Local voltage control in distribution systems: An incremental control algorithm

Inverter-based local volt/var control forms a closed-loop dynamical system whereby the measured voltage determines the reactive power injection, which in turn affects the voltage. There has been only a limited rigorous treatment of the equilibrium and dynamical properties of such feedback systems. In this paper, we expand on our prior result that reverse-engineers a class of non-incremental voltage control schemes and provides a principled way to rigorously engineer the control to incorporate new design goals and/or achieve better dynamical properties. Specifically, it has been observed in the literature that in practical circumstances the droop-based control scheme, a commonly adopted non-incremental voltage control, can lead to undesirable oscillatory behaviors even in the case of a single inverter unit. This motivates us to forward-engineer the local voltage control and apply the (sub)gradient method to design an incremental voltage control algorithm that demands less restrictive condition for convergence. We provide a sufficient condition to ensure convergence of the proposed control algorithm and evaluate its performance on a real-world distribution feeder in Southern California with multiple large PV generation units through simulations.