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Stationary frame linear proportional integral (PI) control has been widely used for current regulation of three-phase voltage-source inverters for a long time, but it has disadvantages of steady-state errors for ac quantities regulation. An attractive solution to eliminate these errors is P+Resonant (PR) control. However, one of its limitations is slow transient response in the startup. So far, no literature has explicitly explained the reason for its slow response phenomena. Therefore this study reveals, for the first time, a clear description of its nature by using classical control theory. To improve the current regulation performance of PR control, a novel proportional complex integral (PCI) control is proposed in this study. Unlike PR control based on the internal model principle, the proposed PCI control is derived from the concept of infinity gain to achieve zero steady-state error. A straightforward well-formulated design procedure for the PCI controller is presented based on system bandwidth criterion. In addition, practical issues such as control delay effects and digital roundoff error mitigations are discussed. Theoretical analysis, continuous-domain simulations in the MATLAB/Simulink environment and discrete-domain digital control experiments based on TMS320F2812 DSP are carried out from the viewpoint of steady-state and dynamic performance comparisons among stationary frame PI, PR and PCI control strategies. In agreement with theoretical analysis, simulation and experimental results indicate that PCI control is the best solution among three strategies to achieve fast and accurate current regulation for three-phase grid-connected voltage-source inverters.