The dynamics of induction motors supplied by non-constant voltage source

A vector model of an induction machine is used to analyze the dynamical behaviour of the machine when the supply is a non-constant, non-linear voltage source. The vector model consists of rotating space vectors that represent, in a very concise manner, relevant electromagnetic variables of the rotating-field electric machine: applied voltages, currents, m.m.f.'s, and flux linkages. The vectors are two-dimensional ones: they are located in a plane that is orthogonal to the axis of the machine. Their magnitude and angular speed vary depending on the operating conditions.;The angular position of the rotor-flux linkage vector is used as the model's frame of reference because that vector tends to be the most stable one, particularly in motors having short-circuited rotor windings. This frame of reference is used when the vector model of the machine is expressed as a set of differential equations that relate the varying coordinates of voltage and current vectors. Steady-state analyses of the machine supplied by a constant AC source, and by a constant DC source via a three-phase inverter, are presented. The analysis of transient conditions with constant or non-constant voltage sources is done using computer-aided time simulation. This approach is illustrated with the results obtained in simulation studies that use: a constant AC source, a constant DC source, and, most importantly, a photovoltaic array as a typical instance of a non-constant, non-linear voltage source.