Document Type : Research paper


Department of Electrical and Computer Engineering, University of Birjand, Birjand, Iran


Utilizing capacitor banks is very conventional in distribution network in order for local compensation of reactive power. This will be more important considering uncertainties including wind generation and loads uncertainty. Harmonics and non-linear loads are other challenges in power system which complicates the capacitor placement problem. Thus, uncertainty and network harmonics have been considered in this paper, simultaneously. Capacitor placement has been proposed as a probabilistic harmonic problem with different objectives and technical constraints in the capacitor placement problem. Minimizing power and energy loss and capacitor prices are considered as objectives. Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithms have been used to solve the optimization problem. Loads are subjected to uncertainty with normal probabilistic distribution function (PDF). Auto Regressive and Moving Average (ARMA) time series and two point estimate method have also been utilized to simulate the wind speed and to perform the probabilistic load flow, respectively. Finally, the proposed method has been implemented on standard distorted test cases in different scenarios. Monte Carlo Simulation (MCS) has also been used to verify the probabilistic harmonic power flow. Simulation results demonstrate the efficiency of the proposed method.


Main Subjects

[1]     S. K. Bhattacharya, S. K. Goswami, “A new fuzzy based solution of the capacitor placement problem in radial distribution system”, Expert Syst. Appl., vol. 36, pp. 4207-4212, 2009.
[2]     M. Ladjavardi, M. A. S. Masoum, “Genetically optimized fuzzy placement and sizing of capacitor banks in distorted distribution networks”, IEEE Trans. Power Delivery,vol. 23, pp. 449-456, 2008.
[3]     V. Farahani, S. H. H. Sadeghi, H. A. Abyaneh, S. M. M. Agah, K. Mazlumi, “Energy loss reduction by conductor replacement and capacitor placement in distribution systems”, IEEE Trans. Power Syst,,vol. 28, pp. 2077-2085, 2013.
[4]      A. A. El-Fergany, “Optimal capacitor allocations using evolutionary algorithms,” IET proc. Gener. Trans. Distrib., vol. 7, no. 6, pp. 593-601, 2013.
[5]     D. Kaur, J. Sharma, “Multiperiod shunt capacitor allocation in radial distribution systems,” Int. J. Electric Power Energy Syst., vol. 52, pp. 247-253, 2013.
[6]     A. Mendes, P. M. Franca, C. Lyra, C. Pissarra, C. Cavellucci, “Capacitor placement in large-sized radial distribution networks,” IET proc. Gener. Trans. Distrib., vol. 152, no. 4, pp. 496-502, 2013.
[7]     Y. Baghzouz, “Effects of nonlinear loads on optimal capacitor placement in radial feeders”, IEEE Trans. Power Delivery, vol. 6, pp. 245-251, 1991.
[8]     Y. Baghzouz and S. Ertem, “Shunt capacitor sizing for radial distribution feeders with distorted substation voltages”, IEEE Trans. Power Delivery, vol. 5, pp. 650-657, 1990.
[9]     G. Bei, A. Abur, “Optimal capacitor placement for improving power quality”, in Proc. of the IEEE Power & Energy Society General Meeting , vol. 1, pp. 488-492, 1998.
[10]  E. Baran, F. Wu, “Optimal capacitor placement in distribution systems”, IEEE Trans. Power Delivery, vol. 25, pp. 725-734, 1989.
[11]  X. Yan, D. Zhao Yang, W. Kit Po, E. Liu, B. Yue, “Optimal capacitor placement to distribution transformers for power loss reduction in radial distribution systems”, IEEE Trans. Power Syst.,, vol. 28, pp. 4072-4079, 2013.
[12]  S. Nojavan, M. Jalali, K. Zare, “Optimal allocation of capacitors in radial/mesh distribution systems using mixed integer nonlinear programming approach”, Electr. Power Syst. Res., vol. 107, pp. 119-124, 2014.
[13]  T. S. Abdel-Salam, A. Y. Chikhani, R. Hackam, "A new technique for loss reduction using compensating capacitors applied to distribution systems with varying load condition," IEEE Trans. Power Deliver, vol. 9, pp. 819-827, 1994.
[14]  M. Sedighizadeh, M. M. Mahmoodi, “Optimal reconfiguration and capacitor allocation in radial distribution systems using the hybrid shuffled frog leaping algorithm in the fuzzy framework”, J. Oper. Autom. Power Eng., vol. 3, no. 1, pp. 56-70, 2015.
[15]  R. Baghipour, S.M. Hosseini, “A hybrid algorithm for optimal location and sizing of capacitors in the presence of different load models in distribution network”, J. Oper. Autom. Power Eng., vol. 2, no. 1, pp. 10-21, 2014.
[16]  S. Sundhararajan, A. Pahwa, “Optimal selection of capacitors for radial distribution systems using a genetic algorithm”, IEEE Trans. Power Syst., vol. 9, pp. 1499-1507, 1994.
[17]  T.-L. Huang, Y.-T. Hsiao, C.-H. Chang, J.-A. Jiang, “Optimal placement of capacitors in distribution systems using an immune multi-objective algorithm”, Int. J. Electr. Power Energy Syst., vol. 30, pp. 184-192, 2008.
[18]  J.-P. Chiou, C.-F. Chang, C.-T. Su, “Capacitor placement in large-scale distribution systems using variable scaling hybrid differential evolution”, Int. J. Electr. Power Energy Syst., vol. 28, pp. 739-745, 2006.
[19]  A. A. El-Fergany, A. Y. Abdelaziz, “Capacitor allocations in radial distribution networks using cuckoo search algorithm,” IET Gener. Transm. Distrib, vol. 8, pp. 223-232, 2014.
[20]  A. Seifi, M. R. Hesamzadeh, “A hybrid optimization approach for distribution capacitor allocation considering varying load conditions,” Int. J. Electr. Power Energy Syst., vol. 31, pp. 589-595, 2009.
[21]  D. Das, "Optimal placement of capacitors in radial distribution system using a Fuzzy-GA method," Int. J. Electr. Power Energy Syst., vol. 30, pp. 361-367, 2008.
[22]  A. A. El-Fergany, A. Y. Abdelaziz, "Efficient heuristic-based approach for multi-objective capacitor allocation in radial distribution networks," IET Gener. Transm. Distrib, vol. 8, pp. 70-80, 2014.
[23]  A. R. Abul’Wafa, “Reliability/cost evaluation of a wind power delivery system,” Electr. Power Syst. Res., vol. 81, pp. 873-879, 2011.
[24]  G. Verbic, C. A. Canizares, “Probabilistic optimal power flow in electricity markets based on a two-point estimate method”, IEEE Trans. Power Syst,, vol. 21, pp. 1883-1893, 2006.
[25]  S. Chun-Lien, “Probabilistic load-flow computation using point estimate method, IEEE Trans. Power Syst,, vol. 20, pp. 1843-1851, 2005.
[26]  R. Billinton, H. Chen, R. Ghajar, “Time-series models for reliability evaluation of power systems including wind energy, Microelectron. Reliab., vol. 36, pp. 1253-1261, 1996.
[27]  R. Billinton, G. Yi, “Multistate wind energy conversion system models for adequacy assessment of generating systems incorporating wind energy,” IEEE Trans. Energy Convers., vol. 23, pp. 163-170, 2008.
[28]  R. Karki, R. Billinton, “Cost-effective wind energy utilization for reliable power supply,” IEEE Trans. Energy Convers, vol. 19, pp. 435-440, 2004.
[29]  P. Giorsetto and K. F. Utsurogi, “Development of a new procedure for reliability modeling of wind turbine generators,” IEEE Trans. Power Appl. Syst, vol. PAS-102, pp. 134-143, 1983.
[30]  D. Xia, G. T. Heydt, “Harmonic power flow studies - part ii implementation and practical application,” IEEE Trans. Power Appl. Syst., vol. PAS-101, pp. 1266-1270, 1982.
[31]  M. A. S. Masoum, E. F. Fuchs, “Transformer magnetizing current and iron-core losses in harmonic power flow,” IEEE Trans. Power Delivery, vol. 9, pp. 10-20, 1994.
[32]  Available online,
[33]  G. Carpinelli, T. Esposito, P. Varilone, P. Verde, “First-order probabilistic harmonic power flow,” in Proc. of the IEEE Int. Conf. Gener. Trans. Distrib., vol. 148, pp. 541-548, 2001.
[34]  A. A. Romero, H. C. Zini, G. Ratta, R. Dib, “Harmonic load-flow approach based on the possibility theory,” IET Gener. Transm. Distrib., vol. 5, pp. 393-404, 2011.
[35]  J. Kennedy, R. C. Eberhart, “Particle swarm optimization”, in Proc. of IEEE Int. Conf. Neural Networks, pp. 1942-1948, 1995.
[36]  D. Zaharie, “Influence of crossover on the behavior of differential evolution algorithms,” Appl. Soft. Comput., vol. 9, pp. 1126–1138, 2009.
[37]  W. M. Grady, M. J. Samotyj, A. H. Noyola, “Minimizing network harmonic voltage distortion with an active power line conditioner,” IEEE Trans. Power Delivery, vol. 6, pp. 1690-1697, 1991.
[38]  M. A. S. Masoum, M. Ladjevardi, A. Jafarian, E. F. Fuchs, “Optimal placement, replacement and sizing of capacitor Banks in distorted distribution networks by genetic algorithms,” IEEE Trans. Power Delivery, vol. 19, pp. 1794-1801, 2004.
[39]  A. Ulinuha, M.A.S. Masoum, S. Islam, “Hybrid genetic-fuzzy algorithm for volt/var /total harmonic distortion control of distribution systems with high penetration of non-linear loads,” IET Gener. Transm. Distrib., vol. 5, pp. 425-439, 2011.
[40]   V. R. Pandi, H. H. Zeineldin, X. Weidong, “Determining optimal location and size of distributed generation resources considering harmonic and protection coordination limits,” IEEE Trans. Power Syst,, vol. 28, pp. 1245-1254, 2013.