Variable gradient-based phase locked loop for accurate frequency estimation of distorted grids

A variable gradient-based phase locked loop (VG-PLL) is developed for distorted grids. Firstly, the large-signal model of the synchronous reference frame phase locked loop (SRF-PLL) with harmonic disturbances is established, and the large-signal model shows that the SRF-PLL has poor filtering effects in estimating the grid frequency. To address this issue, a VG-PLL is then proposed. Based on the variable gradient method, a Lyapunov function is developed to demonstrate that the proposed VG-PLL is input-state stability, even when the grids are distorted. In addition, the performance comparisons between the VG-PLL and SRF-PLL are provided. Compared with the SRF-PLL, the proposed VG-PLL has better filtering capability. Experimental tests also verify the superior performance of the proposed VG-PLL for accurate frequency estimation under grid distortions.