Design and Analysis of Nonlinear Controller for a Standalone Photovoltaic System Using Lyapunov Stability Theory

This paper presents the Lyapunov stability theory-based nonlinear controller design for a standalone photovoltaic (PV) system. The comparative analysis of different nonlinear controllers is also carried out. Due to the nonlinear I-V characteristics of photovoltaic systems, conventional hill-climbing methods like Perturbate and Observe and Incremental Conductance do not show reliable tracking of maximum power under various uncertainties. Therefore, these methods require nonlinear tools to meet control objectives and design specifications. Out of various nonlinear controlling techniques, the one presented in this paper is the sliding mode approach for maximum power point tracking (MPPT). In the context of Lyapunov stability theory, the sliding mode approach uses a switching manifold. In this approach, the system trajectories are made to follow the sliding surface and remain there forever to ensure the stability of equilibrium points. Two types of sliding mode controllers have been simulated, namely, conventional-sliding mode controller (CSMC) and terminal-sliding mode controller (TSMC). The results are analyzed and compared scientifically on various performance parameters including duty cycle ratio, ideal and PV output power, and time taken for error convergence, under varying dynamic conditions. All the control algorithms are developed in matlab/Simulink.