Applied Mathematics, University of Waterloo
Switching Optimal Control with an Application in Maximum Power Point Tracking of Photovoltaic Systems
In recent years, solar energy as a renewable energy source has attracted worldwide attention and many efforts have been spent on developing photo-voltaic(PV) devices and their applications. An effective control algorithm plays an important role in developing efficient solar PV systems. To this objective, various algorithms have already been presented in the literature of power electronics, known as Maximum Power-Point Tracking (MPPT) methods. From a control system’s point of view, solar PV systems can be modeled as a control system for which more complicated and efficient control techniques can be exploited, compared to the classical methods. While the problem of maximizing the output power of PV systems seems fundamentally an optimization problem, the design process of optimal controllers for solar PV systems still remains unclear. In this research, a framework is developed to address the problem of optimal feedback control for solar PV systems. In this way, the switching model of the system is obtained and the stability of the closed-loop nonlinear system is guaranteed by using a Lyapunov function. This Lyapunov function can be considered as an optimal value candidate that satisfies the Hamilton-Jacobi-Bellman equation with a nonquadratic performance functional. Thus, the obtained feedback control law guarantees both optimality and stability conditions, which potentially brings many benefits in the applications. Since the performance of solar PV systems is easily affected by the changing environment, the merits of the proposed control law have been observed under changing ambient temperature and solar radiation power.