Economic Dispatch Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

6.3 Solving the Economic Dispatch Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

Implementing PV Dispatch in a New Economic Dispatch Algorithm •.••.•.••...••.. 138

7.1 Need For a New Approach to Economic Dispatch . . . . . . . . . . . . . . . . . . . . . . . . . . 138

7.2 Proposed Rule-based System Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

7.2.1 Present Functions of the Dispatcher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

7.2.2 A Rule Base Replacing the Dispatcher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

7.2.2.1 PV Dispatch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

7.2.3 Rules in the Rule Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

Table of Contents viii

7.3 Programming Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

7.3.1 Interface With EPRl's GPUC Program ................................ 156

7.3.2 Interface With the Solar Resource Forecast Program . . . . . . . . . . . . . . . . . . . . 159

7.3.3 The Dispatch Combined With the RB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Case Study: Results . . . . • . . . . . • . • . • • . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . • . 164

8.1 Continuous Simulation Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

8.1.1 Generator Data ................................................ 166

8.1.2 Load Data .................................................... 166

8.1.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

8.2 Effect of PV Penetration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

8.3 Static Versus the Dynamic Dispatch Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

Summary and Recommendation 191

9.1 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

Bibliography . . . . . . . • . . . . . . • . . . • . • . . . . . . . . . • . . . . . . . . . • . . . . . . • . . . . • . . . . 198

Solar Geometry . . . . . • . . . . . . . . . . . • . . . . . . . . . . • . . • . . . . . . . . . . . . . . • . . . . . . . . 216

Selected Input-Output for Dispatch Model . . . . . . . . • . . . . . . . . . . . . • . . . . . • • . . . . . . 221

Sample Run . . . . . . . . . . . . . . . . . . . • . . • . • . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . 231

Vita . . . . . . • . • . . . . . . . . . . . . . . . . . • . . . . . . . . . . • . . . • . . . • . . . . . . . . . . . . . . . . • . 255

Table of Contents Ix

List of Illustrations

Figure 1. Utility Integration Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Figure 2. System simulation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Figure 11.

Figure 12.

Figure 13.

Figure 14.

Figure 15.

Figure 16.

Solar irradiance components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Position of the sun relative to an inclined plane . . . . . . . . . . . . . . . . . . . . . . . 42

Array orientation options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

PV output comparisons for fixed tilt, azimuth-optimized and fully tracking arrays for August at Raleigh, NC ....................................... 46

PV output comparisons for fixed tilt, azimuth-optimized and fully tracking arrays for November at Hesperia, CA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Functional blocks in a PV simulation model . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Battery capacity requirement for percent peak load supplied. Site is Raleigh, NC ........................................................ 68

Battery capacity requirement for percent peak load supplied. Site is Hesperia, CA ........................................................ 69

Comparison of depth of charge and discharge of battery with and without PV power at Raleigh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

The simulation process to forecast global irradiance . . . . . . . . . . . . . . . . . . . 94

Execution of the FORECST module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

ACF of March Data in Raleigh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

ACF of the Differenced Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

PACF of the Differenced Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Figure 17. ACF of the residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Figure 18. Global irradiance comparison at Raleigh in March 107

List of Illustrations x

Figure 19. PV output comparison at Raleigh in March . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Figure 20. Global irradiance comparison at Raleigh in June . . . . . . . . . . . . . . . . . . . . . 109

Figure 21. Global irradiance comparison at Richmond in March . . . . . . . . . . . . . . . . . . 110

Figure 22. lrradiance comparisons with updates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Figure 23. A case of model inaccuracy. . ................................... 113

Figure 24. A four-level hierarchy in production control . . . . . . . . . . . . . . . . . . . . . . . . . 117

Figure 25. Relationship of unit commitment to other programs in the control center . . . 118

Figure 26. AGC and economic dispatch functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

Figure 27. System frequency characteristic versus tie-line flow 133

Figure 28. The three computer modules in the proposed operation scheme . . . . . . . . . 144

Figure 29. Operational scenario with PV system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

Figure 30. Rule-set 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Figure 31. Rule-set 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

Figure 32. Rule-set 8

Figure 33. Functional properties of the new dynamic economic dispatch

Figure 34. Components of unit commitment

Figure 35. Execution of the DRIVER module

154

157

158

160

Figure 36. Information exchange in the three modules . . . . . . . . . . . . . . . . . . . . . . . . . 162

Figure 37. Continuous simulation run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

Figure 38. Sample modified load profile and PV output for a day in January . . . . . . . . . 169

Figure 39. Effect of PV output on thermal generation . . . . . . . . . . . . . . . . . . . . . . . . . . 177

Figure 40. Effect of PV output on combustion turbine generation . . . . . . . . . . . . . . . . . . 178

Figure 41. Effect of PV output on spinning reserves

Figure 42. Effect of PV output on system lambda

Figure 43. Effect of PV output on production costs

179

181

182

Figure 44. Effect of PV output on some specific thermal units . . . . . . . . . . . . . . . . . . . . 183

Figure 45. Effect of PV output on some specific CT units . . . . . . . . . . . . . . . . . . . . . . . . 184

Figure 46. Effect of PV penetration on system production cost . . . . . . . . . . . . . . . . . . . 188

List of Illustrations xi

Figure 47. Position of the sun relative to an inclined plane . . . . . . . . . . . . . . . . . . . . . . 217

Figure 48. Generator input data {Generating unit identification) 222

Figure 49. Generator input data {Generating unit performance characteristics) . . . . . . . 223

Figure 50. Generator input data {Generating unit cost data and hourly load) 224

Figure 51. Unit commitment output used as input to the model {Generator unit schedule) 225

Figure 52. Unit commitment output used as input to the model {Partial CT generation data) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

Figure 53. Generator response rates

Figure 54. Partial thermal generator output during simulation

Figure 55. Sample of model output at each interval

Figure 56. Sample of model output at each interval ............................

List of Illustrations

227

228

229

230

xii

List of Tables

Table 1. Some Characteristics of the Four Models ............................ 60

Table 2. Ratio of lrradiance in Raleigh, NC and Orlando, FL . . . . . . . . . . . . . . . . . . . . . 61

Table 3. Ratio of lrradiance in Hesperia, CA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Table 4. Peak shaving characteristics in the four seasons for typical utility in the south-east (assuming 7000 MW annual peak). . . . . . . . . . . . . . . . . . . . . . . . . . 73

Table 5. Peak shaving characteristics in the four seasons for typical utility in the west (assuming 7000 MW annual peak) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Table 6. Comparisons of the three PV array orientation strategies for the south-eastern utility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Table 7. Comparisons of the three PV array orientation strategies for the western utility. 80

Table 8. Fitted ARIMA (p,d,q) Models in Raleigh, NC. . . . . . . . . . . . . . . . . . . . . . . . . . 105

Table 9. Fitted ARIMA (p,d,q) Models in Richmond, VA.

Table 10. Thermal generator data for the synthetic utility

106

167

Table 11. Combustion turbine generator data for the synthetic utility .............. 168

Table 12. System operation without PV during 1st time period ................... 171

Table 13. System operation without PV during 2nd time period ................... 172

Table 14. System operation without PV during 3rd time period . .................. 173

Table 15. System operation with PV during 2nd time period ..................... 174

Table 16. System operation with PV during 3rd time period ..................... 175

Table 17. System regulation limit violations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

Table 18. System operation summary with and without PV . . . . . . . . . . . . . . . . . . . . . . 186

Table 19. Static versus dynamic dispatch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

List of Tables xiii

CHAPTER 1

Introduction

Solar photovoltaics is now an acceptable form of power generation. The clean, simple and

renewable nature of this type of generation is highly desirable, particularly in the context of

depleting conventional fossil fuel resources. Photovoltaics can provide power for electric

utilities, homes, boats, water pumping, and small electronic consumer products. Tremendous

progress has been made in developing PV as a cost effective electrical option for many

diverse applications.

1.1 Historical Perspective

Photovoltaics (PV) has come a long way since being a mere laboratory curiosity in the

1950's,when the Silicon solar cell was discovered at Bell Laboratories in New Jersey. The

beginning of the Space Age in the late 1950s was also the beginning of extensive research

and development into the photovoltaic device. Space satellites needed a light weight, long

Introduction 1

lasting energy source. Photovoltaics were an ideal match to this need, depending only on the

sun for fuel. The age of the PV power source in space began with the launching of the

Vanguard satellite.

Photovoltaics quickly proved themselves to be an ideal source for earth and extraterrestrial

applications. Research improved the device performance and decreased weight. By the early

1970's, large arrays were being developed. While proven as an energy source for space,

photovoltaic cells still remained too expensive for terrestrial use. It was not until the oil

embargo of 1973, that the current program to develop a terrestrial energy source began in

earnest. In the short time since that beginning, tremendous strides in efficiency, reliability and

cost effectiveness have been made. PV is now cost-effective over a wide range of applications

and shows promise for becoming a major world supply source in the future. The advent of

micro-electronics industry has resulted in the use of many megawatts of photovoltaics in

millions of calculators, watches, and other small devices. Battery chargers, auxiliary power

supplies, emergency radio power sources are just some of the new applications of

photovoltaics now being brought on to the market.

Before the end of this century, PV should achieve its long-term goal of becoming a major

power source in the industrialized countries. Its promise of a clean, secure energy source,

combined with its simplicity and modularity make it ideal for future utility connected

applications. Large installations already operating in the United States have verified the

practicality of the energy source. Systems such as the first 1-megawatt (of the planned two

megawatts) installed at the electric utility at Sacramento, CA, have demonstrated that the

systems can indeed operate compatibly with the electric grid producing valuable energy.

Collector costs remain a major obstacle to large scale use of PV on the U.S. utility system.

However, the progress already made in this area has led many utilities as well as third party

investment groups to begin to investigate large scale PV systems today. As a result of these

efforts, it has been possible to verify that today's commercial collectors are extremely reliable.

Introduction 2

The first major utility connected non-utility owned photovoltaic system is the megawatt-sized

Lugo facility installed in Southern California by ARCO Solar in 1982. The plant feeds power into

the Southern California Edison's grid. Another multi-megawatt PV plant was installed by ARCO

Solar, shortly afterward (1983-84) at Carissa Plains, CA. The plant in now interconnected to the

Pacific Gas & Electric Co.

In approximately thirty years, PV has progressed from the laboratory to a proven power

source for both terrestrial and space applications. The modularity of the source allows the

same technology to power calculators or entire cities. Continued research has resulted in a

commercial technology that is used in high reliability applications in space and on earth. PV

is probably the optimal choice for a remote location where it is difficult to get fuel to, or which

may be inaccessible to utility service extensions. Provided some technological problems are

solved, PV will find increased use as a utility power source in the very near future.

1.2 Present PV Status & Future Trends

The basic principles of converting sunlight directly to electricity are well known. However,

there are many photovoltaic materials and devices and their design, fabrication, optimization

and performance vary a great deal from one photovoltaic material to another. The basic power

element of a photovoltaic system is the solar cell. Typical solar cells are made of crystalline

silicon, the material of the semiconductor revolution. Crystalline silicon technology continues

to be an important area of research and development in the photovoltaic community. Recent

achievements in increasing cell and module efficiencies point to silicon's continued potential

as a cost effective technology. Researchers have made impressive progress in identifying,

developing and optimizing new single-crystal cell structures and in improving the performance

of conventional cell structures. For example, over the past five years, the one-sun efficiency

Introduction 3

of laboratory cells has increased from 18% to 22%, while module life expectancy has

increased from less than 10 years to approximately 20 years. However, even though industry

has used the technology base to reduce module costs to less than $500/m 2, the cost of silicon

materials and of processing cells made from single-crystal wafers, remain obstacles to

achieving cost effective crystalline silicon systems for utility applications. On the other hand,

thin film technologies show considerable potential, and must be considered major

competitors. These include amorphous silicon and its alloys, copper Indium diselenide and its

alloys, and thin film, single crystal gallium arsenide. Multijunction devices in flat-plate and

concentrator systems also look like viable options. Amorphous silicon and polycrystalline thin

film cells, which are about a hundred times thinner than crystalline silicon cells use very little

semiconductor material and offer a long term potential for significantly lower cost. Further,

entire thin film modules, rather than individual cells, can be fabricated in an automated

production process.

As a result of advances in these and other technologies, the cost of PV-generated electricity

has decreased from an estimated $1.50 per kilowatt-hour in 1980 to approximately 35 cents

per kilowatt-hour today. Although significant progress has been made in reducing the cost

of PV electricity, commercially available systems and designs are cost effective only for

remote and special high-value applications. The cost of PV-generated electricity must be

reduced approximately six fold to achieve the long term goal of cost competitiveness in the

U.S. bulk power markets.

1.3 Central Station Photovoltaics

There is a growing number and types of remote applications of PV around the world today.

PV systems are pumping water, grinding grain, protecting bridges and pipes from corrosion,

Introduction 4

aiding navigation, helping communications and powering entire buildings or villages. There

is also an increasing number of modern homes that are installing PV systems as a primary

source, as a backup or auxiliary source to the utility, or who want to sell excess power to the

utility. The first type of application is termed stand-alone systems in as much as no utility

interaction is conceived in the design framework. These systems are essentially isolated and

meant to supply the entire load. The second type of application is known as a utility

interactive distributed system. There could be multitudes of such power generations, all

connected to the same power grid.

There is yet another conceivably potential application of photovoltaics. It is the central station

mode of operation of the plant which is either owned by a utility or a third party investor, and

supplies all its power to the utility's grid. It is generally felt in the photovoltaic community, that

the ultimate application of PV will be its use for bulk power generation. Already, large

MW-sized installations are operating in the U.S and Japan. Some are in the construction

phase and some are in the design and planning stages. Southern California Edison Co., Pacific

Gas & Electric Co. and Tennessee Valley Authority among others, are large utilities having a

substantial solar powered generation component in their generation mixes.

1.3.1 Utility Point of View

Within a large utility company, solar technology is viewed in different ways. There are those

who see solar variously as a resource to be planned for, a system to be designed, a

perturbation on the future load curve, and a technology to be developed. In addition, different

utilities see solar differently, depending on their load, and their size and geographic location.

Some see it as an opportunity to ease a critical future problem of fuel cost and availability.

Many utilities, particularly in the Southwest, are actively engaged in collecting solar radiation

Introduction 5

data for their areas. This is evidence that the utilities are looking into the future and strongly

believe that solar applications have real potentials.

At this time, utilities are concerned about a number of problems related to solar photovoltaic

technology. These are economics and operating characteristics.

1.3.2 Economics

An electric utility is an economically driven entity. Therefore, its primary need is to determine

how to supply the load at the least cost, and then arrange to do so. The economic optimization

must be based on a detailed characterization of future electricity usage patterns, the capital

cost, fuel cost, maintenance requirements, efficiency and reliability of various types of power

plants. Evaluating the economic value of a PV system is a difficult job, to say the least. To be

comparable to a utility, two power plants have to be capable of doing the same job. This

means, they not only must produce the same amount of electric energy annually, but they

must have the same effective capacity or power output capability in kilowatts. The problem

with PV is that its effective capacity is not easily related to its peak output, as with other types

of plants. The effective capacity of solar generation depends on how the operation of the PV

plant affects the load on the remainder of the generating system. This, in turn depends on the

relative amount of solar generation as well as on its reliability and availability during periods

of high demands. Load patterns vary from utility to utility and PV plant reliability and

availability are dependent on irradiance patterns which vary geographically. Thus, no two PV

plants will have the exact same effective capacity. The economic value of a PV plant is

calculated as a part of a utility system and then compared to its costs. The economic value

of a PV installation is sensitive to the amount of installed solar capacity as a percentage of the

total generating capacity. The more a utility relies on PV, the less each individual increment

of PV capacity is worth.

Introduction 6

1.3.3 Operating Characteristics

PV power generation from a central station PV plant effects the operation of all existing

generating units in the system. For the PV plant to integrate successfully into the electric

energy system under circumstances which now exist, it becomes necessary to provide the

PV generating plant with control regimes adequate to the demands that will be placed on

them, and the development of such control regimes becomes an integral part of the

integration process. The first step in such a development is the determination of the conditions

under which the controlled plant will operate. When connected to a large power system, PV

plants become an integral part of that system, and are affected by conditions which would not

occur if they were serving an isolated load. Some of these conditions are directly related to

basic physical laws, while others arise because of the manner in which the power systems

are operated. A power system never attains a steady state, so it is always characterized by

dynamic phenomena.

The basic requirement is that of maintaining a balance between energy being absorbed by the

connected loads and energy being provided by the generating units. In addition, since most

power systems are composed of equipment required to operate at given voltage and

frequency, the system is designed to supply energy within constraints of voltage and

frequency. The Automatic Generation Control (AGC) mechanism in the system takes care of

these problems.

The existing conventional generating units, through the use of AGC, are capable of operating

under the dynamic response required to supply the random variations in system load. Such

is not the case with central station PV plants. Frequent weather changes may translate into

extremely high variations in the power generations from the plant. If the plant is constantly

connected to the distribution system, this causes operational problems like load following,

spinning reserve requirements, load frequency excursions, system stability, etc., which the

Introduction 7

conventional AGC system is unable to handle. This calls for modifications of the existing

schedule and control algorithms to incorporate the random variations in PV output.

This dissertation deals with the development of a new strategy for dynamic economic dispatch

that allows the control of PV plant generations and therefore, avoids the penalties because

of load following and spinning reserve requirements and other related real-time operational

problems. Until now, most researchers have used a static analysis of PV generations in the

central station utility concept. In this method, the total system load is modified by the

generations and the net load is scheduled for dispatch by the conventional generating system.

A major disadvantage of the static approach is that, there is no way of knowing ahead of time,

the potential effects the high variations in PV generations might have on generations from the

cycling units in the system.

Judging from the above two points, clearly the real-time operations perspective is just as

important as the economical aspect of central station PV. While economics are constantly

improving and it is only a matter of time before central station PV plants can compete

favorably against conventional peaking or intermediate fossil fuel plants, questions still

remain to be answered in the real-time operations framework and continues to be the weak

link between the PV plant and the utility. An attempt is made in this dissertation to devise an

algorithm that does everything that a standard AGC program accomplishes, with the

additional capability of treating the PV plant as a dispatchable unit, comparable to the dispatch

operation of a combustion turbine unit.

Dispatchability of a central station PV plant is introduced in the next section.

Introduction 8

1.4 PV Dispatchability

Why is dispatchability of a PV plant so Important In the framework of modern AGC? The

answer to that question is rather simple. It provides controllability to an otherwise random

source of generation.

In most power system computer control, which include AGC and economic dispatch (ED)

functions, the ED program computes an economic base value for designated units every few

minutes based on the load change over the time since the last execution of the ED program.

In between computations of this economic base, the frequency deviation and inadvertent

interchange is controlled by an algorithm which distributes the area control error (ACE) over

certain designated regulating units, and linearly distributes the deviation of the units from their

economic limits. In using this approach, the economic base value calculated is usually

restricted not only by the dispatcher-entered economic high and low limits, but also by the rate

at which the unit can respond over the nominal period of the economic dispatch (5 minutes).

Hence, a unit with a response rate of 5 MW/minute, economic high and low limits of 200 and

100 MW respectively, an actual power of 100 MW and an economic dispatch period of 5

minutes, will be restrained in the on-line economic dispatch, by an effective upper and lower

limits of 135 MW and 100 MW respectively. The result of doing this is that each unit is

assigned an economic base, which can be achieved by moving it at its sustained rate of

response from the present value and hence controlling the system in a smooth manner. An

extension to this method, which is now becoming common in power systems, is that of

including a constraint into the ED problem to guarantee that sufficient regulating and/or

reserve margin is maintained over a short (5 minute) period. This method ensures that the

economic base values assigned to the units will be achievable within 5 minutes of operation

and will, if possible, maintain sufficient short term regulating reserve.

Introduction 9

Under the strategy described above, it is well known that the least expensive units will be

allocated close to their limits during the early stages of the load pickup.leaving the more

expensive units for the final stages. This may result in the utility company not being able to

meet its load pickup in the later stages, except by purchasing energy from a neighboring

utility. At present, this is handled by the dispatcher's ramping of the more expensive units

above their economic assignment early in the load pickup period and thus keeping some less

expensive units below their operational limits in the early stages, so that they can help satisfy

the load pickup required at later stages. This requires of course, the dispatcher to make these

decisions at his own discretion. He will tend to choose a safe solution rather than an

economical one.

The problem of dispatching PV under these circumstances, adds a new facet to the entire

problem. First, the dispatcher has no knowledge about the amount of generation, which will

be available at any economic dispatch interval. Secondly, actual observations at various PV

sites in the Southeastern U.S. shows high amount of fluctuations in the solar irradiance within

a 3-minute interval. This variation translates into constantly fluctuating PV generations posing

a serious decision-making problem for the dispatcher. These problems can be resolved by

using a rule-based system approach, which will comprise of all the decision process of an

expert dispatcher plus the speed of a computer processor. The new proposed methodology

provides the following:

• A prediction of the short term sub-hourly solar irradiance thus, giving a look ahead

capability at the PV generations.

• An economic dispatch.

• Decisions on steps to take in case of operating problems

• Area control error correction.

An introduction to the forecast of solar irradiance which is an integral part of the methodology,

follows.

Introduction 10

1.5 Resource Forecast

Dispatch of photovoltaic power is a difficult problem. This is largely due to the fact that short

term prediction of solar irradiance is difficult to predict. The wide variability of the cloud cover

and to some extent, the atmospheric condition makes it hard for any attempt at

parameterization of these phenomena. On the other hand, observed hourly global irradiance

data is available at many locations throughout the SOLMET network [206]. These data, as well

as the typical meteorological year (TMY) [207] data which provide the data for typical months

of a synthetic year, have proven to be useful in the past for PV array performance prediction

[228]. Such weather data are known to be used in many PV performance analysis models.

These models rely for their analysis on the past historical data and are therefore accurate only

in a most general sense with possibilities of wide statistical variability between the actual and

the predicted data.

It therefore seems only logical to assume that a typical synthetic year or a number of years

of historical data may only be useful to predict the average monthly or even daily PV array

performance. A time scale smaller than the day requires knowledge of the cloud cover and

their expected instantaneous changes. Chapter 4 of this dissertation discusses a novel

approach for the prediction of the solar irradiance in the sub-hourly time frame (3-10 minutes)

by means of a Box and Jenkins time-series analysis [37].

Introduction 11

CHAPTER 2

Recent Advances in Utility Integration

A considerable amount of work has been done on the integration of photovoltaic (PV) systems

with the electric utility. Such PV systems studied vary from simple residential systems to large

MW-sized central stations. The existing literature may be divided into three general categories

according to the nature of the study. These are:

• Systems Study

• Operations Study

• Planning and reliability study

Systems study belongs to a group where only the photovoltaic system is examined in the light

of the solar resource. Operational study comprises of the investigation into the specific nature

of the impact of the PV systems into the utility's existing network. Such effects may be

harmonics and power factor effects, generation scheduling effects, frequency control effects,

etc., all of which relate to the short term impacts. Planning and reliability study on the other

hand refers to the long-term impact on the utility. Factors that are of interest in this study are

Recent advances In utility Integration 12

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long term expansion planning , capacity credit, reliability study, etc. The relationship among

these three avenues of research are illustrated in Figure 1.

The following discussion exemplifies the research literature available in each of these areas.

2.1 Systems Research

The survey is initiated with a number of reports from large central station power projects

which are already operating in interconnected mode with electric utilities. Other aspects of the

systems research are then explored.

PATAPOFF (212) discusses the design and construction process for three large photovoltaic

facilities in Lugo, Carissa Plains and Sacramento, California. These plants are operating as

central station power plants providing their host utilities with additional resources in their

energy mix. The Lugo facility is rated at 1 MW built by ARCO Solar and is interfaced with a

12 ·KV distribution system of the Southern California Edison Company at Hesperia, CA. The

monthly capacity factor of this plant has varied between 21% and 37% during its operation.

The author points out an important feature of the system - that of the coincidence of peak load

matching between the Edison company's summer loads and the PV output.

The plant at Carissa Plains is reported by the author to be a 6 MW rated system, also

constructed by ARCO Solar. The design is similar to the plant at Lugo, except that the system

uses reflector enhancements on its two-axis tracking arrays. Use of reflection mirrors

enhances the solar radiation incident on the modules by 80%. The net effect is reduction in

the number of modules needed. The plant is connected to the Pacific Gas & Electric


Company's 115 KV grid. The PV system shows a good match with summer-time peak demands

at this site as well.

The plant at Sacramento is rated at 1 MW and is supplying power to the Sacramento Municipal

Utility District (SMUD). The plant consists of one-axis tracking arrays and was constructed by

Acurex Corp. The author concludes that although some issues remain to be resolved, none

of them represent impediments to widespread use of PV. Low annual capacity factors are not

detrimental if availability is high when demand is the highest.

SPENCER [262) describes the SMUD project as being only a phase of the bigger 100 MW

project which was to be completed in 12 years period. At present, two of the phases are

operating and feeding power into the 12.47 KV SMUD distribution grid. Further development

has essentially been discontinued. The entire project was expected to cost $3.2 million per

MW. Each MW of PV power corresponds to roughly 9 acres of land area.

ARNETT et al. [9) describe the conceptual design, prototype testing, production, assembly and

installation of two MW-sized plants constructed by ARCO Solar. The two plants being the one

at Lugo, CA and the other at Carissa Plains, CA. The facilities employ structural mounting

systems for the photovoltaic modules which provide a means of tracking to enhance the daily

energy production of the PV power plants. Estimates of increased annual energy production

of upto 45% for the two-axis tracking over the fixed tilt arrays were projected.

CHEATHAM et al. [62) in elaborating on the Lugo plant and the Carissa Plains plant,

emphasize on advantages of a large MW-sized central station power plant. These are: (a)

Modularity, (b) environmentally benign, (c) low operating and maintenance costs, (d)

predictable reliability, (e) speed of installation and (f) system life expectancy.

LEONARD [183) attempts to answer some of the questions that need to be addressed before

PV can become economically and technically attractive. The author begins with an overview


of six existing utility interconnected projects and leads to the design study of a 100-200 MW

utility interconnected plant. It is pointed out that although the projected cost of completion of

the 1 MW SMUD plant at Sacramento was $12 million, actual costs incurred were less. This

data provides strong evidence that projections of the cost of a PV plant are likely to be quite

reliable in the future mainly because the cost of PV modules are on a downward trend. The

large-scale system design studies confirm that array fields in PV plants will almost certainly

be divided into a number of subfields, each with its own power conditioning subsystem (PCS).

With only a few exceptions, failure of a component will lead to the shutdown of no more than

one subfield and the loss of only 5-10% of the total plant output. Another conclusion of the

author is that no generally preferred array field design can be defined, because different array

concepts will be optimal in different utility systems (with different diurnal or seasonal demand

profiles).

A study conducted by SHUSHNAR et al [253) reveals that PV and area-related

Balance-of-System (BOS) costs make up 75% to 85% of the total costs in all cases considered

in the study. The study results indicate the high sensitivity of BOS costs to PV efficiency,

system configuration design and identify efficiency and configuration (fixed, tracking, etc.) as

the most effective avenues for system cost reduction.

SMITH (260) examines the economics of large-scale photovoltaic power generation and a

projected break-even cost for photovoltaic cell systems in the light of an electric utility's hourly

energy profile. The author concludes by saying that the PV system may prove to be

economical for utility systems where a substantial reduction in conventional power generation

is realized and the total PV system costs approach $0. 75 per peak watt. The analysis is based

on a 19% cell efficiency.

A number of papers have been devoted to improvements in power conditioning subsystems.

CHU et al (72) have studied several options for central station utility interactive power

conditioning. They have compared the development potential for two PCS designs, 50-500 KW


and 1-10 MW. The 1-10 MW sized PCS employs new switching devices which are faster and

can be switched at higher rates than those existing. Through the use of Pulse Width

Modulation (PWM), chopper waveshaping techniques, the need for magnetic filtering is

significantly reduced. Total harmonic currents are limited to 5% and the power factor is

maintained between 0.95 leading and 0.95 lagging during normal operation. Projected PCS

efficiencies are reportedly greater than 96% from one quarter to full load. PCS cost

projections are made at $0.07 to $0.12/W for the most probable combination of volume,

voltages and ratings.

In a similar study, KEY et al. (161) study and compare the designs of PCS units ranging from

ratings of 2 KW to 5 MW. Both line and self-commutated inverter designs for single and

three-phase applications are described. Both types of inverter designs have been used

successfully. The 1 MW line-commutated unit at SMUD achieved 97% efficiency and power

quality has been reported to be good.

KRAUTHAMER et al. [173) predict that the technical viability and to some extent, the economic

viability of central station PV generation will depend on the availability of large power

conditioners that are efficient, safe, reliable, and economical. The authors go on to overview

the technical cost requirements that must be met to develop economically viable PCS.

PICKRELL et al. (220) discuss the optimization of an inverter/controller design as part of an

overall photovoltaic power system (PPS) designed for maximum energy extraction from the

solar array. The special design requirements for the inverter/controller include: (a) a power

system controller (PSC) to control continuously the solar array operating point at the

maximum power level based on variable solar irradiance and cell temperatures and (b) an

inverter designed for high efficiency at rated load and low losses, at light loadings to conserve

energy. The authors found that although good overall immunity to transients is achieved in

utility line voltages, oscillations in the injected utility line power and solar array voltage are


encountered at low irradiance levels. The hardware manufacture of such a system is

realizable.

WOOD (290] proposes a new scheme for power conditioning in a central station PV plant.

Instead of each array subfield being served by an inverter, the author proposes that the

subfields be served by a de-to-de converter, a boost converter. The de voltage is increased

by a factor of 4-6 through the converter, and the transformed de is collected by an

underground distribution. A single transformation is then used to tie into the utility

sub-transmission or transmission system.

Several authors have discussed detailed design considerations for a multimegawatt-sized

central station photovoltaic system. STRANIX et al. (268] present a conceptual design of a 50

MW PV power plant based on the technology of thin film amorphous silicon (A-si) panels. The

design is for a location in New Jersrey; the performance evaluation based on actual

irradiance. The design criterion minimizes the installed plant cost per annual kilowatt-hour of

energy generated. Based on a design and performance evaluation, the input de voltage is 2000

Vdc while the ac output is 34 KV, 3 phase; the PCS delivers power at unity power factor over

the operating range; the annual energy production is 85.5 GWh at a capacity factor of 19.4%;

the costs are projected at 0.93-1.55 $/Wp (1982 dollars) intermediate and near term goals.

SIMBURGER et al. [255] presents a similar design study for a 200 MW rated central station

PV plant. The plant located at Barstow, CA (southwestern U.S.), uses fixed-tilt Oat plate panels

consisting of 8X20 ft arrays, with single crystal silicon cells. According to the authors, the basic

plant size for a commercial scale central station power plant is in the range of 200 to 300 MW.

The reason for this size selection is that the output of the PV plant is expected to be similar

to an intermediate load conventional fossil-fuel generating station.

JONES et al. (154) discusses a number of guidelines to be followed in the design of large

photovoltaic systems. The guidelines include considerations related to the selection of


collector type, array field configuration, hardware specifications, system installation and

checkout.

LEONARD (184] uses the basic computer simulation approach for the design of a central

station PV plant. The central element of the design process is a computer simulation of the

operation of the photovoltaic system at the assumed location. Hour-by-hour computation of

system performance are carried out with the aid of a mathematical model of the system and

an hourly representation of the irradiance to be expected at the site. The simulations are

carried out for a full year of simulated operations and yield as a figure of merit, the capacity

factor.

DEMEO et al. (89] describes a procedure for estimating capital costs of non-conventional, flat

plate photovoltaic central stations. According to results obtained by the study, acceptable

plant economics will require photovoltaic panel efficiencies in excess of 10%, and panel costs

near $10-$20/m2• Also, a key overall factor affecting the plant economics is the array cost per

unit area per unit plant efficiency. Any modification which reduces the factor without an

offsetting reduction in average irradiance will lower the plant capital cost. Another conclusion

that the authors derive is the fact that concentrator arrays may not be cost effective when

employed solely to reduce required cell areas.

POST et al. [224] provide detailed cost comparisons of five competing photovoltaic system

options for large sized PV power plants. The options include fixed tilt, one-axis tracking and

two-axis tracking flat-plate collectors as well as concentrators, utilizing linear and point-focus

fresnel optics. For a high insolation location, such as the southwest U.S., concentrator systems

offer a slight cost estimate for current PV technology. For the same location, however none

of the competing system options is a clear winner over the others for tomorrow's technologies

(mid 1990s). The system options depend on the site being considered for the installation.


ROSEN (238) calls for attention toward the balance-of-system costs as the next most important

cost element after the array cost. The author discusses development requirements with

regard to array design, de voltage level, array field grounding, power conditioning, operating

and maintenance requirements and system prediction. THOMAS et al. (274] reasserts the fact

that utility owned central station PV plant will constitute a major potential application in the

foreseeable future. The authors also point that solar availability dictates the allowable cost

of the PV system.

TAYLOR (99) in an EPRI report, states that after reaching compatibility between allowable

costs and achievable performance and price, the ultimate limits to penetration are likely to

be set by operational issues, like system reliability, dispatch, etc. The author lists a number

of implications of PV research and development. Among these, an important issue is the

establishment of a better solar data base, which can be used to determine requirements for

regulating capacity. These requirements can also be used to more accurately establish

generation expansion scenarios.

In another EPRI report (98) the authors discuss a new microcomputer based evaluation model

to determine the value of a PV plant to the electric utility. The model consists of a simplified

utility production cost code and a simplified PV system performance code. The model accepts

data on the existing generation mix(unit rating, fuel type, heat rate, forced outage rate and

monthly dispatch order), the electrical demand (hourly demand profile for a typical week in

each month) and the contribution from an alternative generation source (hourly for a typical

day in each month). For any given hour. the model dispatches units in a pre-specified order

to meet the hourly electrical demand (dispatch order in the analysis is based on the principle

of least cost generation). Upon meeting the load, the model checks the amount of available

contribution from the PV plant and displaces an equal amount of the last unit dispatched (the

marginal generation). The procedure is reiterated hour-by-hour for each typical week. The

simulation gives an estimate of the type and quantity of fuels displaced. Using the value


determined from the simplified production cost model, the authors obtain the allowable cost

of PV generation in cents per KWh.

A number of photovoltaic system simulation models are now existing in the literature. Shown

in Figure 2 are some of the better known models with their origins. Most of these models take

as input, the hourly irradiance and weather parameters at any particular site and simulate

hourly or daily photovoltaic output.

2.2 Operational Research

This phase of central station PV plants refers to the situation which is brought about when the

utility has already decided to install the PV plant and the problem is to find out the optimal

way to operate and control the output in real time. The problems associated are manifold.

The more important of those are: generation dispatch, load frequency control, power factor

control and system protection.

SIM BURGER et al. [254] present a new model which was synthesized in order to simulate the

operation of an entire electric power system. This model simulates the operation of the

generation system and the automatic generation control in response to changes in net

demand. When a large, widely varying power generation source like the PV system is added

to an existing system, the impact on this system would be the same as reducing the total

energy required from the remainder of the system while increasing the short term swings in

net system demand. A 24 hour simulation shows that with a 500 MW wind system, some

changes in base operating system need to be made. For example, a peaking unit of 500 MW

capacity would have to operate under AGC for the entire 24-hour period to accommodate the

Recent advances in utility integration 21

Model PV Performance Model Photovoltaic F-Chart Lifetime Cost & Performance Engineering & Reliability TRNSYS/MIT

Photovoltaic Analysis Model PVFORM - System Analysis Program Solar Cell Model (SOLCEL-11) Solar Energy System Analysis TRNSYS/ASU

PV Transient Analysis Prog.

Solar Reliability

Figure 2. System simulation models

Recent advances In utility Integration

Originator Electric Power Research Institute (EPRI) University of Wisconsin Jet Propulsion Laboratory (JPL) JPL University of Wisconsin MIT Lincoln Laboratory Solar Energy Research Institute (SERI) Sandia National Laboratory Sandia National Laboratory Sandia National Laboratory University of Wisconsin Arizona State University Sandia National laboratory BDM Corporation Sandia National Laboratory Battelle-Columbus Laboratory Sandia National Laboratory

22

wind power system. Also, some unscheduled interconnected power will have to be

interchanged, which might create area control error problems.

THOMAS et al. [275) investigate the potential impact of photovoltaic systems on the utility

operations. The results show that a small (1-4%) penetration of photovoltaic systems will not

adversely affect the utility operations even under the "worst case", which is a rapidly moving

cloud front. As individual plant size approaches ;:::- 5% of the control area capacity, difficulties

might arise. Some of the authors' recommendation for alleviating the problems are:

• Reduced energy density of the array field i.e., install 50 MW/mi2 as opposed to 100 MW/

mi2•

• Disperse the array field. Install four 25 MW fields instead of one 100 MW field.

• Forecast approaching cloud fronts via National Weather Service type data or from sensors

located in close proximity of the array field.

• Alter the generating types used for regulation to give an improved ramp rate during times

of problematic cloud movement.

PATAPOFF et al. [213) present the utility experience in the operation of a MW-sized plant. The

plant is the 1 MW PY station at Lugo, CA. The facility is interfaced with the Southern California

Edison utility company through a 12 KV/480 V delta-wye 1 MVA transformer. Protection

equipment include over and under voltage, over and under frequency and overcurrent relays.

During normal operation, either the two 500 KVA self-commutated inverters are operated in

parallel, or the 1000 KVA line-commutated inverter unit is operated. The total harmonic

distortion values ofthe self-commutated inverters are lower than those of the line-commutated

inverter at all power levels, for both current and voltage, but the level is not much of a concern

to the utility.

LEE et al. [182) p~esent a method for estimating the load following and spinning reserve

requirements for a power system containing intermittent generation. The authors incorporate


the generations in an optimal generation expansion planning model which evaluates the effect

of such requirements on the generation mix and the production costs. The authors use the

"negative load" concept in which intermittent generation is deducted from the load demand

at each hour. Load following and spinning reserve requirements are evaluated for the two

cases of with and without intermittent generations. The requirements increase linearly with

penetration of intermittent generations. According to the authors, the overall effect of

integrating the intermittent generations were: it increased the annual production costs,

decreased the annual fixed costs, and substantially reduced the energy and capacity credits

otherwise attributable to intermittent generations.

A number of studies have been devoted solely to the harmonics and power factor effects of

PV systems on the operation of electric utilities. CAMPEN (48], TAKEDA [270], TAKIGAWA et

al. (271], all report analysis of the effect of harmonics at different PV sites. COKKINIDES et al

(76] conducted experiments and simulation studies to investigate problems of interface, such

as harmonic generation and propagation, and safety assessment during faults. The authors

conclude that present technology of power conditioning units generate lower level harmonics

than those existing in the system from other sources. GUESS et al. [123]present the result of

a conceptual design study for a central station PV power conditioning system. The authors

propose promising methods for the power converters to minimize subsystem costs, harmonic

currents, and size, while maximizing efficiency.

2.3 Planning and Reliability Research

This phase of the research on central station PV applications is concerned with incorporation

of the new system into the various utility planning and reliability models. These models are

required prior to making decisions regarding the planning of electric power components,


constructing components, continuing or delaying construction, etc. Two basic objectives have

to be satisfied in any such planning models.

• To serve the load most reliably, that is, with the least probability of losing the load or

failing to serve the entire energy requirement during the period of study.

• To accomplish the above with the least cost of generation.

The following is a discussion of the advances made in the field of incorporation of PV systems

in the planning and reliability models.

DAY et al. [88) discuss model extensions implemented to assist in determining the potential

value and reliability impact of solar plants. The principal computer programs used in the

study are: A production costing model, a reliability model, and a solar plant model. This

general procedure is useful in estimating the lifetime value of a solar plant to a utility system.

The framework provides a vehicle for assessing the value of either a single solar plant or a

number of them, independent of their cost projections. The initial step in the evaluation

process is to project future loads for all years in the expansion period. An optimal generation

expansion program is used to expand the conventional system without any solar plant

installations. The next phase involves the optimal expansion of conventional units in the

presence of a forced solar plant. Comparisons are then made between non-solar and solar

expansion plan installation schedules, capital and operating costs, and present worth of plan

revenue requirements.

SISSINE [257) discusses the issue of capacity credit for wind and other renewable power

sources. Although the paper deals mostly with wind systems, some of the suggestions made

by the author are equally valid for photovoltaic systems. Capacity credit for a conventional

thermal plant is determined on the basis of its capacity factor which ranges between 70 and

80%. However, the traditional capacity factor approach would be erroneous in determining the

capacity credit of wind systems. The major shortcoming of this approach is reportedly, its


failure to capture correlations of wind resource availability with utility loads. It is more

appropriate to use a method based on the reliability of the entire generating system.

Reliability analysis examines the difference in loss-of-load probability (LOLP) between two

arrangements of utility equipment: the existing arrangement (base case) and an expansion

arrangement that adds wind facilities to the base case. The change in LOLP due to the

addition of wind facilities gauges the reliability improvements which is equated to an increase

in system capacity. The ratio of this change in system capacity to the wind facilities' total rated

capacity is defined as their effective load carrying capability (ELCC) and represents their

capacity credit.

PESCHON et al. [219] discuss the development of new mathematical models for the economic

evaluation of intermittent sources of power. The purpose of these mathematical models are

to answer questions related to real-time operational problems, operating savings, economic

characteristics over a typical 20-25 year planning horizon and level of penetration. The

computer model makes feasible the simulation of the hourly operation of the combined system

for a complete snapshot year with and without the non-conventional source. With the reliability

criteria satisfied by the generation mixes with and without the non-conventional source, the

capacity credit is determined.

KU et al. [175] describe a methodology used for and the results obtained from a study for

assessment of the economic viability of long-range applications of PV generations in the

Public Service Electric & Gas (PSE&G) Co. at New Jersey. The authors develop a

mathematical and statistical process to convert actual irradiance data to hourly electric

energy production patterns for average days of each season. Using the PSE&G electric system

as a basis, they develop a long-range generation expansion scenario including advanced

design for combustion turbines (CT). The authors then substitute various amounts of CT

capacity additions with PV generating capacity which corresponds to different levels of PV

penetration. The authors then determine the amount of PV kw capacity required to replace

each kw of CT capacity in order to provide the same level of system reliability.


JORDAN et al. (155] describe the methodology developed for evaluating capacity factor,

effective capacity and total economic value of a PV system, when combined with other

generating units in an electric utility. The authors adopt a total system performance model

which consists of three models: the source performance model (wind or photovoltaics), the

reliability model, and the production costing model. The source model evaluates the total PV

power generations for a given system; the reliability model makes use of the long-established

loss-of-load probability method with modification to represent hourly variations in both load

and PV plant output, and the production cost simulation model is a standard production cost

program which has been in use for years.

DAPKUS et al. (80) describe a planning method which considers the uncertain and dynamic

nature of the decision process. A stochastic dynamic program is used to model uncertainty in

demand, the date of new technology (PV plant) commercialization, and the possible loss of

service of existing technologies due to accident, regulatory action or lack of fuel. In this

methodology, the state of the system at any time is completely defined by the number of units

of each type of technology, the availability status of each technology and the peak level of

demand.

CARAMANIS (50) discusses the methodology used in the software package, Electric

Generation Analysis System (EGEAS) developed for EPRI, by the Massachusetts Institute.of

Technology. EGEAS is a comprehensive planning package which can analyze

"non-dispatchable" (NOT) options in the utility. NOT refers to those generations which depend

on the weather, or nature, e.g., wind, solar, hydrothermal, etc. The author addresses the issue

of an additional source of uncertainty in NDT, besides equipment failure. The uncertainty is

due to energy source availability fluctuations arising from the stochastic nature of wind speed,

irradiance, river flow, etc., affecting the output from a particular NDT. This random variable is

interdependent with system load fluctuations. This particular relationship is identified in the

methodology. The rest of the methodology follows any standard optimal expansion program.


FINGER [109] presents a production costing methodology which can also model solar power

generations as well as other non-conventional sources or energy. The treatment or solar

generations is deterministic. In other words, the hourly load demands are modified

chronologically by solar generations.

SINGH et al. [256] discuss a methodology which evaluates the reliability of electric power

systems having PV plants. Two groups are created, one each for the conventional generation

system and the other for the non-conventional generation system. A generation system is

created for each group. The models of the non-conventional group are modified hourly

depending on the limitations of energy. All the models are combined hourly to find the loss

of load expectations and the frequency of capacity deficiency for the hour in question. This

procedure is accomplished using a discrete state algorithm as well as the method of

cumulants.

STEMBER [265] presents two techniques for modeling the availability and maintenance costs

of photovoltaic power systems. The term 'availability' refers strictly to the hardware system.

The two basic availability models are: a simulation technique using the GASP-IV language,

and an analytical approach using state space techniques. The simulation model developed is

SOLREL [266]. It uses event-by-event simulation to represent the 30 year life of the system

with individual reliability and maintenance events modeled with statistical distributions.

UNIONE et al. [278] discuss the availability as a measure for estimating the expected

performance for solar and wind powered generation systems and for identifying causes of

performance loss. The authors discuss models ranging from simple system models to

probabilistic fault-tree analysis. They develop a methodology incorporating typical availability

models for estimating reliable plant capacity.


2.4 Economic Dispatch With PV Plants

Economic dispatch is defined as the process of allocating generation levels to the generating

units in the mix, so that the system load may be supplied entirely and most economically. A

general survey of the economic dispatch methods now existing, is done along with the studies

done on integration of photovoltaic systems into these dispatch algorithms. The research

study shown here are those published after the comprehensive survey done by HAPP [125)

which was published in 1977. Since then, substantial work has been published in this area,

particularly in the area of modernizing the AGC.

HAPP [125) reviews the progress of optimal dispatch from its inception to its present day

status. As presented by the author, economic dispatch dates back to the early 1920's or even

earlier when engineers already concerned themselves with the problem of the economic

allocation of generation or how to properly divide the load among the generating units

available. Prior to 1930, various methods were in use, such as: (a) the base load method

where the next most efficient unit is loaded to its maximum capability, then the second most

efficient unit is loaded, etc., (b) "best point loading", where units are successively loaded to

their lowest heat rate point, beginning with the most efficient unit and working down to the

least efficient unit, etc. It was recognized as early as 1930, that the incremental method, later

known as the equal incremental method, yielded the most economic results. The theoretical

work on optimal dispatch later led to the development of analog computers for properly

executing the coordination equations in a dispatching environment. A transmission loss

penalty factor computer was developed in 1954 and was used by AEP in conjunction with an

incremental loading slide rule for producing daily ger:ieration schedules in a load dispatching

office. An electronic differential analyzer was developed for use in economic scheduling for

off-line or on-line use by 1955. The use of digital computers for obtaining loading schedules

was investigated in 1954 and is used to this day.

Recent advances in utility Integration 29

BOSE [35) examines the impact of new generation technologies on utility operation practices.

While not dealing in extent with any particular technology, the author discusses the general

characteristics of each potentially viable new generation source. The scheduling practices

considered, range from load frequency control and economic dispatch to the weekly (short

term) and yearly (long term) scheduling of generating units. The impact of new technologies

is predicted to be significant, the exact effects depending on the level of penetration, the

extent of dispersion, ownership, and the weather dependency of the technologies selected.

WAIGHT et al. (285) have used the Dantzig-Wolfe decomposition method to resolve the

economic dispatch problem into a master problem and several smaller linear programming

subproblems. The algorithm that that they have followed is as follows:

• Decompose the problems into n subproblems and a master problem.

• Choose the initial basis of the master problem by introducing artificial variables and

setting up the appropriate Phase I (feasibility) and Phase II (optimality) objective

functions.

• Compute an objective function for each subproblem and solve each subproblem using the

revised simplex method.

• Calculate the relative cost factors for all subproblems. If all are positive, stop since

optimality has been reached. Otherwise, reiterate with new simplex multipliers.

The authors claim that with this decomposition technique, a significant advantage can be

achieved in terms of computer timing and storage.

ISODA (144) recognizes the response limitations of generation units in the mix and assesses

its impact as well the impact of short term load demand forecast on the economic dispatch

scheme. The author claims that with short term load forecasts available, the manual operation

(by operator) to regulate the power generations of the thermal units when the load changes

steeply for a long time is reduced. According to the authors, the optimum forecast period is


approximately one hour in which the load demand should be forecast for a total of 4 to 6

points. Application of the method is also possible in an on-line dispatching control in electric

utilities.

LEE et al. (182] have investigated the load following and spinning reserve penalties for

intermittent generation in the economic evaluation of such sources in the presence of a

conventional generation mix. They present an approach estimating the load following and

spinning reserve requirements for a power system containing intermittent generation. They

incorporate this in an optimal generation expansion planning model which evaluates the effect

of such requirements on the generation mix and the production costs. The authors claim that

the penalties are too high due to the presence of intermittent generation and that all energy

and capacity credits are eliminated due to such penalties. According to a case study

performed by the authors, increasing penetration of intermittent generation (wind powered

system in the case study), causes an increase in the spinning reserve requirements and the

load following requirements, the increase being linear. The effect of penetration on system

costs is found to be non-linear. For their case study, below 5% penetration, the load following

requirement is satisfied by the optimal generation mix, the penalty cost arising primarily due

to increase in spinning reserve requirement. Beyond 5% penetration, the load following

requirement begins to alter the generation mix, with the consequence that the penalty cost is

greatly increased due to the combined effect of higher spinning reserve and the departure

from the optimal generation mix, imposed by the load following constraint.

STADLIN [263] incorporates an additional constraint into the economic dispatch optimization

process, that of regulating margin. He introduces the term µ to be the Lagrange multiplier

representing the incremental cost of regulating margin in dollars per megawatt-hour. This is

used in addition to the Lagrange multiplier A. which is defined' as the incremental cost of

delivered power in dollars per MWh, in the classical /..-dispatch solution of the economic

dispatch problem. Modification of the conventional incremental cost is therefore accomplished

by introducing a regulating margin cost penalty. For example, an increase in µ causes an


increased incremental bus cost for high load levels which will tend to retard normal economic

loading to produce extra "raise" regulating margin.

RAITHEL et al. (230) introduce a successive approximation dynamic programming to obtain

the optimal unit generation trajectories that meet the predicted area load. They use "dynamic"

optimization as compared to the "static" case, as the dispatch program determines the

economic allocation of generation for the entire future period of interest, using knowledge of

both the present and the predicted load . The look-ahead capability provides the advantage

of responding to sudden severe changes in load demand. They adapt the successive

approximations dynamic programming algorithm to handle valve-point loading of units.

Valve-point loading is accomplished via the representation of the valve point in the unit

production cost function.

CHALMERS et al. [60) evaluate the effect on utility operation of photovoltaic generations that

is interconnected to an electric utility grid. The authors study various PV concentrations and

performance characteristics on generation control. Their results show that PV generation can

be integrated into the utility system in substantial amounts without creating any unusual

problems in system operation and control. The most severe condition as reported by the

authors is created when the entire PV array is completely covered and uncovered by a fast

moving cloud cover. Their simulation results show that the NERC limit is exceeded for PV

sizes of 100 MW (5.5% penetration) or more, in the winter, during conditions of the cloud cover

moving away from the sun. The penetration limit for the PV system is somewhat higher for

the case when the sun gets covered suddenly by a large cloud cover.

SAMUAH et al. (243] reformulates the economic dispatch problem by introducing an added

constraint on maximum frequency deviation following a postulated disturbance. The significant

improvement in average system frequency deviation response is found to be at the expense

of increased operating cost. The main difference between the frequency deviation constrained

dispatch and the conventional economic dispatch is the allocation of the total system margin.


In the latter case, the margin allocation is made without explicit consideration of the minimum

frequency following a specified disturbance. The margin is usually carried by a few units. On

the other hand, with a tight minimum frequency limit imposed, the allocation is made so that

the system margin is distributed among more units with the faster units carrying relatively

larger portions. The method of solution adopted by the authors is a Dantzig-Wolfe

decomposition technique followed by several linear programming solutions. An algebraic

formula is developed for the maximum frequency deviation.

KAMBALE et al. (156) discuss the problem of tracking economic target curves, produced by

an economic program. In tracking the target curves, unit dynamics including boiler dynamics,

are taken into account. The problem is decomposed in such a way that the slower bulk control

is based on a fully non-linear and dynamic model of the unit while faster load fluctuations are

traced by fast, dynamic vernier control based on a linearized model. This, according to the

authors, results in fuel economy coupled with tight and smooth control, which demands

moderate computational load. Three stages of control are identified arising out of three

components of load. The first stage has a 24-hour horizon and load needs to computed once

in 24 hours. Stage 2 has a 0.5-1 hour time horizon and the load component estimate is

recomputed every 2-5 minutes on line. The third stage is represented by the random load

generation component having a time horizon of 15-30 seconds. The load component in this

stage is recomputed once every 2-4 seconds. All control operations are divided into these

three stages.

LIN et al. (186) present a real time economic dispatch method by calculating the penalty

factors from a base case data base. The basic strategy of the proposed method assumes that

a base case data base of economic dispatch solution is established according to statistical

average of system operation data of the daily demand curve. Solutions in the data base can

either be calculated by the B-coefficients method or other existing methods in the literature.


PATTON (214) introduces the concept of dynamic optimal dispatch as opposed to the static

optimization, which does not consider the effect of change related costs. The dynamic optimal

dispatch method uses forecasts of system load to develop optimal generator output

trajectories. Generators are then driven along the optimal trajectories by the action of a

feedback controller. Optimal trajectories are first calculated for nominal load forecasts using

quadratic programming or gradient projection methods; then they are updated using

neighboring optimum methods as load forecasts are revised through time. Studies of small

system indicate that the dynamic optimal dispatch may be economically attractive. Savings

of upto 1 % of total fuel consumption is possible with this approach over the static approach.

WOOD (291) proposes a new methodology to incorporate· reserve constraints and goes on to

prove that this methodology is more efficient than that introduced by (Stadlin]. He shows a

technical solution to the reserve constrained problem which can be achieved with a very

efficient use of computer resources. The problem is expressed as a dynamic programming

scheduling problem and a feasible, but suboptimal solution is proposed which eliminates the

usual search space problem. This method reduces the problem to a backward sequence of

dispatch problems, with the generator limits being carefully adjusted between each time

interval in the solution sequence.

BOSCH (35) also presents a solution to a dynamic optimal dispatch constrained by reserve

and power rate limits. The solution is obtained with a special projection having conjugate

search directions that quickly and accurately solves the associated non-linear programming

problem with upto 9600 constraints. The proposed methodology reduces fuel costs by about

0.5%.

RAMANATHAN (231) discusses a fast solution technique for economic dispatch, based on the

penalty factors from Newton's method. The algorithm uses a closed form expression for the

calculation of Lambda (Lagrangian multiplier), as well as takes care of total transmission loss

changes due to generation change, thereby avoiding any iterative processes in the


calculations. In this algorithm, a major portion of the calculation time is spent on performing

penalty factor calculations and is the same regardless of the calculation technique. Since, no

iterations are involved, there are no oscillations or convergence problems in the execution

of the algorithm.

ROSS et al. (239) discuss the application of a dynamic economic dispatch algorithm to AGC.

When coupled with a short term load predictor, look-ahead capability is provided by the

dynamic dispatch, that coordinates predicted load changes with the rate of response

capability of generation units. The dispatch algorithm also enables valve-point loading of

generation units. The method that the authors use in their dispatch algorithm makes use of

successive approximations dynamic programming. The authors claim that the algorithm is an

improvement over the existing dynamic dispatch algorithms, in that the computer resources

required are modest.

AOKI et al. [6] present a new method to solve an economic load dispatch problem with de load

flow type network security constraints. The network security constraints represent the branch

flow limits on the normal network and the network with circuit outages. Hence, the problem

contains a large number of linear constraints. In power systems, only a small number of flow

limits may become active. Computationally, since it is inefficient to deal with such constraints

simultaneously. the authors have extended the quadratic programming technique into the

parametric quadratic programming method using the relaxation method. The memory

requirements and execution times suggest that the method is practical for real-time

applications.

BECHERT et al. [19) point out the problems of applying solutions of static optimization

techniques used for solving economic load allocation, into the feedback control of dynamic

electric power networks. Their research attempts at overcoming the disadvantages of such

controllers by combining economic load allocation and supplementary control action into a

single dynamic optimal control problem. Power interconnection is partitioned into the


electrical network subsystem plus separate control area subsystems, each of which then

constitutes a separate control problem. The electrical network subsystem is solved to find the

shaft power required from each control area, such that network frequency and tie-line power

errors may be minimized. The demand signal then serves as a target toward which each

control area's power output is driven.

BRAZZELL et al. [41) present a computerized algorithm of scheduling generation for

contingency load flows, used in planning studies taking into account the operating constraints

such as economic dispatch and regulating reserves.

VIVIANI et al. (283) present an algorithm to incorporate the effects of uncertain system

parameters into optimal power dispatch. The method employs the multivariate Gram-Charlier

series as a means of modeling the probability density function which characterize the

uncertain parameters. The sources of uncertainty are identified as those emanating from long

and short term forecast errors; measurement or telemetering errors and system configuration

error. The energy system parameters are grouped into state vectors and control vectors. The

Gram-Chartier series is employed to statistically model the control vector, which consists as

elements, the generator power and voltages at each bus.

INNORTA et al. (142) discuss a method of redefining the optimal and secure operation

strategies, a very short period in advance by exploiting the availability of the on-line state

estimation and load forecasting. An H Advance Dispatching" (AD) activity is added in the

system control hierarchy between the day before scheduling and the on-line economic

dispatch. The authors prove that AD can be very effective for supplying security constrained

participation factors to the regulating units when economic dispatch is operating and also

improves system operation when economic dispatch is not available. More precisely, AD

modifies the day before scheduling by supplying the optimal trajectories of the thermal units

over very short time periods, taking into due account, the load predictions (30 minutes ahead)

and the actual security constraints which include dynamic limitations upon the rates of change


of the thermal generator MW outputs. The authors use an on-line parametric linear

programming algorithm for the AD model.

CARPENTIER [54) reviews the potential applications of modern proposals for AGC as opposed

to the conventional methods. The conventional implementations generally use

integro-proportional control derived from the servo-mechanism theory. The modern proposals

employ optimal power flow techniques. The author discusses the primary, secondary (LFC)

and tertiary (ED) controls in a single system using conventional AGC. During the tertiary

control, economic dispatch owns the cost curves in its memory, receives the electric powers

of these units and computes the economic participation factors for each units, in order that

resulting operation should be the most economic possible. The computation is static and is

usually taken into account but not transmission security. Modern AGC systems, on the other

hand, allows system constraints to be taken into account, particularly transmission security

while improving economy and even transients, e.g., through solving the LFC-ED interface

problems. Moreover, optimal power flow techniques may be combined with the results of

optimal control theory to further increase the quality of the transients.

2.5 Conclusions

Two points are very clear from the survey of the recent advances in integration of PV systems

in an electrical utility's generation system.

• Although PV economics, dictated by array costs, has been targeted as a primary concern

for increasing penetration, it is obvious, that many technical problems need to be

answered, particularly in the area of real-time operation of PV systems with a

conventional system.


• At present, the PV generations, if any exist are handled in a static manner in utility

operation. In other words, they are forced on the power system and the latter is expected

to accomodate the presence of PV. Most studies consider hourly PV output during their

operation in the utility and these are assumed to be constant throughout the hour.

Although, this procedure may be adequate on a clear day, it is likely to create problems

on a cloudy or partly cloudy day, when hourly estimates of PV output produces large

errors when compared to the instantaneous values, because of high amount of variations

in the solar irradiance.

• Advanced automatic generation control algorithms utilizing state-of-the-art control

technology are now available. These algorithms may not be appropriate for handling

intermittent power generations from PV systems. Modifications need to be made on the

existing algorithms or new and efficient algorithms need to be developed.

There is no question that the overall utility system planning, including reliability and capacity

credits will depend on the real-time operating characteristics of the PV plants. At this point,

as it stands, central station PV systems have been limited to less than 5% penetration of the

generation capacity before operational problems become significant. This translates to a PV

plant capacity of less than 500 MW or less for large electric utility systems. Although, in the

light of present day's technology standards, this figure seem relatively high, it certainly would

look quite modest in a few years time.


CHAPTER 3

Optimizing PV Output in the Utility

Solar radiation, also termed as irradiance, reaching the surface of the earth is a general term

for the global horizontal lrradiance received on the ground. Global horizontal irradiance can

be decomposed into two general components, the direct normal irradiance component and the

diffuse irradiance component. The relationship is depicted more clearly in Figure 3.

Extraterrestrial radiation refers to the solar radiation above the atmosphere of the earth. The

transmission of solar radiation through the atmosphere is mainly dependent on three factors:

• scattering by the molecules (Rayleigh scattering),

• scattering and absorption by solid and liquid particles, and

• selective absorption by gaseous constituents.

As shown in the figure, the scattered radiation is called diffuse radiation. A portion of this

diffuse radiation goes back to space and a portion reaches the ground. The radiation arriving

on the ground directly in line from the solar disk is the direct normal or beam radiation. A

knowledge of both direct and diffuse irradiance components is very essential for the design

of photovoltaic systems. Unfortunately, solar data availability around the U.S. has been a

Optimizing PV output 39

I I Extra terres t ri a I

Radiation

. . . . . . . . :··Diffuse:.·

: Scattering ... 11·· ...... ·.·· Reflected \ \ Direct

Radiation

Atmospheric Absorption Warming of Air

by Surface Diffuse Raid1ta~tion ____ ... Total

~,___ )-Rad1at1on

Direct, Diffuse, and Total Solar Radiation

Figure 3. Solar lrradiance components.


major constraint in the design of such systems. At most sites, only the global horizontal

irradiance data is measured, at the hourly or daily time scale. Direct and diffuse components

are rarely recorded anywhere. PV system designers therefore have to rely on estimates of the

diffuse irradiance given by prediction techniques. The basic procedure is to develop

correlations between the global irradiance and its diffuse component using measured values

of these two components at those sites which do record both quantities, and then to apply

such correlations at locations where diffuse radiation data are not available. The quantities

which are generally correlated can be divided into the four following groups:

1. Correlations between the daily global irradiance H a~d its diffuse component Hd.

2. Correlations between the monthly mean daily global irradiance Fi and its diffuse

component Hd.

3. Correlations between the monthly mean hourly global irradiance i and its diffuse

component Id.

4. Correlations between the hourly global irradiance I and its diffuse component Id.

Such correlations have been studied by a number of authors over the past few years.

References [77, 103, 187) provide detailed discussion of these relationships.

The diurnal variation of solar irradiance depends on the position of the sun relative to the

receiving plane throughout the day. The seasonal variation is brought about by the difference

in the orientation relative to the sun as seasons change. Figure 4 shows the relationship of

the sun's position with an inclined plane. As will be obvious later in this section, an inclined

plane receives more energy throughout the day, than a horizontal receiving plane.

Mathematical relationships govern the specific geometry shown in the figure. The

relationships are different for the different array orientation employed. Equations governing

this sun-earth geometry are given in Appendix A.


Sun

~ r.e 01 s.1;r.t to the sun-coserver at 0

Figure 4. Position of the sun relative to an Inclined plane

Optimizing PV output

!-'cr1zonta1 suriace

\ \

Hcrizontal ;i1ane c.:i

eartn s st..:r~ace

42

3.1 Array Orientation Strategy

Realistic PV systems are oriented at particular tilt angles so as to optimize the solar

irradiance. There are a number of options that the designer might choose for the system.

These options are generally dictated by cost-benefit ratios. Figure 5 shows the options that

may be used to configure the PV array. Besides, among the systems options, the designer

may choose one of two types: (a) flat plate and (b) concentrators. The choice of the right

option in both the orientation and the system is a matter of simulating the relative

performances throughout the year with long term data at any location. The performance

characteristics are believed to vary considerably from location to location. While the

southwestern U.S is well suited for concentrator technology, the same is not true for the

southeast or northeast. The reason is that, the southwest receives more direct normal

irradiance annually. Array orientation strategies may strictly be based on array structure

costs. While the two-axis tracking array orientation requires a computer controlled automatic

tracker system, the simple fixed surface orientation does not incur the extra costs of tracking.

On the other hand, energy collected by a 2-axis tracking system may prove to be twice as

much as the fixed surface array during the year.

Two mathematical relationships which figure prominently in simulating the performance of an

array oriented in one of the ways described in Figure 5 are shown below:

1. Angle of incidence of solar radiation on a horizontal surface:-

cos eh = sin 0 sin <p + cos 0 cos <p cos co = sin a = cos 0z (3.1)


Option

1. Fixed surface

2. Monthly tilt on Fixed surface

3. Monthly tilt on 2-axis fixed surface

4. North-south axis tracking

5. East-west axis tracking

6. Polar-axis tracking

7. Monthly tilted with vertical axis tracking

8. Two-axis tracking

Figure 5. Array orientation options


Description

PV modules mounted horizontal to the surface

Monthly tilt adjusted on modules facing south

Monthly tilt and azimuth adjustment on PV modules

Modules track the sun about a north-south axis with the entire plane tilted

Modules track the sun about an east-west axis

Modules track the sun about a polar axis

Modules track east-west on a vertical axis with optimal monthly tilts applied on the modules

PV modules constantly updated maintaining it parallel with sun's rays

44

where:

eh = incidence angle on horizontal.

ez = zenith angle.

a = elevation angle of the sun.

5 = solar declination.

<p = latitude at the site.

co = hour angle = cos- 1( - tan <p tan 5)

2. Angle of incidence of solar radiation on a tilted surface:-

COS et = COS a sin p COS(y5 - y) + sin a COS p

where:

e, = incidence angle (angle between direction of the

sun and normal direction of the surface).

Ys = solar azimuth angle.

= sin-1[ cos 5 sin co] cos a

y = surface azimuth angle.

p = slope of the planar array.

(3.2)

(3.3)

Three of the most important array orientations for central station PV systems and results of

actual simulations are discussed next.

3.1.1 South-facing array


320

i 240 ~

~ a.. ~

0

> 0... 160

80

S oulh facing 2 axis traclang

;\ I \ /"-:;

I \t. \ I I I I I I I I I

Op!1mal az1mulhm

\ ~

\ ('.\ '(

'.\

'.\

'.\

'\ '\ \ \

0 .._~..._~..__~..r..:-~...._~....._~_,_~_._~_._~_.__.__._~_._~_, 0 4 8 12 16 20 24

Holl' or day

Figure 6. PV output comparisons for fixed tilt, azimuth-optimized and fully tracking arrays for August at Raleigh, NC


320

i 240 ~

~ a.. ~

0

> a. 160

80

4

s oulh racing 2 axis traclang

I f I i I i I i i

8

/. r

\

12 Ho1r or day

\ \ \ \ I I I \ \

16

I \ \ \

20 24

Figure 7. PV output comparisons for fixed tilt, azimuth-optimized and fully tracking arrays for November at Hesperia, CA


This is the most typical orientation for PV arrays in the northern hemisphere. The installation

requires only a simple tilting structure. Use of the solar geometry and weather data at

Raleigh, NC, latitude 35.75 ° , shows the fact that the optimal tilt angle varies for each month

from 60 ° in January to 5 ° in June and back up to 60 ° in December. The surface azimuth angle

in each case is held at O 0 • Therefore in order to obtain the maximum available solar energy

every month, it is required to change the tilt angles according to the figures obtained. On the

other hand, it may be desirable to leave the array facing south at one specific tilt angle

throughout the year. Then a new tilt angle may be found which optimizes the annual output.

In this case for Raleigh, this angle is 30 °. The curve in Figure 6 shows, among other things

the PV output from a south facing array on a typical day in the month of August at Raleigh.

To show the effect of site diversity , similar results are also shown for a site at Hesperia, CA

in Figure 7. The month shown here is November. An annual tilt angle also of 30 ° is used at

this site as well.

3.1.2 Optimal-Surface-Azimuth Oriented Array

Since maximizing PV output at noon time may not necessarily be of primal importance to a

utility with a load shape peaking at another hour besides noon, it is only natural to try and

maximize the PV output at or close to the hour of peak demand. It is found that this can be

done by changing the surface azimuth angles as required to an angle suitable for maximizing

the PV generations at any prescribed hour of peak load. This strategy is a special case of

option 3 shown in Figure 5. The orientation strategy is of course inherently linked with the fact

that the overall energy generated during the day is less than that generated by a south-facing

array. Also because of the diurnal nature of the solar radiation, optimal orientation is not

possible for peak demands occurring after 1600 hrs and in these situations it is better to leave

the array facing a direction optimal for the 4 PM peak.


Results of maximizing the irradiance at the 16th hour of the day in August at Raleigh is shown

in Figure 6. Similar results of maximizing at the 13th hour of the day in November at the

Hesperia site is shown in Figure 7. Needless to say that the reason why these particular hours

are chosen for maximization is the occurrence of the peak demands at those hours. For the

Raleigh site, the optimal tilt angle and the optimal surface azimuth angle are found to be 40

0 and 80 ° west of south respectively for the month shown in the figure. At the Hesperia site,

these angles are determined to be 50 ° and 10 ° west of south respectively.

3.1.3 Two-axis Tracking Arrays

In this orientation strategy, the array is always facing the direction of the sun for maximum

solar radiation at every hour. In other words, the incidence angle is constantly held at O 0 • This

strategy requires the use of expensive tracking mechanism in both the horizontal and vertical

axes.

The output from a two-axis tracking array model at the Raleigh and Hesperia sites are shown

in Figure 6 and Figure 7 along with the outputs from the other two strategies of array

orientation. From the figures, it is obvious that two-axis tracking provides much more energy

during the day than either the south-facing or the optimal fixed surface azimuth arrays.

However, the peak power generations are the same for all three. It will be seen in a later

analysis that the peak generation at a desired hour is of greater importance than the total

energy generated during the day in the case of utility integrated PV systems combined with

a battery plant meant specifically for supply side load management. More specifically, to

shave an equal percentage of the peak load, the battery size requirement actually increases

with a two-axis tracking array option than either of the other two.


3.2 PV Pet1ormance Simulation Model

Simulation programs are essential for evaluation of the hourly performance of PV systems

given the historically observed irradiance data, the ambient temperature data and in some

cases, the wind speed data. The purpose of the simulation model is to calculate hourly

plane-of-array irradiance at pre-specified tilt and azimuth orientations of PV arrays. Thermal

models are then used to model cell temperatures at each interval of the simulation and

various efficiencies are then calculated with the help of reference efficiencies. DC power

output is calculated as a product of these efficiencies and the modular area of the PV array.

DC/AC inversion efficiencies are either input as a curve or in the form of a regression

polynomial. The major blocks of the performance simulation model are shown in Figure 8.

Block A in the figure, is concerned with the availability of atleast a full year's worth of

irradiance and weather data at the site. The translation of horizontal irradiance on to tilted

surfaces is accomplished in block B. The irradiance on a tilted surface is also known as

plane-of-array irradiance. Each component of the horizontal global irradiance get translated

in a different way. While the direct normal irradiance on the plane-of-array depends only on

the solar zenith angle, the same is not true for the diffuse irradiance component. There are a

number of techniques proposed by different authors for this purpose. Some of the more widely

used models are discussed in the following section.

Block C is the cell temperature model. A cell temperature model is required because the

currents and voltages developed in a solar cell is a function of the cell temperature. Solar

irradiance, ambient temperature and wind speed have a combined effect on the cell

temperature. Some researchers do not consider wind speed in their modeling, and predict a

linear relationship between cell temperature and the solar irradiance. A commonly used

relationship is:


Hourly Gloloo.I Hortzonto.I lrro.dlcrnce, 1 Direct Irraolto.nce, AMlolent T eMpero:ture

o.nd \/Ind Speed

CoMpute Plo.ne-of-o.rro.y 2 Irro.cllo.nce

I CoMpute Module TeMperature 3 I

4 CoMpute DC Power

CoMpute AC Power 5 Using PCU EfflClency Curv1r

Figure 8. Functional blocks in a PV simulation model

51 Optimizing PV output

Tc= Ta+ 0.3A (3.4)

where:

Tc = cell temperature

T. = ambient temperature

A = plane-of-array irradiance

Some consider a more complex thermodynamic relationship between these parameters and

also the wind speed. One of such study is reported by FUENTES (185).

Block D is the array electrical model. This model calculates currents, voltages and peak power

using the output from block C. The power conditioning model is incorporated in block E. Here

de power is converted to ac for use in supplying directly to the grid or after a voltage boost.

3.2.1 Translation of Horizontal lrradiance on the Plane of Array

The plane-of-array irradiance models play a vital role in the design, simulation and

operational studies of a solar photovoltaic system. These models are developed to calculate

the amount of energy available from the sun at a given hour on a surface tilted at any angle

from the horizontal and facing a given direction. The electrical output from a PV system is

directly effected by the amount of insolation received on an inclined plane.

Almost all factors other than the plane-of-array irradiance, are either constants or vary

predictably depending on cell structure, ambient temperature, area of the array, etc. The final

optimal array orientation strategy that must be decided upon, is influenced by the prediction

available from a plane-of-array irradiance model. For example one has to choose one from the

eight array orientation options shown in Figure 5. All of those orientations need translation

of horizontal irradiance onto tilted surfaces. Knowing the importance of plane-of-array


irradiance, it becomes imperative to find a model which can accurately predict the irradiance

on such surfaces.

For design analysis, long-term monthly plane-of-array irradiance models have been found to

be adequate. But analytically, the performance of these models is not known when operational

considerations become important. A change in the time frame is therefore required and daily

and hourly models need to be assessed for their performance. The study sequence adopted

is mentioned below for clarity:

• Four models are compared to determine their applicability on a monthly basis.

• After an acceptable model is found whose predicted output matches the field

observations, a shorter term analysis is performed using models on a daily or hourly

basis to find the best model which matches the observed data.

In choosing the models for study, care is taken so as to include both isotropic and anisotropic

models which are also well known and have been widely used in the literature for solar energy

design and operational studies. The models selected for this study are:

• Liu & Jordan (188)

• Duffie & Beckman (94)

• Klucher [169], and

• Perez (218].

Generally, the direct normal irradiance on a horizontal surface is translated onto tilted

surfaces by multiplying with a factor, (cos i/ cos i) (188), where i is the incidence angle on a

horizontal surface and it, the incidence angle on the tilted surface. The diffuse sky component

is where most authors differ in their opinions. Some have suggested a simplistic isotropic sky

condition (188), and many have presented different forms of anisotropy for the diffuse sky

(169,218,273). It would seem that the translation models ought to be of the split transposition


type where direct and diffuse irradiances are modeled separately assuming the availability

of both types of data. But unfortunately, both the direct and the diffuse irradiance data are

rarely available throughout the U.S., much less the rest of the world. In this situation, only the

global horizontal irradiance (a commonly measured item at numerous locations) are used in

various estimation models given in references (77], (188] to estimate the diffuse component.

Under these circumstances, all translation models are effectively reduced to simple

transposition models considering the global-on-horizontal to global-on-slope relationship

used.

3.2.1.1 Liu and Jordan Model

This model [188] is used in the daily and monthly time frames. This model is valid only for

surfaces facing the equator. The conversion factor R for the daily total radiation is given as;

Hr Hd Hd R = - = (1 - -)Ro + -Rd + R H H H P

where

R0 = conversion factor for the direct normal irradiance

= cos(q> - P) [ si.n C05 - C05 cos co'5 J cos <p sin co5 - co5 cos co5

= cos(<p - P> [ si~ ro'5 - co'5 cos co'5 ]

COS <p Sin C05 - C05 COS C05

Rd = conversion factor for the diffuse sky component

= _!_(1 + cos p) 2

and RP = conversion factor for the ground reflected component


(3.5)

(3.6)

(3.7)

(3.8)

54

= ~ (1 - cos p)p; (3.9)

p = reflectivity (albedo) of ground.

The conversion factor R for the monthly average daily irradiance is the same as 3.10, except

that the daily terms are replaced by the monthly average terms.

3.2.1.2 Duffie and Beckman Model

Duffie and Beckman (94) have presented a model for estimating factor R. They have used an

isotropic diffuse sky model and in contrast to the Liu and Jordan model, this model is claimed

to be able to handle any surface orientations including south-facing, east or west facing arrays

or any other surface azimuth angles. This model, like the Liu and Jordan model also requires

long-term historical data for global irradiance. The diffuse component on the horizontal

surface is determined from equations 3.5 and 3.6, similar to the Liu-Jordan model. The

difference in the two models lies in the treatment of the direct term. Klein and Theilacker

(167), have developed an algorithm for this term. The model is given as follows:

- Fid R =D+-Rd+R H P (3.10)

where

max{O, G(ross,ros,)}

D = (3.11)


Hd a'= a - -=-H

(3.12)

a = 0.409 + 0.5016 sin(ros - 60°) (3.13)

b = 0.6609 - 0.4767 sin(ros - 60°) (3.14)

d . 7t = sin ros - ~s cos ros (3.15)

A = cos p + tan q> cosy sin p (3.16)

B = cos cos cos P + tan o sin P cosy (3.17)

C = sin p sin y/ cos q> (3.18)

i = incidence L = arcos [cos o cos q>{A cos ro - B + C sin ro}] (3.19)

lrosrl = rnin{ros,[arcos(AB + c.J A2 - 8 2 + c2 )/(A 2 + c2)]} (3.20)

- I COsr I if (A > 0 & B > 0) or (A ~ 8)

+ I rosr I otherwise.

lrossl = rnin{ros, [arcos(AB - c.J A2 - a2 + c2 )/(A 2 + C2)]} (3.21)

+ lrossl if(A > O&B > O)or(A ~ B)

COss = - I ross I otherwise.


3.2.1.3 Klucher Model

Klucher (169) developed a model for predicting the irradiance on inclined surfaces using an

anisotropic diffuse sky model. The model he presents is a modification of the Temps and

Coulson model [273) which he found to be valid only for clear sky conditions. The Klucher

model uses hourly measured irradiance data for the global irradiance. The diffuse part of the

model is given below:

where F is the so-called modulating factor defined as

Id 2 F = 1.0 - (-1 )

(3.22)

(3.23)

The second and third terms represent the horizon brightening and the circumsolar brightening

respectively. The direct and ground reflected parts are given by 3.24 and 3.25.

I - I D0 = H. d cos "'

srn a (3.24)

where "' = incidence angle on the inclined plane

(3.25)

It is noteworthy here that under overcast skies when the ratio of diffuse to global irradiance

!JI is unity, the Klucher all sky model reduces to the Liu and Jordan isotropic model, shown

in equation 3.10.


3.2.1.4 Perez Model

Perez, et al. [218) developed a model which uses the anisotropy of the diffuse irradiance by

superimposing upon an isotropic radiance field both a disc and a horizontal band with

increased radiance. This is an attempt to replicate circumsolar and horizon brightening.

The radiance enhancements within these areas were determined by Perez et al. [218) by

analyzing the direct radiation and the global radiation incident upon seven inclined and one

horizontal sensor. The enhancement parameters F1 and F2 are functions of the ratio I/Id, Id and

the zenith angle. The equation for the diffuse component on the inclined surface is given in

terms of the following;

o.5(1 + cos p) + 2(1 - cos WHF1 - 1)Xc(9) cos e· + ~~'(F2 - 1) Ds= ~~~~~~~~~~~~~,;..._~___:,~~~~~~=--~-1 + 2(1 - cos P'HF1 - 1)Xh(z) cos z' + 0.5(1 - cos 2~)(F2 - 1)

where

F, = diffuse irradiance enhancement factor for circumsolar brightening.

F2 = diffuse irradiance enhancement factor for horizon brightening.

W = half angle width of circumsolar disc (assumed equal to 15°)

~ = horizon band angular thickness (assumed equal to 6.5 ° )

~· = altitude of the horizon bandwidth with respect to the sloping plane.

p = slope of the plane.

z = solar zenith angle.

z' = equal to the solar zenith angle if the circular region is totally visible

(3.26)

from the horizontal or equal to the average incidence angle if only partially visible.

Xh = fraction of the circular region visible from the horizontal

e = equivalent of z for the sloping surface.

e· = equivalent of z' for the sloping surface

Xe = equivalent of Xh for the sloping surface.


The direct and the ground reflected parts are identical to Klucher's.

3.2.1.5 Results of the Comparative Study

Three sites representing three regions of the U.S. are selected for evaluating the four models.

These sites are, Raleigh, NC representing eastern U.S., Orlando, FL representing

southeastern U.S. and Hesperia, CA representing the western U.S. General information about

these sites and PV arrays are provided in Appendix B. Data for the Raleigh site comprised

of 3-minute observations for the months of March through July, 1985. That for the Orlando site

are 6-minute observations during the month of December, 1985. Observations for the Hesperia

site are taken at 10-minute intervals for the entire year of 1985.

Some special features of the four models are kept in mind when comparisons are made.

These are shown in Table 1. Table 2 and Table 3 show the comparisons of results obtained

from using the four models. The numbers presented in these tables reflect the monthly

average daily ratios of the irradiance on a tilted surface and that on the horizontal.

Comparisons are made only for the months for which actual data are available at this time.

The column labeled 'Actual' represents the ratios between (measured) plane-of-array and

horizontal irradiances. The four columns that follow represent the same ratio when calculated

by these models using historical data. Table 2 shows the performance comparison of the four

models in Raleigh, NC and Orlando FL. It is seen from this table that the isotropic model of

Liu-Jordan comes close to estimating the actual data in the summer months of June and July

but underestimates by a considerable margin during March. The Klucher model does better

in March but overestimates in June and July. Perez model seems to do better overall. the

comparison at Orlando, FL in December shows that the Duffie-Beckman model is very close

to the actual value while Liu-Jordan overestimates. This is to be expected, because the

Duffie-Beckman model was developed as an improvement over the Liu-Jordan model which


Table 1. Some Characteristics of the Four Models

MODEL NAME

LIU-JORDAN

DUFFIE-BECKMAN

KLUCHER PEREZ


MODELING CHARACTERISTICS

• Monthly average of daily ratios R predicted. • Daily ratio R predicted. • Requires long-term historical data. • Requires only global irradiance data. • Diffuse component on horizontal plane is estimated

• Only monthly average of daily ratios R predicted.

• Requires long-term historical data. • Requires only global irradiance data. • Diffuse component on horizontal plane is estimated

• Hourly ratios RH predicted. _ • Monthly average of daily ratio R predicted. • Daily ratio R predicted. • Does not require long-term historical data if either

direct or diffuse component is available. • Diffuse component is estimated if no observed

data is available.

60

Table 2. Ratio of lrradiance in Raleigh, NC and Orlando, FL

RALEIGH

MONTH ACTUAL KLUCHER PEREZ LIU-JORDAN DUFFIE

MARCH 1.1954 1.188 1.151 1.139 1.125

JUNE 0.9202 0.970 0.955 0.927 0.942

JULY 0.9425 0.982 0.940 0.940 0.953

ORLANDO

MONTH ACTUAL KLUCHER PEREZ LIU-JORDAN DUFFIE

DEC 1.2739 1.324 1.256 1.305 1.269


Table 3. Ratio of lrradiance in Hesperia, CA

MONTH ACTUAL KLUCHER PEREZ

JANUARY 2.210 2.794 2.201

FEBRUARY 1.862 2.026 1.856

MARCH 1.605 2.086 1.472

APRIL 1.491 1.867 1.499

MAY 1.429 1.747 1.405

JUNE 1.400 1.611 1.407

JULY 1.395 1.678 1.362

AUGUST 1.563 1.967 1.554

SEPTEMBER 1.553 1.717 1.584

OCTOBER 1.677 2.215 1.828

NOVEMBER 1.944 2.168 1.649

DECEMBER 2.403 2.767 2.308


was claimed to have come short of accurately estimating the irradiance on tilted surfaces

during the winter. The Perez model provides the next best scenario.

The next site examined is Hesperia which has two-axis tracking arrays. Since

Liu-Jordan and Duffie-Beckman models do not have the capability of modeling tracking arrays,

comparisons for the Hesperia site are confined only to the Klucher and the Perez models.

Table 3 presents the respective irradiance ratios which are compared with the field

measurements for every month of the year. It is seen that the Klucher model always

overestimates the actual data. This is because the Klucher model happens to overestimate

values on clear days when diffuse sunlight is almost negligible. And Hesperia gets more direct

sunlight than any of the other sites in the east or the southeast. On the other hand, Perez

model seems to provide better estimate of the irradiance ratios in Hesperia. However, Perez

model is somewhat off in the month of March.

3.3 Energy Storage With Central Station PV

With the availability of advanced batteries, it is now possible to store large amounts of energy

during off-peak periods of the day for use during the peak periods. This process is called load

leveling. The rationale for this entire scheme revolves around the fact that energy during

off-peak periods is cheaper and easily available whereas that during the peak periods of the

day is very expensive and is derived from fossil fuel. Considerable amount of research and

development work has been performed at the battery test facility (BEST) in New Jersey [221).

Storage batteries are now looked at seriously by electric utilities for load leveling. The

proposed 10 MW battery load leveling project for the Southern California Edison Co. at Chino,

California, is a case in point.


As the storage technology matures and becomes available for electric utility load leveling,

there may be other ways to make it more viable. One such option may be to integrate

batteries and photovoltaic (PV) energy system. Since utilities are in fact looking for the ideal

PV plant which can be as effective as a conventional peaking generating unit, only because

with such a plant, the effective load carrying capacity is the highest. The objective of the

optimization is then to perform a comparative analysis of the benefits of the battery alone

versus the battery-PV hybrid system for load-leveling applications. In order to study the effects

of such a hybrid system in different geographical regions, two different sites - one in the

southeastern and the other southwestern U.S. have been looked at. Results of the study follow

shortly.

3.3.1 Potential For A Combined Photovoltaic/Battery System

The PV plant may be generating power during low-demand periods when the lower

incremental cost machines are operating as base or intermediate capacity. This may not be

the most desirable form of operation as it cannot justify the high installation cost of the PV

plant at certain sites. In cases like this, CHINERY (64) states that it is quite possible that the

operating cash now of some utilities can be adversely affected. This is because they sell

power to many of their customers (especially residential) at the same rate regardless of

whether the sale takes place during on-peak or off-peak periods. Cutting their load during

off-peak periods forces them to sell less power when their profit margin is the greatest. This

act reduces their revenues significantly without reducing their operating expenses.

These problems lead to the general belief that a combined PV and energy storage system set

up with an objective of reshaping the peak demand curve might prove to be an attractive

option for the utility. Photovoltaics, in conjunction with a battery under the peak load

management scheme, would have a unique application in utility peak load restructuring.


Whereas, PV power combined with energy storage in stand-alone mode attempts to supply

all of the load, the central station application of PY/energy storage combination attempts to

shave the peak load where the most fuel savings can be earned by the combined system.

From the point of view of economics, SCHUELER, et al. [248] claim that utility owned energy

storage perform better than dedicated storage for photovoltaic central station application.

Therefore, utilities already planning on having PV power in the generation mix and further

contemplating advanced battery energy storage for peak-shaving might be better off bringing

the two technologies together for a more effective utilization. Details of the performance of

such a system as well as the effect of the nature of PV array orientation on battery

performance are discussed.

3.3.2 Battery Plant Consideration

Sizing a suitable battery adequate for shaving the peak demand hours in every month of the

year is tantamount to determining the size of the battery required to supply the peak load of

the month which contains the annual peak. However, this may not be true for low

peak-shaving requirements. For example, if the month of August contained the annual peak

and assuming that this month had a single daily peak occurring in the afternoons, then for a

peak shaving requirement of upto 6% of the peak load, this particular month will always need

the largest battery size. Any further reduction in the peak shaving requirement will shift the

worse conditions to another month which most probably has double peaks in a day and

therefore the size of the battery is determined according to that required in that month.

For load leveling purposes, advanced batteries are required. These batteries should have the

following features: high efficiency, 70-75%; high cycle life, 3000-4000 cycles; discharge should

be at constant power for 5-8 hours; low demand cost ($/MW) and low capacity cost ($/MWh).


Although, all of these criteria are not met by any of the existing batteries, the following provide

good choices:

1. Sodium-Sulfur,

2. Zinc-Bromine,

3. Hydrogen-Nickel, and

4. Lead-acid.

Out of the above four, only the lead-acid battery has been the front runner in the application

of load leveling. A cycle life of 1000-1500 may easily be reached with the present technology.

For the simulation results presented in this paper, an advanced lead-acid battery

characteristics are used.

Needless to say that the actual size of the battery will depend on the amount of peak-shaving

desired. Some utilities have load profiles which will not allow peak shaving beyond a certain

limit, the constraint being the depth of discharge limitations on the battery itself. A second

factor is the fact that the costs of batteries are largely dependent on the MWh size of the plant

rather than the MW size. Thus, utility planners would opt for a low MWh to MW ratio in sizing

a battery plant. That means a small period of discharge. Also figuring prominently in the

fixation of an optimal amount of peak shaving is the limitation on the total base capacity

available for charging the battery. It so happens that the daily utility load experiences a low

demand period during the early morning hours. Therefore, this period is suitable for charging

the battery with the generating capacity which is available at this time. The operating costs

of this generation, called here, as the base capacity, is minimal. On the other hand, there is

also a limited amount of capacity to be spared, wherefore comes the limitation on the exact

amount of peak shaving possible.

A third constraint on the lower limit of the peak shaving comes from the presence of

photovoltaic power in the grid. The best possible use of PV generation, as pointed out earlier,


is in its utilization during the peak shaving period. This decreases the capacity needed from

battery discharge during these hours and is therefore conducive to the battery sizing.

Reducing the peak load shaving amount certainly precludes the PV power from being

optimally utilized and therefore works against the economics of the utility.

Once the peak shaving period/s has been fixed within the limitations as pointed out,

some additional constraints must be kept in mind before arriving at a final size of the battery.

These are:

1. Battery discharge should be deep enough to supply an entire peak load duration.

2. Base capacity (power taken from the reserve generation during the lowest daily demand

periods on top of any available photovoltaic power) to charge the battery should be

enough for charging at the specific charging rate of the battery.

3. Back-up power, i.e. power outside of the combined capacity of the PV/battery system to

shave the peak should be zero.

4. Usage of PV power outside the peak demand region should be minimized. This is done

in order to earn more fuel and capacity credit.

An iterative computer optimization method to satisfy the above constraints with the maximum

possible peak shaving possible, is employed to yield the results enumerated below. In the two

case studies performed on the typical utilities in the south-east and in the west, it is found that

5% peak load shaving is the optimal amount of load management possible under the

constraints. The size of the battery of course depends on the orientation strategy of the PV

arrays. Figure 9 and Figure 10 illustrate the change in battery capacity for percent peak load

shaved in the southeastern and the western parts of the U.S. respectively. Steeper slopes of

these curves signify the fact that for each percent increase of peak shaving desired, the


,.... c:: :c

4550

~ 3600 >°"' ~ u Ill Q.. nl u

~2650 --nl co

1700

South facing array ~----~~, Optimal array onenbt.1011 0---------.t> T vo axis t.raclang

No PV array

750 ...._~--~---~~-'-~~--~--~~--~~--~--~~....._~_. 0 2 4 6 8 10

Percent. peak load

Figure 9. Battery capacity requirement for percent peak load supplied. Site is Raleigh, NC


4550

...... c:: I i 3600 >-

-t! u

"' 0..

"' u

t2650 --"' co

1700

Soll'lh facing array ))(-(-----"")( Opt.rmal array onent.at.ron ~-----'Z> Tvo axu; !raclang "+"'-------'-P No PV array

750 '--~ ......... ~-......_~-'-~--''--~ ........ ~--'~~ ......... ~-...~~...a.....~~ 0 4 6 8 10

Percent peak load

Figure 10. Battery capacity requirement for percent peak load supplied. Site is Hesperia, CA


number of peak hours increases faster in the case of the western utility thereby requiring

higher battery capacity. This also gives an indication that the peak periods in the western

utility are more flat.

3.3.3 PV/Battery Operating Strategy

Duty Cycle

It is found that a daily duty cycle rather than a weekly cycle would best suit the peak shaving

purposes. This is agreed upon because of the excessive amount of battery capacity required

for longer hours of storage in the weekly cycle application.

Cycle Life

One of the general concerns in battery operation for peak shaving is preserving the cycle life

of the battery. The depth of discharge (DOD) of the batteries has a direct affect on the cycle

life. Generally, an advanced lead-acid battery will last 3000 cycles if its cycling is limited to

50% DOD (99). On the other hand an 80% DOD limits the cycle life to only 1500 cycles.

Besides, temperature also has an affect on the life of the battery. Owing to the dependence

of cycle life on the DOD, it is necessary to maintain the discharge level to a minimum possible.

It will be proved later that PV power can help in preserving the cycle life of the battery through

a combined operation of the two plants for peak shaving.

Combined Operation

The following steps describe how the combined operation of the PY and battery system

is envisaged:


1. During the early morning hours, it is natural to find the battery State Of Charge (SOC)

down to a low level. This is from the preceding day's discharge during peak periods.

Therefore, apply constant power to charge the battery to as high a level possible before

the discharge cycle begins. The charging power is composed of base capacity and

photovoltaic power generation, available only after sunrise, during the charge cycle.

2. Apply all the photovoltaic generations to the peak load during the load management

period. If not sufficient, discharge the battery.

3. The daily duty cycle of the battery consists of one of the following possibilities:

a. Two charge cycles; two discharge cycles:-

• charging is done in the early morning hours.

•charging again done by photovoltaic power in the mid-afternoons when the morning

peak has been shaved and the evening peak is ahead.

• discharge in the morning peak period.

• discharge in the evening peak period.

b. Two charge cycles; one discharge cycle:-

• same as in (a) except that only the morning peak is required to be shaved.

c. One charge cycle; one discharge cycle:-

• charging is done in the early morning hours.

• discharging during one long extended period.

4. During charge periods, if the battery SOC reaches 100%, then all photovoltaic power

available is diverted to supply the load demand at that time even if the load is not within

the peak load period. This is because the PV operating cost is zero and therefore any

available power is an addition to the overall generation capacity with a higher dispatch

priority over the other dispatchable generation.


3.3.4 Comparative Study

Two model utilities from the south-eastern and the western regions of the U.S are selected for

analysis of the load management strategy described in preceding sections. The Load profiles

for these utilities are produced from (98]. The peak load occurs in the month of August for both

utilities and are assumed to be 7000 MW in both cases. The assumption for the annual peak

demand is actually immaterial. The most important factor influencing load management

strategies is the shape of the daily load curve.

The PV array site representing the south-east is chosen to be Raleigh, NC and that

representing the west is Hesperia, CA. Simulations concerning the PV power output itself are

done by using the program PVFORM (198] developed at the Sandia National Laboratories.

Battery (Lead-acid) charging and discharging characteristics are taken from HOOVER (137].

Specifications of the PV battery system can be found in CHOWDHURY and RAHMAN (68].

The optimal load management strategies for both sites are determined by an optimization

routine to be 5% peak shaving for the worst month (in terms of energy capacity requirement).

Because of lower energy requirement in some other months particularly in the spring season,

this translates into a higher (upto 8%) peak shaving capability by the same PY/battery system.

Four representative months, viz., February, May, August and November representing the

winter, spring, summer and fall respectively are chosen for presenting the results of the study.

Table 4 shows the nature of the systems used in the peak load management scheme in the

southeastern utility. Similar results for the western utility are shown in Table 5. The following

observations may be made from these tables:

1. Photovoltaic power combined with battery storage makes a large difference in battery

size compared to the case with no PV power assumed. The differences are:-


Table 4. Peak shaving characteristics In the four seasons for typical utility In the south-east (assuming 7000 MW annual peak).

c Percent Battery Base Cap· A PV array peak Capacity. acity for s orientation. load MW/MWh charging. E shaved. 1 MW

5% - WI 150 - WI 1 South- 6% - SP 350/2050 50 - SP

Facing 5% - SU 50 - SU 6% - FA 0 - FA

5% - WI 125 - WI 2 Optimal 6% - SP 350/1925 50 - SP

surface 5% - SU 75 - SU azimuth 5% - FA 0 - FA

5% - WI 125 - WI 3 Two-axis 6% - SP 350/1925 25 - SP

tracking 5% - SU 50 - SU 5% - FA 0 - FA

5% - WI 175 - WI 4 No PV 5% - SP 350/2350 200 - SP

array 5% - SU 325 - SU 7% - FA 250 - FA

1 WI-Winter; SP-Spring; SU-Summer; FA-Fall


Table 5. Peak shaving characteristics in the four seasons for typical utility in the west (assuming 7000 MW annual peak)

c Percent Battery Base Cap· A PV array peak Capacity acity for s orientation load MW/MWh charging E shaved. 1 MW

5% • WI 0 • WI 1 South- 7% - SP 350/1925 125 - SP

Facing 6% - SU 150 - SU 5% - FA 150 - FA

6% - WI 50 - WI 2 Optimal 7% - SP 350/2025 100 - SP

surface 6% - SU 125 - SU azimuth 5% - FA 150 - FA

6% - WI 25 - WI 3 Two-axis 8% - SP 350/2075 150 - SP

tracking 6% - SU 0 - SU 5% - FA 150 - FA

7% - WI 325 - WI 4 No PV 5% - SP 350/3400 300 - SP

array 5% - SU 475 - SU 5% - FA 225 - FA



• Case 1 vs. case 4:



Saving of 300 MWh in S-E utility

Saving of 1475 MWh in W utility





Obviously, photovoltaics has a bigger impact on load management in the western utility

in terms of battery size requirement.

2. PV/battery combination also has a large impact on base capacity required for charging

the battery as opposed to the case with no PV power assumption. These are as follows:

• For S-E utility:

• For W utility:

25 - 50 MW saving in winter.

150 - 175 MW saving in spring.

275 - 300 MW saving in summer.

250 MW saving in fall.

275 - 325 MW saving in winter.

150 - 175 MW saving in spring.

325 - 475 MW saving in summer.

75 MW saving in fall.

The reductions in base capacity for cases 1,2 and 3 should be examined in the light of

total PV installed capacity. Both utilities had 350 MW of rated PV power in these


simulations, and looking at the above comparisons, the turnaround is quite attractive,

particularly in spring and summer. The savings in summer for the typical western utility

which comes to 475 MW should be compared to the 350 MW of installed PV capacity. The

savings in combined PV/battery case stems from the fact that less base generation

capacity is required to charge a battery with smaller capacity size required compared to

the stand-alone battery case.

3. The fact that PV power can cause low depth of discharge of the battery is evident from the

comparison shown in Figure 11. The "no PV" case shows that the DOD can reach over

70% on a typical day in the month of August at Raleigh while the PV/battery combined

case exhibits a more preferable discharge characteristic, the DOD not reaching 50%.

Similar characteristics are also seen in all the other months at both sites.

4. Another important issue of concern is the cycle life of the battery versus the PV array size.

It is found that the number of charge-discharge cycles do not change significantly for

small changes in the PV array size. Large changes in the latter is not possible in such

applications without losing much of benefits earned in terms of percent of peak load

shaved and amount of base generation capacity saved.

3.3.5 Relative Performance of Array Orientation Strategies

After comparing the attractiveness of PV/battery combination over the battery system

alone, i.e. cases 1,2 and 3 versus case 4, it is useful to compare cases 1,2 and 3 against one

another. In other words, to find out what array orientation strategy is the best for load

management.

Once again from Table 4 (S-E utility):


1.0

0.8 GI f' nl

..&; u

0 0.6 ll .... nl ....

U)

0.4

0.2

4 8

No PV array Opl1mal az1mulh array

.. - - - - - - - -

12 16 20 Ho1r of day

0.0

0.2

0.4

0.6

0.8

Figure 11. Comparison of depth of charge and discharge of battery with and without PV power at Raleigh


GI E'9 nl

..&; u UI

-6 .... 0

..&; ...... D.. GI

0

77



From Table 5 (W utility):



Saving in battery capacity of 125 MWh.

Saving in base capacity of 25 MW

in winter and 25 MW in summer.

Almost identical in all respects to case 2.

Increase in battery capacity of 100 MWh.


in spring and 25 MW in summer.

Increase in battery capacity of 50 MWh.


in winter, 50 MW in spring and

125 MW in summer.

While optimal surface azimuth oriented arrays are better than others in the southeast,

south-facing arrays provide a better perspective of load management strategy in the west. Of

course the final choice of the orientation strategy would have to depend on the economics

involved.

Table 6 and Table 7 show the comparisons for the simulation runs involving the three

strategies for PV array orientation. The indices to look for are the "peak effectiveness ratio"

(column 4) and the "charging effectiveness ratio" (column 6). The former is defined here as the

ratio of array energy supplied by the array to the grid during the peak period to the total

energy supplied by the array to the grid. The "charging effectiveness ratio" is defined as the

ratio of the energy supplied by the PV array to charge the battery to the total energy required


Table 6. Comparisons of the three PV array orientation strategies for the south-eastern utility.

Total Total Peak Total Charging PV array array effec· energy effec· array energy energy tiveness to charge tiveness orient- to load. during ratio battery. ratio a ti on MWh 1 peaks. MWh

MWh

Case 1. 32200 - WI 11200 - WI 0.35 - WI 16770 - WI 0.53 South- 46100 - SP 37100 - SP 0.80 - SP 20460 - SP 0.61 facing 41300 - SU 25900 - SU 0.63 - SU 24570 - SU 0.69

27800 - FA 10500 - FA 0.38 - FA 14000 - FA 1.00

Case 2. 29800 - WI 14000 - WI 0.47 - WI 13270 - WI 0.48 Optimal 47400 - SP 37000 - SP 0.78 - SP 20220 - SP 0.61 azimuth 42700 - SU 31900 - SU 0.75 - SU 18700 - SU 0.41 orient. 29100 - FA 10700 - FA 0.37 - FA 8700 - FA 1.00

Case 3. 43400 - WI 14600 - WI 0.34 - WI 12970 - WI 0.47 2-axis 61600 - SP 45800 - SP 0.74 - SP 17320 - SP 0.77 tracking 61700 - SU 33700 - SU 0.55 - SU 19530 - SU 0.63

41900 - FA 11100-FA 0.26 - FA 9300 - FA 1.00



Table 7. Comparisons of the three PV array orientation strategies for the western utility.

Total Total Peak Total Charging PV array array effec· energy effec· array energy energy tiveness to charge tiveness orient· to load. during ratio battery. ratio a ti on MWh 1 peaks. MWh

MWh

Case 1. 35400 - WI 10300 - WI 0.29 - WI 25600 - WI 1.00 South- 78600 - SP 66900 - SP 0.85 - SP 24500 - SP 0.28 facing 75700 - SU 6090 - SU 0.80 - SU 23800 - SU 0.20

48200 - FA 37900 - FA 0.79 - FA 13000 - FA 0.18

Case 2. 38000 - WI 16900 - WI 0.44 - WI 29200 - WI 0.75 Optimal 78700 - SP 70200 - SP 0.89 - SP 22500 - SP 0.36 azimuth 7520 - SU 62900 - SU 0.84 - SU 21800 - SU 0.22 orient. 50100 - FA 39600 - FA 0.79 - FA 13200 - FA 0.20

Case 3. 50500 - WI 18200 - WI 0.36 - WI 31000 - WI 0.88 2-axis 111000- SP 91200 - SP 0.82 - SP 31700 - SP 0.44 tracking 99100 - SU 75700 - SU 0.76 - SU 21900 - SU 1.00

59000 - FA 44100 - FA 0.75 - FA 12800 - FA 0.18



for charging. Column 3 in The tables also show the total energy supplied by the PV array

during the period of load management. Column 2 presents the PV energy used to supply the

overall load and column 5 shows the PV and base energy used to charge the battery. Column

4 is the ratio of column 3 over column 2 whereas column 6 is the ratio of the PV array energy

used to charge the battery over column 5.

Higher values in columns 4 and 6 indicate a more desirable feature. A higher "peak

effectiveness ratio" means that the array power is used more effectively during the load

management period in terms of the amount of energy being supplied. A higher "charging

effectiveness ratio" signifies the fact that lesser base capacity is used for charging the battery

and that most of the charging power came from the existing PV array. Evidently, from

Table 6 and Table 7, case 2 in which the array is optimally oriented for maximum power

during peak shaving periods, is the best option in this perspective.


CHAPTER 4

Resource Forecast

The dispatching of photovoltaic power has always posed a major problem to electric utility

system operators. This has been largely due to the fact that the short term prediction of solar

irradiance is difficult to predict. The wide variability of the cloud cover and to some extent, the

atmospheric condition makes it hard for any attempt at parameterization of these phenomena.

On the other hand, observed hourly global irradiance data is available at many locations

throughout the SOLMET network [206). These data, as well as the typical meteorological year

(TMY) [207] data which provide the data for typical months of a synthetic year, have proven

to be useful in the past for PV array performance prediction [198). Such weather data are

known to be used in many PV performance analysis models. Examples of such models are

shown in Figure 2 on page 22. These models rely for their analysis on the past historical data

and are therefore accurate only in a most general sense with possibilities of wide statistical

variability between the actual and the predicted data (Refer to Reference [228) for a detailed

comparative analysis).

It therefore seems only logical to assume that a typical synthetic year or a number of years

of historical data may only be useful to predict the average monthly or even daily PV array

Resource Forecast 82

performance. A time scale smaller than the day requires knowledge of the cloud cover and

their expected instantaneous changes.

In applications such as utility grid connected systems. it is important to be able to dispatch the

PV output in the same fashion as any conventional generators. like coal and oil-fired units.

That means the dispatcher has to have the information about the general availability of PV

power plant 24 hours in advance (for unit commitment), and expected fluctuations in PV output

in 10 minute time frame (for economic dispatch). The expected weather conditions of the next

day, will determine the availability of PV power in the 24-hour time frame. However, for the

economic dispatch considerations the prediction of PV output in 10 minute (or less) intervals

is necessary. Failure to do so will cause the PV power to remain non-dispatchable and will

inhibit its penetration in the utility grid.

This was the incentive for undertaking a study which would enable prediction of sub-hourly

solar irradiance and prove its usefulness to not only the photovoltaic community, but the

electric utility industry as well. In this chapter, A novel approach is presented, for the

prediction of the solar irradiance in the sub-hourly time frame (3-10 minutes) by means of a

Box and Jenkins time-series analysis [37).

4.1 Background Information

A number of authors have previously presented models to estimate the global solar

irradiance. Of these some are stochastic in nature and the rest use some form of

parameterization of known phenomena. GLANH et al. [117), have used Model Output

Statistics (MOS) to predict, among other weather variables, the variation of the cloud amount.

MOS is a weather forecasting technique which consists of determining a statistical


relationship between a predictand and variables forecast by a numerical model at some

projection time. The lead time of projection varied from 6 hours to a day. The predictions

depend on empirical relationships derived from observations of numerous weather variables

on the hour.

PURI [225) has introduced a statistical Markovian irradiance model for predicting the

time-sequence of half-hour solar radiation values on a horizontal surface, which uses hourly

irradiance values. He finds a half-hour transition density function from the hourly transition

density function and predicts the joint cumulative distribution function for several successive

normalized half-hour values.

ATWATER, et al. [12). have developed a parametric model which accounts for atmospheric

phenomena. Parameterizations were used to account for Rayleigh and Mie scattering and for

absorption by permanent gases, water vapor and aerosols. Cloud cover was incorporated into

their model by using cloud transmission functions developed by HAURWITZ (128). Their

models estimate the global horizontal irradiance at any time of the day with an a-priori

assumption that cloud cover amount at every layer is known.

BRINKWORTH (44) recognizes the sequential characteristics in the past solar irradiance data

and introduces a stochastic model which generates future irradiance sequences. He uses the

autocorrelation function of the irradiance time-series based on long-term averaged data. This

model is dependent on a reference year of irradiance measurement and although useful for

solar-thermal system design, may not be very useful for the photovoltaic performance study

as pointed out earlier.


4.2 Time Series Modeling in lrradiance Prediction

4.2.1 Choosing the Model

The most fundamental time series models are the autoregressive model and the moving

average model (37). In the autoregressive model AR(p), the current value of the process is

expressed as a linear combination of p previous values of the process and a random shock.

(4.1)

In order to write this in a more convenient form, the following operators are introduced.

So that equation (4.1) can be written as:

(4.2)

In the moving average model MA(q), the current value of the process is expressed as a linear

combination of q previous random shocks.

(4.3)


Introducing the operator

equation (4.3) can be written as:

(4.4)

The general mixed autoregressive-moving average model ARMA (p, q) is a combination of (4.2)

and (4.4)

(4.5)

Writing (4.5) is the operator notation

(4.6)

Equation (4.6) can only be used to model stationary processes where the roots of the

polynomial q>(B) and 0(8) lie outside the unit circle. Non-stationary processes can be modeled

by differencing the original process i; to obtain a stationary process, wt . Multiple differencing

may sometimes be required in order to achieve stationarity. This results in an autoregressive

integrated moving average ARIMA (p,d,q) model, which is expressed as:

(4.7)

where Vd is the differencing operator of order d.


It is a well known fact that the hourly solar irradiance data presents a diurnal as well as an

annual periodicity. To model such data in its raw form would mean using a seasonal ARIMA

model which recognizes the dependence of a particular hour's data on the same hour of all

the previous day's and all previous year's data. Needless to say, the dimensionality of this

seasonal modeling appears to have unwieldy proportions. To make things less complicated,

it becomes necessary to pre-whiten the solar irradiance data so that all periodicities may be

stripped. The underlying principle is the recognition of the fact that the randomness found in

the global solar irradiance data received on earth's surface is caused by changes in the cloud

cover and the aerosol content in the air. A clear day's (cloudless sky) irradiance data may

be estimated accurately by atmospheric parameterization (85], and is therefore deterministic

in nature. It is the stochastic behavior of constant cloud movement which makes the radiation

on a cloudy day difficult to predict. It was therefore decided to model the cloud cover, or in

computational terms, the cloud transmissivity coefficients by an ARIMA (p,d,q) model of the

form shown in equation 4. 7 where i; represents the transmission coefficients.

4.2.2 The Pre-whitening Process

This is the process of obtaining i; as described above from past observations of the global

solar irradiance. Global irradiance under cloudless skies is written as the sum of a direct

beam component 18 and diffuse components from Rayleigh scatter l0 R and scattering by

aerosol 10 A (85]:

18 = S' cos 9z[T,(O)T,(R) - awJT,(a) (4.8)

loR = S' cos 9zT,(0)[1 - T,(R)]/2 (4.9)

loA = S' cos 9z[T,(O)T,(R) - aw][1 - T,(a)]ro0 f (4.10)


where: S' = the solar constant (1353 W/m2)

corrected for departure of the actual

Sun-Earth distance from the mean value

ez = the solar zenith angle

aw = the absorptivity of water vapor

co0 = the spectrally averaged single scattering

albedo for aerosol

f = the ratio of forward to total scatter by

aerosol.

T,(O) = the transmissivity after absorption by ozone

T,(R) = the transmissivity after Rayleigh scatter

T,(a) = the transmissivity after extinction by aerosol

The parameterization used in the prediction strategy follows in part, that used in the MAC

model [84), which has been used in the estimation of solar irradiance and its components.

The derivation of these parameters are described in the following sub-section.

4.2.2.1 Parameterization for the Prewhitening Process

Optical Air-mass

m, = ____ 35 ___ _

(1224 cos2 ez + 1) 112 (4.11)

Transmittance after Ozone Absorption

0.1082 X0 0.00658 X0 0.002118 X0 T,(O) = 1 - + ___ __..;;_ + ______ ....:.,_ __ _ (1 + 13.86 X0 )o.sos 1 + (10.36 X0 )3 1 + 0.0042 X0 + 0.00000323 X!

(4.12)

X0 = m,U0 , U0 = 3.5mm


Water Vapor Absorptivity

Water vapor absorption is given by the equation:

a = w (1 + 141.5 Xw)0'635 + 5.925 Xw

In Uw = (0.1133 - In(/... + 1)) + 0.0393td

(4.13)

(4.14)

Where td is the dew point temperature (°F) and A. is a variable exponent by which the

atmospheric water vapor path length is modified. A. is a variable depending on the season and

the latitude of the site. Values of A. for different seasons and latitudes have been computed

and reported in (259).

Transmissivity after Extinction by Aerosol

The transmissivity after extinction by aerosol is calculated from:

T,(a) = exp( - µ8 m,) = kmr (4.15)

Values of the extinction coefficient µ. for a particular site is found by using an equation given

in reference (279). This equation is:

µ8 = - ~ In [l/1(0)) r

(4.16)

where I is the measured direct beam flux density for the whole spectrum and 1(0) is the

spectrally integrated value of /"(/...), which is the flux density beneath an aerosol free

atmosphere. 1(0) can be calculated [277) as:


1(0) = S[T,(R)T,(O) - Bw] (4.17)

Rayleigh Scatter

Davies et al [85) have presented the following table for relating the Rayleigh scatter and the

optical air mass:

m, 0.5 1.0 1.2 1.4 1.6 1.8 2.0 3.0

T,(R) 0.9385 0.8973 0.8830 0.8696 0.8572 0.8455 0.8344 0.7872

m, 3.5 4.0 4.5 5.0 5.5 6.0 10.0 30.0

T,(R) 0.7673 0.7493 0.7328 0.7177 0.7037 0.6907 0.6108 0.4364

Aerosol Scatter

The aerosol scatter is calculated from a relationship of the ratio of the forward to total scatter

for aerosol. This relationship is also found in a tabular form in (85).

25.8 36.9 45.6 53.1 60.0 66.4 72.5 78.5 90.0

f 0.92 0.91 0.89 0.86 0.83 0.78 0.71 0.67 0.60 0.60

Since global irradiance le on a clear (cloudless) sky assumption is given by

le = Is + loA + loR (4.18)

we have,


T (0) le= S' cos 0z[T,(O)T,(R) - aw)T,(a) + Tl1 - T,(R)]

(4.19)

Also, since

(4.20)

where 10 = extraterrestrial irradiance

'ta = total transmissivity on a clear day.

Comparing (4.20) with (4.19),

T (0) 'ta= T,(a)[T,(O)T,(R) - aw][1 - roof]+ T(1 - T,(R)) + 2T,.(R)roof - awroof (4.21)

For a cloudy sky, 'ta is modulated by the transmissivity of the clouds at any given instant of

time. Therefore the total all-sky transmissivity 't, on a cloudy day would be

(4.22)

where 'tc = transmissivity of the cloud.

If 't is already known, and since 't• may be calculated as described in equations 4.8 to 4.21,

we already have the input time-series 'tc, to the ARIMA (p,d,q) model.

Commensurate with equation 4.18, we may also write the all-sky global irradiance, IA on

earth's surface as:


(4.23)

Using long-term historical observations of IA at any site, t may then be found from equation

4.23.

We can now generate the stationary time series tc = _.!... which is Gaussian by nature. t.

4.3 Simulation

The pre-whitened time-series tc is used in the ARIMA (p.d.q) model given by equation 4.7 to

estimate the values of the autoregressive and moving average parameters. The latter are

used in a forecast model originating directly from the ARIMA model itself. The forecast model

requires at least one previous hour's data and the data at the top of the hour at which

simulation is desired. Simulation continues for all the sub-intervals within the hour. Forecast

updates may be done at any interval during simulation. The forecasted values of the solar

irradiance at those intervals is found by the anti-mapping technique which is the reverse of

the transformation described in equations 4.22 and 4.23.

The entire simulation process consists of separate simulations for the direct beam irradiance

component, the irradiance component after Rayleigh scattering and the irradiance component

after aerosol absorbtion and scattering. These are described next.

• Beam Component

1. Optical air mass.


2. Ozone path length (for transmissivity through ozone layer).

3. Dew point temperature (to determine atmospheric water vapor path length).

4. Spectrally averaged single scattering albedo ro0 for aerosol.

For scattering aerosols: ro0 = 1

For absorbing aerosols: ro0 = 0

For urban areas: ro0 = 0.75

5. Aerosol extinction coefficient which depends on the climatic conditions at the site.

6. Sun-earth geometrical relationships.

• Diffuse Component After Rayleigh Scatter


• Diffuse Component After Aerosol Scatter


2. Single scattering albedo for aerosol.

3. Aerosol extinction coefficient.

4. Sun-earth geometrical relationships.

The flow chart in Figure 12 shows the simulation process.

4.3.1 Predicting the Output from a Photovoltaic System

The computer simulation program PVFORM (198) is modified to take in the sub-hourly

irradiance data generated, and to calculate the output from a given photovoltaic system.

Additional input requirements for PVFORM are temperature and wind speed measurements.


SYNTHETICALLY J GENERATED

IRRADIANCE DATA

H PRE - 'JHJTEN I 3

HISTORICALL ye:. OBSERVED STATlONARY

lRRADlANCE DAT A TIME-SERIES CLOUD i.--

TRANSHISSIVI TIES 4

I AR IMA MODELS I t

SUB-HOURLY FORECASTED

CLOUD TRANSH1SSIVITIES 6

SUB-HOURLY FDRECASTED GLOBAL INVERSE 7

IRRADIANCE TRANSFDRHA TIDN DATA 8

Figure 12. The simulation process to forecast global irradiance


Although the program also requires observed direct irradiance data, these are synthetically

generated as shown in box 1 of Figure 12.

4.3.2 Programming Considerations

The PV output forecast strategy is an integral part of an extended scheme, that of dispatching

the PV generations in the electric utility's power system operation. the PV output forecast is

coded into a computer module called FORECST. The latter consists of two sub-modules called

SIMUL and PREDIC. The relationship between these computer modules and their input and

output are shown in Figure 13. SIMUL generates a simulated global irradiance and direct

normal irradiance data on clear days during the period of interest. Input for SIMUL consists

of:

• Dew point temperature at the site

• Turbidity at the site

• Actual direct normal data (if turbidity at the site is not known)

• Actual global irradiance

Output from the sub-module SIMUL consists of:

• Simulated global irradiance on clear days

• Simulated direct normal irradiance data

• Simulated cloud cover data at the site

Sub-module PREDIC generates the forecasted sub-hourly PV generations which is used

by the DRIVER module. The inputs for sub-module PREDIC are the following:


Irro.dlo.nce Do. to. SIMulo. t1on

I TAPE

Dew point tel"lpero.ture

a.t site

Turbidity o.t site

l l ACTUAL DIRECT NDRHAl DATA

DATA BAS!

I TAPE

+

SIM UL

PV a.rro.y TeMpero.ture

Wind speed

TAPE I

PV output forcrco.sts

Sub-hourly PV Output Foreco.s-t

Figure 13. Execution of the FORECST module


• Time series parameters at the site

• PV array data

• Wind speed and temperature at the site

• Simulated global irradiance on clear days

• Simulated direct normal irradiance data

• Simulated cloud cover data at the site

The forecasts generated by SIMUL are based on the specific ARIMA (p,d,q) model applicable

for the site and period of the month. According to reference [37), the forecast equation is

derived from the ARIMA (p,d,q) model as follows:

Equation 4.7 can be written as:

(4.24)

where '1'(8) is called the generalized autoregressive operator. It is a non-stationary operator

with d of the roots of the polynomial '1'(8) equal to unity.

Equation 4.8 can be written directly in terms of the difference equation [37) by:

Substituting t + I in (4.25), we have

(4.26)

Taking conditional expectations at time t, in (4.26), we obtain,

(4.27)


To calculate conditional expectations, we note that if j is a non-nagative integer

[Zt+ j1 = E[Zt+ j1 = ~t(J); j = 0, 1,2, ...

(at-11 = E[at-11 = at-l = Zt-l - ~t-j- 1 (1); j = 0,1,2, ...

(at+ 11 = E[Bt+ 11 = 0; j = 0, 1,2, ...

Therefore, to obtain forecasts ~(/), one would write down .the model for z.+ 1 in the form shown

in equation 4.26 and treat the terms on the right according to the following rules (371:

• The z._1 U = 0,1,2, .. ) which have already happened at origin t, are left unchanged.

• The z.+1 U = 0,1,2, .. ) which have not yet happened, are replaced by their forecasts~(/)

at origin t. /\ • The a1 _ 1 U = 0,1,2, .. ) which have happened are available from z._1 - z._1_ 1(1).

• The a,+1 U = 0,1,2, .. ) which have not yet happened are replaced by zeroes.

4.4 Simulation Results

Two sites representing the Southeastern United States were selected for evaluating the

forecast model. These sites are, Raleigh, NC and Richmond, VA. General information about

these sites and PV arrays are provided in Appendix B.

Data for the Raleigh site comprised of 3-minute observations for a 12-month period, March

1985 through February 1986. That for the Richmond site were 10 minute observations during


the months of June 1986 through March 1987. The Virginia Power site has the Sandia National

Laboratory designed on-site data acquisition system (ODAS). The Carolina Power and Light

site has an industry standard data acquisition system very similar to the ODAS. To assure

proper data quality, some reasonableness checks on the observed data are made and missing

data are filled in by interpolation.

4.4.1 Identification of the ARIMA Model (p,d,q)

For a better presentation of existing conditions, the time series data are resolved into weeks

rather than an entire season's or a full month's data. This gives a more realistic and accurate

estimate of the parameters in the model. Techniques for preliminary identification of time

series models rely on the analysis of autocorrelation function (ACF) and partial autocorrelation

functions (PACF). Figure 14 shows the ACF of the undifferenced time-series data for the 1st

week of March in Raleigh.

The non-decaying function indicates that differencing is required. The reason for persistence

of non-stationarity of the pre-whitened data is the discontinuity in the series during night-time

and early morning hours, during which times, irradiance is obviously inexistent. Figure 15

shows the ACF of the same data after differencing of the first order (V 1) is applied to the data.

Figure 15 shows the PACF of the same data. These figures suggest a moving average model

of order 2, considering the relatively large autocorrelations at lags 1 and 2. No autoregressive

parameters need to be included as is apparent from these figures. The parameters in the

initial model are estimated using maximum likelihood techniques and the model is checked

for goodness of fit. An accurate model produces residuals (one-step ahead forecasting errors)

that are white and will therefore have zero autocorrelations at lags 1 to oo. Figure 17 shows

that ACF of the residuals. From the figure it is evident that the fitted model is adequate except


1. 0] 0.8

0.6

~ O. LI

.... 0.2 < -' ~ -0.0 ~ 8 -0.2 .... :::> < -0.Ll

-0.6

-0.8

-1. 0 0 3 6 9

Figure 14. ACF of March Data in Raleigh.

Resource Forecast

12 LAGS

15 18 21 2Y

100

I. 0

0.8

0.6

~ 0.4

... < 0.2 ...J

~ -0.0 ~ 8 -0.2 ... ::::> < -0.li

-0.6

-0.8

-1. 0 0 3 6

Figure 15. ACF of the Differenced Data

Resource Forecast

9 12 LAGS

15 18 21

101

I. 0

0.8

0.6

0:: 0.4 0:: 0 <.> 0.2 0 t-::> < -0.0 _, < ;: -0.2

11 I I ~ Q. -0.4

-0.6

-0.8

- i. 0 0 3 6

Figure 16. PACF of the Differenced Data

Resource Forecast

9 12 LAGS

1 5 18 21

102

1. 0

0.8

0.6

~ 0.4

.... 0.2 < _, ~ -0.0 ~ 8 -0.2 .... ::> < -0. Li

-0.6

-0.8

-1. 0 0 3 6 9 12 15 18 21

LAGS

Figure 17. ACF of the residuals


that the model needs autoregressive factors at lags 4, 7 and 19, suggested by the spikes at

these lags.

Similar procedure was followed for all months of data available at each site. Table 8 and

Table 9 show the models fitted for the data in Raleigh and Richmond respectively.

Forecasted global irradiance are compared against the actual data at both sites. Also, the

photovoltaic power output as simulated by PVFORM are compared against actual PV output

data at both sites.

Figure 18 shows the comparison of the global irradiance data as forecasted by the ARIMA

model and measured global irradiance data at Raleigh for the 1st week of March. The figure

shows simulations at hours 12, 13 and 14. Forecasts are issued at the top of each hour for

all the ensuing intervals throughout the hour. For the site at Raleigh, each interval

corresponds to 3 minutes.

Figure 19 shows the predicted PV output for the same time intervals at the same site. Both

figures suggests that the forecasts are accurate most of the time except when there are

sudden transitional changes in the cloud cover moving across the sun. In other words, the

randomness involved in sudden extreme changes in the sun's intensity (e.g. bright sun to fully

shaded sun and back to bright sun again) during an interval will not be picked up by the

forecast model.

Figure 20 shows the comparison of modeled and observed data in the month of June at

Raleigh. The intervals in the figure are also equal to 3 minutes and the hours shown are 9, 10

and 11. Figure 21 provides the same comparative information for Richmond in March.

Forecasts are issued at intervals of 10 minutes at this site. The figure shows comparison for

the hours of 11,12 and 13. The transitional change from a clol!dY to a clear sky is evident but


Table 8. Fitted ARIMA (p,d,q) Models In Raleigh, NC.

Week Month d Autoregressive Moving Average Parameters Parameters

MAR 1 q>, = 0.085 (j)7 = 0.059 01 = 0.331 (j)19 =0.091 02= 0.163

1 q>5=0.089 q>8 =0.089 01 =0.491 JUN 1 q>,=0.092 q>g=0.117

(j)11 =0.086 MAR 1 q>5=0.102 01 = 0.332

02= 0.221 2 JUN 1 None 01=0.577

02 =0.212 (j)3 =0.123 (j)9 =0.093 01 =0.462

MAR 1 q>7=0.091 (j)14 =0.118 (j)15=0.090

3 JUN 1 q>3=0.085 01 =0.482 (j)g =0.120

MAR 1 q>4 =0.102 q>8 =0.106 01=0.391 (j)19 =0.070 02=0.132

4 JUN 1 q>2=-0.191 01 =0.415 q>5=0.110 02=0.397 q>8 =0.121 q>7=0.135 01=0.445

MAR 1 q>g=0.171 q>1,=0.108 02 =0.186 5 q>,g=0.147

JUN 1 q>3=-0.149 0, =o.306 <P12 = -0.148 02=0.181


Table 9. Fitted ARIMA (p,d,q) Models In Richmond, VA.

Week Month d Autoregressive Moving Average Parameters Parameters

1 MAR 1 None 01 = 0.265

2 MAR 1 q>, = 0.093 <p5 = 0.099 None <Jl11 =-.099 <j)19 =-.110

3 MAR 1 <Jl2 = 0. 143 <p5 = 0.078 None q>14 = 0.115 <p18 =-.099

4 MAR 1 <p4 = 0.093 <p8 = 0.157 None <p13 =-0.167

5 MAR 1 None 01 =0.189 02=0.249


N I: ...... :!

GI ~ Ill

-ij

~ -Ill ..c ,.Sil l.!J

800

600

400

200

Ob;erved - - - - Forecast

-\)\f'v

\\/ \ /"-- '\

0 '--~~~-'-~~~--I'--~~~-'-~~~-"~~~~-"-~~~-' 0 20 40 60

Intervals

Figure 18. Global lrradiance comparison at Raleigh In March


3750

3000

~ 2250 ~

0

> a.. 1500

750

-v----.:..

Observed - - - - Forecast

----

0 ...._~~~ ........ ~~~~--~~~---~~~~--~~~~.._~~~--0 20 40 60

I nlervals

Figure 19. PV output comparison at Raleigh in March


800

N ~

600 ' ;;§

II ~ 111

-6

~ - 400 111 ..ll _g l!)

200

I I I

\-v /\,-1

Observed ---- Forecast

0 '--~~~ ........ ~~~---'"--~~~..Jo-~~~--'~~~~_._~~~-' 0 20 40 60

Intervals

Figure 20. Global irradiance comparison at Raleigh in June


N l: ..... ;;s

Cll ~ RI

-ij

~ RI

...0

.Ji! l.!J

BOD

600

400

200

Ob;erved - - - - Forecast

3 6 9 Intervals

Figure 21. Global irradiance comparison at Richmond in March

Resource Forecast

12 15 18

110

is not very abrupt, and the forecasts therefore, follow the actual data with a fair amount of

accuracy.

Figure 22 shows the improvement in the accuracy of the forecasts when forecast updates are

applied at the half-hour mark. Hours 10, 11 and 12 are shown in the figure. Each interval

corresponds to 3 minutes. The RMSE (Root Mean Squared Errors) for the months of March

and June at Raleigh are 21.82% and 20.93% respectively. The MBE (Mean Bias Errors) for the

same two months at this site are 2.5% and 2.57%. At Richmond, the RMSE for the month of

March is 19.7%, while the MBE is 1.88%.

4.5 Conclusions on the Forecast Strategy

The following observations can be made about the predictive model and the results presented

in this chapter.

1. An accurate and relatively simple method (compared to other statistical methods) to

predict solar irradiance is proposed.

2. A comprehensive model is presented which can forecast the irradiance value for any lead

time from a few minutes to an hour.

3. Input requirements are not very restrictive. Only requirements are past global horizontal

irradiance measurement at a site.

4. Results show that when compared to actual data measured at several locations, the

forecasts are quite accurate and the model is site independent.


--N l:: ...... ~

cu g Ill

-6

~ Ill ...c _g

l!J

800

600

400

200

/\

Obi:erved - - - - Forecast

0 ,__~~~--'-~~~~..._~~~--"~~~~ ........ ~~~~..__~~~-' 0 20 40 60

Intervals

Figure 22. lrradiance comparisons with updates


800

N

~ 600 :!

Cll ~ Ill

-ij

~ Ill 400

...0

...5il l!l

200

Obi;;erved - - - - Forecast

0 '--~--'~~ ......... ~~--~~.L-~--'---~.....L.~~-'-~~..&.-~---JL...-~-' 0 4 8 12 16 20

Intervals

Figure 23. A case of model Inaccuracy.


5. Forecasts are found to be inaccurate only when there are sudden transitional changes in

the cloud cover moving across the sun. In other words, the randomness involved in

sudden extreme changes in the sun's intensity (e.g. bright sun to fully shaded sun and

back to bright sun again) during an interval will not be picked up by the forecast model

and is generally considered impossible to predict by any forecast model. Figure 23

illustrates an example of model inaccuracy. The hour shown is 10 A.M. It starts as a very

clear day and within one interval dark clouds cover the sun. As obvious, the model cannot

predict this situation.

6. One of the many applications of the forecast methodology is that, it may effectively be

used to predict photovoltaic power output at a lead time tL assuming a certain origin t0.

A PV plant may therefore be considered as a dispatchab/e generation unit comparable to

the operation of a combustion turbine unit in the generation scheduling scheme of electric

utilities.


CHAPTER 5

Unit Commitment

Unit commitment is the process of selecting a combination of generating units that will supply

a future expected load of the system over a required period of time, at minimum cost as well

as provide a specified margin of the operating reserve known as the spinning reserve. The

determination of the units to be operated in parallel in a given interval depends on their

operating costs as well as technical merits. While the operating cost consists of fuel and

maintenance costs, the technical merits include governor characteristic, stability limitation,

voltage regulation, etc., of the units.

As a matter of practice, generating units are broadly divided into two groups: (a) thermal and

(b) hydro. The operation of thermal units involves both fuel and maintenance cost, but that of

hydro generators require only maintenance costs. Thermal units include conventional steam

plants, nuclear plants, and diesel and gas turbine units. Of these four categories, the latter two

types are mostly used as peaking units, i.e., units are put to service during peak load periods

only. The other two types based on fossil and nuclear fuel respectively, run throughout the

load cycle, and are called base load units.

Unit Commitment 115

Unit commitment is a part of the production control scheme in power systems. The main

objective of production control is to minimize the cost of generated power while maintaining

its quality and satisfying the system security constraints. This implies directly that losses in

both the generation and the transmission of electrical energy must be as small as possible.

All participating generators are run at high efficiencies, the mix of production resource is

exploited economically and the energy is transmitted optimally.

The activities in the production control field have traditionally been based on planning. The

aim is to break down the overall objectives into detailed plans, normally on an hourly basis,

that can be carried out by the operator in the control center. Thus, several steps are taken

in a hierarchical scheme to support the operator's ambition always to have production

resources available to meet the load demand and guide him to operate the generating units

so that the most economic alternatives are chosen.

The long term off-line production planning takes all available generating plants into

consideration - hydro power plants, oil and coal-fired power plants as well as nuclear power

units; and then determines the set of generating units which meets the expected load demand.

This implies the requirement of load prediction functions to predict the future load demands,

both in the long and short term basis.

The active power production control is accomplished by the cooperation of several on-line and

off-line application functions in a four level hierarchy as outlined in Figure 24. Other programs

such as data acquisition, state estimation, security management functions, etc., are also part

of the production control package. Production control thrives on data transfer between each

level of the hierarchy and is therefore dependent on error-free operation of each of the

functions.

In most modern power system control centers, all functions are part of a man-machine

interface, the man being the dispatcher and the machine being a number of digital computers.

Unit Commitment 116

UlCAL CDHTRllL

RESOURCE SCHEDULING • Time interval - year/weeks • Weekly hydro generation • Fuel management.

UNIT COMMITMENT •Time interval - day/hours. •Hourly generation schedule. •Interchange schedule.

AGC •Time interval - minute/seconds. •Set points for plants or units. •Control of inadvertent tie-line flow.

ECONOMIC DISPATCH •Time interval - hour/minutes. •Base points selection. •Participation factors.

LOCAL CONTROL •Time interval - seconds/milliseconds. •Control orders for units. •System frequency control.

Figure 24. A four-level hierarchy In production control

Unit Commitment 117

c ::I ;::; 0 0 3 3 ;::; 3 111 a

..... CD

Dn-lln• CoMput•r Bo.ck-up CoMputer

St!curlt:t:'. Functions SysteM Support

Alo.rMs Logging AutoMo. tic Genera. tlon Control Buy I sell Ne go tlo. tlon

Sto. te Estll'lo. tton Un11: COMMl1:Ment

Contingencies I I I Loo.d Flow

EconoMlc Dlspo. tch Loo.d F oreco.stlng

Supervisory Control o.nd Do. to. Acquisition

<SCADA>

Short Circuit

I Sto.blllty

Figure 25. Relationship of unit commitment to other programs In the control center

Figure 25 shows a functional block diagram of the control center. The relationship between

unit commitment and the other programs in the production control hierarchy is evident from

the figure.

5.1 Solving the Unit Commitment problem

At present, unit commitment algorithms consider the following generic constraints:

• Initial unit operating conditions

• Unit maximum/minimum output levels

• Unit minimum up-time and minimum down-time

• Crew constraints

• Must-run and must-out constraints

• Spinning reserve constraints

While the purpose of this dissertation is not to solve the unit commitment problem, it will be

worthwhile to mention the existing solution techniques. The most talked about techniques for

the solution of the unit commitment problem are linked to six types of methods:

1. partial enumeration method (of the branch and bound type)

2. dynamic programming (DP) method

3. Benders partitioning method

4. heuristic method (e.g. priority list scheme)

5. Lagrangian relaxation method

6. Mixed integer-linear programming (MILP) method

Unit Commitment 119

Of these methods, the priority list scheme is the most popular. DP algorithms are the only

ones that approach an optimum solution for large systems. MILP algorithms are just

beginning to be researched and are not widely used on large system problems. Besides the

above solution techniques, a new solution methodology has been introduced in (194). The

author proposes an expert system approach in this methodology.

Results of a unit commitment program are an integral part of this dissertation. This is used in

the proposed economic dispatch program discussed in a later chapter. In the development

of this model for incorporating central station PV systems, a priority based unit commitment

program was used. The specific program used is the "Unit Commitment and Production

Costing Program (GPUC)" developed by Boeing Computer Services for the Electric Power

Research Institute (EPRI), (29,30). A brief discussion of the program is given below, details can

be found in (29,30).

5.2 EPRl's Unit Commitment Program

The program is designed to analyze the operations of generation and transmission systems

consisting primarily of thermal committable generating units and with possible additional

capacity in the form of non-committable combustion turbines, pumped storage hydro and

hydro units. Its main function is to schedule generation and interchange on an hourly basis

for periods ranging upto a week. Given a profile of the expected integrated hourly loads, a

description of the generation system and a set of scheduling constraints, the program

generates a unit commitment schedule such that the expected system load is met at suitably

low cost without violating any of the numerous operating constraints. Once a schedule has

been determined, the total production costs (fuel plus any start-up costs) are estimated. The

Unit Commitment 120

program also monitors fuel consumption by generating unit, station and fuel type and

compares this usage with any fuel usage constraints.

The following subsections highlight the scheduling process used by the program.

5.2.1 Input Data

The input data required by GPUC consists of:

• processing options such as spinning reserve requirements, priority list generation

options, load specification option, etc.

• unit identification, cost and performance data such as unit id, heat rate curve, startup

time, minimum downtime, maximum up time, boiler cool down time, etc.

• load models for a week. The load for each 24 hour period is assumed to start at 8:00 a.m.

and the loads specified have to be hourly integrated loads.

• manual scheduling data for hydro, pumped hydro and thermal units and interchange.

• transmission loss data appropriate to the option exercised. GPUC allows three options for

this purpose:

• ignore transmission losses;

• compute transmission losses using the 8-constants provided; or

• use a quadratic function of the load for computing losses.

5.2.2 Priority List Generation

Commitment of dispatchable units proceeds on the basis of a single priority list which may

be provided by the user or generated by GPUC. The priority list generation is based on the

Unit Commitment 121

operating cost of a unit at a user specified fraction of the generator set capacity. Units are

removed from the set as their priorities are assigned. The process stops when the capacity

of the reduced generator set is a specified fraction of the total generation capacity. The units

remaining in the set are then assigned priorities based on the relative operating costs at their

maximum capacity.

5.2.3 Hourly Generation Maximum Capacity

This quantity is central to the scheduling of non-committable capacity. It is determined as the

summation of:

1. the maximum capacities of all on-line committable units

2. the maximum capacities of any combustion turbines which are user-scheduled to be

on-line; and

3. any user-scheduled interchange and hydro capacity.

5.2.4 Reserve capacity From Non-committable Sources

All non-committable sources contribute to two types of reserves (ten minute and spinning

reserves) as a function of the unit type and status during the hour. The reserve capacity from

non-committable sources is required in order to compute:

1. the ten minute and spinning reserve capacity from such sources; and

2. an estimate of the additional reserve capacity from the committable sources.

Unit Commitment 122

5.2.5 Precommitment of Peaking Units

The purpose of this process is to schedule combustion turbines and interchange on an hourly

basis such that, for each hour:

1. there is sufficient on-line generating capacity and interchange to meet the expected load

plus losses;

2. if possible there is sufficient capacity and interchange to meet the load plus losses and

reserve requirements; and

3. if desired by the user, peaking units are scheduled to displace the more expensive

thermal units.

For each hour, two inflated estimates of required capacity are made:

1. an estimate of load plus losses computed by multiplying the hourly load by a user

specified factor. This estimate is denoted as TLOAD1.

2. TLOAD1 is further inflated to TLOAD2 by the addition of

• a user-specified non-negative factor called ADDPK which can cause GPUC to

schedule combustion turbines to displace the more expensive committable units; and

• a measure of potential spinning reserve deficit for the hour.

Peaking capacity or interchange is then scheduled according to whether GMAX, the hourly

maximum dispatchable capacity, lies above, below or between TLOAD2 and TLOAD1.

Unit Commitment 123

5.2.6 Hourly Regulation Requirement

GPUC does not require ramp rate inputs for the generating units. However, it attempts to

provide sufficient regulating margin during periods of load pickup. The policy followed in the

program is, that 'in the average system, bringing additional capacity on-line at a given hour,

equal to the load pickup the next hour, should ensure a system response rate sufficient to

meet the increased demand'. The regulation requirement for hour h is found by calculating

the increase in the dispatchable load, DELPWR.

DELPWR = (FL(h + 1) - FL(h)) x GENMIN + PNON(h) - PNON(h + 1) (5.1)

and

DISREG(h) = REGFAC x DELPWR, forDELPWR > 0

or

DISREG(h) = 0 for DELPWR < 0

where

FL(I) = the integrated MW load for hour I

PNON(I) = the total non-committable generation for hour I

DISREG(I) = regulation requirement for hour I

REGFAC = user-input regulation factor.

Unit Commitment

(5.2)

124

5.2.7 Committable Unit Commitment Schedule

The dispatchable unit commitment schedule is basically arrived at by considering a shutdown

decision for each unit on an hour by hour basis. The default status of all dispatchable units

is the Economic Run status. Then at every hour a decision is made whether to shut down a

unit or not. The decision is first based on a comparison of GMAX versus the load, loss,

reserve and regulation requirement for each hour that the unit would be shutdown, upto its

minimum down time. If this comparison allows the unit to be shut down, an economic

comparison is made. This is done by prorating the unit's startup cost over the shutdown

period and the up-time. A comparison of an hour's fuel costs plus the hour's prorated value

of start-up costs will allow the determination of the most economical set of on-line generators.

Once the schedule of committable and non-committable units has been determined, an

economic dispatch is done and production costs are calculated and fuel usage is logged.

Unit Commitment 125

CHAPTER 6

Economic Dispatch

Among the major economic-security functions in power systems operation, economic dispatch

is unanimously ranked very high by most power system engineers. This is a procedure for the

distribution of total thermal generation requirements among alternative sources for optimal

system economy with due consideration of generating costs, transmission losses, and several

recognized constraints imposed by the requirements of reliable service and equipment

limitations.

It is important to emphasize that the problem to be considered in this chapter is the problem

of minimizing production costs in real-time under the assumption that the generators available

have already been specified {i.e., we know which generators are on-line or committed at a

given moment) by a unit commitment program. The optimization is therefore concerned with

a particular set of generators. The economic dispatch problem has historically been the most

researched topic in power systems operation [125). One of the earliest methods to be adopted

is the base load procedure, whereby units are successively loaded to their lowest heat rate

point beginning with the most efficient unit.

Economic Dispatch 126

The incremental cost method was first formally derived by STEINBERG and SMITH (264) in

1934, even though it was recognized as early as 1930. The idea is that the next increment in

the load should be picked up by the unit with the lowest incremental cost. Loss inclusion in

the formulation and solution, received a boost in 1943 by the publication of the derivation of

a loss formula by GEROGE (116). The classic coordination equations were discovered by

KIRCHMAYER and STAGG (165), in 1951. These results form the backbone of today's economy

operation methodology. The classic book by KIRCHMAYER (166), published in 1958, gives a

comprehensive treatment of the loss formula derivations and the conventional economic

dispatch problem. Chapter 2 of this dissertation discusses in detail, the current status of

economic dispatch and the inclusion of PV systems in such algorithms.

The developments cited so far find their mathematical background in the classical

optimization results employing classical theory of maxima and minima in the static case and

variational calculation in the dynamic case. The solution of further problems has been

enhanced by the development of powerful optimization and computational techniques.

Bellman's principle of optimality and dynamic programming in 1950's, gave an impetus to

problems involving discrete and discontinuous variables. The introduction of Kuhn-Tucker

theorem in 1951 to the optimization literature, made it possible to include inequality

constraints in the problem formulation.

6.1 AGC and Economic Dispatch

Today's major power systems are not isolated entities. They are usually connected to a

number of neighboring utilities' power system and therefore power flows in all directions.

Needless to say, there are legal constraints and agreements enforced to govern the power


flow over the tie-lines. Yet, inadvertent flows are not uncommon and consequently cause

departures of the area control error (ACE) from its zero setting.

Let Pd denote the demand power, 'P;. the total system losses, and P5 , the total intertie power

(P5 > 0 implies net injection of active power flow). Then one would expect that P9.,n, the total

power generation required from the economic dispatch routine will be:

(6.1)

With inadvertent intertie flows, then,

(6.2)

becomes non-zero for short periods of time. If the ACE is positive, there is excessive

generation and machines will accelerate, while negative ACE results in machine deceleration.

The ACE, expressed in megawatts is a very important system parameter. It is usually

displayed to the dispatch operator together with system lambda.

There is a relationship between the ACE and system frequency. The ACE can also be

expressed as:

ACE= M - S +BM (6.3)

where

M = metered interchange, MW

S = scheduled interchange, MW

B = frequency bias, MW/HZ [74)

~f = frequency deviation from 60 HZ (system frequency), HZ

It is a function of the automatic generation control (AGC) algorithm of the power system to

take remedial measures to correct the ACE back to zero within a stipulated period of time.


m n 0 ~ 0 3 er c iii

"C I» -n ':S'

.... w 0

Load Precl1ct1on

Predicted

Bus Loads

EconoMlc Dispatch

Base Points Po.rtlclpo. tlon

Fo.ctors

'-------• Bus loads ._ __ ..,. ___ _

Unit CoMMltMent or Opero.tor Entered

Vo.lues

Bo.lo.nee

AutoMo.tlc Genera. tlon

Control

Bo.se Points to o.ll other

Production Units

Figure 26. AGC and economic dispatch functions

Generator Setpolnts to Plo.nts

f>o.rt1c1po. ting In AGC

6.1.1 Load Frequency Control

The load frequency control (LFC) system, deals with the control of loading of the generating

units vis-a-vis the system frequency. The loading in a power system is never constant and the

system frequency remains at its nominal value only when there is matching between the

active generation and the active demand. During changing demand condition, the frequency

error, that is, the deviation of frequency from its nominal value, is therefore, an index of

mismatch and can be utilized to send the appropriate command to adjust generation.

The function of the LF system is to basically control the opening of the inlet valves of the prime

movers according to the loading condition of the system. In the case of a multi-area system,

the above control system also maintains the specified interchanges between the participating

areas. In smaller and simpler systems, the control is generally exerted manually, but in large

systems, automatic control devices are used in the loop of the LFC system.

Single-area system

A single-area system is one which is not connected to any other system and hence the

demand on the system is fully met by its own generation. Sudden load changes are

accommodated in such systems in the following way:

1. Change in stored energy - The sudden load increment is initially supplied from the stored

energy of the spinning capacity of the system by bringing down the frequency of the

system.

2. Change in effective load - Due to the drop of the frequency, the total load on the system

effectively decreases (due to the frequency dependence nature of the load), thus allowing

the already available generation to partly serve the added demand.


3. Change in generation - The reduced frequency actuates the inherent speed-governing

system of the generating units which then increases the input to the prime-movers

causing increased generation which prevents any further drop in frequency. The units

behave coherently, thereby maintaining equal frequency deviations among them.

For a sudden drop in demand, the above behavior follows a reverse sequence, i.e., the

frequency will increase and thereby the effective load on the system will be slightly increased.

These will then be followed by decreased generation due to the actuation of the governing

system of the units.

Multi-area system

In the operation of areas interconnected to one another, a step-load change in any area

belonging to the system, causes a non-zero static error of the frequency and area interchange.

For such systems, a control strategy that will set both frequency and interchange deviations

ultimately to zero, is therefore, needed. An integral control scheme is usually applied with an

input to the integral controller of each area, of the form:

The above input is known as the area control error of area i. B; represents the frequency bias

of the area, and ~S; indicates the interchange error. The above control scheme is known as

the tie-line frequency bias control. The control causes each area to absorb its own load

changes during the normal operating condition and thus to take part in the control of the

system frequency. During emergency, when one or more areas are unable to absorb their own

load changes, the remaining areas assist the affected areas by permitting power transfer

beyond scheduled values, provided the interconnection remains synchronous. The frequency

will be deviated from normal to the extent needed to provide the necessary assistance.


ZDNE-2 ZDNE-1 N c I

:>. ~ f O Q.I ::s 0- N Cl.I t.

Li..

ZDNE-3 ZDNE-4 c

1 IN - TO ., OUT

Are<l net lntercha.nge, M\J

Figure 27. System frequency characteristic versus tie-line flow


The frequency bias 8, is generally expressed in MW per 0.1 per Hz and its recommended

value varies from 0.5 ~ (~ = area frequency response characteristic) to ~ of the area. The

characteristic of the tie-line frequency bias control, which operates to reduce the area control

error to zero, is shown by the straight line CC in Figure 27. The line CC has a slope given by

the reciprocal of 8, the frequency bias. The horizontal line through fo (nominal frequency) and

the vertical line through T0 (scheduled interchange) cross at the point N on the line CC and

thus N defines the scheduled net interchange at the normal frequency. When the operating

condition of the concerned area is such that it falls on the line CC, the ACE will be zero. But

if the point does not fall in the line, then its horizontal distance from CC represents ACE. To

actuate the control, the point should be in the proper zone. Thus, for an area which is sending

power out of the area, zone 4 in the figure is an inoperative area. This is because the errors

in the zone are of opposite sign - the frequency error is negative while the interchange error

is positive. Hence, such an operating condition of the area, although not normal, will not

actuate its control. On the other hand, when the point falls in zone 3, such as N', the control

will act to increase the area generation. Similarly, zone 1 is an operating zone and the control

will act to reduce the area generation.

6.2 Formulating the Economic Dispatch Problem

The classical approach to formulating the economic dispatch problem is the calculation of

generator outputs from on-line (committed) units to satisfy the system load plus losses at the

minimum cost. The cost of operating a unit may be expressed as the product of fuel cost and

heat rate:

(6.4)


where F1 = fuel cost and H1 = heat rate (input to the unit as heat energy requirements).

The heat rate of a thermal unit relates the unit's efficiency to the unit's total MW generation.

One popular method of representing this relationship relates the required energy input to the

MW output by an quadratic expression of the form:

- 2 H; - a; + bf; + cf 1 (6.5)

where a,, b1 and c, are the heat rate coefficients and P1 is the MW output of the unit. This results

in the following relationship between the cost of a unit and its MW output:

The economic dispatch problem can now be stated as:

n Minimize z = ! C,{P;)

i=1

such that !P1 - system load = 0

(6.6)

(6.7)

(6.8)

Realistic dispatching requires consideration of many more constraints than the primary power

balance constraint shown in equation 6.8. These are:

1. GENERATION LOSSES Considering line losses, the power balance constraint shown in

equation 6.8 is modified to:

p ! p;. - system load - losses = 0

I

where PF1 = penalty factor for unit i

= 1 (PL = systemload) 1 - oP/oP,

2. SPINNING RESERVE

Economic Dispatch

(6.9)

135

n l: min(G; - P1 S;) :::?: R j I

(6.10)

Where G1 = capacity of unit i

S; = maximum spinning reserve allowed on unit I

R = total spinning reserve required for the system.

3. UP-RAMP CONSTRAINT

(6.11a)

4. DOWN-RAMP CONSTRAINT

(6.11b)

Where llT = the economic dispatch interval.

y,1 .Yu = increase and decrease response rates in %/min.

5. CAPACITY LIMITS

P min,i S:: P;j S:: P max,/ (6.12)

6.3 Solving the Economic Dispatch Problem

An examination of the economic dispatch problem formulated in equations 6.7 through 6.12,

it is clear that it is a non-linear optimization problem. Several methods have been introduced

for its solution [289).

1. Penalty methods


2. Gradient projection

3. Linearizing

4. Lagrangian methods

5. Direct search

Of the above five, perhaps the most widely used method is on that belongs to the fourth

category. Also known as /..-dispatch, the Lagrangian multiplier method is based on the

Incremental cost rule. The rule states that the minimum generation cost occurs when the

incremental costs of all units are equal. In other words, the cost of generating an aditional MW

is the same for all units.

A.= dC1 = dC2 = ... = dCn (6.13) dP1 dP2 dPn

Equation 6.13 portrays the essential significance of the incremental cost rule. Iterative

algorithms to solve the economic dispatch problem may be found in reference (289).


CHAPTER 7

Implementing PV Dispatch in a New Economic

Dispatch Algorithm

In this chapter, the proposed strategy for the dynamic economic dispatch incorporating

photovoltaic (PY) generations is discussed in detail. The strategy is a combination of a

conventional economic dispatch and a rule-based system replacing the dispatcher. A case

study using the proposed strategy will be presented in the next chapter.

7.1 Need For a New Approach to Economic Dispatch

Optimal dispatch of photovoltaic (PY) power in its true meaning, is actually non-existent in the

current status of the research on the integration of this relatively new technology in the utility's

power system. This fact is clearly portrayed in the survey done in Chapter 2. The most

effective utilization of PV power can be envisaged in the three following roles:

Implementing PV In an ED Program 138

• Directly serving the load

• Reliability service (equivalent to spinning reserve)

• Load frequency control

For a thermal plant, these functions are inherently built-in, but for a PV plant, with the present

technology, it has not been possible to play all the above roles, simply because of lack of

control.

The need for definite control strategies becomes evident when one examines the role of PV

plants at present. PV operation in power systems has essentially been limited to hourly

system load modifications by PV output and then scheduling the conventional generations to

supply the net load. In other words, PV generation is only used to get a modified unit

commitment output (88,175,245). The unit commitment programs generally provide the

information on thermal, hydro and combustion turbine (CT) units scheduled for a period of 24

hours to a week. Besides, a production costing sub-program computes the cost of generation

to supply the expected loads during the same period. The program is executed twice, once

with PV power output and then again without the same. The difference in production costs

revealed by these two runs, indicates the fuel credit attributable to the PV system. This

approach has several disquieting characteristics. These are:

1. PV output over the day or week of the unit commitment period is simulated using typical

weather data at the site. While load forecasts during this period follow a particular trend

and are generally considered accurate to a certain degree, the same cannot be said for

the PV output. The reason is that, PV plant performance depends on the highly variable

weather phenomena and are liable to extreme changes during the week. Weather

forecasts as far ahead as one week can not be considered reliable. Therefore, the amount

of uncertainty introduced into the unit commitment program output is considerably

increased because of the presence of PV power.


2. With this approach, PV power is considered to be forced on the system. No care is taken

to see whether the PV plant might be operating during a period of time when the

base-load units are operating. The latter are required to operate at the same level of

generation throughout the day, in order to be most economic. Also, no care is taken to

see whether there is enough cycling capacity available at any time during which the net

load changes substantially because of the forced PV generations.

3. The penetration level (capacity rating of PV plant compared to total system capacity) of

PV power is not well defined. Apparently, the phrase "the more the better" applies to this

case. Increased PV generations causes increased fuel savings. Therefore, the larger the

PV plant, the better or more economic it is for the entire system as a whole. But with

increasing amount of PV power, there comes a situation when some conventional

dispatch units will not be scheduled by the unit commitment (UC) program which

otherwise would have been scheduled because the UC program is led to believe there is

enough firm capacity. This change in the generation schedule is not acceptable because

of uncertainties involved with PV plant operation and the potential severity in the system

security because of loss of valuable spinning reserve. As mentioned in (1), PV power is

only as reliable as the weather, and decommitting a unit means loss of valuable spinning

reserve and possible regulating capacity for a number of successive hours. (Once a

steam unit is brought down, it cannot be brought back up immediately). Considering this

probable outcome, we are led to the contradictory statement that PV penetration should

be limited. (In (164) though, the authors using a static approach, have found that the

penetration of a PV plant is prevented from increasing beyond a certain limit because of

adverse economic affects.)


7.2 Proposed Rule-based System Approach

Clearly a more qualitative approach is desirable for treating the presence of PV power in the

power system. PV plants are capital intensive and the cost of producing energy from such

plants can only be justified if the energy produced is used to serve more functions than just

reducing the load by a small amount, which in most cases, appears to be mere noise in the

presence of large utility loads. Whenever PV penetration exceeds 5% of the total system

capacity, it is no longer considered to be just noise and definite control regimes must be set

in order to accomplish trouble-free operation of the integrated system.

7.2.1 Present Functions of the Dispatcher

Dispatchers (operators) have to make decisions regularly when they operate and control the

power system. Even in the absence of unusual and emergency situations, many of the

decisions still are non-trivial in their nature. Therefore, a successful operation depends on the

ability of the dispatcher to interpret information and to execute proper control orders.

Today, the work of the system operator is eased in many ways, for example, a computerized

control system can improve the interpretation of the vast amounts of data which are

transmitted and collected in control centers. Application functions of various types also

contribute to helping the dispatcher in the decision making process, but the requirement is

that he must have the expertise or experience to use them.

An economic dispatch program is run at every 3-10 minute interval. The dispatcher has to

work from the hourly committed dispatch units and use standard procedures to allocate

generation levels, maintain the right amount of regulating capacity, maintain the system


frequency, maintain the area control error at zero in case of interconnected systems, bring

up fast start-up units like peaking hydro or gas turbines in case of emergencies, etc. The work

of the power system dispatcher has changed significantly due to technical developments

which have taken place in the field of computerized control systems. Routine and tedious data

manipulations are handled automatically and application functions are introduced

successively into the control systems repertoire. Hence, the world of the dispatcher becomes

confined to more and more unique abilities which humans possess. For example, he is

required:

• To distinguish known patterns among large amounts of data and thereby to choose

appropriate strategies and approaches; and

• To inject intuition and common sense into the control of the power system.

To master his task skillfully, the dispatcher must be taught:

• Basic facts

• Methodological knowledge

• Active competence

Using these features, which are developed with time, the dispatcher makes his decisions. An

example of a situation where his experience is called upon is during the morning load pick-up

period when the constraints of power balance and operating reserve are stretched to their

limits. The situation is handled by the dispatcher's ramping of the more expensive units above

their economic assignment early in the load pick-up period and thus keeping some less

expensive units below their operational limits in the early stage, so that they can help satisfy

the load pick-up required at the later stages. In this case, the dispatcher chooses to go with

the safe solution than an economical one.


It is conceivable to represent the knowledge of the dispatcher as a rule-based computer

algorithm. The decision making process of the dispatcher renders itself perfectly to a set of

*If-Then" rule structures for use by a rule-based system. This rule base (RB) approach to

economic dispatch becomes almost a necessity when the dispatch algorithm has to deal with

the operation of a photovoltaic system. This is discussed next.

7.2.2 A Rule Base Replacing the Dispatcher

A rule base will be defined as an intelligent combination of procedures that uses knowledge

and inference techniques of the human expert to solve problems in an algorithmic manner.

In narrow problem domains, the rule base can provide high performance, equalling or even

exceeding that of human individual experts.

In the proposed dynamic economic dispatch incorporating PV, a rule base is introduced to

operate, either by itself or in tandem with a conventional economic dispatch algorithm. The

functions of the two are coordinated by another algorithm which overlooks the flow of

information and records them. This functional relationship between the three computer

program modules are shown in Figure 28. Details of each module are discussed later in this

chapter. At this time, it is worthwhile to examine the nature of the problem introduced by the

presence of PV power in the mix before rules are established for an RB approach to the

solution.

7.2.2.1 PV Dispatch

The treatment of PV generations is considered, in this economic dispatch approach to be

similar to that of combustion turbines (CT). The essential similarities are the fact that CTs can

be brought on-line within a very short period of time whenever there is need for extra capacity,


ECDl\JDMIC DISPATCH

DRIVER

RULE BASE

Figure 28. The three computer modules in the proposed operation scheme

Implementing PV in an ED Program 144

and they can be backed off whenever desired. Proceeding along those lines, provided PV

power is forecasted to be available at say 100 MW, the PV plant may be controlled to produce

anywhere from Oto 100 MW as and when required. Dissimilarities exist in the operation of the

two plant types though. Whereas, a CT plant operates on a low capacity factor (average

capacity of operation over the rated capacity) because of high cost of fuel, a PV plant is

expected to run on as high a capacity factor as possible in order to compete favorably against

conventional thermal units. Therefore, the PV plant will be required to not only supply the peak

loads as CTs, but also during intermediate load periods.

Unquestionably, the single most important parameter that is the cause of PV dispatch

problems is the response rate of thermal units. During dispatch, the fundamental constraint

becomes:

At any time t, expected power generation required from the thermal generators must equal expected load at t minus the sum of generation from non-conventional sources minus the PV output at t.

(7.1)

implying:

(7.2)

where G, = the total thermal generation at time t

G,_, = the total thermal generation at time t-1

D, = the total demand at time t

D,_, = the total demand at time t-1

4 = the total losses at time t

4-, = the total losses at time t-1

lmplementlng PV In an ED Program 145

c, = the total combustion turbine generation at time t

c,_ 1 = the total combustion turbine generation at time t-1

H, = the total hydro generation at time t

H,_ 1 = the total hydro generation at time t-1

PSH, = the total pumped-storage hydro generation at time t

PSH,_ 1 = the total pumped-storage hydro generation at time t-1

IC, = the total interconnected power flow at time t

IC,_ 1 = the total interconnected power flow at t-1

PV, = the total photovoltaic generation at time t

PV,_ 1 = the total photovoltaic generation at time t-1

Normally, differences in losses and other load-generation mismatches in the absence of PV

power are easily picked up by cycling (load following) units and the system maintains a

matched load condition. With PV power on the other hand, large variations in PV output can

cause the thermal plants to reach their response limits before load matching constraint is met.

Therefore, two conditions might arise:

• Thermal generation increase not possible in the dispatch interval.

This situation may arise because of a sudden drop in PV power in the mix, causing the

thermal generators to attempt to make up the loss. Using the up-ramp response

constraint of each cycling thermal unit, the total system response capability (regulating

capacity) in the Hup" direction should be greater than or equal to the change in generation

required of the units. Mathematically,

(7.3)

where l!.T = dispatch interval

Pit_, = MW output of unit i at interval t-1


y,; = response rate of unit i In the raise direction (%/min)

Violation of equation 7.3 implies corrective action has to be taken to reach optimality.

• Thermal generation decrease not possible in the dispatch interval.

This situation is brought about when there is a sudden increase in PV generation in the

mix possibly by movement of clouds away from the area. The thermal generators are

expected to back-off part of their generations (unload) in order to accommodate the

additional PV power. Once again, the response rate of the thermal generators plays an

important role, this time in the "lower" direction. According to the down-response rate of

each unit, the total system response capacity in the lower direction should be greater

than or equal to the change in generations required from the generators. Mathematically,

(7.4)

where y11 = response rate of unit i in the lower direction (%/min.)

Violation of equation 7.4 once again implies corrective action has to be taken, by the

dispatcher.

The corrective actions are channeled into "rules" or "if-then" logic structures. These rules are

described next.

7.2.3 Rules in the Rule Base

Problems in operation require corrective actions so that the system may be brought back to

an optimal state. Figure 29 shows the situations where rules are applied for corrective action.

The following is a list of the set of rules written for the RB.


THERMAL UNITS UNABLE TO PICK UP INCREASED NET DEMAND

1. Increase PV generation input 2. Increase hydro generation 3. Increase pumped storage plant output 4. Increase CT generation 5. Start-up unscheduled hydro unit 6. Start-up unscheduled PSH unit 7. Start-up unscheduled CT unit 8. Buy more unscheduled interconnected power

THERMAL UNITS UNABLE TO UNLOAD

1. Decrease CT generation 2. Decrease pumped storage output 3. Decrease hydro generation 4. Shut-down scheduled CT unit 5. Shut-down scheduled PSH unit 6. Shut-down scheduled hydro unit 7. Release scheduled interconnection 8. Decrease PV generation input

Choose the 'best' option

Redo the Dispatch Program. Get new system Lambda Set artificial maximums and minimums Recalculate reserve capacity Change status of units if applicable

Figure 29. Operational scenario with PV system


RULE-SET 1 If thermal units are unable to pick up the increased net demand of the system, and

if the PV plant was operating at below maximum capacity in the last interval of the dispatch,

then increase PV generation.


if RULE-SET 1 is not satisfied, then increase hydro generation.


if RULE-SET 2 is not satisfied, then increase pumped storage hydro generation.


if RULE-SET 3 is not satisfied, then increase combustion turbine generation.


if RULE-SET 4 is not satisfied, then start-up unscheduled hydro unit(s).


if RULE-SET 5 is not satisfied, then start-up unscheduled pumped storage unit(s).


if RULE-SET 6 is not satisfied, then start-up unscheduled CT unit(s).

RULE-SET 8 If thermal units are unable to pick up the increased net demand of the system,

and if RULE-SET 7 is not satisfied, then buy unscheduled interconnected power.

RULE-SET 9 If thermal units are unable to unload the extra generation because of a decrease

in net system demand, then decrease CT generation.



in net system demand and if RULE-SET 9 is not satisfied, then decrease pumped storage hydro

generation.


in net system demand and if RULE-SET 10 is not satisfied, then decrease hydro generation.


in net system demand and if RULE-SET 11 is not satisfied, then shut down scheduled CT

unit(s).


in net system demand and if RULE-SET 12 is not satisfied, then shut down scheduled pumped

storage hydro unit(s).


in net system demand and if RULE-SET 13 is not satisfied, then shut down scheduled hydro

unit(s).


in net system demand and if RULE-SET 14 is not satisfied, then decrease tie-line interchange

flow.


in net system demand and if RULE-SET 15 is not satisfied, then decrease photovoltaic power.

The set of rules 1 through 8 are valid for the situation when there is a significant reduction in

the non-committable generations causing the thermal generators to attempt to pick up


Comment Check to see if PV plant is present in the generation mix. If (PV_STATUS = 0) then

else

begin Comment No PV plant is present. Therefore, set flag to false

and go to rule 2. FLAG1 : = false; end

begin Comment PV plant is present in the mix. Check if the plant

is running at maximum capacity. If (PV_GEN_NOW = PV_GEN_MAX) then

begin

endif

Comment Change in PV generation not possible. Diagnosis: plant is running at full capacity or plant is down.

FLAG1 : = false; end

If (PV_GEN_MAX - PV_GEN_NOW < INC_AMOUNT) then begin

else

Comment Possible increase in PV generation is less than the increase required by the system (INC_AMOUNT). So increase PV power by whatever amount possible and go to rule-set 2.

FLAG1 : = false; PV_GEN_NOW := PV_GEN_MAX; end

begin Comment Increase in PV generation is possible. PV GEN NOW : = PV GEN NOW + INC AMOUNT; FLAG1 : ;, true; - - -end

end If end

endif

Figure 30. Rule-set 1.


generation. Response limitations of thermal units therefore require other measures to be

taken. Rule-set 1 receives the highest priority as logical reasoning dictates that PV power

ought to be optimally utilized. Therefore, it will be the purpose of the RB to supervise the

presence of maximum possible PV power which is the most favorable scenario from the

production costs point of view. Rule-set 1 is illustrated in Figure 30. Although, the rules are

written in FORTRAN, the style of a declarative language is used to represent the logic.

Rule-set 2 through 4 are similar although concerning different unit types. Hence these are not

repeated here. Rule-set 5 through 8 are apparently violations of the optimal solution given by

the unit commitment program. There is nothing so alarming about this violation. The only

concern under this action, that of departure from optimality, is quite unwarranted, because the

system is already in a sub-optimal state considering the fact that the thermal units are not

able to follow the economic trajectory. The only legitimate concern under this situation should

be that starting up unscheduled units may violate some constraints, e.g., minimum up-time

or minimum down-time requirements. The rules to be established are therefore required to

examine these constraints before starting unscheduled units. As for start-up time itself, the

units to be considered by the RB for start-up are fast-start units, like peaking hydro, pumped

storage hydro and combustion turbines, which need little warm-up time. Figure 31 shows the

logic for rule-set 5. Once again, for avoiding repetition of similar characteristics, rule-sets 6

and 7 are not shown. The logic for these set of rules is centered on locating the optimal

capacity unit which matches the generation increment requirement INC_AMOUNT. If that is

not possible, multiple units are searched for, whose combined capacity adds up to the variable

INC_AMOUNT. A sub-program called PRIORITY locates these units and "pushes" these units

into a "stack", with the highest priority unit residing at the top of the stack. A sequential "pop"

operation then brings out these units from the "stack".

Rule-set 8 is somewhat different from other rules, as it involves buying unscheduled power

from interconnected systems. This action advocates caution because it involves more than

one area. Area control error (ACE) problem is one criterion that must be looked into before


Comment Check to see If a hydro plant Is present in the generation mix. If (NUM HYDRO = 0) then

begin

else

Comment No hydro plant Is present. Therefore, set flag to false and go to rule 6.

FLAG2 : = false; end

begin Comment Hydro plant is present In the mix. Search for units which are down.

If found, locate the unit with a capacity which matches the MW amount of increase required by the system.

UNIT FOUND:= O; NUM-LOOP := 1; N := -NUM HYDRO; While (N >-0) do

begin If (UP _HYD_STATUS(NUM_LOOP) = 1) then

begin Comment The hydro unit is up. Check the next one. NUM LOOP := NUM LOOP + 1; N:=-N-1; -end

else begin Comment Check for up-time and down-time constraint violations. call UNIT_VIOLATE (NUM_LOOP, VIO_FLAG); If (VIO FLAG = true) then

begin Comment Constraint violated. Check next unit. NUM LOOP:= NUM LOOP + 1 N := -N - 1; -end

else begin UNIT FOUND:= UNIT FOUND + 1; CONTRIB (UNIT_FOUND) := MAX_CAP (NUM_LOOP); NUM LOOP:= NUM LOOP + 1; N:=-N-1; -end

end if end

endif end

end endif If (UNIT FOUND = 0) then

FLAG2 : = false; else

begin Comment Prioritize the hydro units selected. call PRIORITY (CONTRIB, INC_AMOUNT, UNIT_ORDER) Comment The order of the selected hydro units according to descending order

of capacity is stacked in the UNIT _ORDER stack. This stack is popped sequentially to schedule the units.

TOTAL CAP:= O; While (TOT_CAP < > INC_AMOUNT) do

begin UNIT:= pop (UNIT_ORDER); TOTAL_CAP := TOTAL_CAP + MAX_CAP (UNIT) Comment Upgrade status of the unit to ·up· mode. STATUS (UNIT):= 1; end

end endif



Comment Check to see if tie-lines are present. If (NUM_ TIES = 0) then

else

begin Comment No tie-lines are present. Therefore, set flag to false. FLAGS : = false; end

begin Comment Tie lines are present. Search for tie lines not scheduled at this hour. TIE_FOUND : = O; NUM_LOOP := 1; N : = NUM TIES; While (N >-0) do

begin If (UP _TIE_STATUS(NUM_LOOP) = 1) then

begin Comment The tie line is already scheduled. Check the next one. NUM_LOOP: = NUM_LOOP + 1; N:=N-1; end

else begin Comment Tie-line is available. Get out of loop TIE FOUND : = NUM LOOP; N : ;,, O; -end

endif end

end end if If (TIE_FOUND = 0) then

FLAGS : = false; else

begin Comment Check if area control error can be controlled. UNIT (TIE_FOUND): = INC_AMOUNT call ACE (SCHED, INC_AMOUNT, ACE_FLAG) If (ACE_FLAG = true) then

begin Comment ACE is not controllable with the interchange. Set flag. FLAGS : = false; UNIT (TIE_FOUND) : = O; end

endif end

endif



scheduling any interchange company or a tie-line. The set of rules governing these actions is

shown in Figure 32.

The RB follows these sets of rules sequentially whenever there is not enough regulating

capacity in the system. At any point in time, a part of any set of rules may be satisfied, in which

case a coordinated decision is taken. For example, during dispatch operation, it was found

that thermal generation could not be increased any further to match the total load demand.

The RB finds a hydro unit to be scheduled which can only satisfy part of the increase in

generation required. None of the other rule-sets 1 through 7 can be satisfied. In this case, the

RB will schedule interconnected power to make up the rest of the increment. In situations like

these, human interaction produces delay and may take longer than the dispatch interval itself.

The RB provides solutions within seconds.

It should be noted that a tie-line may be receiving power from a number of interchange

companies. The sub-program ACE checks for NERC (North-American Electric Reliability

Council) regulation violations related to area control error. The tie-line bias [75), should be

such that the ACE is brought back to zero within the dispatch interval.

Rule-sets 9 through 16 employ inverse logic to what is used in rule-sets 1 through 8. For

example rule-set 14 is concerned with shutting down a scheduled hydro unit as compared to

rule-set 5 which is valid for starting up unscheduled hydro units. The set of rules effecting

change in the photovoltaic operation in the scenario of the presence of "unloadable

generation" is given a low priority. Following along the same reasoning as before, one would

like to maintain as much PV generation in the system, until it comes down to a "last resort"

to reduce the PV generation level.


7.3 Programming Considerations

Summing up the functions of the dynamic economic dispatch as proposed in the dissertation,

there are a number of possible steps to take in case the system reaches a point where the

economic trajectory cannot be followed. Figure 33 illustrates the flow of information in the

dispatch algorithm. It is clear from the figure that as a result of the presence of photovoltaic

systems, the solution of the unit commitment may have to be modified in order to arrive at

an economic solution.

7.3.1 Interface With EPRl's GPUC Program

It was explained earlier that the dynamic economic dispatch algorithm proposed here starts

from a given unit commitment (UC) solution provided by EPRl's computer program namely,

Generation Production Unit Commitment. The UC program is slightly modified in order to

produce a particular set of data in a form which is useful to the dispatch program. The data

in question, comprises of the unit schedule throughout the commitment period, and the

amount of non-committable generation every hour, from units such as combustion turbines,

hydrothermal units, pumped storage units and also the hourly interchange schedule. The

period of UC considered most effective for this application is 24 hours. Figure 34 illustrates the

application of EPRl's GPUC program in the proposed scheme. Input to GPUC are hourly load

data and the generator data. The hourly load data are simulated by a computer module called

AVHR which takes in the raw sub-hourly load data input and produces a) the dispatchable

sub-hourly load data, and b) normalized hourly load data. Output (b) is directly input to GPUC

and the latter yields commitment schedules for all hours in the schedule and the participation


3 .,, ii" 3 Ill ::I -:; cc "V < :; DI ::I m c "V ... 0 cc ... DI 3

.... "' ......

I

OPTIMAL PV OUTPUT

prHR/VfEK LOAD H DAILY/WEEKLY FORECAST UNIT COMMllMENT

I -11 SHORT-TERM DYNAUIC ECONOMIC I~ SUB-HOURLY

LOAD FORECAST LOAD DISP ATCl-1 PHOTOVOLTAIC

OPTIMAL THERMAL

GENERATION

I

OP11MAL COMBUSllON

TURBINE GENERATI~

* OPllMAL HYDRO (RUN-OF-RIVER'

PLANT GENERATION

OUTPUT PREDICllONS

* PUMPED-STORAGE

PLANT GENERATION

Figure 33. Functional properties of the new dynamic economic dispatch

rt

BUY/SEU POWER

Hourly Loo.d SiMulo. tlon

AVHR

Unit CoMMitMent

GPUC

Figure 34. Components of unit commitment

Implementing PV In an ED Program

To DRIVER

CoMMltMent Schedule

158

factors from combustion turbines, hydro units, pumped storage units and the interchange

schedule.

7.3.2 Interface With the Solar Resource Forecast Program

Figure 13 on page 96 shows the input output requirements for the FORECST module used for

forecasting PY output during the dispatch interval. The module is linked to the DRIVER module

described tater. The FORECST module consists of two sub-modules, SIMUL and PREDIC.

SIMUL generates a simulated global irradiance and direct normal irradiance data on clear

days during the period of interest. Sub-module SIMUL generates:

• global irradiance on clear days

• direct normal irradiance data

• cloud cover data at the site

Sub-module PREDIC takes in as input, the output of sub-module SIMUL and generates the

forecasted sub-hourly PV generations which is used by the DRIVER module.

The prediction of the photovoltaic power generations for the economic dispatch period is

dependent on the forecast of the global irradiance. The dispatch program accepts data from

this forecast generating algorithm. The tatter has been explained in Chapter 4. The resource

forecast is updated at the beginning of every dispatch interval.

7.3.3 The Dispatch Combined With the RB


3 .,, ii" 3 CD a S" ca ~ S" Ill ;:,

"' 0 -a .. 0 ca Dl 3

.. °' 0

Sp1nn1n9 reserves Po.rt1c1po. tlon fo.ctors

Col"ll'll"trlen-t sch&dule C Therl'lo.l 9enero.t100

Sub-hourly loo.ct do. to.

Genera.tor do.to.

CT o.nd Hydro genera. tlon

PV output f oreco.s-ts

lntercho.nge

Figure 35. Execution of the DRIVER module

In order to be compatible with the UC program, the generation data input requirement for the

dispatch algorithm is quite similar to EPRl's GPUC program. The input data for both programs

is shown in greater detail, in Appendix C. Figure 35 provides an insight into the operation of

the DRIVER module which is the heart of the proposed dynamic economic dispatch scheme.

Input to the module consists of:

• Generator participation factors

• Commitment schedule for all generators

• Sub-hourly load data

• Generator data

• Forecasted PV output for the dispatch interval.

The output from the program consists of the following:

• Spinning reserve

• Thermal generation

• PV generation

• Production costs

• Pumped storage hydro generation

• Hydro generation

• Combustion turbine generation

• Interchange

Figure 36 shows the combined operation of the dynamic economic dispatch and the rule base

which can be used as a dispatcher's aid. The operations of the economic dispatch and the

rule base are coordinated by the module called DRIVER. The module makes sure that there

is enough reserve margin as required by the system. It computes the contributions from all

non-committable sources, computes artificial minimum and maximum limits dictated by


3 "1:1 ii' 3 CD :;, -S" ca ~ S" DI :;,

"' c .,, 0 ca DI 3

.... 0 N

I --- D R I VE R

I I I

,-----____,1 Inter-cho.nge

CT Genera. taon

Hydro Genero. taor

Reserve Mo.rgln

P. Storo.ge Genera. taon

PV .Genero. t101

Ro.Mp Conditions

TherMo.l G.rnero. tlon

L_ ----- ---~ :;Ql -::s ~Sy=" =b: i-;1 11 -:hQ:-hy= ::rQ:ns - i I I C I Loss Estl"Q tlon i I I 1

1 [ Cho.nge puMped storo.ge gen. I I

0 s I R .. B I RequlreMent f'or

1 1 U I Cho.nge CT genera. taons I A 1 M I cllspo. tcho.ble genera. tlons DISREQ P _ ~

0

M

Mo.xlMuM avo.llo.ble A I I L ( Cho.nge PV genero.taons IS I dlspo. tenable genero. taon DISHAX --.._._._._._._ ______ _.T E E

MlsMo. tches between o.ctual I I ( Modlf'y unit coMMl1:Ment schedulel I I dlspo. tcho.lole genero. taon a. DISREQ C

I __ J

I C ( 1 H I I I Ch4n9e 1nterch4n9e schedule i _ Syst•" lo.Mlodo. ~ -L ______ J L ---

Figure 36. Information exchange In the three modules

response rates of thermal units and passes the information to ECONOMIC DISPATCH module.

The driver then, receives back information on the mismatches between the possible

dispatchable generation under constraints and that required by the system. This is then

passed on to the RULE-BASE module which makes the necessary decisions to correct the

situation. The RB at this stage communicates directly with the ED module.

An example of the operation of the PV plant in the proposed dispatch scheme follows. This

will illustrate the maximum potential of the plant in combined operation with other plants in

the mix.

During normal operation of the dispatch algorithm, assume a sudden drop in instantaneous

load by an amount of 60 MW at the beginning of the dispatch interval. Assuming that the total

non-committable generation output (consisting of combustion turbine units, hydro units,

pumped storage units and the PV plant), as well as system losses remain constant throughout

the interval, it is found that that the system on-line regulating capacity at this time is not

enough to unload the thermal generations during the interval. The RB takes over control and

decides that the PV generation may be reduced by 15 MW to bring the system back to a

balanced state. This is an illustration of how the PV plant may be used for maintaining system

security. Detailed results of a case study are presented in Chapter 8.


CHAPTER 8

Case Study: Results

This chapter presents results of a case study using the PV output forecast strategy and the

rule based dispatch algorithm. The data used for the study represents a location in Virginia.

This is a typical location in the southeastern United States and has moderate weather

throughout the year.

The generation mix used for the study is derived from the EPRI synthetic utility system [98],

southeastern U.S. integrated by personal communication with a number of utility operations

personnel in the region. The results presented in this chapter are targeted toward bringing

out the differences in a power system with and without a photovoltaic power plant. Also the

differences in a static approach and a dynamic rule based strategy are pointed out.

8.1 Continuous Simulation Run

Case Study Results 164

l. 0 ~-d d > ... l. d ., ,,~ ,, ., d .c _g ....

Updo.te PV foreco.sts

No

START

Reo.d dlspo.tch 1ntervo.l T

Reo.d sto.rt "tlMe for SIMulo. t1on 10

=

Issue PV f oreco.sts for the next hour

o.t eo.ch lntervo.l

Do o.n econoMIC dlspo. tch

1Jr1te results for thtr lntervo.l

IncreMent lnterco.l count l = I + T

Figure 37. Continuous simulation run

Case Study Results

No

Yes

Yes

165

For the purpose of presenting the results, a continuous simulation procedure was followed.

The algorithm of this process is shown in Figure 37. At the outset, parameters such as,

generator data, generator schedule, dispatch interval, etc., are read in. PV output forecasts

are issued only if the interval of simulation falls within the daytime hours. After reading in the

interval's load demand, an economic dispatch calculation is performed. In case of any

dispatch problems, e.g., inadequate regulating capacity or spinning reserve, the rule-based

system takes over and matches the generation and demand maintaining system security, and

an economic dispatch calculation is redone. When there are no problems, the results are

written out for the interval and the time counter is incremented by one interval. If the time

coincides with the end of the hour, program control is handed back to the PV output forecast

routine which issues new forecasts for the upcoming hour of simulation. If on the other hand,

the time is within the hour, PV generation forecasts are updated with the newly available

actual irradiance in the last interval before control is transferred directly to the economic

dispatch program.

8.1.1 Generator Data

Table 10 and Table 11 list the characteristics of generators and combustion turbine

generators respectively, that are used in the study. Also shown in the figures are the minimum

and maximum generations possible as well as the ramp (response) rates for each generator.

It should be mentioned here that only the dis patchable thermal units belonging to the synthetic

utility are listed in Table 10. The base load units are supposed to run almost throughout the

day and are therefore considered non-dispatchable for all practical purposes.

8.1.2 Load Data


Table 10. Thermal generator data for the synthetic utility

NAME TYPE OF UNIT PMAX(MW) PMIN(MW) LOAD/UNLOAD RATE TUNIT1 COAL 760 250 3%/MIN TUNIT2 COAL 760 174 3%/MIN

TUNIT3 COAL 420 125 5%/MIN TUNIT4 COAL 190 50 7%/MIN

TUNIT5 COAL 190 50 7%/MIN


TUNIT7 COAL 210 70 5%/MIN TUNIT8 COAL 210 70 5%/MIN TUNIT9 COAL 115 35 7%/MIN TUNIT10 COAL 450 136 3%/MIN TUNIT11 COAL 450 136 3%/MIN













Table 11. Combustion turbine generator data for the synthetic utility

NAME TYPE OF UNIT PMAX(MW) PMIN(MW) LOAD/UNLOAD RATE CUNIT1 OIL 18 12 100%/MIN CUNIT2 GAS 18 12 100%/MIN CUNIT3 OIL 18 12 100%/MIN CUNIT4 GAS 44 16 100%/MIN

CU NITS GAS 44 16 100%/MIN CUNIT6 GAS 64 46 100%/MIN

CUNIT7 GAS 64 46 100%/MIN


CUNIT9 GAS 64 46 100%/MIN CUNIT10 OIL 17 11 100%/MIN CUNIT11 OIL 17 11 100%/MIN CUNIT12 OIL 17 11 100%/MIN

CUNIT13 OIL 17 11 100%/MIN

CUNIT14 GAS 42 28 100%/MIN CUNIT15 OIL 18 22 100%/MIN

CUNIT16 OIL 32 21 100%/MIN



3700

~ 2900

l! .. E II

-0

-0

~ 2100

1300

1 I nlerval • 10 M rules

,, 1

1,1 I

I 1' 1 I 1 I 1' , 1

1' 1'

I

, , I I I I I , , I

I I I I I I I I I I I I I ; I I I I

v

Load ---------- PV

800

600

400

200

500'--~--~--~----~------~--~--~~---~--~-- 0 o 29 58 87 116 145 I nlervak

Figure 38. Sample modified load profile and PV output for a day In January

Case Study Results

::r ~ ~ .. 0... ~ D

> 0.

169

Load demand data at 30 seconds interval are available from a Virginia utility. These are used

to create an hourly load data (for generation scheduling purposes) and a sub-hourly load data

base (for the dynamic economic dispatch program). The sub-hourly data consists of load

demands at every 3 to 10 minute intervals.

Figure 38 shows the sub-hourly load demand and PV plant generations for a sample day in

the month of January. This day is particularly selected to show the variable nature of the PV

generations. Such extreme variations in PV output may occur during sudden movement of

thick, dark clouds covering the sun for several minutes before moving away again. It should

be mentioned here that the figure shows only the dispatchable load. In other words, the base

load is subtracted from the total load.

8.1.3 Simulation Results

The day is divided into three time spans for presenting the results. These three time spans

represent the three important regions of the daily load profile. Hour 0 (midnight) through hour

8 (8 AM) is used to fill in the first time span. This period consists of the base period of the day

during which mostly the base load units are operating. The demand profile experiences its

first valley period (winter loads may have a second valley later in the day). The end of this

period is marked by a sharply increasing load shape indicating the morning load pick-up. The

next time span comprises of hours 8 through 16. This is the period which experiences high

variability in the demand and at the same time, photovoltaic generations are increasing with

the sun gradually approaching its noon-time position of maximum radiation. Hours 16 through

24 (midnight) represents the third time span of the day. This period normally means a rapid

reduction in load demand during summer-time in most parts of the U.S., or a second increase

in demand during winter.


Table 12. System operation without PV during 1st time period

INT 1 LOAD LOSS DISP CT GEN PV GEN SPIN A. COST X1 boo$ 1 2110.00 105.50 2215.50 0.00 0.00 2030.50 19.19 7.61 2 1997.00 99.85 2096.78 0.00 0.00 1014.10 19.01 7.23 3 1982.00 99.10 2081.03 0.00 0.00 894.53 18.99 7.19 4 1964.00 98.20 2062.19 0.00 0.00 895.46 18.96 7.13 5 1945.00 97.25 2042.25 0.00 0.00 893.99 18.93 7.06 6 1912.00 95.60 2007.60 0.00 0.00 905.97 18.87 6.95 7 1891.00 94.55 1985.54 0.00 0.00 888.65 18.84 6.88 8 1872.00 93.60 1965.60 0.00 0.00 883.52 18.81 6.82 9 1847.00 92.35 1939.35 0.00 0.00 887.10 18.77 6.74

10 1833.00 91.65 1924.64 0.00 0.00 871.97 18.75 6.69 11 1821.00 91.05 1912.05 0.00 0.00 867.85 18.73 6.65 12 1804.00 90.20 1894.20 0.00 0.00 871.39 18.70 6.60 13 1792.00 89.60 1881.59 0.00 0.00 863.70 18.68 6.56 14 1789.00 89.45 1878.45 0.00 0.00 852.53 18.67 6.55 15 1787.00 89.35 1876.34 0.00 0.00 851.05 18.67 6.54 16 1774.00 88.70 1862.70 0.00 0.00 862.31 18.65 6.50 17 1761.00 88.05 1849.05 0.00 0.00 860.45 18.63 6.46 18 1765.00 88.25 1853.25 0.00 0.00 840.73 18.64 6.47 19 1765.00 88.25 1853.25 0.00 0.00 845.51 18.64 6.47 20 1765.00 88.25 1853.25 0.00 0.00 845.51 18.64 6.47 21 1778.00 88.90 1866.90 0.00 0.00 831.86 18.66 6.51 22 1781.00 89.05 1870.05 0.00 0.00 844.22 18.66 6.52 23 1791.00 89.55 1880.55 0.00 0.00 837.30 18.68 6.56 24 1792.00 89.60 1880.55 0.00 0.00 849.24 18.68 6.56 25 1807.00 90.35 1897.34 0.00 0.00 832.44 18.70 6.61 26 1835.00 91.75 1926.74 0.00 0.00 822.13 18.75 6.70 27 1845.00 92.25 1937.24 0.00 0.00 845.05 18.77 6.73 28 1872.00 93.60 1965.60 0.00 0.00 828.63 18.81 6.82 29 1903.00 95.15 1998.14 0.00 0.00 828.31 18.86 6.92 30 1953.00 97.65 2049.63 0.00 0.00 813.81 18.94 7.09 31 2038.00 101.90 2139.89 0.00 0.00 977.07 18.78 7.55 32 2154.00 107.70 2261.57 0.00 0.00 794.84 18.97 7.94 33 2238.00 111.90 2349.02 0.00 0.00 845.70 19.10 8.21 34 2320.00 116.00 2435.99 0.00 0.00 858.31 19.22 8.49 35 2427.00 121.35 2548.35 0.00 0.00 845.09 19.39 8.85 36 2533.00 126.65 2659.65 0.00 0.00 859.47 19.56 9.21 37 2691.00 134.55 2825.54 0.00 0.00 856.71 19.73 9.86 38 2900.00 145.00 3046.46 0.00 0.00 768.61 20.09 10.59 39 3100.00 155.00 3256.13 0.00 0.00 801.16 20.42 11.30 40 3287.00 164.35 3453.14 0.00 0.00 765.18 20.79 11.97 41 3462.00 173.10 3636.31 0.00 0.00 710.94 21.38 12.61 42 3580.00 179.00 3759.00 0.00 0.00 741.67 21.80 13.05 43 3700.00 185.00 3358.00 527.00 0.00 684.89 20.32 18.58 44 3886.00 194.30 3554.42 527.00 0.00 278.00 21.08 19.25 45 3977.00 198.85 3648.65 527.00 0.00 270.14 21.36 19.58 46 3992.00 199.60 3662.84 527.00 0.00 306.40 21.40 19.63 47 3980.00 199.00 3653.21 527.00 0.00 323.67 21.37 19.60 48 3954.00 197.70 3624.70 527.00 0.00 347.00 21.28 19.50

1 1 interval = 10 minutes. Interval 1 = > 0:10 A.M.


Table 13. System operation without PV during 2nd time period

INT 1 LOAD LOSS DISP CT GEN PV GEN SPIN /.. COST X1 :>OO $

49 3905.00 195.25 3572.95 527.00 0.00 383.37 21.13 19.32 3~4.00

50 3908.00 195.40 3576.28 527.00 0.00 352.69 21.14 19.33 3~4.00

51 3866.00 193.30 3533.89 527.00 0.00 396.75 21.02 19.18 3~4.00

52 3835.00 191.75 3500.82 527.00 0.00 397.97 20.93 19.06 53 3814.00 190.70 3478.34 527.00 0.00 388.24 20.87 18.99 54 3805.00 190.25 3468.50 527.00 0.00 376.18 20.84 18.95 55 3775.00 188.75 3562.58 402.00 0.00 397.52 21.10 17.41 56 3763.00 188.15 3549.20 402.00 0.00 499.57 21.06 17.36 57 3753.00 187.65 3538.67 402.00 0.00 500.04 21.03 17.33 58 3731.00 186.55 3515.58 402.00 0.00 512.88 20.97 17.25 59 3694.00 184. 70 3476.64 402.00 0.00 529.32 20.86 17.11 60 3675.00 183.75 3456.84 402.00 0.00 511.19 20.80 17.04 61 3650.00 182.50 3499.43 334.00 0.00 517.38 20.92 16.18 62 3648.00 182.40 3496.33 334.00 0.00 561.90 20.92 16.17 63 3645.00 182.25 3493.18 334.00 0.00 562.03 20.91 16.16 64 3632.00 181.60 3479.29 334.00 0.00 572.84 20.87 16.11 65 3608.00 180.40 3454.13 334.00 0.00 584.48 20.80 16.03 66 3584.00 179.20 3429.49 334.00 0.00 584.71 20.72 15.94 67 3550.00 177.50 3586.10 142.00 0.00 596.43 21.17 14.31 68 3545.00 177.25 3579.88 142.00 0.00 740.68 21.15 14.28 69 3482.00 174.10 3514.10 142.00 0.00 803.35 20.97 14.05 70 3456.00 172.80 3484.81 142.00 0.00 779.71 20.88 13.95 71 3414.00 170.70 3442.65 142.00 0.00 793.33 20.76 13.80 72 3394.00 169.70 3422.29 142.00 0.00 772.89 20.71 13.73 73 3347.00 167.35 3514.35 0.00 0.00 804.75 20.97 12.18 74 3280.00 164.00 3443.82 0.00 0.00 962.95 20.77 11.94 75 3252.00 162.60 3415.55 0.00 0.00 922.74 20.69 11.84 76 3229.00 161.45 3390.45 0.00 0.00 923.71 20.64 11.76 77 3221.00 161.05 3382.05 0.00 0.00 913.66 20.62 11.73 78 3208.00 160.40 3369.48 0.00 0.00 920.05 20.59 11.68 79 3187.00 159.35 3346.35 0.00 0.00 935.22 20.56 11.60 80 3445.00 172.25 3617.91 0.00 0.00 650.07 21.74 12.55 81 3219.00 160.95 3378.49 0.00 0.00 1120.93 20.61 11.71 82 3201.00 160.05 3361.55 0.00 0.00 925.37 20.58 11.66 83 3207.00 160.35 3367.35 0.00 0.00 909.56 20.59 11.68 84 3195.00 159.75 3354.74 0.00 0.00 925.57 20.57 11.63 85 3162.00 158.10 3320.10 0.00 0.00 952.81 20.52 11.51 86 3123.00 156.15 3279.14 0.00 0.00 973.41 20.45 11.37 87 3097.00 154.85 3251.85 0.00 0.00 976.64 20.41 11.28 88 3095.00 154.75 3249.74 0.00 0.00 962.72 20.40 11.27 89 3060.00 153.00 3213.00 0.00 0.00 998.22 20.34 11.15 90 3041.00 152.05 3193.05 0.00 0.00 996.59 20.31 11.08 91 3030.00 151.50 3181.49 0.00 0.00 996.42 20.29 11.04 92 3070.00 153.50 3223.50 0.00 0.00 947.63 20.36 11.19 93 3030.00 151.50 3181.49 0.00 0.00 1014.31 20.29 11.04 94 3017.00 150.85 3167.85 0.00 0.00 1003.28 20.27 11.00 95 3004.00 150.20 3154.20 0.00 0.00 1008.91 20.25 10.95 96 3046.00 152.30 3198.30 0.00 0.00 956.79 20.32 11.10

1 1 interval = 10 minutes. Interval 1 = > 0:10 AM


Table 14. System operation without PV during 3rd time period

INT 1 LOAD LOSS DISP CT GEN PV GEN SPIN A. COST Tl N SP

97 3042.00 152.10 3194.10 0.00 0.00 986.91 20.31 11.09 98 3085.00 154.25 3239.24 0.00 0.00 939.29 20.39 11.24 99 3124.00 156.20 3280.20 0.00 0.00 924.86 20.45 11.38

100 3157.00 157.85 3314.85 0.00 0.00 914.26 20.51 11.50 101 3168.00 158.40 3326.39 0.00 0.00 923.08 20.53 11.54 102 3224.00 161.20 3386.39 0.00 0.00 869.86 20.63 11.74 103 3001.00 150.05 3152.18 0.00 0.00 1140.54 20.24 10.94 104 3412.00 170.60 3547.91 36.00 0.00 570.00 26.82 12.80 105 3302.00 165.10 3432.50 36.00 0.00 961.98 20.73 12.38 106 3334.00 166.70 3464.61 36.00 0.00 826.80 20.83 12.50 107 3393.00 169.65 3526.65 36.00 0.00 795.66 21.00 12.71 108 3437.00 171.85 3572.84 36.00 0.00 809.90 21.13 12.87 109 3469.00 173.45 3373.21 270.00 0.00 812.71 20.59 15.02 110 3514.00 175.70 3419.87 270.00 0.00 598.59 20.70 15.18 111 3597.00 179.85 3506.88 270.00 0.00 540.45 20.95 15.48 112 3646.00 182.30 3560.29 270.00 0.00 569.19 21.10 15.67 113 3651.00 182.55 3563.65 270.00 0.00 615.98 21.10 15.68 114 3662.00 183.10 3575.45 270.00 0.00 605.86 21.14 15.72 115 3671.00 183.55 3519.93 334.00 0.00 603.29 20.98 16.26 116 3671.00 183.55 3519.93 334.00 0.00 558.27 20.98 16.26 117 3679.00 183.95 3529.12 334.00 0.00 549.08 21.01 16.29 118 3678.00 183.90 3529.12 334.00 0.00 558.03 21.01 16.29 119 3652.00 182.60 3500.10 334.00 0.00 587.05 20.93 16.19 120 3631.00 181.55 3478.09 334.00 0.00 580.79 20.86 16.11 121 3612.00 180.60 3586.98 206.00 0.00 578.45 21.17 15.04 122 3599.00 179.95 3572.32 206.00 0.00 684.68 21.13 14.98 123 3594.00 179.70 3567.48 206.00 0.00 682.17 21.12 14.97 124 3549.00 177.45 3520.45 206.00 0.00 726.78 20.98 14.80 125 3512.00 175.60 3481.60 206.00 0.00 725.10 20.87 14.67 126 3457.00 172.85 3424.82 206.00 0.00 744.04 20.71 14.47 127 3404.00 170.20 3574.54 0.00 0.00 746.42 21.14 12.40 128 3375.00 168.75 3543.74 0.00 0.00 913.02 21.05 12.29 129 3340.00 167.00 3507.00 0.00 0.00 928.40 20.95 12.16 130 3279.00 163.95 3442.79 0.00 0.00 956.81 20.76 11.94 131 3197.00 159.85 3356.85 0.00 0.00 980.46 20.57 11.64 132 3122.00 156.10 3278.10 0.00 0.00 996.04 20.45 11.37 133 3074.00 153.70 3228.10 0.00 0.00 934.78 20.45 11.11 134 3040.00 152.00 3191.99 0.00 0.00 970.89 20.39 10.99 135 2968.00 148.40 3116.39 0.00 0.00 1025.28 20.27 10.73 136 2901.00 145.05 3046.04 0.00 0.00 1051.22 20.15 10.49 137 2812.00 140.60 2952.05 0.00 0.00 1087.48 20.00 10.18 138 2750.00 137.50 2887.63 0.00 0.00 1053.51 19.90 9.96 139 2706.00 135.30 2841.30 0.00 0.00 1026.41 19.82 9.81 140 2627.00 131.35 2758.34 0.00 0.00 1058.57 19.70 9.54 141 2582.00 129.10 2711.10 0.00 0.00 1021.49 19.63 9.38 142 2517.00 125.85 2642.85 0.00 0.00 1041.71 19.53 9.16 143 2428.00 121.40 2549.39 0.00 0.00 1065.79 19.39 8.86 144 2291.00 114.55 2405.54 0.00 0.00 1114.64 19.18 8.39



Table 15. System operation with PV during 2nd time period

INT 1 LOAD LOSS DISP CT GEN PV GEN SPIN A. COST X1 t>oo s 49 3905.00 195.25 3155.87 527.00 416.73 800.45 19.61 17.89 50 3908.00 195.40 3023.61 527.00 553.08 641.51 19.94 17.44 51 3866.00 193.30 2962.83 527.00 569.19 537.82 19.94 17.24 52 3835.00 191.75 2922.32 527.00 578.07 512.08 19.87 17.10 53 3814.00 190.70 2885.61 527.00 592.83 502.66 19.82 16.98 54 3805.00 190.25 2872.12 527.00 596.13 477.00 19.80 16.94 55 3775.00 188.75 2944.59 402.00 618.45 515.82 19.91 15.31 56 3763.00 188.15 2894.64 402.00 656.31 643.99 19.83 15.14 57 3753.00 187.65 2865.18 402.00 673.47 618.13 19.79 15.04 58 3731.00 186.55 2860.49 402.00 655.05 592.87 19.78 15.03 59 3694.00 184.70 2791.07 402.00 685.62 657.52 19.68 14.80 60 3675.00 183.75 2782.92 402.00 673.83 595.11 19.66 14.77 61 3650.00 182.50 2810.21 334.00 688.29 627.52 19.70 13.86 62 3648.00 182.40 2810.21 334.00 687.21 655.27 19.70 13.86 63 3645.00 182.25 2803.39 334.00 689.85 662.09 19.69 13.83 64 3632.00 181.60 3186.55 558.00 67.85 48.00 27.31 18.21 65 3608.00 180.40 3162.54 558.00 67.85 467.30 20.26 18.11 66 3584.00 179.20 3167.99 558.00 37.21 434.01 20.27 18.12 67 3550.00 177.50 2947.43 142.00 638.46 1073.77 19.91 12.13 68 3545.00 177.25 2947.43 142.00 633.93 854.43 19.91 12.13 69 3482.00 174.10 3322.10 334.00 0.00 287.77 22.73 15.58 70 3456.00 172.80 3294.76 334.00 0.00 658.77 20.47 15.48 71 3414.00 170.70 3250.69 334.00 0.00 652.98 20.40 15.33 72 3394.00 169.70 3229.69 334.00 0.00 648.09 20.37 15.26 73 3347.00 167.35 3309.70 0.00 205.66 889.74 20.50 11.48 74 3280.00 164.00 2880.49 0.00 564.77 1365.96 19.04 10.04 75 3252.00 162.60 2731.24 0.00 681.96 1167.59 19.46 9.55 76 3229.00 161.45 2709.80 0.00 680.64 1015.76 19.56 9.48 77 3221.00 161.05 2700.92 0.00 681.12 996.49 19.54 9.45 78 3208.00 160.40 2672.58 0.00 695.82 1015.81 19.50 9.36 79 3187.00 159.35 2658.39 0.00 687.96 1001.18 19.48 9.31 80 3445.00 172.25 2939.05 0.00 679.32 706.09 20.05 10.23 81 3219.00 160.95 2697.87 0.00 682.08 1240.18 19.54 9.44 82 3201.00 160.05 2680.01 0.00 681.03 1005.27 19.51 9.38 83 3207.00 160.35 2690.28 0.00 677.07 976.85 19.53 9.41 84 3195.00 159.75 2683.41 0.00 671.34 994.15 19.52 9.39 85 3162.00 158.10 2646.83 0.00 673.26 1023.75 19.46 9.27 86 3123.00 156.15 2608.91 0.00 670.23 1024.49 19.41 9.15 87 3097.00 154.85 2585.13 0.00 666.72 1009.72 19.37 9.07 88 3095.00 154.75 2577.45 0.00 672.30 993.23 19.36 9.05 89 3060.00 153.00 2557.07 0.00 655.92 1005.61 19.33 8.98 90 3041.00 152.05 2524.19 0.00 668.85 1015.27 19.28 8.88 91 3030.00 151.50 2521.53 0.00 659.97 980.46 19.28 8.87 92 3070.00 153.50 2570.25 0.00 653.25 928.70 19.35 9.02 93 3030.00 151.50 2523.66 0.00 657.84 1030.83 19.28 8.87 94 3017.00 150.85 2508.57 0.00 659.28 992.80 19.26 8.83 95 3004.00 150.20 2508.57 0.00 645.81 975.61 19.26 8.83 96 3046.00 152.30 2560.55 0.00 637.74 923.62 19.34 8.99

1 1 interval = 10 minutes. Interval 1 = > 0:10 AM.


Table 16. System operation with PV during 3rd time period

INT 1 LOAD LOSS DISP CT GEN PV GEN SPIN A. COST X1 t>oo s 97 3042.00 152.10 2925.95 270.00 0.00 347.48 22.79 13.53 98 3085.00 154.25 2969.99 270.00 0.00 689.49 19.96 13.66 99 3124.00 156.20 3009.99 270.00 0.00 689.92 20.02 13.79

100 3157.00 157.85 3044.85 270.00 0.00 700.37 20.07 13.91 101 3168.00 158.40 3056.40 270.00 0.00 728.66 20.09 13.95 102 3224.00 161.20 3115.20 270.00 0.00 682.94 20.19 14.14 103 3001.00 150.05 3151.04 0.00 0.00 970.55 20.24 10.94 104 3412.00 170.60 3547.24 36.00 0.00 570.00 26.83 12.80 105 3302.00 165.10 3432.46 36.00 0.00 961.32 20.73 12.38 106 3334.00 166.70 3464.61 36.00 0.00 826.77 20.83 12.50 107 3393.00 169.65 3526.65 36.00 0.00 795.66 21.00 12.71 108 3437.00 171.85 3572.84 36.00 0.00 809.90 21.13 12.87 109 3469.00 173.45 3373.21 270.00 0.00 812.71 20.59 15.02 110 3514.00 175.70 3419.87 270.00 0.00 598.59 20.70 15.18 111 3597.00 179.85 3506.88 270.00 0.00 540.45 20.95 15.48 112 3646.00 182.30 3560.29 270.00 0.00 569.19 21.10 15.67 113 3651.00 182.55 3563.65 270.00 0.00 615.98 21.10 15.68 114 3662.00 183.10 3575.45 270.00 0.00 605.86 21.14 15.72 115 3671.00 183.55 3519.93 334.00 0.00 603.29 20.98 16.26 116 3671.00 183.55 3519.93 334.00 o".oo 558.27 20.98 16.26 117 3679.00 183.95 3529.12 334.00 0.00 549.08 21.01 16.29 118 3678.00 183.90 3529.12 334.00 0.00 558.03 21.01 16.29 119 3652.00 182.60 3500.10 334.00 0.00 587.05 20.93 16.19 120 3631.00 181.55 3478.09 334.00 0.00 580.79 20.86 16.11 121 3612.00 180.60 3586.98 206.00 0.00 578.45 21.17 15.04 122 3599.00 179.95 3572.32 206.00 0.00 684.68 21.13 14.98 123 3594.00 179.70 3567.48 206.00 0.00 682.17 21.12 14.97 124 3549.00 177.45 3520.45 206.00 0.00 726.78 20.98 14.80 125 3512.00 175.60 3481.60 206.00 0.00 725.10 20.87 14.67 126 3457.00 172.85 3424.82 206.00 0.00 744.04 20.71 14.47 127 3404.00 170.20 3574.54 0.00 0.00 746.42 21.14 12.40 128 3375.00 168.75 3543.74 0.00 0.00 913.02 21.05 12.29 129 3340.00 167.00 3507.00 0.00 0.00 928.40 20.95 12.16 130 3279.00 163.95 3442.79 0.00 0.00 956.81 20.76 11.94 131 3197.00 159.85 3356.85 0.00 0.00 980.46 20.57 11.64 132 3122.00 156.10 3278.10 0.00 0.00 996.04 20.45 11.37 133 3074.00 153.70 3228.10 0.00 0.00 934.78 20.45 11.11 134 3040.00 152.00 3191.99 0.00 0.00 970.89 20.39 10.99 135 2968.00 148.40 3116.39 0.00 0.00 1025.28 20.27 10.73 136 2901.00 145.05 3046.04 0.00 0.00 1051.22 20.15 10.49 137 2812.00 140.60 2952.05 0.00 0.00 1087.48 20.00 10.18 138 2750.00 137.50 2887.63 0.00 0.00 1053.51 19.90 9.96 139 2706.00 135.30 2841.30 0.00 0.00 1026.41 19.82 9.81 140 2627.00 131.35 2758.34 0.00 0.00 1058.57 19.70 9.54 141 2582.00 129.10 2711.10 0.00 0.00 1021.49 19.63 9.38 142 2517.00 125.85 2642.85 0.00 0.00 1041.71 19.53 9.16 143 2428.00 121.40 2549.39 0.00 0.00 1065.79 19.39 8.86 144 2291.00 114.55 2405.54 0.00 0.00 1114.64 19.18 8.39



Table 12, Table 13 and Table 14 show the parameters involved during operation of the power

system during the three time periods respectively. These tables show results of the case

before PV is added. Column 1 in these tables lists the intervals during the period with interval

1 being 10 minutes after midnight. Column 2 shows the modified load demand at each interval

while column 3 gives the transmission losses, both in MW. The latter is determined by

providing constant penalty factors for each unit. Column 4 provides information on

dispatchable generation. Columns 5 and 6 show the generations in MW, from combustion

turbines and the PV plant respectively. The spinning reserve (MW) at each interval is listed in

column 7 while the system lambda ($/MWh) is shown in column 8. Production cost (1000 $)

appears in column 9.

Table 15 and Table 16 are introduced to bring out the differences if a photovoltaic plant is

added to the system. These tables are counterparts ofTable 13 and Table 14 which shows the

"no PV" case. The PV plant is rated at 750 MW de.

A graphical representation of the net effect of having a PV plant in the generation mix is shown

in Figure 39. The particular feature shown in the figure is the effect on the dispatchable

thermal generations during the entire 24 hour period. Also shown in the figure are the load

profile and the photovoltaic generation on the same scale. The thermal generations follow the

load (transmission losses not shown in the figure) consistently until the PV plant starts

generating power. Dispatch problems that cannot be handled by the thermal units are picked

up by combustion turbine units as shown in Figure 40.

The effect of PV output on the spinning reserve is evident in Figure 41. The obvious impact is

during high variations in the PV plant output. In the morning, when the plant starts up, there

is a sudden decrease in thermal generation which contributes to an increase in the spinning

reserve. This happens during a time when the system is experiencing a shortage in reserves

without the PV plant being considered. In the afternoon, when the PV plant shuts off, the


:x ~

3200

~ 2400 ....... Ill ... ~ Cll t7l

..Jl

...c Ill ~ 1600 Ill Q.. !!

0

800 1 I ntervaJ. 10 miMes

' I\. I

--------------

r> I\ r~\ r \ /1 I

\ \

Without PV With PV Load PV output

~ \

\

Li I 0 .__~---~--~~ .......... ~--~---~--'------~---~-----___,

0 29 58 87 116 145 Intervals

Figure 39. Effect of PV output on thermal generation


1-u

800

600

400

200

1 I nt.erval- 1 amvles

I' I I I I I I I I

I

Wrlhout PV - - - - - - - - - - w 1th p v

~ - I I

0 .._~~....__~~.__~_....._~__..__~__.,__~__..___...~..._~__..__~ ............... ~__.J D 29 58 87 116 145

I nt.ervals

Figure 40. Effect of PV output on combustion turbine generation


QI

~ QI LI

E en c ~ a.

U1

1500

1200

900

600

300

0 0

1 I nterval- 1

29

111rutes

~ II

1'.

: I f\ ~ /~ I I I 11 V I

----+--'- __..___ I I I

I ',1 I I I

58

I ~I ,, 11

,, 11 11 ,,

I nlervals

Figure 41. Effect of PV output on spinning reserves

Case Study Results

87

1thoul PV With PV Req11red

116 145

179

reverse condition of that of the morning start-up occurs, thus reducing the reserves

significantly for a short period of time.

Figure 42 provides a look at the change in system lambda because of the presence of PY

generations. System lambda goes up whenever the thermal generations cannot follow the

economic trajectory. In other words, lambda increases when there are sudden changes in the

PY generations. Figure 43 shows the effect on the overall production costs incurred by the

system. Figure 44 and Figure 45 show the net impact of PY output on some specific thermal

and combustion turbine units respectively.

Shown in Table 17, is a list of the system regulating capacity violations during the day. Also

evident from the table are the reasons of the violations which may be PY induced or

otherwise. These violations occur when inadequate generation capacity is present in the

system during times when the net load varies by a large amount during two successive

intervals. Net load is derived from the actual load minus the non-committable (CT, hydro,

pumped storage and interchange) generations minus the PY generations (if present). In

columns 2 and 3 are shown the total number of thermal units which have either reached their

minimum limit or maximum limit set by their response rates. Also shown in column 3 within

parentheses, are the changes in PY generations from the previous interval and the changes

in actual loads from the previous interval. It is seen that only in extreme variations of PY plant

output does the system experience loading or unloading problems. Other than that, the only

cases when the system might have problems are when the load itself varies during the

interval, by a large amount.

Table 18 gives a summary of the operation of the power system with and without the addition

of the PY plant. Total dispatchable thermal generation is reduced by 6.7% with the addition

of the 750 MW PY plant. On the other hand, CT picks up by 18.4%. The PY plant operates with

a capacity factor of 58.4%. The daily total spinning reserves is increased somewhat and the

production costs fall by about 3.5% indicating a saving of more than $60,000 during the day.


111

" ..D E

..Ill

24

e 12 .S 1 I nt.ervaJ. 10 m1nule; Ill >-

Ul

6

ii /I

I I .... I .... ' ,- - ....... _, .... \ /\ ,, - - -- -- '

W1thou! PV ---------- w 1th p v

0 '--~--'~~-"'~~--~~--~~--~~--~-----~--~~--~~-0 29 58 87 116 145

I ntervak:

Figure 42. Effect of PV output on system lambda


f ~

0 C>

24

C> 18 C> C> d -+"

I.II 0 u c 1! 12 ~

""'C e a.

6

0 0

1 I nlerval- 10 111nulec

29

W1thoui PV - - - - -- - - - - w 1th p v

\ 1' -.... \. -

58 87 116 I nt.ervals

Figure 43. Effect of PV output on production costs

Case Study Results

145

182

.JI ..c I'll

640

ij 320 -+' I'll 0.... !!

0

160

1 I nlerval- 10 111111ies

c:Jf------El TUN I T 2 v1lhout P V C9 e:i TUN I T2 v1lh PV 6 6 TUN I T3 v1lhout PV -+------------+- TUN I T 3 v1lh P V

>-< ------>( TUN I T '1 v1lhout P V <!>----<> TUN IT '1 v1lh PV

0 ,__~_._~__.,__~_._~__..__~ ......... ~--'~~ ......... ~--'~~-'-~--' 0 29 58 87 116 145

I nlerval&

Figure 44. Effect of PV output on some specific thermal units


100 1 I nlervalo 10 111rlltei: cg E'.J CUN IT 1 vrthout PV

Ql e:J CUNITl vrth PV 6 6 CUNITS vrlhout PV

CUN ITS vrlh PV 80 )( >< CUNI T7 vrlhout PV

0 ~ CUNIT1 vrlh PV

:x 60 ~ c 0

...j:i

~ ~ Cll en

~ 40 u

20

58 87 116 I nlervals

Figure 45. Effect of PV output on some specific CT units


Table 17. System regulation limit violations

Time Total Thermal Units Affected Remarks CASEI CASE II Without PV With PV

6:20 AM 3 3 (0 1) (209 2) No system problem 6:30 AM 1 1 (0) (200) No system problem 6:50 AM 3 3 (0) (175) No system problem 7:10 AM 7 7 (0) (120) No system problem 8:10 AM 0 12 (416)(-59) PV starts producing. No system problem 8:20 AM 0 2 (136)(+3) No system problem

10:40 AM 0 20 (-622)(-13) Thermal loading problem in Case II 11:30 AM 0 20 (-634)(-63) Thermal loading problem in Case II 12:20 PM 0 14 (360)(-67) Thermal unloading problem in Case II 1:20 PM 7 5 (-9) (258) No system problem 4:10 PM 0 21 (-638) (-4) PV plant shuts off. Thermal loading problem 4:20 PM 0 1 (0) (43) No system problem 5:20 PM 18 18 (0) (411) Thermal loading problem 6:10 PM 2 2 (0) (32) No system problem

1 MW change in PV generation from last interval; ( + = > increase) 2 MW change in load demand from last interval; ( + = > increase)


Table 18. System operation summary with and without PV

Parameter No PV With PV Total daily dispatchable generation 72757.50 MWhr 67866.24 MWhr Total daily CT generation 2772.00 MWhr 3282.00 MWhr Total daily PV generation 0.00 MWhr 4381.54 MWhr Total daily pumped storage generation 0.00 MWhr 0.00 MWhr Total daily hydro generation 0.00 MWhr 0.00 MWhr Total daily interchange 0.00 MWhr 0.00 MWhr Total daily spinning reserve 19144.49 MWhr 19267.19 MWhr Total energy under daily load curve 71931.00 MWhr 71931.00 MWhr Total daily losses 3596.50 MWhr 3596.50 MWhr Total daily production costs $1, 725,526.90 $1,664,892.80 Total daily CT schedule 76 (Unit-hrs) 83 (Unit-hrs) Total daily Hydro schedule 0 (Unit-hrs) 0 (Unit-hrs) Total daily pumped storage schedule 0 (Unit-hrs) 0 (Unit-hrs) Total daily interchange schedule 0 (Unit-hrs) O (Unit-hrs)


The extra operation time seen by the combustion turbines in the absence of hydro or pumped

storage generators is evident from the statistic on unit-hrs of operation time in the two cases.

8.2 Effect of PV Penetration

An important factor to be considered in the integrated operation of PV plants and conventional

generating units is the effect of the PV plant rating as a fraction of the system capacity on the

overall production costs. This is shown in Figure 46. In the figure, each percent of penetration

represents 56.5 MW of generating capacity. The fact that production costs decrease with each

additional penetration of PV plant is evident in the figure. Also featured in the figure is the fact

that the costs level off after the penetration reaches a certain limit. The limit in the case study

is found to be 13.27%. Beyond this point, system operational problems make it more

expensive than the base case, to run a PV plant.

8.3 Static Versus the Dynamic Dispatch Case

A static dispatch algorithm would be one where no PV output forecasts are available. A typical

day's irradiance data is selected in this case to yield PV output which would be expected on

a typical day during the month. (Solar irradiance data for typical days of the year may be found

in TMY weather tapes (207)). Therefore no care is taken to include the instantaneous changes

in the weather. Under this strategy, hourly expected PV generations are subtracted from

hourly load data and the thermal and non-thermal generations are forced to follow the net


1740

...... ~

,.!I 0 -a

-g 1680 " ~ D

_r;

t; .....

UI 0 u c 1620 D

.+i g -a e a_

1560

1 Percent penetration • 56 MW 1500 .__~....._~__..~~-'-~-i..~~.i.......~ ......... ~--i~~...._~_._~__,

a 3 6 9 12 15 Percent penehbon

Figure 46. Effect of PV penetration on system production cost


Table 19. Static versus dynamic dispatch

Parameter Static Case Dynamic Case Total daily dispatchable generation 70786.00 MWhr 67866.24 MWhr Total daily CT generation 2467.00 MWhr 3282.00 MWhr Total daily PV generation 2041.44 MWhr 4381.54 MWhr Total daily pumped storage generation 0.00 MWhr 0.00 MWhr Total daily hydro generation 0.00 MWhr 0.00 MWhr Total daily interchange 0.00 MWhr 0.00 MWhr Total daily spinning reserve 28455.00 MWhr 19267.19 MWhr Total energy under daily load curve 71793.00 MWhr 71931.00 MWhr Total daily losses 3488.00 MWhr 3596.50 MWhr Total daily production costs $1,659,572.00 $1,664,892.80 Total daily thermal schedule 497 (Unit-hrs) 497 (Unit-hrs) Total daily CT schedule 46 (Unit-hrs) 76 (Unit-hrs) Total daily Hydro schedule 0 (Unit-hrs) 0 (Unit-hrs) Total daily pumped storage schedule O (Unit-hrs) O (Unit-hrs) Total daily interchange schedule 0 (Unit-hrs) 0 (Unit-hrs)


load. The proposed dynamic dispatch case has already been described in Chapter 7 and

results presented in this chapter. A comparison of the two cases in shown in Table 19. Both

cases assume the existence of a 750 MW PV power plant operating in the same generation

mix. Day shown in the figure is January 15th. The PV plant output in the static case during the

day is found to be more than 53% less than what is actually generated. The thermal

generations are up by 4% in the static case compared to the dynamic case. Rest of the

parameters show an overly optimistic scenario. CT generations in the static case are lower

by about 25% than the dynamic case; spinning reserves are up by about 52% and the

production cost is lower than the dynamic case. Another statistic in the comparison is the daily

thermal schedule measured in unit-hours. The two cases show similar schedules mainly

because the same hourly load data is used. The conclusion that is derived from these results

is that, although the dynamic dispatch case shows a more conservative result, these are more

realistic figures and are to be expected in real-time operation in the power system. The static

case is adequate for planning and reliability studies with PV plants in the generation mix. But,

for real-time integrated operation, a dynamic study as proposed in this chapter is required.


CHAPTER 9

Summary and Recommendation

The value of solar photovoltaics to an electric utility will remain a widely debated topic in

research circles for the next few years. But before the "value" can be established, it is

imperative that the operation of the PV plant be studied in the context of the utility's

generation scenario. The utility's power system operations is a complex scheme to say the

least and to add the highly variable PV generations in the pot, obviously makes it more

complicated. But a solution needs to be found in order to make PV more competitive against

other emerging new technologies, or even against conventional fossil fuel-based generation

systems.

This dissertation has put forward a new operational tool for integrating a PV system with the

utility. It is recognized at the outset, that much of the existing research concentrated on the

central PV system and its operations have concluded that technical problems in PV operation

will override any value or credit that can be earned by a PV system, and that penetration of

a PV plant in the utility will be severely limited. These are real problems and their solutions

are sought in this dissertation. The following points are believed to be the major obstacles

Conclusions 191

that are plaguing the cause of PV systems, and for that matter, all renewable sources which

depend on the weather or any random phenomenon. These are:

• At present, the PV generations, if any exist in the generation mix, are handled in a static

manner in utility operations. PV output over the day or week of the commitment period is

simulated using typical weather data at the site. While typical load demand trends during

this period follow a particular trend and are generally considered accurate to a certain

degree, the same cannot be said for the PV output. The reason is that, PV plant

performance depends on the highly variable weather phenomena and are liable to

extreme changes during the week. Weather forecasts as far ahead as one week cannot

be considered reliable. Therefore, the amount of uncertainty introduced into the unit

commitment output is considerably increased because of the presence of PV power.

• With the static approach, PV power is considered to be forced on the system. No care is

taken to see whether the PV plant might be generating during a period of time when the

base load units are operating. The latter are required to operate at the same level of

generation throughout the day, in order to be most economic. Also, no care is taken to

see whether there is enough cycling capacity available at any time during which the net

load changes substantially because of the forced PV generations.

Judging from the drawbacks of the static approach, it seems obvious that a new approach or

methodology needs to be developed which would give a central station PV plant its due share

of credit.

This dissertation dealt mainly, with the development and implementation of this new approach

- a dynamic rule-based dispatch algorithm which takes into account all the problems faced

by the dispatch operator during a dispatch interval and channels those into a knowledge base

for use by a rule base (RB).

Conclusions 192

The new dynamic dispatch requires forecasts of photovoltaic generations at the beginning of

each dispatch interval to build the more realistic scenario. A Box-Jenkins time-series method

was used to model the sub-hourly solar irradiance. The irradiance data at any specific site can

be stripped of its periodicities using a pre-whitening process which involves parameterization

of certain known atmospheric phenomena. The pre-whitened data series can be considered

stationary, although some non-stationarity might be introduced by the discontinuities in the

data collection during night hours. This model is extended to yield forecast equations which

are then used to predict the photovoltaic output expected to occur at certain lead times

coinciding with the economic dispatch intervals. The following observations can be made

about the predictive model:

1. An accurate and relatively simple method (compared to other statistical methods) to

predict solar irradiance.

2. A comprehensive model which can forecast the irradiance value for any lead time from

a few minutes to an hour.

3. Input requirements are not very restrictive. Only requirements are past global horizontal

irradiance, wind speed and temperature measurements.

4. Results show that when compared to actual data measured at several locations, the

forecasts are quite accurate and the model is site independent.

5. Forecasts are found to be inaccurate only when there are sudden transitional changes in

the cloud cover moving across the sun. In other words, the randomness involved in

sudden extreme changes in the sun's intensity (e.g. bright sun to fully shaded sun and

back to bright sun again) during an interval will not be picked up by the forecast model

and is generally considered impossible to predict by any forecast model.

In the rule-based dispatch algorithm that was developed in this dissertation, the rule based

system is introduced to operate as a substitute for the dispatch operator. A dispatcher works

from the hourly committed dispatch units and uses standard procedures to allocate generation

levels, to maintain the system frequency, to maintain the area control error at zero in case

Conclusions 193

of interconnected systems and to bring up fast start-up units like peaking hydro or gas

turbines in case of emergencies. Some of these are routine jobs, while some require

specialized knowledge or experience. The RB is given these two qualities through a number

of rules. The RB works in tandem with a conventional economic dispatch algorithm. The

functions of the two are coordinated by another algorithm which overlooks the flow of

information and records them.

With the sub-hourly PV output forecasts available, the treatment of PV plants in the economic

dispatch algorithm becomes similar to that of combustion turbines (CT). The essential

similarities are the fact that CT's can be brought on-line within a very short time, whenever

there is need for extra capacity, and they can be backed off whenever desired. Dissimilarities

in the operation of the two plant types are that a CT plant operates at a low load factor,

whereas, a PV plant is expected to run at as high a load factor as possible in order to compete

favorably against conventional units.

It was found that inclusion of PV generations caused two forms of the same problem - that

of response limitation of thermal units. The problems were:

• Thermal generations were not able to increase and attain the economic trajectory as

dictated by the unit economics and net load.

• Thermal generations were not able to decrease and attain the economic trajectory as

dictated by the unit economics and net load.

The RB gives one of 16 possible solutions as and when required. These solutions are written

as rules which manipulate the non-committable generation to achieve an optimal solution. The

RB during its operation overlooks the fact that the PV generation are kept at the maximum

level possible under all constraints. The case study revealed that the thermal generating units

which are scheduled by the unit commitment are able to absorb most of the small to medium

variations present in the PV generations. In cases of large variations during a single interval,

Conclusions 194

for example, when the PV plant starts up from zero to a substantial amount in the morning,

or when the plant shuts-off in the evening, the thermal generators reach their response limits

before they can reach their maximum or minimum generation, thus causing mismatches in the

load and generation. The mismatches are then picked up by the non-committable sources of

generation (in the case study, combustion turbine units only), comprised of pumped storage

units, hydro generation plant, or by interconnection tie-lines. If none of these are sufficient,

changes are made in the PV generation schedule.

The effect on spinning reserve is markedly present during high variations in PV plant output.

In the morning when the PV plant starts up, there is a sudden decrease in thermal generation

which contributes to an increase in the spinning reserve. This is beneficial to the system

because, the time of PV plant start-up coincides with the morning load pick-up and therefore,

the system would experience a potential reserve shortage without PV at this particular time.

the situation reverses in the evening when the PV plant shuts off, and the load is also dropping

significantly, so that the thermal units would have to pick up generation, thus reducing the

reserves.

The case study revealed that during a single day's operation:

1. thermal plant generation was reduced by 6.7%,

2. CT generations picked up 18.4%,

3. the PV plant operated with a load factor of 58.4%,

4. total spinning reserves increased insignificantly,

5. production costs fell by 3.5%, indicating a saving of $60,000 during the day, and

6. the worst situation occurred when the demand decreased, but at the same time, the PV

generations increased substantially from one interval to another and vice versa.

The results obviously depend on the time of the year and the specific utility. The time of the

year information is reflected in the load demand profile. Most utilities in the U.S. have single

Conclusions 195

peaks in summer and double peaks in winter. Also, the time of the peak load occurrence,

varies with season. The utility generating capacity mix influences the results a great deal. A

utility with a generation mix having a combination of a number of non-committable plant types,

for example, pumped storage, CT, hydro, and interconnection, would incur lower production

costs since the extra non-committable generation required because of the presence of PV

could be shared by all the plant types.

For the utility selected in the case study, penetration of PV was limited to 13.27% before

operating mismatches were no longer possible to be resolved. Once again, the penetration is

a function of the utility and the location.

9.1 Recommendations

The concepts and algorithms developed in the dissertation are part of an integration process

dealing with photovoltaic power plants and electric utilities. Although, central station

photovoltaics is not a new concept, the methodology of integration presented here is. An effort

has been made to develop a model of power system operations incorporating the dispatch of

PV generations. The model, while serving to concretize the ideas presented and providing

validity, requires more development to be regarded as an operational tool.

Some issues which need to be researched further are:

• Resource forecast strategy

1. A more extensive data base may be created.

2. Grouping of similar days into day types may prove to be useful as irradiance

forecasts may become more accurate.

Conclusions 196

• Rule-based dispatch algorithm

1. Number of rules used in the rule base needs to be increased in order to make the

algorithm site independent.

2. A random firing of the rules in the rule base may be explored. This approach will

certainly have a distinct advantage over the hierarchical approach followed in this

dissertation. An expert system may be employed for this purpose.

• Overall Methodology

1. An economic analysis of the integration of PV systems with utilities needs to be

performed over the lifetime of the PV plant, before any value can be established for

the plant in the planning context.

2. Statistical availability and reliability modeling for the PV plant should be done in

order to perform the next stage of the value determination process -- that of

long-term planning in the utility's planning process.

Conclusions 197

Abbreviations

AIEE ASH RAE

EMNEA EPES EPRI IECEC ISES PAS PES PICA PSCC PVSC PWRS SERI

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Bibliography 214

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Bibliography 215

Appendix A

Solar Geometry

In order to calculate the solar irradiance reaching a horizontal surface on the earth, it is

necessary to write down the trigonometric relationships between the solar position in the sky

and the surface coordinates on earth. The position of the sun is expressed in terms of the

following solar angles as illustrated in Figure 47which is the same figure as Figure 4 on page

42 and is repeated here for convenience.

1. Solar elevation angle (Solar altitude): The angular distance of the sun above the horizon

at a specified time of the year and time of day from a particular location. This is angle f3

in the figure.

where B = declination

L = latitude

ro = hour angle

Solar Geometry

sin f3 = sin L sin B + cos L cos B cos ro (A.1)

216

L..r.e JI 5,gnt :o :ne sun-ocserver at 0

~-

Figure 47. Position of the sun relative to an Inclined plane

Solar Geometry

\ Hcrizontal ;>1ane c.:i

~arth s :urrace

217

2. Solar azimuth: The angular distance from due south to the sun's projection on the horizon,

measured from due south (northern hemisphere). This is angle <p in the figure. It is

measured east positive, west negative and south zero.

cos o sin ro sin<p =----cos p (A.2)

3. Surface azimuth: (angle required for tilted surfaces) Angular distance from due south to

the normal to a vertical surface. This is angle 'I' in the figure.

4. Solar declination: Angular distance of the sun north latitudes (positive) or south latitudes

(negative) of the equator at a specified time of the year.

(A.3)

where dn = julian date

5. Sun's hour angle: (apparent solar time) Angular distance in degrees of the sun from its

highest position at solar noon. Mornings are considered positive and evenings negative.

Apparent solar time = local standard time + longitude correction + equation of time

6. Zenith angle: Angle between the local zenith and the line joining the observer and the

sun. This is eH In the figure.

COS 0H =sin~ (A.5)

7. Sunrise and sunset angles: The hour angle at sunrise and sunset.

cos ros = - tan L tan o (A.6)

8. Incidence angle: The incidence angle i is defined as the angle between the normal to a

surface and a line collinear with the sun's rays.

Solar Geometry 218

• South-facing Horizontal and Vertical Surfaces (Fixed):

cos i = - sin o cos L + cos o sin L cos ro (A.6)

• South-facing Titled Surfaces

cos i = sin(L - r) sin o + cos(L - r) cos o cos ro (A.7)

where r = tilt angle

• Non-south-facing Titled Surfaces: If a tilted surface has a direction other than due

south, the following equation is used to calculate the incidence angle:

cos i = cos(q> - 'Vl cos P sin r + sin P cos r (A.8)

• Generalized Equation for Fixed Planar Surfaces

cos i = sin o( sin L cos r - cos L sin r cos 'Vl

+ cos o cos ro( cos L cos r + sin L sin r cos 'I')

+ cos o sin r sin 'I' sin ro (A.9)

9. Extraterrestrial lrradlance: The irradiance on a horizontal surface on top of the

atmosphere.

10 = lscE0( sin o sin L + cos o cos L cos ro1)

where /0 = extraterrestrial irradiance for 1 hour

centered around the hour ro;

lsc = solar constant = 1353 w/m2

E0 = eccentricity correction factor of the earth's orbit

Solar Geometry

(A.10)

219

= (rof r)2 = 1 + 0.033 cos[(27td,,f365)] (A.11)

r0 = mean earth-sun distance.

Solar Geometry 220

Appendix B

Selected Input-Output for Dispatch Model

Selected Input-Output for Dispatch Model 221

1 101 1. 24. 13. 1.1 1. 20. 102 1. 1. 1. 1. 1. 1. 1. 103 3915. 3915. 3915. 3915. 3915. 3915. 3915. 104 1. 10. 5. 107 1. 109 50.

2 2 1 TUNIT1 1 1 1 760. 250. 2 2 TUNIT2 1 1 1 760. 174. 2 3 TUNIT3 1 1 1 420. 125. 2 4 TUNIT4 1 2 1 190. 50. 2 5 TUNIT5 1 2 1 190. 50. 2 6 TUNIT6 1 3 1 270. 65. 2 7 TUNIT7 1 4 1 210. 70. 2 8 TUNIT8 1 4 1 210. 70. 2 9 TUNIT9 1 5 1 115. 35. 2 10 TUNIT10 1 5 1 450. 136. 2 11 TUNIT11 1 5 1 450. 136. 2 12 TUNIT12 1 5 1 110. 35. 2 13 TUNIT13 1 5 1 110. 35. 2 14 TUNIT14 1 5 1 90. 25. 2 15 TUNIT15 1 6 1 55. 25. 2 16 TUNIT16 1 6 1 55. 25. 2 17 TUNIT17 1 6 1 85. 33. 2 18 TUNIT18 1 6 1 55. 25. 2 19 TUNIT19 1 6 1 55. 25. 2 20 TUNIT20 1 3 1 90. 35. 2 21 TUNIT21 1 3 1 90. 35. 2 22 TUNIT22 1 7 1 76. 25. 2 23 TUNIT23 1 8 1 80. 25. 2 24 TUNIT24 1 6 1 85. 33. 2 25 CUNIT1 2 9 1 3 18. 12. 2 26 CUNIT2 2 2 2 2 18. 12. 2 27 CUNIT3 2 1 3 3 18. 12. 2 28 CUNIT4 2 10 4 2 44. 16. 2 29 CUNIT5 2 10 5 2 44. 16. 2 30 CUNIT6 2 10 6 2 64. 46. 2 31 CUNIT7 2 10 7 2 64. 46. 2 32 CUNIT8 2 10 8 2 64. 46. 2 33 CUNIT9 2 10 9 2 64. 46. 2 34 CUNIT10 2 7 10 3 17. 11. 2 35 CUNIT11 2 7 11 3 17. 11. 2 36 CUNIT12 2 7 12 3 17. 11. 2 37 CUNIT13 2 7 13 3 17. 11. 2 38 CUNIT14 2 6 14 2 42. 28. 2 39 CUNIT15 2 3 15 3 18. 12. 2 40 CUNIT16 2 3 16 3 32. 21. 2 41 CUNIT17 2 5 17 2 33. 22.

Figure 48. Generator Input data (Generating unit Identification)


3 3 1 680.941472 7.189709 0.00185289 24. 24. 3 2 702.962766 7.681645 0.00137080 24. 24. 3 3 401.805713 7.245143 0.00425294 24. 24. 3 4 118.276158 8.117995 0.00448263 8. 8. 3 5 120.276158 8.117995 0.00448263 8. 8. 3 6 162.333586 7.643047 0.00326549 24. 24. 3 7 269.422099 6.091183 0.00938761 24. 24. 3 8 248.665264 6.544131 0.01010862 24. 24. 3 9 156.272943 6.122496 0.02577877 8. 8. 3 10 391.128891 7.463225 0.00306321 24. 24. 3 11 396.128891 7.463225 0.00306321 24. 24. 3 12 117.296959 7.903477 0.01579254 8. 8. 3 13 117.296959 7.903477 0.01579254 8. 8. 3 14 49.930167 13.002987 0.00435611 8. 8. 3 15 32.600426 10.016945 0.01324790 8. 8. 3 16 32.600426 10.016945 0.01324790 8. 8. 3 17 85.080842 7.489352 0.01736940 8. 8. 3 18 32.600426 10.016945 0.01324790 8. 8. 3 19 32.600426 10.016945 0.01324790 8. 8. 3 20 118.552580 7.590891 0.02703001 8. 8. 3 21 103.900210 7.517778 0.02761267 8. 8. 3 22 52.503344 12.188683 0.01718860 8. 8. 3 23 47.585357 8.994592 0.01746156 8. 8. 3 24 85.080842 7.489352 0.01736940 8. 8. 3 25 87.876 9.217 3 26 87.468 9.245 3 27 87.036 9.259 3 28 236.716 8.631 3 29 236.716 8.631 3 30 236.716 8.631 3 31 236.716 8.631 3 32 236.716 8.631 3 33 236.716 8.631 3 34 71.181 10.862 3 35 71.181 10.862 3 36 71.181 10.862 3 37 71.181 10.862 3 38 291.83 9.745 3 39 87.876 9.217 3 40 135.828 9.943 3 41 262.112 9.363

Figure 49. Generator input data (Generating unit performance characteristics)


4 4 1 2.11 4000. 24. 4 2 2.11 4000. 24. 4 3 2.11 2000. 12. 4 4 2.11 450. 10. 4 5 2.11 450. 10. 4 6 2.11 750. 10. 4 7 2.11 530. 10. 4 8 2.11 430. 10. 4 9 2.11 2800. 10. 4 10 2.11 3600. 24. 4 11 2.11 3600. 24. 4 12 2.11 2250. 10. 4 13 2.11 2250. 10. 4 14 2.11 300. 10. 4 15 2.11 100. 10. 4 16 2.11 100. 10. 4 17 2.11 300. 10. 4 18 2.11 100. 10. 4 19 2.11 100. 10. 4 20 2.11 460. 10. 4 21 2.11 300. 10. 4 22 2.11 300. 10. 4 23 2.11 300. 10. 4 24 2.11 300. 10. 4 25 5.90 100. 4 26 5.53 100. 4 27 5.90 100. 4 28 5.53 100. 4 29 5.53 100. 4 30 5.53 100. 4 31 5.53 100. 4 32 5.53 100. 4 33 5.53 100. 4 34 5.90 100. 4 35 5.90 100. 4 36 5.90 100. 4 37 5.90 100. 4 38 5.53 100. 4 39 5.90 100. 4 40 5.90 100. 4 41 5.53 100. 7 7 1 1 30 -1 8 8 1 0.507 0.471 0.454 0.454 0.477 0.584 0.810 1.000 0.985 0.953 0.927 0.887 0.832 0.828 0.791 0.775 0.800 0.846 0.917 0.936 0.908 0.839 0.747 0.645

12 VA. TECH SAMPLE SYSTEM (FROM EPRI REGIONAL SYSTEM S.E. AND CP&L DATA).

Figure 50. Generator Input data (Generating unit cost data and hourly load)


-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Figure 51. Unit commitment output used as input to the model (Generator unit schedule)


0.00 0.00 0.00 0.00 0.00 0.00 0.00 18.00 18.00 18.00 18.00 18.00 0.00 0.00 0.00 0.00 0.00 0.00

18.00 18.00 18.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 18.00 18.00 18.00 18.00 18.00 0.00 0.00 0.00 0.00 0.00 0.00

18.00 18.00 18.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 18.00 18.00 18.00 18.00 18.00 0.00 0.00 0.00 0.00 0.00 0.00

18.00 18.00 18.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 44.00 44.00 44.00 44.00 44.00 0.00 0.00 0.00 0.00 0.00 0.00

44.00 44.00 44.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 44.00 44.00 44.00 44.00 44.00 0.00 0.00 0.00 0.00 0.00 0.00

44.00 44.00 44.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64.00 64.00 64.00 64.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

64.00 64.00 64.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64.00 64.00 64.00 64.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

64.00 64.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64.00 64.00 64.00 64.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64.00 64.00 64.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 17.00 17.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 17.00 17.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 17.00 17.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 17.00 17.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Figure 52. Unit commitment output used as Input to the model (Partial CT generation data)


UP DOWN

TUNIT1 .03 .03 TUNIT2 .03 .03 TUNIT3 .05 .05 TUNIT4 .07 .07 TUNIT5 .07 .07 TUNIT6 .05 .05 TUNIT7 .05 .05 TUNIT8 .05 .05 TUNIT9 .07 .07

TUNIT10 .03 .03 TUNIT11 .03 .03 TUNIT12 .07 .07 TUNIT13 .07 .07 TUNIT14 .10 .10 TUNIT15 .10 .10 TUNIT16 .10 .10 TUNIT17 .10 .10 TUNIT18 .10 .10 TUNIT19 .10 .10 TUNIT20 .10 .10 TUNIT21 .10 .10 TUNIT22 .10 .10 TUNIT23 .10 .10 TUNIT24 .10 .10 CUNIT1 1.0 1.0 CUNIT2 1.0 1.0 CUNIT3 1.0 1.0 CUNIT4 1.0 1.0 CUNIT5 1.0 1.0 CUNIT6 1.0 1.0 CUNIT7 1.0 1.0 CUNIT8 1.0 1.0 CUNIT9 1.0 1.0

CUNIT10 1.0 1.0 CUNIT11 1.0 1.0 CUNIT12 1.0 1.0 CUNIT13 1.0 1.0 CUNIT14 1.0 1.0 CUNIT15 1.0 1.0 CUNIT16 1.0 1.0 CUNIT17 1.0 1.0

Figure 53. Generator response rates


HRINT UNIT# GEN CHANGE MORE REQD. STATUS

7 2 2 0.59809E + 02 0.50698E+01 ramp-up limit 7 2 10 0.27933E + 02 0.22856E + 00 ramp-up limit 7 2 11 0.27933E +02 0.22856E + 00 ramp-up limit 7 3 2 0.63461E +02 0.37961E +01 ramp-up limit 7 5 10 0.40542E +02 0.54078E + 01 ramp-up limit 7 5 11 0.40542E + 02 0.54078E +01 ramp-up limit 7 5 23 0.75663E +01 0.6631 SE-01 ramp-up limit 8 1 3 -. 73862E + 02 -.19441E+02 ramp-down limit 8 1 8 -.31076E +02 -.29781E +01 ramp-down limit 8 1 10 -.84423E + 02 -.43923E +02 ramp-down limit 8 1 11 -.84423E +02 -.43923E +02 ramp-down limit 8 1 12 -.19891E +02 -.37502E + 01 ramp-down limit 8 1 13 · -.19891E +02 -.37502E+01 ramp-down limit 8 1 23 -.13272E + 02 -.17904E + 01 ramp-down limit 8 1 2 -.80593E +02 -.12193E+02 ramp-down limit 8 2 2 0.68400E +02 0.61562E+01 ramp-up limit 8 2 4 0.34790E +02 0.21956E +01 ramp-up limit 8 2 5 0.34790E +02 0.21956E +01 ramp-up limit 9 1 2 -.69601E +02 -.12014E +01 ramp-down limit 9 1 3 -.50089E + 02 -.14989E + 01 ramp-down limit 9 1 10 -.69543E + 02 -.32270E + 02 ramp-down limit 9 1 11 -.69543E + 02 -.32270E +02 ramp-down limit 9 1 4 -.42900E + 02 -.29996E + 01 ramp-down limit 9 1 5 -.42900E + 02 -.29996E + 01 ramp-down limit 9 1 8 -.27883E + 02 -.22383E +01 ramp-down limit 9 1 12 -.17847E + 02 -.39048E +01 ramp-down limit 9 1 13 -.17847E+02 -.39048E + 01 ramp-down limit 9 1 7 -.33984E + 02 -.27511E +01 ramp-down limit 9 2 10 -.48620E +02 -.14701E+02 ramp-down limit 9 2 11 -.48620E +02 -.14701E +02 ramp-down limit

11 4 2 0.15745E +03 0.10322E + 03 ramp-up limit 11 4 3 0.55359E + 02 0.18529E + 02 ramp-up limit 11 4 4 0.52522E +02 0.24048E + 02 ramp-up limit 11 4 5 0.52522E + 02 0.24048E +02 ramp-up limit 11 4 8 0.23291E +02 0.25946E +01 ramp-up limit 11 4 10 0. 76860E + 02 0.49383E + 02 ramp-up limit 11 4 11 0. 76860E + 02 0.49383E + 02 ramp-up limit 11 4 12 0.14908E + 02 0.53997E +01 ramp-up limit 11 4 13 0.14908E+02 0.53997E + 01 ramp-up limit 11 4 7 0.37303E + 02 0.11399E +02 ramp-up limit 11 4 9 0.39247E +02 0.26168E + 02 ramp-up limit 11 4 15 0.25580E +02 0.18080E + 02 ramp-up limit 11 4 16 0.25580E + 02 0.18080E + 02 ramp-up limit 11 4 17 0.31911E +02 0.15984E+02 ramp-up limit 11 4 18 0.25580E +02 0.18080E + 02 ramp-up limit 11 4 19 0.25580E +02 0.18080E + 02 ramp-up limit 11 4 20 0.34667E +02 0.24167E +02 ramp-up limit 11 4 21 0.34521E +02 0.24021E +02 ramp-up limit 11 4 23 0.42649E + 02 0.35149E +02 ramp-up limit

Figure 54. Partial thermal generator output during simulation


VA. TECH SAMPLE SYSTEM (FROM EPRI REGIONAL SYSTEM S.E.)

ECONOMIC DISPATCH AND PRODUCTION COST SUMMARY

11:00 AM 11:10AM 11:20 AM 11:30 AM 11:40 AM

LOAD DEMAND (MW) 3584.00 3550.00 3545.00 3482.00 3456.00 TRANSMISSION LOSSES (MW) 179.20 177.50 177.25 174.10 172.80 DISPATCHABLE GEN (MW) 3167.99 2947.43 2947.43 3322.10 3294.76 COMBUST. TURB. GEN (MW) 558.00 142.00 142.00 334.00 334.00 PV POWER GENERATION (MW) 37.21 638.46 633.93 0.00 0.00 PUMPED STORAGE GEN (MW) 0.00 0.00 0.00 0.00 0.00 HYDRO GENERATION (MW) 0.00 0.00 0.00 0.00 0.00 INTERCHANGE (MW) 0.00 0.00 0.00 0.00 0.00 SPINNING RESERVES (MW) 434.01 1073.77 854.43 287.77 658.77 TEN MINUTE RESERVES (MW) 1318.00 2502.00 2502.00 2502.00 2502.00 SYSTEM LAMBDA ($/MWH 20.27 19.92 19.92 22.73 20.47 FUEL COSTS ($/H) 18124.20 12127.99 12127.99 15582.55 15478.89 CUMULAT. PROD.COST ($) 729933.62 742061.56 754189.50 769772.00 785250.87

11:50AM 12:00 PM 12:10 PM 12:20 PM 12:30 PM

LOAD DEMAND (MW) 3414.00 3394.00 3347.00 3280.00 3252.00 TRANSMISSION LOSSES (MW) 170.70 169.70 167.35 164.00 162.60 DISPATCHABLE GEN (MW) 3250.69 3229.69 3309.70 2880.49 2731.24 COMBUST. TURB. GEN (MW) 334.00 334.00 0.00 0.00 0.00 PV POWER GEN (MW) 0.00 0.00 205.66 564.77 681.96 PUMPED STORAGE GEN (MW) 0.00 0.00 0.00 0.00 0.00 HYDRO GENERATION (MW) 0.00 0.00 0.00 0.00 0.00 INTERCHANGE (MW) 0.00 0.00 0.00 0.00 0.00 SPINNING RESERVES (MW) 652.98 648.09 889.74 1365.96 1167.59 TEN MINUTE RESERVES (MW) 2502.00 2502.00 3546.00 3546.00 3546.00 SYSTEM LAMBDA ($/MWH) 20.40 20.37 20.50 19.04 19.46 FUEL COSTS ($/H) 15328.77 15257.42 11478.66 10043.20 9548.11 CUMULAT.PROD.COST ($) 800579.62 815837.00 827315.62 837358.81 846906.87

Figure 55. Sample of model output at each Interval


Characteristics of the two selected sites.

Site Latitude Altitude Location Climate Longitude

RALEIGH 35.46 °N 134 m South-east Moderate 78.38 °W U.S

RICHMOND 37.75 °N 50 m South-east Moderate 77.33 °W U.S

Characteristics of the two PV Arrays.

Site Size Array Azimuth Operated of Orientation by

PV Array

RALEIGH 4KW Fixed Monthly South CP & L Tilt

RICHMOND 25KW 2-axis Tracking N/A VA POWER

Figure 56. Sample of model output at each interval


= = = > Enter dispatch interval

10

Appendix C

Sample Run

= = = > Input status of PV plant. 0 - None; 1 - Present; Default: 0

1

= = = > Enter multiplication factor for PV plant

30.0000000

Sample Run

More non-thermal generation required

Hour: 11 Minute: 40. Amount 109.19 MW

231

= = = > Switch to manual (Y/N)

y

= = = > Choose a number from the following choices

1. Display status of the entire system

2. Increase PV generation input

3. Increase hydro generation

4. Increase pumped storage plant output

5. Increase CT generation

6. Start-up unscheduled hydro unit

7. Start-up unscheduled PSH unit

8. Start-up unscheduled CT unit

9. Buy more unscheduled interconnected power

1

SYSTEM STATUS

TOTAL LOAD: 3632.00 MW. LOSSES: 181.60 MW.

VA. TECH SAMPLE SYSTEM (FROM EPRI REGIONAL SYSTEM S.E. ).

Sample Run 232

Thermal Generation summary for 10:40 A.M.

NAME STATUS POWER

1 ROXBOR03 UNIT DOWN 0.00

2 ROXBOR04 ART MAXIMUM 656.78


4 ROBNSON1 ART MAXIMUM 164.06


6 LEEUNIT3 ART MAXIMUM 270.00

7 ASHEVLE1 MAXIMUM GEN 210.00

= = = > Review more screens (Y /N)

y



NAME STATUS POWER

8 ASHEVLE2 ART MAXIMUM 158.67

9 SUTTON 2 DIS PATCHABLE 101.53

10 SUTTON 3 ART MAXIMUM 332.77


12 SUTTON1B ART MAXIMUM 54.79


14 SUTTON1A MINIMUM GEN 25.00

15 WTHSPN 1 DIS PATCHABLE 50.58


17 WTHSPN 3 MAXIMUM GEN 85.00



Sample Run 233

20 LEE UNT2 DISPATCHABLE 69.67

21 LEE UNT1 DISPATCHABLE 69.52

22 BLEWETT1 MINIMUM GEN 25.00

23 CFHREC DISPATCHABLE 67.65


y



NAME STATUS POWER

24 WTHSPN 7 MAXIMUM GEN 85.00

Total Thermal Generation: 3411.74 MW

= = = > Review more screens (Y/N)

y


Non-dispatchable Generation Summary for 10:40 A.M.

NAME STATUS POWER

25 MOREHD1A MAXIMUM GEN 18.00

26 ROBNSN1A MAXIMUM GEN 18.00

27 ROXBR01A MAXIMUM GEN 18.00

28 DRLNGTN1 MAXIMUM GEN 44.00




Sample Run 234

32 DRLNGTNS MAXIMUM GEN 64.00

33 DRLNGTN6 UNIT DOWN 0.00

34 BLEWET1A UNIT DOWN 0.00




38 WTSPNIC1 UNIT DOWN 0.00

39 LEE IC1 UNIT DOWN 0.00



y



NAME

41 SUTONIC2

STATUS

UNIT DOWN

POWER

0.00

Non-dispatchable Generation at this point: 334.00 MW

Photovoltaic Plant Generation: 67.85 MW

Total Non-dispatchable Generation: 401.85 MW


y

System Summary

Sample Run 235

System Load:

System Losses:

Thermal Generation Capacity:

Total Thermal Generation:

Total Non-dispatchable Gen:

Total Combustion Turbine Gen:

Total Hydro Gen:

Total Pumped Hydro Gen:

Total lntertie:

Total Photovoltaic Gen:

Last System Lambda:

Spinning Reserve:

Choose a number from the following choices










2

3632.00 MW

181.60 MW

3612.06 MW

3411.74 MW

401.85 MW

334.00 MW

0.00 MW

0.00 MW

0.00 MW

67.85 MW

0.25 $/MWh

257.00 MW

PV plant generating 67.85 MW. Increment desired 109.19 MW

Sample Run 236

•••••• Change in PV generation not possible. ••••••

•••••• Plant is down or running at full capacity ••••••











4

••• No PSH plant present in the system •••

••• Try another choice ...




Sample Run 237








5

•••••• Change in CT generation not possible. ••••••

•••••• Units are down or running at full capacity ••••••











8

Sample Run 238

••• CT unit DRLNGTN6 Rescheduled •••

••• CT unit BLEWET1A Rescheduled •••

•••CT unit BLEWET2A Rescheduled •••

••• CT unit BLEWET3A Rescheduled •••



Switch to manual (Y /N)

y







Sample Run 239





1

SYSTEM ST A TUS

TOTAL LOAD: 3632.00 MW. LOSSES: 181.60 MW.



NAME STATUS POWER

1 ROXBOR03 UNIT DOWN 0.00





6 LEEUNIT3 ART MAXIMUM 270.00



y

Sample Run 240

VA. TECH SAMPLE SYSTEM {FROM EPRI REGIONAL SYSTEM S.E. ).


NAME STATUS POWER





12 SUTTON1B ART MAXIMUM 54.79


14 SUTTON1A MAXIMUM GEN 90.00

15 WTHSPN 1 ART MAXIMUM 32.50





20 LEE UNT2 ART MAXIMUM 45.50

21 LEE UNT1 ART MAXIMUM 45.50

22 BLEWETT1 DIS PATCHABLE 70.99

23 CFHREC ART MAXIMUM 32.50


y



NAME STATUS POWER


Sample Run 241

Total Thermal Generation: 3297.54 MW


y



NAME STATUS POWER

25 MOREHD1A MAXIMUM GEN 18.00

26 ROBNSN1A MAXIMUM GEN 18.00

27 ROXBR01A MAXIMUM GEN 18.00







34 BLEWET1A MAXIMUM GEN 17.00




38 WTSPNIC1 UNIT DOWN 0.00




y


Sample Run 242


NAME

41 SUTONIC2

STATUS

UNIT DOWN

POWER

0.00

Non-dispatchable Generation at this point: 449.00 MW

Photovoltaic Plant Generation: 67.85 MW

Total Non-dispatchable Generation: 626.05 MW


y

System Summary

System Load:

System Losses:

Thermal Generation Capacity:

Total Thermal Generation:

Total Non-dispatchable Gen:

Total Combustion Turbine Gen:

Total Hydro Gen:

Total Pumped Hydro Gen:

Total lntertie:

Total Photovoltaic Gen:

Last System Lambda:

Spinning Reserve:

Sample Run

3632.00 MW

181.60 MW

3302.55 MW

3297.54 MW

626.05 MW

449.00 MW

0.00 MW

0.00 MW

0.00 MW

67.85 MW

0.25 $/MWh

257.00 MW

243











0

Invalid Choice 0









Sample Run 244



8

... CT unit BLEWET4A Rescheduled •••

••• CT unit WTSPNIC1 Rescheduled •••

••• CT unit LEE IC1 Rescheduled •••

••• CT unit LEE IC2 Rescheduled •••



Switch to manual (Y/N)

N


...... Change in PV generation not possible ...... .


Sample Run 245

••• No hydro present in the system •••

••• Try another choice •••






••• for rescheduling •••




Sample Run



246


N

PY plant generating 0.00 MW. Increment desired 97.24 MW

•••••• Change in PY generation not possible. ••••••










Sample Run 247




••• CT unit DRLNGTNS Rescheduled •••

Excessive non-thermal generation present



N


•••••• Units are down or running at minimum capacity ••••••



Sample Run 248

*** No hydro present in the system ***

*** Try another choice ***

****** Change in CT schedule not possible. ******

****** Reason: Violation of up-time constraints ******

*** No PSH plant present in the system ***

*** for rescheduling ***

... No hydro present in the system ***


*** No tie lines present in the system ***


PV plant generating 675.51 MW. Reduction desired 110.74 MW

*** Generation in PV plant decreased ***

Sample Run



249


N


...... Change in PV generation not possible. ••••••










Sample Run 250


*** for rescheduling *"*

••• CT unit MOREHD1A Rescheduled •••

**" CT unit ROBNSN1A Rescheduled •••

**" CT unit ROXBR01A Rescheduled *"*

*"* CT unit DRLNGTN1 Rescheduled *"*

*"* CT unit DRLNGTN2 Rescheduled •••




N


...... Change In PV generation not possible. ••••••

•••••• Plant is down or running at full capacity ***"**

Sample Run 251














Sample Run 252


Switch to manual (YIN)

N


...... Change in PV generation not possible ...... .



... Try another choice •••

*** No PSH plant present in the system ***



•••••• Units are down or running at full capacity ******

*** No hydro present in the system ***


Sample Run 253

... No PSH plant present in the system •••

... for rescheduling •••

••• CT unit MOREHD1A Rescheduled ...

••• CT unit ROBNSN1A Rescheduled ...

Sample Run 254

The vita has been removed from the scanned document

1987 - virginia tech · 2020. 9. 28. · photovoltaic output expected to occur at certain lead...

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