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some Exam problems


Lisa Thomson

Jan 1, 1970
next week we have a exam in Power Systems. Our Professor gave us some
problems to practise but without solutions. If anybody wants to help
me here are the problems:

A shops receives power through a 2.5km long, 4160V transmission line.
Following is the list of machines with their ratings:
Power(kW) Power Factor
nr1 60 0.76(lagging)
nr2 50 0.75(lagging)
nr3 37.5 0.78(lagging)
nr4 60 0.8(lagging)

a) What is the overall power factor?
b) Design a delta connected capacitor bank across the 4160V terminals
to raise the power factor to 0.9(lagging).
Calculate the power rating, capacitance per phase and the rated
per-phase voltage of the capacitor bank.
c) Calculate the savings on energy and its cost over a period of 1
year if the per phase resistance of the 4160V transmission line is 1.5
Ohm/km and the shop is in operation everyday, 24h hours a day. The
cost of electrical energy is 7.8cents/kWh.

| |
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B3 B4
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T3 T4
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G3 G4

Generator G1=G2 30MVA 6.3kV Xd"=12%
Transformer T1=T2 35MVA 6.3kV/110kV Xt=7%
Generator G3 150MVA 12kV Xd"=15%
Generator G4 50MVA 13.8kV Xd"=10%
Transformer T3 150MVA 12kV/110kV Xt=8%
Transformer T4 50MVA 13.8kV/110kV Xt=7%

Transmission line 1 TL1 X=10 Ohm
Transmission line 2 TL2 X=18 Ohm
Transmission line 3 TL3 X=26 Ohm
The above system has been operation at no load when a 3 phase power
short circuit occurs on Bus B4. Calculate the short circuit current in
amperes on Bus B4. Choose Vb=110kV and Sb=100MVA as the base values in
the TL 2.


G1 12MVA, 6.3kV Y (neutral grounded) X"d=X2=14%; X0=5%
G2 50MVA, 12kV Y (neutral grounded) X"d=X2=16%; X0=6%
G3 45MVA, 13.8kV Y (neutral grounded) X"d=X2=15%; X0=4%
T1 15MVA, 6.3kV Y (neutral grounded)/138kV Y(neutral grounded)
T2 50MVA, 12kV Delta connected/138kV Y(neutral grounded) Xt=X2=X0=8%;
T3 50MVA, 13.8kV Delta connected/138kV Y(neutral grounded)
TL1 X1=X2=38 Ohm, X0=105 Ohm
TL2 X1=X2=26 Ohm, X0=58 Ohm

Consider 50MVA and 138kV as the bases in the transmission line

In a thounderstorm day the circuit breaker CB of the above system
opened and remained open after a 3 phase short circuit in the system.
Another lightning hits a phase conductor and caused a single phase to
ground fault at Bus B2.
Determine the fault current in amperes, and phase voltages in volts at
Bus B2. neglect the pre fault current in the system.