0195136047.pdf

13.3 SYNCHRONOUS MACHINES 585

Solution

Per-phase terminal voltageVt=

6. 6 × 1000

√

3

=3811 V

Full-load per-phase armature currentIa=

2. 5 × 106

√

3 × 6. 6 × 1000

= 218 .7A

(a) Referring to Figure 13.3.2(a) for an overexcited generator operating at 0.8 power factor

lagging, and applying Equation (13.3.2), we have

E ̄f= 3811 +j 218. 7 ( 0. 8 −j 0. 6 )( 10 )= 5414  tan−^10. 3415

% voltage regulation =

5414 − 3811

3811

× 100 = 0. 042 × 100 = 4 .2%

(b) Referring to Figure 13.3.2(b) for an underexcited generator operating at 0.8 power factor

leading, and applying Equation (13.3.2), we have

E ̄f= 3811 +j 218. 7 ( 0. 8 +j 0. 6 )( 10 )= 3050  tan−^10. 7

% voltage regulation=

3050 − 3811

3811

× 100 =− 0. 2 × 100 =−20%

As we have just seen, the voltage regulation for a synchronous generator can become

negative.

Power Angle and Other Performance Characteristics

The real and reactive power delivered by a synchronous generator, or received by a synchronous
motor, can be expressed in terms of the terminal voltageVt, the generated voltageEf, the
synchronous impedanceZs, and the power angle or torque angleδ. Referring to Figure 13.3.2,
it is convenient to adopt a convention that makes positive the real powerPand the reactive
powerQdelivered by an overexcited generator. Accordingly, the generator action corresponds
to positive values ofδ, whereas the motor action corresponds to negative values ofδ. With
the adopted notation it follows thatP>0 for generator operation, whereasP<0 for motor
operation. Further, positiveQmeans delivering inductive VARs for a generator action, or receiving
inductive VARs for a motor action; negativeQmeans delivering capacitive VARs for a generator
action, or receiving capacitive VARs for a motor action. It can be observed from Figure 13.3.2
that the power factor is lagging whenPandQhave the same sign, and leading whenPandQ
have opposite signs.
The complex power output of the generator in volt-amperes per phase is given by
S ̄=P+jQ=V ̄tI ̄a∗ (13.3.4)

whereV ̄tis the terminal voltage per phase,I ̄ais the armature current per phase, and*indicates a
complex conjugate. Referring to Figure 13.3.2(a), in which the effect of armature resistance has
been neglected, and taking the terminal voltage as reference, we have the terminal voltage,

V ̄t=Vt+j 0 (13.3.5)

the excitation voltage or generated voltage,

E ̄f=Ef(cosδ+jsinδ) (13.3.6)