A graph theory-based solution method for capacitor bank and voltage regulator allocation problems in an unbalanced distribution system

Abstract

This paper presents a graph theory-based method to solve voltage and reactive power (voltage/var) control problems for a three-phase unbalanced distribution system (UDS). Multi-point fixed and switched capacitor bank (CB), solar distributed generation (SDG) and voltage regulator (VR) location are determined by simple and straightforward graph theory-based measures. The main contribution of this paper is – a single-stage optimisation-based voltage/var control method for UDS unlike commonly used two-stage optimisation methods; to find the location and optimal size of the CB. As the proposed graph theory method used power flow outputs to determine the most suitable nodes for CB and SDG connection, optimisation is needed only for optimal sizing at a certain location which reduces the computational burden. Secondly, optimal placement of VR is used to maintain the voltage level/voltage unbalance of the system. Multiple test cases with optimal configurations of switched CBs and optimal power factor operation-based SDG are used to demonstrate the effectiveness of proposed optimal operation techniques for overall improvement of performance parameters of UDS.