INTRODUCTION
It is important to begin by stressing that although readers who can absorb the material in this chapter will undoubtedly be better versed in induction motor matters than those who decide to skip it, it should be seen as a bonus in terms of the added understanding it can provide, rather than an essential.
Nothing on the equivalent circuit was included in the Wrst two editions of the book, because it was feared that readers might Wnd it too daunting. But on reXection there are three reasons why it is logical to include such a potentially illuminating topic. Firstly, the parameters that appear in the equivalent circuit (e.g. leakage reactance, magnetising reactance) are common currency in any serious discussion of induction motors, and understanding what they mean is necessary if we wish to engage eVectively with those who use the language. Secondly, a knowledge of the structure and behaviour of the circuit brings a new perspective to support the ‘physical’ basis followed in the rest of the book, and in this respect it can be an excellent aide-memoire when attempting to recall aspects of motor performance. And Wnally, it provides the only simple method for quanti- tative performance predictions and thereby permits us to justify some of the qualitative statements made in Chapters 5 and 6.
As elsewhere in the book a knowledge of elementary circuit theory is required, together with an understanding of the material on magnetic circuits introduced in Chapter 1. In addition, readers whose basic know- ledge of steady-state a.c. circuits (reactance, impedance, power-factor and phasors) and introductory-level calculus have become rusty will Wnd it helpful to brush-up on these topics before reading on.
Outline of approach
So far in this book we have not referred to the parallels between the induction motor and the transformer, not least because the former is designed to convert energy from electrical to mechanical form, while the latter converts electrical power from one voltage to another. Physically, however, the construction of the wound-rotor induction motor has striking similarities with that of the 3-phase transformer, with the stator and rotor windings corresponding to the primary and secondary windings of a transformer. In the light of these similar- ities, which are discussed in Section 7.2, it is not surprising that the induction motor equivalent circuit is derived from that of the transformer.
The behaviour of the transformer is covered in Section 7.3, beginning with the ‘ideal’ transformer, for which the governing equations are delightfully simple. We then extend the equivalent circuit so that it includes the modest imperfections of the real transformer. In the course of this discussion we will establish the meaning of the terms magnetising reactance and leakage reactance, which also feature in the induction motor equivalent circuit. And perhaps even more importantly for what comes later, we will be in a position to appreciate the beneWt of being able to assess what eVect a load connected to the secondary winding has on the primary winding by making use of the concept of a ‘referred’ secondary load impedance. This concept will be central when we reach the induction motor.
The emphasis throughout will be on how good a transformer is, and how for most purposes a very simple equivalent circuit is more than adequate. The approach taken diVers from that taken in many text- books, which begin with the all-singing, all-dancing circuit which can not only look frighteningly complicated to a newcomer, but also tends to give the erroneous impression that the transformer is riddled with serious imperfections.
We will reach the induction motor equivalent circuit in Section 7.4.
This is where a really clever leap of the imagination is revealed. We have already seen that the magnitude and frequency of the rotor currents depend on the slip, and that they interact with the air-gap Xux to produce torque. So how are we to represent what is going on in the rotor in a single equivalent circuit that must necessarily also include the stator variables, and in which all the voltages and currents are at mains frequency? We will discover that, despite the apparent complexity, all of the electromechanical interactions can be represented by means of a transformer equivalent circuit, with a hypothetical slip-dependent ‘electromechanical resistance’ connected where the secondary ‘load’ would normally be. The equivalent circuit must have created quite a stir when it was Wrst developed, but is now taken for granted. This is a pity because it represents a major intellectual achievement.