Using Simplified Distflow-Based Mixed-Integer Quadratically Constrained Programming Formulation for Optimum Selection of Conductor Size in Electrical Distribution Networks

Abstract

Determining conductor size is a subproblem that plays a vital role in the planning process of distribution systems. The problem of selecting the conductor cross-sectional area is usually made a model of mixed-integer non-linear programming (MINLP). It is important to note, however, that the MINLP model is not always capable of ensuring convergence to a solution that is globally optimum. In this research, a mixed-integer quadratically constrained programming (MIQCP) formulation is developed as a method for determining the conductor cross-sectional area in power distribution networks in an optimal manner. The goal function aims at minimizing the lifetime cost of lines, including initial capital cost together with operational expenses. The suggested optimization model's constraints consist of power balance equations, thermal loading capacity of branches, nodal voltage restrictions, budget limitations for investment, and the need to have the same wire size in the main feeder. By using the simplified DistFlow approach for electrical distribution networks and precisely linearizing the product of a binary variable and a continuous variable, the MIQCP formulation is derived from the MINLP model. It is likely possible to solve the MIQCP formulation efficiently in the GAMS environment by using available commercial solvers like CPLEX. The developed MIQCP model is validated using three medium voltage distribution grids of IEEE 33 buses, IEEE 85 nodes, and the Vietnamese real 102 buses. The calculation results revealed the accuracy along with the efficacy of the proposed optimization procedure.