Closed form solution of the isolated open circuit operation of induction machines

Abstract EN

This paper presents a closed form solution of induction machines when disconnected from their main supply.

Using time complex variables, expressed in the rotor reference frame, and the fact that the stator current is zero during this mode of operation, the differential equations that describe the dynamic behavior of the symmetrical induction machine were transformed into first order linear differential equations which could be easily solved in closed form.

The performance of the closed form solution was evaluated using several induction machines with different horse power ratings ranging from 3 hp to 2250 hp.

In all simulated cases, the closed form solution and the detailed dlq model results were identical.

This is expected, since the closed form solution was obtained directly from the detailed dlq formulation.

However, the closed form solution is faster than the detailed dlq model.

Furthermore, the closed form solution can directly determine the dynamic response of induction machines at any time during their isolated open circuit mode of operation.

However, in the case of the detailed d/q model, being a numerical solution, the time step must be properly selected in order to obtain reasonable accuracy.