Scheduling electric power generators using particle swarm optimization combined with the Lagrangian relaxation method

Balci, H. H. ; Valenzuela, J. F.

International Journal of Applied Mathematics and Computer Science, Tome 14 (2004) no. 3, pp. 411-421.

Résumé

This paper describes a procedure that uses particle swarm optimization (PSO) combined with the Lagrangian Relaxation (LR) framework to solve a power-generator scheduling problem known as the unit commitment problem (UCP). The UCP consists of determining the schedule and production amount of generating units within a power system subject to operating constraints. The LR framework is applied to relax coupling constraints of the optimization problem. Thus, the UCP is separated into independent optimization functions for each generating unit. Each of these sub-problems is solved using Dynamic Programming (DP). PSO is used to evolve the Lagrangian multipliers. PSO is a population based search technique, which belongs to the swarm intelligence paradigm that is motivated by the simulation of social behavior to manipulate individuals towards better solution areas. The performance of the PSO-LR procedure is compared with results of other algorithms in the literature used to solve the UCP. The comparison shows that the PSO-LR approach is efficient in terms of computational time while providing good solutions.

Détail

Keywords: particle swarm optimization (PSO), unit commitment, Lagrange relaxation
Mots-clés : optymalizacja rojem cząstek, jednostka wytwórcza, relaksacja Lagrange'a

Bibliographie

[1] Abido M.A. (2002): Optimal power flow using particle swarm optimization.—Int. J. Electr. Power Energy Syst., Vol. 24, No. 7, pp. 563–571.

[2] Bard J.F. (1988): Short-term scheduling of thermal-electric generators using lagrangian relaxation. — Opers. Res., Vol. 36, No. 5, pp. 756–766.

[3] Bertsekas D.P. (1982): Constrained Optimization and Lagrange Multiplier Methods.—New York: Academic Press.

[4] Bertsekas D.P., Lauer G.S., Sandell N.R. Jr. and Posbergh T.A. (1983): Optimal short-term scheduling of large scale power systems. — IEEE Trans. Automat. Contr., Vol. 28, No. 1, pp. 1–11.

[5] Blackwell T.M. and Bentley P. (2002): Don’t push me! Collision avoiding swarms.—Proc. Congress Evolutionary Computation, Honolulu, USA, pp. 1691–1696.

[6] Carter M.W. and Price C.C. (2001): Operations Research: A Practical Introduction. — Boca Raton: CRC Press.

[7] Eberhart R.C. and Hu X. (1999): Human tremor analysis using particle swarm optimization.—Proc. Congress Evolutionary Computation, Piscataway, NJ, pp. 1927–1930.

[8] Fischer M.L. (1973): Optimal solution of scheduling problems using lagrange multipliers: Part I.—Opers. Res., Vol. 21, No. 5, pp. 1114–1127.

[9] Garver L.L. (1963): Power generation scheduling by integer programming—Development of theory. — AIEE Trans., No. 2, pp. 730–735.

[10] Kazarlis S.A., Bakirtzis A.G. and Petridis V. (1996): A genetic algorithm solution to the unit commitment problem. — IEEE Trans. Power Syst., Vol. 11, No. 1, pp. 83–90.

[11] Kennedy J. and Eberhart R.C. (1995): Particle swarm optimization. — Proc. IEEE Int. Conf. Neural Networks, Perth, Australia, pp. 1942–1948.

[12] Kennedy J. and Eberhart R.C. (2001): Swarm Intelligence. — San Francisco: Morgan Kaufmann.

[13] Lee F.N. (1988): Short term unit commitment—A new method. — IEEE Trans. Power Syst., Vol. 3, No. 2, pp. 421–428.

[14] Muckstadt J.A. and Koenig S.A. (1977): An application of Lagrangian relaxation to scheduling in power generating systems. — Opers. Res., Vol. 25, No. 3, pp. 387–403.

[15] Naka S., Genji T., Yura T. and Fukuyama Y. (2003): A hybrid particle swarm optimization for distribution state estimation. — IEEE Trans. Power Syst., Vol. 18, No. 1, pp. 60–68.

[16] Orero S.O. and Irving M.R. (1997): A combination of the genetic algorithm and Lagrangian relaxation decomposition techniques for the generation unit commitment problem.— Electr. Power Syst. Res., Vol. 43, No. 3, pp. 149–156.

[17] Reynolds C.W. (1987): Flocks, herds and schools: A distributed behavioral model. — Comput. Graph., Vol. 21, No. 4, pp. 25–34.

[18] Salman A., Ahmad I. and Al-Madani S. (2002): Particle swarm optimization for task assignment problem. — Microprocess. Microsyst., Vol. 26, No. 8, pp. 363–371.

[19] Sheble G.B. and Fahd G.N. (1994): Unit commitment literature synopsis. — IEEE Trans. Power Syst., Vol. 9, No. 1, pp. 128–135.

[20] Shi Y. and Eberhart R.C. (1999): Empirical study of particle swarm optimization.—Proc. Congress Evolutionary Computation, Piscataway, NJ, pp. 1945–1950.

[21] Shi Y. and Krohling R.A. (2002): Co-evolutionary particle swarm optimization to solve min-max problems. — Proc. IEEE Congress Evolutionary Computation, Honolulu, Hawaii, USA, pp. 1682–1687.

[22] Su C.C. and Hsu Y.Y. (1991): Fuzzy dynamic programming: An application to unit commitment. — IEEE Trans. Power Syst., Vol. 6, No. 3, pp. 1231–1237.

[23] Suzannah Y.W.W. (1998): An enhanced simulated annealing approach to unit commitment.—Int. J. Electr. Power Energy Syst., Vol. 20, No. 5, pp. 359–368.

[24] Takriti S., Birge J.R. and Long E. (1996): A stochastic model for the unit commitment problem.—IEEE Trans. Power Syst., Vol. 11, No. 3, pp. 1497–1508.

[25] Tandon V. (2000): Closing gap between CAD/CAM and optimized CNC and milling. — M.Sc. Thesis, Purdue School of Engineering and Technology, Purdue University, Indiana, USA.

[26] Ting T.-O., Rao M.V.C., Loo C.K. and Ngu S.S. (2003): Solving unit commitment problem using hybrid particle swarm optimization.—J. Heuristics, Vol. 9, No. 6, pp. 507–520.

[27] Tseng C.L., Li C.A. and Oren S.S. (2000): solving the unit commitment problem by a unit decommitment method. — J. Optim. Theory Applics., Vol. 105, No. 3, pp. 707–730.

[28] Valenzuela J. and Smith A. (2002): A seeded memetic algorithm for large unit commitment problems.—J. Heuristics, Vol. 8, No. 2, pp. 173–195.

[29] Virmani S., Adrian E.C., Imhof K. and Mukherjee S. (1989): Implementation of a Lagrangian relaxation based unit commitment problem. — IEEE Trans. Power Syst. Vol. 4, No. 4, pp. 373–1380.

[30] Wood A.J. and Wollenberg B.F. (1996): Power Generation, Operation and Control, 2-nd Ed..—New York: Wiley.

[31] Xiaomin B. and Shahidehpour S.M. (1997): Extended neighborhood search algorithm for constrained unit commitment. — Int. J. Electr. Power Energy Syst., Vol. 19, No. 5, pp. 349–356.

[32] Yoshida H., Kawata K., Fukuyama Y. and Nakanishi Y. (2001): A particle swarm optimization for reactive power and voltage control considering voltage security assessment. — IEEE Trans. Power Syst., Vol. 15, No. 4, pp. 1232–1239.