Mixed integer conic programming approach for optimal capacitor placement in radial distribution networks.

Abstract

The flow of reactive power in radial power systems increases the losses and reduces the line voltages particularly at heavy loads. In order to minimize those losses and to maintain the voltage profile within acceptable limits, capacitor banks have been used to provide reactive power compensation. The amount of reactive power compensation is linked to the location, size, and number of capacitor banks to be placed in the power system. This thesis introduces a mixed-integer conic programming (MICP) approach to solve the optimal capacitor placement problem in radial distribution networks. The problem is formulated to allow optimally placing fixed and switched type capacitors; its objective is to minimize the peak power losses, the energy losses, and the costs associated with the required capacitor banks while satisfying the physical and technical constraints on the network. The proposed solution is based on the conic quadratic format of the power flow equations. As a result of using the conic format, the relaxation becomes convex and therefore a global solution to the capacitor planning problem can be obtained using a branch-and-cut algorithm. The method is tested on three radial test systems with 9, 34 and 83 nodes having up to 12 load levels and is validated by comparison with previously published solution results. The MICP method consistently gave better quality solutions and unlike previous techniques, it gives assurance of the quality of the solution.