On the basis of “cleaning” the power electronics interfaces in power system, and in order to achieve fast and accuracy grid currents tracking the references, parallel structure repetitive control (PSRC) and its control system are discussed. PSRC employs a parallel combination of categorized nk+i (i=0,1,2,…,n-1) order harmonic frequency internal models to achieve the zero-error tracking or disturbance elimination for all harmonics. Compared with conventional RC (CRC), PSRC has less time delay, faster error convergence rate, same tracking accuracy and same digital data memory cells. PSRC is applied into constant-voltage constant-frequency (CVCF) pulse-width-modulation (PWM) converter system, including three/single-phase rectifier/grid-connected inverter systems. Experimental results validate the effectiveness and advantages of PSRC. This work is supported by National Natural Science Foundation of China (No. 51407084) and Fundamental Research Funds for the Central Universities (No. JUSRP11461).