Exercise 01

The characteristics of a three-phase alternator are as follows:

- Star-connected stator windings at the frequency of 50Hz .

- No-load characteristic: E = 175. I_e

- Resistance of one phase of the armature equal to 0.25 Ω.

- Synchronous reactance equal to 1.5 Ω.

1. Determine the synchronous impedance of the machine.

2. The alternator supplies a balanced three-phase inductive load with a power factor of 0.8. The RMS line voltage at the armature terminals is 2.6 kV. The RMS line current is 440 A.

2.1 What is the intensity of the excitation current?

2.2 Calculate the copper losses in the armature.

2.3 A no-load test gave the total no-load losses equal to 80 kW. What is the efficiency of the alternator?

Exercise 02

A three-phase alternator with star-connected stator windings. On a pure resistive load, it delivers a current of 20 A at a voltage of 230 V between two terminals of the armature. The resistance of the inductor is 50 Ω and that of the armature winding is 1 Ω. The excitation current is 2 A. The collective losses are equal to 400 W.

- Find :

1. The useful power P_U.

2. The absorbed power P_A.

3. The copper losses in the armature.

4. The efficiency of the alternator.

Exercise 03

A three-phase alternator delivers a current of 20 A with a phase-to-phase voltage (line voltage) of 230 V and a power factor of 0.85.

The inductor, supplied by a DC voltage of 200 V, has a resistance of 100 Ω. The alternator receives a mechanical power of 7.6 kW.

- Find:

1. The useful power P_U delivered by the alternator.

2. The absorbed power P_A.

3. The efficiency.