Problem 1. (a) With reference to the phasor diagram, state what is meant by the load angle of a synchronous motor.
(b) What is the value of this angle when the motor runs on no-load?
Problem 2. (a) Sketch the curve of the power factor characteristic of a synchronous motor as the excitation current changes.
(b) (i) With reference to the curve in part (a), when the excitation is increasing initially state whether the power factor is leading or lagging.
(ii) Explain, with the help of a phasor diagram for one phase, briefly what happens as the excitation increases further.
Problem 3. Explain briefly with the aid of phasor diagrams, how the synchronous machine stator current can be varied if the load is constant.
Problem 4. (a) State and explain briefly the main methods of excitation of a synchronous induction motor.
(b) Identify which method of excitation is most commonly used in modern machines.
Problem 5. A 30 kW star-connected synchronous motor is supplied from a 415 volt 50 Hz source. When fully loaded and running at unity power factor the input power is 35 kW. The excitation current under these conditions is 10 A.
What will be the value of input power if the load remains constant and the excitation
(i) is reduced to 5 A
(ii) is increased to 20 A?
Problem 6. (a) A three-phase delta-connected synchronous induction motor has a six pole stator winding and is connected to a 415 volt 50 Hz supply. The winding resistance is negligible and the synchronous reactance per phase is 3 ohms. The input power is 25 kW and the motor has a leading power factor of 0.8.
Calculate the stator reactive voltage drop IXs and hence with reference to a phasor diagram calculate the magnitude of the generated voltage E.
(b) Confirm the calculated value of E by constructing the phasor diagram to scale and measuring E.
Problem 7. A factory has an average demand of 520 000 units per week. The maximum demand is 25 MVA at 0.8 power factor and the minimum power factor of 0.6 occurs when the demand is 11 MVA.
The factory is charged at 2.5 pence per unit with a surcharge of 0.2 pence per unit for each 500 kW by which the maximum demand exceeds 18 MW and a further surcharge of 3% (of charge, plus surcharge) for every increment of 0.05 by which the minimum power factor falls below 0.8.
There is a large drive which operates continuously and is powered by an induction motor with draws 2 MW at a power factor of 0.8 lagging.
This motor is replaced by a synchronous motor which draws the same power but runs at a power factor of 0.8 leading.
Assuming the maximum demand penalty does not change
(i) Show that the maximum demand power is 20 MW.
(ii) Show that the total weekly charge for the factory is £19 219.20.
(iii) Calculate the new power factor and reactive penalty charge when demand is 11 MVA.
(iv) Show that the new total weekly cost is £17 644.50.
(v) If the synchronous motor costs £250 000, calculate the time required to recover the cost of the motor.
Problem 8. (i) A star-connected, three-phase synchronous induction motor takes a current of 10 amps from a 415 volt supply at unity power factor when supplying a steady load. If the synchronous reactance is 5 ohms/phase and the resistance is negligible, draw the phasor diagram and calculate the value of the generated emf and the load angle.
(ii) If the excitation is reduced by 10% and, as a consequence the generated e.m.f. is reduced by 10%, calculate the new value of the generated e.m.f E, the stator current, the power factor and the load angle, assuming that the load does not change.
(iii) Comment very briefly on the effect that reducing the excitation has on the power factor, stator current and the load angle.