Reactive power planning using convex line‐wise power balance equations for radial distribution systems

Abstract

Optimal capacitor placement for radial distribution systems (RDSs) considers minimising the total cost of new fixed capacitors, switchable capacitors, and losses, while satisfying power balance equations, limits on bus voltages and capacitor limits. It is a non-convex mixed-integer non-linear programming (MINLP) challenge. In this study, the authors propose a solution method using a line-wise model (LWM) of power balance equations. First, equations for LWM are presented with their Jacobian for solving the power flow problem using Newton–Raphson method. Then, an optimal non-convex MINLP capacitor placement formulation with LWM power balance equations is presented. Thereafter, it is transformed into a convex mixed-integer conic programming formulation using second-order conic relaxation. Both the non-convex and convex optimal capacitor placement formulations are used to study 69-bus and 136-bus RDS. The results are compared with a formulation that uses the branch flow model (BFM) for power balance equations. Results show that the non-convex LWM-based formulation is twice as fast when compared with the BFM-based formulation. The convex LWM-based formulation is from 4 to 30 times as fast when compared with the BFM-based formulation, demonstrating the benefits of the use of the LWM-based formulation for enhancing the solution space of the optimisation problem.