Induction Machines at Steady State

Abstract

In this chapter, steady state operation of induction machines is studied with the aim to derive the equivalent circuit and mechanical characteristic of induction machine. The steady state model is derived from the dynamic model, developed and explained in the previous chapter. The voltage balance equations at steady state are used to develop the steady state equivalent circuit of the machine with squirrel cage rotor. At the same time, the concept of the equivalent transformer is introduced to derive the same steady state equivalent circuit. The equivalent circuit is used to determine the steady state currents, torque, power, losses, and fluxlinkages. Typical resistances and inductances of the equivalent circuit are explained and discussed, along with typical experimental procedures for their measurement and estimation. The system of relative units is introduced and explained, along with benefits that come from its use. Characteristic examples are studied to develop skills in working with relative units and selecting the base quantities used in scaling the absolute values into relative values. The functions that approximate the mechanical characteristic of induction machine and typical mechanical loads are introduced and explained. Natural mechanical characteristic is analyzed along with the start-up mode, rated operation, and no load operation. Breakdown torque is studied and explained in both motor and generator modes. Stable and unstable equilibrium points on mechanical characteristic are discussed and explained. The influence of machine resistances and reactances on the start-up torque, breakdown torque, breakdown slip, and coefficient of efficiency is analyzed and explained. This chapter proceeds by summarizing energy losses in windings, magnetic circuits, and mechanical losses due to rotation. Calculation of steady state losses is explained on the basis of the steady state equivalent circuit. The losses are presented in the form of power balance chart drawn for induction machine that operates in motoring mode. Simplified power balance is derived by splitting the air-gap power into rotor losses and mechanical power, according to the relative slip s. This chapter ends with deriving power balance chart for induction generator and discussing generator operating mode of induction machines.