Photovoltaic System Allocation Using Discrete Particle Swarm Optimization with Multi-level Quantization

  • Song, Hwa-Chang (Dept. of Electrical Engineering, Seoul National University of Technology) ;
  • Diolata, Ryan (School of Electronic and Information Engineering, Kunsan National University) ;
  • Joo, Young-Hoon (School of Electronic and Information Engineering, Kunsan National University)
  • Published : 2009.06.30


This paper presents a methodology for photovoltaic (PV) system allocation in distribution systems using a discrete particle swarm optimization (DPSO). The PV allocation problem is in the category of mixed integer nonlinear programming and its formulation may include multi-valued dis-crete variables. Thus, the PSO requires a scheme to deal with multi-valued discrete variables. This paper introduces a novel multi-level quantization scheme using a sigmoid function for discrete particle swarm optimization. The technique is employed to a standard PSO architecture; the same velocity update equation as in continuous versions of PSO is used but the particle's positions are updated in an alternative manner. The set of multi-level quantization is defined as integer multiples of powers-of-two terms to efficiently approximate the sigmoid function in transforming a particle's position into discrete values. A comparison with a genetic algorithm (GA) is performed to verify the quality of the solutions obtained.


  1. Trends in Photovoltaic Applications: Survey Report of Selected IEA Countries between 1992 and 2007, IEA Annual Report, Aug. 2008. Available:
  2. Paatero, J. V, and Lund, P. D., 'Effects of large-scale photovoltaic power integration on electricity distribution networks', Renewable Energy, vol. 32, no. 2, Feb. 2007, pp.216-234
  3. Hemandez, J. C., Medina, A., and Jurado, F., 'Optimal allocation and sizing for profitability and voltage enhancεment of PV systems on feeders', Renewable Energy, vol. 32, no. 10, Aug. 2007, pp. 1768-1789
  4. Ide, A., and Yasuda, K., 'A Basic Study of Adaptive Particle Swarm Optimization', Electrical Engineering in Japan, vol. 151, no. 3, 7 March 2005, pp. 41-49
  5. EI-Dib, A. A., Youssef, H. K. M., EI-Metwally, M. M., and Osman, Z., 'Optimum VAR sizing and allocation using particle swarm optimization', Electric Power Systems Research, vol. 77, no. 8, June 2007, pp. 965-972
  6. Eberhart, R., and Kennedy, J., 'A New Optimizer Using Particle Swarm Theory', Proceedings of Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, 4-6 October 1995
  7. Veeramachaneni, K., Osadciw, L., and Kamth, G., 'Probabilistically Driven Particle Swarms for Optimization of Multi-valued Discrete Problems: Design and Analysis', Proceedings of IEEE Swarm Intelligence Symposium, Honolulu, Hawaii, 1-5 April 2007, pp.141-149
  8. Kennedy, J., and Eberhart, R., 'A Discrete Binary Version of Particle Swarm Optimization Algorithm', Proceedings of the IEEE International Conference on Systems. Man and Cybernetics, Orlando, Florida, USA, vol. 5, 12-15 Oct. 1997, pp. 4104-4108
  9. Yang, S., Wang, M., and Jiao, L., 'A Quantum Particle Swarm Optimization', Proceedings on IEEE Congress on Evolutionary Computation, Portland, Oregon, vol. 1, 19-23 June 2004, pp. 320-324
  10. Khanesar, M. A., Teshnehlab, M., and Shoorehdeli, M. A., 'A Novel Binary Particle Swarm Optimization', Proceedings of Mediterranean Confrence on Control and Automation, Athens, Greece, 27-29 July 2007
  11. Pampara, G., Franken, N., and Engelbrecht, A. P., 'Combining Particle Swarm Optimisation with angle modulation to solve binary problems', Proceedings of IEEE Congress on Evolutionary Computing, Edinburgh, Scotland, vol. 1, 5 Sept. 2005, pp. 89-96
  12. Sadri, J., and Suen, C. Y., 'A Genetic Binary Particle Swarm Optimization Model', Proceedings of IEEE Congress on Evolutionary Computation, Vancouver, BC, Canada, 16-21 July 2006, pages 656-663
  13. Lee, S., Soak, S., Oh, S., Pedrycz, O., and Jeon, M., 'Modified Binary Particle Swarm Optimization', Progress in Natural Science, vol. 18, no. 9, 10 Sept. 2008, pp. 1161-1166
  14. Rastegar, R., Meybodi, M. R., and Badie, K., 'A New Discrete Binary Particle Swarm Optimization Based on Leaming Automata', Proceedings of IEEE nternational Conference on Machine Learning and Applications, Louisville, KY, USA, 16-18 Dec. 2004, pp. 456-462
  15. Moradi, A., and Fotuhi-Firuzabad, M., 'Optimal Switch Placεment in Distribution Systems using Trinary Particle Swarm Optimization Algorithm', IEEE Transactions on Power Deliven, vol. 23, no. 1, Jan. 2008, pp. 271-279
  16. Pugh, J., and Martinoli, A., 'Discrete Multi-Valued Particle Swarm optimization', Indianapolis, Indiana, USA, 12-14 May 2006, pp. 103-110
  17. Kennedy, J., and Eberhart, R., 'Particle swarm optimization', IEEE International Coηference on Neural Network, Perth, Australia, 1995
  18. Shi, Y., and Everhart, R., 'A modicied Particle Swam Pptimizer.' Preceeding of IEEE International Conference on Evlutation, Anchorage, AK, 409 May 1998
  19. Clerc, M., 'The Swarm and the Queen: Towards a Deterministic and Adaptive Particle Swarm Optimization' IEEE Proceedings on Congress on Evolutonary Computation, Washington DC, USA, 6-9 July 19999
  20. Yoshidι H., Kawata, K., Fukuyama, Y., Takayama, S., and Nakanishi, Y., 'A Particle Swarm Optimization for Reactive Power and Voltage Control Considering Voltage Security Assessment', IEEE Transactzons on Power Systems, vol. 15, no. 4, Nov. 2000, pp. 1232-1239
  21. Ko, J. H., Joo, J. S., and Lee, Y. H., 'On the Use of Sigmoid Functions for Multistage Detection in Asynchronous CDMA Systems', IEEE Trransactions on Vehicular Technology vol. 48, no. 2, March 1999, pp. 522-526
  22. AI-Hinai, A., Sedhisigarchi, K., and Feliachi, A., 'Stability Enhancement of a Distribution Network Comprising a Fuel Cell and a Microturbine', Proceedings on IEEE Power Engineering Society General Meeting, Denver, CO., USA, 6-10 June 2004
  23. Urfalioglu, O., 'Robust Estimation of Camera Rotation, Translation and Focal Length at High Outlicr Rates'', Canadian Conference on Computer and Robot Vision, Canada, 17-19 May 2004
  24. Leζ K. H., Baek, S. w., and Kim, K. w., 'Inverse Radiation Analysis Using Repulsive Particle Swarm Optimization AIgorithm', Internαtional Journal of Heat and Mass Transfer, vol. 51, no. 11-12, June 2008, pp.2772-2783

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