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

2020-03-262020-03-2620182018 IEEE 19th Workshop on Control and Modeling for Power Electronics, COMPEL 20189781538655412https://hdl.handle.net/20.500.12585/8867In 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.Recurso electrónicoapplication/pdfenghttp://creativecommons.org/licenses/by-nc-nd/4.0/Nonlinear Analysis for the Three-Phase PLL: A New Look for a Classical Probleminfo:eu-repo/semantics/conferenceObject10.1109/COMPEL.2018.8460081Exponential stabilityHamiltonian systemsNon-linear analysisPassivity-based controlSynchronous reference frame phase-locked-loopAsymptotic stabilityDifferential equationsHamiltoniansLocks (fasteners)Nonlinear analysisNonlinear equationsPower controlPower electronicsSystem stabilityClassical problemsDissipative hamiltonian systemHamiltonian systemsNonlinear differential equationPassivity based controlPhase Locked Loop (PLL)Stability propertiesSynchronous reference framePhase locked loopsinfo:eu-repo/semantics/restrictedAccessAtribución-NoComercial 4.0 InternacionalUniversidad Tecnológica de BolívarRepositorio UTB57204100992364492235005691956410014833891400