Induction Machine Transient Model Using Complex Variables and Trapezoidal Integration

Abstract

This paper presents a model which predicts, with a high degree of accuracy, the dynamic response of induction machines. The model is simple, fast, accurate and numerically stable. Using the complex form of the induction machine equations along with trapezoidal integration and the fact that mechanical transients are much slower than electrical transients, the differential equations that describe the dynamic behavior of the symmetrical induction machine were transformed into algebraic equations which could be easily solved. The performance of the proposed model was evaluated using several induction machines with different horse power ratings ranging from 3 hp to 2400 hp. In all simulated cases, the proposed model was very accurate and duplicated faithfully the detailed d/q model results with a computation time as little as 25% of that required by the full-order model. Moreover, because of the numerical stability of the proposed model, computation time can be drastically reduced by using a larger time step in the simulation while maintaining reasonable accuracy.