Abstract
One of the most principle optimization problems which gained the attention of power system operators around the world is optimal power flow (OPF) . The OPF basically performs an intelligent power flow and optimizes the system operation condition by optimally determination of control variables. It also considers a specific set of operational constraints and technical limits for this aim, which guaranties both feasibility and optimality of the scheduled operation condition. Generally, this problem can be categorized into two main sub-problems, i.e. optimal reactive power dispatch (ORPD) and optimal real power dispatch, which are differ in their aims and control variables. This chapter deals with the first one, ORPD, which has significant impact on power system security. ORPD is modeled as an optimization problem with nonlinear functions and mixed continuous/discrete variables. Thus, it is a complicated optimization problem. The multi-objective ORPD (MO-ORPD) problem is studied, taking into account different operational constraints such as bus voltage limits, power flow limits of branches, limits of generators voltages, transformers tap ratios and the amount of available reactive power compensation at the weak buses. Three different objective functions are considered in the proposed MO-ORPD framework, which are minimizing total active power losses , minimizing voltage variations and minimizing voltage stability index (L-index). These conflicting objectives are optimized via ε-constraint method. In order to model the stochastic behavior of demand and wind power generation, it is necessary to modify the MO-ORPD problem, and develop a probabilistic approach to handle the uncertainties in MO-ORPD problem. Hence, a two-stage stochastic MO-ORPD (SMO-ORPD) is suggested to handle the load and wind power uncertainties in the MO-ORPD problem. In the proposed two-stage stochastic optimization model, the decision variables are classified into two categories, namely, “here and now” and “wait and see” variables. The optimal values of “here and now” variables should be known before realization of scenarios, and therefore, their values are the same for all scenarios while the optimal values of “wait and see” variables are based on the realized scenario, and hence their values are scenario dependent. Moreover, in order to examine performance of the proposed SMO-ORPD and the impact of wind power generation on the results of SMO-ORPD, deterministic ORPD (DMO-ORPD) has also been solved in two modes: DMO-ORPD without wind farms (WFs) and any uncertainty, for the sake of comparison with the available methods in recent literature, and DMO-ORPD with WFs. In this chapter the reactive power compensation devices are modeled as discrete/continuous control variables. DMO-ORPD and SMO-ORPD are formulated as mixed integer non-linear program (MINLP) problems, and solved by General Algebraic Modeling System (GAMS). Also, the IEEE 30-bus standard system is utilized for evaluation of the proposed MO-ORPD models.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
B. Zhao, C. Guo, Y. Cao, A Multiagent-Based Particle Swarm Optimization Approach for Optimal Reactive Power Dispatch, IEEE Transactions on Power Systems, vol. 20, pp. 1070–1078, 2005.
C. Dai, W. Chen, Y. Zhu, X. Zhang, Seeker Optimization Algorithm for Optimal Reactive Power Dispatch, IEEE Transactions on Power Systems, vol. 24, pp. 1218–1231, 2009.
A. Khorsandi, A. Alimardani, B. Vahidi, S. Hosseinian, Hybrid Shuffled Frog Leaping Algorithm and Nelder-Mead Simplex Search for Optimal Reactive Power Dispatch, IET Generation, Transmission & Distribution, vol. 5, pp. 249–256, 2011.
M. Ghasemi, S. Ghavidel, M.M. Ghanbarian, A. Habibi, A New Hybrid Algorithm for Optimal Reactive Power Dispatch Problem with Discrete and Continuous Control Variables, Applied Soft Computing vol. 22, pp. 126–40, 2014.
M. Ghasemi, M.M. Ghanbarian, S. Ghavidel, S. Rahmani, E. Mahboubi Moghaddam, Modified Teaching Learning Algorithm and Double Differential Evolution Algorithm for Optimal Reactive Power Dispatch Problem: A Comparative Study, Information Sciences, vol. 278, pp. 231–249, 2014.
M. Martinez Rojas, A. Sumper, O. Gomis Bellmunt, A. Sudria Andreu, Reactive Power Dispatch in Wind Farms Using Particle Swarm Optimization Technique and Feasible Solutions Search, Applied Energy, vol. 88, pp. 4678–4686, 2011.
R. Mallipeddi, S. Jeyadevi, P.N. Suganthan, S. Baskar, Efficient Constraint Handling for Optimal Reactive Power Dispatch Problems, Swarm and Evolutionary Computation, vol. 5, pp. 28–36, 2012.
C.M. Huang, S.J. Chen, Y.C. Huang, H.T. Yang, Comparative Study of Evolutionary Computation Methods for Active-Reactive Power Dispatch, IET Generation, Transmission & Distribution, vol. 6, pp. 636–645, 2012.
A. Rajan, T. Malakar, Optimal Reactive Power Dispatch Using Hybrid Nelder-Mead Simplex Based Firefly Algorithm, International Journal of Electrical Power & Energy Systems, vol. 66, pp. 9–24, 2015.
R.P. Singh, V. Mukherjee, S. Ghoshal, Optimal Reactive Power Dispatch by Particle Swarm Optimization with an Aging Leader and Challengers, Applied Soft Computing, vol. 29, pp. 298–309, 2015.
M.H. Sulaiman, Z. Mustaffa, M.R. Mohamed, O. Aliman, Using the Gray Wolf Optimizer for Solving Optimal Reactive Power Dispatch Problem, Applied Soft Computing, vol. 32, pp. 286–292, 2015.
D. Thukaram, G. Yesuratnam, Optimal Reactive Power Dispatch in a Large Power System with AC-DC and FACTS Controllers, Generation, Transmission & Distribution, IET, vol. 2, pp. 71–81, 2008.
A. Rabiee, M. Vanouni, M. Parniani, Optimal Reactive Power Dispatch for Improving Voltage Stability Margin Using a Local Voltage Stability Index, Energy Conversion and Management, vol. 59, pp. 66–73, 2012.
C. Dai, W. Chen, Y. Zhu, and X. Zhang, Reactive Power Dispatch Considering Voltage Stability with Seeker Optimization Algorithm, Electric Power Systems Research, vol. 79, pp. 1462–1471, 2009.
A. Ela, M. Abido, S. Spea, Differential Evolution Algorithm for Optimal Reactive Power Dispatch, Electric Power Systems Research, vol. 81, pp. 458–464, 2011.
A. Khazali, M. Kalantar, Optimal Reactive Power Dispatch Based on Harmony Search Algorithm, International Journal of Electrical Power & Energy Systems, vol. 33, pp. 684–692, 2011.
S. Duman, Y. Sonmez, U. Guvenc, N. Yorukeren, Optimal Reactive Power Dispatch Using a Gravitational Search Algorithm, IET Generation, Transmission & Distribution, vol. 6, pp. 563–576, 2012.
J.M. Ramirez, J.M. Gonzalez, T.O. Ruben, An Investigation about the Impact of the Optimal Reactive Power Dispatch Solved by DE, International Journal of Electrical Power & Energy Systems, vol. 33, pp. 236–244, 2011.
E.M. Soler, E.N. Asada, G.R. Da Costa, Penalty-Based Nonlinear Solver for Optimal Reactive Power Dispatch with Discrete Controls, IEEE Transactions on Power Systems, vol. 28, pp. 2174–2182, 2013.
M. Abido, J. Bakhashwain, Optimal VAR Dispatch Using a Multi-Objective Evolutionary Algorithm, International Journal of Electrical Power & Energy Systems, vol. 27, pp. 13–20, 2005.
L. Zhihuan, L. Yinhong, D. Xianzhong, Non-Dominated Sorting Genetic Algorithm-II for Robust Multi-Objective Optimal Reactive Power Dispatch, Generation, Transmission & Distribution, IET, vol. 4, pp. 1000–1008, 2010.
S. Jeyadevi, S. Baskar, C. Babulal, M. Willjuice Iruthayarajan, Solving Multi-Objective Optimal Reactive Power Dispatch Using Modified NSGA-II, International Journal of Electrical Power & Energy Systems, vol. 33, pp. 219–228, 2011.
A. Saraswat, A. Saini, Multi-Objective Optimal Reactive Power Dispatch Considering Voltage Stability in Power Systems Using HFMOEA, Engineering Applications of Artificial Intelligence, vol. 26, pp. 390–404, 2013.
G. Chen, L. Liu, P. Song, Y. Du, Chaotic Improved PSO-Based Multi-Objective Optimization for Minimization of Power Losses and L Index in Power Systems, Energy Conversion and Management, vol. 86, pp. 548–560, 2014.
B. Mandal, P.K. Roy, Optimal Reactive Power Dispatch Using Quasi-Oppositional Teaching Learning Based Optimization, International Journal of Electrical Power & Energy Systems, vol. 53, pp. 123–134, 2013.
A. Ghasemi, K. Valipour, A. Tohidi, Multi-Objective Optimal Reactive Power Dispatch Using a New Multi-Objective Strategy, International Journal of Electrical Power & Energy Systems, vol. 57, pp. 318–334, 2014.
B. Zhou, K. Chan, T. Yu, H. Wei, J. Tang, Strength Pareto Multi-Group Search Optimizer for Multi-Objective Optimal VAR Dispatch, IEEE Transactions on Industrial Informatics, vol. 10, pp. 1012–1022, 2014.
Z. Hu, X. Wang, G. Taylor, Stochastic Optimal Reactive Power Dispatch: Formulation and Solution Method, International Journal of Electrical Power & Energy Systems, vol. 32, pp. 615–621, 2010.
S. M. Mohseni Bonab, A. Rabiee, S. Jalilzadeh, B. Mohammadi Ivatloo, and S. Nojavan, “Probabilistic Multi Objective Optimal Reactive Power Dispatch Considering Load Uncertainties Using Monte Carlo Simulations, Journal of Operation and Automation in Power Engineering, vol. 3(1), pp. 83–93, 2015.
S. M. Mohseni Bonab, A. Rabiee, B. Mohammadi Ivatloo, Load Uncertainty Analysis in Multi Objective Optimal Reactive Power Dispatch Considering Voltage Stability, Majlesi Journal of Energy Management, vol. 4(2), pp. 23–30, 2015.
A. Brooke, D. Kendrick, A. Meeraus, GAMS Release 2.25: A User’s Guide: GAMS Development Corporation Washington, DC, 1996.
P.E. Gill, W. Murray, M.A. Saunders, SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization, SIAM Journal on Optimization, vol. 12, pp. 979–1006, 2002.
The GAMS Software Website, http://www.gams.com/dd/docs/solvers/sbb.pdf, 2013.
A. Soroudi, T. Amraee, Decision Making under Uncertainty in Energy Systems: State of the Art, Renewable and Sustainable Energy Reviews, vol. 28, pp. 376–384, 2013.
A. Rabiee, A. Soroudi, B. Mohammadi Ivatloo, M. Parniani, Corrective Voltage Control Scheme Considering Demand Response and Stochastic Wind Power, IEEE Transactions on Power Systems, vol. 29, pp. 2965–2973, 2014.
A. Soroudi, B. Mohammadi Ivatloo, A. Rabiee, Energy Hub Management with Intermittent Wind Power, in Large Scale Renewable Power Generation, Springer, pp. 413–438, 2014.
A. Rabiee, A. Soroudi, Stochastic Multiperiod OPF Model of Power Systems with HVDC-Connected Intermittent Wind Power Generation, IEEE Transactions on Power Delivery, vol. 29, pp. 336–344, 2014.
A. Soroudi, A. Rabiee, A. Keane, Stochastic Real-Time Scheduling of Wind-Thermal Generation Units in an Electric Utility, IEEE System Journal, 2014.
R.D. Zimmerman, C.E. Murillo Sanchez, D. Gan, A MATLAB Power System Simulation Package, 2005.
S. Wen, H. Lan, Q. Fu, D. Yu, L. Zhang, Economic Allocation for Energy Storage System Considering Wind Power Distribution, IEEE Transactions on power Systems, vol. 30(2), pp. 644–52, 2015.
C.A. Canizares, Voltage Stability Assessment: Concepts, Practices and Tools, Power System Stability Subcommittee Special Publication IEEE/PES, thunderbox.uwaterloo. ca/~claudio/claudio.html#VSWG, 2002.
F. Jabbari, B. Mohammadi Ivatloo, Static Voltage Stability Assessment Using Probabilistic Power Flow to Determine the Critical PQ Buses, Majlesi Journal of Electrical Engineering, vol. 8, pp. 17–25, 2014.
H. Xiong, H. Cheng, H. Li, Optimal Reactive Power Flow Incorporating Static Voltage Stability Based on Multi-Objective Adaptive Immune Algorithm, Energy Conversion and Management, vol. 49, pp. 1175–1181, 2008.
R. Raghunatha, R. Ramanujam, K. Parthasarathy, D. Thukaram, Optimal Static Voltage Stability Improvement Using a Numerically Stable SLP Algorithm, for Real Time Applications, International Journal of Electrical Power & Energy Systems, vol. 21, pp. 289–297, 1999.
X. Wang, Y. Gong, C. Jiang, Regional Carbon Emission Management Based on Probabilistic Power Flow with Correlated Stochastic Variables, IEEE Transactions on Power Systems, vol. 30, pp. 1094–1103, 2014.
M. Alipour, B. Mohammadi Ivatloo, K. Zare, Stochastic Risk-Constrained Short-Term Scheduling of Industrial Cogeneration Systems in the Presence of Demand Response Programs, Applied Energy, vol. 136, pp. 393–404, 2014.
R.D. Zimmerman, C.E. Murillo Sanchez, R.J. Thomas, MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education, IEEE Transactions on Power Systems, vol. 26, pp. 12–19, 2011.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Appendix
Appendix
See Table 12.15.
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Mohseni-Bonab, S.M., Rabiee, A., Mohammadi-Ivatloo, B. (2017). Multi-objective Optimal Reactive Power Dispatch Considering Uncertainties in the Wind Integrated Power Systems. In: Mahdavi Tabatabaei, N., Jafari Aghbolaghi, A., Bizon, N., Blaabjerg, F. (eds) Reactive Power Control in AC Power Systems. Power Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-51118-4_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-51118-4_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-51117-7
Online ISBN: 978-3-319-51118-4
eBook Packages: EnergyEnergy (R0)