Orthogonal Decoupling Control of the Error of a New-Type Phase-Locked Loop under Unbalanced Grid Conditions

This paper proposes a new-type phase-locked loop (PLL) based on Tan-Sun coordinate transformation system, which can realize the fast synchronization under unbalanced grid conditions. The phase detector’s (PD) error of the proposed PLL is selected as the linear function of three-phase grid voltages, which can be further expressed as the linear function of the estimated parameter errors by using Taylor expansion. In Hilbert space, by selecting the unit vector perpendicular to the other estimated parameter errors’ coefficients of PD’s error, the result derived by making the inner product of the unit vector and PD’s error is related to only one estimated parameter error, which means the decoupling control for each estimated parameter value becomes possible. Therefore, the standard first-order or second-order closed-loop control system can be designed for each estimated parameter value with the same settling time. The simulation and experimental results in the end indicate the effectiveness and speediness of the proposed Tan-Sun based PLL under unbalanced grid conditions.