Final answer:
To calculate the percentage regulation for a three-phase star-connected alternator, you need to calculate the synchronous voltage first. Then, for a given load and power factor, you can calculate the armature current and the output voltage to determine the percentage regulation.
Step-by-step explanation:
To calculate the percentage regulation for a three-phase star-connected alternator, we need to calculate the synchronous voltage first. The synchronous voltage (E) can be calculated using the formula: E = V / root3, where V is the line voltage. In this case, V = 13.8 kV, so the synchronous voltage is 13.8 / root3 = 7.97 kV.
a) For a 45% load at 0.9 power factor lagging, the load power is given by P = (0.45 * 1750 kVA) = 787.5 kVA. The armature current (Ia) can be calculated using the formula: Ia = P / root3 * V, where V is the line voltage. The output voltage (Eo) can be calculated using the formula: Eo = E - Ia * R, where R is the armature resistance. The percentage regulation is then given by: (E - Eo) / E * 100%.
b) For a 65% load at 0.75 power factor leading, the load power is given by P = (0.65 * 1750 kVA) = 1137.5 kVA. The armature current (Ia) can be calculated in the same way as in part a. The output voltage (Eo) can be calculated using the formula: Eo = E + Ia * X, where X is the synchronous reactance. The percentage regulation is then given by: (E - Eo) / E * 100%.