J.W. Lynn

Electrical machine dynamics

In this chapter, we shall look at the dynamic performance of some typical machines using approximate methods of solution. The analytical technique developed in the previous chapter leads to more exact solutions and will be used later, in the form of generalised machine theory. There is, however, the danger that by formulating equations in a ‘mechanical manner’ and solving them by using a digital computer, one may lose sight of the physical processes that are involved. The approximate methods often help us to obtain a physical insight into the behaviour of the systems.

Synchronous machine oscillations

We have seen that the dynamical stability of an electromechanical system is determined by the damping and synchronising torque coefficients and the inertia constants. In a mechanical system damping and spring constants can be easily visualised—damping, for instance arises due to friction. In an electrical system, mechanical friction constitutes a small part of the total damping, the main damping torque being of electrical origin. In trying to understand the electrically generated damping, we can tell intuitively that this is caused by power dissipation due to copper loss. In a machine, during steady-state operation, copper loss takes place continually and largely accounts for the power difference between input and output. If, however, the rotor begins to oscillate about its steady-state angular velocity, oscillating currents induced as a result, generate additional copper loss. For instance, if an oscillating current ∆I sin (ωot + α) in a winding is superimposed upon a 50 Hz steady-state current 1 sin ωt, where ω0 = hω, then the additional average copper loss is (8.1) where the integration period is the common repetition time for the two oscillatory currents. This additional copper loss appears to be the only dissipation (neglecting mechanical damping) which may suppress the rotor oscillation and bring it back to its normal uniform angular velocity. This argument, however, cannot explain why the rotor oscillations may sometimes build up, indicating the presence of negative damping—apparently produced by copper loss which is always positive. We shall see presently that the physical nature of damping is more complicated than that.

A review of basic machine theory

There are many types of rotating electromechanical energy converter. When these transform mechanical energy to electrical energy, they are called generators. When they convert electrical to mechanical energy, they are operating as motors. Most energy converters can operate either as generators or motors. We shall, however, refer to these rotating electromechanical energy converters simply as electrical machines.

Electrical machine dynamics continued

In Chapter 4 we have seen that the general dynamical analysis of a machine involves the determination of the initial steady state conditions of operation, the magnitude, nature, and duration of the disturbing forces, and the calculation of the dynamical response. It is thus necessary to have detailed information about the parameters of the machine and the nature of nonlinear functions and saturation effects associated with them.

Electrodynamical equations and their solution

In Chapter 2, we dealt with mutually coupled stationary coils (Section 2.7). This was followed by a review of the performance characteristics of a.c. and d.c. generators and motors.

PAIRWISE ANALYSIS OF DYNAMIC STABILITY IN LARGE POWER SYSTEMS

The method suggested involves computation of synchronizing and damping torque coefficients of oscillating generators selected in pairs in a large interconnected system and the use of these values to construct a model to represent the dynamics of the entire system. This method, shown to give acceptable results, saves a considerable amount of storage space and computation time.