A New Hybrid Optimization Method for Optimum Distribution Capacitor Planning
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.
[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.
[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.
@article{"International Journal of Electrical, Electronic and Communication Sciences:53363", author = "A. R. Seifi", title = "A New Hybrid Optimization Method for Optimum Distribution Capacitor Planning", 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", volume = "2", number = "10", pages = "2217-6", }
