Question

Note: For three-phase synchronous machine problems, the given voltages generally refer to the per-phase equivalent circuit. Hence, they are phase voltages of wye-connected synchronous machine. However, if a problem has explicitly stated that the voltage is line voltage, you need to convert it, at first, into the phase voltage (assuming wye-connection) before applying the voltage to the per-phase equivalent circuit.

A 2GW synchronous generator is connected to an infinite bus through a transmission line. The infinite bus voltage (per phase) is 240kV (reference voltage), the inductive reactance of the transmission line is 6Ω, the synchronous reactance of the generator is Xs = 9Ω. If the generator delivers its rated power at unity power factor to the infinite bus, compute the terminal voltage of the generator

Answer 1

To compute the terminal voltage of the generator, we need to consider the power factor and use the power equation, V = P/I. Substituting the given values, the terminal voltage is approximately 4.17 kV.

Step-by-step explanation:

To compute the terminal voltage of the generator, we need to consider the power factor of the generator. Since the generator delivers its rated power at unity power factor, the current flowing in the generator is equal to the current flowing in the transmission line. We can use the power equation, P = IV, where P is the power output of the generator, I is the current flowing in the generator, and V is the voltage. Rearranging the equation gives us V = P/I. Substituting the given values, we have V = (1000 MW)/(240 kV), which gives a terminal voltage of approximately 4.17 kV.