**Commenced**in January 2007

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**Edition:**International

**Paper Count:**30184

##### A New Hybrid Optimization Method for Optimum Distribution Capacitor Planning

**Authors:**
A. R. Seifi

**Abstract:**

This work presents a new algorithm based on a combination of fuzzy (FUZ), Dynamic Programming (DP), and Genetic Algorithm (GA) approach for capacitor allocation in distribution feeders. The problem formulation considers two distinct objectives related to total cost of power loss and total cost of capacitors including the purchase and installation costs. The novel formulation is a multi-objective and non-differentiable optimization problem. The proposed method of this article uses fuzzy reasoning for sitting of capacitors in radial distribution feeders, DP for sizing and finally GA for finding the optimum shape of membership functions which are used in fuzzy reasoning stage. The proposed method has been implemented in a software package and its effectiveness has been verified through a 9-bus radial distribution feeder for the sake of conclusions supports. A comparison has been done among the proposed method of this paper and similar methods in other research works that shows the effectiveness of the proposed method of this paper for solving optimum capacitor planning problem.

**Keywords:**
Capacitor planning,
Fuzzy logic method,
Genetic Algorithm,
Dynamic programming,
Radial Distribution feeder

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1331801

**References:**

[1] M.E. Baran, and F.F. Wu, "optimal capacitor placement in distribution systems," IEEE Trans. Power Delivery, vol. 4(1), pp. 725-734, 1989.

[2] T.S. Abdel-Salam, A. Y. Chikhani, and R. Hackam, "A new technique for loss reducing using compensating capacitors applied to distribution systems with varying load condition," IEEE Trans. Power Delivery, Vol.9(2), pp. 819-827, 1994

[3] M. Chis , M.M.A. Salama, and S. Jayaran," capacitor placement in distribution systems using heuristic search strategies," in Proc. 1997 IEE Generation, Transmission and Distribution Conf., pp. 225-230.

[4] M.Y. Cho, and Y.W., "Chen Fixed/switched type shunt capacitor planning of distribution systems by considering customer load patterns and simplified feeder model," in Proc. 1997 IEE Generation, Transmission and Distribution Conf., pp. 533-540.

[5] H. N. Ng, and M.M.A, "Salama. Fuzzy optimal capacitor sizing and placement," in Proceedings of the Canadian conference on electrical and computer engineering; pp. 684-687

[6] C.T. Su, and C.C. Tsai, "A new fuzzy-reasoning approach to optimum capacitor allocation for primary distribution systems," in Proceedings of the IEEE international conference on industrial technology, pp. 237-41, 1996.

[7] K.H. Abdul-Rahman, and S.M. Shahidepour, "A fuzzy-based optimal reactive power control," IEEE Trans. Power System, Vol. 8(2): pp. 662- 70, 1993.

[8] H. D. Chiang, J. C. Wang, and O. Cockings, "Optimal capacitor placements in distribution systems: part 1: a new formulation and the overall problem," IEEE Trans. Power Delivery, Vol. 5(2), pp. 634- 42,1990.

[9] H.T. Yang, Y.C. Huang, C.L. Huang, "Solution to capacitor placement problem in radial distribution system using tabu search method," in Proceedings of the international conference on energy management and power delivery; pp. 388-93, 1995.

[10] V. Ajjarapu, and Z. Albanna, "Application of genetic based algorithms to optimal capacitor placement," in Proceedings of the first international forum on applications of neural networks to power systems; pp. 251- 5,1991.

[11] S. Sundharajan, and A. Pahwa, "optimal selection of capacitors for radial distribution systems using a genetic algorithm," IEEE Trans. Power System, Vol. 9(3), pp. 1499-507.1994.

[12] H. Chin, and W. Lin, "Capacitor placement for distribution systems with fuzzy algorithm," in Proc. 1994 IEEE Region 10-s Ninth Annu. Int. Conf., vol. 2, pp. 1025-1029.

[13] C. Su and C. Tsai, "A new fuzzy-reasoning approach to optimum capacitor allocation for primary distribution systems," in Proc. IEEE Int. Conf. Ind. Technol., pp. 237-241, 1996.

[14] H. N. Ng, M. M. A. Salama, and A. Y. Chikhani, "Capacitor placement in distribution systems using fuzzy technique," in Proc. Canadian Conf. Elect. Comput. Eng., vol. 2, pp. 790-793, 1996.

[15] H. N. Ng and M. M. A. Salama, "Fuzzy optimal capacitor sizing and placement," in Proc. Canadian Conf. Elect. Comput. Eng., vol. 2, pp. 680-683, 1995.

[16] M. E. El-Hawary, Electric Power Applications of Fuzzy Systems. Piscataway, NJ: IEEE Press, 1998.

[17] H. N. Ng, M. M. A. Salama, and A.Y. Chikhani, "Capacitor allocation by approximate reasoning: Fuzzy capacitor placement," IEEE Trans. Power Delivery, vol. 15, pp. 393-398, Jan. 2000.

[18] R. E. Bellman and L. A. Zadeh, "Decision-making in a fuzzy environment," Manage. Sci., vol. 17, no. 4, pp. 141-164, Dec. 1970.

[19] H.-J. Zimmermann, Fuzzy Set Theory and its Application, 2nd ed. Norwell, MA: Kluwer, ch. 12, pp. 241-272, 1990.

[20] R. E. Bellmen, S. E. Dreyfus, applied Dynamic programming, Princeton University press, Princeton, N.J., 1962.

[21] A. S. Chung, and F. Wu, " An extensile genetic algorithm framework for problem solving in a common environment," IEEE Trans. On power systems, vol.15, no.1, Feb.2000.

[22] J. H. Holland, "Genetic Algorithm," Scientific American, Vol. 267,No. 1, , pp.66-73, July 1992.

[23] D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison Wesley, 1989.

[24] A S. Chung, and F. Wu, "An Extensile Genetic Algorithm Framework for Problem Solving in a Common Environment," IEEE Trans. On power systems, vol.15, no.1, Feb.2000.

[25] T. Yokota, M. Gen, and Y. X. Li, "Genetic Algorithm for Non-linear Mixed Integer Programming Problems and its Applications," computers ind. Eng., Vol.30, No.4 ,pp.905-917, 1996.

[26] S. F. Mekhamer, S. A. Soliman, M. A. Moustafa, and M. E. El-Hawary, " Application of Fuzzy Logic for Reactive-Power Compensation of Radial Distribution Feeders", IEEE Transaction on Power Systems, Vol.18, No.1, Februry 2003.

[27] J. J. Grainger and S. H. Lee, "Optimal size and location of shunt capacitor for reduction of losses in distribution feeders," IEEE Trans. Power App. Syst., vol. PAS-100, pp. 1105-1118, Mar. 1981.

[28] M. Chis, M. M. A. Salama, and S. Jayaram, "Capacitor Placement in Distribution Systems using Heuristic Search Strategies," in Proc. Inst. Elect.Eng., vol.144, No.3, pp.225-230, 1997.

[29] T. S. A.Salama, A. Y. Chikhani, and R.Hackam, "A new technique for loss reduction using compensating capacitors applied to distribution systems with varying load condition," IEEE Trans. On Power Delivery, vol.9, pp.819-827, Apr.1994.

[30] C. Su and C. Tsai, "A New Fuzzy-reasoning Approach to Optimum Capacitor Allocation for Primary Distribution Systems." in Proc. IEEE Int. Conf. Ind. Technol, pp.237-241, 1996.

[31] H. C. Chin and W. M. Lin, "Capacitor Placements for Distribution Systems with Fuzzy Algorithm",in Proceedings of 1994 IEEE Region 10-s Ninth Annual International Conference, 94CH3417-3, Vol.2, pp.1025- 1029.

[32] M. M. A. Salama and A. Y. Chikhani, "A simplified network approach to the VAr control problem for radial distribution systems," IEEE Trans. Power Delivery, vol. 8, pp. 1529-1535, July 1993.

[33] H. N. Ng, M. M. A. Salama, and A.Y. Chikhani, "Capacitor allocation by approximate reasoning: Fuzzy capacitor placement," IEEE Trans. Power Delivery, vol. 15, pp. 393-398, Jan. 2000.