Research Article A Comprehensive Modeling of a Three-Phase Voltage Source PWM Converter Juan Segundo-Ramírez, 1 Rafael Peña-Gallardo, 1 Aurelio Medina, 2 Ciro Núñez-Gutiérrez, 1 and Nancy Visairo-Cruz 1 1 Facultad de Ingenier´ ıa, Universidad Aut´ onoma de San Luis Potos´ ı, Manuel Nava No. 8, Zona Universitaria, 78290 San Luis Potos´ ı, SLP, Mexico 2 Facultad de Ingenier´ ıa El´ ectrica, Divisi´ on de Estudios de Posgrado, Universidad Michoacana de San Nicol´ as de Hidalgo, Ciudad Universitaria, 58030 Morelia, MICH, Mexico Correspondence should be addressed to Rafael Pe˜ na-Gallardo; rafael.pena@uaslp.mx Received 22 December 2014; Revised 29 April 2015; Accepted 3 May 2015 Academic Editor: Ivanka Stamova Copyright © 2015 Juan Segundo-Ram´ ırez et al. Tis 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. Tis 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. Te 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 coefcients are calculated by explicit mathematical formulas. Te 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 benefts of the proposed VSC model. 1. Introduction Tis contribution describes a time domain model of the voltage source converter (VSC) that can be used in the transient and steady state analysis of nonlinear power sys- tems including linear or nonlinear control schemes. With the proposed model, the original discontinuous nonlinear power system can be transformed into a continuous system while keeping the underlying discontinuous nature of the VSC and avoiding undesirable numerical problems associ- ated with the large derivatives during the switching transi- tions. Additionally, the computation of the periodic steady state solution is obtained with a Newton method; in this paper, an enhanced numerical diferentiation method is used [1]. Te VSC is the heart of many components in industrial applications due to its modular design, controllability, and the ability to build some multilevel topologies for low and high power applications [2, 3], high voltage direct current (HVDC) transmission system [4], electric motor speed drives, interconnection of wind energy systems, and fexible AC transmission systems (FACTS) [5], among others. For these reasons, the three-phase VSC is the common building block in FACTS technologies, custom power equipment, active flters, variable speed drives, PWM rectifers, HVDC links, and power electronic interfaces for interconnection of renewable energy sources. However, the analyses of electric networks including VSC-based components still represent important challenges, since the VSC-based components are in general nonlinear and incorporate both continuous and discontinuous time dynamics and discrete time events. Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2015, Article ID 426245, 11 pages http://dx.doi.org/10.1155/2015/426245