A New Voltage Regulator for Distribution Networks With Stability and Robustness Certificates

This letter considers the voltage regulation problem of a radial and balanced distribution network, in which the impedance values (i.e., resistance and reactance) are uncertain. To solve this problem, we introduce an optimization-based robust control method leveraging tools from Control Lyapunov Function (CLF) and Quadratic Programming (QP). We first show that by selecting a suitable control gain, we can regulate the network voltage towards an arbitrary non-zero sub-level set after a large initial disturbance. Then we provide guidelines for choosing an appropriate CLF such that the aforesaid sub-level set coincides with the voltage safe limits, and thus, ensure voltage stability. Finally, we transform the voltage regulation problem to an equivalent QP-based optimization framework and translate the above conditions to obtain a feasible solution for voltage stability. We also empirically verify the efficacy of our method by performing experiments on the IEEE-33 bus distribution network.