January Paper_Answers(1)

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load power for three-wire system using only two Wattmeters. Provide the required equations to support your answer. Solution: Figure should be provided.
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c)
Design the network of Figure 7 such that the system will turn on 10 s after the switch is closed.
e)
Draw the equivalent circuit of a power transformer. Sketch a phasor diagram for the power transformer on an inductive load and explain the physical meaning of each variable listed in the phasor diagram a) n 120 f rpm , we have, f
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3.
a)
The circuit shown in Figure 5 employs a multimeter with an internal resistance of 10 MΩ in the voltmeter mode. The switch is closed at t=0 s.
i) ii) iii)
Find the voltage across the coil the instant after the switch is closed. What is the final value of the current iL? How much time must pass before iL reaches 10 mA? What is the voltmeter reading at t=12 ms?
4.
a)
A 4-pole synchronous generator is driven by a prime mover at a speed of 1800 rpm. Calculate the frequency of the terminal voltage. What is spinning reserve? Explain briefly why it is needed The line voltage at the terminals of a 3-phase load is 33(1+j0) kV and the line current is 10-30o kA. Determine the complex power delivered to the load.
1 1.25 103 0.625 kW/m2 2
ii)
iii)
Find the total power delivered. Answer: PT =9000 W
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2.
a)
Given a three-phase unbalanced-Y load, show how to measure the total real
3
Figure 2 c i)
Explain in details, with the aid of circuit diagrams and equations, a method of how to measure the mutual inductance M practically in a laboratory environment. Solution: Using series adding circuit: . V VR +V1 V2
=IR (j L1I j MI ) ( j L2 I j MI )
RR
.
L L1 L2 2M
and series opposing circuits:
V 2 jMI j( L1 L2 ) I I ( R1 R2 ) R R1 R2 L L1 L2 2 M Hence:
January 2013 EXAMINATIONS Answers
1. a)
Find the total inductance of the series coils shown in Figure 1.
Figure 1 Answer: 6.4 H b)
For the residential supply shown in Figure 2 (assuming a totally resistive load) :
b) c)
d)
The wind turbines at North Hoyle, off the Welsh coast, are each rated at 2 MW maximum output. For a wind speed of 10 m s-1 the electrical output is 1.34 MW. Given that the area swept by the blades of the turbine is 5027 m 2 and the density of air is 1.25 kg m-3, determine the overall efficiency of the energy conversion process.
p
pn 4 1800 60 Hz. 120 120
b) Large generators cannot be started very quickly – they need a time measured in hours, not seconds, to start from cold, thus the generator companies MUST keep some machines operating at no load or part load – this is called “spinning reserve”. Once a machine is rotating and synchronised and the boilers up to temperature the load can be increased quickly to meet the demand of the consumers. This is because that the power supply and power demand in a power system need to be balanced. Otherwise, the frequency and/or voltage of the system will change. c) S 3VI * 3 33 1030 571.630 495 j 285.8 MVA. d) The wind power per m2 is: P
LA L1 L2 2M LB L1 L2 2M
M
ii)
LA LB 4
For the circuit shown in Figure 3, find the maximum power delivered to the speaker. Answer: I1= 0.83 A Power=2.78 W.
4 4 4 3 2
ii) iii)
iv) v)
Answers:
Figure 4 Total 20
i. Zero. Balanced load, Z1=Z2=Z3. ii. PL=1200 W. Total power=3600 W.
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i)
Design the system to ensure a balanced load (i.e. find the value of R). Answer: 1920 Ω Find the magnitude of the currents I1 and I2 and the line voltage VL. Answers: I1=5A I2 =8.33 A VL =4152 V
p u Ai A u B iB uC iC i Au AC iB u BC i A u A uC iB u B uC
iC i A iB
b)
For the Y-connected load of Figure 4:
i)
What is the net current and voltage at the neutral point n and why? Use a phasor diagram to support your answer. Find the average real power to each phase and the total real power each phase and the total reactive power. Find the apparent power to each phase and the total apparent power. Find the power factor of the load.