2006 International Conference on Power System Technology

A New Approach to Determine Base,

Intermediate and Peak-Demand in an ElectricPower System

A. Salimi-beniIran Grid Management Company-IGMC

Beni(tavanir.org.ir

D. FarrokhzadIran Grid Management Company-IGMC

farokhzadgtavanir.org.ir

Abstract--Electricity demand varies from place to place and fromcountry to country depending on the mix of demand, the climate,and other factors. A typical load curve of a power electricitysystem through one period of time is normally divided into threeparts as base, intermediate and peak-load. While havingaccurate information for the three parts of a load curve is veryimportant, it is not an easy task to calculate the base,intermediate and peak-load of a particular system. This paperpresents a new statistical approach to calculate the three mainparts of a system load demand; base, intermediate and peak-loadusing a cluster analysis which is one of the statistical methods toin data categorizing. The main advantage of the proposedtechnique is that it can be applied to situations in which LDC orsystem load factor varies. The applicability of the proposedtechnique is illustrated by determining the base, intermediateand peak-load for different seasons of Iran power network.

Index Terms--Base load, cluster analysis, Intermediate load,Load Division Curve(LDC), Peak load.

I. INTRODUCTION

T HE importance of electricity in our economy and in allaspects of our lives is constantly growing. Modemsociety because of its pattern of social and working habits

has come to expect the supply to be continuously available ondemand. This can only be achieved by focusing on all aspectsof an electric power system from the generating units throughthe transmission system down to the customer at the end ofthe distribution system. At the same time, electric powerutilities are required to operate their systems more efficientlyand economically and therefore the planning process isbecoming a critical factor in determining the performance anddesign of power systems. One of the main issues in this regardis to acknowledge that reliable forecasting of the expectedgrowth in electric energy demand is the fundamentaldeterminant of the necessity for system development and/orreinforcement.

M. Fotuhi-FiruzabadDepartment of Electrical Engineering

Sharif University of Technologyfotuhi@sharif.edu

S. J. AlemohammadKhozestan Electric Power Regional Company

Accurate load forecasting is an important issue as itensures the availability of supply and also provides a mean toavoid over or under utilization of generation, transmission anddistribution facilities. Electricity demand fluctuatesthroughout every 24-hour period as well as through the week,and also seasonally. It also varies from place to place andfrom country to country depending on the mix of demand, theclimate, and other factors. A typical load curve of a powerelectricity system through one period of time is normallydivided into three parts as base, intermediate and peak-load.Figure 1 shows these three main parts. The shape of such acurve will vary markedly according to the kind of demand.While having accurate information for the three parts of aload curve is very important, it is not an easy task to calculatethe base, intermediate and peak-load of a particular system.Determination of these three main parts of system demand isone of the major issues in power system planning.

Because of the large fluctuations in demand over thecourse of the day, it is normal to have several types of powerstations broadly categorized as base-load, intermediate-loadand peak load stations. The base load stations [4] are usuallysteam- driven and run more or less continuously at near ratedpower output. Coal and nuclear power are the main energysources used. Intermediate-load and peak-load stations mustbe capable of being brought on line and shut down quicklyonce or twice daily. A variety of techniques are used forintermediate and peak-load generation including gas turbines,gas-and oil-fired steam boilers and hydro-electric generation.Peak-load equipment tends to be characterized by low capitalcost, and relatively high fuel cost is not a great problem.

1-4244-0111-9/06/$20.00c02006 IEEE.

I

2

LDC Iran Network 2001

Peak load

Intermediate load

Base load

1 1441 2881 4321Time

d(P, Q) = (x1 - Y1)2 + (x2 - Y2 )2 + + (x_y_ )2

=^\/X - )' X - Y ) (1)The statistical distance between the same two observations

can be expressed in the form of:

d(X,Y)= (- (-Y)

_N Ordinarily, A = S 1 , where S contains the sample variances

5761 7201 8641and co-variances. Another distance measure is theMinkowski metric:

Fig 1. Iran load duration curve for 2001

The base load demand [1] for reliable, continuous supplyof large amounts of electricity is the key factor in any system.The main investment of any electric utility is to meet that kindof demand. As well as daily and weekly variations in demandthere are gradual changes occurring in the pattern ofelectricity demand from year to year. In most literature,attempt has not been devoted to develop a technique tocalculate base, intermediate and peak-load. [5] - [8]

This paper presents a new statistical approach to calculate thethree main parts of a system load demand; base, intermediate andpeak-load. This technique is based on a cluster analysis which is oneof the statistical methods in data categorizing. The main advantageof the proposed technique is that it can be applied to situations inwhich LDC or system load factor varies. The applicability of theproposed technique is illustrated by determining base, intermediateand peak-load for different seasons of Iran power network.

II. METHODOLOGY

A. Cluster analysis

Grouping or clustering is distinct from the classificationmethods. Classification pertains to a known number ofgroups, and the operational objective is to assign new

observations to one of these groups. Cluster analysis isconcerned with forming groups of similar objects based on

several measurement of different kinds made on the objects.The key idea is to identify classifications of the objects thatwould be useful for the aims of the analysis. This idea hasbeen applied in various areas. Before implementing any

technique for clustering, it is required to define a measure fordistances between utilities so that similar utilities are a shortdistance apart and dissimilar. Ones are far from each other, a

popular distance measure based on variables that take on

values is to standardize the values by dividing by the standarddeviation (sometimes other measures such as range are used)and then to compute the distance between objects using theEuclidean metric method.

B. Similarity measure

The straight-line distance between two arbitrary points Pand Q with coordinatesP= (XI x2 ... , ) and (YI,Y2. ,)is given by

Il/m

(2)d (P, Q) = x i-yilm

i=l

For m=1, d(X,Y) measures the " city-block" distancebetween two points in p dimensions. For m=2, d(X,Y)becomes the Euclidean distance. In general, varying mchanges the weight is given to the larger and smallerdifferences. The construction of distances and similarities hasbeen described. It is always possible to construct similaritiesfrom distances. For example, we might set

Sik(3)

1 + dik

Where 0 < Sik < 1 is the similarity between items i and k

and di. is the corresponding distance. The less subjective

schemes for creating clusters will be discussed in more detail.In general, there are two main approaches for clustering andthey are [2]:

1. Hierarchical cluster methods2. Nonhierarchical cluster methods

The second approach is used in this paper.

Nonhierarchical clustering techniques are designed to group

items into a collection of k clusters, rather than variables. Thenumber of clusters, k, may either be specified in advance or

determined as part of the clustering procedure. Because a

matrix of distances (similarities) does not have to bedetermined and the basic data do not have to be stored duringthe computer run, nonhierarchical methods can be applied tomuch larger data sets than hierarchical techniques. One of themore popular nonhierarchical procedures known as the k-means is investigated in the following subsection.

C. K-means method:

This algorithm [3] assigns each item to the cluster havingthe nearest centroid (mean). In its simplest version, theprocess is composed of these three steps:

1. Partition the items in to k initial cluster.2. Proceed through the list of items, assigning an item to the

cluster whose centroid (mean) is nearest. (Distance isusually computed using Euclidean distance with eitherstandardized or unstandardized observations) recalculatethe centriod for the cluster receiving the new item and forthe cluster losing the item.

25000

200001-ect

15000

10000

3. Repeat step 2 until no more reassignments take place.Rather than starting with a partition of all items into kpreliminary groups in step 1. We could specify k initialcentroids (seed points) and then proceed to step 2.The final assignment of items to clusters will be, to some

extent, dependent upon the initial partition or the initialselection of seed points. Experience shows that most majorchanges in assignment occur with the first reallocation step.

III. APPLICATION

Using the approach described in the previous sections, thethree main parts of the system load demand, base load,intermediate load and peak load, are calculated using an

statistical software SPSS. Hourly peak loads of Iran networkas well as Khozestan region are used for the study resultspresented in this paper.

A. Calculating base, intermediate and peak load of Irannetwork

1 2

LOAD2001 20318 15003

30000

25000

-20000 a0

15000

100001 1441 2881 4321 5761 7201 864

Time

Fig. 2. Hourly peak load of Iran in year 2001.

Using the nonhierarchical cluster algorithm and K-Meanstechnique presented in the previous section, the intervalsassociated with the base and peak load of Iran network arecalculated. The hourly peak load of Iran network for the year2001 are used for the analysis presented in this section. In thefirst step, the number of cluster is assumed to be 2 and basedon the first step of the proposed algorithm initial clustercenters are determined. These values are shown in Table I.

TABLE I

Initial Cluster Centers

Cluster

1 2

LOAD2001 26385 10453

In the second step, the algorithm is converged after 7iterations. The results associated with each iteration are

presented in Table II. After convergence, based on the thirdstep of the proposed algorithm, final clusters are obtained as

shown in Table III. The values lower than the minimumcluster; here 15003 MW, are considered as base load whilethe values upper than the maximum cluster; here 20318 MW,are considered to be the peak load. The distance between thepeak and base load is the intermediate load as shown inFigure 2.

TABLE II

As noted earlier,[9] having accurate information on the base,intermediate and peak load is an important issue as it ensures theavailability of supply and also provides a mean to avoid over or

under utilization of generation, transmission and distributionfacilities. Figure 3 shows that the system requires base loadstations for 27.45% of the time during a year. Thermal andnuclear units are appropriate for the base load. 54.111% of thetime period, this system requires generating units appropriatefor the intermediate load. Combined cycle units are

considered to be appropriate for the intermediate load. Finallythe system should have sufficient peak load stations for18.44% of the year. Hydro and gas turbine units are in thepeak load station categories.

30000

25000

- 20000ct0

15000

10000 L

Peak load18.44%

Base load27.45%

1 1441 2881 4321 5761

Time

7201 8641

Fig. 3. Load duration curve of Iran network for 2001

Iteration HistoryChange in Cluster Centers

Iteration 1 21 5608.275 4861.2532 216.329 146.0223 113.640 76.8184 66.440 45.4435 34.363 23.7216 18.600 12.8647 6.691 4.621

TABLE III

Final Cluster Centers

Cluster

B. Calculating Base, Intermediate and Peak load ofKhozestan Region Network

Khozestan is located in the south west of Iran and has a

very hot climate. This is the main reason in selecting thisregion separately from the whole country presented inSubsection A. In addition, the study results presented in thissection can be compared with those obtained for the wholecountry to show the impacts of weather climate on thepercentage of base, intermediate and peak load. Similar to theprevious study, the hourly peak load of 2001 for Khozestanregion is used for the analysis of this section.

3

4

Using the nonhierarchical cluster algorithm and K-Meanstechnique, the intervals associated with the base and peak loadof Khozestan region are calculated. In the first step, thenumber of cluster is assumed to be 2 and based on the firststep of the proposed algorithm initial cluster centers aredetermined as shown in Table IV.

TABLE IV

Initial Cluster CentersCluster

1 2

LOAD2001 798 3735

In the second step, the algorithm is converged after 5iterations. The results associated with each iteration arepresented in table V. After convergence, final clusters areobtained as shown in table VI. The values lower than theminimum cluster; here 1709 MW, are considered as base loadwhile the values upper than the maximum cluster; here 2932MW, are considered to be the peak load. The distancebetween the peak and base load is the intermediate load asshown in Figure 4.

TABLE V

Iteration History

Iteration 1 2

1 895.787 833.085

2 9.344 17.982

3 3.808 7.204

4 1.917 3.607

5 .427 .802

4250

3400

W 2550

ct 17000

Peak load

I850 T

o1 1441 2881 4321 5761 7201 8641

Time

Fig 4. Load hourly khoozestan network 2001

Figure 5 shows that Khozestan region requires base loadstations for 35.54% of the time during a year. 47.24% of thetime period, this region requires generating units appropriatefor the intermediate load. Finally the system should havesufficient peak load stations for 17.22% of the year.

It can be seen from this figure that Khozestan region needsbase load stations for 35.54% of time compared to that of thewhole country which was 27.45%; i.e. about 7% more. Thisindicates that a region with the hot weather climate requiresmore base load stations.

ct

4000

3500

3000

2500

2000

1500

Peak load17.22%

Intermediat load=47.24%

1000 Base load

500 35.54%

time 1 1441 2881 4321 5761 7201 8641

TABLE VI

Final Cluster Centers

Fig 5. LDC khozestan network 2001

IV. CONCLUSIONS

A new statistical approach is presented in this paper tocalculate the three main parts of a system load demand; base,intermediate and peak-load using a cluster analysis. Thecluster analysis is one of the statistical methods in datacategorizing. The main advantage of the proposed techniqueis that it can be applied to situations in which LDC or systemload factor varies. The applicability of the proposed techniqueis illustrated by determining base, intermediate and peak-loadfor two different case studies. The results are presented andcompared for the two cases. The results presented indicatethat regions with the hot weather climate require more baseload stations.

Change in Cluster Centers

5

V. ACKNOWLEDGMENT

Financial support provided by Khozestan Electric RegionalCompany is gratefully acknowledged.

VI. REFERENCES

[1] Rahman, S., Rinaldy, " An efficient load model for analyzing demandside management impacts," Power Systems, IEEE Transactions, pp:1219-1226, 1993,Vol.8, ISSN: 0885-8950

[2] Richard A. Johnson, Dean W. Wichern, "Applied MultivariateStatistical Analysis ", Prentice Hall prentice-Hall 1988.

[3] William R. Dillon, Matthew Goldstein, "Multivariate Analysis Methodsand Applications," John Willy & Sons1384.

[4] Koval, D.O. and Chowdhury, A.AJ. L. Alqueres and J. C. Praca, "Baseload generator unit operating characteristics," Industrial andCommercial Power Systems Technical Conference, 1994. ConferenceRecord, Papers Presented at the 1994 Annual Meeting, 1994 IEEE, pp.225-230.

[5] Davis, M.W.a, Gifford. A.H and Krupa. T.J, "Micro turbines-aneconomic and reliability evaluation for commercial, residential, andremote load applications," in Power Systems, IEEE Transactions pp1556- 1562, ISSN: 0885-8950.

[6] Singh. S.N, Srivastava. S.C, Kalra. P.K., Rao. M.V, " Voltage andreactive power distribution fractors for line, transformer and generatoroutage studies, " in Advances in Power System Control, Operation andManagement, 1993. APSCOM-93., 2nd International Conference, pp:794 - 800 vol.2, 1993, ISBN: 0-85296-569-9.

[7] Ansari. S.H, Patton. A.D, "A new Markov model for base-loaded unitsfor use in production costing," in Power Systems, IEEE Transactions,pp: 797 - 804, 1990, ISSN: 0885-8950.

[8] Shwehdi. M.H, Hughes. C.M, Quasem. M.A, "Base load fuelconsumption with radiant boiler simulation," in Energy Conversion,IEEE Transaction, pp: 677-683, 1992, Vol.7, Issue:4, ISSN: 0885-8969.

[9] Gangloff. W.C, " New US nuclear plants: one scenario, " NuclearScience Symposium and Medical Imaging Conference, 1991,Conference Record of the 1991 IEEE, pp: 1373-1376, Vol.2, ISBN: 0-7803-0513-2.

VII.

VIII. BIOGRAPHIES

A. Salimi Beni was born in Iran. Obtained B.Sc. andM.Sc. degrees in statistics from Shahid Beheshtiuniversity and Amir Kabir university (poly techniqueof Tehran) in 1998 and 2002 respectively. Worked inIran Grid Management Company (IGMC) in the

;_ department of load forecasting where he conductedm1111_ research in the area of load forecasting.

M. Fotuhi-Firuzabad (IEEE Senior Member, 99) wasborn in Iran. Obtained B.Sc. and M.Sc. degrees inelectrical engineering from Sharif university oftechnology and Tehran university in 1986 and 1989respectively and M.Sc. and Ph.D. degrees in electricalengineering from the university of Saskatchewan in1993 and 1997 respectively. Dr. Fotuhi-Firuzabadworked as a postdoctoral fellow in the department ofelectrical engineering, university of Saskatchewan

from Jan. 1998 to Sept. 2000 and from Sept. 2001 to Sept. 2002 where heconducted research in the area of power system reliability. He worked as anassistant professor in the same department from Sept. 2000 to Sept. 2001.Presently he is an associate professor and head of the Department of ElectricalEngineering, Sharif University of technology, Tehran, Iran.

Davood Farrokhzad was born in 1963 in Tehran, Iran.He received the B.Sc. degree in electrical engineeringand M.Sc. degree in industrial engineering from SharifUniversity of Technology, in 1990 and 1996respectively. He received his PHD degree in industrialengineering from Sharif University of Technology in2001. He has been working in Iran Power Generationand Transmission Company (TAVANIR) for about ten

years and has been responsible for power system planning and reliabilityevaluations. In addition he has been engaged in hydro- thermal system studiesfor Iran Ministry of Energy. His current research interests are in application ofoptimization methods to power system planning and operation problems aswell as in simulation techniques for stochastic modeling of power systemreliability.

S. J. Alemohammad was born in Iran. Obtained his B.Sc. degree in physicsfrom Tehran University in 1979. Presently he is manager of research andplanning office in Khozestan electric regional company.