Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31819
Evolutionary Techniques for Model Order Reduction of Large Scale Linear Systems

Authors: S. Panda, J. S. Yadav, N. P. Patidar, C. Ardil


Recently, genetic algorithms (GA) and particle swarm optimization (PSO) technique have attracted considerable attention among various modern heuristic optimization techniques. The GA has been popular in academia and the industry mainly because of its intuitiveness, ease of implementation, and the ability to effectively solve highly non-linear, mixed integer optimization problems that are typical of complex engineering systems. PSO technique is a relatively recent heuristic search method whose mechanics are inspired by the swarming or collaborative behavior of biological populations. In this paper both PSO and GA optimization are employed for finding stable reduced order models of single-input- single-output large-scale linear systems. Both the techniques guarantee stability of reduced order model if the original high order model is stable. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example from literature and the results are compared with recently published conventional model reduction technique.

Keywords: Genetic Algorithm, Particle Swarm Optimization, Order Reduction, Stability, Transfer Function, Integral Squared Error.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2553


[1] M.J.Bosley and F.P.Lees, "A survey of simple transfer function derivations from high order state variable models", Automatica, Vol. 8, pp. 765-775, !978.
[2] M.F.Hutton and B. Fried land, "Routh approximations for reducing order of linear time- invariant systems", IEEE Trans. Auto. Control, Vol. 20, pp 329-337, 1975.
[3] R.K.Appiah, "Linear model reduction using Hurwitz polynomial approximation", Int. J. Control, Vol. 28, no. 3, pp 477-488, 1978.
[4] T. C. Chen, C.Y.Chang and K.W.Han, "Reduction of transfer functions by the stability equation method", Journal of Franklin Institute, Vol. 308, pp 389-404, 1979.
[5] Y.Shamash, "Truncation method of reduction: a viable alternative", Electronics Letters, Vol. 17, pp 97-99, 1981.
[6] P.O.Gutman, C.F.Mannerfelt and P.Molander, "Contributions to the model reduction problem", IEEE Trans. Auto. Control, Vol. 27, pp 454- 455, 1982.
[7] Y. Shamash, "Model reduction using the Routh stability criterion and the Pade approximation technique", Int. J. Control, Vol. 21, pp 475-484, 1975.
[8] T.C.Chen, C.Y.Chang and K.W.Han, "Model Reduction using the stability-equation method and the Pade approximation method", Journal of Franklin Institute, Vol. 309, pp 473-490, 1980.
[9] Bai-Wu Wan, "Linear model reduction using Mihailov criterion and Pade approximation technique", Int. J. Control, Vol. 33, pp 1073-1089, 1981.
[10] V.Singh, D.Chandra and H.Kar, "Improved Routh-Pade Approximants: A Computer-Aided Approach", IEEE Trans. Auto. Control, Vol. 49. No. 2, pp292-296, 2004.
[11] D.E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, 1989.
[12] S.Panda and N.P.Padhy, "Comparison of Particle Swarm Optimization and Genetic Algorithm for FACTS-based Controller Design", Applied Soft Computing. Vol. 8, Issue 4, pp. 1418-1427, 2008.
[13] S.Panda and N.P.Padhy, "Application of Genetic Algorithm for PSS and FACTS based Controller Design", International Journal of Computational Methods, Vol. 5, Issue 4, pp. 607-620, 2008.
[14] S.Panda and R.N.Patel, "Transient Stability Improvement by Optimally Located STATCOMs Employing Genetic Algorithm" International Journal of Energy Technology and Policy, Vol. 5, No. 4, pp. 404-421, 2007.
[15] S.Panda and R.N.Patel, "Damping Power System Oscillations by Genetically Optimized PSS and TCSC Controller" International Journal of Energy Technology and Policy, Inderscience, Vol. 5, No. 4, pp. 457- 474, 2007.
[16] S.Panda and R.N.Patel, "Optimal Location of Shunt FACTS Controllers for Transient Stability Improvement Employing Genetic Algorithm", Electric Power Components and Systems, Taylor and Francis, Vol. 35, No. 2, pp. 189-203, 2007.
[17] J. Kennedy and R.C.Eberhart, "Particle swarm optimization", IEEE Int.Conf. on Neural Networks, IV, 1942-1948, Piscataway, NJ, 1995.
[18] S.Panda, N.P.Padhy, R.N.Patel, "Power System Stability Improvement by PSO Optimized SSSC-based Damping Controller", Electric Power Components & Systems, Taylor and Francis, Vol. 36, No. 5, pp. 468- 490, 2008.
[19] S.Panda and N.P.Padhy, "Optimal location and controller design of STATCOM using particle swarm optimization", Journal of the Franklin Institute, Elsevier, Vol.345, pp. 166-181, 2008.
[20] S.Panda, N.P.Padhy and R.N.Patel, "Robust Coordinated Design of PSS and TCSC using PSO Technique for Power System Stability Enhancement", Journal of Electrical Systems, Vol. 3, No. 2, pp. 109- 123, 2007.
[21] C. B. Vishwakarma and R.Prasad, "Clustering Method for Reducing Order of Linear System using Pade Approximation", IETE Journal of Research, Vol. 54, Issue 5, pp. 326-330, 2008.
[22] S.Mukherjee, and R.N.Mishra, Order reduction of linear systems using an error minimization technique, Journal of Franklin Inst. Vol. 323, No. 1, pp. 23-32, 1987.
[23] S.Panda, S.K.Tomar, R.Prasad, C.Ardil, "Reduction of Linear Time- Invariant Systems Using Routh-Approximation and PSO", International Journal of Applied Mathematics and Computer Sciences, Vol. 5, No. 2, pp. 82-89, 2009.
[24] S.Panda, S.K.Tomar, R.Prasad, C.Ardil, "Model Reduction of Linear Systems by Conventional and Evolutionary Techniques", International Journal of Computational and Mathematical Sciences, Vol. 3, No. 1, pp. 28-34, 2009.
[25] R.Parthasarathy, and K. N. Jayasimha, System reduction using stability equation method and modified Cauer continued fraction, Proc. IEEE Vol. 70, No. 10, pp. 1234-1236, Oct. 1982.
[26] L.S. hieh, and Y.J.Wei, A mixed method for multivariable system reduction, IEEE Trans. Autom. Control, Vol. AC-20, pp. 429-432, 1975.
[27] R.Prasad, and J.Pal, Stable reduction of linear systems by continued fractions, J. Inst. Eng. India, IE (I) J.EL, Vol. 72, pp. 113-116, Oct. 1991.
[28] J. Pal, Stable reduced -order Pade approximants using the Routh- Hurwitz array, Electronics letters, Vol. 15, No. 8, pp. 225-226, April 1979.