Robust Repetitive Controller Design Based on S/SK Problem for Single-phase Grid-connected Inverters

Proportional-integral multi-resonant (PIMR) controller can provide high gains in the fundamental frequency and its integer multiples of the fundamental frequency, so it has excellent harmonic rejection capability and is widely used in grid-connected inverters. However, PIMR requires an accurate model of the inverter system. In a distributed grid, multiple inverters are connected to the grid at the same time, and with the combined effect of a large number of nonlinear loads and line impedance, the grid cannot continue to be considered as an ideal grid, but a weak grid with background harmonics and grid impedance. Then it will be difficult for PIMR to retain the excellent harmonic suppression capability, which in turn leads to the threat to the stability of grid-connected system. Considering that the robust controller is not obvious to parameter uptake, the robust controller is combined with the PIMR to form a robust proportional-integral multi resonant (RPIMR) controller. In the paper, the stability of RPIMR is analyzed, the design process of RPIMR is given, and finally, the effectiveness and feasibility of the control strategy are simulated.