State Equations of Dynamic Systems with Time Varying Coefficients

The state equations of Kron's primitive machine (KPM) are derived. In turn, the describing equations of the classical energy converters that have time varying coefficients are transformed to corresponding equivalent state equations. These state equations have time independent coefficients and describe the two and three phase primary (with damping windings) synchronous energy converters and the two and three phase primary induction energy converters, all referred to a stationary d-q reference frame. In effect, the state equations describe KPM-equivalents of the above-mentioned devices. The parameters of these equivalents are functions of the real parameters of the physical devices as they are used in practice.