Question

A 45-MVA, 13.8 kV synchronous machine is operating as a synchronous
condenser, as discussed in Appendix D (section D.4.1). It’s short-circuit ratio
is 1.68 and the field current at rated voltage, no load is 490 A. Assume the
generator to be connected directly to an 13.8 kV source

a. What is the saturated synchronous reactance of the generator in per unit
and in ohms per phase?
The generator field current is adjusted to 260 A.
b. Draw a phasor diagram, indicating the terminal voltage, internal voltage,
and armature current.
c. Calculate the armature current magnitude (per unit and amperes) and its
relative phase angle with respect to the terminal voltage.
d. Under these conditions, does the synchronous condenser appear inductive
or capacitive to the 11.5 kV system?

Answer 1

Short circuit ratio is given as

Single phase rated voltage is given by

Single phase rated power is given by

Now, base value of impedance is

Now, base value of current is given by

a.

The saturated synchronous reactance in per units is given by

The saturated synchronous reactance in ohms per phase is given by

b.

where, is armature current

is internal voltage

is external votage

is synchronous saturated reactance

c.

Since generator field current is adjusted to 260 A, internal voltage in per unit will, therefore, be

Rated terminal voltage in per unit is

Now, armature current in per unit value is given by

and armature current in amperes is given by

d.

In this part 11.5 kV sytem is given whereas in rest of the question 13.8 kV system is provided. So, I think there must be some mistake.