Time Domain Response of Induction Motors with PWM Supplies

Induction motors may be excited by rectangular voltage waves which are pulsewidth modulated according to a wide variety of strategies. The determination of performance directly in the time domain has hitherto been regarded as a complex task requiring considerable mathematical knowledge, and solution in the frequency domain has been preferred. The way is described in which the time domain response can be generated by any engineer with some programming experience provided there is access to a computer with subroutines which produce system eigenvalues and eigenvectors and which permit the manipulation of complex matrices. The solution is generated directly in the stator three-phase reference frame in terms of the stator phase currents. Transformation of stator variables to an orthogonal reference frame or so as to diagonalize the system matrix is not required. A key to the solution is the generation of two switching arrays which define the switching instants and voltage levels of the voltage waveforms applied to the machine. The switching instants can be random, pseudorandom, or follow a specific pattern. The method can therefore be applied to sinusoidally modulated waves where the ratio of carrier-to-signal frequency is nonintegral or even irrational and to the transition from pure PWM to pure six-step through the intermediate stages involving dwell time limiting. The solution can either be transient, following the behavior from some specified starting point, or steady-state where the starting point is unknown but the excitation follows a recurring sequence of arbitrary length. Sample computations are given.