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Mathematical Problems in Engineering
Volume 2015, Article ID 426245, 11 pages
Research Article

A Comprehensive Modeling of a Three-Phase Voltage Source PWM Converter

1Facultad de Ingeniería, Universidad Autónoma de San Luis Potosí, Manuel Nava No. 8, Zona Universitaria, 78290 San Luis Potosí, SLP, Mexico
2Facultad de Ingeniería Eléctrica, División de Estudios de Posgrado, Universidad Michoacana de San Nicolás de Hidalgo, Ciudad Universitaria, 58030 Morelia, MICH, Mexico

Received 22 December 2014; Revised 29 April 2015; Accepted 3 May 2015

Academic Editor: Ivanka Stamova

Copyright © 2015 Juan Segundo-Ramírez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This contribution reports the development of a time domain model of a three-phase voltage source converter (VSC) that can be used in the transient and steady state analysis of nonlinear power systems including their associated closed-loop control schemes. With this proposed model, the original discontinuous nonlinear power system can be transformed into a continuous system, while keeping the underlying harmonic nature of the VSC and avoiding typical and undesirable numerical problems associated with the large derivatives during the switching transitions. The development of this model was based on the dynamic Fourier series of the switching functions under a sinusoidal PWM modulation scheme, which require the calculation of the switching instants at each integration step; the switching instants and the dynamic Fourier series coefficients are calculated by explicit mathematical formulas. The proposed model of the VSC is suitable for the fast computation of the periodic steady state solution through the application of Newton method. Simulations were carried out in order to illustrate the benefits of the proposed VSC model.