Reference no: EM13749941

QUESTION 1.

A series resistive inductive load is energised from a 240V(RMS), 50Hz single phase AC supply, such that the load draws 1200W at a power factor of 0.8.

a) Calculate the reactive power and the current supplied to the load.

b) Sketch a phasor diagram for this load condition, showing all circuit voltages and currents.

c) Calculate the capacitance value (μf) required to be placed in shunt with the RL load so as to achieve unity power factor as seen by the supply.

QUESTION 2.

A 7.2kVA single phase 50Hz, 480Vrms : 240Vrms transformer can be modelled using the primary referred approximate equivalent circuit shown in Figure 1 below.

Req = 0.84Ω, Xeq = 1.6Ω, Xo = 360Ω, Ro = 800Ω.

Characterisation tests on the transformer have determined the circuit parameters for this transformer as:

a) Calculate the primary current and real power measurements that would result when an open circuit test is carried out on this transformer at rated primary voltage.

b) Calculate the primary voltage and real power measurements that would result when a short circuit test is carried out on this transformer at rated primary current.

c) Calculate the transformer secondary voltage for rated secondary current at a lagging power factor of 0.95, when the transformer is supplied at rated primary volts.

QUESTION 3.

A DC, separately excited motor is supplied from a 240-V source. When the motor is unloaded, it draws 1A of current from the source. When the motor is loaded, it draws 25A of current and it rotates at 1560 rpm. The field current supplied to the motor remains unchanged and the armature reaction can be neglected. The motor armature resistance is equal to 0.4 Ω. Calculate the following:

a) The armature voltage of the motor under the load.

b) The amount of mechanical power developed by the motor under the load.

c) The no-load speed of the motor.

d) The amount of rotational losses of the motor.

e) The motor efficiency under the specified load if the field circuit power loss is equal to 360 W.

QUESTION 4.

A 3-phase, 15-kV, 4-pole, cylindrical rotor synchronous generator is connected to a 50-Hz infinite bus. The synchronous reactance of the machine is Xs = 0.6 ohms per phase and the excitation voltage is set to E0 = 12 kV line-to-neutral.

a) Draw single-phase equivalent circuit representing the machine connected to infinite bus.

b) Consider the machine running as a synchronous condenser.

(i) What is the amount of active power generated by the machine?

(ii) Calculate the amount of current injected by the machine to the infinite bus.

(iii) Calculate the amount of reactive power generated by the machine.

Now, the excitation voltage has been reduced to 8.66 kV and the steam turbine supplies mechanical torque on the shaft such that the torque angle of the machine is equal to +30°.

c) Draw phasor diagram for this operating conditions showing clearly the bus voltage, the excitation voltage and the stator current.

d) Calculate the machine power factor.

QUESTION 5.

a) Draw the approximate equivalent circuit for a single phase power transformer. Identify all circuit elements and briefly explain their physical relevance.

b) Short Circuit and Open Circuit tests have been conducted on a single-phase 19.2 kVA 480V/120V 50 Hz transformer, and the following values have been calculated from the results of these tests for the primary referred approximate equivalent circuit for this transformer:

                                        R_eq = 0.4Ω   X_eq = 0.88Ω   R_o = 512Ω   X_o = 360

[i] Calculate the voltage, current and power readings that would be expected from the open-circuit test on this transformer if the primary side was energised at rated voltage.

[ii] Calculate the voltage, current and power readings that would be expected from the short-circuit test on this transformer if the primary side was energised at rated current.

c) The transformer of part (b) is supplied at rated primary voltage, and supplies a load current of 128A (measured on the secondary output side) with a lagging power factor of 0.866. Determine:

[i] the secondary output voltage.

[ii] The transformer efficiency.

d) The tertiary, delta-connected winding in a Yy-connected three-phase transformer has a dual role. Explain briefly the two reasons for its existence.

QUESTION 6.

A 4- pole DC motor is operated as a separately excited motor.

When the motor is externally driven at 1800 rpm with rated field current and zero armature current, the armature voltage is 250V DC.

When the motor is supplied from a 250VDC supply with the same field current, and is providing rated mechanical output torque to a load, the input current is 50A, and the motor speed has dropped to 1701 rpm.

(a) Calculate the armature resistance for the motor.

(b) If the motor rotational losses are 2 kW at these operating conditions, calculate the efficiency of the motor in this load situation.

(c) Calculate the actual mechanical output torque of the motor under these load conditions.

(d) If the motor is required to rotate at 900 rpm, with a reduced armature current of 20 A, calculate the armature voltage needed to achieve this operating condition. Assume the field current is unchanged.

(e) Discuss the two possible ways of achieving variable speed operation for a DC machine. Show the torque speed characteristics of a DC motor operating under both these types of speed control strategies, and discuss how they relate to the concepts of the "constant torque" and "constant power" regions of variable speed operation. Discuss the advantages and disadvantages of each speed control strategy.

QUESTION 7.

Characterisation tests have been performed on a four pole, 415 V (line to line), three phase, star connected, 50Hz induction motor, with the following results:

- No-load test : 415Vl-l, 3.76A, 234.3 W/phase. (obtained at synchronous speed with a drive motor supplying the rotational losses of the drive system)
- Locked rotor test : 163.8 Vl-l, 30A, 603 W/phase.

a) Draw the per phase approximate equivalent circuit model of the induction motor, with all elements "stator-referred". Identify the physical significance of each element in the model.

b) Using the characterisation data, calculate the "stator-referred" induction motor parameters. Assume that the shunt elements are much larger than the series terms. Remember that the measured input voltages are "line-to-line", not phase voltages.

c) A load test is performed on the induction motor, which is fed from a 415Vl-l 50Hz supply, and the rotor speed is measured to be 1410rpm. Calculate the output mechanical power and mechanical torque for this test if the rotational losses constitute 880W for this condition. [Hint : Assume that the stator and rotor winding resistances are split equally].

d) Calculate the induction motor efficiency for the load test described in (c).

e) It is required to run the induction motor at a no-load zero slip speed of 900 rpm. Neglecting rotational losses, what must the supply voltage and frequency be in order to achieve this speed?

QUESTION 8.

A three phase squirrel cage induction motor has the nameplate data shown in Table I below

No. of Poles	4	Stator Configuration	Wye (Star)
Rated Stator Voltage	415 V (line - line)	Rated Frequency	50 Hz
Rated Stator Current	32.5 A	Rated Power	23.4 kW
Rated Speed	1420 rpm	Rated Torque	160 \m

Table I : Induction Motor Nameplate Data.

Characterisation tests have been performed on this motor, with the following results:

- Locked rotor test : ω_r = 0 rpm, 100.9 Vl-l, 32.5A, 739.4 W/phase.
- No-load test : ω_r = 1496 rpm, 415Vl-l, 3.74A, 552.3 W/phase.
- Zero Slip test: ω_r = 1500 rpm, 415Vl-l, 2.98A, 138.5 W/phase.

a) Using the characterisation data above, calculate the "stator-referred" induction motor parameters, and the total power losses in the mechanical drive train when operating near synchronous speed.

b) A load test is performed such that the induction motor speed droops to 1440 rpm, when supplied with 3-phase 415 Vl-l at 50Hz. Calculate the output mechanical power and the associated mechanical torque for this load condition.

c) Calculate the induction motor efficiency for the load test described in (b).

d) It is required to supply the same torque at a speed of 1200rpm. Approximately, determine the supply voltage and frequency required to achieve this speed and torque condition.

e) Sketch the approximate torque speed curves for the conditions defined in (b) and (d). Explain why the supply frequency must change from 50Hz in order to achieve the loading condition in (d).

QUESTION 9.

(a) What are the four operating conditions that must be satisfied before a synchronous machine can be synchronised to an electrical grid?

(b) A three phase Y-connected cylindrical rotor synchronous generator is operating into a grid at its rated l-l voltage of 6000V, with a rated stator current of 200A at a 0.8 lagging power factor. If the generator has a synchronous reactance of Xs = 10 Ω/phase and negligible stator winding resistance, find:

i. The real and reactive power flow into the grid.

ii. The internal back-emf Eo.

iii. The machine torque angle δ (in electrical degrees).

(c) Calculate the new torque angle, stator current and machine power factor if the field excitation is changed to reduce the generator internal back-emf to 1.2 pu. Is the generator supplying or sinking reactive power? Sketch a phasor diagram for this operating condition.

(d) Sketch the capability diagram for this synchronous machine for 1 pu and 1.5 pu excitation levels, and show how the practical operating region can be identified on this diagram by considering various machine operating limits.

QUESTION 10.

A 4- pole DC motor is known to have an armature resistance of 0.5 Ω, and is operated as a separately excited motor.

(a) When the motor is connected to a 250V DC supply with no external mechanical load and with rated field current, it runs at a speed of 1488 rpm with an armature current of 4A. Calculate the no load rotational losses under these conditions.

(b) The motor is now mechanically loaded until the armature current reaches 40A, under which conditions the DC supply voltage sags to 245V. Calculate the motor speed if the field current is unchanged.

(c) Assuming that the motor rotational losses vary proportionally with speed, calculate the motor efficiency under the load condition of (b).

(d) The motor field current is now accidentally set to half rated value. Calculate the DC supply voltage that is required to return to the same no load operating conditions of part (a) (HINT: remember that the rotational power losses must stay the same if the speed is unchanged).

(e) Discuss the two possible ways of achieving variable speed operation for a DC machine. Show the torque speed characteristics of a DC motor operating under both these types of speed control strategies, and discuss how they relate to the concepts of the "constant torque" and "constant power" regions of variable speed operation. Discuss the advantages and disadvantages of each speed control strategy.

QUESTION 11.

(a) An electric heating element is rated at 4.0kW when connected to a single phase 240Vrms, 50 Hz AC supply, and is known to have a power factor of 0.833 lagging.

[iii] Calculate the current supplied to the heating element when connected to the 240Vrms AC source. Hence or otherwise determine the resistance and inductance of the heating element.

[iv] Sketch a phasor diagram for this operating condition, showing the applied voltage, load current and the voltages across the equivalent load resistance and reactance.

[v] Determine the value of a shunt connected capacitance (μf) required to achieve unity power factor as seen by the supply. Determine the supply current and the real power absorbed by the heating element/capacitor combination for this operating configuration.

(b) A balanced three phase delta-connected load with an element impedance of 28.28 + j28.28Ω is connected to a 400V (line to line) 50Hz AC supply. Calculate:

i. The current that flows in each of the delta load elements.

ii. The supply line current that feeds the delta load.

iii. The total real and reactive power absorbed by the load, and its corresponding power factor.

iv. The load elements are accidentally connected in star rather than delta. Calculate the total real and reactive power absorbed by the load for this configuration and its resultant power factor.

QUESTION 12.

(a) A single phase series resistive-inductive heating element draws a measured current of 15A when connected to a 225V single phase 50 Hz AC supply.

Tests have shown that a minimum supply current of 13A can be achieved when a 106.2μF capacitor is connected in parallel across this heating element.

Calculate:

(i) the real power consumed by the heating element
(ii) the power factor of the heating element
(iii) the resistance of the heating element
(iv) the inductance of the heating element

(b) A balanced star-connected load is connected across a three phase 450V 50 Hz AC supply. Each load element has an impedance of 5+j12Ω.

Calculate:

(i) the power factor of the load

(ii) the supply line current

(iii) the reactive power consumed by the load

(iv) The delta-connected capacitor values required to restore the system power factor to unity

QUESTION 13.

A DC shunt motor rotating at 1560 RPM is supplied from a 240-V source. The line current supplied to the motor is equal to 27 A. The shunt field resistance of the motor is equal to 120 Ω and the armature resistance is equal to 0.6 Ω. Calculate the following:

(a) The armature current of the machine.

(b) The back-emf.

(c) The output mechanical power and the net torque developed by the motor if its mechanical losses are equal to 280 W.

QUESTION 14.

A 415 V, 5 kW, 50 Hz, 4-pole, 3-phase wound-rotor induction motor has the following characteristics:

- stator winding resistance R1 = 2.1 Ω,
- referred rotor winding resistance R'2 = 1.8 Ω,
- stator leakage reactance X₁ = 2.25 Ω.
- referred rotor leakage reactance X'₂ = 2.25 Ω.

The magnetising current, core losses and rotating losses can be neglected for this question.

The motor is started direct on-line from a 415 V 50 Hz three phase supply.

(a) Calculate the starting current.

(b) Calculate the starting torque.

(c) Discuss how the starting current could be limited for this wound-rotor motor.

(d) If the motor is running at a speed of 1450 rpm, calculate the mechanical output power.

QUESTION 15.

A 3-phase, 15 kV, 4-pole, cylindrical rotor synchronous generator is connected to infinite bus running at 50 Hz. The synchronous reactance of the machine is X_s = 0.6 Ω per phase and the excitation voltage is set to E₀ = 12 kV line-to-neutral. The mechanical torque applied to the generator is equal to 1591 kNm.

Considering these operating conditions:

(a) calculate the power generated under these conditions

(b) calculate the power angle at which the generator is operating

(c) sketch a phasor diagram showing the excitation voltage, the bus voltage and the stator current of the generator

(d) determine from the phasor diagram whether the power factor is leading or lagging under these conditions

(e) calculate the amount of active and reactive power exchanged between the generator and the infinite bus