Nonlinear Controller Design and Stability Analysis for Single-Phase Grid-Connected Photovoltaic Systems

Abstract

In this paper, the control problem of single phase grid tied to the photovoltaic (PV) systems is presented. The proposed system involves two main controllers: three-phase inverter with LCL filter controller and the DC/DC boost converter controller. These controllers are designed to achieve the following three control objectives: (i) the PV voltage must be controlled to achieve the maximum power point; (ii) maintaining the intermediate voltage to a constant reference value; (iii) Providing a grid current with sinusoidal form and in phase with the grid voltage by means of controlling DC/AC converter (Power Factor Correction). To meet these threefold objectives, a cascade nonlinear controllers is developed making use of Backstepping technique with the Lyapunov function. So as to guarantee the stability of the whole system, these objectives should be achieved simultaneously. A nonlinear controller is designed using Backstepping approach for PFC and PV voltage regulator design. to achieve DC voltage regulation a filtered PI regulator type is used. The stability of the system is formally analysed using averaging theory. The controller performances are illustrated by simulation in MATLAB/Simulink environment.