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The analysis and numerical results of a current controlled three-phase Space Vector Modulated (SVM) Voltage Source Converter (VSC) are presented. The aim of the current controller of VSC is to track the sinusoidal reference currents in each phase. The current controller includes a saturation function in order to avoid overmodulation in the SVM. Due to this strong nonlinearity the study leads to rather unexpected system states. An approximate Poincare map is derived using stroboscopic sampling with the modulation period of the SVM. The paper reports that saddle-nodes and coexisting chaotic and spiral attractors appear at some parameter settings.