代写-NATIONS 2019/20
时间:2022-01-17
PAPER CODE ........ELEC209............ PAGE .. ..... 1.............. OF ....9..........................CONTINUED.
FIRST SEMESTER EXAMINATIONS 2019/20
ELECTRICAL CIRCUITS & POWER SYSTEMS
TIME ALLOWED: Three Hours
INSTRUCTIONS TO CANDIDATES
The numbers in the right hand margin represent an approximate guide to the marks available for that
question (or part of a question). Total marks available are 100.
Answer All Questions.
Additional Information:
Formula Table
PAPER CODE NO. EXAMINER: Dr. A. Al-Ataby
ELEC209 DEPARTMENT: EE&E TEL. NO.: 48045
PAPER CODE ........ELEC209........ PAGE
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1. a) i)
State why in a three-phase system, transformers in the distribution and
local substations must have a secondary winding connected as Y (start)
rather than Δ (delta).
2
ii)
State, with a proper justification, a possible and quick way to check if
there is a fault in a three-phase system that is arranged as four-wire Y.
2
b) i) A three-phase Y-connected load is supplied by a balanced three-phase
Y-connected source with a phase voltage of 120 V. If the line
impedance and load impedance per phase are 1 + j1 Ω and 20 + j10 Ω,
respectively, determine the line currents and load voltages.
6
ii) A balanced three-phase delta-connected load with per phase impedance
10 + j7.54 Ω is connected to a balanced three-phase Y voltage source
with phase voltage of 220 V. Determine the line currents and load
(phase) currents.
6
c) Two three-phase balanced loads are connected to a 240 kV line. Load 1 draws
30 kW at a power factor of 0.6 lagging, while load 2 draws 45 kVAR at a
power factor of 0.8 lagging.
i) Calculate the complex power consumed by each three-phase load.
4
ii) Calculate the total apparent power consumed by both three-phase loads.
2
iii) Calculate the line currents drawn by each load.
3
Total
25
PAPER CODE ........ELEC209........ PAGE
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................7..............CONTINUED
2. a) It is required to measure the mutual inductance M formed between two coils
practically. With the aid of suitable circuit diagrams and equations, design a
laboratory experiment to fulfil this requirement.
4
b) For the transformer circuit shown in Figure Q2 below:
i) Find the input impedance of the transformer Zi.
2
ii) Find the primary voltage Ep and the secondary voltage Es.
5
iii) Find the currents in each loop of the transformer circuit.
2
c) A magnetically coupled pair has a resulting fluxes Φell1 and Φ21 are 0.3 mWb and
0.8 mWb, respectively. If the number of turns for each coil is to be selected as
N1 = 500 and N2 = 1000, design the magnetically coupled circuit (i.e. determine
L1, L2, M and the coefficient of coupling k) if the driving current is required to be
3 A.
8
d) The primary coil of a transformer is connected to a 6 V battery. The turns ratio is
1:3 and the secondary load, RL, is 100 ohms. Find the voltage across the load.
2
e) A transformer with N1 = N2 has a specific application in electrical engineering.
Briefly explain why it is needed in electrical system.
2
Total
25
PAPER CODE ........ELEC209........ PAGE
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................7..............CONTINUED
3. a) For the circuit shown in Figure Q3a:
Figure Q3
i) Calculate vC, iC, and vR1 at 0.5 s after the switch makes contact
with position 1.
6
ii) The circuit sits in position 1 10 minutes before the switch is moved
to position 2. How long after making contact with position 2 will it
take for the current iC to drop to 8 μA? How long will it take for vC
to drop to 10 V?
6
b) A 50 Hz alternating (sinusoidal) voltage supply with 100 V peak voltage
and 50o phase shift is suddenly applied to a circuit which consists of a
resistance R in series with an inductance L = 1 mH.
i) Design the circuit such that the transient has no effect on the circuit. 5
ii) With proof, re-design the circuit such that the maximum current in
the circuit due to transient does not exceed 80 A.
8
Total
25
PAPER CODE ........ELEC209........ PAGE
...........5............... OF
................7..............CONTINUED
4. a) A 20 MVA transformer with 11 kV and 66 kV primary and secondary
voltages, respectively, has a reactance of 0.242 ohms referred to the primary.
What is the per-unit reactance on the primary side? What is the per-unit
reactance referred to the secondary?
4
b) Part of a power system is illustrated in Figure Q4. Two synchronous
generators are connected in parallel to the same 6.6 kV bus-bars (Gl: 5 MVA,
0.2 pu; G2: 15 MVA, 0.3 pu). The feeder has a reactance of 0.05 Ω/km and is
40 km long. Select 75 MVA as a common power base. Determine generators
and feeder per-unit reactances for the given common power base and draw the
equivalent circuit of the system.
Figure Q4
8
c)
A 600 MVA synchronous generator is star-connected, with 4 poles and a
synchronous reactance of 3 Ω. It is supplying 500 MW to an infinite bus at 22
kV, 50 Hz and 0.9 pf (lagging). Calculate the excitation voltage Vo and the
load angle δ.
5
d)
Classify overhead transmission lines according to their length and illustrate the
equivalent circuit for each class.
4
e) The turns ratio of a transformer is 20:1 and a peak primary current value of 10
A. Given that the coefficient of coupling k between the primary and secondary
coils is 0.6, calculate the secondary current and the referred load to the
primary side when the load connected to the secondary winding is + )110( j .
4
Total
25
G1
G2
Feeder
Load
PAPER CODE ........ELEC209........ PAGE
...........6............... OF
................7..............CONTINUED
2
pu1 B1 B2
2
pu 2 B2 B1
Z S V
Z S V
=
Formula Table
Φ = BA
v = L di/dt
λ = NΦ = Li
λ1=N1 Φ1 = N1 Φ11 + N1 Φ12
L1 i1= N1 Φ11
N1 Φ12 =M12 i2
N2 Φ21 =M21 i1
Voltage Ratio: V1/V2 = N1/N2
Current Ratio: I1/I2 = N2/N1
Impedance Ratio: Z1/Z2 = (N1/N2)
2
vC = Vf c+ (Vi - Vf) e
-t/τ , where τ = RC
iL = If + (Ii - If) e
-t/τ , where τ = L/R
f = n/60 × p/2
,
Volume =
( )sins mi I t = +
0 ( )1 4ln H/m.
4
d r
L
r
−
= +
END
1 1 1 2
2 2 2 1
V j L I j MI
V j L I j MI
=
=
21 12
11 22
k
= =
1 2
Mk
L L
=
( )
( )
R
t
L
s t mi i i I sin t Ae
−
= + = + − +
( )t t tti e Ae Be
− −= +0
2 2
0 = −
0 = ( )
t
ti e A Bt
−= +
2
2
where
1
m
m
v
I
R L
C
=
+ −
=
2
1
2221
1211
2
1
V
V
YY
YY
I
I
=
2
1
2221
1211
2
1
I
I
ZZ
ZZ
V
V
−
=
2
2
2221
1211
1
1
I
V
TT
TT
I
V
F/m
ln
2
C 0
−
=
r
rd
Tscsc2
Tsc2
)( VjXRI
VZIVg
++
=
+
=
T
sceff
sceff
V
XR
jXR
I
)(
222
+
+
=
vA
3
2
1
vP =
1
2 R
s
R
Reff −
=
2B
1B
2pu
1pu
S
S
Z
Z
=