Question 5.5: For the 45-kVA, three-phase, Y-connected synchronous machine......
For the 45-kVA, three-phase, Y-connected synchronous machine of Example 5.4, at rated armature current (118 A) the short-circuit load loss (total for three phases) is 1.80 kW at a temperature of 25°C. The dc resistance of the armature at this temperature is 0.0335 Ω/phase.
Compute the effective armature resistance in per unit and in ohms per phase at 25°C.
The short-circuit load loss is 1.80/45 = 0.040 per unit at I_a = 1.00 per unit. Therefore,
R_{a,\text{eff}} = \frac{0.040}{(1.00)^2} = 0.040 per unit
On a per-phase basis the short-circuit load loss is 1800/3 = 600 W/phase and consequently the effective resistance is
R_{a,\text{eff}}=\frac{600}{(118) ^2}= 0.043 Ω/\text{phase}
The ratio of ac-to-dc resistance is
\frac{R_{a,\text{eff}}}{R_{a,\text{dc}}}=\frac{0.043}{0.0335}=1.28
Because this is a small machine, its per-unit resistance is relatively high. The effective armature resistance of machines with ratings above a few hundred kilovoltamperes usually is less than 0.01 per unit.