Revista Eletrônica de Potência (Brazilian Journal of Power Electronics)

Palavras Chaves: Conversor trifásico, Critério generalizado de Nyquist, estabilidade, Linearização, PLL

Resumo

Este artigo realiza a análise da influência do sistema de sincronismo sobre a estabilidade de conversores trifásicos conectados à rede elétrica combinando equações de espaço de estado e funções de transferência matriciais. Fundamentado no método das impedâncias, divide-se o sistema de geração em dois elementos representados por funções de transferência matriciais em eixos síncronos dq. O primeiro representa a admitância equivalente do conversor, que é obtido ao considerá-lo conectado à uma rede ideal. Neste caso, são considerados as dinâmicas do phase-looked loop (PLL) e do controlador de corrente. O segundo representa a impedância equivalente da rede. O modelo não-linear obtido foi, então, linearizado por perturbações de pequenos sinais. A interconexão entre os dois elementos é realizada em matrizes função de transferência e representada na forma de digrama de blocos. A análise da estabilidade do sistema se dá pela utilização do critério generalizado de nyquist (GNC). Além disso, o método dos autovalores é utilizado no sistema completo em espaço de estados para elucidar a escolha dos ganhos do PLL. A fim de verificar a análise teórica, resultados de simulação são apresentados, mostrando uma boa correção com a análise matemática no domínio da frequência.

Title: Synchronism method influence on three-phase grid-tied converters stability

Keywords: Generalized Nyquist criteria, Linearization, PLL, stability, Three-phase converter

Abstract

This paper analyzes the influence of the synchronism system on the stability of three-phase grid-tied converters, combining state space equations and matrix transfer functions. Based on the impedance method, the generation system was divided into two elements represented by matrix transfer functions on dq synchronous axis. The first represents the equivalent admittance of the converter, which is obtained by considering it connected to an ideal grid. Here, the dynamics of the phase-looked loop (PLL) and of the current controller are considered. The second represents the grid equivalent impedance. In addition, the resulting non-linear model was linearized by the small-signal method. The interconnection between these two elements is performed in transfer function matrices and represented in the block diagram form. The analysis of the stability of the system is given by the use of the Generalized Nyquist Criterion (GNC). Moreover, the eigenvalues method is used in the complete state space system to elucidate the choice of PLL gains. In order to validate the theoretical analysis, simulations results are presented, showing a good agreement with the mathematical analysis in the frequency domain.

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