Journal of Optimization Theory and Applications

, Volume 179, Issue 1, pp 283–310 | Cite as

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

  • Salman KhodayifarEmail author
  • Mohammad A. Raayatpanah
  • Abbas Rabiee
  • Hamed Rahimian
  • Panos M. Pardalos


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.


Combinatorial optimization Distributed generation Multi-period optimal power flow Non-convex mixed-integer nonlinear programming Semi-definite programming Benders’ decomposition 

Mathematics Subject Classification

90C11 90C06 90C30 90C27 



The authors are grateful to the editors for their constructive comments, which helped us improve the presentation of this paper substantially.


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Authors and Affiliations

  1. 1.Department of MathematicsInstitute for Advanced Studies in Basic Sciences (IASBS)ZanjanIran
  2. 2.Faculty of Mathematical Sciences and ComputerKharazmi UniversityTehranIran
  3. 3.Department of Electrical EngineeringUniversity of ZanjanZanjanIran
  4. 4.Department of Integrated Systems EngineeringThe Ohio State UniversityColumbusUSA
  5. 5.Department of Industrial and Systems Engineering, Center for Applied OptimizationUniversity of FloridaGainesvilleUSA

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