Stationary Frame Equivalent Model of Proportional-Integral Controller in dq Synchronous Frame

This letter establishes the stationary frame equivalent model of proportional-integral (PI) controller in dq synchronous frame. Although both PI controller in dq synchronous frame and proportional-resonant (PR) controller in stationary frame achieve zero steady-state error when tracing fundamental frequency reference, their amplitude and phase characteristics differ greatly from each other except for fundamental frequency. Using stationary frame PR controller to replace PI controller in dq synchronous frame directly leads to analytical errors, especially in low frequency stage. Another straightforward analysis method is to use stationary frame PI controller to replace PI controller in dq synchronous frame, however the coupling terms in dq synchronous frame are ignored and the approximation is not accurate. The accurate stationary frame equivalent model of PI controller is established. For system controlled in dq synchronous frame, the established model can be used to precisely predict system performance and thus guides control parameters design process. Theoretical analysis is presented and validity of the model is evaluated by simulation.