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THE MANCHESTER METROPOLITAN UNIVERSITY
FACULTY OF SCIENCE AND ENGINEERING
DEPARTMENT OF ENGINEERING AND TECHNOLOGY
SESSION 2004/
Examination for the BEng (HONS) ELECTRICAL AND ELECTRONIC ENGINEERING FULL TIME/PART TIME YEAR TWO
UNIT 64EE2106B : ELECTRICAL POWER ENGINEERING
Thursday 12 May 2005
9.30 am to 11.30 am
Instructions to Candidates
Answer FOUR questions (80 marks). All questions carry equal marks. The marks for each question are shown in parenthesis. Students may use their own calculators according to Faculty regulations.
S149 25/08/
- (a) The total power, P, in a three-phase electrical system is the sum of the phase powers. For a balanced three-phase system, connected in star or delta formation, the equation shown below applies. Where; VL is the line voltage, IL is the line current and cosφ is the power factor. Derive this equation using the power per phase as the starting point. P = 3 VLILcos φ [8] (b) A 6.6 kV/400 V transformer that is delta/star connected supplies a three-phase and neutral 400 V, 0.3 MW variable power factor load. Power supplied to the load is balanced.
(i) Calculate the magnitudes of the transformer currents for a balanced power factor of 0.85 lagging. [4] (ii) Calculate the magnitude of the neutral conductor current for unbalanced phase power factors of; phase 1, unity; phase 2, 0.85 lagging; phase 3, 0.6 lagging. [8]
- A three-phase electricity generating station consists of three generators and three transformers connected to a 6.6 kV bus bar. Each load, with its own 400 V bus-bar, is connected to a transformer by a cable. A layout of the system is shown below in figure Q2 together with the equipment ratings and impedances.
(a) Calculate the per unit impedances, to a base of 10 MVA, for all the system equipment. [6] (b) A three-phase symmetrical short circuit fault could occur anywhere in the system. Where the fault level would be at its greatest, state its location and calculate its MVA fault level. [6] (c) A three-phase symmetrical short circuit fault could occur on any one of the 400 V bus-bars. State which one of the bus-bars when faulty would create the greatest fault level and calculate the fault level in MVA. [8]
Cable 3 400 V 2 × 10 -3^ Ω
Transformer 3 5 MVA 0.05 p.u.
Generator 3 4 MVA 0.2 p.u.
Bus-bar Load 3
Cable 1 400 V 1 × 10 -3^ Ω
Transformer 1 10 MVA 0.05 p.u.
Bus-bar Load 1
Generator 1 8 MVA 0.2 p.u. 6.6 kV bus-bar
Cable 2 400 V 0.67 × 10 -3^ Ω
Transformer 2 15 MVA 0.05 p.u.
Generator 2 12 MVA 0.2 p.u.
Bus-bar Load 2
Figure Q
Continued
- A forward converter is shown in Figure Q5.
(a) Show that the mean output voltage is given by where D is the duty cycle ratio of the converter.
V out =DVin
[12]
(b) Assuming that the converter has the particulars shown below, determine the minimum operating frequency, f , of the converter.
Input voltage Vin=24 V Output voltage Vout=12 V Smoothing inductor value L=75 μH
Maximum ripple component of inductor current ∆ I = 2 A
[8]
R
Vin C
L
D
Vout
Figure Q
Continued
- (a) The armature of a four-pole dc machine is wound with 564 conductors and when driven at 800 rpm, the flux per pole is 20 mWb and the current in each conductor is 60 A. Calculate the emf and the electrical power generated in the armature if the armature conductors are wave-connected. [8] (b) The magnetic circuit shown in Figure Q6 is made from sheet steel laminations whose B-H curve is also included in Figure Q6. The cross−sectional area of the circuit is 8 cm^2. Calculate the current required to establish a flux of 0.8 mWb in the air−gap. You may make any reasonable assumptions. [12]
a=1 cm, b=6 cm, c=8 cm. μ o = 4 π x 10 −^7 Hm −^1
a
a
a
a
b
c
N=100 l (^) g =0.1 cm
I
Sheet Steel
0
1
0 500 1000 1500 2000 2500 3000 H (A/m)
B(T)
Figure Q
END
