A Study on the Impact of DE Population Size on the Performance Power System Stabilizers
Abstract The population size of DE plays a significant role in the way the algorithm performs as it influences whether good solutions can be found. Generally, the population size of DE algorithm is a user-defined input that remains fixed during the optimization process. Therefore, inadequate selection of DE population size may seriously hinder the performance of the algorithm. This paper investigates the impact of DE population size on (i) the performance of DE when applied to the optimal tuning of power system stabilizers (PSSs); and (ii) the ability of the tuned PSSs to perform efficiently to damp low-frequency oscillations. The effectiveness of these controllers is evaluated based on frequency domain analysis and validated using time-domain simulations. Simulation results show that a small population size may lead the algorithm to converge prematurely, and thus resulting in a poor controller performance. On the other hand, a large population size requires more computational effort, whilst no noticeable improvement in the performance of the controller is observed.
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Abdel – Magid, Y. L., Abido, A., and Mantaurym, H., 1999. Simultaneous stabilization of Multimachine Power System via genetic algorithm. In IEEE Trans. Power Sys., pages 1428–1438.
Bibaya, L., and Liu, C., 2016. Optimal tuning and placement of power system stabilizers based eigenvalues. In Indonesia Journal of Elec. Eng. And Comput. Sciences, pages 273–281.
Brest, J., Greiner, S., Boskovic, B., Mernik, M., and Zumer, V., 2006. Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. In IEEE Trans. on Evolutionary Computation, pages 646–657.
Brest, J., Boškovi?, B., and Žumer, V., 2010. An improved self-adaptive differential evolution algorithm in single-objective constrained real-parameter optimization. In Proc. of the IEEE Congress on evolutionary computation.
Brown, C., Jin, Y., Leach, M., and Hodgson, M., 2016. µJADE: Adaptive Differential Evolution with a Small Population. In Soft Computing, pages 4111–4120.
Das, S., and Suganthan, P. N, 2011. Differential evolution: a survey of the state-of-the-art. in IEEE Trans. On Evol. Comput., pages 4–31.
Duan, M., Yang, H., Wang, S., and Liu, Y., 2019. Self-adaptive Dual-strategy Differential Evolution Algorithm. In Plos One 14(10). https://doi.org/10.1371/Journal.pone.0222706.
Eltaeib, T., and Mahmood, A., 2018. Differential evolution: a survey and analysis. Applied Sciences, MDPI. 7, 1945. https://doi.org/10.3390/app8101945.
Folly, K. A., 2005. Multimachine power system stabilizer design based on a simplified version of genetic algorithm combined with learning. In Proc. of International Conference on Intelligent Systems Application to Power Systems (ISAP).
Folly, K. A., and Mulumba, T., 2020. Impact of population size on the performance of DE-based Power System Stabilizers. In proc. of 24th European conference in Artificial Intelligence (ECAI), workshop on artificial- intelligence-in-power-and-energy-systems-(AIPES), paper ID No.8, 2020.
Georgioudakisa M., and Plevris, V., 2020. On the Performance of Differential Evolution Variants in Constrained Structural Optimization. In Procedia Manufacturing, pages 371–378.
Kundur, P., Klein, M., Rogers G., and Zywno, M., 1989. Application of power system stabilizers for enhancement of overall system stability. In IEEE Trans. Power Syst., pages 614–626.
Lui J., and Lampinen, J., 2005. A Fuzzy adaptive differential evolution algorithm. In Soft Computation: Fusion Found Method Appl., pages 448–462.
Mallipeddi R., and Suganthan, P. N., 2008. Empirical Study on the Effect of Population Size on Differential. In Proc. of IEEE Congress on Evolutionary Computation.
Mitra, P., Yan, C., Grant, L., Venayagamoorthy, G. K., and Folly, K., 2009. Comparison study of population-based techniques for power system stabilizer design. In Proc. of the 15 th Int. conf. on Intelligent, Curitiba, Brazil.
Mohamed, A. W., 2017. Solving large-scale global optimization problems using enhanced adaptive differential evolution algorithm’, In Complex Intell. Syst., pages 205–231.
Montgomery, J., 2010. Crossover and the different faces of differential evolution searches. In Proc. of IEEE Congress on Evolutionary Computation.
Mulumba, T., and Folly. K. A., 2011. Design and comparison of Multi-machine Power System Stabilizer based on Evolution Algorithms. In Proc. of. Universities’ Power Engineering Conference (UPEC).
Mulumba, F., 2012. Application of Differential Evolution to Power System Stabilizer Design. MSc Dissertation, University of Cape Town, Cape Town.
Mulumba, T. F., and Folly, K. A., 2020. Application of Evolutionary Algorithms to Power System Stabilizer Design. In Implementations and Applications of Machine Learning, Studies in Computational Intelligence 782, Subair S, Thron, C, Eds., pages 29–62. Springer.
Peng, S., and Wang, Q., 2018. Power system stabilizer parameters optimization using immune genetic algorithm. In IOP Conf. Series: Materials Sci. and Eng., 394. https://www.doi.org/10.1088/1757-899X/394/4/042091.
Price, K. V., 1997. Differential evolution vs. the functions of the 2nd ICEO. In Proc. IEEE Int. Conf. Evol. Comput. pages 153–157.
Shafiullah, Md., Juel Rana, Md., and Abido, M. A., 2017. Power system stability enhancement through optimal design of PSS employing PSO. Fourth Int. Conf. on Adv. In Elec. Eng. (ICAEE).
Shayeghi, H., Shayanfar, H. A., Safari, A., and Aghmasheh, R., 2010. A robust PSSs design using PSO in a multi-machine environment. Energy Convers. and Manag. pages 696–702.
Sheetekela, S., and Folly, K., 2009a. Multimachine power system stabilizer design based on evolutionary algorithms, The 44th international Universities. Power Engineering Conference (UPEC).
Sheetekela, S. P. N., and Folly, K. A., 2009b. Optimization of Power System Stabilizers using Genetic Algorithm Techniques based on Eigenvalue analysis. 18th Southern African Universities’ Power Engineering Conference (SAUPEC).
Soeprijanto, A., Putra, D. F. U., Fenno, O., Suyanto, Ashari, H. S. D., and Rusilawati., 2016. Optimal tuning of PSS parameters for damping improvement in SMIB model using random drift PSO and network reduction with losses concept. In Int. Seminar of Intelligent Technology and Appl. (ISITIA) 2016.
Storn, R., and Price, K., 1997. Differential Evolution: a simple and effective heuristic for global optimization over continuous spaces. Journal of global optimization, pages 341–359.
Suganthan, P. N., and Quin, A. K., 2005. Self-Adaptive Differential Evolution Algorithm for numerical optimization. In Proc. of the IEEE Congres on Evolutionary Computation.
Teo, J., 2006. Exploring dynamic self-adaptive populations in differential evolution. In Soft. Comput. pages 673–686.
Vesterstroem J., and Thomsen, R., 2004. A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems. In Proc. of the IEEE Congress on Evolutionary Computation.
Bibaya, L., and Liu, C., 2016. Optimal tuning and placement of power system stabilizers based eigenvalues. In Indonesia Journal of Elec. Eng. And Comput. Sciences, pages 273–281.
Brest, J., Greiner, S., Boskovic, B., Mernik, M., and Zumer, V., 2006. Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. In IEEE Trans. on Evolutionary Computation, pages 646–657.
Brest, J., Boškovi?, B., and Žumer, V., 2010. An improved self-adaptive differential evolution algorithm in single-objective constrained real-parameter optimization. In Proc. of the IEEE Congress on evolutionary computation.
Brown, C., Jin, Y., Leach, M., and Hodgson, M., 2016. µJADE: Adaptive Differential Evolution with a Small Population. In Soft Computing, pages 4111–4120.
Das, S., and Suganthan, P. N, 2011. Differential evolution: a survey of the state-of-the-art. in IEEE Trans. On Evol. Comput., pages 4–31.
Duan, M., Yang, H., Wang, S., and Liu, Y., 2019. Self-adaptive Dual-strategy Differential Evolution Algorithm. In Plos One 14(10). https://doi.org/10.1371/Journal.pone.0222706.
Eltaeib, T., and Mahmood, A., 2018. Differential evolution: a survey and analysis. Applied Sciences, MDPI. 7, 1945. https://doi.org/10.3390/app8101945.
Folly, K. A., 2005. Multimachine power system stabilizer design based on a simplified version of genetic algorithm combined with learning. In Proc. of International Conference on Intelligent Systems Application to Power Systems (ISAP).
Folly, K. A., and Mulumba, T., 2020. Impact of population size on the performance of DE-based Power System Stabilizers. In proc. of 24th European conference in Artificial Intelligence (ECAI), workshop on artificial- intelligence-in-power-and-energy-systems-(AIPES), paper ID No.8, 2020.
Georgioudakisa M., and Plevris, V., 2020. On the Performance of Differential Evolution Variants in Constrained Structural Optimization. In Procedia Manufacturing, pages 371–378.
Kundur, P., Klein, M., Rogers G., and Zywno, M., 1989. Application of power system stabilizers for enhancement of overall system stability. In IEEE Trans. Power Syst., pages 614–626.
Lui J., and Lampinen, J., 2005. A Fuzzy adaptive differential evolution algorithm. In Soft Computation: Fusion Found Method Appl., pages 448–462.
Mallipeddi R., and Suganthan, P. N., 2008. Empirical Study on the Effect of Population Size on Differential. In Proc. of IEEE Congress on Evolutionary Computation.
Mitra, P., Yan, C., Grant, L., Venayagamoorthy, G. K., and Folly, K., 2009. Comparison study of population-based techniques for power system stabilizer design. In Proc. of the 15 th Int. conf. on Intelligent, Curitiba, Brazil.
Mohamed, A. W., 2017. Solving large-scale global optimization problems using enhanced adaptive differential evolution algorithm’, In Complex Intell. Syst., pages 205–231.
Montgomery, J., 2010. Crossover and the different faces of differential evolution searches. In Proc. of IEEE Congress on Evolutionary Computation.
Mulumba, T., and Folly. K. A., 2011. Design and comparison of Multi-machine Power System Stabilizer based on Evolution Algorithms. In Proc. of. Universities’ Power Engineering Conference (UPEC).
Mulumba, F., 2012. Application of Differential Evolution to Power System Stabilizer Design. MSc Dissertation, University of Cape Town, Cape Town.
Mulumba, T. F., and Folly, K. A., 2020. Application of Evolutionary Algorithms to Power System Stabilizer Design. In Implementations and Applications of Machine Learning, Studies in Computational Intelligence 782, Subair S, Thron, C, Eds., pages 29–62. Springer.
Peng, S., and Wang, Q., 2018. Power system stabilizer parameters optimization using immune genetic algorithm. In IOP Conf. Series: Materials Sci. and Eng., 394. https://www.doi.org/10.1088/1757-899X/394/4/042091.
Price, K. V., 1997. Differential evolution vs. the functions of the 2nd ICEO. In Proc. IEEE Int. Conf. Evol. Comput. pages 153–157.
Shafiullah, Md., Juel Rana, Md., and Abido, M. A., 2017. Power system stability enhancement through optimal design of PSS employing PSO. Fourth Int. Conf. on Adv. In Elec. Eng. (ICAEE).
Shayeghi, H., Shayanfar, H. A., Safari, A., and Aghmasheh, R., 2010. A robust PSSs design using PSO in a multi-machine environment. Energy Convers. and Manag. pages 696–702.
Sheetekela, S., and Folly, K., 2009a. Multimachine power system stabilizer design based on evolutionary algorithms, The 44th international Universities. Power Engineering Conference (UPEC).
Sheetekela, S. P. N., and Folly, K. A., 2009b. Optimization of Power System Stabilizers using Genetic Algorithm Techniques based on Eigenvalue analysis. 18th Southern African Universities’ Power Engineering Conference (SAUPEC).
Soeprijanto, A., Putra, D. F. U., Fenno, O., Suyanto, Ashari, H. S. D., and Rusilawati., 2016. Optimal tuning of PSS parameters for damping improvement in SMIB model using random drift PSO and network reduction with losses concept. In Int. Seminar of Intelligent Technology and Appl. (ISITIA) 2016.
Storn, R., and Price, K., 1997. Differential Evolution: a simple and effective heuristic for global optimization over continuous spaces. Journal of global optimization, pages 341–359.
Suganthan, P. N., and Quin, A. K., 2005. Self-Adaptive Differential Evolution Algorithm for numerical optimization. In Proc. of the IEEE Congres on Evolutionary Computation.
Teo, J., 2006. Exploring dynamic self-adaptive populations in differential evolution. In Soft. Comput. pages 673–686.
Vesterstroem J., and Thomsen, R., 2004. A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems. In Proc. of the IEEE Congress on Evolutionary Computation.
Agbenyo Folly, K., & Fa Mulumba, T. (2022). A Study on the Impact of DE Population Size on the Performance Power System Stabilizers. ADCAIJ: Advances in Distributed Computing and Artificial Intelligence Journal, 11(1), 97–109. https://doi.org/10.14201/adcaij.27955
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