4. Modelling and Simulating Transformers

Chapter 4 describes how a transformer is merely a special case of a set of magnetically coupled windings wound on the same core, with the objective being to maximize the transfer of energy from one winding to the others. Since transformers are essentially magnetically coupled coils, the mathematical model of coupled inductors in Chap. 2 will continue to be used. The difference between a transformer and a random set of magnetically coupled coils is that a transformer is an electrical machine that has specifications similar to any other machine like a motor or generator. For example, a transformer will have a rated maximum power and rated maximum voltages that can be applied to each winding. The chapter will describe how using these specifications, an equivalent circuit can be formulated and the parameters of this equivalent circuit can be estimated. Using this equivalent circuit, we will extract the values of inductances that are necessary to use the simulation model of the coupled inductors. We will examine several simulations to understand the working of the transformer. Simulations will examine the magnetizing current and the other components in the no-load current of the transformer. Simulations will also examine the effect of turns ratio in transforming voltages and currents by simulating step-up and step-down transformers.