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ADVANCED COMPUTATIONAL
APPROACHES FOR POWER SYSTEM
OPERATIONS CONSIDERING WIND
POWER AND EMISSION PROBLEM
BY
FANG YAO
B.E. (Honours)
M.E
A thesis submitted for the degree of Doctor of Philosophy at
The University of Western Australia
December 2011
School of Electrical, Electronics and Computer Science Engineering
i
Declaration by Author
This thesis is composed of my original work, and contains no material previously
published or written by another person except where due reference has been made in the
text. I have clearly stated the contribution by others to jointly-authored works that I have
included in my thesis.
I have clearly stated the contribution of others to my thesis as a whole, including
statistical assistance, survey design, data analysis, significant technical procedures,
professional editorial advice, and any other original research work used or reported in
my thesis. The content of my thesis is the result of work I have carried out since the
commencement of my research higher degree candidature and does not include a
substantial part of work that has been submitted to qualify for the award of any other
degree or diploma in any university or other tertiary institution. I have clearly stated
which parts of my thesis, if any, have been submitted to qualify for another award.
I acknowledge that copyright of all material contained in my thesis resides with the
copyright holder(s) of that material.
FANG YAO
ii
Statement
Statement of Contributions to Jointly Authored Works Contained in the Thesis
[1]. F. Yao, Z. Y. Dong, J. H. Zhao, Z. Xu, H. Iu and K. P. Wong, ―Advanced statistical
approaches to wind power interval prediction,‖ IEEE Transactions on Sustainable
Energy. (First Revision)
F. Yao, Z. Y. Dong, J. H. Zhao were responsible for conception design, data analysis
and interpretation;
F. Yao was responsible for writing;
H. Iu and K. P. Wong were responsible for reviewing.
[2]. F. Yao, Z. Y. Dong, K. Meng, Z. Xu, H. Iu and K. P. Wong, ―A computational
framework for power system operations considering emissions and wind power,‖ IEEE
Transactions on Smart Grid. (Second Revision)
F.Yao, Z. Y. Dong, K. Meng were responsible for conception design, data analysis and
interpretation;
F. Yao was responsible for writing;
Z. Xu, H. Iu and K. P. Wong were responsible for reviewing.
[3]. F. Yao, Z. Y. Dong, K. Meng, Z. Xu, H. Iu and K. P. Wong, ―Quantum-inspired
Particle Swarm Optimizations considering wind power uncertainty and carbon tax in
Australia,‖ IEEE Transactions on Industry Informatics. (Accepted for publication)
F.Yao, Z. Y. Dong, K. Meng were responsible for conception design, data analysis and
interpretation;
F. Yao was responsible for writing;
Z. Xu, H. Iu and K. P. Wong were responsible for reviewing.
[4]. Z.Y. Dong, K.P. Wong, K. Meng, F.J. Luo, F. Yao, and J.H. Zhao, ―Wind power
impact on system operations and planning,‖ IEEE PES Gen. Meeting, Minneapolis, USA,
Jul. 2010.
iii
Z. Y. Dong, K. P. Wong, K. Meng and F. J. Luo were responsible for conception design,
data analysis and interpretation;
Z. Y. Dong and K. Meng were responsible for writing;
F. Yao and J. H. Zhao were responsible for reviewing.
[5]. F. Yao, K. Meng, Z.Y. Dong, Z. Xu, H. Iu, J.H. Zhao, and K.P. Wong, ―Differential
evolution algorithm for multi-objective economic load dispatch considering minimum
emission costs,‖ IEEE PES Gen. Meeting, Detroit, USA, Jul. 2011.
F.Yao, Z. Y. Dong, K. Meng and J. H. Zhao were responsible for conception design,
data analysis and interpretation;
F. Yao was responsible for writing;
Z. Xu, H. Iu and K. P. Wong were responsible for reviewing.
[6]. F. Yao, R. C. Bansal, Z. Y. Dong, ―wind power generation system knowledge: theory,
design and application‖, book chapter was published on World Scientific Publishing,
Singapore, 2010.
F. Yao, R.C. Bansal and Z. Y. Dong were responsible for conception design, data
analysis and interpretation;
F. Yao was responsible for writing;
R. C. Bansal and Z. Y. Dong were responsible for reviewing.
[7]. F. Yao, Z. Y. Dong, Ke Meng, Yan Xu, H. Iu and K. P. Wong, ―Unit commitment
considering probabilistic wind generation‖, IEEE PES Gen. Meeting, San Diego, USA,
Jul. 2012.
F.Yao, Z. Y. Dong and K. Meng were responsible for conception design, data analysis
and interpretation;
F. Yao was responsible for writing;
Yan Xu, H. Iu and K. P. Wong were responsible for reviewing.
Statement of Contributions by Others to the Thesis as a Whole
No contribution by others.
iv
Statement of Parts of the Thesis Submitted to Qualify for the Award of Another
Degree
None.
Published Works by the Author Incorporated into the Thesis
[1]. F. Yao, Z. Y. Dong, J. H. Zhao, Z. Xu, H. Iu and K. P. Wong, ―Advanced statistical
approaches to wind power interval prediction,‖ IEEE Transactions on Sustainable
Energy. (First Revision)
Partially incorporated as Chapter 4.
[2]. F. Yao, Z. Y. Dong, K. Meng, Z. Xu, H. Iu and K. P. Wong, ―A computational
framework for power system operations considering emissions and wind power,‖ IEEE
Transactions on Smart Grid. (Second Revision)
Partially incorporated as Chapter 5.
[3]. F. Yao, Z. Y. Dong, K. Meng, Z. Xu, H. Iu and K. P. Wong, ―Quantum-inspired
Particle Swarm Optimizations considering wind power uncertainty and carbon tax in
Australia,‖ IEEE Transactions on Industry Informatics. (Accepted for publication)
Partially incorporated as Chapter 6.
[4]. F. Yao, R. C. Bansal, Z. Y. Dong ―wind power generation system knowledge: theory,
design and application‖, book chapter was published on World Scientific Publishing,
Singapore, 2010.
Partially incorporated as Chapter 2.
[5]. F. Yao, Z. Y. Dong, Ke Meng, Yan Xu, H. Iu and K. P. Wong, ―Unit commitment
considering probabilistic wind generation‖, IEEE PES Gen. Meeting, San Diego, USA,
Jul. 2012. Partially incorporated as Chapter 7.
v
Additional Published Works by the Author Relevant to the Thesis but not
Forming Part of it
[1]. Z.Y. Dong, K.P. Wong, K. Meng, F.J. Luo, F. Yao, and J.H. Zhao, ―Wind power
impact on system operations and planning,‖ IEEE PES Gen. Meeting, Minneapolis, USA,
Jul. 2010.
[2]. F. Yao, K. Meng, Z.Y. Dong, Z. Xu, H. Iu, J.H. Zhao, and K.P. Wong, ―Differential
evolution algorithm for multi-objective economic load dispatch considering minimum
emission costs,‖ IEEE PES Gen. Meeting, Detroit, USA, Jul. 2011.
vi
Acknowledgements
I finish this thesis based on the research during my Ph.D. study with School of Electrical,
Electronics and Computer Engineering, The University of Western Australia, from 2009
to 2011. Coming to the University of Western Australia to pursue a Ph.D. has been a
richer experience than I could have hoped for. In these three years, many people have
helped me with my research, thus made significant contributions to this thesis. I would
therefore like to sincerely acknowledge them.
First and foremost, I would like to give my great appreciation to my supervisors Prof.
Herbert Ho-Ching Iu, Prof. Zhao Yang Dong and Prof. Victor Sreeram for giving me an
opportunity to reach this goal, for their direction, support, and advice over the course of
my candidature. It is impossible for me to finish this thesis without their enthusiasm,
inspiration, and guidance.
Secondly, I appreciate my parents for their constant love, support and encourage through
years. I would also like to thank Prof. Kit Po WONG, Dr. Jun Hua ZHAO, Dr. Ke
MENG, who significantly contribute to my research through discussions and suggestions.
Special thanks are given to the University of Western Australia for giving me the
Australian Postgraduate Award Scholarship (APA) and UWA Top-up Scholarship as the
financial support for my Ph.D. study.
Finally, I would thank all my friends and fellow students at the School of Electrical,
Electronics and Computer Engineering who have helped me in one way or another.
vii
Abstract
Nowadays, the electric power systems which are electrical and mechanical controlled
systems play the fundamental role in the modern society. No one can doubt the essential
fact that the electric power industry is undergoing restructuring and the competitive
markets will take place of the monopolistic industry structure. As a result, competitive
markets pose severe challenges to power system. The first one is the electric power
system stability. It is clear that the power system stability was spotlighted by many
blackouts around the world. The second is that the conventional energy will tend to be
exhausted and is the primary factor of the environmental pollution. Thirdly, lots of
power operation constraints such as system security, emission reduction and associated
government regulations need to be taken into considered. One consequence is that more
advanced power system data analysis and system operational methods are required in the
deregulated, market-oriented environment. In the same time, the computational power of
modern computers and the application of databases have facilitated the effective
employment of new data analysis techniques. As a result of deregulated markets and
global warming, renewable energy and reliable energy supplies also play a key role in
the government’s energy policy.
In this thesis, the research work is directed at developing computational intelligence
based techniques to solve several power system problems that emerge in deregulated
electricity markets. Four major contributions are included in the thesis: (1). Advanced
statistical approaches to wind power interval prediction; (2). A novel hybrid optimization
algorithm connecting interior point method (IPM) and particle swarm optimization (PSO)
for solving combined economic and emission dispatch (CEED) problem with valve point
effects and stochastic wind power; (3). A newly proposed quantum-inspired particle
swarm optimization for solving economic dispatch considering wind power and carbon
tax; (4). A unit commitment framework considering probabilistic wind power and
emission. Furthermore, a wind speed forecasting (WSF) tool and a load forecasting tool
(OptiLoad), both developed at the Hong Kong Polytechnic University, are incorporated
for corresponding forecasts.
As one of the renewable energy, wind energy is being widely used in the entire world.
However, the most serious problems many power industry enterprisers talk about centers
on the intermittency and uncertainty of wind power. Those problems make it difficult to
viii
integrate wind power into power system. Wind power forecasting system is
indispensable to the integration process of the system operators who rely on accurate
wind power forecasts to design everyday operational plans and assess system security.
So wind power prediction system is of vital importance. Normally, the wind power
predictions are provided in the form of point forecasts in a majority of research works.
Here, a statistical method for wind power interval forecasting is developed. A time series
model is formulated as the theoretical basis of the method. The proposed model takes
into account two important characteristics of wind speed, the nonlinearity and the
time-changing distribution. Based on the proposed model, linear regression and five data
mining algorithms are employed to forecast the prediction interval of wind power output.
The six methods are tested using real wind data collected at a wind station in Australia.
For the wind speed forecasting, the Lazy IBK algorithm outperforms other five
algorithms. In terms of the prediction interval, the five data mining algorithms show
superior performances. The case study proves that, combined with an appropriate
nonlinear regression algorithm, the proposed methodology is effective in wind power
interval forecasting.
Economic dispatch is a crucial process in the power system operation, which aims to
allocate power generation to match load demand at minimal possible cost while
satisfying all generators and system constraints. In the present content, we describe a
novel hybrid optimization algorithm connecting interior point method (IPM) and particle
swarm optimization (PSO) for solving combined economic and emission dispatch
(CEED) problem with valve point effects as well as stochastic wind power. The problem
aims to minimize the scheduling cost and greenhouse gases (GHGs) emission cost. Here
the GHGs include carbon dioxide (CO2) and nitrous oxides (N2O). A dispatch model
including both thermal generators and a wind farm is developed. The probability of
stochastic wind power based on the Weibull distribution is included in the CEED model.
The model is tested for a standard system involving six thermal units and one wind farm.
A set of numerical experiments is reported. The effectiveness of the hybrid
computational method is validated by comparing with other optimization algorithms on
the test system.
In today’s society, global warming is becoming a matter of concern for more and more
people, especially for governments and electric power experts. As a result, carbon tax is
applied in many countries to reduce the carbon emission. In this research work, a
computational framework for economic dispatch (ED) considering wind power
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uncertainty and carbon tax is presented. The probability of stochastic wind power based
on non-linear wind power curves and Weibull distribution is included in the unit
commitment (UC) and economic dispatch (ED) model. Given the complexity of the
model, a solution approach based on quantum-inspired particle swarm optimization
(QPSO) is also proposed. QPSO has very strong search ability and high convergence
speed. The dispatch model is tested on a standard system involving six thermal units and
two wind farms using the real wind speed data obtained from two meteorological
stations in Tasmania, Australia. The effectiveness of the QPSO is validated by
comparing with other optimization algorithms on the test system.
For given known wind speed data, wind power output can be derived through wind
turbine curve. However, the derived result is probabilistic, which makes the wind power
integration a probabilistic problem. UC is an optimization problem of determining
operational schedules for generating units in a power system with a number of
constraints. The main objective of UC is to decide the on/off statuses of generators over
the scheduling period to meet the system load demand and reserve requirements at
lowest cost. Basically, the UC outputs are on/off statuses on an hourly basis for a given
time horizon, such as 24 hours. In the proposed UC framework, a practical load
forecasting (LF) tool called OptiLoad and a practical wind speed forecasting (WSF) tool,
both developed at the Hong Kong Polytechnic University, are incorporated for
corresponding forecasts. The OptiLoad relies on several state-of-the-art forecasting
methods including ANN, SVM, and k-NN for minutely to weekly ahead load forecasting.
During its implementation, the forecasting results provided respectively by the three
methods are strategically combined as the final result. According to the practical on-line
performance, the weight for each method is dynamically updated.
In summary, the research reported in this thesis provides computational frameworks for
power system operation with wind power and environment problem, which are validated
effectively for proposed power test systems. It also covers advanced power system
random and probabilistic data analysis techniques that can provide more accurate
forecasting and simulation results.
Key Words:
x
Power System Operation, Wind Power, Emission, Economic Dispatch, Unit
Commitment, Computational Approaches, Wind Power Forecasting
Australian and New Zealand Standard Research Classifications (ANZSRC)
090607 - Power & Energy System Engineering 50%
090608 – Renewable Power and Energy Systems Engineering 50%
xi
Table of Contents
Declaration by Author ........................................................................................................................ i Statement............................................................................................................................................. ii Acknowledgements ............................................................................................................................ vi Abstract ............................................................................................................................................. vii Table of Contents ............................................................................................................................... xi List of Figures .................................................................................................................................. xiv List of Tables ...................................................................................................................................... xv Chapter 1. Introduction ................................................................................................................... 1
1.1. Overview ................................................................................................................................ 1 1.2. Motivation .............................................................................................................................. 1 1.3. Challenges .............................................................................................................................. 4 1.4. Objectives ............................................................................................................................... 5 1.5. Outline .................................................................................................................................... 5 1.6. Original Contributions ......................................................................................................... 6
Chapter 2. Wind energy resources: theory, design and application ............................................ 7 2.1. Introduction ........................................................................................................................... 7 2.2. Power in the Wind ................................................................................................................. 8
2.2.1. Aerodynamics principle of wind turbine .......................................................... 8 2.2.2. Power available in the wind ..................................................................................... 9 2.2.3. Rotor efficiency ............................................................................................... 10 2.2.4. Factors affecting wind power .......................................................................... 10 2.2.5. Impact of tower height ...................................................................................... 11 2.2.6. Wind turbine sitting ......................................................................................... 12 2.2.7. Idealized wind turbine power curve ............................................................... 12 2.2.8. Speed control for maximum power ................................................................. 15
2.3. Wind Turbine Design Considerations ............................................................................... 15 2.3.1. Basic design philosophies ................................................................................. 16 2.3.2. Choice between two and three blade rotors ................................................... 16 2.3.3. Weight and size considerations........................................................................ 17
2.4. Grid Connected Wind Farms ............................................................................................. 17 2.4.1. Wind farms ....................................................................................................... 17 2.4.2. Problems related with grid connections ......................................................... 17 2.4.3. Latest trend of wind power generation ........................................................... 19
2.5. Hybrid Power Systems ........................................................................................................ 19 2.6. Economics of Wind Power Systems ................................................................................... 22 2.7. Conclusion ........................................................................................................................... 23
Chapter 3. Wind Power System Data Analysis Methodologies .................................................. 24 3.1. Introduction ........................................................................................................................ 24 3.2. Wind power data analysis .................................................................................................. 24
3.2.1. Wind power forecasting ......................................................................................... 24 3.2.2. Power System Operation with Wind Power ......................................................... 25 3.2.3. Future Needs of Data Analysis in Wind Power System ................................. 27
3.3. Evolutionary Algorithms .................................................................................................... 28 3.3.1. Genetic Algorithm .................................................................................................. 28 3.3.3. Immune Algorithm ........................................................................................... 30 3.3.4. Particle Swarm Optimization .......................................................................... 32 3.3.5. Comparison ....................................................................................................... 36
3.4. Machine Learning Methods .............................................................................................. 37 3.4.1. Artificial Neural Networks .................................................................................... 37 3.4.2. Extreme Learning Machine ................................................................................... 38 3.4.3. Support Vector Machine ........................................................................................ 39 3.4.4. Relevance Vector Machine ..................................................................................... 41
3.5. Time Series Models ............................................................................................................ 44 3.5.1. ARIMA .................................................................................................................... 45 3.5.2. GARCH ................................................................................................................... 45 3.5.3. Comparisons ........................................................................................................... 45
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3.6. Conclusion ........................................................................................................................... 45 Chapter 4. Wind Power Interval Forecasting .............................................................................. 47
4.1. Introduction ........................................................................................................................ 47 4.2. A Review of Wind Power Interval Forecasting ................................................................ 47 4.3. The Statistical Model of Wind Speed Time Series ........................................................... 49 4.4. Data Mining Methods for Wind Power Interval Forecasting ......................................... 52
4.4.1. Introduction to Data Mining ................................................................................. 52 4.4.2. Regression Algorithms Employed in This Paper ................................................. 53
4.5. Converting Wind Speed to Wind Power .......................................................................... 57 4.6. Performance Evaluation .................................................................................................... 58 4.7. Australian Regional Wind Power Interval Forecasting .................................................. 58
4.7.1. Data Collection ....................................................................................................... 58 4.7.2. Results of Wind Speed Forecasting ....................................................................... 59 4.7.3. Results of Wind Power Interval Forecasting ....................................................... 60
4.8. Conclusions ......................................................................................................................... 63 Chapter 5. Economic Dispatch Considering Wind Power and Emission .................................. 64
5.1. Nomenclature ...................................................................................................................... 64 5.2. Introduction ........................................................................................................................ 64 5.3. Economic Dispatch with Wind Power and Emission ...................................................... 65 5.4. Probability of Wind Power ................................................................................................ 67 5.5. Mathematical Model of Economic Dispatch with Wind Power and Emission .............. 69
5.5.1. Objective Function ................................................................................................. 69 5.5.2. System Constraints ................................................................................................. 71
5.6. Hybrid Optimization Algorithm ....................................................................................... 71 5.6.1 Interior Point Method (IPM) .................................................................................. 72 5.6.2 Particle Swarm Optimization (PSO) ..................................................................... 73 5.6.3 Hybrid Optimization Method................................................................................. 74
5.7. Australian Regional Reference Case Studies ................................................................... 74 5.7.1. Economic Dispatch Model without and with Wind Farm .................................. 76 5.7.2. CEED Model without and with Wind Power ....................................................... 78 5.7.3. Hybrid Optimization Methods Compare with Other Approaches..................... 79
5.8. Conclusion ........................................................................................................................... 80 Chapter 6. Power System Operations Considering Wind Power Uncertainty and Carbon Tax
in Australia ......................................................................................................................................... 81 6.1. Nomenclature ...................................................................................................................... 81 6.2. Introduction ........................................................................................................................ 81 6.3. Probability Analysis of Wind Power based on non-linear wind power curve ............... 84 6.4. Stochastic Economic Dispatch Formulation .................................................................... 85
6.4.1. Objective Function ................................................................................................. 85 6.4.2. System Constraints ................................................................................................. 87
6.5. Quantum-Inspired Particle Swarm Optimization ........................................................... 87 6.5.1. Particle Swarm Optimization ................................................................................ 87 6.5.2. Quantum-Inspired Particle Swarm Optimization ............................................... 87 6.5.3. Procedure of QPSO ................................................................................................ 91
6.6. Case Studies ........................................................................................................................ 91 6.6.1. Economic Dispatch with and without Carbon tax ......................................... 93 6.6.2. Comparisons with Other Approaches ............................................................. 95
6.7. Conclusion ........................................................................................................................... 95 Chapter 7. Unit Commitment Considering Probabilistic Wind Generation and Emission
Problem .............................................................................................................................................. 97 7.1. Nomenclature ...................................................................................................................... 97 7.2. Introduction ........................................................................................................................ 98 7.3. A Review of Probability of Wind Power ........................................................................... 99 7.4. Wind Power and Load Demand Forecasting ................................................................... 99 7.5. Mathematical Formulation of UC Problem with Wind Power and Emission ............. 102 7.6. A Brief of Interior Point Method (IPM) ......................................................................... 104 7.7. Case Studies ...................................................................................................................... 104 7.8. Conclusion ......................................................................................................................... 108
Chapter 8. Conclusions and Future Work ................................................................................. 109 8.1. Conclusions ....................................................................................................................... 109
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8.2. Future Work ..................................................................................................................... 112 8.3. Summary ........................................................................................................................... 113
Bibliography .................................................................................................................................... 114
xiv
List of Figures
Figure 1. (a) the result of faster air sliding over the top of the wind foil. (b) the
combination of actual wind and the relative wind . .............................................. 8 Figure 2. Increase the angle of attack can cause a wing to stall . .................................... 8 Figure 3. Idealized power curve. ...................................................................................... 12 Figure 4. (a) Increasing rotor diameter gives rate power at lower wind speed .............. 14
(b) increasing the generator size increases rates power . ................................. 15 Figure 5. Schematic diagram of general isolated wind-diesel hybrid power system .. 20 Figure 6. Contribution of various sub-systems towards capital cost of wind turbine. 23 Figure 7. Flowchart of a typical GA ................................................................................ 29 Figure 8. Flowchart of a typical IA ................................................................................. 32 Figure 9. Flowchart of a typical PSO .............................................................................. 33 Figure 10. Flowchart of a typical DE ................................................................................ 36 Figure 11. Diagram of a Multilayer Perceptron Network ............................................... 54 Figure 12. Structure of the RBF Network ........................................................................ 55 Figure 13. The Power curve for VESTAS V90-3.0 MW, 60Hz, 106.7 ............................. 57 Figure 14. Distributions of the Errors of Linear Regression, Lazy IBK and Regression
Tree……………………………………………………………………………..60 Figure 15. The 95% level prediction intervals forecasted by six data mining methods 62 Figure 16. The 99% level prediction intervals forecasted by six data mining methods 63 Figure 17. Simplified Wind Turbine Power Curve .......................................................... 67 Figure 18. Wind Speed Distribution and Weibull Fitting ............................................... 75 Figure 19. Solutions of ELD Models without and with Wind Farm .............................. 77 Figure 20. Solutions of CEED Models without and with Wind Farm............................ 78 Figure 21. Computational Framework Considering Wind Power Uncertainties ......... 83 Figure 22. Nonlinear wind power curve ........................................................................... 84 Figure 23. The Quantum Rotation Gate ........................................................................... 89 Figure 24. Flowchart of Quantum-inspired Particle Swarm Optimization................... 91 Figure 25. Wind Speed Distribution for Wind Farm #1 .................................................. 93 Figure 26. Wind Speed Distribution for Wind Farm #2 .................................................. 93 Figure 27. Solutions of ED Models without and with Carbon Tax ................................. 94 Figure 28. Wind Power Forecasting Model .................................................................... 101 Figure 29. User interface of OptiLoad (v1.0b) ............................................................. 102 Figure 30. Wind Speed Distribution and Weibull Fitting ............................................. 105 Figure 31. Modefied IEEE 30-bus system ...................................................................... 105 Figure 32. (a). Forecasted System Demand (b). Forecasted wind power
vs. scheduled wind power .............................................................................. 107
xv
List of Tables
Table 1 Friction coefficient for various terrain characteristics . .......................................... 11 Table 2 Offshore wind farms in Europe . ............................................................................. 19 Table 3 Comparisons of the EAs .......................................................................................... 36 Table 4 The Results of the Lagrange Multiplier Test.......................................................... 59 Table 5 Prediction Errors of Different Methods ................................................................. 59 Table 6 The Mape of Different Methods for Wind Power Forecasting ............................. 60 Table 7 Performances of Different Methods on Wind Power Interval Forecasting ......... 61 Table 8 Wind Power Factors ................................................................................................. 75 Table 9 Fuel Cost Coefficients .............................................................................................. 75 Table 10 Fuel Consumption Coefficients and Generator Limits ................................. 76 Table 11 Emission Factors of Units ................................................................................ 76 Table 12 Emission Prices ................................................................................................. 76 Table 13 Solution of ELD without Wind Farm ............................................................. 76 Table 14 Solution of ELD with Wind Farm ................................................................... 77 Table 15 Solution of CEED without Wind Farm .......................................................... 78 Table 16 Solution of CEED with Wind Farm ................................................................ 78 Table 17 Comparison of Different Approaches ............................................................. 80 Table 18 Generator Parameters...................................................................................... 92 Table 19 Wind Farm Parameters ................................................................................... 92 Table 20 Emission Factors of Generating Units ............................................................ 92 Table 21 Forecast System Demand and Wind Farm Outputs ...................................... 92 Table 22 Solution of ED Without and With Carbon Tax .............................................. 93 Table 23 Comparison of Different Approaches ............................................................. 95 Table 24 Wind Power Factors ....................................................................................... 105 Table 25 Generator Parameters.................................................................................... 106 Table 26 Generator Constraints ................................................................................... 106 Table 27 Forecasted Wind Power and System Demand ............................................. 106 Table 28 Generation Schedules ..................................................................................... 107
1
Chapter 1. Introduction
1.1. Overview
Over the last decades, under the circumstances of competitive power markets and global
warming problems, many countries are trying to exploit clean energy in order to solve
the energy crisis and mitigate the greenhouse effects. Wind power is one of the
renewable energy sources, and it has been widely developed in recent years. Wind
energy has a number of advantages such as no pollution, relatively low capital cost
involved and the short gestation period required. As mentioned above wind power has
many advantages, however it has the intermittent and volatile character which may
impact on power system security and stability. As a result, the decreasing power system
stability margins will lead to unacceptable operating conditions and power system
collapses. In addition, the uncontrollable nature of wind power will lead to an additional
cost of managing the intermittency.
On the other hand, more advanced power system data analysis and system operational
methods are required in the deregulated and market-oriented environment, which can
ensure the success of the wind power integration process. Data analysis can be used to
extract and recognize the features or patterns of power system information that can make
possible correct predictions of future behaviour and provide effective directions for
decision makers.
The aim of this research is to develop a preliminary analytical framework and a
mathematical model of wind power systems for resolving the operation problems and
minimize the power system operation costs. Moreover, novel advanced and effective
data analysis techniques will to be developed.
1.2. Motivation
In order to solve the problems of today’s power system operation, it is necessary to use
the new techniques, numerical analysis, control methodologies and equipment modeling
to improve the operation efficiency, and minimize the wind power operation cost.
The wind power forecasting system can greatly help integrate wind power into the power
system, since system operators rely on accurate wind power forecasts to design
operational plans and assess system security [1]. A number of methods for wind power
2
forecasting have been proposed in the literature. Depending on the different inputs,
existing methods can be divided into three groups: physical approaches, statistical
approaches and the combination of both. The physical methods forecast wind power
based on the physical characteristics of the wind flow around and inside the wind farm,
and the power curve of the wind turbine. The main idea is to improve the results of
numerical weather prediction (NWP) models by physical information about the terrain
(roughness, orography, obstacles) and wind turbines characteristics (hub height, power
curve, thrust coefficient). Statistical methods, such as recursive least squares or artificial
neural networks, are based on the relation between historical and future values of wind
power. A combination of both physical and statistical methods usually will improve the
forecasting accuracy. Physical methods will be used to predict the future values of
relevant weather variables, statistical approaches can then be employed to improve the
prediction accuracy and provide useful statistical information.
Extensive researches have been conducted to develop wind power forecasting methods.
A short-term forecasting model based on physical reasoning was developed by Landberg
in 1990 [2]. This model uses NWP to forecast the wind speed and direction, then
transform the wind to a local site, using the power curve to correct the wind with peak
efficiency. The University of Oldenburg developed a similar model namely Previento [3].
They use the Deutschlandmodell (DM) or nowadays the Lokalmodell (LM) of the
German Weather Service as the NWP model. The Wind Power Prediction Tool (WPPT)
has been developed by the Institute of Informatics and Mathematical Modeling (IMM),
the Technical University of Denmark. WPPT uses adaptive recursive least squares
estimation with exponential forgetting to provide half an hour to 36 hours forecasts [4].
Ecole de Mines de Paris (ARMINES) and Rutherford Appleton Laboratory (RAL) have
developed short-term wind power forecasting models since 1993. ARMINES has tested
different wind power forecasting approaches based on Auto-Regressive and Moving
Average Model (ARMA) and various neural networks, such as fuzzy neural networks
and wavelet networks. The models based on fuzzy neural networks were proved to have
outstanding performance [5, 6]. Institute of Solare Energieversorgungstechnik (ISET)
has developed Deutscher Wetterdienst (DWD) and neural networks based models for
short-term forecasting since 2000. The model was now renamed as Advanced Wind
Power Prediction Tool (AWPT) [7]. EWind is an US wind prediction model developed
by TrueWind, Inc. These models use the output of ForeWind (an energy company)
numerical weather models to apply a once-and-for-all parameterization for the local
3
effect [8]. The University Carlos III of Madrid developed the Short-term Prediction
System (SIPREOLICO) tool, which is based on Spanish High Resolution Local Area
Model (HIRLAM) forecast and takes into account hourly Supervisory Control and Data
Acquisition (SCADA) data from 80% of wind turbines in Spain. These inputs are then
fed into adaptive non-parametric statistical models and different power curve models to
give wind power forecasts [9,10].
Previous works were mainly limited by the predicting wind power value. This research
work proposes to use Advanced Statistical Interval Forecasting to improve the
forecasting accuracy. Wind power is stochastic in nature and errors will always exist in
wind power forecasts. Therefore, besides predicting the expected value of future wind
power, it is also important to estimate its prediction interval. Generally speaking, a
prediction interval is a stochastic interval, which contains the true value of wind power
with a pre-assigned probability. Because the prediction interval can quantify the
uncertainty of the forecasted wind power, it can be employed to evaluate the investment
risks of the decisions made by market participants.
Another technique used to improve the wind power system operation is economic
dispatch (ED). Economic dispatch deals with the minimum cost of power production in
electrical power system analysis [11]. The main task of ED is to try to find the optimal
allocation of the electrical power output from various available generators. Normally, the
ED problem includes two or three energy power generators, and only one is a depletable
resource such as fuels. Nowadays, it is a trend to use alternative energy resources to
thermal energy power generation. Wind and solar energy are the most popular choices.
One of the major benefits of the renewable resources is there is no extra cost in the
production of power after the initial land and capital cost.
There are many research works about the economics of wind-thermal coordination. In
the Hellenic interconnected system, the cost of wind power from independent producers
is governed by guaranteed and interruptible contracts [12]. Sometimes, the wind power
operator should dispatch all available power produced by the wind generator by the
guaranteed contracts. Furthermore, interruptible contracts of wind generation maybe
applied to avoid the power system instability. A direct search method to the solution of
the wind-thermal coordination problem was developed by Chen et al [13]. Miranda and
Hang [14] researched a solution with fuzzy wind constraints and attitudes of dispatchers.
In this solution, the interruptible contracts of wind generation are modeled through
4
compensation payments to private owners if all available wind power is not utilized [14].
In Wang and Singh’s work, they use a solution with a similar fuzzy model of particle
swarm optimization [15]. Hetzer et al provided an extension of the classical ED model
with wind power generators [16].
However, those research works did not consider the emission issue and wind power
prediction overestimation/underestimation situations, which would be very critical in a
wind power system. Here, complete optimization-based economic dispatch models with
wind power and emission problems are presented. Both wind turbines and conventional
generators are taken into account in the power generation.
1.3. Challenges
The challenges of this research project are given below:
1) In terms of wind power interval forecasting
There are two main challenges for accurate interval forecasting of wind power: (i) The
expected value of wind power should be accurately predicted. This is difficult since wind
power is a nonlinear time series, and is therefore highly volatile. (ii) The probability
distribution of forecasting errors should also be accurately estimated. This is even more
difficult since the error distribution can be time-changing. Existing methods discussed
above cannot effectively handle wind power interval forecasting, since they mainly focus
on predicting the expected value of wind power. In [17,18], statistical analyses have
been conducted to study the distribution of wind power forecasting errors. These studies
however, fail to establish proper statistical models for interval forecasting of wind power,
and also fail to take into account the time-changing effect of the error distribution.
2) In terms of power system economic dispatch with wind power and emission
The challenges for hybrid power ED are: (i) There are two wind power supply situations
that should be considered. Firstly, if a certain amount of wind power is assumed and that
power is not available at that time, the system must get more power from an alternative
energy source. Secondly, if the available wind power is more than the assumed power, a
certain amount of wind power will be wasted. So the operator should pay an extra cost to
the wind power producer. (ii) In this project, the wind speed will be assumed to follow
Weibull distribution. How to analyze the uncertainty of wind power by probabilistic
method is the key part of the problem. (iii) Due to the intermittent and stochastic
5
characteristics of wind energy, how to coordinately dispatch traditional generation
sources and wind power while satisfying all the determined and probabilistic constraints
becomes more complicated. One of the consequences is that more advanced and reliable
computation approaches are required.
1.4. Objectives
The intention of the present research is to develop a computational framework for power
system data analysis considering wind power and emission problem. Specifically, the
objectives of the thesis comprise the following:
Development of advanced statistical approaches to wind power interval forecasting.
Development of an novel hybrid optimization method to power system operation
with wind power and emission problem
Development of Evolutionary Algorithms based approaches to model and operate a
tested power system considering wind power and carbon tax
All these objectives are to be achieved with full reference to extant scientific research
publications and the application of available useful software tools and algorithms.
1.5. Outline
The research reported in this thesis is presented as follows. Chapter 2 introduces the
wind energy resources: theory, design and application. This chapter provides a
description of the fundamental topics which are essential to understand the wind energy
conversion and its eventual use. Chapter 3 is concerned with power system data analysis
methodologies for wind power integration and operation. The emphasis is on data
analysis for wind power system prediction, operation and management in a deregulated
market environment. This is followed by a comprehensive review of some popular data
analysis approaches. Chapter 4 presents wind power interval forecasting problem which
is essential in the wind power integration process. This is shown to be perfectly solved
by advanced statistical prediction approaches. The basic concept of data mining and five
data mining algorithms for wind power forecasting are introduced. Chapter 5 emphasizes
the economic dispatch problem considering wind power, together with the global
warming topic. A hybrid optimization algorithm is developed to solve the newly
proposed computational framework. Chapter 6 is concerned with power system
operation with wind power integration and carbon tax, which can find the least-cost
6
economic dispatch of available generation resource to meet the electrical load. Chapter 7
discusses the Unit Commitment (UC) problem that is important in the operation of
thermal power plants. This is shown to be perfectly solved by the proposed IPM. Chapter
8 concludes the thesis and suggests the future research direction.
1.6. Original Contributions
The main contributions of the research reported in this thesis are set out below:
New advanced statistical approaches to wind power interval forecasting.
A novel computational framework for power system economic dispatch considering
wind power and emission
A novel computational framework for power system operation with power and
carbon tax.
A new quantum-inspired particle swarm optimization that is to be used for solving
economic dispatch/unit commitment and other optimization problems.
Both available scientific research methods and industrial software tools are used
throughout this research to achieve theoretical advances, while at the same time
maintaining significant industrial practicality. The complete outcomes of the present
research extend to 6 publications in major international journals, refereed conference
proceedings, and invited book chapters.
7
Chapter 2. Wind energy resources: theory,
design and application
2.1. Introduction
Wind power is one of the renewable energy sources which have been widely developed
in recent years. Wind energy has many advantages such as no pollution, relatively low
capital cost involved and the short gestation period. The first wind turbine for electricity
generation was developed at the end of the 19th century. From 1940 to1950, two
important technologies, i.e., three blades structure of wind turbine and the AC generator
which replaced DC generator were developed [19]. During the period of 1973 to 1979,
the oil crises led to lots of research about the wind generation. At the end of 1990s, wind
power had an important role in the sustainable energy. At the same time, wind turbine
technologies were developed in the whole world, especially in Denmark, Germany, and
Spain. Today, wind energy is the fastest growing energy source. According to Global
Wind Energy Council (GWEC), global wind power capacity has increased from 7600
MW at the end of 1997 to 195.2 GW by 2009. However wind power accounts for less
than 1.0% of world’s electrical demand. It is inferred that the wind power energy will
develop to about 12% of the world’s electrical supply by 2020[20].
A lot of developments have been taken place in the design of wind energy conversion
systems (WECS). Modern wind-turbines are highly sophisticated machines built on the
aerodynamic principles developed from the aerospace industry, incorporating advanced
materials and electronics and are designed to deliver energy across a wide-range of wind
speeds. The following sections will discuss the different issues related to wind power
generation and wind turbines design.
The rest of the chapter is organized as follows. A number of important topics including
aerodynamic principle of wind turbine, power available in the wind, rotor efficiency,
factors affecting power in the wind, wind turbine power curve, optimizing rotor diameter
and generator rated power have been presented in Sec. 2. Section 3 discusses a number
of design considerations such as choice between two and three blades turbine, weight
and size considerations. Grid connected wind farms, problems related with grid
connections and latest trends of wind power generation are described in Sec. 4. Section 5
8
discusses hybrid power system and economics of wind power system. The conclusion is
presented in Sec. 7, followed by references at the end of chapter.
2.2. Power in the Wind
2.2.1. Aerodynamics principle of wind turbine
Figure 1(a) shows an airfoil, where the air moving the top has a greater distance to pass
before it can rejoin the air that takes the short cut under the foil. So the air pressure on
the top is lower than the air pressure under the airfoil. The air pressure difference creates
the lifting force which can hold the airplane up.
Lift
Drag
(a)
Wind Relative
wind (for
blade
motion)
Resulting wind
Blade
motion
lift
(b)
Figure 1. (a) the result of faster air sliding over the top of the wind foil. (b) the combination of actual
wind and the relative wind [21].
Figure 2. Increase the angle of attack can cause a wing to stall [21].
In terms of the wind turbine blade, it is more complicated than the aircraft wing. From
Fig. 1(b) we can find that a rotating turbine blade sees air moving toward it not only
from the wind itself, but also from the relative motion of the blade. So the combination
of wind and blade motion is the resultant wind which moves toward the blade at a certain
angle.
Angle between the airfoil and the wind is called angle of attack as shown in Fig. 2.
Increasing the angle of attack can improve the lift at the expense of increased drag.
9
However, if we increase the angle of attack too much the wing will stall and the airflow
will have turbulence and damage the turbine blades.
2.2.2. Power available in the wind
The total power available in wind is equal to the product of mass flow rate of wind wm ,
and 2 / 2V . Assuming constant area or ducted flow, the continuity equation states that
wm AV , where is the density of air in 3/kg m , A is the blades area in 2m , and
V is velocity in /m s .
Thus, the total wind power,
Pw = (mw V 2 )/2 = (ρAV 3 )/2. (2.1)[22]
Here, the is a function of pressure, temperature and relative humidity. Let us assume
the inlet wind velocity is iV and the output velocity is
oV , then the average velocity is
( ) / 2i oV V .
The wind power recovered from the wind is given as
2 2 2 2
2 3
( ) / 2 ( / 4)( )( )
( / 2)(1 )
out w i o i o i o
w
P m V V A V V V V
P x x x
(2.2)[22]
where /o ix V V . Differentiating Eq. (2.2) with respect to x and setting it to zero gives
the optimum value of x for maximum power output
d(Pout )/dx = 0 = (1 − 2x − 3x2 ) (2.3)[22]
and then we can get max 1/ 3px .
Substituting the value of max px in Eq. (2.2), the maximum power recovered is
Pout max = 16/27Pw = 0.593Pw . (2.4)[22]
It can be found that the maximum power from a wind system is 59.3% of the total wind
power.
The electrical power output is,
Pe = Cp ηm ηg Pw, (2.5)[22]
where pC is the efficiency coefficient of performance when the wind is converted to
mechanical power. m is mechanical transmission efficiency and g is the electricity
10
transmission efficiency [23]. The optimistic values for these coefficients are 0.45pC ,
0.95m and 0.9g , which give an overall efficiency of 38%. For a given system, wP
and Pe will vary with wind speed.
2.2.3. Rotor efficiency
For a given wind speed, the rotor efficiency is a function of rotor turning rate. If the rotor
turns too slowly, the efficiency drops off because the blades are letting too much wind
pass by unaffected. However, if the rotor turns too fast, efficiency will reduce as the
turbulence caused by one blade increasingly affects the blade that follows. The tip-speed
ratio (TSR) is a function which can illustrate the rotor efficiency. The definition of the
tip-speed-ratio is:
TSR = rotor tip speed/wind speed = (πdN)/60v (2.6)
Where N is rotor speed in rpm, d is the rotor diameter (m); and v is the wind speed (m/s)
upwind of the turbine.
2.2.4. Factors affecting wind power
2.2.4.1. Wind statistics
Wind resource is a highly variable power source, and there are several methods of
characterizing this variability. The most common method is the power duration curve
[24]. Another method is to use a statistical representation, particularly a Weibull
distribution function [25]. Long term wind records are used to select the rated wind
speed for wind electric generators. The wind is characterized by a Weibull density
function.
2.2.4.2. Load factor
There are two main objectives in wind turbine design. The first is to maximize the
average power output. The second one is to meet the necessary load factor requirement
of the load. Load factor is very important when the generator is pumping irrigation water
in asynchronous mode [26]. Commonly assumed long-term average load factors may
be anywhere from 25% to 30%.
11
2.2.4.3. Seasonal and diurnal variation of wind power
It is clear that the seasonal and diurnal variations have significant effects on wind. The
diurnal variation can be reduced by increasing the height of wind power generator tower.
In the early morning, the average power is about 80% of the long term annual average
power. On the other hand, in early afternoon hours, the average power can be 120% of
the long term average power.
2.2.5. Impact of tower height
Wind speed will increase with the height because of the friction at earth surface is large
[27]. The rate of the increase of wind speed that is often used to characterize the impact
of the roughness of the earth’s surface on wind speed is given as:
o o
v H
v H
(2.7)
where V is the wind speed at height H , Vo is the nominal wind speed at height Ho , and
α is the friction coefficient. This can be translated into a substantial increase in power at
greater heights. Table 1 gives the typical values of friction coefficient for various terrain
characteristics.
Table 1 Friction coefficient for various terrain characteristics [28].
Terrain characteristics Friction coefficient α
Smooth hard ground, calm water
0.10 Tall grass on ground 0.15 High crops and hedges 0.20 Wooded countryside, many trees 0.25 Small town with trees 0.30 Large city with tall buildings 0.40
It is known that power in the wind is proportional to the cube of wind speed, so even the
modest increase in wind speed will cause significant increase in the wind power. In order
to get higher speed winds, the wind turbines will be mounted on a taller tower. The air
friction is also an important aspect to be considered, in the first few hundred meters
above the ground, wind speed is greatly affected by the friction that air experiences. So
smoother is the surface, lesser is the air movement friction.
12
2.2.6. Wind turbine sitting
The factors that should be considered while installing wind generator are as follow:
(1) Availability of land.
(2) Availability of power grid (for a grid connected system).
(3) Accessibility of site.
(4) Terrain and soil.
(5) Frequency of lighting strokes.
Once the wind resource at a particular site has been established, the next factor that
should be considered is the availability of land [29-31]. Area of the land required
depends upon the size of wind farm. In order to optimize the power output from a given
site, some additional information is needed, such as wind rose, wind speeds, vegetation,
topography, ground roughness, etc. In addition other information such as convenient
access to the wind farm site, load bearing capacity of the soil, frequency of cyclones,
earthquakes, etc. should also be considered.
2.2.7. Idealized wind turbine power curve
The power curve is an important item for a specific wind turbine. The wind power curve
also shows the relationship between wind speed and generator electrical output.
Rated power Shedding the wind
Cut in wind speed Rated wind speedFurling or cut out
wind speed
wind speed (m/s)
Vc VR VF
PR
Po
wer
del
iver
ed (
kw
)
Figure 3. Idealized power curve.
13
2.2.7.1. Cut-in wind speed
When the wind speed is below cut-in wind speed (VC) shown in Fig. 3, the wind
turbines cannot start [32, 33]. Power in the low speed wind is not sufficient to
overcome friction in the drive train of the turbine. Generator is not able to generate any
useful power below cut in speed.
2.2.7.2. Rated wind speed
We can see from Fig. 3, we can see that as the wind speed increases, the power delivered
by the generator will increase as the cube of wind speed. When the wind speed reached
VR the rated wind speed, the generator can deliver the rated power. If the wind speed
exceeds VR, there must be some methods to control the wind power or else the generator
may be damaged. Basically, there are three control approaches for large wind power
machines: active pitch-control, passive stall-control, and the combination of the two
ways.
In pitch-control system, an electronic system monitors the generator output power. If the
power exceeds the rated power, the pitch of the turbine blades will adjust to shed some
wind. The electronic system will control a hydraulic system to slowly rotate the blades
about the axes, and turn them a few degrees to reduce the wind power. In conclusion,
this strategy is to reduce the blade’s angle of attack when the wind speeds over the rated
wind speed.
For the stall-controlled machines, the turbine blades can reduce the efficiency
automatically when the winds exceed the rated speed. In this control method, there are
no moving parts, so this way is a kind of passive control. The most of the modern, large
wind turbines use this passive, stall-controlled approach.
For large (above 1.0 MW), when the wind speed exceed the rated wind speed, the
turbine machine will not reduce the angle of attack but increase it to induce stall.
For the small size wind turbines, there are a variety of techniques to spill wind. The
common way is the passive yaw control that can cause the axis of the turbine to move
more and more off the wind. Another way relies on a wind vane mounted parallel to the
plane of the blades. As winds get strong, wind pressure on the vane rotate the machine
away from the wind.
14
From Fig. 3 we can see that there is no power generated at wind speeds below VC ; at
wind speeds between VR and VF , the output is equal to the rated power of the
generator; above VF the turbine is shut down [32, 33].
2.2.7.3. Cut-out or furling wind speed
Sometimes, the wind is too strong to damage the wind turbine. In Fig. 3 this wind speed
is called as cut-out or the furling wind speed. Above VF, the output power is zero. In
terms of active pitch-controlled and passive stall-controlled machines, the rotor can be
stopped by rotating the blades about their longitudinal axis to create a stall. However, for
the stall-controlled machines, there will be the spring-loaded on the large turbine and
rotating tips on the ends of the blades. When it is necessary, the hydraulic system will
trip the spring and blade tips rotate 90◦ out of the wind and stop the turbine.
2.2.7.4. Optimizing rotor diameter and generator rated power
Figure 4 shows the trade-offs between rotor diameter and generator size as methods to
increase the energy delivered by a wind turbine. In terms of Fig. 4(a), increasing the
rotor diameter and keep the same generator will shift the power curve upward. In this
situation, the turbine generator can get the rated power at a lower wind speed. For Fig.
4(b), keeping the same rotor but increasing the generator size will allow
Vc Vr
Pr
Po
wer
(K
W)
Wind speed (m/s)
Increased rotor
diameter
Original rotor
diameter
Figure 4. (a) Increasing rotor diameter gives rate power at lower wind speed
15
Vc Vr
Pr
Po
wer
(K
W)
Wind speed (m/s)
Large generator
Original
generator
(b) increasing the generator size increases rates power [28].
2.2.8. Speed control for maximum power
It is known that the rotor efficiency Cp depends on the tip-speed ratio (TSR). Modern
wind turbines operate optimally when their TSR is in the range of around 4–6 [34]. In
order to get the maximum efficiency, turbine blades should change their speed as the
wind speed changes. There are different ways to control the rotor blades speed:
2.2.8.1. Pole-changing induction generators
In terms of the induction generator, the rotor spins at a frequency which is largely
controlled by the number of poles. If it is possible for us to change the number of poles,
we can make the wind turbine spin at different operating speeds. The stator can have
external connections that switch the number of poles from one value to another without
change in the rotor.
2.2.8.2. Variable slip induction generators
It is known that the speed of a normal induction generator is around 1% of the
synchronous speed. The slip in the generator is a function of the dc resistance in the rotor
conductors. If we add a variable resistance to the rotor, then the slip can range up to
about 10% [34].
2.3. Wind Turbine Design Considerations
A wind turbine consists of rotor, power train, control and safety system, nacelle structure,
tower and foundations, etc. the wind turbine manufacturer must consider many factors
before selecting a final configuration for development.
16
First of all, the intended wind location environment is the most important aspect. The
turbines for high turbulent wind sites should have robust, smaller diameter rotors.
International Electro-technical Commission (IEC) specified design criteria which are
based on the design loads on the mean wind speed and the turbulence level.
Secondly, minimizing cost is the next most important design criteria. In fact electricity
generated by wind is more expensive than the electrical power from fuel- based
generators. So the cost is a very important factor that restrains the wind power
generation diversifies. If the cost of wind energy could be reduced by an additional 30%
to 50%, then it could be globally competitive. In order to reduce the cost of wind energy,
the wind energy designers can increase the size of wind turbine, tailor the turbines for
specific sites, explore new structural dynamic concepts, and develop custom generators
and power electronics [35].
2.3.1. Basic design philosophies
There are three wind turbine design principles for handing wind loads: (i) with- standing
the loads, (ii) shedding or avoiding loads and (iii) managing loads mechanically and/or
electrically [36]. For the first design philosophy, the classic Danish configuration was
originally developed by Paul La Com in 1890. These kinds of designs are reliability,
high solidity but non-optimum blade pitch, low tip speed ratio (TSR) and three or more
blades. For the wind turbines based on the second design philosophy, these turbines have
design criteria such as optimization for performance, low solidity, optimum blade pitch,
high TSR, etc. In terms of the designs based on the third philosophy, these wind turbines
have design considerations like optimization for control, two or three blades, moderate
TSR, mechanical and electrical innovations.
2.3.2. Choice between two and three blade rotors
Wind turbine blades are one of the most important components of a wind turbine rotor.
Nowadays, fiber glass rotor blades are very popular. Rotor moment of inertia is the main
difference between two and three blades. For the three bladed rotors mass movement has
polar symmetry, whereas the two bladed rotor mass movements do not have the same, so
the structural dynamic equations for the two bladed turbine system are more complex
and have periodic coefficients [36]. In terms of the three bladed systems, the equations
have constant coefficients which make them easier to solve. In conclusion, the three
blade turbines are more expensive than the two blades. However, three blades can
provide lower noise and polar symmetry.
17
2.3.3. Weight and size considerations
Wind tower is the integral component of the wind system. In order to withstand the
thrust on the wind turbine, the wind tower must be strong enough. In addition, the wind
tower must also support the wind turbine weight. It is common to use the tall wind
towers because they can minimize the turbulence induced and allow more flexibility in
siting. The ability of a wind tower to withstand the forces from the high wind is an
important factor of a wind tower. The durability of the wind tower depends on the rotor
diameter of wind turbine and its mode of operation under such conditions. In terms of
the wind tower cost, the cost of operation and maintenance (O&M) and the cost of major
overhauls and repairs also needed to be considered.
2.4. Grid Connected Wind Farms
2.4.1. Wind farms
Nowadays, a single wind turbine is just used for a particular site, such as an off-grid
home in rural places or off-shore areas. In a good windy site, normally there will be lots
of wind turbines which are often called as a wind farm or a wind park. The advantages of
wind farm are reduced site development costs, simplified connections to transmission
lines, and more centralized access for operation and maintenance.
How many wind turbines can be installed at a wind site? If the wind turbines are located
too close, it will result in upwind turbine interfering with the wind received by those
located downwind. However, if the wind turbines are located too far, it means site space
is not properly utilized.
When the wind pass the turbine rotor, the energy will be extracted by the rotor and the
power which is available to the downwind machines will be reduced. Recent studies
show that the wind turbines performance will degrade when the wind turbines are too
close to each other [28, 34].
2.4.2. Problems related with grid connections
For wind power generation, there must be a reliable power grid/transmission network
near the site so that the wind generated power can be fed into the grid. Generally, the
wind turbine generates power at 400 V, which is stepped up to 11–110 kV, depending
upon the power capacity of the wind system. If the wind power capacity is up to 6 MW,
the voltage level is stepped up to 11/22 kV; for a capacity of 6–10 MW, the voltage level
18
is increased up to 33 kV; and for capacity higher than 10 MW, it is preferred to locate a
66 or 110 kV substation at the wind farm site [37]. An unstable wind power generation
system may have the following problems:
2.4.2.1 Poor grid security and reliability
From economic point of view, the poor grid stability may cause 10–20% power loss [37],
and this deficiency may be the main reason for low actual energy output of wind power
generation.
In China, many wind farms are actually not connected to the power grid because of the
stability issues and difficulties in dispatching by the system operators. Major wind power
researches are being conducted in aspects of dispatch issues, and long distance
transmission issues.
In the Australian National Electricity Market (NEM), before the connection of a wind
farm to a power grid, the (wind) generation service provider must conduct connectivity
studies by itself and/or with the transmission network service provider for which the
wind farm is to be connected. The connectivity study needs to check if the proposed
wind generator can be hosted by the existing power grid in view of stability as well as
reliability aspects. Depending on the study results conducted by the transmission
network service provider, the cost associated and the suitability of the connection point
of the proposed wind farm will be given for the generation company to make further
decisions regarding its investment.
2.4.2.2 Low frequency operation
There is no doubt that the low frequency operation of the wind generation will affect the
output power. Normally, when the frequency is less than 48 Hz, many wind power
generations do not cut in. The power output loss could be around 5–10% on account of
low frequency operation [37].
2.4.2.3 Impact of low power factor
A synchronous generator can supply both active and reactive power. However, reactive
power is needed by the wind power generation with induction generator for the
magnetization. However, in terms of wind power generator with induction generators,
instead of supplying reactive power to the grid, they will absorb reactive power from
19
grid. As a result, suitable reactive power compensation device is required to supply the
reactive power to wind generator/grid [38,39].
Table 2 Offshore wind farms in Europe [40].
Country Project name Capacity
(MW)
Number
of
turbines
Wind turbine
manufacturer
Denmark Horns Rev 1 160 80 Vestas
Denmark Nysted 165.6 72 Siemens
Denmark Horns Rev 2 209 91 Siemens
Netherlands Egmond Aan zee 108 38 Vestas
Netherlands Prinses Amaila 120 60 Vestas
Sweden Lillgund 110.4 48 Siemens
Gunfleet sands 1 and 2 Clacton-on Sear 104.4 29 Siemens
2.4.3. Latest trend of wind power generation
In Europe, offshore projects are now springing up off the coasts of Denmark, Sweden,
UK, France, Germany, Belgium, Irelands, Netherlands, and Scotland. The total offshore
wind farm installed capacity in 2009 has reached 2055 MW. Table 2 shows operational
offshore wind farms having installed of more than 100 MW in Europe till 2009 [40].
2.5. Hybrid Power Systems
There are still many locations in different parts of the world that do not have electrical
connection to grid supply. A power system which can generate and supply power to such
areas is called a remote, decentralized, standalone, autonomous, isolated power system,
etc. It is a common way to supply electricity to these loads by diesel power plants. The
diesel system is highly reliable which is proved for many years. The main problems of
diesel system are that the cost of fuel, transportation, operation and maintenance are very
high.
The cost of electricity can be reduced by integrating diesel systems with wind power
generation. This system has another advantage of reductions in size of diesel engine and
battery storage system, which can save the fuel and reduced pollution. Such systems
having parallel operation of diesel with one or more renewable energy based sources
(wind, photovoltaic, micro hydro, biomass, etc.) to meet the electric demand of an
isolated area are called autonomous hybrid power systems. Figure 5 shows a typical
wind-diesel hybrid system with main components [41]. A hybrid system can have
20
various options like wind-diesel, wind-diesel-photovoltaic, wind-diesel- micro hydro,
etc.
Control system
WT IG
Wind system
DG SG
Diesel generator set
Reactive power supply
Dump loads
Storage system
Bus line
Figure 5. Schematic diagram of general isolated wind-diesel hybrid power system
The operation system of a diesel engine is very important. Normally there are two main
modes of system operation which are running diesel engine either continuously or
intermittently. Continuous diesel system operation has the advantage of technical
simplicity and reliability. The main disadvantage of this approach is low utilization of
renewable energy sources (wind) and not very considerable fuel savings. Basically, the
minimum diesel loading should be 40% of the rated output, and then minimum fuel
consumption will be around 60% of that at full load [42]. In order to get large fuel
savings, it is expected that diesel engine runs only when wind energy is lower than the
demand. Nevertheless unless the load is significantly less than the energy supplied by the
wind turbine, the diesel generator will not be able to stay off for long time. The start-stop
can be reduced by using the energy storage methods. To make the supply under these
circumstances continuous, it is required to add complexity in the architecture or control
strategy.
As wind is highly fluctuating in nature and it will affect the quality of supply
considerably and even may damage the system in the absence of proper control
mechanism. Main parameters to be controlled are the system frequency and voltage,
which determine the stability and quality of the supply. In a power system, frequency
deviations are mainly due to real power mismatch between generation and demand,
21
whereas voltage mismatch is the sole indicator of reactive power unbalance in the
system. In the power system active power balance can be achieved by controlling the
generation, i.e., by controlling the fuel input to the diesel electric unit and this method is
called automatic generation control (AGC) or load frequency control (LFC) or by
scheduling or management of the output power. The function of load frequency
controller is to generate, raise or lower command, depending upon the disturbance, to the
speed-gear changer of the diesel engine which in turn changes the generation to match
the load. Different methods of controlling the output power of autonomous hybrid power
systems are dump load control, priority load control, battery storage, flywheel storage,
pump storage, hydraulic/pneumatic accumulators, super magnetic energy storage, etc
[43].
It is equally important to maintain the voltage within specified limits, which is mainly
related with the reactive power control of the system [28, 29]. In general, in any hybrid
system there will be induction generator for wind/hydro system. An induction generator
offers many advantages over a synchronous generator in an autonomous hybrid power
system. Reduced unit cost, ruggedness, brushless (in squirrel cage construction), absence
of separate DC source for excitation, ease of maintenance, self-protection against severe
overloads and short circuits, etc., are the main advantages [44].
However the major disadvantage of the induction generator is that it requires reactive
power for its operation. In case of grid-connected system induction generator can get the
reactive power from grid/capacitor banks, whereas in case of isolated/autonomous
system reactive power can only be supplied by capacitor banks. In addition, most of the
loads are also inductive in nature, therefore, the mismatch in generation and
consumption of reactive power can cause serious problem of large voltage fluctuations at
generator terminals especially in an isolated system. The terminal voltage of the system
will sag if sufficient reactive power is not provided, whereas surplus reactive power can
cause high voltage spikes in the system, which can damage the consumer’s equipment
and affect the quality of supply. To take care for reactive power/voltage control an
appropriate reactive power compensating device is required [38, 41, 43]. Another
approach available from ENERCON27 consists of a wind turbine based on an annular
generator connected to a diesel generator with energy storage to form a stand-alone
power system.
22
2.6. Economics of Wind Power Systems
It is no doubt that the purpose of all types of energy generation ultimately depends on the
economics. The wind power generation costs have been falling over recent years. It is
estimated that wind power in many countries is already competitive with fossil fuel and
nuclear power if social/environmental costs are considered [45].
The installation cost of a wind system is the capital cost of a wind turbine (see Fig. 6 for
the normalized contribution of an individual sub-system towards total capital cost of a
wind turbine), land, tower, and its accessories, and it accounts for less than any state or
federal tax credits.
The installation cost of wind system is the cost of wind turbine, land, tower, and its
accessories and it accounts for less than any state or federal tax credits. The maintenance
cost of wind system is normally very small and annual maintenance cost is about 2% of
total system cost [48]. The cost of financing to purchase the wind system is significant in
the overall cost of wind system. Furthermore the extra cost such as property tax,
insurance of wind system and accidents caused from the wind system. One of the main
advantages of generating electricity from the wind system is that wind is free. The cost
of wind system just occurs once. On the other hand, the cost of non-renewable energies
is more and more expensive, which is required for the renewable energies such as wind
power.
Nowadays, research and development make the wind power generation competitive with
other non-renewable fuels such as fossil fuel and nuclear power. Lots of efforts have
been done to reduce the cost of wind power by design improvement, better
manufacturing technology, finding new sites for wind systems, development of better
control strategies (output and power quality control), development of policy and
instruments, human resource development, etc [46,47].
23
Figure 6. Contribution of various sub-systems towards capital cost of wind turbine.
2.7. Conclusion
Wind power generation is very essential in today’s society development. Lots of wind
power technologies have been researched and numbers of wind farms have been
installed. The performance of wind energy conversion systems depends on the
subsystems such as wind turbine (aerodynamic), gears (mechanical), and generator
(electrical). In this chapter a number of wind power issues, such as power in the wind,
impact of tower height, maximum rotor efficiency, speed control for maximum power,
some of the design considerations in wind turbine design, wind farms, latest trend of
wind power generation from off shore sites, problems related with grid connections and
hybrid power systems have been discussed.
24
Chapter 3. Wind Power System Data Analysis
Methodologies
3.1. Introduction
A survey of state-of-the-art research techniques that facilitate wind power system
prediction and operation is provided in this chapter. The relevant literature review
comprises broadly the two parts outlined below. In the first part, research on the
importance of data analysis approaches for wind power system prediction and operation
is discussed. The basic concepts of wind power forecasting and operation are first
reviewed and this is followed by comprehensive discussions of existing techniques. Then,
the respective benefits and drawbacks of these techniques are summarized. Finally, the
availability of new computational intelligence based methods for wind power system
prediction and operation is studied and discussed. The second part reviews a series of
popular evolutionary algorithms. The advantages and disadvantages of each algorithm
are discussed in detail, with a number of machine learning methods and time series
models also presented. This is followed by comprehensive comparisons of these
approaches.
3.2. Wind power data analysis
In this section, the importance of wind power system data analysis is discussed, with the
focus being on existing approaches and their detailed comparisons. The importance of
introducing advanced computational intelligence based methods for wind power system
data analysis is then emphasised. Finally, the future needs of data analysis for wind
power systems forecasting and operation in a deregulated market environment are
discussed.
3.2.1. Wind power forecasting
Wind power forecasting is to estimate the expected produced power of wind turbines in
the future. Depending on the forecasting time scales, wind power prediction can be
classified into three groups: very short-term forecasts, short-term forecasts and long-term
forecasts.
The time scales concerning very short-term prediction are from milliseconds up to a few
minutes. The forecasted results can be used for the wind turbine active control. For
25
short-term wind power prediction, the time scales are in the order of some days and from
minutes to hours. Its purpose is to serve for power system management or energy trading,
which mainly include unit commitment and economic dispatch. The long-term wind
power forecasts are required for planning the maintenance of wind farms, or
conventional power plants or transmission lines, in which the time scales up to 5~7 days
ahead.
A number of methods for short-term wind power forecasting have been proposed in the
literature. Depending on the different inputs, existing methods can be divided into three
groups: physical approaches, statistical approaches and the combination of both. The
physical methods forecast wind power based on the physical characteristics of the wind
flow around and inside the wind farm, and the power curve of the wind turbine. The
main idea is to improve the results of numerical weather prediction (NWP) models by
physical information about the terrain (roughness, orography, obstacles) and wind
turbines characteristics (hub height, power curve, thrust coefficient). Statistical methods,
such as recursive least squares or artificial neural networks, are based on the relation
between historical and future values of wind power. A combination of both physical and
statistical methods usually will improve the forecasting accuracy. Physical methods will
be used to predict the future values of relevant weather variables, statistical approaches
can then be employed to improve the prediction accuracy and provide useful statistical
information.
Wind power forecasting is the very important topic in a deregulated market, which can
greatly help the wind power integration process. In previous study, fuzzy logic and
neuro-fuzzy (NF) [49-51], neural networks (NNs) [52-56], data mining [57] and some
hybrid methods [58-60] based techniques have been employed for this purpose. Also the
statistic time series models autoregressive integrated moving average (ARIMA) [61] and
general autoregressive conditionally heteroscedastic (GARCH) models [62] have been
proved to be effective with satisfactory prediction performance.
3.2.2. Power System Operation with Wind Power
Power systems normally include an abundance of conventional fossil-fired generators,
which can control their output power following the system load schedules or vary the
output in accordance with system demand. Due to the uncertainty and intermittency of
wind resource, it is a challenge to integrate wind power into power system. At the same
time, the variability of wind generation should be considered in the power system over
26
different time scales. Under the normal circumstance of thermal power system, every
conventional generator will be scheduled to meet the system load and reserve
requirements at minimum operating cost. It is necessary for the units to vary output
power to match the system load changes over the scheduling time, which requires the
generators to have the capability to meet the load fluctuation as well as sudden,
unexpected changes in the system demand [63].
Along with the integration of wind power come more complicated control, requirements
and reserves should be considered. If the wind generation is involved into the thermal
power system, the system operators may be forced to alter the generator loading levels,
ramping requirements, spinning reserve and other relevant issues. Having recognized the
wind power integration problem, it follows that the power system operators must
develop a plan of action.
Here, the emphasis is on to two important problems of operational planning for power
systems with wind power generation, namely economic load dispatch and unit
commitment.
Economic load dispatch (ELD) [64] is an important topic in the operation of thermal
power plants which can help to build up effective generating management plans. It aims
to allocate power generation to match load demand at minimal possible cost while
satisfying all the units and system constraints. In previous research, different approaches
have been suggested, including linear programming and non-linear programming
[65]-[67]. Linear programming methods are fast and reliable, but the main drawback is
that it is associated with the piecewise linear cost approximation [65]. The non-linear
programming methods have a problem of algorithm convergence and complexity [67].
Recently, different heuristic approaches have been proved to be effective with promising
performance, such as evolutionary programming (EP) [68]-[70], SA [71], tabu search
(TS) [72], pattern search (PS) [73], GAs [74],[75], DE [76], and PSO [77]. EP can be a
quite powerful evolutionary method; however, it is rather slow converging to a near
optimum for some function optimization problems [78]. Both SA and TS can be quite
useful in solving complex reliability optimization problems, but SA is very time
consuming, and cannot easily be utilised to tune the control parameters of the annealing
schedule. TS is difficult in defining effective memory structures and strategies which are
problem dependent. Although GAs can ensure the colony evolves and the solutions
change continually, they often lack a strong capacity of producing the best offspring
27
individuals and thus cause the slow convergence near global optimum and sometimes
may be trapped into local optima. DE is no doubt a very powerful method, but the
greedy updating method and intrinsic differential property usually leads the computing
process to be trapped by local optima. The PSO converges quickly, but has a slow
fine-tuning ability of the solution. Once it gets stuck into the local optima, it is very hard
to jump out of it.
In nowadays society, power system generation scheduling problem can be divided into
two relevant optimization sub-problems: unit commitment (UC) and economic dispatch
(ED). The main objective of the unit commitment is to decide the ON/OFF statuses of
generators over the scheduling period to meet the system load demand and reserve
requirements at the lowest cost. Basically, the unit commitment outputs are ON/OFF
statuses on an hourly basis for a given time scales, such as 24 hours. In addition, a unit
commitment is an optimization problem that determines which and when a generator is
to be work and for how long. Unit commitment schedule is approached by satisfying the
system constraints such as ramp rate limits, spinning reserve as well as minimum up and
down time limits.
In the literatures, many researchers have shown the interests to unit commitment
methods and various numerical optimization techniques have been employed to solve the
unit commitment problems. In the traditional UC problem, many mathematical methods
have been proposed such as priority list (PL) [79,80] approaches, dynamic programming
(DP) [81], branch-and-bound (BB) [82] methods, mixed-integer programming (MIP) [83]
and Lagrangian Relaxation (LR) [84,85] methods. Recently, optimization solvers based
on heuristics techniques have been proved to be effective with promising performance,
including genetic algorithm (GA) [86-89], evolutionary programming (EP) [90], fuzzy
logic (FL) [91], artificial neural network (ANN) [92], simulated annealing (SA) [93],
particle swarm optimization (PSO) [94] as well as hybrid techniques [95-97]. Many
researchers are attracted by heuristic optimization methods. Apart from providing local
optimal solutions, those approaches provide global optimal solution and easily dealing
with various difficult nonlinear constraints.
3.2.3. Future Needs of Data Analysis in Wind Power System
Along with the introduction of wind power forecasting and wind power system operation,
the amount of data associated from power system considering wind power has been
increasing sharply. This has introduced difficulties for wind power system data analysis
28
with the traditional approaches. As a result, it is necessary to introduce advanced
approaches into wind power system data analysis.
3.3. Evolutionary Algorithms
In this section, a group of EAs will be reviewed, which take inspirations from
evolutionary or adaptive systems in the biological and physical world, using to solving
optimization problems. In the EAs, normally a population of candidates is generated
randomly within search spaces first, and then evolves according to kinds of distinguished
implementations, such as selection, crossover, mutation, or recombination. With fitness
function evaluation, the population evolves towards global optimum in the search space.
Four kinds of popular EAs are introduced as follows, to namely the GA, IA, PSO, and
DE.
3.3.1. Genetic Algorithm
GAs [98] are one of the most famous families of EAs. It is implemented as a computer
simulation of gene evolution in which a population of gene representations of candidate
solutions to a specific problem evolves toward better solutions. Originally, these
solutions are represented in binary as strings ―0‖ and ―1‖. GAs usually begin with a
randomly generated population of individuals within the search space. In each generation,
the fitness of every individual is evaluated, and then undergoes selection, crossover, and
mutation to form a new population. Commonly, GA terminates when either a maximum
number of generations or satisfactory fitness value has been reached. In this section, the
procedures of the classical binary-coded GA are represented.
Step-1. Initialization. Each unit is a value decoded from a gene which can be represented
as a binary string. For a five-digit binary string and unit range is 10,10 , the gene
0,0,0,0,0 can be decoded to -10, and gene 1,1,1,1,1 can be decoded to 10.
Step-2. Selection. From the theory of natural evolution selection, the individuals with
higher fitness values are more likely to produce better offspring. Normally, the roulette
selection is used in the selection procedure. A roulette wheel on which each member of
the population is given a sector whose size is proportional to the fitness of individual is
constructed [98]. Then the wheel is spun and the selected individual becomes parent.
Step-3. Crossover. Crossover is a random implementation of recombination in which
each parent contributes part of its genetic structure to offspring. Here the single-point
29
crossover is employed. Based on the crossover possibility, individual exchange of
characters between two strings is performed.
1 1 0 | 0 1 0
2 1 1 | 0 1 1
S
S
(3.1)
Suppose in choosing a random integer in 1,4 , if in case of 2, the crossover occurs after
the second number can be seen below
'
'
1 1 0 | 0 1 1
2 1 1 | 0 1 1
S
S
(3.2)
Step-4. Mutation. Mutation is the implementation of occasional tunning of the value.
With the binary string representation, this simply means change a bit to different
representation. Then the parents will be replaced by their offspring, and a new
population will be generated. An example can be seen as follows.
'3 1 0 0 1 1 3 1 0 1 1 1S S (3.3)
A flow chart of a basic GA is given in Figure 7, [98].
Start
Generate the initial population,
Gen = 0
Gen=Gen+1
Fitness function evaluation
Crossover
Selection
Reproduction Mutation
Stop?
Form new population
Output
Yes
No
Mutation
probabilityReproduction
probability
Crossover
probability
Figure 7. Flowchart of a typical GA
30
3.3.3. Immune Algorithm
With the development of immunology, the mechanism of biologic immune system has
been gradually discovered by researchers. Because of the powerful capability of
information processing and special characteristics such as diversity, adaptive trait,
biologic immune system has become a hot spot of artificial intelligence research.
Immune algorithm (IA) [99]-[101] imitates the principle of the defence system
annihilates foreign disease-causing bacteria or viruses through self-learning and
self-adjusting mechanism. Although IA is very similar to GA, there are essential
differences in the production theory for population. Compared to GA and other kinds of
EAs, IA enhances searching ability through the mechanism of memory pool. Meanwhile,
it achieves self-adjusting by introducing two distinguished discriminators, affinity and
concentration. To some extent, it can avoid premature convergence. It should be noted
that similar techniques, such as sharing function method, have been used with other EAs
to discount the fitness values of closely located individuals in the search domain, in
order to achieve higher diversity in the search process. The evolutionary procedures of
IA are represented as follows.
Step-1. The antigens and antibodies in IA represent the objective functions and feasible
solutions, respectively. The affinity and concentration are used as discriminators of the
quality of solutions, which are calculated by
1
1i
i t r r
As (3.4)
where,
r random number in 0,1 ;
i location index of antibodies in current population which are rearranged in terms of
the values in ascending sequence, 1,i p , where p is population size.
1
1 p
i mn
i
t Ksp
Cs (3.5)
1,
0,
m n
mn
Ab t Ab t lKs
otherwise
(3.6)
where,
31
Euclidean distance;
l distance threshold;
Step-2. Then, a roulette selection is implemented based on the selection probabilities for
the antibodies. This allocates each antibody a probability of being selected
proportionally according to affinity and concentration. The selection rates can be
calculated by
1
i
i
i pi
i i
t
tt
t
t
As
CsPs
As
Cs
(3.7)
Step-3. After that, crossover and mutation are implemented. Crossover is one of the
primary IA operators that promote the new region exploration ability in the space.
Generally, crossover rate should be chosen comparatively large, between 0.7 and 1.0.
Mutation is another operator which guarantees the population diversity. And the
mutation rate should be chosen between thousandths and hundredths.
An arithmetic crossover operator is described as follows
' 1i m nt b t b t Ab Ab Ab (3.8)
And mutation operator can be selected in the algorithm are described as the following
formulae
1
' 1 1
rt
t T
i i m nt t b t t
Ab Ab Ab Ab (3.9)
Step-4. Finally, antibodies which have high affinity values will evolve into next
generation and be added into memory pool. Given number of new antibodies will be
inserted into population, replacing those with low affinity values.
A flow chart of a basic IA is given in Figure 8, [101].
32
Start
Generate the initial population,
Gen = 0
Gen=Gen+1
Affinity values evaluation
Selection
Mutation
Stop?
Form new population
Output
Yes
No
Mutation
probability
Crossover
probability
Crossover
Insert given number of
new individuals
Figure 8. Flowchart of a typical IA
3.3.4. Particle Swarm Optimization
PSO is a global search technique originally introduced by Kennedy and Eberhart [102].
It simulates the social evolvement knowledge, probing the optimum by evolving the
population which may include candidate solutions. Compared with other EAs, PSO
shows incomparable advantages in computational speed and precision [103]. In short,
the PSO is characterized as a simple heuristic of well balanced mechanism with
flexibility to enhance and adapt to both global and local exploration abilities, which
gains lots of attention in power system applications [104],[105]. In order to improve the
global search ability, voiding trapped into local optima in solving multimodal problems;
many revised versions of PSO appeared, mainly concentrating in improving the
evolution implementations and exploring the best parameters combinations.
The origins of PSO are best described as sociologically inspired, since the algorithm was
based on the sociological behaviour associated with bird flocking [103]. In the
conventional PSO, each individual is treated as a particle in the space, with position and
velocity vectors. The algorithm maintains a swarm of particles, where each particle
represents a potential solution to the objective problem. For a given n-dimensional
problem, the position and velocity vectors of a particle in the PSO can be represented as
33
,1 ,2 ,
,1 ,2 ,
, , ,
, , ,
j j j j n
j j j j n
t x t x t x t
t t t t
x
υ (3.10)
The core idea of classical PSO is the exchange of information among the global best,
population best, and current particles, which can be done as follows
1 21
1 1
j j pb j gb j
j j j
t t r t t r t t
t t t
υ υ p x p x
x x υ (3.11)
where,
, parameters;
1 2,r r random number in 0,1 ;
inertia weight;
pbp local best particle;
gbp global best particle;
jυ velocity vectors;
The flow chart of a typical PSO is given in Figure 9, [102].
Start
Generate the initial population,
Gen = 0
Gen=Gen+1
Fitness values evaluation
Stop?
Update global and local best particles
Output
Yes
No
Update particles and velocities
Figure 9. Flowchart of a typical PSO
DE is a heuristic optimization method with efficient search and optimization capabilities
developed relatively recently [106]. Like other EAs, DE is able to handle nonlinear,
non-differentiable, and non-convex optimization problems. However, DE is more
34
efficient and reliable compared with other EAs [107]. There are different variations of
DE; hereby the self-adaptive DE is reviewed for completeness.
For a given d-dimensional problem to be optimized in continuous search space , the
DE probes the optimum by evolving a population 1 2, ,i i i idw w w w , 1,2, ,i NP ,
where NP is population size, as candidate solutions. The initial population is obtained
by randomly distributing each parameter of an individual vector with uniform
probability distribution. In each generation g , every individual vector , ,i gw undergoes
mutation and crossover operations to produce a trial vector , ,i gv and then the greedy
selection decides which one will enter the next generation.
Step-1. Mutation. The most distinguished characteristic of DE is self-organizing scheme
to generate offspring. Traditionally, for each target vector ,i gw , mutant vector is
generated according to
, , , ,i g a g b g c gm w F w w (3.12)
where the integer indexes , , [1, ]a b c NP , a b c i , and [0,2]F is a scaling
factor. Due to the uncertainty of the mutation rate F which is a very important parameter
in DE, a self-adaptive method [108] is used. A small mutation rate may lead to
premature convergence, while a large one may result in lower calculation precision and
speed. The self-adaptive mutation implementation can be used to choose the proper
mutation rate, as described below
max
max
, , 0 , ,
11
0
2
, 0.6,1.2
i g a g b g c g
G
G g
m w F w w
e F
(3.13)
where,
maxG maximum evolution iteration;
g current iteration.
Therefore, in the beginning, the mutation rate is relatively large 02F F , which
guarantees the diversity of population; later on 0F F , which makes the algorithm
converges at optimal solutions ultimately.
35
Step-2. Crossover. To increase the diversity of the individuals, the mutant vectors are
combined with the target vector, and the trial vector is produced similar to independent
binominal trials
,
,
,
[0,1], 1,2, ,
ji g j
ji g
ji g
m if rand CR j dv j d
w otherwise
(3.14)
where [0,1]CR is the crossover constant, and let j d to ensure that ,ji gw get at
least one parameter from ,ji gv .
Step-3. Selection. The selection scheme in DE also differs from other evolutionary
algorithms. The trial vector is not compared to not to all individuals in the current
population, but only to one individual- the target vector according to cost function value
, , ,
, 1
,
i g i g i g
i g
i g
v if E v E ww
w otherwise
(3.15)
The above operations will be repeated until stop criteria is met. Notice that there are two
user-defined control variables, which are population size and crossover constant.
Selection of these values depends on the associated problem, for example, to optimize
difficult thirty dimensional functions; population size 200 and crossover constant 0.9 can
be used [109]. For multi-modal and non-separable problems such as in neural networks
training, too small value of CR may result in intolerable computational time, while too
large value may make population stagnate since the pool size of potential trial vectors is
limited. According to the benchmark functions test [110], the range [0.4, 0.9] is a
common option.
The flow chart of a typical DE is given in Figure 10, [106].
36
Start
Generate the initial population,
Gen = 0
Gen=Gen+1
Fitness values evaluation
Stop?
Mutation and crossover
Output
Yes
No
Selection and update population
Figure 10. Flowchart of a typical DE
3.3.5. Comparison
Although the heuristic methods do not always guarantee discovering globally optimal
solutions in finite time, they often provide a fast and reasonable solution. Generally
speaking, all these algorithms are same, only with different theory background and
evolutionary implementations. Each method has its own merits and drawbacks, and the
problem of local optima is unavoidable. Consequently, the research emphasis may focus
on how to improve search capability and computing efficiency. Many attempts try to
merge some of their individual implementations together into a new algorithm, so that it
can overcome individual disadvantages as well as benefit from each others’ advantages.
Based on previous algorithms research experience, compared with other alternatives,
PSO is computationally inexpensive in terms of memory and speed. The most attractive
features of PSO can be summarized as: simple concept, easy implementation, fast
computation, and robust search ability [111].
Table 3 Comparisons of the EAs
EAs Theory Speed Accuracy Variations
GA Gene evolution ★★ ★★ ★★★
IA Immunology ★ ★★★ ★
PSO Social evolvement ★★★ ★ ★★★
DE Greedy updating ★★★ ★★ ★★
★: Represents the degree or the score of each class.
37
3.4. Machine Learning Methods
Machine learning is another significant research field of artificial intelligence which is
about the design of algorithms and techniques that make computers to study and learn
automatically. Machine learning methods have been used in over a wide range of
applications including classification and regression, extracting rules and patterns out of
available massive historical or real-time data sets. They form an essential part of
techniques used in this research for power system data analysis. In this section, several
state-of-the-art machine learning methods are investigated.
3.4.1. Artificial Neural Networks
ANN is an information processing paradigm which is inspired by the biological nervous
systems. The key element of this paradigm is the information processing units. It is
composed of a number of mutually interconnected neurones working in unison to solve
specific problems [112]. ANNs, with their remarkable ability to derive meaning from
complicated or imprecise data, can be applied to extract patterns and forecast trends
[113]. A trained ANN can work as an expert in the category of analyzed information.
Other advantages include
1. Adaptive learning: ability to learn based on the data given for initial experience [114].
2. Self-organisation: ability to create own organisation or representation of the
information [70].
3. Real time operation: ability to carry out parallel computations [114].
The two kinds of most popular neural networks are: Feed-forward networks and
Feedback networks.
1. Feed-forward ANNs allow signals to travel one way from input to output.
Feed-forward ANNs tend to be straight forward networks that associate inputs with
outputs, which are extensively used in pattern recognition [115]. This type of
organisation is also referred to as bottom-up or top-down. The feed-forward ANNs are
like Back-Progagation (BP) neural network, Radius Basis Function (RBF) neural
network, and Multi-Layer Perceptrons (MLP).
38
2. Feedback ANNs can have signals travelling in both directions by introducing loops in
the network, which are very powerful and can get extremely complicated. Feedback
ANNs are dynamic; their 'state' is changing continuously until they reach an equilibrium
point [116]. They remain at the equilibrium point until the input changes and a new
equilibrium needs to be found. Feedback architectures are also referred to as interactive
or recurrent, although the latter term is often used to denote feedback connections in
single-layer organisations [116]. The Recurrent neural network is one kind of feedback
ANNs.
3.4.2. Extreme Learning Machine
Extreme learning machine (ELM) was proposed in [117]. It is a single hidden layer
feed-forward network (SLFN), with input weights and hidden bias randomly generated
and output weights analytically calculated. Theoretically, the activation function for
hidden nodes of ELM should be infinitely differentiable in any interval [117], such as
sigmoid functions as well as sine, cosine, exponential and radial basis functions.
However, in practice, a wider range of activation functions, like non-differentiable and
non-continuous, can be adopted if the incremental constructive method is used [118].
Therefore, ELM has no limitations for activation functions of hidden nodes. However,
the activation functions of output neurons are restricted to be linear.
The critical idea behind ELM is to transform many difficult issues arising from nonlinear
optimization, like the optimal determination for input weights, hidden bias, and output
weights, to a simple least square problem of calculating the optimal output weights. This
idea is completely different from the traditional iterative learning methods since it makes
the learning process so easy. Huang has proposed the theorem and given a rigid proof
[117],[119]. The mechanism of ELM can be described as used in practice below.
Suppose an ELM with k hidden neurons and activation function to learn distinct
samples ,i iyx , where d
i Rx is the input, and iy is the output. In ELM, the input
weights and hidden bias are randomly generated; therefore the output matrix of hidden
layer can be computed by
ijhH (3.16)
1,2, ,
,1,2, ,
ij j i j
i nh g w b
j k
x (3.17)
39
where,
ijh output of jth hidden neuron with respect to ix ;
jw input weights connecting the jth hidden neuron and input neurons;
jb bias of jth hidden neuron.
With the given target vector iyY and calculated hidden layer output H , the
output weight matrix connecting the hidden neurons and output neurons jβ can
be represented as
†β YH (3.18)
where †H is the Moore-Penrose (MP) generalized inverse of H . There are several
methods to calculate the MP generalized inverse of H , and Huang suggested that
singular value decomposition (SVD) be the most appropriate method due to its
universality.
The ELM has been theoretically proven to be capable of universal approximation in a
satisfactory sense [118], and also it has been shown to have good generalization
properties and have extremely fast speed. From its algorithm, it can be seen that the only
job left for users is to select activation function and the number of hidden neurons, which
make it easy for use. Moreover, it avoids many difficulties faced by conventional
learning methods such as learning rate, learning epochs, stopping criteria and local
minima.
3.4.3. Support Vector Machine
Support Vector Machine (SVM) is a universal classification algorithm proposed by
Vapnik [120] in the middle of 1990s, it is thought of a new innovation of learning
machine, which uses the statistical learning theory. It approximates the relation curve by
using only a small amount of training data, which are known as the support vectors
(SVs). SVM can effectively avoid the over-fitting problem, by reaching a proper
trade-off between empirical accuracy and model complexity [120]. Therefore, SVM
usually show better performance than many traditional regression methods. SVM is
noisy insensitive and has a fast training speed, which is believed as a strong candidate of
best machine learning algorithm.
40
Classification is a common need in machine learning. Suppose some given data
points each belong to one of two classes, and the goal is to decide which class a new data
point will be in [120]. For given data set 1
,l
i i iy
x , d
i Rx , 1, 1iy . Select
proper kernel function , iK x x and parameter C , solving the optimization problem
2
, ,1
1
2
. . 1, 0, 1,2,
i
l
iw b
i
i i i i
min E w w C
s t y w x b i l
＋ (3.19)
The dual problem is
1 1 1
1
1min
2
. . 0,0 , 1,2,
l l l
i j i j i j j
i j j
l
i i i
i
y y K x x
s t y C i l
(3.20)
The optional solution is * * * *
1 2, ,T
l and calculates
*
1
l
i i i i i
i
b y y K x x
(3.21)
Therefore the optional classification function can be represented as
*
1
sgn ,l
i i i
i
f x y K x x b
(3.22)
Regression: In statistics, regression analysis is any of a number of techniques for the
modeling and analysis of numerical data consisting of values of a dependent variable and
of one or more independent variables, which can be used for prediction, inference,
hypothesis testing, and modeling of causal relationships [120].
For regression function estimation problem, SVM introduces the following loss function
, , ,L y f x L y f x
(3.23)
where,
41
0, ,,
,
if y f xy f x
y f x
(3.24)
For given data set 1
,l
i i iy
x , d
i Rx , 1, 1iy . Select proper kernel
function , iK x x and parameter C , solving the optimization problem
*
, ,1
*
*
1 1,
2
. .
, 0, 1,2,
i
l
i iw b
i
i i i
i i i
i i
min E w w w Cl
w x b y
s t y w x b
i l
＋
(3.25)
The dual problem is
*
* * * *
,1 1 1 1
* *
1
1
2
. . 0,0 , , 1,2,
l l l l
i i j j i j i i i i i
i j i i
l
i i i i
i
min K x x y
Cs t i l
l
(3.26)
The optional solution is * *
1 1, , ,T
l l α and gets the decision function
*
1
,l
i i i
i
f x K x x b
(3.27)
where the b can be calculated by one of the flowing formulae
*
1
*
1
l
i i i i j
i
l
k i i i k
i
b y x x
b y x x
(3.28)
3.4.4. Relevance Vector Machine
Relevance Vector Machine (RVM) is a statistical learning technique developed recently
by Tipping [121] based on Bayesian estimation for regression and classification
problems. Its key feature is that it can yield a solution function that depends on only a
42
very small number of training samples, relevance vectors (RVs). It is reported that in
several benchmark studies RVM can yield nearly identical performance to, if not better
than, that of SVM while using far fewer relevance vectors than the number of support
vectors for SVM [121]. Compared to SVM, RVM does not need the tuning of a
regularization parameter during the training phase. The detailed learning procedures of
RVM can be summarised as follows.
For given dataset 1
,l
i i it
x , d
i Rx and it R , the output can be expressed as
0
1
, ,
,
l
i i
i
i i i
y K
t y
x ω x x
x ω
(3.29)
where,
l sample number;
K kernel function;
i model weights;
i output noise.
Assume |p t x is Gaussian 2| ,N t y x . The likelihood function of the dataset
can then be written as
2
/22 2
2, 2 exp
2
l
p
t -Φωt |ω ＝ (3.30)
with,
1, , lt tt ; 0 , , l ω ; 11 ll l Φ = φ x ,L,φ x ;
11, , , , ,i i i i lK K φ x φ x x x x .
From the structural risk minimization theory of statistics learning, maximum-likelihood
estimation of value ω and 2 without constraints will generally lead to severe
over-fitting. In order to improve model generalization ability, RVM defines Gaussian
prior probability distribution over the weights [122], which is the key feature of RVM
and is ultimately responsible for its sparsity properties [121].
43
1
0
| | 0,l
i i
i
p N
ω α (3.31)
where,
α vector of hyperparameters.
For the given prior probability distribution and likelihood distribution, posterior
probability distribution for calculating the weights by Bayesian inference can be
expressed as
2
2
2
2
| , || , ,
| ,
| , , ,
p pp
p
p N
t ω ω αω t α
t α
ω t α μ Σ
(3.32)
with, 2 T μ ΣΦ t ; 1
2 T
Σ Φ Φ A ; 0 1, , , ldiag A , when
i , 0i .
The weights estimation can be achieved by the mean value of posterior probability
distribution μ , and uncertainty of best weights values Σ can be used to represent the
uncertainty of model prediction. In order to estimate the model weights, the best values
of hyperparameters need to be estimated, whose likelihood distribution can be calculated
according to Bayesian framework which is the marginal likelihood [123],[124]
2 2| , | , | 0,p p p d N t α t ω ω α ω C (3.33)
with, 2 1 T C I ΦA Φ .
The best possible hyperparameters 2,MP MPα can be solved by the type II maximum
hyperparameters likelihood method [123]. Here an iterative re-estimation approach is
adopted, using the direct differentiation and rearranging
2
new ii
i
(3.34)
with, 1 Σi i ii .
For the noise variance, the re-estimate can be calculated by
44
2new
i
i
l
t Φμ (3.35)
In practice, many of the i approach infinity and according to (2-31), 2| , ,p ω t α
becomes in finitely peaked at zero. The i corresponding to these values can be
regarded equal to 0. And the dataset corresponding to the non-zero i are the relevance
vectors, like the support vectors in SVM.
If the above hyperparameters estimation converges, the new dataset *x can be predicted
according to weights posterior and best hyperparameters 2,MP MPα . The prediction
distribution can be calculated by
2 2 2, , , , ,MP MP MP MP MPp t p t p d * *| | |t α ω ω t α ω (3.36)
Because the two integral parts are all Gauss distribution, so
2 2
* *, , ,MP MPp t N * | t α (3.37)
with, * *
T μ φ x and 2 2
* * *
T
MP φ x Σφ x . The prediction values
are *;y x μ .
3.5. Time Series Models
The previously discussed methods do not consider the sequential information of data,
which might be very useful for time series analysis. The time series models, which allow
inherently for the specification of dynamic relationship of time series and automatically
handle the statistical consequences, are proposed to better solve time series forecasting
[125]. Time series can be classified into two categories. A time series is said to be
stationary if there is no systematic change in mean (no trend), no systematic change in
variance and no periodic variations [125]. The time series which do not satisfy the above
conditions are nonstationary time series. Nonstationary time series contains more
uncertainties and thus more difficult to be predicted [125]. Because the time series
models are not the emphasis of this thesis, just a general introduction is provided in the
following sections.
45
3.5.1. ARIMA
ARIMA models are among the most widely used time series models [126], which use
Box-Jenkins’s approaches for time series prediction. There are several variations of the
ARIMA models, including autoregressive (AR) model, moving average (MA) model and
mixed autoregressive/moving average (ARMA) model [126]. Box and Jenkins
generalized the ARMA model to ARIMA handling nonstationary time-series, whose
statistical properties depends on time [127].
3.5.2. GARCH
Volatility model is another type of time series analysis model which aims at modelling
the changes in variance, [127]. There are several famous volatility models [135], namely
the autoregressive conditionally heteroscedastic (ARCH) model [128], GARCH model
[129], and exponential GARCH model [130]. Other volatility models [135] include
conditional heteroscedastic ARMA (CHARMA) [131] model, random coefficient
autoregressive (RCA) model [132], stochastic volatility model [133] and long-memory
stochastic volatility model [134].
3.5.3. Comparisons
ARMA estimation, the basic assumptions on the error terms include zero mean, constant
variance, and uncorrelatedness [135]. The homoskedastic assumption of constant
variance does not necessarily hold in the heteroskedastic estimation using GARCH
models [129].
3.6. Conclusion
This chapter has described the importance of data analysis for wind power forecasting
and wind power operation. It is clear that despite the many hundreds of approaches that
have been developed for these problems. However each method has its own advantages
and disadvantages, the comprehensive comparisons have provided after detailed
discussion of these techniques.
Due to the deregulation and growth of power system and market, the existing approaches
can not only provide satisfactory performance any longer. More advanced data analysis
techniques should be introduced into power system problems. Meanwhile, the
computational power of modern computers enables the employment of new data analysis
46
techniques to be practical and effective. The possibility and availability of employing
new computational intelligence based methods for wind power prediction and wind
power system operation has been studied and discussed.
In the following chapters, advanced computational methods will be developed for wind
power forecasting and power system operations with stochastic wind power, which will
reversely result in a deeper understanding of the performance of different algorithms and
allow more meaningful comparisons and choices in practical situations.
47
Chapter 4. Wind Power Interval Forecasting
4.1. Introduction
Based on the comprehensive review of data analysis techniques for power system with
wind power, this chapter is concerned with advanced statistical approaches to wind
power interval forecasting. A time series model is formulated as the theoretical basis of
method. The proposed model takes into account two important characteristics of wind
speed, the nonlinearity and the time-changing distribution. Based on the proposed model,
linear regression and five data mining algorithms are employed to forecast the prediction
interval of wind power output. The six methods are tested using real wind data collected
at a wind station in Australia. For the wind speed forecasting, the Lazy IBK algorithm
outperforms other five algorithms. In terms of the prediction interval, the five data
mining algorithms show superior performances. The case study proves that, combined
with an appropriate nonlinear regression algorithm, the proposed methodology is
effective in wind power interval forecasting.
4.2. A Review of Wind Power Interval Forecasting
Wind energy is being increasingly made use of by human around the world. However,
the intermittency and uncertainty of wind make it a challenge to integrate wind power
into the power system. The wind power forecasting system can greatly help the
integration process, since system operators rely on accurate wind power forecasts to
design operational plans and assess system security [136, 137]. Predictions of wind
power output are traditionally provided in the form of point forecasts. The advantage of
point forecasts is that they are easily understandable. The single value is expected to tell
everything about future power generation. Nowadays, the majority of the research efforts
on wind power forecasting are still focused on point prediction only. These efforts try to
increase forecast accuracy by decreasing the level of prediction error. The reviews of the
state of the art in wind power prediction can be found in [138] and [139]. A book on
physical approaches to short-term wind power forecasting also partly discusses the state
of art in wind power forecasting [140].
However, even by better understanding and modeling both the meteorological and power
conversion processes, there will always be an inherent and irreducible uncertainty in
every prediction. The epistemic uncertainty corresponds to the incomplete knowledge
one has of the processes that influence future events [141]. The uncertainty of a wind
48
power forecast mainly depends on the predictability of the current meteorological
situation and the level of the predicted wind speed [142]. To assist with management of
the uncertainty of the forecasts, Extensive researches have been conducted to develop
wind power forecasting methods. Quantile regression methods have been introduced in
[142-144]. Those approaches use probabilistic forecasts through different quantile
regression methods to achieve the complete future wind production information. A
time-series and ensemble-based method was developed by J. W. Taylor et al. in [145].
This method provides a description of the expected future value and the associated
uncertainty though prediction of the wind power probability density function. P. Pinson
et al. developed a nonparametric probabilistic forecast approach which can avoid
assumptions on the shape of predictive distributions [146]. One popular approach is to
use ensemble-based probabilistic forecasting methodology, which enable better wind
power management and trading purposes [147,148]. In [149, 150], statistical analysis
have been conducted to study the distribution of wind power forecasting errors. Because
wind power is stochastic in nature, errors will always exist in wind power forecasts.
Therefore, besides predicting the expected value of future wind power, it is also
important to estimate its prediction errors.
The above studies however fail to establish proper statistical models for interval
forecasting of wind power, and also fail to take into account the time-changing effect of
the error distribution. Generally speaking, a prediction interval is a stochastic interval,
which contains the true value of wind power with a pre-assigned probability. Because
the prediction interval can quantify the uncertainty of the forecasted wind power, it can
be employed to evaluate the risks of the decisions made by market participants. Existing
methods discussed above cannot effectively handle wind power interval forecasting,
since they mainly focus on predicting the expected value of wind power.
There are two main challenges for accurate interval forecasting of wind power: (i) The
expected value of wind power should be accurately predicted. This is difficult since wind
power is a nonlinear time series, and is therefore highly volatile. (ii) The probability
distribution of forecasting errors should also be accurately estimated. This is even more
difficult since the error distribution can be time-changing. In this chapter, a novel
approach is proposed to forecast the prediction interval of wind power. A statistical
model is firstly formulated to properly model the time series of wind speed. Based on the
proposed model, a number of different data mining algorithms are introduced to predict
the expected value of wind speed and the parameters of forecasting error distribution.
49
Prediction intervals of wind speed are then constructed based on the predicted wind
speed value and error distribution. The wind speed prediction interval is finally
transformed into wind power prediction interval with the wind turbine power curve.
Comprehensive studies are performed to compare the performances of linear regression
and five data mining algorithms in wind power interval forecasting.
4.3. The Statistical Model of Wind Speed Time Series
To forecast the power output of a wind turbine, a widely used approach is to predict the
wind speed firstly, and then transform the predicted wind speed into wind power with
the power curve. Therefore, in this section a statistical model of wind speed is firstly
formulated. We will also briefly explain how to integrate the proposed model with
nonlinear regression techniques to forecast the prediction intervals of wind speed.
The wind speed time series can usually be assumed to be generated by the following
stochastic process:
ttttt XYYfY )...,,( 21
, (4.1)
where tY denotes the random wind speed, and ty is the observed value of tY at time t.
m
t RX
is a m-dimensional explanatory vector. Each element itX , of tX
represents an
explanatory variable which can influence tY , for example the temperature and humidity.
The current value of tY can be determined by its lagged values ..., 21 tt YY and the
explanatory vector tX
. Note that the mapping )(f from ttt XYY
...,, 21 to tY can be any
linear or nonlinear function. Most existing methods essentially forecast wind speed by
estimating mapping )(f ; the forecasted value )(ˆ f of )(f can be called the point
forecast of wind speed. According to (4.1), the wind speed tY contains two components,
)(f is a deterministic component; and t is a random component, which is also
known as noise. Detailed statistical studies [136] show that t can be assumed to follow
a normal distribution. We therefore have:
),(~ 2 Nt. (4.2)
Because )(f is a deterministic function, we should be able to approximate it with
arbitrary accuracy by employing a powerful nonlinear regression technique (e.g. Neural
50
Network). Most existing wind speed forecasting methods mainly focus on estimating
)(f and select its estimated value as the predicted wind speed. On the other hand,
because of the uncertainty introduced by noise t , errors will always exist in wind speed
forecasts. Therefore, estimating and 2 is essential for estimating the uncertainty of
tY .
In model (4.1)-(4.2), parameters and 2 are assumed to be constant. In practice, the
model parameters can usually be time-changing. We therefore introduce the following
time-changing distribution model of wind speed:
(4.3.1)
(4.3.2)
(4.3.3)
(4.3.4)
(4.3.5)
(4.3.6)
Similar to )(f , mappings )(g and )(h can also be either linear or nonlinear.
According to model (4.3.1~4.3.6), the uncertainty of wind speed is time-changing. The
mean and variance of noise t are determined by the previous noises and the explanatory
vector. Note that model (4.3.1~4.3.6) is a generalization to traditional ARCH
(AutoRegressive Conditional Heteroscadesticity) model, since by setting 0tu and
assume )(f and )(h are linear functions, model (4.3.1~4.3.6) will be identical to the
ARCH model.
To more strictly justify our model, the Lagrange Multiplier (LM) test can be employed
to verify that the wind speed has a time-changing distribution [151]. In the case study,
we will test whether the actual wind speed data of Australia have time-changing
distribution by performing the LM test.
Based on the statistical model (4.3.1~4.3.6) of wind speed, we can construct the
prediction interval, which contains the true value of wind speed with any pre-assigned
probability. The definition of prediction interval can be given as:
,1 ,2 ,' ( , ... )t t t t mX X X X
1 2( , ,... )t t t tu g X
1 2( , ,... )t t t th X
1 2( , ..., )t t t t tY f Y Y X
t t t tv
~ (0,1)tv N
51
Definition 1: Given a time series }{ tY which is generated with model (4.3.1~4.3.6), an
level prediction interval (PI) of tY is a stochastic interval ],[ tt UL calculated from }{ tY ,
such that 1]),[( ttt ULYP .
Because noise t is usually assumed to be normally distributed, the level prediction
interval can therefore be calculated as:
tattt zfL 2/)1()( , (4.4)
tattt zfU 2/)1()( , (4.5)
Where )(tf represents the value of the deterministic component )(f at time t ; is the
confidence level and 2/)1( az is the critical value of the standard normal distribution.
Based on (4.4) and (4.5), to calculate the prediction interval, we should firstly obtain
three quantities, the wind speed forecast )(tf , the mean and variance 2 of the
noise.
In practice, traditional time series models, such as ARIMA and GARCH usually perform
poorly on short-term wind speed forecasting since they are linear models and therefore
cannot handle the complex nonlinear patterns of wind speed data. To give accurate wind
speed forecasts, the three mappings )(f , )(g and )(h in model (4.3.1~4.3.6) should
be accurately estimated with nonlinear regression techniques. In this paper, we introduce
six different regression methods to estimate )(f , )(g and )(h . To apply regression
methods to estimate )(g and )(h , an unsolved problem is how to obtain the estimates of
mean t and variance 2
t of the noise. In this paper the moving window method is
employed. Given the noise series }{ t , the estimates of t and 2
t can be calculated as:
nt
nts
stn
12
1ˆ (4.6)
nt
nts
sstn
22 )ˆ(2
1ˆ (4.7)
By combining a nonlinear regression method with the proposed model (4.3.1~4.3.6), the
main procedure of wind power interval forecasting is given as follows:
52
1. Given the historical wind speed data }{ tY and the explanatory vector data }{ tX
for
time period ],0[ T , employing a regression technique to estimate function
)...,( 21 tttt XYYfY
. Denote the estimate of )(f as )(ˆ f .
2. Calculate the forecasting errors )...,(ˆ21 ttttt XYYfYe
for period ],0[ T . Note that
te can be considered as the estimate of noise t .
3. Based on error series }{ te , calculating the estimates of t and 2
t with Equations
(4.6) and (4.7).
4. Based on error series }{ te , mean and variance estimate series }ˆ{ t and }ˆ{ 2
t ,
employing a regression technique to estimate functions ),,(ˆˆ21 tttt Xeeg
and
),,(ˆˆ21 tttt Xeeh
, and use them as the estimates of )(g and )(h .
5. To forecast the wind speed at t , firstly employ )(ˆ f , )(ˆ g and )(ˆ h to calculate
)(ˆ tf , t and 2ˆt ; then calculate the wind speed prediction interval with Equations (4.4)
and (4.5).
6. Transform wind speed prediction interval into wind power prediction interval with
the wind turbine power curve, which will be discussed in the following sections.
4.4. Data Mining Methods for Wind Power Interval
Forecasting
In this section, we firstly provide a brief introduction to data mining and regression,
which is an important research area in data mining. Five data mining algorithms used in
this paper are then presented. The power curve for converting wind speed into wind
power is introduced. We finally discuss how to evaluate the performance of wind power
interval forecasting methods.
4.4.1. Introduction to Data Mining
Data Mining (or Knowledge Discovery in Data) is the process of extracting useful
information from a large amount of data. Data mining is the exploration and analysis of
large quantities of data by automatic or semi-automatic means in order to discover
meaningful patterns or rules [151]. The patterns or relations discovered by data mining
53
should be novel, in that these patterns have not been discovered or assumed before the
data mining process is performed. In this sense, data mining is a tool to discover new
knowledge rather than validating existing knowledge.
In a large database, there are many different types of patterns that can be discovered by
different approaches and techniques. Based on the patterns that we are searching for,
data mining can be classified into several major research areas, such as classification,
clustering, correlation and regression [152, 153].
Regression [154] is a process to estimate a functional mapping between a data vector and
a target variable. Regression aims at determining a continuous target variable, which is
usually named as dependent variable, while the data item itself is usually called
independent variables, explanatory variables or predictors. For example, in wind speed
forecasting, the predictors can be historical wind speed, temperature and humidity, while
the independent variable is the future wind speed. Regression usually estimates the
mapping based on a training dataset in which the independent variables of all data items
have been given. Regression is therefore a supervised learning problem in the sense that
the estimation of the mapping is supervised by the training data.
Regression is also an important research area of statistics. The most important statistical
method is linear regression, which assumes that the independent variable is determined
by a linear function of predictors. In recent years, the data mining society has proposed
many other regression methods, such as neural networks and support vector machine. In
this chapter, we will introduce six different regression techniques and integrate them
with the proposed statistical model to perform wind power interval forecasting.
4.4.2. Regression Algorithms Employed in This Paper
1). Linear Regression
Linear regression is a traditional and widely-used statistical technique for regression. It
is selected as the baseline technique in this chapter and will be compared with five
nonlinear techniques. Linear regression models the relationship between the dependent
variable iy and the vector of predictors ix
. Linear regression assumes that the
independent variable y is linearly dependent on the predictors x plus a noise term i .
The model can be written as:
54
(4.8)
where T
ix ' is the inner product between vectors ix and . And these n equations
can be written in the vector form as:
, Xy T (4.9)
where
ny
y
y
y2
1
,
'
'
2
'
1
nx
x
x
X
,
p
T
1
,
n
2
1
(4.10)
The is usually assumed to follow a normal distribution with a zero mean and varianc
2 . We therefore have:
)0(~ 2 ，N (4.11)
is a p-dimensional parameter vector, which specifies how much each component of
X contributes to the output y [155].
2). Multilayer Perceptron Network
A multilayer perceptron (MLP) network is a feed-forward artificial neural network
model that maps sets of input data onto a set of appropriate outputs. Based on the
standard linear perceptron, MLP uses three or more layers nodes with nonlinear
activation functions. An MLP network consists of a set of source nodes as the input layer,
one or more hidden layers of computation nodes, and an output layer of nodes.
F
F
F
F
F
∑
∑∑
∑∑
∑
Input Layer
Hidden
LayerOutput
Layer
Figure 11. Diagram of a Multilayer Perceptron Network
Figure 11 shows the signal flow process of a feed-forward neural network. A MLP
network has two stages: a forward pass and a backward pass. The forward pass includes
'
1 1 ... , 1,2,...,T
i i p ip i i iy x x x i n
55
presenting a sample input to the network and letting activations flow until they reach the
output layer [156, 157].
3). Radial Basis Function (RBF) Network
A radial basis function (RBF) network is an artificial neural network (NN), which uses
radial basis functions as activation functions. The RBF network has three layers: an input
layer, a hidden layer with a number of non-linear RBF activation functions, and a linear
output layer. The hidden layer is used to determine the behavior structure of network. In
RBF network, the response from the hidden unit is activated by the Gaussian function or
other functions. The output layer provides the response from the hidden layer to the
activation pattern of the input layer [158].
The functional relationship modeled by RBF networks can be written as:
(4.12)
where nj ,...,2,1 , n is the number of output nodes in the output layer, Ni ,...,2,1 , N is
the number of input nodes in the input layer, K is the number of RBFs used. KC are the
center value vector and K are the width value vector of RBFs. jkw are the weights of
connections between RBFs and output nodes.
⋮ ⋮
x1
X2
Xk
Ф(x,c,σ)
1
2
k
w1
w2
Wk
y
Figure 12. Structure of the RBF Network
Fig. 12 illustrates the basic structure of the RBF network. In the hidden layer, the term
(.) represents the activation function in a node.
1
( ) [ ( ), , ]k
j k kjkk
y i x i cw
56
4). Lazy IBK
Lazy IBK is one of the widely-used lazy learning methods. Lazy Learning methods
defer the decision of how to assign the dependent variable until a new query explanatory
vector is inputted. When the query explanatory vector is received, a set of similar data
records is retrieved from the available training dataset and is used to assign the
dependent variable to the new instance [159]. In order to choose the similar data records,
lazy methods employ a distance measure that will give nearby data records higher
relevance. Lazy methods choose the k data records that are nearest to the query instance.
The dependent variable of the new instance is determined based on the k nearest
instances.
Lazy learning algorithms have three basic steps:
(1). Defer: Lazy learning algorithms store all training data and defer processing until a
new query is given.
(2). Reply: A local learning approach developed by Bottou and Vapnik in 1992 is a
popular method to determine the dependent variables for news queries [160]. In Bottou
and Vapnik learning approach, instances are defined as points in a space and a similarity
function is defined on all pairs of these instances.
(3). Flush: After solving a query, the answer and any intermediate results are discarded.
5). Regression Tree
A regression tree is one of the widely-used decision tree algorithms. A decision tree
is a data-mining tool designed to extract useful information from a large data sets and
use the information to help decision-making processes. A regression tree consists of a set
of nodes that can assign the value of the dependent variable to an explanatory vector.
Regression tree constructs a tree style decision rule set and divides the training data into
the leaf nodes of the decision tree according to the numerical or categorical values of
explanatory variables. The regression rules of each leaf node are derived from a
mathematical process that minimizes the regression errors of the leaf nodes [161].
6). Decision Table
Similar to regression tree, decision table also determines the value of the dependent
variable with a set of decision rules [162]. However, the decision table arranges decision
rules as a table, rather than a tree. A decision table usually consists of a number of
57
parallel decision rules. Similar to regression tree, the training data will be divided into
several groups, each of which will be represented by a decision rule. For a given
explanatory vector (input), an appropriate decision rule will be firstly selected based on
the values of its explanatory variables. The dependent variable for this input will be
assigned as the average of the dependent variables of all training data vectors in the
corresponding group. The dependent variable can also be determined by performing
linear regression on the corresponding group of training data. Empirical studies show
that decision table has similar performance to regression trees.
4.5. Converting Wind Speed to Wind Power
An elementary method is used in this paper to convert the predicted wind speed to the
predicted wind power output of a wind turbine or wind farm. The predicted wind speed
is provided by one of the six regression methods discussed above. The wind speed is
then input into the certified wind turbine power curve and transformed into the wind
power.
The VESTAS V90-3.0 MW wind turbine is selected for the case studies in this paper.
The VESTAS V90-3.0 MW is a pitch regulated upwind wind turbine with active yaw
and a three-blade rotor. It has a rotor diameter of 90 m with a generator rated at 3.0 MW.
The VESTAS V90-3.0 MW is widely used in Australia wind power plants and has a
proven high efficiency. The typical power curve of VESTAS V90-3.0 MW 60HZ
106.7dB(A) is shown in Figure 13. It can be clearly observed that the wind power
output )(up is proportional to 3u for small wind speed u . Moreover, The power curve is
steep for medium wind speeds and flat for large wind speeds. The cut-in speed is 3.5 m/s
and the cut-out speed is 25 m/s [163].
Figure 13. The Power curve for VESTAS V90-3.0 MW, 60Hz, 106.7
58
4.6. Performance Evaluation
Before proposing the case study results, several criteria are introduced for performance
evaluation. Given T historical wind power values tp , 1 ≤ t ≤ T of a time series tp
which are converted from T historical wind speed observations, and the corresponding
forecasted power values
tp , 1 ≤ t ≤ T, Mean Absolute Percentage Error (MAPE) is
defined as :
*
1
| |1 Tt t
t t
p pMAPE
T p
(4.13)
MAPE is a widely used criterion for time series forecasting. It will also be employed to
evaluate the proposed method in the case studies.
Another two criteria are presented to evaluate the interval forecasting. Given T wind
power values tp , 1 ≤ t ≤ T of a time series yP
, and the corresponding forecasted α
level prediction intervals tt ul , , 1 ≤ t ≤ T, the empirical confidence [164] and the
Absolute Coverage Error (ACE) are defined as:
T
ulpfrequence ttt ],[ˆ
(4.14)
ACE (4.15)
where is the number of observations, which fall into the forecasted prediction interval
(PI), divided by the sample size. It should be as close to α as possible.
4.7. Australian Regional Wind Power Interval Forecasting
4.7.1. Data Collection
In the experiments, the wind power forecasting model has been evaluated using the wind
speed data from the Devonport Airport Wind Station, Tasmania, Australia. The data was
provided by the Australian Bureau of Meteorology. The training data is from 1st
February 2008 to 1st March 2008, while the test data is from 1st February 2009 to 1st
March 2009
To empirically prove the validity of our model, we will firstly verify that the wind speed
data exhibit time-changing distribution effect by performing the Lagrange Multiplier test.
The results of the LM test with 95% significance level on the data from 1st February
2009 to 1st March 2009 are given as follows:
59
Table 4 The Results of the Lagrange Multiplier Test
Dataset Order P-value LM Statistics Critical Value
Feb 2008 to Mar 2008 1 0 1913.6 3.8415
Feb 2008 to Mar 2008 5 0 1964.6 11.0705
Feb 2008 to Mar 2008 10 0 1969.3 18.307
Feb 2009 to Mar 2009 1 0 2898.9 3.8415
Feb 2009 to Mar 2009 5 0 3057.2 11.0705
Feb 2009 to Mar 2009 10 0 3077 18.307
As illustrated in Table 4, setting the significance level as 0.05, P-value of the LM test is
zero in all six cases. Moreover, the LM statistics are significantly greater than the critical
value of the LM test in all occasions. These two facts strongly indicate that the wind
speed data have strong effect of time-changing distribution. In the test, a order of 10
means that the variance 2
t is correlated with its lagged values up to at least 2
10t . In
other words, the wind speed at 10 time units before time t can still influence the
uncertainty of the wind speed at time t.
4.7.2. Results of Wind Speed Forecasting
Wind speed forecasting is the first step of wind power forecasting. Six regression
methods are firstly employed to perform half an hour wind speed forecasting in this
paper. The performances of six algorithms are shown as follows:
Table 5 Prediction Errors of Different Methods
Regression Methods MAPE
Linear Regression 12.81%
Multilayer Perceptron 12.32%
RBF Network 29.34%
Lazy IBK 10.46%
Decision Table 15.10%
Regression Tree 11.26%
As illustrated in Table 5, the MAPEs of Lazy IBK and regression tree are smaller than
other methods. Moreover, the MAPEs of Lazy IBK and regression tree are around 10%,
which is sufficiently good considering the very high volatility of wind speed. The results
indicate that these two nonlinear regression methods perform well in the wind speed
forecasting.
60
-20 -10 0 10 200
200
400
600
800
1000
1200
1400
Errors [m/s]
Dis
trib
ution o
f err
ors
[%
]
Distribution of errors for Linear Regression
-20 -10 0 10 200
200
400
600
800
1000
1200
1400
Errors [m/s]
Dis
trib
ution o
f err
ors
[%
]
Distribution of errors for Lazy IBK
-20 -10 0 10 200
200
400
600
800
1000
1200
1400
Errors [m/s]
Dis
trib
ution o
f err
ors
[%
]
Distribution of errors for Regression Tree
Figure 14. Distributions of the Errors of Linear Regression, Lazy IBK and Regression Tree
The forecasting errors of these three methods are graphically shown in Figure 14. In
Figure 14, the visual inspection suggests that the forecasting errors of the three
algorithms have a normal distribution. It is very important to know the type of the error
distribution to ensure that the proposed statistical model has a valid assumption. To
empirically prove that the wind speed forecasting errors are normally distributed, the
forecasting errors of all six methods are checked for normality by performing the
Kolmogorov-Smirnov Normality Test. The test results also show that all the six
forecasting methods have normally distributed errors. These results again verify the
validity of the assumptions of our model.
4.7.3. Results of Wind Power Interval Forecasting
Table 6 The Mape of Different Methods for Wind Power Forecasting
Regression Methods MAPE
Linear Regression 37.62%
Multilayer Perceptron 42.48%
RBF Network 53.73%
Lazy IBK 28.09%
Decision Table 35.58%
Regression Tree 30.05%
The wind speed forecasts given by the six regression algorithms are then converted into
wind power forecasts as discussed in Section 4.5. Similarly, Mean Absolute Percentage
Error (MAPE) is used to evaluate the performances of different methods. From Table 6,
it is observed that for wind power forecasting, the MAPEs of Lazy IBK and regression
tree are still lower than other four algorithms.
61
Based on Tables 5 and 6, the Lazy IBK method is selected as the wind speed point
forecasting method (the estimator of )(f ). The procedure discussed in Section II is
then employed to give the prediction intervals of wind power. We will employ all six
regression methods to estimate )(g and )(h , then compare their performances in
wind power interval forecasting.
In Table 7, for 95% and 99% confidence levels, the ACEs of different regression
methods are presented. As seen in Table 7, the ACEs of five nonlinear methods are
similar regardless of the confidence level. On the other hand, the five nonlinear
regression algorithms all outperform linear regression. This is a clear proof that strong
nonlinearity exists in the wind power data.
Table 7 Performances of Different Methods on Wind Power Interval Forecasting
Regression Methods ACE for 95%
Confidence
ACE for 99%
Confidence
Linear Regression 5.37% 3.34%
Multilayer Perceptron 3.19% 0.39%
RBF Network 3.02% 0.16%
Lazy IBK 3.16% 0.38%
Decision Table 3.16% 0.43%
Regression Tree 3.2% 0.39%
The 95% level and 99% level prediction intervals given by different methods are
illustrated in Figures 15 and 16. As illustrated, the prediction intervals given by the five
nonlinear algorithms all perfectly contain the true values of wind power. These results
clearly prove the effectiveness of the proposed statistical model. Moreover, the results
also show that, nonlinear regression methods are suitable candidates in wind power
interval forecasting.
460 480 500 520 540 560 580 6000
500
1000
1500
2000
2500
3000
3500
Time (5 mins)
Win
d P
ow
er
(MW
)
95% PI of Linear Regression
Observed Wind Power
Lower Bound of PI
Upper Bound of PI
460 480 500 520 540 560 580 600
0
500
1000
1500
2000
2500
3000
3500
Time (5 mins)
Win
d P
ow
er
(MW
)
95% PI of Multilayer Perceptron
Observed Wind Power
Lower Bound of PI
Upper Bound of PI
62
460 480 500 520 540 560 580 6000
500
1000
1500
2000
2500
3000
3500
Time (5 mins)
Win
d P
ow
er
(MW
)
95 % PI of RBF Network
Observed Wind Power
Lower Bound of PI
Upper Bound of PI
460 480 500 520 540 560 580 600
0
500
1000
1500
2000
2500
3000
3500
Time (5 mins)
Win
d P
ow
er
(MW
)
95 % PI of Lazy IBK
Observed Wind Power
Lower Bound of PI
Upper Bound of PI
460 480 500 520 540 560 580 6000
500
1000
1500
2000
2500
3000
3500
Time (5 mins)
Win
d P
ow
er
(MW
)
95% PI of Decision Table
Observed Wind Power
Lower Bound of PI
Upper Bound of PI
460 480 500 520 540 560 580 6000
500
1000
1500
2000
2500
3000
3500
Time (5 mins)
Win
d P
ow
er
(MW
)
95% PI of REPTree
Observed Wind Power
Lower Bound of PI
Upper Bound of PI
Figure 15. The 95% level prediction intervals forecasted by six data mining methods
460 480 500 520 540 560 580 6000
500
1000
1500
2000
2500
3000
3500
Time( 5 mins)
Win
d P
ow
er
(MW
)
99% PI of Linear Regression
Observed Wind Power
Lower Bound of PI
Upper Bound of PI
460 480 500 520 540 560 580 600
0
500
1000
1500
2000
2500
3000
3500
Time (5 mins)
Win
d P
ow
er
(MW
)
99% PI of Multipayer Perceptron
Observed Wind Power
Lower Bound of PI
Upper Bound of PI
460 480 500 520 540 560 580 6000
500
1000
1500
2000
2500
3000
3500
Time (5 mins)
Win
d P
ow
er
(MW
)
99% PI of RBF Network
Observed Wind Power
Lower Bound of PI
Upper Bound of PI
460 480 500 520 540 560 580 600
0
500
1000
1500
2000
2500
3000
3500
Time (5 mins)
Win
d P
ow
er
(MW
)
99% PI of Lazy IBK
Observed Wind Power
Lower Bound of PI
Upper Bound of PI
63
460 480 500 520 540 560 580 6000
500
1000
1500
2000
2500
3000
3500
Time (5 mins)
Win
d P
ow
er
(MW
)
99% PI of Decision Table
Observed Wind Power
Lower Bound of PI
Upper Bound of PI
460 480 500 520 540 560 580 600
0
500
1000
1500
2000
2500
3000
3500
Time (5 mins)
Win
d P
ow
er
(MW
)
99% PI of REPTree
Observed Wind Power
Lower Bound of PI
Upper Bound of PI
Figure 16. The 99% level prediction intervals forecasted by six data mining methods
4.8. Conclusions
Accurate wind power interval forecasting is essential for the efficient planning and
operation of power systems. Wind energy is characterised by its nonlinearity and
intermittency, which pose significant challenges for wind power forecasting. Traditional
linear time series models cannot appropriately handle these challenges and therefore
cannot achieve satisfactory performances. In this chapter, we propose a statistical
approach, which can handle nonlinear time series with time-changing distributions, thus
is suitable for wind power interval forecasting. Two major contributions of this chapter
are: (i) a comprehensive statistical model is introduced, which forms the theoretical basis
for wind power interval forecasting; (ii) linear regression and five data mining methods
are incorporated into the proposed model. The comparison of different regression
algorithms in wind power forecasting is presented. Experimental results show that lazy
IBK and regression tree are suitable candidates for wind power forecasting. Moreover,
the effectiveness of the proposed model in wind power interval forecasting is also
proven with the case studies.
64
Chapter 5. Economic Dispatch Considering
Wind Power and Emission
5.1. Nomenclature , ,i i ia b c Cost coefficients of thermal generator i .
, ,i i id e f Fuel consumption coefficients of thermal unit i .
iC Cost function of thermal generator i .
,u jC Cost coefficient for not using all generated wind power due to the
underestimation case.
,o jC Cost coefficient for purchasing reserve power from other source due to
overestimation case.
,s jC Government subsidy parameter of turbine j .
,w jC Cost coefficient of wind turbine j .
ief Fuel emission factor of thermal unit i .
i iEM p GHGs emission function of thermal unit i .
,GHG i iF p Emission cost of thermal unit i .
h Price factor of GHGs emission.
M Number of thermal power generators.
N Number of wind turbines.
ip Actual power generated by thermal generator i .
dp Total system loads.
lossp Total transmission losses.
, ,in r outv v v Cut-in, rated, and cut-out wind speeds.
jw Predicted wind power generated by turbine j .
,j avW Actual wind power generated by wind turbine j .
,r jw Rated wind power from wind turbine j .
5.2. Introduction
In this chapter, we describe a novel hybrid optimization algorithm connecting interior
point method (IPM) and particle swarm optimization (PSO) for solving combined
economic and emission dispatch (CEED) problem with valve point effects as well as
stochastic wind power. The problem aims to minimize the scheduling cost and
greenhouse gases (GHGs) emission cost. Here the GHGs include carbon dioxide (CO2)
and nitrous oxides (N2O). A dispatch model including both thermal generators and a
wind farm is developed. The probability of stochastic wind power based on the Weibull
distribution is included in the CEED model. The model is tested for a standard system
involving six thermal units and one wind farm. A set of numerical experiments is
reported. The effectiveness of the hybrid computational method is validated by
comparing with other optimization algorithms on the test system.
65
5.3. Economic Dispatch with Wind Power and Emission
Economic dispatch (ED) is an important task in the power system operation, which aims
to allocate power generation to match load demand at minimal possible cost while
satisfying all the units and system constraints [165]. Suitable improvements in the unit
outputs scheduling can contribute to significant cost savings. Nowadays, with the
awareness of environmental pollution contributed by the combustion of fossil fuels,
building a low-carbon world has attracted widespread attentions. Many countries are
trying to exploit clean energy in order to mitigate the greenhouse effects. The primary
source of greenhouse gases (GHGs) is the combustion of fossil fuels. Coal, oil, and gas
are the three major types of fossil fuels, which produce emissions represented by GHGs,
such as COx, NxO, and SOx. In order to reduce the GHGs emissions, the combined
economic emission dispatch (CEED) was proposed, which can take account of fuel cost
and emission tax together. Because the amount of emission from fossil-based thermal
generators depends on the amount of generated power, thus the emission cost increase
leads to reduced overall power generated by thermal units, which in turn lowers
emissions. Moreover, the natural economic forces will also help to catalyze the move to
greater energy efficiency and use of renewable sources.
Wind energy is among the major contributors to an overall reduction in GHGs emissions.
Wind farms have been installed worldwide with a motive of finding some respite from
GHGs emissions and energy crisis [166]. The pace with which the global wind power
capacity has increased, it is evident that majority of countries around the world are
resorting to the same, for wind energy - it’s projected to have taken over the global
growth of other traditional sources. Wind energy will play a vital role in doing away
with the fossil fuels and it’s presumed that wind power could largely reduce the global
emissions in the future. In the literatures, many researchers have shown great interests to
incorporate wind power with traditional dispatch problems. For instance, an economic
emission dispatch model with wind power generation was studied in [167], and the
simulation results proved that significant GHGs emission reduction was achieved. In
[168], the authors studied an economic dispatch model coordinating wind power to
mitigate NOx emission impacts. From the results, we can find that with wind power, the
total emissions can be reduced. However, due to the intermittent and stochastic
characteristics of wind energy, how to coordinately dispatch traditional generation
sources and wind power while satisfying all the determined and probabilistic constraints
66
becomes more complicated. One of the consequences is that more advanced and reliable
computation approaches are required.
In terms of the solvers, different heuristic techniques have been proved to be effective
with promising performance in the researches, including evolutionary programming (EP)
[169]-[172], simulated annealing (SA) [173], tabu search (TS) [174], pattern search (PS)
[175], genetic algorithm (GA) [176]-[178], differential evolution (DE) [179], and
particle swarm optimization (PSO) [180]-[182]. Although the heuristic approaches do
not always guarantee discovering globally optimal solutions in finite time, they often
provide a fast and reasonable solution. In general, each method has its own strengths and
weaknesses. Many attempts try to merge some of the individual implementations
together into a new method, so that it can overcome individual shortages and benefit
from each others’ advantages [182]. Recently, hybrid optimization methods combining
different techniques receive widespread concerns. In [183], the authors presented a
hybrid EP and sequential quadratic programming (SQP) for solving the ED problem with
non-smooth fuel cost function. And a hybrid self-tuning DE was proposed to solve the
ED problem with kinds of constraints in [184]. In [185], a hybrid approach combining
DE with biogeography-based optimization (DE/BBO) was developed to address both
convex and non-convex ELD problem. Those hybrid optimization methods were found
to be more effective and accurate.
In this chapter, a CEED model incorporating wind power to minimize the total cost is
proposed. Because of the stochastic characteristic of wind speed, wind power output is
not deterministic. As a sequence, the probability distribution of wind speed must be
taken into account in the CEED model. A huge number of research works have indicated
that wind speed approximately follows Weibull distribution [186]-[189]. In our CEED
model, wind power is described as the three-parameter Weibull distribution. As ED
problem in consideration of emission issue, there are many works reducing the N2O, as
well as SO2, however, there are few papers on CEED in consideration of the CO2
emission. In this paper, the reduction of CO2 emission is one of the main concerns in the
CEED model. In terms of the optimization method, we present a hybrid technique which
combines interior point method (IPM) and particle swarm optimization (PSO) together.
In the proposed algorithm, IPM is firstly used in the stage to solve the CEED problem
without considering the valve point loading, and then PSO is deployed to further
optimize the solution.
67
5.4. Probability of Wind Power
Wind power, one of the most appealing renewable energy sources, has been widely
developed in the recent years. Wind power energy has lots of advantages such as no
pollution, relatively low capital cost involved, and the short gestation period required.
However, the wind resource changes with locations and climates resulting in high
uncertainties in the produced energy. The total power available from a wind turbine is
equal to the product of the mass flow rate of the wind Wm , and 2 / 2V Assuming
constant area or ducted flow, the continuity equation states that Wm AV where is
the density of the air in 3/kg m , A is the blades area in 2m , and V is the velocity in
m/s. Thus, the total wind power becomes PW=(mWV2)/2=(ρAV
3)/2 (MW). In this equation,
the wind speed V is a random variable. The most commonly available representation of
the output curve identifies four zones of performance for any make of wind energy
conversion systems (WECS), namely, 1) zero power output at speeds below cut-in, 2)
approximately linear variation of output power with speed between cut-in and rated wind
speed values, 3) rated power output between rated wind speed values and cut-out speed
values, and 4) zero power output above cut-out speed. The simplified wind turbine curve
ignores the minor nonlinearities, and the simplification will not lead to large bias
[190,191]. The function relation between a given wind speed and power output can be
described in Fig. 17.
inv rv outv
Wind Speed m s
Win
dP
ow
erM
W
rw
Figure 17. Simplified Wind Turbine Power Curve
In the above figure, w (MW) is the wind energy conversion systems (WECS) output
power; wr (MW) is the WECS output rated power; vin (m/s), vr (m/s), vout (m/s) is the
WECS cut-in speed, rated speed, and cut-out speed, respectively. From Fig. 17, we can
see that there is no power generated at wind speeds below vin or above vout ; at wind
speeds between vr and vout , the output is equal to the rated power of the generator; at
wind speeds between cut-in wind speed and rated wind speed, the output is a linear
function power.
Therefore, the wind power output can be described as,
0,
,
,
in out
in r
r r out
W V v or V v
W aV b v V v
W w v V v
(5.1)
where,
r
r in
wa
v v
,
in r
r in
v wb
v v
.
68
Weibull distribution is the most popular density function that can be used to describe the
wind speed frequency curve. Using a three-parameter Weibull distribution, the CDF
(cumulative distribution function) and pdf (probability density function) of wind speed V
are as follow,
1 exp , 0
k
V
vF v v
c
(5.2)
1
exp
k k
V
k v vf v
c c c
(5.3)
where, k>0 is the shape parameter, c>0 is the scale parameter and θ is the location
parameter of the distribution. When θ=0, this reduces to two-parameter Weibull
distribution. In this thesis, the author assumed that the wind speed data from the same
wind farm. So the location parameter can be assumed to be zero.
According to Eq. (5.1), three portions of WECS power output can be analyzed and the
corresponding probabilities (CDF or pdf) can be calculated.
(1) For inV v or outV v ,
0
1
1 exp exp
in out
V in V out
k k
in out
P W P V v P V v
F v F v
v v
c c
(5.4)
(2) For in rv V v ,
in r
r in
V v wW aV b
v v
, depending on the definition of cumulative
distribution function (CDF), the CDF of WECS output power can be described as
in r
W
r in
r in r in
in V in
r r
V v wF w P W w P W w
v v
v v w v v wP V v F v
w w
(5.5)
We can obtain the pdf of W by differentiating with respect to w. The chain rule for
derivatives can be used,
dF dF du
dw du dw
, where u is the argument of F,
r in
in
r
v v wu v
w
,
and we then obtain
69
1
exp
kk
r in r in
in in
r in r rW
r
v v w v v wv v
k v v w wf w
cw c c
(5.6)
(3). For r outv V v ,
exp exp
r r out
V out V r
kk
outr
P W w P v V v
F v F v
vv
c c
(5.7)
5.5. Mathematical Model of Economic Dispatch with Wind
Power and Emission
This section describes the problem formulation of CEED model including wind power.
The model aims at minimizing the operation costs (including fuel cost, wind power cost)
and emission cost while satisfying the given constraints. In [192], an economic dispatch
(ED) model incorporating wind power is developed. In order to accurately characterize
the uncertainty in the availability of wind energy, penalty costs functions for both
underestimation and overestimation cases were added. Inspired by the previous work, a
similar CEED model is developed with an additional term incorporated to account for
government wind farm subsidy. To address the uncertainties in wind power production,
the wind speed distribution probability functions are applied in formulating the
optimization model.
5.5.1. Objective Function
The objective function is formulated to minimize the total system operation costs and
greenhouse gases (CO2 and N2O) emission costs. A cost function is obtained based on
the ripple curve for more accurate modeling which contains higher order nonlinearity
and discontinuity due to the valve point effect and should be refined by a sine function
[193]. The overall objective function can be expressed as the sum of these two terms,
1 2.Min Cost Cost (5.8)
70
(1). Total system scheduling costs
1 , ,
1 1
, ,
1
, ,
1
,
M N
i i w j j av
i j
N
p j j av j
j
N
s j j av
j
Cost C p C w
C w w
C w
……..………………………(5.9)
2
,minsini i i i i i i i i i iC p a b p c p d e p p (5.10)
where, i iC p is the fuel cost function of thermal generator i.
, ,w j j avC w is the wind
power cost of the wind farm. If the wind farm is owned by the system operator, this term
may not exist which is considered in the case studies of this paper later on.
Here, ,p jCis the cost coefficient which can be either the underestimation cost coefficient
,u jCor the overestimation cost coefficient ,o jC
. Depends on different situations,
, ,( , )p j j av jC w wmay have two different mathematical expressions.
When actual wind power is larger than predicted power:
, , , ,( , ) ( )p j j av j u j j av jC w w C w w (5.11)
When actual wind power is smaller than predicted power:
, , , ,( , ) ( )p j j av j o j j j avC w w C w w (5.12)
The underestimation cost , ,u j j av jC W w
occurs if the actual generated wind power is
more than the predicted, thus the system operator should compensate for the surplus
wind power cost. On the other hand, if the actual wind power is less the scheduled power,
the operator needs to purchase from an alternate source and pay the overestimation cost
, ,o j j j avC w W. The last term in the Eq. (5.9) is the wind power subsidy cost
, ,s j j avC w.
As one of the renewable energy subsidy projects, wind farms in many countries receive a
largely covert subsidy. An excellent example is the Renewables Obligation (RO) in UK.
The RO is designed to encourage generation of electricity from eligible renewable
sources in the UK [194]. In this paper, the wind farm was assumed to receive a fix cost
subsidy for generating every MW wind power.
According to [192], the cost of underestimation will be assumed as follow,
,
, ,
, , ,
,
r j
j
r j r j
j j
w
u j j av j u j j Ww
w w
u j W j Ww w
C W w C w w f w dw
C w f w dw w f w dw
. (5.13)
In terms of overestimation case, the cost equation will be in the similar manner,
71
, , ,0
,0 0
j
j j
w
o j j j av o j j W
w w
o j j W W
C w W C w w f w dw
C w f w dw w f w dw
. (5.14)
The Eqs. (5.11) and (5.12) can be solved through the wind power probability Eqs.
(5.4)-(5.7).
(2). Greenhouse gases (GHGs) emission costs
2 ,
1
M
GHG i i
i
Cost F p
(5.15)
where,
,GHG i i i iF p h EM p (5.16)
2( )i i i i i i i iEM p ef d e p f p (5.17)
Eq. (5.13) represents the fuel cost function of thermal generators. Eq. (5.14) expresses
the GHGs emission cost function, h is the given GHGs emissions price which is
determined by regulations and markets. ( )i iEM p is the GHGs emissions of thermal
generator i and is calculated by Eq. (5.15). efi is the fuel emission factor of GHGs for
thermal generator i. di, ei, and fi are fuel consumption coefficients, the GHGs are CO2
and N2O in this paper.
5.5.2. System Constraints
,min ,maxi i ip p p (5.18)
,0 j r jw w (5.19)
1 1
M N
i j d loss
i j
p w p p
(5.20)
Inequality constraint Eq. (5.16) defines the limitations of thermal units output from the
lower to the upper bound. Constraint Eq. (5.17) shows the wind power output limitations,
while Eq. (5.18) gives the power balance between generations and loads including the
transmission losses.
5.6. Hybrid Optimization Algorithm
In this section, a hybrid optimization algorithm is presented, which combines IPM and
PSO together. Compared with other classical approaches, IPM provides better
computational performance for large-scale problems and PSO is computationally
inexpensive in terms of memory and speed. The most attractive features of PSO could be
summarized as, simple concept, easy implementation, fast computation, and robust
72
search capability [183]. This combination can overcome individual disadvantages and
benefit from each others’ advantages. The corresponding computation time can be
largely reduced and the quality of final solutions can be improved as well.
5.6.1 Interior Point Method (IPM)
Interior point method approach to constrained minimization is to solve a sequence of
approximate minimization problems [195],[196]. This algorithm was firstly developed
by Narendra Kamarkar in 1984 [197]. One of the variants of these interior point methods
is the affine-scaling primal method [198].
Consider a linear programming problem, expressed as
.
. .0
TMin c x
Ax bs t
x
. (5.21)
Assume that a starting feasible solution vector x0 is available, for the new iterate x-new,
to make an improvement, x must move in a descent direction while maintaining
feasibility. Consequently, the new iterate x-new should satisfy the following constraints,
0
T T
new
new
c x c x
Ax b
. (5.22)
If the new iterate x-new, and the current iterate x0 are related through x-new=x0+dx,
where dx is the step direction vector, then the following two conditions must hold
0 0
0
0
0
T T T
new
T
new
c x c x dx c x
c dx
Ax A x dx b
Adx
. (5.23)
Given a starting vector, 1 2[ , , , ] ,T
nx x x x its components are scaled in some manner to
yield the scaled vector x1 whose components are at equal distance from all the walls.
The diagonal of scaling matrix D is
D diag x . (5.24)
With these definitions, original vector x and the scaled vector x1, are related through
1
1 0x D x . (5.25)
Scaling the original linear programming problem shown in Eq. (5.19) leads to the scaled
linear programming problem given by
73
1 1
1 1
1
.
. .0
TMin c x
A x bs t
x
. (5.26)
where, 1A AD , 1c Dc .
With the step direction vector dx , we take a step in that direction and obtain the next
iterate of the solution vector x. This is found from the updating formula given by
0x x dx . (5.27)
By using a maximum allowable step size α in that direction and a step size factor ρ, the
new iterate of the solution vector x becomes
0 ,0 1x x dx . (5.28)
5.6.2 Particle Swarm Optimization (PSO)
PSO is a global search technique originally introduced by Kennedy and Eberhart [199].
It simulates the social evolvement knowledge, probing the optimum by evolving the
population which may include candidate solutions. In the classical PSO, each individual
is treated as a particle in the space, with position and velocity vectors. The algorithm
maintains a swarm of particles, where each particle represents a potential solution to the
objective problem.
For a given n-dimensional problem, the position and velocity vectors of a particle in the
PSO can be represented as
,1 ,2 ,
,1 ,2 ,
, , ,
, , ,
j j j j n
j j j j n
x t x t x t x t
t t t t
(5.29)
The core idea of the classical PSO is the exchange of information among the global best,
population best, and current particles, which can be done as follows
1
2
1
1 1
j j pb j
gb j
j j j
t t r p t x t
r p t x t
x t x t t
(5.30)
where, j is velocity vectors, is inertia weight, pbp is local best particle, gbp
is
global best particle, 1.65 , 1.81 ;
74
5.6.3 Hybrid Optimization Method
The procedures of the proposed hybrid algorithm are summarized as the follows,
Step-1. Load history wind data, generators and wind turbines settings, emission
parameters, and forecasted wind farm data;
Step-2. Solve the CEED problem without valve-point effects incorporating wind power
using IPM;
Step-3. Calculate the updated constraints using Eq. (5.29) [200], and randomly generate
initial population around the solution obtained from IPM for PSO;
'
,min ,min
'
,max ,max
max ,
min ,
1
i i i i
i i i i
i i
p p p
p p p
e
(5.31)
Step-4. Solve the CEED problem with valve-point effects incorporating wind power
using PSO;
Step-5. Save and output final solution.
Application of this approach in CEED problem incorporating wind power will be
presented in the following section.
5.7. Australian Regional Reference Case Studies
In the case study part, the CEED model with wind power was evaluated using the
historical wind speed dataset from a wind observation station in Tasmania, Australia.
The data was provided by the Australian Bureau of Meteorology [201]. Here we assume
that the wind speed data from a large wind farm and use the data to estimate the
generated wind power. The wind speed distribution frequency and the corresponding
Weibull distribution parameters are presented in Fig. 18.
The Vestas V90 3.0 MW wind turbine is selected for the case studies. It is a pitch
regulated upwind wind turbine with active yawing and a three-blade rotor. It has a rotor
diameter of 90 m with a generator rated at 3.0 MW. The Vestas V90 3.0MW is widely
used in the wind plants in Australia and has a proven high efficiency. The parameters of
the associated Weibull distribution factor and wind farm parameters can be calculated
from the wind speed data and are given in Table 8.
75
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Wind Speed (m/s)
Fre
quency
Weibull Fitting: y=(k/c)*(x/c)(k-1)*exp(-(x/c)k) --- k = 1.89, c = 5.49 (m/s)
Wind Distribution
Weibull Fitting
Figure 18. Wind Speed Distribution and Weibull Fitting
Table 8 Wind Power Factors
c k ө vin vout vr wr Cw,j Cu,j Co,j Cs,j
5.5 1.89 0 4 25 16 3 0 60 20 10
The proposed algorithm is implemented for a test system including 6 thermal generators
and 1 large wind farm. There are 3 coal-fired units, 2 gas-fired units, and 1 oil-fired unit
in this system. The wind farm totally consists of 100 Vestas V90 3.0 MW wind turbines
located in a coherent geographic area. The predicted wind power for the wind farm is
denoted as wj and is 15% of the rated power, which is 0.45 MW. Depended on the actual
generated wind power, the extra cost will be determined by overestimation case or
underestimation case. According, the maximum capacity of the system under
investigation is 2030 MW and 2330 MW incorporating with wind power. The fuel cost
coefficients, generator limits, and fuel consumption coefficients are shown in Tables 9
and 10, [202].
Table 9 Fuel Cost Coefficients
Unit Fuel Cost Coefficients
ai bi ci di ei
G1 (Coal) 2000 10 0.002 200 0.084
G2 (Coal) 2500 15 0.0025 300 0.035
G3 (Coal) 6000 9 0.0018 400 0.042
G4 (Gas) 923.4 18 0.00315 150 0.063
G5 (Gas) 950 20 0.0032 100 0.084
G6 (Oil) 124.8 23.4 0.00343
2
80 0.098
Note: The coefficients of ai, bi, and ci are in $, $/MW and $/MW2.
76
Table 10 Fuel Consumption Coefficients and Generator Limits
Unit Fuel Consumption Coefficients
Pmin Pmax fi gi hi
G1
(Coal) 40 0.2 0.00004 20 110
G2
(Coal) 50 0.3 0.00005 20 100
G3
(Coal) 80 0.12
0.00002
4 120 600
G4 (Gas) 2462.4 48 0.0084 110 520
G5 (Gas) 2500 50 0.009 110 500
G6 (Oil) 1.248 0.234 3.43e-05 40 200
G7
(Wind) 0 0 0 0 300
Note: The coefficients of fi, gi, and hi are in t, t/MW and t/MW2 for coal/oil units. The coefficients of fi, gi,
and hi are in m3, m
3/MW and m
3/MW
2 for gas unit.
In this paper, two of the most concerned GHGs emissions, CO2 and N2O are considered
in the model. The emission characteristics of the units and emission allowance price are
shown in the Tables 11 and12.
Table 11 Emission Factors of Units
Emission
Factor Coal (kg/kg) Gas (kg/m
3) Oil (kg/kg)
efco2 3.1604 1.84 2.8523
efn2o 1.29e-03 3.4e-04 3.3e-04
Table 12 Emission Prices
Fuel CO2 ($/t) N2O ($/kg)
Price 1.5 5.0
5.7.1. Economic Dispatch Model without and with Wind Farm
In this case study, the total system load is 1200 MW and the system loss is assumed to
be zero for simplicity. The basic ELD model with and without wind farm are tested on
the system and the simulation results are shown in Tables 13, 14 and Fig. 19.
Table 13 Solution of ELD without Wind Farm
Unit Power
(MW)
Operation Cost
($)
G1 (Coal) 96.1420 3002.41
G2 (Coal) 99.6707 4123.64
G3 (Coal) 593.5137 12320.25
G4 (Gas) 259.2695 5805.12
G5 (Gas) 111.3000 3226.54
G6 (Oil) 40.1041 1069.57
Total 1200.0000 29547.53
Overall
Cost 29547.53
77
Table 14 Solution of ELD with Wind Farm
Unit Power
(MW)
Operation Cost
($)
G1 (Coal) 94.9404 2969.79
G2 (Coal) 99.6663 4123.62
G3 (Coal) 593.9294 12328.37
G4 (Gas) 258.7817 5800.15
G5 (Gas) 111.4298 3230.31
G6 (Oil) 40.4079 1079.15
G7 (Wind) 0.8446 1586.53
Total 1200.0000 31117.92
Overall
Cost 31117.92
It can be seen that the solution of ELD with wind farm succeeds in reducing generated
power and operation costs of some fuel units (G1, G3, G4 and G6). However, the
outputs and scheduling costs of generators G2, G5 were increased slightly. The reason is
that although wind power generators have lots of advantages such as no emission, the
operation cost is really expensive. With the wind power generator, part of the load of
high cost units (G1, G3, G4, G6) is shifted to comparative low cost units (G2 and G5).
The operation cost of solution of ELD with wind farm is highly increased in comparison
with solution of ELD without wind farm. In addition, the wind power government
subsidy is just a little bit due to the little output wind power.
G1 G1 G2 G2 G3 G3 G4 G4 G5 G5 G6 G6 G70
200
400
600Solution of ELD without and with Wind Farm
Genera
ted P
ow
er
(MW
)
G1 G1 G2 G2 G3 G3 G4 G4 G5 G5 G6 G6 G70
5000
10000
15000
Opera
tion C
ost
($)
Without Wind Farm
With Wind Farm
Without Wind Farm
With Wind Farm
Figure 19. Solutions of ELD Models without and with Wind Farm
The real generated wind power in this case is 0.8446 MW which is far less than the
predicted wind power (45MW), and the cost incurred by overestimation will be applied.
The operator needs to purchase more power from another source. Furthermore, the
common ELD model does not take in account the emission issue. The incorporation of
wind power in simple ELD problem is not an economic solution due to the really high
operation cost of wind power.
78
5.7.2. CEED Model without and with Wind Power
In this case study, the system load is 1600 MW and the system loss power is assumed to
be zero. The CEED model with and without wind farm are performed on the test system
and the simulation results are shown in Tables 15, 16 and Fig. 20.
Table 15 Solution of CEED without Wind Farm
Unit Power
(MW)
Operation
Cost
($)
Emission Cost
($)
G1 (Coal) 95.5408 2986.10 3202.99
G2 (Coal) 20.7747 2820.83 3029.61
G3 (Coal) 598.7496 12414.63 8641.41
G4 (Gas) 509.7226 10924.30 852.97
G5 (Gas) 333.1363 7978.45 590.56
G6 (Oil) 42.0759 1131.62 495.65
Total 1600.0000 38255.93 16813.19
Overall
Cost 55069.12
Table 16 Solution of CEED with Wind Farm
Unit Power
(MW)
Operation
Cost
($)
Emission Cost
($)
G1 (Coal) 95.3455 2980.80 3200.81
G2 (Coal) 21.3548 2835.68 3039.05
G3 (Coal) 569.0520 11708.60 8404.66
G4 (Gas) 507.6528 10885.02 849.54
G5 (Gas) 296.0316 7159.18 530.05
G6 (Oil) 40.0636 1068.30 474.47
G7 (Wind) 70.4998 3230.97 0.00
Total 1600.0000 39868.55 16498.57
Overall
Cost 56367.12
G1 G1 G2 G2 G3 G3 G4 G4 G5 G5 G6 G6 G70
200
400
600Solution of CEED without and with Wind Farm
Genera
ted P
ow
er
(MW
)
G1 G1 G2 G2 G3 G3 G4 G4 G5 G5 G6 G6 G70
0.5
1
1.5
2
2.5x 10
4
Tota
l C
ost
($)
Without Wind Farm
With Wind Farm
Without Wind Farm
With Wind Farm
Figure 20. Solutions of CEED Models without and with Wind Farm
79
The system load is increased to 1600 MW in case 2. But the load is still less than the
maximum capacity for both thermal units and system with wind power. The objective of
CEED is to minimize the total system operation costs and greenhouse gases (CO2 and
N2O) emission costs. It is clear that part of the load of highly polluted fuel fired units
(G1~G6) is shifted to no emission polluted wind power generator (G7). Although the
wind power cost is expensive, emission cost were decreased in the solution of CEED
with wind farm. The reason is that the government wind power subsidy is directly
proportional to the output wind power.
In this case, the real generated wind power is 70.4998 MW which is larger than the
predicted wind power (45MW). The underestimation situation will be considerate and
the cost for not using all wind power available from wind turbine should be applied.
From Tables 15 and 16, we can find that the CEED model with wind farm reduces the
emission cost dramatically in comparison with CEED solution without wind power
because of the no-emission character of wind energy.
In Eq. (5.9), the government wind power subsidy is directly proportional to the output of
wind power. Thus, the overall cost is acceptable from a standpoint of wind power system
operation. Therefore, the simulation results have shown that the proposed CEED with
wind energy gives a better emission solution efficiently and economically.
5.7.3. Hybrid Optimization Methods Compare with Other
Approaches
In order to evaluate the performance of the proposed method, GA, IA, and PSO are
employed in the case studies. For comparison purposes, these algorithms are used
directly to solve the CEED problem with wind power. For the proposed IPM-PSO
algorithm, the population size is 100 and maximum iteration is 3 for PSO. Meanwhile, in
order to make a fair comparison of the other approaches, we fixed the same population
size as 100 and tested them to approach maximum iteration 100. The initial crossover
and mutation rates for GA and IA were all set as 80% and 5%. All the programs were
run on a 2.66 GHz, Intel Core 2, with 4G RAM desktop. Table 17 shows the results out
of 50 runs with each method.
80
Table 17 Comparison of Different Approaches
Algorithm Best Solution
($)
Average
Solution ($)
Average Time
(s)
GA 57369.97 57916.20 13.28
IA 57180.98 57669.57 12.57
PSO 56714.06 57417.04 8.01
IPM+PSO 56367.12 56567.02 1.31
A comparison with other approaches is made to evaluate the proposed algorithm which
is shown in Table 17. As is shown, we can conclude that, the proposed method can
greatly enhances the searching ability, ensures quality of average solutions, saves
computation time, and also efficiently manages the system constraints.
5.8. Conclusion
This paper developed a hybrid method combining the IPM and PSO to achieve a faster
and better optimization performance. The method was successfully applied to solve the
power system ELD problem considering GHGs emissions and wind power in an
integrated CEED model, where the valve point loading is also taken into account. In the
present work, the wind speed distribution probability functions are applied in
formulating the optimization model to address the uncertainties involved.
The proposed hybrid method was applied to solve the CEED problem of a test system
involving 6 thermal units and 1 wind farm. The comparisons were made between the
classical ELD and the proposed CEED model with and without wind farm. The proposed
CEED model with wind farm shows a better performance in terms of less emission cost.
In addition, the resultant overall dispatching cost is also optimized considering the
government subsidy. Furthermore, the proposed hybrid optimization method was
compared with other optimization approaches for the studied case. The simulation results
show that the hybrid method is better in terms of the speed and accuracy. Compared to
the classical PSO and other methods, it can be concluded that the hybrid method greatly
enhances the searching ability and efficiently manages the system constraints, therefore
providing a new and efficient tool for the CEED problem.
81
Chapter 6. Power System Operations
Considering Wind Power Uncertainty and
Carbon Tax in Australia
6.1. Nomenclature , ,i i ia b c Cost coefficients of thermal unit i .
,i id e Valve-point effects coefficients of thermal unit i .
c Scale factor of Weibull distribution.
,o jC Cost coefficients for purchasing reserve power from other source due to
overestimation case.
,u jC Cost coefficients for not using all generated wind power due to
underestimation case.
, ,i i if g h Fuel consumption coefficients of thermal unit i .
k Shape factor of Weibull distribution.
m Population size.
M Number of thermal power units.
n Population dimension.
N Number of wind plants.
dp Total system demand.
lp Total transmission losses.
,t ip Actual power generated by thermal unit i .
jw Predicted power generated by wind turbine j .
,av jw Scheduled power generated by wind turbine j .
, ,in r outv v v Cut-in, rated, and cut-out wind speeds.
,r jw Rated power of wind turbine j .
6.2. Introduction
In the recent years, due to the impacts of greenhouse gases (GHGs) on the global
warming, many countries are placing enormous pressure on the energy sector to reduce
carbon emissions. The combustion of fossil fuels including coal, oil, and gas is the main
source of GHGs. COx, NxO, and SOx are the three major GHGs, and CO2 is the most
important one of these gases to produce greenhouse effects. In order to curb GHGs and
build a clean energy economy, carbon tax has been widely used in many countries.
Carbon tax is an environmental tax that is levied on the carbon content of fuels. Because
Australia is one of the world’s worst greenhouse gas polluters, due to its heavy reliance
on coal for electricity, the Australian government has proposed the detailed carbon tax
82
policies. In 2011, the Gillard government has announced publicly that 500 largest
polluters in Australia would be imposed a carbon tax at A$23/t of carbon emission,
effective from July 01, 2012. Through this carbon tax policy, the government encourages
the power industry to invest cleaner forms of power like wind and solar energy.
Although it imposes great impacts on the traditional coal industry, for the renewable
energy sector this tax is a positive kick start.
The increasing environmental challenges force enterprises to modify their system
operation routines to reduce carbon emissions. Economic dispatch (ED) aims to allocate
power generation to match load demand and minimize total operational cost while
satisfying all the power units and system constraints [203]. Better dispatch strategies
normally can provide quick solutions to improve the current situation of system
operation and reduce carbon emissions dramatically. On the other hand, exploiting
renewable energy is another effective way to mitigate energy source deficiency, control
GHGs emissions, and achieve smart grid visions [204],[205]. Wind power, one of the
most appealing renewable energy resources has gained widespread concerns during the
last decade. Along with the introduction of various emission reduction schemes,
increasing number of wind turbines have been installed around the world [206].
However, due to the intermittent and stochastic characteristics of wind resource, wind
power brings great challenges to power system economic dispatch problem. One of the
major challenges is how to effectively accommodate the wind forecasting errors.
Because variations of wind speed directly influence the power output of wind farms,
which then causes difficulties in estimating suitable system reserve margin to ensure
secure and reliable system operations. As a sequence, high penetration of wind power
also causes high potential risks and more difficulties in power system operation.
Although wind speed is difficult to forecast by single predictor, composite forecast
model can statistically produce an optimal forecast by computing prediction results from
a number of different methods. The fundamental concept is that if the errors in the
forecasts produced by different methods are unbiased and have a low degree of
correlation with each other, the random errors from the individual forecasts will tend to
offset each other, with the result that a composite of the forecasts will have lower errors
than any individual forecast. Moreover, huge number of researches has indicated that
wind speed follows Weibull distribution approximately [207]. In order to assist with
management of the uncertainties of wind forecasts, extensive researches have been
conducted to develop kinds of probabilistic optimization strategies [208],[209]. In this
83
paper, a computation framework for power system daily operations considering wind
power uncertainties is proposed, and is shown in Fig. 21, which includes two major steps,
wind power forecasting and stochastic unit commitment/economic dispatch.
Wind Farm &
Observation
Stations
Wind Data
Processing
Numerical
Weather
Prediction
Data Mining &
Machine
Learning
Assembled
Prediction
Model
Wind Farm
Aggregated
Power Curve
Turbine Model
& Wind Farm
Layout
Historical
Wind
DatabaseMeasurement
Wind Speed
Samples
History Wind
Speed and
Direction
Terrain,
Location,
Wake Effects
System
Demand
Predictor
Unit
Commitment
Economic
Load
Dispatch
System
Security
Constraints
On / Off
States
Power
Generating
Units
Setting Points
Wind Power
Uncertainty
Stochastic
Optimization
Load Curve
Figure 21. Computational Framework Considering Wind Power Uncertainties
In order to accommodate the revised dispatch strategy, more efficient solvers are needed.
Different heuristic techniques have been developed to solve the classical ED problems
with constraints, to namely simulated annealing (SA) [210], genetic algorithm (GA)
[211], evolutionary programming (EP) [212],[213], tabu search (TS) [214], pattern
search (PS) [215], particle swarm optimization (PSO) [216],[217], as well as differential
evolution (DE) [218],[219]. Based on our experience, when compared with other
approaches, the PSO is computationally inexpensive in terms of memory and speed.
However, these heuristic methods do not always guarantee discovering globally optimal
solutions in finite time, especially when being applied into large-scale optimization
problems. Therefore, more sophisticated computational tools are required. The
quantum-inspired evolutionary algorithms (QEAs), first proposed in [220], are based on
the principles of quantum computing, which can strike right balance between exploration
and exploitation more easily when compared with the conventional EAs. Quantum bit is
used as probabilistic representation of particles, defined as the smallest information unit.
A string of quantum bits consist of a quantum bit individual. Quantum rotation gate is
defined as an implementation to drive individuals moving toward better solutions, and
eventually find the global optimum. The QEAs can explore the target space with a
84
smaller number of individuals and exploit global solution within a short span of time
[221]-[223]. In this paper quantum-inspired particle swarm optimization (QPSO) is used.
6.3. Probability Analysis of Wind Power based on non-linear
wind power curve
In last chapter, we have developed three portions of WECS power output. Compared
with the wind power curve that we have discussed in last chapter, here the typical wind
power curve is non-linear. As a result, the wind power turbine’s output power can not be
described as what we have used in last chapter. A new portions of WECS power output
and the corresponding probabilities (CDF or pdf) should be derivate again. The
nonlinear wind power curve is shown in Fig. 22.
Wind Speed (m/s)vin vr vout
wr
Win
d P
ow
er (
MW
)
Figure 22. Nonlinear wind power curve
The total wind power becomes PW=(mWV2)/2=(ρAV
3)/2 (MW). As a result, wind power
output can be described as,
3
0,
1,
2
,
in out
in r
r r out
W V v or V v
W AV v V v
W w v V v
(6.1)
The derivation can be analyzed in a similar manner as last chapter. Here we directly give
three portions of WECS power output and the corresponding probabilities (CDF or pdf).
(1) For inV v or outV v ,
0
1
1 exp exp
in out
V in V out
k k
in out
P W P V v P V v
F v F v
v v
c c
(6.2)
85
(2) For in rv V v ,
31
2W AV
, depending on the definition of cumulative distribution
function, the CDF of WECS output power can be described as, the result is totally
different with what we have discussed in last chapter:
3
1 1
3 3
1
2
2 2
W
V
F w P W w P W AV w
w wP V F
A A
(6.3)
We can obtain the pdf of W by differentiating with respect to w. The chain rule for
derivatives can be used,
dF dF du
dw du dw
, where u is the argument of F,
1
32wu
A
, and then
we obtain,
3 31
32 1 2exp
3
k kk
W k k
k wf w w
A Ac c
(6.4)
(3) For r outv V v ,
exp exp
r r out
V out V r
kk
outr
P W w P v V v
F v F v
vv
c c
(6.5)
6.4. Stochastic Economic Dispatch Formulation
This section describes the problem formulation of stochastic ED model considering wind
power and carbon tax. The model aims at minimizing operational costs (including fuel
cost, wind power cost) and carbon emission tax while satisfying the given constraints.
To address the uncertainties in wind power generation prediction, the wind speed
distribution probability functions are applied in formulating the optimization model.
6.4.1. Objective Function
The objective function is formulated to minimize the expected value of the total system
operational costs, which can be represented as follows,
86
,
, , , ,, 1 1 1
, ,
1 1
.i av j
M M N
Total t i i e i i w j av jp w i i j
N N
u j ue o j oe
j j
Min E C C p C p C w
C E W C E W
(6.6)
The first item ,t i iC p is the cost function of thermal generator i. A cost function is
obtained based on the ripple curve for more accurate modeling, which contains higher
order nonlinearity and discontinuity due to valve point effects [224]. It can be defined as,
2
, ,minsint i i i i i i i i i i iC p a b p c p d e p p (6.7)
The second item in the objective function is the carbon tax and it can be represented as,
,
1
M
e i i Tax i i
i
C p C EM p
(6.8)
2
i i i i i i i iEM p ef f g p h p (6.9)
Eq. (6.8) expresses the carbon emission cost function, TaxC is the given carbon tax price
which is determined by Australian regulations and markets. i iEM p is the carbon
emissions of thermal unit i , which can be calculated by Eq. (6.9). ief is the fuel
emission factors of CO2 for thermal generator i . if , ig , and ih are fuel consumption
coefficients.
The third component , ,w j j avC w
represents the production cost of wind power. If the
wind farm is owned by the system operator, this term may not exist.
Due to the uncertainty of wind power forecasts, the predictions normally have some
errors. The fourth component of Eq. (6.6) is the underestimation cost ,u j ueC E W. The
underestimation situation occurs if the actual generated wind power is more than the
predicted, thus the system operator should compensate for the surplus wind power cost.
On the other hand, if the actual wind power is less than the scheduled power, the
operator needs to purchase power from an alternate source and pay the overestimation
cost ,o j oeC E W which is the fifth component in Eq. (6.6). Because the fourth and fifth
components in Eq. (6.6) contain random variable, depending on the definition of
expected value of an arbitrary function [192], the expected value of underestimation cost
will be assumed as follow,
87
,
, ,
, ,
,
r j
j
r j r j
j j
w
u j ue u j j Ww
w w
u j W j Ww w
C E W C w w f w dw
C wf w dw w f w dw
(6.10)
In terms of overestimation case, the expected value of cost equation will be in the similar
manner,
, ,0
,0 0
j
j j
w
o j oe o j j W
w w
o j j W W
C E W C w w f w dw
C w f w dw wf w dw
(6.11)
The Eq. (6.10) and (6.11) can be solved through the wind power probability Eqs.
(6.2)-(6.5).
6.4.2. System Constraints
,min ,maxi i ip p p (6.12)
, ,0 av j r jw w (6.13)
,
1 1
M N
i av j d loss
i j
p w p p
(6.14)
Inequality constraint in Eq. (6.12) defines the limitations of thermal units output from
the lower to the upper bounds. Constraint Eq. (6.13) shows the wind power output
limitations, while Eq. (6.14) gives the power balance between generation and loads
including the transmission losses.
6.5. Quantum-Inspired Particle Swarm Optimization
6.5.1. Particle Swarm Optimization
The introduction of Particle Swarm Optimization (PSO) has been discussed in Section
5.6.2.
6.5.2. Quantum-Inspired Particle Swarm Optimization
QPSO has stronger search ability and quicker convergence speed since it not only
introduces the concepts of quantum bit and rotation gate but also the implementation of
self-adaptive probability selection and chaotic sequences mutation. In the QPSO, the
88
state of a particle is depicted by quantum bit and angle, instead of particle position and
velocity in classical PSO.
Quantum bit, the smallest unit in the QPSO, is defined as a pair of numbers,
1,2, ,,
1,2, ,
ji
ji
t j m
i nt
(6.15)
The modulus
2
ji tand
2
ji tgive the probabilities that the quantum bit exists in
states ―0‖ and ―1‖, respectively, which must satisfy,
2 2
1ji jit t (6.16)
A string of quantum bits consists of a quantum bit individual, which can be defined as,
1
1
1
, , , ,
, , , ,
, , , ,
j ji jn
j
j ji jn
j ji jn
t t tq t
t t t
q t q t q t
(6.17)
A quantum bit is able to represent a linear superposition of all possible solutions due to
its probabilistic representation [222]. Totally 2n kinds of individuals can be represented
by combinations of different quantum bit states. This quantum bit representation has
better characteristics of generating diversity in population than other representations.
Because of the normalization condition, the quantum angle can be represented as,
| cos | 0 sin |1
arctan
ji ji ji
ji
ji
ji
q t t t
tt
t
(6.18)
The quantum bit individual can be represented in the form of quantum angles,
1
1
, , , ,
, , , ,
j j ji jn
j j ji jn
q t q t q t q t
t t t t
(6.19)
The fundamental update mechanism of QPSO is evolving quantum bits and angles, by
which the updated quantum bits should still satisfy the normalization condition. The
quantum rotation gate update equation could be calculated by,
89
1 2
1j j
pb j gb j
t t
r t r t
(6.20)
where, j is angle change, j is current angles, pb is local best angles, and gb
is
global best angles.
1 cos 1 sin 1
1 sin 1 cos 1
ji ji ji ji
ji ji ji ji
t t t t
t t t t
(6.21)
And quantum rotation gate can be illustrated in Fig. 23, [220].
Figure 23. The Quantum Rotation Gate
Although the quantum bit and rotation gate representation has better characteristics of
population diversity, the premature convergence problem could still appear. In order to
address this problem, the implementations of self-adaptive probability selection and
chaotic sequences mutation are adopted.
The individual affinity value can be defined as follows. We calculate the fitness value of
every individual in current population and rearranged the population in terms of fitness
value in ascending sequence. The affinity is designed by using location index of
quantum bit individual.
1
1j
jAs q t r r
(6.22)
where, r is random number in 0,1. The most attractive feature of this definition is
that the affinity value is only relevant to the location index rather than real fitness value.
The individual concentration can be defined as,
90
1
,m
j a
a
j
Ks q t q t
Cs q tm
(6.23)
1, ,
,0,
j a
j a
q t q t lKs q t q t
otherwise
(6.24)
Roulette selection is implemented based on the computed selection probabilities. This
allocates every quantum bit individual a probability of being selected proportionally
according to selection probabilities. The selection probabilities are,
1
j
j
jm
j
j j
As q t
Cs q tPs q t
As q t
Cs q t
(6.25)
Therefore, the quantum bit individuals can be selected according to individuals selection
probabilities, guaranteeing that individuals having high affinity values are selected; and
the one that has high concentration value could be rejected, which helps the algorithm
converge at optimal solutions ultimately.
Chaotic sequences mutation is implemented next. A widely used system evidencing
chaotic behavior is the logistic map, which can be expressed as follows,
1 1 , 0,4g t g t g t (6.26)
The behaviour of the above chaotic system is greatly influenced by the parameter [225].
A small difference in the initial value causes substantial differences in long time
behavior. Here we select μ=4, and the mutation implementation can be defined as,
1 4 1
0,1 , 1,2, ,
i i i
i
g t g t g t
g t i n
(6.27)
And,
' 1 1t
q t q t s g tT
(6.28)
Notice that there is a user-defined control variable s, which is the mutation control
constant. Selection of this value depends on practical problem. In general, with little
91
knowledge about global optimum, it is difficult to constrain the mutation size to a
sufficiently small region. Initial solutions are usually far from the global optimum; hence
larger mutation may prove to be beneficial. But as the evolution progresses, later
solutions may be nearer to the global optimum and the mutation size should be reduced
gradually to help quick convergence. Here according to our experience, the range
[0.1,0.5] is suitable.
6.5.3. Procedure of QPSO
The above steps are shown in Fig. 24, for completeness.
Termination Criterion
Satisfied for Run?
End
No
Yes
Run=0
Create Initial Population for Run
Gen=0
Evaluate Fitness Value of Each Individual in Population
Update Global Best and Local Best Individuals
Global Best Individual Remain
Same for Gens?
Evolve Individuals by Quantum Bit and Rotation Gate
Insert New Individual into Population
Gen=Gen+1
Calculate Affinity and Concentration Values
Roulette Selection
Chaotic Sequence Mutation
Update Quantum Bits and Angles
Designate Result for Run
Run=Run+1
Run=N?
Yes
No
Figure 24. Flowchart of Quantum-inspired Particle Swarm Optimization
6.6. Case Studies
The proposed method is implemented on a benchmark system including 6 thermal
generators and 2 wind farms. These thermal generators include 3 coal-fired units, 2
gas-fired units, and 1 oil-fired unit. These 2 wind plants consist of 30 Vestas V90 3.0
MW wind turbines and 20 Sinovel SL3000 3.0 MW wind turbines respectively, locating
in two coherent geographic areas. Both of these two types of machines are pitch
92
regulated upwind wind turbines with active yaw and three-blade rotor. For simplicity,
the wind turbine power curve is linearized in the computation. The fuel cost coefficients,
generator limits, fuel consumption coefficients, and emission factors are shown in Tables
18 [226]. Accordingly, the maximum capacity of the test system under investigation is
2330 MW without wind power and 2480 MW with wind power. The historical wind
dataset was obtained from two wind observation stations, which was provided by the
Australian Bureau of Meteorology [227]. The wind speed distribution and Weibull
fitting is given in Fig. 25. The characteristics of wind turbine and penalty cost
parameters are provided in Table 19. According to the current exchange rate, the carbon
tax is fixed as USD$20/t.
Table 18 Generator Parameters
Unit Type pmin pmax Fuel Cost Coefficients Fuel Consumption Coefficients
a b c d e f g h
G1 Coal 20 110 2000 10 0.002 200 0.08 40 0.2 0.00004
G2 Coal 20 100 2500 15 0.0025 300 0.04 50 0.3 0.00005
G3 Coal 120 600 6000 9 0.0018 400 0.04 80 0.12 0.000024
G4 Gas 110 520 923.4 18 0.00315 150 0.06 2462.4 48 0.0084
G5 Gas 110 500 950 20 0.0032 100 0.08 2500 50 0.009
G6 Oil 40 200 124.8 23.4 0.00343
2 80 0.10 1.248 0.234
0.0000343
2
G7 Wind 0 90 0 0 0 0 0 0 0 0
G8 Wind 0 60 0 0 0 0 0 0 0 0
Note: (1) The coefficients of ai, bi, ci, and ei are in $, $/MW, $/MW2, and $/MW.
(2) The coefficients of fi, gi, and hi are in t, t/MW, and t/MW2 for coal/oil units, are in m
3, m
3/MW,
and m3/MW
2 for gas unit.
Table 19 Wind Farm Parameters
Plant Model No c k vin vout vr wr Cw,j Cu,j Co,j
1 Vestas 30 4.6024 1.8862 4 25 16 3 0 70 20
2 Sinovel 20 4.4363 1.7128 3 25 13 3 0 60 20
Table 20 Emission Factors of Generating Units
Emission Factor Coal (kg/kg) Gas (kg/m3) Oil (kg/kg)
efco2 3.1604 1.84 2.8523
Table 21 Forecast System Demand and Wind Farm Outputs
Case Index Case I Case II Case III
Demand (MW) 1200 1400 1600
Wind #1 (MW) 15 20 18
Wind #2 (MW) 12 5 15
93
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Wind Speed (m/s)F
requency
Weibull Fitting: Wind Farm #1
Wind Distribution
Weibull Fitting
Figure 25. Wind Speed Distribution for Wind Farm #1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Wind Speed (m/s)
Fre
quency
Weibull Fitting: Wind Farm #2
Wind Distribution
Weibull Fitting
Figure 26. Wind Speed Distribution for Wind Farm #2
Table 22 Solution of ED Without and With Carbon Tax
Units Case I Case II Case III
Power (MW) Power (MW) Power (MW) Power (MW) Power (MW) Power (MW)
G1 (Coal) 93.09 22.72 94.11 43.86 94.65 95.76
G2 (Coal) 83.63 20.58 77.81 20.72 78.02 20.32
G3 (Coal) 583.71 578.13 578.89 577.90 579.84 577.97
G4 (Gas) 221.80 390.79 416.91 477.07 500.78 510.13
G5 (Gas) 111.49 110.91 110.66 173.87 214.38 295.42
G6 (Oil) 41.94 40.66 40.55 41.08 40.37 40.75
G7 (Wind) 63.46 3.27 79.28 40.91 45.64 58.33
G8 (Wind) 0.88 32.95 1.78 24.59 46.33 1.32
Total (MW) 1200.00 1200.00 1400.00 1400.00 1600.00 1600.00
Cost ($) 28703.62 48141.95 32361.06 52286.27 36400.77 56632.80
6.6.1. Economic Dispatch with and without Carbon tax
In this thesis, the transmission distance is assumed short. In this circumstance, the
transmission loss is quite small relative to the real power. So the transmission loss can be
assumed to be zero for simplicity. The forecasted system load and the outputs of two
wind farms are given in Table 21. The ED model with and without carbon tax is tested
on the benchmark system and the simulation results are shown in Table 22 and Fig. 27.
94
G1 G1 G2 G2 G3 G3 G4 G4 G5 G5 G6 G6 G7 G7 G8 G80
200
400
600Solution of ED without and with Carbon Tax
Pow
er
(MW
)
Without Carbon Tax
With Carbon Tax
G1 G1 G2 G2 G3 G3 G4 G4 G5 G5 G6 G6 G7 G7 G8 G80
200
400
600
Pow
er
(MW
)
Without Carbon Tax
With Carbon Tax
G1 G1 G2 G2 G3 G3 G4 G4 G5 G5 G6 G6 G7 G7 G8 G80
200
400
600
Pow
er
(MW
)
Without Carbon Tax
With Carbon Tax
Figure 27. Solutions of ED Models without and with Carbon Tax
From Table 22 and Fig. 27, it is clear that if the carbon tax is included in the proposed
ED model, the generating outputs of all the units will be affected, but the carbon
emission is reduced respectively. It shows that part of the load of highly polluted fuel
fired units (G1~G3) is shifted to no emission polluted wind generators (G7, G8), less
polluted gas generators (G4, G5), and oil generator (G6). For example, the generation
outputs of G2 in Table 22 are 83.63 MW, 77.81 MW, and 78.02 MW without carbon tax.
If a carbon tax is considered in the ED process, the generating power of G2 will decrease
to 20.58 MW, 20.72MW, and 20.32 MW, respectively. For G4, the generating power
increase from 221.80 MW to 390.79MW, from 416.91 MW to 477.07 MW, and from
500.78 MW to 510.13 MW respectively in the three cases.
In Case I where carbon tax is not considered, the real generated wind power of G7 is
63.46 MW which is larger than the predicted wind power 15 MW. The underestimation
situation will be considered and the cost for compensating for the surplus wind power
should be applied. Although the wind power prediction error penalty cost is expensive,
carbon tax penalty is decreased in the solution of ED with wind farm because of the
no-emission character of wind energy. In all the cases, because of the forecasted low
wind power outputs and high penalty cost, the final real generated wind power is not
very high. However the high overestimation and underestimation compensation cost of
wind turbines will make it difficult for the power generation enterprises to convert wind
energy to electricity. From Table 22, added with carbon tax, the minimal cost objective
will choose more cheap conventional generators such as G4 rather than wind farms (G7,
G8). The reason is that increasing more wind output power will raise the wind power
estimation deviation dramatically. As a result, it is crucial to improve the wind power
95
forecasting system which can greatly help the integration process, since system operators
rely on accurate wind power forecasts to design operational plans and assess system
security. However, as one of the renewable energy subsidy projects, wind farms in many
countries receive a largely covert subsidy. An excellent example is the Renewables
Obligation (RO) in UK. The RO is designed to encourage generation of electricity from
eligible renewable sources in UK [228]. Thus, the wind farms will produce more power
if receiving subsidy from governments.
6.6.2. Comparisons with Other Approaches
In order to evaluate the performance of the proposed method, GA and PSO are employed
in the case studies. For comparison purposes, these algorithms are used directly to solve
the Case I with carbon tax. Meanwhile, in order to make a fair comparison of the other
methods, we fixed the same population size as 100 and tested them to reach maximum
iteration 500. The initial crossover and mutation rate for GA was set as 80% and 5%.
Table 23 shows the results out of 100 runs with each method.
Table 23 Comparison of Different Approaches
Algorithm Best Solution ($) Average Solution ($)
GA 49676.05 50242.72
PSO 48652.87 49041.22
QPSO 48141.95 48522.51
A comparison with other approaches is made to evaluate the proposed algorithm which
is shown in Table 23. As is shown, we can conclude that, QPSO can greatly enhance the
searching ability, ensures quality of average solutions, and also efficiently manages the
system constraints.
6.7. Conclusion
This chapter developed a novel method for power system ED problem to achieve faster
and better optimization performance. The method was successfully applied to solve the
ED problem considering wind power and carbon tax in an integrated model, where the
valve-point effects are also taken into account. In the present work, the wind speed
distribution probability functions are applied in formulating the optimization model to
address the forecast uncertainties involved. The proposed QPSO method was applied to
solve the ED problem of a testing system involving six thermal units and two wind
farms.
The comparisons were made between the proposed ED models without and with carbon
tax. When the carbon tax is considered in the ED process, the output of higher emission
96
units will be substituted with the lower emission ones. The proposed optimization
method was compared with other optimization approaches in the studied cases.
Compared to the classical PSO and other methods, it can be concluded that the QPSO
method greatly enhances the searching ability and efficiently manages the system
constraints, therefore providing a new and efficient tool for ED with wind power and
carbon tax.
The case studies indicate three points of views, (1) Embedding carbon tax in the ED
problem can effectively reduce the GHGs emission. However it will impose impacts to
the traditional fossil-based generation enterprises. Government subsidies are necessary
for establishing a carbon tax model for power enterprises. (2) Due to the uncertainty of
wind energy, it is crucial to improve wind power forecasting accuracy. (3) Energy store
techniques can relieve the intermittent and stochastic characteristic of the renewable
energy such as wind power and solar power. Corresponding researches will be discussed
in our successive publications.
97
Chapter 7. Unit Commitment Considering
Probabilistic Wind Generation and Emission
Problem
7.1. Nomenclature , ,i i ia b c Production cost coefficients of thermal unit i .
, ,i i id e f Fuel consumption coefficients of thermal unit i .
,
p
i tC Production cost of thermal unit i at time t .
,
w
j tC Production cost of wind unit j at time t .
,
u
j tC Underestimation cost of wind unit j at time t .
,
o
j tC Overestimation cost of wind unit j at time t .
,
s
j tC Government subsidy of wind unit j at time t .
,
susd
i tC Start up and shunt down cost of thermal unit i at time t .
i Cost function of thermal unit i .
,u j Cost coefficient for not using all generated wind power due to the
underestimation case.
,o j Cost coefficient for purchasing reserve power from other source due to
overestimation case.
,s j Government subsidy coefficient of power generated by wind unit j .
,w j Production cost coefficient of wind unit j .
i Emission function of thermal unit i .
,I i t The on/off status of thermal unit i at time t .
M Number of thermal units.
N Number of wind units.
,p i t Actual power generated by thermal unit i at time t .
dp t Total system demand.
lossp t Total transmission losses.
,Q j t The on/off status of wind unit j at time t .
,sr i t The spinning reserve of thermal unit i at time t .
sR t The spinning reserve requirement at time t .
,SU i t The start up cost of thermal unit i at time t .
,SD i t The shunt down cost of thermal unit i at time t .
, ,in r outv v v Cut-in, rated, and cut-out wind speeds.
,w j t Predicted wind power generated by wind unit j at time t .
,avW j t Actual power generated by wind unit j at time t .
,r jw Rated wind power from wind turbine unit j .
98
7.2. Introduction
Power system generation scheduling problem can be divided into two sub-problems, unit
commitment (UC) and economic dispatch (ED). UC is an optimization problem of
determining operational schedules for generating units in a power system with a number
of constraints [229]. The main objective of UC is to decide the on/off statuses of
generators over the scheduling period to meet the system load demand and reserve
requirements at lowest cost. Basically, the UC outputs are on/off statuses on an hourly
basis for a given time horizon, such as 24 hours. In addition, UC schedule is approached
by meeting the system constraints such as ramp rate limits, spinning reserve, as well as
minimum up and down time limits.
Wind power, one of the most appealing renewable energy sources has gained widespread
concerns during the last decade. Wind farms have been installed worldwide with a
motive of finding some respite from energy crisis [230]. Wind energy plays a major role
in easing the energy shortage and reducing the globe emissions in the entire world. In the
literatures, many researchers have shown great interests in incorporating wind power
with UC problems. For instance, an approach to evaluate the contribution that wind
power can make to the load carrying capability of a power generating system in an
operating scenario was studied in [231]. A novel UC formulation for a power system
with significant levels of wind generation was proposed in [232]. In [233], the authors
proposed an approach to evaluate the uncertainties of the balancing capacity, ramping
capability, and ramp duration requirements.
Furthermore, various numerical optimization methods have been employed to solve the
UC problems. Traditionally, many mathematical approaches have been proposed, such
as priority list (PL) techniques [234],[235], dynamic programming (DP) [236],
branch-and-bound (BB) methods [237], mixed-integer programming (MIP) [238], and
Lagrangian Relaxation (LR) methods [239],[240]. Recently, optimization solvers based
on the heuristics techniques have been proved to be effective with promising
performance, which include genetic algorithm (GA) [241]-[244], evolutionary
programming (EP) [245], fuzzy logic (FL) [246], artificial neural network (ANN) [247],
simulated annealing (SA) [248], particle swarm optimization (PSO) [249] as well as
hybrid techniques [250]-[252]. Many researchers are attracted by the heuristic
optimization methods because they can provide a fast and reasonable solution, and they
can deal with the constraints easily.
99
In this chapter, a computational UC framework incorporating stochastic wind power is
proposed. Because of the stochastic characteristic of wind speed, wind power output is
not deterministic. As a sequence, the probability distribution of wind speed must be
taken into account in the UC model. A huge number of research works have indicated
that wind speed approximately follows the Weibull distribution [253]. In our UC model,
wind power is described as the three-parameter Weibull distribution. In terms of the
optimization method, we present interior point method (IPM) to solve the proposed UC
model.
7.3. A Review of Probability of Wind Power
As we have discussed in the previous chapters, for a nonlinear wind turbine power curve,
the wind power output and the corresponding probabilities can be presented as follows:
(1) For inV v or outV v ,
0
1
1 exp exp
in out
V in V out
k k
in out
P W P V v P V v
F v F v
v v
c c
(7.1)
(2) For in rv V v ,
in r
r in
V v wW aV b
v v
,
1
exp
k
r in
in
r in rW
r
k
r in
in
r
v v wv
k v v wf w
cw c
v v wv
w
c
. (7.2)
(3). For r outv V v ,
exp exp
r r out
V out V r
kk
outr
P W w P v V v
F v F v
vv
c c
(7.3)
7.4. Wind Power and Load Demand Forecasting
In this chapter, our wind power generation forecasting strategy is to predict the wind
speed firstly, and then convert the wind speed data to wind power data against the wind
turbine power curve. Generally speaking, wind speed forecasting can be classified into
100
two categories: Numerical Weather Prediction (NWP) model and Data-Driven model.
Where the former models the wind speed within the domain of aerodynamics and the
latter relies on the statistically learning of the historical wind speed data. In this chapter,
we developed a forecasting model following the second category. In terms of the data
driven model, it would be subdivided into two groups: time series methods and artificial
intelligence method. In our wind speed forecasting model, both the time series and
artificial intelligence methods have been used. For the time-series models, there are
k-Nearest Neighbour (k-NN), Autoregressive Integrated Moving Average (ARIMA), and
Generalized Autoregressive Conditional Heteroskedasticity (GARCH) having been used;
for the artificial intelligence models, there are ANN, SVM, and Relevance Vector
Machine (RVM) having been studied in our forecasting model [254].
The initial results have demonstrated that the result from a composite of forecast
techniques is often superior to those produced by any individual of the ensemble. The
reason is that if the errors in the forecasts produced by different methods are unbiased
and have a low degree of correlation with each other, then the random errors from the
individual forecast unit will tend to offset each other, therefore a composite of the
forecasts will have lower errors than any individual forecast. As a result, each technique
used in the wind speed forecast model will be assigned a weight, which can be adjusted
automatically according to its forecast performance.
The wind power forecasting structure can be presented in Fig. 29.
101
Figure 28. Wind Power Forecasting Model
For the load demand forecasting, a practical load forecasting tool called OptiLoad [255]
developed at the Hong Kong Polytechnic University is incorporated for the
corresponding forecasts. The OptiLoad relies on several state-of-the-art forecasting
methods including ANN, SVM, and k-NN for minutely to weekly ahead load forecasting.
During its implementation, the forecasting results provided respectively by the
mentioned three methods are strategically combined as the final result. According to the
practical on-line performance, the weight for each method is dynamically updated. Fig.
30 shows the user interface of OptiLoad (version 1.0b).
102
Figure 29. User interface of OptiLoad (v1.0b) [253]
7.5. Mathematical Formulation of UC Problem with Wind
Power and Emission
This section describes the problem formulation of UC model including wind power and
emission. The model aims at finding the solution that minimizes the total operation costs
(including fuel cost, wind power cost, emission cost) while satisfying the given
constraints. In [192], an economic dispatch (ED) model incorporating wind power is
developed. In order to accurately characterize the uncertainty in the availability of wind
energy, penalty costs functions for both underestimation and overestimation cases were
added. Inspired by the previous work, a similar UC model is developed. To address the
uncertainties in wind power production, the wind speed distribution probability functions
are applied in formulating the optimization model.
A. Objective Function
The objective function is formulated to minimize the total system operation costs,
103
, , , , , , ,. p e susd w u o s
i t i t i t j t j t j t j t
t i j
Min C C C C C C C
(7.4)
where,
, , ,p
i t iC I i t p i t (7.5)
, , ,e
i t iC I i t p i t (7.6)
, , ,susd
i tC SU i t SD i t (7.7)
, ,, ,w
j t w j avC Q j t W j t (7.8)
, ,, , ,u
j t u j avC Q j t E W j t w j t (7.9)
, ,, , ,o
j t o j avC Q j t E w j t W j t (7.10)
, ,, ,s
j t s j avC Q j t W j t (7.11)
where, ,i p i t is the fuel cost function of thermal generator i at time t , and
,i p i t is the emission function of thermal generator i at time t .
2
, , ,, , ,i i t i t i tp i t a b p i t c p i t (7.12)
2
, , ,, , ,i i t i t i tp i t d e p i t f p i t (7.13)
,
w
j tC is the wind power cost of the wind farm. If the wind farm is owned by the system
operator, this term may not exist which is considered in the case studies of this paper
later on. The underestimation cost ,
u
j tC occurs if the actual generated wind power is
more than the predicted, thus the system operator should compensate for the surplus
wind power cost. On the other hand, if the actual wind power is less the scheduled power,
the operator needs to purchase from an alternate source and pay the overestimation cost
,
o
j tC.
When we have determined the operation status and the time t , the on/off status and the
subscript t can be dropped. According to [192], the cost of underestimation will be
assumed as follow,
,
, ,
,
r j
j
r j r j
j j
wu u
j j av j j j Ww
w wu
j W j Ww w
E W w w w f w dw
w f w dw w f w dw
. (7.14)
In terms of overestimation case, the cost equation will be in the similar manner,
,0
0 0
j
j j
wo o
j j j av j j W
w wo
j j W W
E w W w w f w dw
w f w dw w f w dw
. (7.15)
104
The Eq. (7.17) and (7.18) can be solved through the wind power probability Eqs.
(7.4)-(7.7).
B. System Constraints
Unit generator limits
,min ,max,i ip p i t p (7.16)
Wind power unit limits
,0 j r jw w (7.17)
System real power balance
1 1
, , , ,M N
av d loss
i j
I i t p i t Q j t W j t p t p t
(7.18)
System spinning reserve requirements
, ,s sI i t r i t R t (7.19)
Thermal unit minimum starting up/down times
1 1 0
1 1 0
on on
i i i i
off off
i i i i
X t T I t I t
X t T I t I t
(7.20)
Ramp rate limits
, , 1
, 1 ,
p i t p i t UR i
p i t p i t DR i
(7.21)
7.6. A Brief of Interior Point Method (IPM)
A brief introduction of Interior Point Method (IPM) has been provided in Section 5.6.1.
7.7. Case Studies
In the case study part, the UC model with wind power was evaluated using the historical
wind speed dataset from a wind observation station in Tasmania, Australia. The data was
provided by the Australian Bureau of Meteorology [256]. Here we assume that the wind
speed data from a large wind farm and use the data to estimate the generated wind power.
The wind speed distribution frequency and the corresponding Weibull distribution
parameters are presented in Fig. 31.
The Vestas V90 3.0 MW wind turbine is selected for the case studies. It is a pitch
regulated upwind wind turbine with active yawing and a three-blade rotor. It has a rotor
diameter of 90 m with a generator rated at 3.0 MW. The Vestas V90 3.0MW is widely
used in the wind plants in Australia and has a proven high efficiency. The parameters of
the associated Weibull distribution factor and wind farm parameters can be calculated
from the wind speed data and are given in Table 24.
105
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Wind Speed (m/s)
Fre
quency
Weibull Fitting: y=(k/c)*(x/c)(k-1)*exp(-(x/c)k) --- k = 1.89, c = 5.49 (m/s)
Wind Distribution
Weibull Fitting
Figure 30. Wind Speed Distribution and Weibull Fitting
Table 24 Wind Power Factors
c k Ө vin vout vr wr αw,j αu,j αo,j αs,j
5.5 1.89 0 4 25 16 3 0 60 20 10
The proposed method is implemented on a modified IEEE 30-bus system. The
benchmark system consists of 6 thermal generators, 2 wind farms, 41 branches, and 21
loads. These thermal generators include 3 coal-fired units, 2 gas-fired units, and 1
oil-fired unit. The test system is shown in Fig. 31, [257]. The wind farm totally consists
of 100 Vestas V90 3.0 MW wind turbines located in a coherent geographic area.
Depended on the actual generated wind power, the extra cost will be determined by
overestimation case or underestimation case. According, the maximum capacity of the
system under investigation is 2030 MW and 2330 MW incorporating with wind power.
Figure 31. Modefied IEEE 30-bus system
106
Table 25 Generator Parameters
Unit Type pmin pmax Fuel Cost Coefficients Fuel Consumption Coefficients
a b c d E f g H
G1 (01) Coal 20 110 2000 10 0.002 200 0.08 40 0.2 0.00004
G2 (02) Coal 20 100 2500 15 0.0025 300 0.04 50 0.3 0.00005
G3 (13) Coal 120 600 6000 9 0.0018 400 0.04 80 0.12 0.000024
G4 (22) Gas 110 520 923.4 18 0.00315 150 0.06 2462.4 48 0.0084
G5 (23) Gas 110 500 950 20 0.0032 100 0.08 2500 50 0.009
G6 (27) Oil 40 200 124.8 23.4 0.00343
2 80 0.10 1.248 0.234
0.0000343
2
G7 (14) Wind 0 90 0 0 0 0 0 0 0 0
G8 (19) Wind 0 60 0 0 0 0 0 0 0 0
Note: (1) The coefficients of ai, bi, ci, and ei are in $, $/MW, $/MW2, and $/MW.
(2) The coefficients of fi, gi, and hi are in t, t/MW, and t/MW2 for coal/oil units, are in m3, m3/MW, and m3/MW2 for gas unit.
Table 26 Generator Constraints
Unit p
min
(MW)
pmax
(MW)
Ramp
Up
Rate
(MW/h)
Ramp
Down
Rate
(MW/h)
Tup
(h)
Tdn
(h)
Start Up
Cost
(Cold)
($)
Start Up
Cost
(Hot)
($)
Shut
Down
Cost
($)
Initial
Status
G1
(Coal) 20 110 40 55 5 5 800 400 3000 -5
G2
(Coal) 20 100 30 55 4 2 720 360 3000 -6
G3
(Coal) 120 600 80 120 6 4 4500 2250 3000 1
G4
(Gas) 110 520 100 150 4 3 7200 3600 3000 1
G5
(Gas) 110 500 100 120 4 3 6600 3300 3000 -1
G6
(Oil) 40 200 50 60 3 4 4260 2230 3000 -1
G7
(Wind) 0 90 0 0 0 0 0 0 0 0
Table 27 Forecasted Wind Power and System Demand
Time 01 02 03 04 05 06 07 08 09 10 11 12
Wind
(m/s) 42 70 72 79 89 81 90 88 43 40 68 60.7
Demand
(MW) 612 502 430 395 384 421 574 736 925 1113 1353 1504
Time 13 14 15 16 17 18 19 20 21 22 23 24
Wind
(m/s) 56 53 46.3 24 3 5 8 10 6 46 58 63
Demand
(MW) 1600 1636 1563 1480 1500 1521 1527 1467 1292 1082 885 715
107
Table 28 Generation Schedules
Unit 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
G1
(Coal) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
G2
(Coal) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
G3
(Coal) 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
G4 (Gas) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
G5 (Gas) 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
G6 (Oil) 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0
G7
(Wind) 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24200
400
600
800
1000
1200
1400
1600
1800Forecasted System Demand Curve
Time (Hour)
Dem
and (
MW
)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240
10
20
30
40
50
60
70
80
90
100Scheduled Wind Power Generation
Time (Hour)
Win
d P
ow
er
(MW
)
Predicted Wind Power
Scheduled Wind Power
Figure 32. (a). Forecasted System Demand (b). Forecasted wind power vs. scheduled
wind power
The generator constraints, production cost coefficients, and fuel consumption
coefficients are shown in Tables 25 and 26, the load curve during 24 hours is shown in
Fig. 32(a). The predicted wind power and system demand of 24 hours are given in Table
27. Table 28 shows the schedules of 7 units for 24 hours by minimizing the cost. In this
table, the value of ―1‖ represents an on-line state of each unit, and the value of ―0‖
represents an off-line state of each unit. From this table, it is clear that wind turbines
were not scheduled for 20 hours. The reason is that the wind power generating cost is
comparative high. The Fig. 32(b) presents the scheduled wind power generation. The
blue line presents the forecasted wind power for 24 hours and the red line presents the
scheduled wind power.
108
7.8. Conclusion
In this chapter, we have presented an IPM approach to solve the UC problem
considering wind power and emission. The proposed optimization framework was tested
on a benchmark system, including six thermal generators and one wind farm. The effects
of the wind distribution and forecasted wind power values were studies in the case.
Based on the analytic probability of stochastic wind power, the final scheduled outputs
of wind farm have been calculated.
109
Chapter 8. Conclusions and Future Work
8.1. Conclusions
Wind power has been playing an increasing important role in today’s power system
industries. It has brought us a lot of benefits such as no pollution, relatively low capital
cost and short gestation period. However, the integration of wind power is a big
challenge due to the intermittency and uncertainty wind resource. Consequently,
data-mining based techniques have been used to form a comprehensive statistical
method for wind power interval forecasting. A hybrid optimization method connecting
interior point method (IPM) and particle swarm optimization (PSO) was developed to
solve the combined economic and emission dispatch (CEED) problem with stochastic
wind power. A quantum-inspired particle swarm optimization (QPSO) has been
proposed so as to overcome many drawbacks that affect the original PSO and solve the
economic dispatch (ED) problem considering probabilistic wind power and carbon tax.
Furthermore, a wind power forecasting tool that combines different forecast techniques
was used for a unit commitment (UC) with wind power and emission issue.
Chapter 2 discussed the background of wind energy resources: theory, design and
application. Wind power generation is more and more essential in today’s society
development. Lots of wind power technologies were researched and developed. The
performance of wind energy conversion systems depends on the subsystems such as
wind turbine (aerodynamic), gears (mechanical), and generator (electrical). In this
chapter, wind power issues, such as types of wind turbines, power in the wind, impact of
tower height, maximum rotor efficiency, wind generators, speed control for maximum
power, average power in the wind and wind farms have been discussed. Wind turbine
power curve is important technical information for a specific wind turbine. The power
curve can show the relationship between wind speed and generator power output. It is no
doubt that the design of wind power system is a very complex task and needs lots of
knowledge and skills, such as civil, mechanical, electrical and electronics, geography,
aerospace, environmental etc. Here we attempt to give a basic idea about design aspects
of the wind power system such as factors affecting wind power, their classification,
choice of generators, main design considerations in wind turbine design, problems
related with grid connections, hybrid wind power generation, environmental aspects of
power generation, latest trend of wind power generation from off shore sites.
110
Chapter 3 provided the basic introductions of wind power forecasting and power system
operations with considering wind power. It also introduced the existing techniques
relevant to solving wind power system problems. Then the field of evolutionary
algorithms was discussed, focusing in particular on comparisons between these
algorithms. It has been shown that all these algorithms are effectively the same except
for their different background theories and evolutionary implementations. Each method
has its own merits and drawbacks and the problem of local optima is unavoidable. In
addition, a number of feature extraction machine learning approaches were studied and
their advantages and disadvantages were detailed. Although some guidelines have been
developed and effective techniques have been suggested, it is difficult to choose a
method in a given situation because this choice is problem dependent. Last but not least,
two time series models namely ARIMA and GARCH were presented. This is followed
by comprehensive comparisons of these approaches.
In Chapter 4, a time series model which is composed of linear regression and five data
mining algorithms was developed. Two important characteristics of wind speed, the
nonlinearity and the time-changing distribution, were taken into account in the proposed
model. In the previous research works, many researchers mainly focus on predicting
wind power point value. Nevertheless, wind power is stochastic in nature and errors will
always exist in wind power forecasts. Therefore, besides predicting the expected point
value of the future wind power, it is also necessary to estimate its forecasting interval. In
the case study, the 95% level and 99% level prediction intervals were presented. From
the forecasting results, it is clear that the prediction intervals given by the five nonlinear
algorithms all perfectly contain the true values of wind power. In addition, the results
clearly prove the effectiveness of the proposed statistical model in wind power interval
forecasting.
Chapter 5 considered the combined economic and emission dispatch (CEED) with wind
power. Nowadays, hybrid optimization methods combining different techniques have
received widespread concerns. The previous research works have proved that the result
from a composite of optimization methods is often superior to those produced by any
individual approaches. The reason is that the combination of optimization techniques can
overcome individual disadvantages and benefit from each other’s advantages. In this
chapter, we developed a novel hybrid optimization algorithm connecting interior point
method (IPM) and particle swarm optimization (PSO) for solving combined economic
and emission dispatch (CEED) problem with valve point effects as well as stochastic
111
wind power. The probability of stochastic wind power based on the linear wind power
output curve is involved in the proposed CEED model. The test system is composed of
six thermal units and one wind farm. A set of numerical experiments have proved the
effectiveness of the hybrid computational method.
Chapter 6 focused on the power system operations with wind power and carbon tax in
Australia. The newly proposed quantum-inspired particle swarm optimization (QPSO)
was researched. QPSO has stronger search ability and quicker convergence speed since
it not only introduces the concepts of quantum bit and rotation gate, but also involves the
implementation of self-adaptive probability selection and chaotic sequences mutation. It
was shown here that the QPSO has superior search capability and speed. The simulation
results show that the QPSO improves on other versions of evolutionary algorithms in
terms of both speed and accuracy. Compared to the original PSO, it greatly enhances the
searching ability and also efficiently manages system constraints. The successful
optimizing performance on the validation data set illustrates the efficiency of the
approach and shows that it can be used as a reliable tool for economic dispatch (ED)
problem solving. In terms of the uncertainty of wind power, the wind speed distribution
probability functions based on the un-linear wind power output curve are applied in
formulating the optimization method.
Chapter 7 proposed a unit commitment (UC) considering probabilistic wind power and
emission problem. In the proposed wind power and load demand forecasting framework,
a practical wind speed forecasting (WSF) tool and load forecasting (LF) tool called
OptiLoad, both developed at the Hong Kong Polytechnic University, are incorporated
for corresponding forecasts. The WSF tool is composed of time-series models including
k-NN, ARIMA and GARCH as well as artificial intelligence models involving ANN,
SVM and RVM. For the OptiLoad, this tool relies on several state-of-the-art forecasting
methods including ANN, SVM and k-NN for minutely to weekly ahead load forecasting.
Lots of relevant research works have proved that the forecasted results from a composite
of forecast techniques is often more robust than those produced by any individual of the
ensemble. The reason is that the random errors from individual forecasting approach will
tend to offset each other in a compound forecast method. In addition, each technique
used in the forecast model will be assigned a weight, which can be adjusted
automatically according to its forecast performance. The proposed optimization
framework was tested on a benchmark system including six thermal generators and one
112
wind farm. Based on the analytic probability of stochastic wind power, the final
scheduled outputs of wind farm have been calculated.
8.2. Future Work
This thesis has reported on an investigation into the techniques of data analysis
appropriate for power system operations with wind power and emission problems. Ideas
from a number of disparate fields have been drawn together for the research that was
carried out and it is apparent that data analysis in power systems considering stochastic
wind power is an area that encompasses much more scope for development and
elaboration. Several directions for further research that are suggested by the work of this
thesis are set out below.
1. Combined unit commitment of electricity and heat in a microgrid under volatile
wind power and solar power
The paper will develop an optimization model for scheduling electricity and heat
production for a microgrid considering the operation constraints as well as volatility of
wind and solar power generation. The stochastic nature of wind power will be solved by
the derived cumulative distribution function. In terms of the solar power, we assume that
the solar energy will be converted into electricity by semiconductor materials. Three key
aspects that should be considered are:
(1) Solar electric energy generation
Before supply the electric power, the current went through a full bridge inverter, the
filter inductor, and transformer. And the solar power generation can work with off-gird
or on-grid forms, so it can be very flexible and convenient. The output power of
photovoltaic cells is affected by the intensity of sunshine, and the battery junction
temperature and other factors.
(2) Storage equipment
The storage equipment of wind power and solar power generation equipments mainly
achieve two purposes, namely power balancing and load balancing. Using power storage
equipment, we can charge it as electrical load when the grid’s electricity is surplus, and
discharge it as electrical source when the grid’s electricity is scarce.
(3) Evaluate the electric power quality
113
Because wind energy and solar energy will be affected by climate, environment, time
and many other factors which with strong randomness. The output hybrid power exist
many uncertainties in operation. There are many evaluation methods as such fuzzy
comprehensive method. In this paper, the operation constraints will include power
balance constraint, limits of generator power constraint and storage battery runs
constraint. For the optimization method, we will use the professional optimization
software which is AIMMS to solve the unit commitment problem.
2. Wind power + solar power dispatch/unit commitment considering emission
problem
In this paper, the stochastic nature of wind power and solar power will be solved by the
derived cumulative distribution function and Monte Carlo sampling technique. The
results of two simulation methods will be compared. For the Monte Carlo sampling,
Variance Reduction such as Importance Sampling and Latin Hypercube Sampling will
be applied. Unlike simple random sampling, IS and LHS ensure a full converge of the
range of variable by maximally satisfying marginal distribution.
In the case study part, the model with wind power was evaluated using the historical
wind speed dataset from a wind observation station in Tasmania, Australia. The data was
provided by the Australian Bureau of Meteorology. And we assume that the wind speed
data from a large wind farm and use the data to estimate the generated wind power. The
solar power distribution will be assumed as Normal distribution and we will use the data
from Newcastle solar power station. In terms of the optimization method, a new hybrid
approach such as Fuzzy GA combined Improve PSO will be applied.
8.3. Summary
This chapter concludes the thesis and highlights the contributions and main
achievements of the research reported. It also identifies directions for future work
involving the methods proposed in the thesis. Overall, the work done here provides a
comprehensive framework for wind power system data analysis which enhances the
wind power system operations, integration, and the planning functionality of its
operators.
114
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