Extremum Seeking for Plants With a Time-Varying Disturbance: Application to Photovoltaic Maximum Power Point Tracking

Abstract

This paper presents an extremum seeking controller for photovoltaic maximum power point tracking (MPPT). The controller belongs to the broad family of “perturb and observe” algorithms, where the terminal voltage of a photovoltaic system is adjusted to maximize its output power. One critical challenge with these algorithms is that it can be difficult to distinguish between changes in photovoltaic power resulting from changes in irradiation versus the control input. With regard to this challenge, we develop an extremum seeking algorithm that uses least-squares estimation to explicitly separate the effect of the control input from the effect of time-varying disturbances. While the use of least-squares estimation in the context of extremum seeking is not new, our separation of time-varying effects is. In addition, our formulation retains much of the structure of traditional extremum seeking, thereby allowing us to perform a stability analysis comparable to the existing literature. This stability analysis assumes the time-varying disturbance to be slow, but we test the controller beyond this limit in simulation for photovoltaic MPPT. We compare our controller to two benchmarks (a similar controller that does not separate time-varying effects and a traditional extremum seeking controller), and our controller outperforms both.