216 M. Younes — M. Rahli — A.
Koridak: ECONOMIC POWER DISPATCH USING EVOLUTIONARY ALGORITHM
Fig. 6. Evolution of the GA (30 bus). Fig. 7. Evolution of the GA (57 bus).
Table 6. Result of the study Subject to constraints
methods GA Matpower PG1 + PG2 + PG3 + PG4 + PG5 + PG6 = 192.1 MW (22)
opt
PG1 [MW] 43.204228 41.53
opt
PG2 [MW] 58.642223 55.39 QG1 + QG2 + QG3 + QG4 + QG5 + QG6 = 105.1 MW (23)
opt
PG3 [MW] 21.551666 16.19 Testing parameters for the IEEE 57 bus test system are
opt
PG4 [MW] 37.439453 22.74 as follows:
opt
PG5 [MW] 17.576327 16.25
opt Table 8. Parameter values for GA.
PG6 [MW] 13.684809 39.96
opt
QG1 [MWAR] –5.420000 –5.42
Population size 60
Qopt
G2 [MWAR] 1.730000 1.73 Number of generations 2500
Qopt Crossover probability 0.8
G3 [MWAR] 35.920000 35.92
Mutation probability 0.05
Qopt
G4 [MWAR] 34.200000 34.20
Generation-elitism 10
Qopt
G5 [MWAR] 6.960000 6.96 Number of bit for encode active power generation 32
Qopt
G6 [MWAR] 31.660000 31.66
Coût [$/h] 576.629286 576.83 Table 9. Result of the study
Characteristic values of the IEEE 57 bus test system methods GA Matpower
are as follows: opt
PG1 [MW] 296.94 265.33
opt
Table 7. Generator operating limits and quadratic cost function PG2 [MW] 100.00 100.00
coefficients. opt
PG3 [MW] 140.00 140.00
opt
PG4 [MW] 99.99 100.00
Bus Pmin Pmax Qmin Qmax a b c
opt
1 0.00 575.88 –200 300 0.01 0.30 0.20 PG5 [MW] 343.88 276.97
opt
2 0.00 100.00 –17 50 0.01 0.30 0.20 PG6 [MW] 100.00 100.00
3 0.00 140.00 –10 60 0.01 0.30 0.20 opt
PG7 [MW] 189.11 287.56
6 0.00 100.00 –8 25 0.01 0.30 0.20 opt
QG1 [MWAR] 176.22 72.73
8 0.00 550.00 –140 200 0.01 0.30 0.20
9 0.00 100.00 –3 9 0.01 0.30 0.20 Qopt
G2 [MWAR] 49.99 50.00
12 0.00 410.00 –150 155 0.01 0.30 0.20 Qopt
G3 [MWAR] 59.72 36.74
Qopt
G4 [MWAR] 24.99 6.37
Losses are respectively Qopt
G5 [MWAR] 199.98 55.78
PL = 2.86 MW, QL = 31.13 MVAR (20) Qopt
G6 [MWAR] –2.99 9.00
The problem is minimize the objective function Qopt
G7 [MWAR] –90.57 48.25
n X o
Min f PG = fi PG (21) Coût [$/h] 3120.87 3176.39
Journal of ELECTRICAL ENGINEERING 57, NO. 4, 2006 217
6 CONCLUSION [14] MÜHLENBEIN, H.—SCHLIERKAMP-VOOSEN, D. : Predic-
tive Models for the Breeder Genetic Algorithm, Evolutionary
Computation 1 No. 1 (1993), 25–49.
GA as a solution to the economic dispatch problem of
[15] KAYNAK, O.—ZADEH, L. A.—TURKSEN, B.—RUDAS, I.
the IEEE 9 bus, 30 bus and 57 bus test system have been
J. : Computational Intelligence: Soft Computing and Fuzzy-
presented. Although genetic algorithms are generally con- Neuro Integration with Applications, 1998.
sidered to be offline optimisation algorithms, owing to the [16] TINNEY, W. F.—HART, C. E. : Power Flow Solution by New-
large amount of CPU time that need to converge to an ton’s Method, IEEE Transactions on Power Apparatus and Sys-
optimal solution, they can exhibit very good online per- tems PAS-86 No. 11 (Nov. 1967), 1449–1460.
formance, when a suitable combination of operators is [17] STOTT, B.—ALSAC, O. : Fast Decoupled Load Flow, IEEE
employed. The basic advantage of GA is that they can be Transactions on Power Apparatus and Systems PAS-93 (June
1974), 859–869.
very effectively coded to work on parallel machines. Po-
[18] van AMERONGEN, R. : A General-Purpose Version of the Fast
tential application of GA include unit commitment and Decoupled Loadflow, IEEE Transactions on Power Systems 4
optimal power flow. With the recent advances in parallel No. 2 (May 1989), 760–770.
computing, the on line solution optimal power flow with [19] MÉSZÁROS, C. : The Efficient Implementation of Interior
nonconvex generator cost functions may soon be possible. Point Methods for Linear Programming and their Applications,
PhD Thesis, Eötvös Loránd University of Sciences, 1996.
References Received 19 September 2005
[1] HOGAN, W. W. : Contract Networks for Electric Power Trans- Mimoun Younes was born in 1965 in Sidi Belabbes,
mission, Journal of Regulatory Economics 4 (1992), 211–242. Algeria. He received his BS degree in electrical engineering
[2] DOMMEL, H. W. : Optimal Power Dispatch, IEEE Transac- from the Electrical Engineering Institute of The University
tions on Power Apparatus and Systems PAS93 No. 3 (May/june of Sidi Belabbes (Algeria) in 1990, the MS degree from the
1974), 820–830. Electrical Engineering Institute of The University of Sidi Be-
[3] ALSAC, O.—BRIGHT, J.—PARIS, M.—STOTT : Further De- labbes (Algeria) in 2003. He is currently Professor of electrical
velopments in LP-Based Optimal Power Flow, IEEE Transaction engineering at The University of Sidi Belabbes (Algeria). His
of Power Systems 5 No. 3 (August 1990), 697–711.
research interests include operations, planning and economics
[4] NANDA, J.—KOTHARI, D. P.—SRIVATAVA, S. C. : New of electric energy systems, as well as optimization theory and
Ptimal Power-Dispatch Algorithm Using Fletcher’s Quadratic
its applications.
Programming Method, Procedings of the IEE 136 No. 3 (May
1989), 153–161. Mostefa Rahli was born in 1949 in Mocta Douz, Mascara,
[5] BJORNDAL, M.—JORNSTEN, K. : Zonal Pricing in a Dereg- Algeria. He received his BS degree in electrical engineer-ing
ulated Electricity Market, The Energy Journal 22 No. 1 (2001). from the Electrical Engineering Institute of The University of
[6] ZIMMERMAN, R. D.—GAN, D. : MATPOWER — A MAT- Sciences and Technology of Oran (USTO) in 1979, the MS
LAB Power System Simulation Package, User’s Manual, School degree from the Electrical Engineering Institute of The Uni-
of Electrical Engineering, Cornell University, 1997, available: versity of Sciences and Technology of Oran (USTO) in 1985,
http://www.pserc.cornell.edu/matpower/manual.pdf. and the PhD degree from the Electrical Engineering Institute
[7] HIMMELBLAU, D. M. : Applied Linear and Nonlinear pro- of The University of Sciences and Technology of Oran (USTO)
gramming, McGraw-Hill, New York, 1972. in 1996. From 1987 to 1991, he was a visiting professor at the
[8] RAHLI, M. : Applied Linear and Nonlinear Programming to University of Liege (Monte ore’s Electrical Institute) Liege
Economic Dispatch, PhD Thesis, Electrical Institute, Usto, (Belgium ) where he worked on Power Systems Analysis anal-
Oran, Algeria, 1996. ysis under Professors Pol Pirotte and Jean Louis Lilien. He
[9] STAGG, G. W.—ABIADH, A. H. El : Computer Methods in is currently Professor of electrical engineering at The Univer-
Power System Analysis, New York, 1968. sity of Sciences and Technology of Oran (USTO), Oran, Al-
[10] GOLDBERG, D. E. : Genetic Algorithms in Search, Optimiza- geria. His research interests include operations, planning and
tion & Machine Learning, Addison-Wesley, Reading, 1989. economics of electric energy systems, as well as optimization
[11] GOLDBERG, D. E. : Sizing Populations for Serial and Parallel theory and its applications.
Genetic Algorithms, In J.D. Schaffer, editor, Proceedings of the
Lahouari Abdelhakem Koridak was born in 1966 in
Third International Conference on Genetic Algorithms, Morgan
Oran, Algeria. He received his BS degree in electrical engineer-
Kaufmann, 1989, pp. 70–79.
ing from the Electrical Engineering Institute of The University
[12] MIKAC, B.—INKRET, R. : Application of a Genetic Algo-
rithm to the Availability-Cost Optimisation of a Transmission
of oran (Algeria) in 1993, the MS degree from the Electrical
Network Topology, Proceedings ICANNGA’97 Third Interna- Engineering Institute of The University of Sidi Be-labbes (Al-
tional Conference on Artificial Neural Networks and Genetic geria) in 2003. He is currently Professor of electrical engineer-
Algorithms, Norwich, U.K., Springer Verlag Wien, New York, ing at The University of Sidi Belabbes (Algeria). His research
1997, pp. 306–310. interests include operations, planning and economics of elec-
[13] HOLLAND, J. H. : Adaptation in Natural and Artificial Sys- tric energy systems, as well as optimization theory and its
tems, University of Michigan Press, Ann Arbor, Michigan, 1975. applications.
