Design Optimal Feedback Control Using Evolutionary Particle Swarm Optimization in Multi- Machine Power System

Ardyono Priyadi, Mauridhy Hery Purnomo, Margo Pujiantoro


This This paper proposes an application of Evolutionary Particle Swarm Optimization (EPSO) to design weighting matrices Q and R elements in Linear Quadratic Regulator (LQR) optimization process. Solving optimal feedback control has already established by LQR method. However, there still has some problem to find the weighting matrices Q and R.
These weighting matrices are the most important components in LQR optimization method. Weighting matrices are calculated using trial and error, Particle Swarm Optimazation (PSO), and EPSO techniques and simulation results are compared. Static and Dynamic loads are considered and comparison is illustrated.

Full Text:



E.P. De Mello & Concordia, “Concepts of Synchronous Machine Stability by Excitation Control”, IEEE, Vol. Pas-88, No.4, April 1969.

Hamdy A.M. Moussa and Yao-Nan Yu, “Optimal Power System Stabilization through Excitation and/or Governor Control”, IEEE, Vol.Pas-91, N0.3, 1972

IEEE Committee Report, “Computer Representation of Excitation Systems”, IEEE Trans., Vol. Pas-87, No.6, 1968

IEEE Committee Report, “Dynamic Models for Steam and Hydro Turbines in Power System Studies”, IEEE Trans., Pas-92, Pp. 1904- 1915, 1973

Anderson P.M and Fouad A.A, “Power System Control and Stability”, The Iowa State University Press, 1977

IEEE Committee Report, “Excitation System Models For Power System Stability Studies”, IEEE Trans., Vol. Pas-100, No.2, 1981

Prabha Kundur, Power System Stability and Control, Mc Graw Hill, 1994

Yau-Nan Yu and Vongsuriya, “Aplication of an Optimal Control Theory to a Power System”, IEEE, Vol.Pas-89, No.1, 1970

Charles E. Fosha, Jr., And Olle I. Elgerd, “The Megawatt-Frequency Control Problem: A New Approach via Optimal Control Theory", IEEE Trans. Vol. Pas, No.4, 1970

J.C. Geromel and J. Bernussou, “An Algorithm for Optimal Decentralized Regulation of Linear Quadratic Interconnected System", Automatica, Vol.15, Pp. 489-491, 1979

Lim Choo Min and S. Elangovan, “Output Feedback Controller for Improved Dynamic Stability in Power Systems”, Int. J. Elect. Enging. Educ., Vol.22, Pp. 83-92, 1985

M.A. Johnson & M.J. Grimble, “Recent Trends In Linear Optimal Quadratic Multivariable Control System Design”, IEEE Proc. Vol.134, Pt.D., No.1, January 1987.

Imam Robandi, Katsumi Nishimori Ryo Nishimura, Nagamori Ishihara, Optimal Feedback Control Design Using Genetic Algorithm in Multimachine Power System, Elsevier Electrical Power and Energy Systems, Vol. 23, Pp. 263-271, 2001

Imam Robandi, Katsumi Nishimori Ryo Nishimura, Nagamori Ishihara, and Ardyono Priyadi, A Q & R Weighting Matrix Improvement in Power System Optimization Using Genetic Algorithm, Proceedings of Industrial Electronic Seminar, Vol. 1, Pp. 32 – 35, Surabaya, Indonesia , 1999

Adi Soeprijanto, Naoto Yorino, Hiroshi Sasaki, Hiroaki Sugihara, “Solving The Unstable Zero Problem In Designing Coordinated H¥- PSS’s Caused by Dynamic Loads”, Proceeding of The Eleven Annual Conference of Power & Energy Society IEE of Japan, Vol. A, pp. 428- 429, 2000

IEEE Task Force on Load Representation for Dynamic Performance, “Load Representation for Dynamic Performance Analysis”, IEEE Transaction on Power Systems, Vol. 8, No.2, 1993

Jovica V. Milanovic, I.A. Hiskens, “Effects of Load Dynamics on Power Systems Damping”, IEEE Transaction on Power Systems, Vol 10, No.2, 1995

J.Kennedy and R.Eberhart, “Particle swarm optimization,” in proceedings of IEEE International conference on Neural Networks, Vol. IV, Perth, Australia, 1995, pp. 1942-1948.

Hirotaka Yoshida, Kenichi Kawata, Yoshikazu Fukuyama, Shinichi Takayama, and Yosuke Nakanishi, “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, Nov. 2000.

Vladimiro Miranda, and Nuno Fonseca, “EPSO-Best-of-Two-Worlds Meta-Heuristic Applied to Power System Problems,” in Proc. Of the IEEE congress on Evolutionary Computation, June 2002, pp.1080-1085.

Vladimiro Miranda, and Nuno Fonseca, “EPSO-Evolutionary Particle Swarm Optimization, a New Algorithm with Application in Power Systems,” in Proc. Of the IEEE congress on Evolutionary Computation, June 2002, pp.745-750.

Vladimiro Miranda, and Nuno Fonseca, “New Evolutionary Particle Swarm Algorithm (EPSO) Applied to Voltage/VAR Control,” in Proc. Of 14the PSCC, Sevilla, June 2002, session 21, paper 5, pp.1-6.

Y.Shi and R. Eberhart, “A Modified Particle Swarm Optimizer”, Proc. Of IEEE International conference on Evolutionary Computation (ICEC`98), Anchorage, Alaska, May 4-9, 1998.

Zheng,Y., Ma, L., Zhang, L., and Qian, J.,”On the convergence analysis and parameter selection in particle swarm optimization”, in Proc. Of international conference on Machine Learning and Cybernetics 2003, pp.1802-1807.

Y.Shi and R. Eberhart, “Parameter selection in Particle Swarm Optimization”,in Proc. Of the 1998 Annual Conference on Evolutionary Programming, San Diago, 1998.

R.C. Eberhart , and Y.Shi, “Comparing Inertia Weights and Costriction Factors in Particle Swarm Optimization”, in Proc. Of the 2000 congress on Evolutionary Computation, Vol.1, pp.84-88.

Ardyono priyadi, Yoshifumi Zoka, Naoto Yorino,”A Design for Robust Power System Stabilizer by Means of Particle Swarm Optimization Method”, in Proceedings of IEEJ Conference, Osaka, 2006.


  • There are currently no refbacks.