0195136047.pdf

590 ROTATING MACHINES

position. The effects of saliency are taken into account by thetwo-reactance theory, in which

the armature currentI ̄ais resolved into two components:Idin the direct or field axis, andIqin

the quadrature or interpolar axis.Iqwill be in the time phase with the excitation speed voltage

E ̄f, whereasIdwill be in time quadrature withE ̄f. Direct- and quadrature-axis reactances (Xd

andXq) are then introduced to model the machine in two axes. While this involved method of

analysis is not pursued here any further, the steady-state power-angle characteristic of a salient-

pole synchronous machine (with negligible armature resistance) is shown in Figure 13.3.4. The

resulting power has two terms: one due to field excitation and the other due to saliency. The

maximum torque that can be developed is somewhat greater because of the contribution due to

saliency.

Saturation factors and saturated reactances can be developed to account approximately for

saturation, or more involved field-plotting methods may be used if necessary. Such matters are

obviously outside the scope of this text.

Parallel Operation of Interconnected Synchronous Generators

In order to assure continuity of the power supply within prescribed limits of frequency and voltage

at all the load points scattered over the service area, it becomes necessary in any modern power

system to operate several alternators in parallel, interconnected by various transmission lines, in

a well-coordinated and optimized manner for the most economical operation. A generator can be

paralleled with an infinite bus (or with another generator running at rated voltage and frequency

supplying the load) by driving it at synchronous speed corresponding to the system frequency and

adjusting its field excitation so that its terminal voltage equals that of the bus. If the frequency of

the incoming machine is not exactly equal to that of the system, the phase relation between its

voltage and the bus voltage will vary at a frequency equal to the difference between the frequencies

of the machine and the bus voltages. In normal practice, this difference can usually be made quite

small, to a fraction of a hertz; in polyphase systems, it is essential that the same phase sequence be

+δ

P

−P

Generator

0

Power due to saliency

Power due to field excitation

sin δ

−δ

Resultant power P

Motor

−π π

VtEf

Xd

− sin 2δ

Vt^2

2

1

Xq

1

()Xd

−π/2 π/2

Figure 13.3.4Steady-state power-angle characteristic of a salient-pole synchronous machine (with negli-

gible armature resistance).