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Three‐Time‐Scale Singular Perturbation Stability Analysis of Three‐Phase Power Converters
Author(s) -
Umbría Francisco,
Aracil Javier,
Gordillo Francisco,
Salas Francisco,
Sánchez Juan Antonio
Publication year - 2014
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.818
Subject(s) - control theory (sociology) , equilibrium point , operating point , nonlinear system , singular perturbation , rectifier (neural networks) , exponential stability , converters , mathematics , electric power system , power (physics) , voltage , computer science , engineering , physics , differential equation , mathematical analysis , electronic engineering , stochastic neural network , control (management) , electrical engineering , quantum mechanics , artificial intelligence , machine learning , recurrent neural network , artificial neural network
Abstract This paper analyzes the stability of the well‐known three‐phase two‐level power converter. Focusing on the rectifier operating mode, the dynamics of the system, when the instantaneous power and dc‐link voltage controllers are included, are described by a set of complex equations that results in a nonlinear autonomous singularly perturbed system. Hence, the closed‐loop system can be studied under the assumption of separate time scales. The analysis proposed in this work follows a novel three‐time‐scale approach, where the fast time scale corresponds with the instantaneous power dynamics, the mid‐range time scale is related to the dc‐link voltage dynamics, and the slow time scale is associated with the dc‐link voltage regulator dynamics. In this way, the analysis leads to the decomposition of the closed‐loop system into three simpler subsystems: fast, medium, and slow subsystems. These subsystems approximate the closed‐loop system behavior over the three different time scales. Finally, since the equilibrium point of each subsystem is exponentially stable and some other conditions are satisfied, it is shown that the equilibrium point of the closed‐loop system also presents exponential stability. Experimental results for a synchronous three‐phase power rectifier prototype are included to corroborate the analysis carried out.