Download Department of Electrical and Computer Engineering Power Systems Name:__________________________________

Department of Electrical and Computer Engineering
CANDIDACY EXAM: Power Systems
Time: 3 hours (9:00 AM – 12:00 noon)
Name:__________________________________
Student number:____________
Student’s signature:_________________________________
General Instructions:
1. This is a closed-book exam. One single-sided formula sheet is allowed.
2. There are a total of seven problems, Q1-Q7, in this exam. You are to choose only five
problems for marking. On the list below circle the problems you want marked and only
those will be marked. If none are circled the first five will be marked.
3. No large memory programmable calculators are permitted.
4. Cell phones and other wireless devices must be turned off.
5. You will be provided with scrap paper.
6. Make sure that your name, student number, and signature are written on this page.
Q1: ___________/20
Q2: ___________/20
Q3: ___________/20
Q4: ___________/20
Q5: ___________/20
Q6: ___________/20
Q7: ___________/20
TOTAL: ___________/ 100
Q1 [20 marks] T1
1
2
L12
G1
T2
G2
L23
3
Fig. 1
ThereactancedataforthepowersystemshowninFig.1isgiveninthefollowingtable.All
dataareinpuonacommonbase.
Item
X1
X2
X0
G1
0.15
0.15
0.05
G2
0.1
0.1
0.05
T1
0.25
0.25
0.25
T2
0.2
0.2
0.2
L12
0.3
0.3
0.75
L23
0.29
0.29
0.74
GroundingreactanceoftransformerT2 =0.05
GroundingreactanceofgeneratorG2 =0.1
a) A bolted (Zf = 0) line to ground (LG) fault occurs at bus‐3. Compute the fault current. [8
marks]
b) CalculatethePhase‐Avoltageatbus‐1afterthefault.[6marks]
c) What would happen to the magnitude of fault current, if the grounding reactance of
transformerT2iszero?Aqualitativeanswerissufficient.[3mark]
d) What would be the effect on fault current, if the grounding reactance of generator G2 is
zero?Aqualitativeanswerissufficient.[3mark]
Q2 [20 marks] a) Compare the Newton‐Raphson and the decoupled NR load flow solution methods
highlighting the advantages and disadvantages of each method. Give at least one example
wherede‐coupledloadflowsolutionisuseful.[4marks]
Asimple3buspowersystemisshowninFig.2.Alladmittancesaregiveninpuonacommon
base.Voltageatbus‐1iscontrolledat1.0puandthatofbus‐2iscontrolledat1.05pu.Inorder
to perform de‐coupled NR load flow, consider bus‐1 as the slack bus and start with initial
estimatesofV2=1.050oandV3=1.00o.
b) Determinethebusadmittancematrix.[3mark]
c) DeterminethevectorsofunknownsandthecorrespondingbussusceptancematricesB’and
B”requiredforperformingthefastdecoupledNRloadflowsolution.[4marks]
d) Calculatethemismatchvectors[P/|V|]and[Q/|V|]forthefirstiteration.[5marks]
e) Computethenewvalueof|V3|.[4marks]
|V2|=1.05 pu
V1=1.00opu
G1
1
y12 = -j40 pu
2
G2
PG2=4 pu
y23 = -j20 pu
y13 = -j10 pu
3
Sload = 5 +j4 pu
Fig. 2
Q3 [20 marks] A275kV,three‐phasetransmissionlineshowninFig3hasthefollowinglineparameters:
A=0.931.5oB=11577o
The source G2 supplies 100 MW of real power at unity power factor while maintaining the
receivingendvoltageat275kV.
VR
G1
G2
Line
[A B C D]
VS
Load
Fig 3 a) Determinethesending‐endvoltagerequirediftheloadbeingdeliveredatthereceivingend
is200MWat0.85laggingpf.[8marks]
b) Theloadofatthereceivingendischangedto300MVAat0.8laggingpfwhilethesending
end voltage being held at 290 kV. Determine the additional reactive power that has to be
suppliedbyG2inordertomaintainthereceivingendvoltageat275kV.[8marks]
c) Calculatethetransmissionefficiencyofthelineundertheconditionin(b).[4marks]
Q4 [20 marks] a) Explainwhatisthe“surgeimpedanceloading”ofatransmissionline.Whatisitsrelevance
to line compensation? Sketch the voltage profile along a lossless transmission line under
surgeimpedanceloading.[4marks]
b) A50MVA,24kV,60Hz,generatorhasthereactances:Xd= 1.0pu,Xd’=0.3pu,andXd”=
0.15pu.Thegeneratorisoperatingatnoloadandratedvoltagewhenathree‐phaseshort
circuitoccursattheterminals.Consideringthefaultcurrentjustaftertheshortcircuit,find
i) Initialsymmetricalrmscurrent[2marks]
ii) Maximumpossibledccomponent[2marks]
iii) Maximumpossibleasymmetricalrmscurrent[2marks]
Youmayusethefollowingequation:
t
 1  1
1   Td  1
1
e
i(t )  E m 
 

 


 X d  X d X d 
 X "d X ' d
t
t

  Td 
Em
Ta
e  cos(t   ) 
cos( )e 
X d


c) Explain why the make duty (closing duty) of a circuit breaker is different from its break
duty(openingduty).Whichdutyislarger?[3marks]
d) In the power system shown in Fig. 4, two 30 kV generators are connected to a 400 kV
transmissionlinethrougha30/400kVtransformer.Impedancesofthegeneratorsandthe
transformer are given in pu based on their own ratings. Find the fault level (short circuit
MVA)atbus‐3.[7marks]
60MVA,
30kV
Xd1’=24%
1
G1
40MVA G2
30kV
Xd2’=24%
2
1
100MVA
30/400kV
Xt=16%
Fig. 4 XL=160
3
Q5 [20 marks] Considerthefollowingdc‐acconverter.Thefrequencyofthecarrierwaveformissetto6kHz.
Thereferencewaveformhasafrequencyof60Hz.Thecut‐offfrequencyofthefilterissetto1
kHz.Drawandfullylabelthewaveformoftheload’sterminalvoltage(v0).
Q6 [20 marks] A three‐phase induction machine operates under constant terminal V/f. While the machine is
accelerating to its reference speed, the speed controller remains in saturation and hence the
machineoperateswithaconstantslipspeed.Showthatunderoperationwithaconstantslipspeed
thetorqueproducedbythemachineisproportionaltotheratio(E/f)2,whereEistheinternalemf
ofthemachineacrossitsmagnetizationbranch.
Q7 [20 marks] AsalientpolesynchronousgeneratorwithsaturatedsynchronousreactancesXd=1.72puandXq=
1.47 pu is connected to an infinite bus through an external impedance of X = 0.09 pu on the
generator base. The generator is operating at rated voltage and rated MVA at 0.95 power factor
laggingasmeasuredatthegeneratorterminals.
a)Drawaphasordiagram,indicatingtheinfinitebusvoltage,thearmaturecurrent,thegenerator
terminalvoltage,theexcitationvoltageandrotorangle(measuredwithrespecttotheinfinitebus);
b)Calculatetheputerminal,infinitebusandgeneratedvoltagesandtherotorangleindegreesas
measuredwithrespecttotheinfinitebus.