Research on phase-locked loop technique based on three-dimensional coordinate transformation

Abstract

The traditional phase-locked loop (PLL) technique widely used in three-phase four-wire system can only obtain one phase angle, and cannot obtain other parameters of unbalanced voltages, such as the amplitude and phase angle of each phase voltage. In order to improve the performance of PLL in unbalanced three-phase four-wire system with disturbance and reduce the order of PLL to improve the stability of the system, a PLL technique based on three-dimensional (3D) coordinate transformation was proposed in this paper. Firstly, the phase detector error of three-phase unbalanced voltage was deduced based on the 3D coordinate transformation. The error can be regarded as the expression form in Hilbert space after linearizing of it. Based on the correspondence between the orthonormal basis in Hilbert space and the unit vectors in Euclidean space, the error can be mapped to Euclidean space, and the detection control law for each voltage parameter can be designed respectively based on the principle of perpendicular decoupling. Then, the voltage parameter detection control law in Euclidean space is mapped back to Hilbert space, so the PLL technique scheme can be obtained which is beneficial to the implementation in the actual system. The control law of each unbalance indices, such as the amplitude and initial phase of each phase voltage, can be decoupled into a first-order or second-order system, so the system structure is simple, and the control parameter design is convenient. The detection of unbalance indices of the three-phase unbalanced voltages with zero-sequence component can be realized with fast and stable characteristics. The simulation and experiments of the proposed PLL technique are carried out finally under several transient conditions of grid voltages, stable within a quarter cycle at the fastest and always stable in 50 ms, so as to validate the rapidness and stability of the proposed PLL technique.