Fixed-Time Voltage Regulation in Distribution Networks with Impedance Awareness

Abstract

This letter introduces an optimization-based fixed time control algorithm for solving the voltage regulation problem of a radial and balanced power distribution network. The proposed algorithm requires no prior knowledge of the exact network impedance (resistance and reactance), yet guarantees voltage convergence to the predefined safe limit within a fixed time-window. We embrace results from Fixed-time stability (FxTs) and Control Lyapunov function (CLF) to analyze the stability and robustness of the underlying algorithm and then synthesize it leveraging the Quadratic Programming (QP) approach. We first analytically provide sufficient conditions on the control gains and the design parameters, that can ensure voltage regulation in fixed-time. Thereafter we transform the existing voltage regulation problem into an equivalent QP-based optimization framework and translate the aforesaid conditions to find feasible solutions for voltage stability. We empirically verify the efficacy of our proposed algorithm on the IEEE-33 bus distribution network and compare its performance against other existing robust control methods.