Steady state performance of inverter fed induction machines by means of time domain complex variables

An induction machine model in which the order of the electrical differential equations is one half of the conventional real variable model is obtained by using the complex time variables introduced by Ku and Lyon in the 1950's. Since the stepped excitation waveforms associated with polyphase inverters are also well suited to complex representation, the method provides a powerful means of exploiting the symmetry inherent in inverter-machine systems. After a brief introduction to the concept of complex time variables, the steady state analysis of six-step voltage and current source inverter driven induction machines is presented. Closed form solutions for the instantaneous voltages, currents and torques are derived. For small slip the current fed machine solutions are reduced to simple expressions involving rotor frequency sinusoidal functions and the relationships between these waveforms and the fundamental component equivalent circuit solutions are demonstrated. The solutions for the voltage fed machine are more complicated, however, hand computation of peak values is feasible or extremely simple computer programs can be written to yield the instantaneous current and torque waveforms.