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ECX 3232-FINAL-2004,2005

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The Open University of Sri Lanka
Diploma in Technology
ECX 3232-Electrical Power
Final Examination-2004
Duration Three Hours
Date: May 22nd 2005
Time: 0930-1130 hrs.
This paper contains Eight (8) questions. Answer any five (5). All questions carry equal
marks. Graph papers will be available on your request.
1. Show that the voltage drop V=(VS-VR) of a distribution line as shown below can be
estimated as:
VS
VR
R+jX
(Impedance)
P + jQ (Load)
(VS-VR) = V  PR+QX
VR
An industrial customer is located 6 km. far from the main source substation and a 11 kV, 1
overhead line connects it. The maximum load consumed by the customer is 1200 kW and
1000 kvar respectively. Resistance and reactance per kilometer of the overhead line are 0.6
/km. and 0.4 /km. What would be the voltage drop at full load of the customer? Find out
the reactive power of the capacitor bank (11 kV name plate rating), which is needed to
reduce the voltage drop to 5% of the nominal voltage.
2.
A 10 kVA single phase transformer, for 2000V/400V at no load, has resistances and leakage
reactances as follows:
Primary winding:
Resistance, 5.5;
Reactance, 12.
Secondary winding:
Resistance, 0.2;
Reactance, 0.45.
Determine:
 The approximate value of the secondary voltage at full load and 0.8 power factor
 The percentage voltage regulation
 Efficiency of the transformer at full load
3. Show that the most economical phase angle to which a given load should be improved is
given by Sin-1(B/A), where A is the annual cost per kVA of demand and B is the annual cost
per kvar of loss-free, power factor correction device. If B is 1/3 of A, find the required
capacitor kvar to correct a load of 400 kW at power factor 0.8 for annual minimum operating
cost.
4.
Why are single-phase motors not self started? What are the methods of starting single-phase
induction motor? Explain with diagram in details any one of them?
As measured at 50 Hz., the two windings of a single-phase motor show the following
impedances.
Page [1] of [3]
Starter Wdg. Capacitor
Main Wdg.
Supply
Voltage
Rotor
Zm = 3.1 + j 2.9 
Zs = 7.0 + j 3.1 
Main winding
Starter Winding
Find the capacitor size that will produce the phase angel shift =900.
5. What non-linear equipments installed in power system, generate harmonic frequencies?
Define the term Total harmonic Distortion (THD)?
A circuit consists of a resistance (R=10), an inductance (L=1.0 H) and a Capacitance
(C=500F). They are connected in series and connected to a system voltage of having 1st, 3rd
and 5th Harmonics. The voltage waveform is given as:
V(t)=90 sin t + 30 sin (3t-1000) + 20 sin (5t+450) Volts.
The frequency of the fundamental Harmonic is 50 Hz.
(i)
(ii)
(iii)
Calculate the current in each harmonic
Determine the Total harmonic distortion factor of current and Voltage
Sketch the time variation of the current
6. Variation of daily load pattern (including week-ends & holidays) of an industrial customer
“ABC” metered at 400V/230V (working on 3 shifts) is as given under. The industry operates
at 0.7 power factor.
Industry “ABC” Load
Shift-1
6.00 a.m.------7.00 a.m.
7.00 a.m.------1.00 p.m.
1.00 p.m.------2.00 p.m.
10 kW
45 kW
10 kW
Shift-2
2.00 p.m.------3.00 p.m.
3.00 p.m.------9.00 p.m.
9.00 p.m.-----10.00 p.m.
10 kW
45 kW
10 kW
Shift-3
10.00 p.m.----11.00 p.m.
11.00 p.m.----- 5.00 a.m.
5.00 a.m.----- 6.00 a.m.
10 kW
45 kW
10 kW
Page [2] of [3]
a) Draw the daily load pattern of customer “ABC”?
b) What would be the industry “ABC” annual energy consumption?
c) Calculate the annual cost and the average price per unit for “ABC”? (You may use the
following tariff chargeable for industrial customers)
d) What would be the annual energy savings, if customer improves his power factor to 0.9?
Tariff table for Q6, chargeable for industrial customers
Customer
Category
Maximum
demand
charge
(Rs./kVA)
per month
Conditions
Industrial
Time-of-day
option
Metered at 400V/230V,
contract demand less than
42 kVA
Metered at 400V/230V,
contract demand more
than 42 kVA
Metered
above
at
11kV
or
Energy Charge
(Rs./kwh)
Fixed Charge
(Rs./Month)
None
15.00 bet 7-10 p.m.
6.90 at other times
30.00 up to 10 kVA
230.00 above 10 kVA
380.00
14.70 bet 7-10 p.m.
6.50 at other times
800.00
360.00
14.00 bet 7-10 p.m.
6.10 at other times
800.00
7. (a) What are the different types of D. C. motors? Explain with diagrams.
(b) A 6-pole DC generator has 400 armature conductors and useful flux is 0.06 Wb. If this
generator is lap wound and running at 1000 r.p.m., what e.m.f. it will induce.? If this
generator is wave wound, at what speed it should run so that it may induce the same
voltage?
(c) Find the speed of a 4-pole 440 V wave wound D.C. shunt motor having flux per pole of 3
mega lines. The armature is having 39 slots with 12 conductors per slot. Armature
resistance is 0.25 Ohms. Current taken by the motor is 42 Amps. (Assume 1 Wb=108 flux
lines)
8. The power input to the rotor (i.e. air gap power) of a 440 V, 50 Hz, 6 pole 3 phase induction
motor is 80 kW. The rotor electromotive force (rotor E.M.F) is observed to make 120
complete alternates per minute. Calculate:
a)
b)
c)
d)
e)
The motor slip (s)
The rotor speed (Nr)
The Mechanical power (Pm) developed (assume stator core loss is negligible)
The rotor copper loss per phase
The rotor resistance per phase, if the rotor current is 65 A
Page [3] of [3]
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