Optimal Long-Term Distributed Generation Planning and Reconfiguration of Distribution Systems: An Accelerating Benders’ Decomposition Approach

In this paper, we study the multi-period distributed generation planning problem in a multistage hierarchical distribution network. We first formulate the problem as a non-convex mixed-integer nonlinear programming problem. Since the proposed model is non-convex and generally hard to solve, we convexify the model based on semi-definite programming. Then, we use a customized Benders’ decomposition method with valid cuts to solve the convex relaxation model. Computational results show that the proposed algorithm provides an efficient way to solve the problem for relatively large-scale networks.

[1]  Stefan Nickel,et al.  A stochastic multi-period capacitated multiple allocation hub location problem: Formulation and inequalities , 2018 .

[2]  Jean-François Cordeau,et al.  Simultaneous Assignment of Locomotives and Cars to Passenger Trains , 1998, Oper. Res..

[3]  F. Pilo,et al.  A multiobjective evolutionary algorithm for the sizing and siting of distributed generation , 2005, IEEE Transactions on Power Systems.

[4]  Dheeraj Kumar Khatod,et al.  Techno-economic and environmental approach for optimal placement and sizing of renewable DGs in distribution system , 2017 .

[5]  S. Rebennack.  Handbook of power systems , 2010 .

[6]  P. Chiradeja,et al.  Benefit of Distributed Generation: A Line Loss Reduction Analysis , 2005, 2005 IEEE/PES Transmission & Distribution Conference & Exposition: Asia and Pacific.

[7]  Babak Hossein Khalaj,et al.  Minimum cost multiple multicast network coding with quantized rates , 2013, Comput. Networks.

[8]  Colin Neil Jones,et al.  An Alternating Trust Region Algorithm for Distributed Linearly Constrained Nonlinear Programs, Application to the Optimal Power Flow Problem , 2017, J. Optim. Theory Appl..

[9]  Jizhong Zhu,et al.  Optimization of Power System Operation , 2009 .

[10]  Alysson M. Costa,et al.  Two-level network design with intermediate facilities: An application to electrical distribution systems , 2011 .

[11]  M. Laughton,et al.  Large-scale mixed integer programming: Benders-type heuristics , 1984 .

[12]  Santanu S. Dey,et al.  Inexactness of SDP Relaxation and Valid Inequalities for Optimal Power Flow , 2014, IEEE Transactions on Power Systems.

[13]  Jean-François Cordeau,et al.  An integrated model for logistics network design , 2006, Ann. Oper. Res..

[14]  Pascal Van Hentenryck,et al.  Strengthening the SDP Relaxation of AC Power Flows With Convex Envelopes, Bound Tightening, and Valid Inequalities , 2017, IEEE Transactions on Power Systems.

[15]  A. M. Geoffrion.  Generalized Benders decomposition , 1972 .

[16]  P. S. Davis,et al.  A branch‐bound algorithm for the capacitated facilities location problem , 1969 .

[17]  Panos M. Pardalos,et al.  An accelerating Benders’ decomposition approach to the integrated supply chain network design with distributed generation , 2018 .

[18]  J. F. Benders.  Partitioning procedures for solving mixed-variables programming problems , 1962 .

[19]  Alysson M. Costa.  A survey on benders decomposition applied to fixed-charge network design problems , 2005, Comput. Oper. Res..

[20]  A. M. Geoffrion,et al.  Multicommodity Distribution System Design by Benders Decomposition , 1974 .

[21]  Tony Q. S. Quek,et al.  Electric Vehicle Charging in Smart Grid: Optimality and Valley-Filling Algorithms , 2014, IEEE Journal of Selected Topics in Signal Processing.

[22]  Sahand Ghavidel,et al.  Multi-objective optimal electric power planning in the power system using Gaussian bare-bones imperialist competitive algorithm , 2015, Inf. Sci..

[23]  Jean-François Cordeau,et al.  A Benders Decomposition Approach for the Locomotive and Car Assignment Problem , 1998, Transp. Sci..

[24]  Panos M. Pardalos,et al.  Optimization Problems in Multicast Tree Construction , 2006, Handbook of Optimization in Telecommunications.

[25]  K. Tomsovic,et al.  Placement of dispersed generation systems for reduced losses , 2000, Proceedings of the 33rd Annual Hawaii International Conference on System Sciences.

[26]  Yasuhiro Hayashi,et al.  Application of tabu search to optimal placement of distributed generators , 2001, 2001 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.01CH37194).

[27]  J. Lavaei,et al.  Convex relaxation for optimal power flow problem: Mesh networks , 2013, 2013 Asilomar Conference on Signals, Systems and Computers.

[28]  S. Low,et al.  Zero Duality Gap in Optimal Power Flow Problem , 2012, IEEE Transactions on Power Systems.

[29]  Paulo Morelato França,et al.  LONG-RANGE PLANNING OF POWER DISTRIBUTION SYSTEMS: SECONDARY NETWORKS , 1996 .

[30]  R D Zimmerman,et al.  MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education , 2011, IEEE Transactions on Power Systems.

[31]  N. Zareen,et al.  A review of optimum DG placement based on minimization of power losses and voltage stability enhancement of distribution system , 2016 .