Optimal DG Placement for Power Loss Minimization in Radial Power Distribution Networks using Mixed-Integer Quadratic Programming Method based on Modified DistFlow

This paper aims at the optimal siting and sizing of distributed generation (DG) units in radial power distribution systems. The objective function to be minimized is real power losses of power distribution grids. The considered constraints encompass the power flow equations, voltage magnitude bounds, the number of buses selected to place DG units, active power limits of each DG and branch power flow confinements. This original optimization formulation is an intricate mixed-integer nonlinear programming (MINLP) model. This MINLP model is recast into mixed-integer quadratic programming (MIQP) formulation by exploiting the modified DistFlow method and exact linearization of the product of a real and binary variable, which can be easily solved with commercial solver CPLEX under GAMS software. The modified DistFlow in which the active and reactive powers are taken the place of their ratios to voltage magnitude as state variables is a cold-start linear branch power flow model. An IEEE 33-node system and a realistic distribution network are employed to study the effects of DG units on active power loss and voltage magnitudes using the proposed model. Calculated results reveal that optimally locating and sizing of DG units make a substantial contribution to decreasing power loss and improving the voltage profile in radial distribution systems.