Design and Analysis of an $H_{\infty}$ Controller for a Single Phase Grid Connected Photovoltaic System with Parametric Uncertainties

Abstract

This paper presents the synthesis of a $\mathrm{H}_{\infty}$ controller for a single phase single stage grid connected photovoltaic (PV) system. The PV array is integrated to the utility grid using an inverter and a filter. Many a times while deriving the mathematical model of a system, there exists some discrepancy between the actual and the derived model of the system. Hence these uncertainties should be taken into account while deriving the controller for the system in order to achieve robust stability. Here the robust controller is designed taking into consideration the uncertainty in the parameters R, L and C. An appropriate state space model of the system is derived in order to facilitate the controller design with the perturbations. Here the controller is designed to as to meet the required objective of good reference tracking, disturbance rejection and robust stability. The controller design step involves the proper selection of weighing function and solution of the cost functions. The cost functions in this case are transfer function from exogenous inputs to output of the system to be minimized. It was observed that in order to achieve the required performance criteria the infinity norm of the cost functions should be less than unity. For this an h infinity optimization problem was solved using the hinfsyn command in MATLAB. A transient analysis was done in MATLAB simulation to see the effect of output disturbance on the system performance. A $\mu$ -synthesis was further done to test whether the system is robustly stable under parametric uncertainties. It was found that the designed controller is robustly stable, effectively track the reference input given to the system. Also the effect of disturbances in the system output is minimized.