Maximum Power Point Tracking in an Uncertain Photovoltaic System Utilizing Finite-Time Nonlinear Control Approach

In this paper, by utilizing the finite-time robust nonlinear control approach, the maximum power point tracking problem is discussed and investigated for a closed-loop photovoltaic system. First, a comprehensive dynamical model for the photovoltaic system is introduced and elaborated. Next, to achieve the maximum power point, reference values for current and voltage of the photovoltaic module are determined by mathematical analysis. By defining tracking errors and two auxiliary variables, it is mathematically demonstrated that the maximum power point tracking problem of an uncertain photovoltaic system is equivalent to the global finite-time stabilization problem of an equilibrium point associated with an uncertain second order nonlinear system. By developing the terminal sliding mode control and defining several innovative sliding manifolds, three different types of finite-time robust nonlinear controllers are designed and proposed to accomplish the maximum power point tracking goal for the closed-loop photovoltaic system. By applying several lemmas, it is proven that all proposed controllers are able to guarantee the mentioned stability of the closed-loop photovoltaic system in the presence of uncertainties. In proposed control schemes, the convergence finite time depends on the values of arbitrary constants and, in consequence, by choosing proper values for these constants, the aforementioned finite time would be reduced significantly. Eventually, three proposed control schemes are numerically simulated onto the photovoltaic system and simulation results illustrate that the suggested controllers properly fulfill and provide the maximum power point tracking objective.