0195136047.pdf

13.3 SYNCHRONOUS MACHINES 587

Tmax=

Pmax

ωm

=

Pmax

2 πns/ 60

(13.3.12)

wherensis the synchronous speed in r/min.
In the steady-state theory of the synchronous machine, with known terminal bus voltageVt
and a given synchronous reactanceXs,the six operating variables areP, Q,δ,φ,Ia,andEf. The
synchronous machine is said to have two degrees of freedom, because the selection of any two,
such asφandIa,PandQ,orδandEf, determines the operating point and establishes the other
four quantities.
The principal steady-state operating characteristics are the interrelations among terminal
voltage, field current, armature current, real power, reactive power, torque angle, power factor,
and efficiency. These characteristics can be computed for application studies by means of phasor
diagrams, such as those shown in Figure 13.3.2, corresponding to various conditions of operation.
Theefficiencyof a synchronous generator at a specified power output and power factor is
determined by the ratio of the output to the input; the input power is given by adding the machine
losses to the power output. The efficiency is conventionally computed in accordance with a set
of rules agreed upon by ANSI. Six losses are included in the computation:

• Armature winding copper lossfor all phases, calculated after correcting the dc resistance
  of each phase for an appropriate allowable temperature rise, depending on the class of
  insulation used.


• Field copper loss,based on the field current and measured field-winding dc resistance,
  corrected for temperature in the same way armature resistance is corrected. Note that the
  losses in the field rheostats that are used to adjust the generated voltage are not charged to
  the synchronous machine.


• Core loss,which is read from the open-circuit core-loss curve at a voltage equal to the
  internal voltage behind the resistance of the machine.


• Friction and windage loss.


• Stray-load losses,which account for the fact that the effective ac resistance of the armature
  is greater than the dc resistance because of the skin effect, and for the losses caused by the
  armature leakage flux.


• Exciter loss,but only if the exciter is an integral component of the alternator, i.e., shares a
  common shaft or is permanently coupled. Losses from a nonintegral exciter are not charged
  to the alternator.

EXAMPLE 13.3.2

A 1000-hp, 2300-V, wye-connected, three-phase, 60-Hz, 20-pole synchronous motor, for which
cylindrical-rotor theory can be used and all losses can be neglected, has a synchronous reactance
of 5.00/phase.

(a) The motor is operated from an infinite bus supplying rated voltage and rated frequency,

and its field excitation is adjusted so that the power factor is unity when the shaft load

is such as to require an input of 750 kW. Compute the maximum torque that the motor

can deliver, given that the shaft load is increased slowly with the field excitation held

constant.