Capacitor planning for large distribution systems with wind generators using successive fuzzy MILP

Distribution systems (DS) are a focal connection point for existing and new renewable energy sources. DS have increasing sizes; they connect increasing numbers of renewable energy sources and have a mandate to operate as financial entities seeking to maximize their profits in an electricity market. To achieve these goals, DS require highly efficient planning tools. In this paper, we propose a successive fuzzy mixed integer linear programming (MILP) method for optimally placing and sizing capacitors in a DS that explicitly models induction run wind electric generators (WEGs). The optimization problem is linearized, transformed into a fuzzy MILP model and is solved successively while updating the solution vector. The fuzzy MILP method employs fuzzy models of voltage constraints that are often violated in a planned system that lacks reactive power support. The use of fuzzy constraints makes the proposed solution method very robust by avoiding infeasibility and reducing the need for user expertise. Further, the fuzzy MILP method represents the dual objectives of capacitor cost and annual energy loss minimization as fuzzy sets with individual satisfaction functions. The method maximizes the minimum of these satisfaction functions during optimization. Tests on 69-bus and 2002-bus DS show that the method performs well and is robust.