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The analysis, design aspects, 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 the VSC is to track the sinusoidal reference currents in each phase. The current controller includes a complex saturation function in order to avoid overmodulation in the SVM. Due to this strong nonlinearity, the study leads to system states not treated so far. An approximate Poincare map is derived. The paper reports saddles in the state space as a consequence of fold bifurcation and other phenomena in conjunction with saddles. Design conditions are derived to avoid undesired operation.