Estimation-Based Extremum-Seeking Control: A Real-Time Approach for Improving Energy Efficiency in Photovoltaic Systems

This paper presents a novel real-time algorithm to find unknown maximum power of photovoltaic (PV) systems. The maximum power of a typical PV system is continuously changing with variations in solar irradiance and PV module temperature. There is no precise mathematical equation to show relation between PV output power and environmental variables. Since power of a PV cell/module is unknown nonlinear and time-varying function of irradiance and temperature, real-time approaches are required to find maximum power values through time. Based on strong concavity feature of PV output power, one can consider this measurable signal as an unknown objective function that needs to be maximized. Hence, an estimation-based extremum-seeking control algorithm is proposed to solve this nonlinear and uncertain optimization problem. First, gradient of the objective function with respect to the PV voltage is treated as an unknown time-varying parameter. An adaptive estimation technique is utilized to identify this parameter. Then, a direct gradient-based adaptive controller is designed to find optimum voltage value and the corresponding maximum power point at uniform and uncertain weather condition in real time. Unlike most model-free approaches, the proposed algorithm has proof of convergence with precise steady-state and fast-transient performance.