Imposing Radiality Constraints in Distribution System Optimization Problems

Distribution systems commonly operate with a radial topology, so all models of optimization problems in these distribution systems should consider radiality in their formulation. This work presents a literature review, a critical analysis, and a proposal for incorporating the radiality constraints in mathematical models of optimization problems for radial distribution systems. The objective is to show that the radiality constraints on such optimization problems can be considered in a simple and efficient way. The reconfiguration and expansion planning problems of distribution systems are used to test and verify the proposed radiality constraints. A generalization of radiality constraints is also examined.

[1]  Hanif D. Sherali,et al.  Linear Programming and Network Flows , 1977 .

[2]  D.L. Wall,et al.  An Optimization Model for Planning Radial Distribution Networks , 1979, IEEE Transactions on Power Apparatus and Systems.

[3]  Turan Gonen,et al.  Optimal Multi-Stage Planning of Power Distribution Systems , 1987, IEEE Transactions on Power Delivery.

[4]  D. Shirmohammadi,et al.  Reconfiguration of electric distribution networks for resistive line losses reduction , 1989 .

[5]  Felix F. Wu,et al.  Network reconfiguration in distribution systems for loss reduction and load balancing , 1989 .

[6]  K. Aoki,et al.  New approximate optimization method for distribution system planning , 1990 .

[7]  Koichi Nara,et al.  Distribution systems expansion planning by multi-stage branch exchange , 1992 .

[8]  Vladimiro Miranda,et al.  Genetic algorithms in optimal multistage distribution network planning , 1994 .

[9]  Swapan Kumar Goswami.  Distribution system planning using branch exchange technique , 1997 .

[10]  Suresh K. Khator,et al.  Power distribution planning: a review of models and issues , 1997 .

[11]  José Luis Bernal Agustín,et al.  Aplicación de algoritmos genéticos al diseño óptimo de sistemas de distribución de energía eléctrica , 1998 .

[12]  Ignacio J. Ramirez-Rosado,et al.  Genetic algorithms applied to the design of large power distribution systems , 1998 .

[13]  E. Miguez,et al.  An Improved Branch Exchange Algorithm for Large Scale Distribution Network Planning , 2002, IEEE Power Engineering Review.

[14]  H.M. Khodr,et al.  Ant colony system algorithm for the planning of primary distribution circuits , 2004, IEEE Transactions on Power Systems.

[15]  N. Bretas,et al.  Main chain representation for evolutionary algorithms applied to distribution system reconfiguration , 2005, IEEE Transactions on Power Systems.

[16]  C. Su,et al.  Variable scaling hybrid differential evolution for solving network reconfiguration of distribution systems , 2005 .

[17]  Ying-Yi Hong,et al.  Determination of network configuration considering multiobjective in distribution systems using genetic algorithms , 2005 .

[18]  A. G. Expósito,et al.  Path-based distribution network modeling: application to reconfiguration for loss reduction , 2005, IEEE Transactions on Power Systems.

[19]  J. A. Domínguez-Navarro,et al.  Integral planning of primary-secondary distribution systems using mixed integer linear programming , 2005, IEEE Transactions on Power Systems.

[20]  H. P. Schmidt,et al.  Fast reconfiguration of distribution systems considering loss minimization , 2005, IEEE Transactions on Power Systems.

[21]  E. Lopez,et al.  Minimal loss reconfiguration using genetic algorithms with restricted population and addressed operators: real application , 2006, IEEE Transactions on Power Systems.

[22]  S. Carneiro,et al.  A new heuristic reconfiguration algorithm for large distribution systems , 2005, 2006 IEEE Power Engineering Society General Meeting.

[23]  Jorge Nocedal,et al.  Knitro: An Integrated Package for Nonlinear Optimization , 2006 .

[24]  S. Carneiro,et al.  A New Distribution System Reconfiguration Approach Using Optimum Power Flow and Sensitivity Analysis for Loss Reduction , 2006, IEEE Transactions on Power Systems.

[25]  Zhengcai Fu,et al.  An improved TS algorithm for loss-minimum reconfiguration in large-scale distribution systems , 2007 .

[26]  J.M. Nahman,et al.  Optimal Planning of Radial Distribution Networks by Simulated Annealing Technique , 2008, IEEE Transactions on Power Systems.

[27]  R. Romero,et al.  An Efficient Codification to Solve Distribution Network Reconfiguration for Loss Reduction Problem , 2008, IEEE Transactions on Power Systems.

[28]  L.S. Barreto,et al.  Multistage Model for Distribution Expansion Planning With Distributed Generation—Part I: Problem Formulation , 2008, IEEE Transactions on Power Delivery.

[29]  Ariovaldo V. Garcia,et al.  A Constructive Heuristic Algorithm for Distribution System Planning , 2010, IEEE Transactions on Power Systems.

[30]  Jose Roberto Sanches Mantovani,et al.  Reactive power dispatch and planning using a non-linear branch-and-bound algorithm , 2010 .