Comparative Study of Discretization Methods for Non-Ideal Proportional-Resonant Controllers in Voltage Regulation of Three-Phase Four-Wire Converters with Vehicle-to-Home Mode

Vehicle-to-home (V2H) technology enables electric vehicles (EVs) to supply power to residential loads, offering enhanced energy self-sufficiency and backup capabilities. Accurate voltage regulation is essential in such systems, especially under nonlinear and time-varying load conditions. The control method for three-phase four-wire (3P4W) converters plays a vital role in addressing these challenges. In the control configuration of such systems, the non-ideal proportional-resonant (PR) controller stands out due to its ability to reject periodic disturbances. However, the comprehensive study on the discretization of this controller for digital implementation in 3P4W systems has not been available in the literature to date. This paper presents a comparative study of several discretization methods for non-ideal PR controllers. The continuous-time complete transfer function of the integral term of non-ideal PR controllers is discretized using techniques such as Forward Euler, Backward Euler, Tustin, Zero-Order Hold, and Impulse Invariance. Additionally, the discretization methods based on two discrete integrators for the non-ideal PR controller, such as Forward Euler and Backward Euler, Backward Euler and Backward Euler plus computational delay, and Tustin and Tustin, are also evaluated. In the MATLAB/Simulink platform, through evaluating the performance of the non-ideal PR controllers, which are discretized using the above discretization methods, in controlling the output voltage of the 3P4W converter in the V2H application under nonlinear load scenarios, including substantial and sudden changes in load, the discretization method Backward Euler and Backward Euler plus delay is recommended.