Nonlinear Analysis for the Three-Phase PLL: A New Look for a Classical Problem

Abstract

In this paper we investigate the dynamics of the classic synchronous reference frame phase-locked-loop (PLL) from a non-linear perspective. First, we demonstrate the nonlinear differential equations that describe the PLL under balanced conditions can be represented as a dissipative Hamiltonian system (DHS). After that, we find the equilibrium points of this system and their stability properties. Additional properties are investigated such as the attraction region, the conditions for exponential stability and the performance for small unbalances an d/or transients in the grid. Simulations results complement the theoretical analysis. We do not propose a new type of PLL, instead, we propose a non-linear analysis for the classic synchronous reference frame PLL. This analysis is useful for theoretical and practical studies since this PLL is widely used in industrial applications. In addition, it can give insights for better understanding of the dynamics of the phase-locked-loop1 1The presentation of this paper in the COMPEL2018 was partially supported by the Maestrfa en Ingeniería Eléctrica Universidad Tecnologica de Pereira. © 2018 IEEE.