Model-Free Optimal Control of VAR Resources in Distribution Systems: An Extremum Seeking Approach

Distributed power electronic reactive power sources-such as smart PV inverters-may play an important role in regulating customer voltages and reducing system losses in future distribution systems. Though it is natural to consider model-based optimal control algorithms to coordinate these resources, those strategies typically require relatively large communications capabilities and accurate models. In this paper we present an alternative way to implement the optimization problem that circumvents these communications and modeling challenges. We present an Extremum Seeking (ES) control algorithm to modulate the reactive power output of VAR resources to minimize total real power delivery at the feeder substation subject to voltage magnitude constraints, without an explicit feeder model. We present results that guarantee a variety of distribution feeder objective functions are convex over a broad range of power flows and perform an analysis showing the convergence of the ES approach. Simulation results demonstrate that the method is equivalent to recently developed convex relaxations used to solve distribution optimal power flow problems.