Stability of distributed, asynchronous VAR-based closed-loop voltage control systems

Due to the proliferation of smart inverters, there have been recent proposals to perform automatic, fast, closed-loop voltage control via VAR injection/absorption. The stability of such feedback loops has only been briefly investigated, either experimentally, or theoretically but under the assumption that all smart inverters act synchronously. This paper attempts to fill a theoretical gap with a rigorous mathematical analysis of the stability criterion of distributed and asynchronous VAR injection over an arbitrary radial feeder, where each unit (out of potentially 100s) faces different impedances and independently runs closed-loop control based on its local voltage, with no global knowledge. We employ Lyapunov analysis, modified to allow non-deterministic system evolution. Our main theorem is a simple and intuitive stability criterion that allows arbitrary sequence of actions (periodic or aperiodic) by the distributed smart inverters. We also show that while both synchronous and asynchronous cases exhibit a tradeoff between voltage correction and stability, the asynchronous case has a much larger stability region and therefore allows much better voltage correction.