This paper aims to present the design and implementation of a three-phase and modular direct matrix converter, controlled by the Singular Value Decomposition (SVD) modulation strategy, which offers several operational advantages. A prototype that emulates a Wind Energy Conversion System (WECS) that incorporates the matrix converter as the main element that links the electrical generator and the electrical grid is presented. The simulation and experimental results corroborate that the matrix converter is a convenient option to take into account for this type of application.