0195136047.pdf

13.3 SYNCHRONOUS MACHINES 593

Generator

Bus

Infinite bus

Es ∠ δs

jXe

Eg ∠ δg

Figure 13.3.5Generator connected to an infinite bus.

P=

EgEs

X

sinδgs (13.3.13)

whereδgsis the angular difference betweenδgandδs, andX=Xd+Xe, withXdbeing the
direct-axis reactance of the synchronous generator. The power angle characteristic given by
Equation (13.3.13) is plotted in Figure 13.3.6. The peak of the power-angle curve, given by
Pmax, is known as thesteady-state power limit(shown by pointbin Figure 13.3.6), representing
the maximum power that can theoretically be transmitted in a stable manner. A machine is
usually operated at less than the power limit (such as at pointain Figure 13.3.6), thereby
leaving a steady-state margin, as otherwise even a slight increase in the angleδgs(such as at
pointcin Figure 13.3.6) would lead to instability. Installing parallel transmission lines [which
effectively reducesXin Equation (13.3.13)] or adding series capacitors in lines raises the stability
limit.

Applications for Synchronous Motors

With constant-speed operation, power factor control, and high operating efficiency, three-phase
synchronous motors are employed in a wide range of applications. An overexcited synchronous
motor, known as a synchronous condenser, is used to improve the system power factor. Syn-
chronous motors are used as prime movers of dc generators and variable-frequency ac generators.
Typical applications include pumps, compressors, mills, mixers, and crushers.
Single-phase reluctance motors find application in such devices as clocks, electric shavers,
electric clippers, vibrators, sandpapering machines, and engraving tools. A hysteresis motor is
employed for driving high-quality record players and tape recorders, electric clocks, and other
timing devices. The horsepower range is up to 1 hp for hysteresis motors, and up to 100 hp for
reluctance motors.

δgs

P

Generator

90 °

Motor

a

b

c

Pmax

Figure 13.3.6Power-angle curve of

Equation (13.3.13).