Analytical Closed-Form Solution of a Space-Vector Modulated VSI Feeding an Induction Motor Drive

This paper presents the analysis of the time response of the stator and rotor currents in an induction motor fed by a space-vector pulse-width modulated voltage source inverter. This mathematical model uses the Laplace and modified Z-transform. The solution is made in two steps: 1) finding the Laplace transform of the stator voltage space vectors and 2) finding the inverse transform of the load currents (original function) using the modified Z-transform. The solution is not dependent on the number of the pulses of the PWM pattern. All the analytical waveforms were visualized from the derived relations with the program MATHCAD. Experimental results prove the feasibility of the proposed mathematical model.