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Most variable-speed AC generation systems use back-to-back converters to supply electrical energy, with fixed electrical frequency and voltage, to a stand-alone load or grid. Matrix converters (MCs) are a good alternative to back-to-back converters because they have several advantages in terms of size and weight. Therefore, MCs can be advantageously used in any variable-speed generation system where high efficiency, reliability, small size, and low weight are considered important factors. Nevertheless, to interface an MC-based generation system to an unbalanced 3φ stand-alone load, a four-leg MC is required to provide a path for the zero-sequence load current. Space-vector-modulation (SVM) algorithms for the operation of four-leg MCs have been proposed in the literature. However, these modulation methods have high computational burdens, and they are difficult to implement, even in fast DSP-based control platforms. Therefore, only simulation results have been reported in these publications. In this paper, an SVM algorithm is optimized and experimentally tested. Moreover, the harmonics produced in the input current when a four-leg MC is feeding an unbalanced or nonlinear load are also mathematically analyzed in this paper, with experimental verification being provided.