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?
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.
3. Explain briefly with the aid of phasor diagrams, how the synchronous machine stator current can be varied if the load is constant.
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.
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?
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.
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.
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
1. (a) What is a Vector grouping?
(b) How does the knowledge of vector grouping assist in connecting transformers to operate in parallel?
(c) What additional information is needed to ensure that transformers are capable of parallel operation?
(d) What are the only phase displacements in degrees with which it is possible to parallel the secondaries of two transformers?
(e) Draw the phase relationships and connections for
(i) Dd0 connection
(ii) Yy6 connection.
2. (a) Name the types of on-load tap changer.
(b) Which is the most commonly used and why?
3. (a) What is the advantage of monitoring winding temperature as a method of overload protection?
(b) Name two other types of overcurrent protection.
4. (a) What is a conservator?
(b) How does this device protect against pollution of the transformer oil?
5. List the symbols, and their meaning, used to classify the methods of cooling a transformer and state the types of cooling of an ONAF transformer.
6. Describe, with the aid of a diagram, the process involved in tap changing using a centre-tapped reactor.
7. (a) Describe, with the aid of a diagram, the method of operation of a Buchholz relay.
(b) State which faults can be detected by this relay and in what way they activate the relay.
(c) What is the major advantage of this relay over other forms of transformer protection?
8. An oil-filled transformer has a c.m.r. of 500 kVA which allows it to run continuously in an ambient of 35°C with an oil temperature rise of 50°C. The transformer has a time constant of 1.5. hours and the ratio of copper losses to iron losses at c.m.r. is 1.5:1. After switch-on, the transformer supplies a load of 600 kVA for one hour and the load then rises to 750 kVA. Calculate the period of time that the transformer can supply this load without exceeding its rated maximum temperature. Sketch the heating curves for the two loads.
These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.1.
A) With reference to the phasor diagram, state what is meant by the load angle of a synchronous motor.
The angle of load is between stator magnetic field rotor magnetic field. If the magnitude of load increases, load angle increases and the speed of rotor does not change. The phasor voltage and back EMF value per phase are same when the load angle increases and the distance of back EMF from its ideal position increases.
• When Ef is equal to Vt this shows the full excitation and the current Ia lag behind Vt with a load angle.
• When Ef < Vt as shown in b, is happened, the excitation is less than full excitation and power factor decreases
• When Ef > Vt as shown in a, the excitation is called over excitation. The motor needs leading current
(a) What is a Vector grouping? (b) How does the knowledge of vector grouping assist in connecting transformers to operate in parallel? (c) What additional information is needed to ensure that transformers are capable of parallel operation? (d) What are the only phase displacements in degrees with which it is possible to parallel the secondaries of two transformers? (e) Draw the phase relationships and connections for (i) Dd0 connection (ii) Yy6 connection.
A) Three-phase transformer windings can be connected to each other in various ways. Depending on the connection of the windings, the vector group of the transformer is determined. The transformer vector group is shown on the name plate of the transformer of the manufacturer. The vector group basically shows the phase difference between the primary and secondary sides inserted due to the special configuration of the transformer windings connection. The vector group table as shown below....
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