Exercice 01

A 6-pole three-phase synchronous machine operates as a synchronous motor. The stator resistance is neglected and the synchronous reactance is equal to 8 Ω. A voltage of 230V at a frequency of 50Hz is applied to the terminals of each stator winding. The motor provides 5kW useful power. All losses are neglected.

1. Give phasor diagram of the equivalent single-phase model

2. Calculate the rotor speed n_s

3. Calculate the useful torque T_U

4. In the case of an inductive 0.6 power factor

            4.1 Calculate the current absorbed by the motor

            4.2 Calculate the reactive power Q

            4.3 Represent the back e.m.f of the motor E₀ in the Fresnel diagram

            4.4 the motor is underexcited or overexcited ?

5. In the case of a capacitive 0.8 power factor

            5.1 Calculate the current absorbed by the motor

            5.2 Calculate the reactive power Q

            5.3 Represent the back e.m.f of the motor E₀ in the Fresnel diagram

            5.4 the motor is underexcited or overexcited ?

 

Exercise 02

A three-phase alternator, with a star-connected stator winding, provides a current of 200 A at a phase-to-phase voltage of 400 V at 50 Hz, with a power factor of 0.866 (inductive load).

1. Calculate the useful power of the alternator.

2. The resistance measured between phase and the neutral point of the stator (single phase resistance) is 30 mΩ. Calculate the stator copper losses.

3. The total collective and rotor copper losses are 6 kW. Calculate the efficiency of the alternator.