Problem 1 -

This problem is about a hydroelectric power station in South East Asia operating at 50 Hz. The synchronous generator has the following technical specifications as prescribed by the manufacturer are: rated voltage: 16.5 kV, rated frequency: 50 HZ and rated speed: 500 RPM. The nominal power conditions are P = 50 MW and Q = 75 MVAR. You are appointed as an Electrical Engineer and responsible for the operation of the power station during your shift.

Task 1: Synchronizing with the grid - the rotary valve has been partly opened for water flow and the synchronous generator is brought up to the rated speed. The excitation is adjusted to 32 A such that the generator generates a line voltage of 16.5 KV. The generator's line voltage, frequency, phase sequence, and phase angle are in match with the grid and the synchronizing switch is closed to connect with the grid.

(a) What is the real and reactive power output of the generator? What is the power angle (8) under the mentioned operating conditions?

Task 2: Due to the increase in grid demand, the load dispatching center instructs you to increase real power generation by 25 MW at unity power factor. So the water inlet is increased by controlling the rotary valve to obtain 25 MW power output and simultaneously the field excitation is increased to 38.5 A such that unity power factor is achieved.

(b) What is the power angle (δ) under this condition?

Task 3:

In order to meet the peak hour demand, you are instructed to increase the real power generation to the nominal value of 50 MW.

(c) What is the power angle (δ) under the nominal load condition?

Problem 2 -

A 4160 V, 2500 hp, 2 pole, 3 phase, Y-connected, 3580 rpm, 60 Hz squirrel-cage induction motor is driving a boiler-feed pump. The motor parameters are:

X₁ = X₂ = 0.72 ohm/phase, X_φ = 3 ohm/phase, neglect all resistances.

Open-circuit transient time constant= 3.6 sec

Short-circuit time constant = 0.12 sec

The motor is operating fully loaded at rated voltage and draws 2160 kVA at 0.9 power factor from the mains.

(a) Compute the transient reactance and draw the constant voltage behind transient reactance model.

(b) Compute the current and E' (magnitude and phase angle).

(c) Determine the time required after interruption of the normal supply for the residual voltage to decay to 25 percent of the normal bus voltage. Note that when the normal source is tripped, flux linkages are "trapped" with the closed rotor circuits of the operating motors, producing a voltage at the terminals (often called the residual voltage) which may require an appropriate time to decay to zero. Determine the speed to which the motor decelerates in this interval (computed in part c). The inertia of the motor and the pump impeller is 76 kg.m² and the load torque varies as the square of the speed. (Neglect all losses are neglected. 1 hp=746 W.)