# AC Optimal Power Flow Problem Considering Wind Energy by an Improved Particle Swarm Optimization

Keywords:
AC optimal power flow, wind energy, IPSO, velocity mirror effect

### Abstract

This paper presents an AC optimal power ﬂow (AC-OPF) problem of a power system, considering wind energy. Wind energy is an environmental-friendly energy source to produce electrical power and it includes less operating costs compared with other sources of electrical power production. Wind generators also affect the operation cost of a power system as well as transmission losses, based on generators locations and speed of wind. In addition, wind speed is a parameter with uncertainty and considering this uncertainty is an important issue in operation of wind generators in the AC-OPF problem. The proposed AC-OPF formulation includes the integer variables in addition to continuous variables and studies the effects of wind energy, transformer tap settings, and shunt capacitors on fuel cost, transmission losses as well as up and down spinning reserves. To solve the AC-OPF model, an improved particle swarm optimization (IPSO) is presented. The IPSO algorithm in this work includes velocity mirror effect that causes improvement in the quality of the results. The proposed method is applied on modified IEEE 30 bus test system, and obtained results approve the validity and effectiveness of the proposed method.### References

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[12] Pudjianto, D., S. Ahmed, and G. Strbac,“Allocation of VAR support using LP and NLP based optimal power flows.” IEE Proceedings-Generation, Transmission and Distribution, 2002. 149(4): pp. 377-383.

[13] Habibollahzadeh, H., G.-X. Luo, and A. Semlyen,“Hydrothermal optimal power flow based on a combined linear and nonlinear programming methodology.” IEEE Transactions on Power Systems, 1989. 4(2): pp. 530-537.

[14] Torres, G.L. and V.H. Quintana,“An interior-point method for nonlinear optimal power flow using voltage rectangular coordinates.” IEEE Transactions on Power Systems, 1998. 13(4): pp. 1211-1218.

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[17] AlRashidi, M. and M. El-Hawary,“Hybrid particle swarm optimization approach for solving the discrete OPF problem considering the valve loading effects.” IEEE transactions on power systems, 2007. 22(4): pp. 2030-2038.

[18] Younes, M., M. Rahli, and L. Abdelhakem-Koridak,“Optimal Power Flow Based on Hybrid Genetic Algorithm.” Journal of Information Science & Engineering, 2007. 23(6): pp.1801-1816.

[19] Kumari, M.S. and S. Maheswarapu,“Enhanced genetic algorithm based computation technique for multi-objective optimal power flow solution.” International Journal of Electrical Power & Energy Systems, 2010. 32(6): pp. 736-742.

[20] Chen, P.-H. and H.-C. Chang,“Large-scale economic dispatch by genetic algorithm.” IEEE transactions on power systems, 1995. 10(4): pp. 1919-1926.

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[23] Kumar, S. and D. Chaturvedi,“Optimal power flow solution using fuzzy evolutionary and swarm optimization.” International Journal of Electrical Power & Energy Systems, 2013. 47: pp. 416-423.

[24] Khaled, U., A.M. Eltamaly, and A. Beroual,“Optimal Power Flow Using Particle Swarm Optimization of Renewable Hybrid Distributed Generation.” Energies, 2017. 10(7): pp. 1013-1019.

[25] Attous, D.B. and Y. Labbi,“Particle swarm optimization based optimal power flow for units with non-smooth fuel cost functions”. in Electrical and Electronics Engineering, 2009. ELECO 2009. International Conference on. 2009. IEEE.

[26] Abido, M.,“Optimal power flow using particle swarm optimization.” International Journal of Electrical Power & Energy Systems, 2002. 24(7): pp. 563-571.

[27] Nakawiro, W. and I. Erlich,“A combined GA-ANN strategy for solving optimal power flow with voltage security constraint”. in Power and Energy Engineering Conference, 2009. APPEEC 2009. Asia-Pacific. 2009. IEEE.

[28] Syai’in, M., A. Soeprijanto, and E.M. Yuniarno,“New algorithm for neural network optimal power flow (nn-opf) including generator capability curve constraint and statistic-fuzzy load clustering.” International Journal of Computer Applications, 2011. 36(7): pp. 1-8.

[29] Sumpavakup, C., I. Srikun, and S. Chusanapiputt,“A solution to the optimal power flow using artificial bee colony algorithm”. in Power System Technology (POWERCON), 2010 International Conference on. 2010. IEEE.

[30] Khorsandi, A., S. Hosseinian, and A. Ghazanfari,“Modified artificial bee colony algorithm based on fuzzy multi-objective technique for optimal power flow problem.” Electric Power Systems Research, 2013. 95: pp. 206-213.

[31] Afandi, A.N. and H. Miyauchi,“Improved artificial bee colony algorithm considering harvest season for computing economic dispatch on power system.” IEEJ Transactions on Electrical and Electronic Engineering, 2014. 9(3): pp. 251-257.

[32]. dos Santos Coelho, L. and V.C. Mariani,“Improved differential evolution algorithms for handling economic dispatch optimization with generator constraints.” Energy conversion and management, 2007. 48(5): pp. 1631-1639.

[33] Abido, M. and N. Al-Ali,“Multi-objective optimal power flow using differential evolution.” Arabian Journal for Science and Engineering, 2012. 37(4): pp. 991-1005.

[34] Amjady, N. and M.R. Ansari,“Non‐convex security constrained optimal power flow by a new solution method composed of Benders decomposition and special ordered sets.” International Transactions on Electrical Energy Systems, 2014. 24(6): pp. 842-857.

[35] Abdi, H., S.D. Beigvand, and M. La Scala,“A review of optimal power flow studies applied to smart grids and microgrids.” Renewable and Sustainable Energy Reviews, 2017. 71: pp.742-766.

[36] Marini, F. and B. Walczak,“Particle swarm optimization (PSO). A tutorial.” Chemometrics and Intelligent Laboratory Systems, 2015. 149: pp. 153-165.

[37] Todorovski, M. and D. Rajicic,“An initialization procedure in solving optimal power flow by genetic algorithm.” IEEE transactions on power systems, 2006. 21(2): pp. 480-487.

[2] Frank, S., I. Steponavice, and S. Rebennack,“Optimal power flow: a bibliographic survey I.” Energy Systems, 2012. 3(3): pp. 221-258.

[3] Mukherjee, S.K., A. Recio, and C. Douligeris,“Optimal power flow by linear programming based optimization”. in Southeastcon'92, Proceedings., IEEE. 1992. IEEE.

[4] Lobato, E., et al.,“An LP-based optimal power flow for transmission losses and generator reactive margins minimization”. in Power Tech Proceedings, 2001 IEEE Porto. 2001. IEEE.

[5] Chung, T. and G. Shaoyun,“A recursive LP-based approach for optimal capacitor allocation with cost-benefit consideration.” Electric Power Systems Research, 1996. 39(2): pp. 129-136.

[6] Peschon, J., D.W. Bree, and L.P. Hajdu,“Optimal power-flow solutions for power system planning.” Proceedings of the IEEE, 1972. 60(1): pp. 64-70.

[7] Alsac, O. and B. Stott,“Optimal load flow with steady-state security.” IEEE transactions on power apparatus and systems, 1974. 93(3): pp. 745-751.

[8] Reid, G.F. and L. Hasdorff,“Economic dispatch using quadratic programming.” IEEE Transactions on Power Apparatus and Systems, 1973. 92(6): pp. 2015-2023.

[9] Momoh, J.A.,“A generalized quadratic-based model for optimal power flow”. in Systems, Man and Cybernetics, 1989. Conference Proceedings., IEEE International Conference on. 1989. IEEE.

[10] Grudinin, N.,“Reactive power optimization using successive quadratic programming method.” IEEE Transactions on Power Systems, 1998. 13(4): pp. 1219-1225.

[11] Zhu, J. and J.A. Momoh,“Multi-area power systems economic dispatch using nonlinear convex network flow programming.” Electric Power Systems Research, 2001. 59(1): pp. 13-20.

[12] Pudjianto, D., S. Ahmed, and G. Strbac,“Allocation of VAR support using LP and NLP based optimal power flows.” IEE Proceedings-Generation, Transmission and Distribution, 2002. 149(4): pp. 377-383.

[13] Habibollahzadeh, H., G.-X. Luo, and A. Semlyen,“Hydrothermal optimal power flow based on a combined linear and nonlinear programming methodology.” IEEE Transactions on Power Systems, 1989. 4(2): pp. 530-537.

[14] Torres, G.L. and V.H. Quintana,“An interior-point method for nonlinear optimal power flow using voltage rectangular coordinates.” IEEE Transactions on Power Systems, 1998. 13(4): pp. 1211-1218.

[15] Granville, S.,“Optimal reactive dispatch through interior point methods.” IEEE Transactions on power systems, 1994. 9(1): pp. 136-146.

[16] Castronuovo, E.D., J.M. Campagnolo, and R. Salgado,“New versions of interior point methods applied to the optimal power flow problem.” Optmization [Online] Digest, 2001.

[17] AlRashidi, M. and M. El-Hawary,“Hybrid particle swarm optimization approach for solving the discrete OPF problem considering the valve loading effects.” IEEE transactions on power systems, 2007. 22(4): pp. 2030-2038.

[18] Younes, M., M. Rahli, and L. Abdelhakem-Koridak,“Optimal Power Flow Based on Hybrid Genetic Algorithm.” Journal of Information Science & Engineering, 2007. 23(6): pp.1801-1816.

[19] Kumari, M.S. and S. Maheswarapu,“Enhanced genetic algorithm based computation technique for multi-objective optimal power flow solution.” International Journal of Electrical Power & Energy Systems, 2010. 32(6): pp. 736-742.

[20] Chen, P.-H. and H.-C. Chang,“Large-scale economic dispatch by genetic algorithm.” IEEE transactions on power systems, 1995. 10(4): pp. 1919-1926.

[21] Bakirtzis, A., V. Petridis, and S. Kazarlis,“Genetic algorithm solution to the economic dispatch problem.” IEE proceedings-generation, transmission and distribution, 1994. 141(4): pp. 377-382.

[22] Yoshida, H., et al.,“A particle swarm optimization for reactive power and voltage control considering voltage security assessment.” IEEE Transactions on power systems, 2000. 15(4): pp. 1232-1239.

[23] Kumar, S. and D. Chaturvedi,“Optimal power flow solution using fuzzy evolutionary and swarm optimization.” International Journal of Electrical Power & Energy Systems, 2013. 47: pp. 416-423.

[24] Khaled, U., A.M. Eltamaly, and A. Beroual,“Optimal Power Flow Using Particle Swarm Optimization of Renewable Hybrid Distributed Generation.” Energies, 2017. 10(7): pp. 1013-1019.

[25] Attous, D.B. and Y. Labbi,“Particle swarm optimization based optimal power flow for units with non-smooth fuel cost functions”. in Electrical and Electronics Engineering, 2009. ELECO 2009. International Conference on. 2009. IEEE.

[26] Abido, M.,“Optimal power flow using particle swarm optimization.” International Journal of Electrical Power & Energy Systems, 2002. 24(7): pp. 563-571.

[27] Nakawiro, W. and I. Erlich,“A combined GA-ANN strategy for solving optimal power flow with voltage security constraint”. in Power and Energy Engineering Conference, 2009. APPEEC 2009. Asia-Pacific. 2009. IEEE.

[28] Syai’in, M., A. Soeprijanto, and E.M. Yuniarno,“New algorithm for neural network optimal power flow (nn-opf) including generator capability curve constraint and statistic-fuzzy load clustering.” International Journal of Computer Applications, 2011. 36(7): pp. 1-8.

[29] Sumpavakup, C., I. Srikun, and S. Chusanapiputt,“A solution to the optimal power flow using artificial bee colony algorithm”. in Power System Technology (POWERCON), 2010 International Conference on. 2010. IEEE.

[30] Khorsandi, A., S. Hosseinian, and A. Ghazanfari,“Modified artificial bee colony algorithm based on fuzzy multi-objective technique for optimal power flow problem.” Electric Power Systems Research, 2013. 95: pp. 206-213.

[31] Afandi, A.N. and H. Miyauchi,“Improved artificial bee colony algorithm considering harvest season for computing economic dispatch on power system.” IEEJ Transactions on Electrical and Electronic Engineering, 2014. 9(3): pp. 251-257.

[32]. dos Santos Coelho, L. and V.C. Mariani,“Improved differential evolution algorithms for handling economic dispatch optimization with generator constraints.” Energy conversion and management, 2007. 48(5): pp. 1631-1639.

[33] Abido, M. and N. Al-Ali,“Multi-objective optimal power flow using differential evolution.” Arabian Journal for Science and Engineering, 2012. 37(4): pp. 991-1005.

[34] Amjady, N. and M.R. Ansari,“Non‐convex security constrained optimal power flow by a new solution method composed of Benders decomposition and special ordered sets.” International Transactions on Electrical Energy Systems, 2014. 24(6): pp. 842-857.

[35] Abdi, H., S.D. Beigvand, and M. La Scala,“A review of optimal power flow studies applied to smart grids and microgrids.” Renewable and Sustainable Energy Reviews, 2017. 71: pp.742-766.

[36] Marini, F. and B. Walczak,“Particle swarm optimization (PSO). A tutorial.” Chemometrics and Intelligent Laboratory Systems, 2015. 149: pp. 153-165.

[37] Todorovski, M. and D. Rajicic,“An initialization procedure in solving optimal power flow by genetic algorithm.” IEEE transactions on power systems, 2006. 21(2): pp. 480-487.

Published

2020-02-03

How to Cite

*Majlesi Journal of Electrical Engineering*,

*14*(3). Retrieved from http://mjee.iaumajlesi.ac.ir/index/index.php/ee/article/view/3425

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