Mathcad - L27 examples - uidaho.edu · 2020. 1. 15. · ECE 524: Transients in Power Systems...
Transcript of Mathcad - L27 examples - uidaho.edu · 2020. 1. 15. · ECE 524: Transients in Power Systems...
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ECE 524: Transients in Power Systems
Session 27; Page 1/28 Spring 2018
Three Phase Travelling Wave Examples
132kV LL
VS VSEND
I
100km line
VRECVVV
R0 0.32ohmkm
R1 0.025ohmkm
L0 3.2mHkm
L1 0.91mHkm
C0 0.008μFkm C1 0.0125
μFkm
Zc0L0C0
Zc0 632.46 Ω Zc1L1C1
Zc1 269.81 Ω
Applied voltage: Vm 107.8kV
Balanced three phase set with close at peak of phase: Vabc0
Vm
Vm
2
Vm
2
Vabc0
107.8
53.9
53.9
kV
Clarke Transform:
Ti1
3
1
1
1
2
1
2
1
2
0
32
32
Te Ti Te TiT
1
0
0
0
1
0
0
0
1
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ECE 524: Transients in Power Systems
Session 27; Page 2/28 Spring 2018
Vmodal0 Te1 Vabc0 Vmodal0
0
132.03
0
kV
Close into open circuit, we expect receiving end voltage to double for each mode, and the convert back to ABC
Voltages when close all three poles
(file lect27.pl4; x-var t) v:VSENDA v:VSENDB v:VSENDC v:VRECA v:VRECB v:VRECC 0.094 0.096 0.098 0.100 0.102 0.104[s]
-200
-100
0
100
200
300
[kV] Note that each individual phase doublesthe initial applied voltageSuggests only one mode excited, asimplied above
Initial modal currentVmodal01
Zc1489.33A Ti
0
Vmodal01Zc1
0
399.53
199.77
199.77
A
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ECE 524: Transients in Power Systems
Session 27; Page 3/28 Spring 2018
(file lect27.pl4; x-var t) c:VSA -VSENDA c:VSB -VSENDB c:VSC -VSENDC 0.096 0.098 0.100 0.102 0.104 0.106 0.108[s]
-500
-350
-200
-50
100
250
400
[A]
Consistent with the resultsabove for the initial transient
Single phase close to open circuited line:
Voltage
Vmodal_single0 Te1
107.8kV
0kV
0kV
Vmodal_single0
62.24
88.02
0
kV Note the cross-coupling, the first term is a ground mode term.
Receiving end: Vrecmodal 2 Vmodal_single0
Vabc_rec Te Vrecmodal Vabc_rec
215.6
0
0
kV
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ECE 524: Transients in Power Systems
Session 27; Page 4/28 Spring 2018
Sending end voltages
( fi le le c t2 7 .p l4 ; x-va r t) v :V S E N D A v :V S E N D B v :V S E N D C 0 .0 9 7 0 .0 9 8 0 .0 9 9 0 .1 0 0 0 .1 0 1 0 .1 0 2 0 .1 0 3 0 .1 0 4 0 .1 0 5[s ]
- 4 0
- 2 0
0
2 0
4 0
6 0
8 0
1 0 0
1 2 0[k V ]
Phases B and C show a zero mode response(same voltage on each).
(fi le le c t27 .p l4 ; x-va r t) v:V RE C A v:V RE C B v:V RE C C 0.095 0.097 0.099 0.101 0.103 0.105 0.107[s]
-100
-50
0
50
100
150
200
250
[kV ]Receiving endvoltages: Note effect of two different
propagation times for ground andline mode
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ECE 524: Transients in Power Systems
Session 27; Page 5/28 Spring 2018
Current
(f ile lec t25.pl4; x -v ar t ) c :VSA -VSEN D A c :VSB -VSEN D B c :VSC -VSEN D C 0.096 0.098 0.100 0.102 0.104 0.106 0.108[s ]
-400
-300
-200
-100
0
100
200
300
[A ]
Close 1 phase, with load 3 phase short.....
(f ile lec t25 .p l4 ; x -v a r t ) c :V S A -V S E N D A c :V S B -V S E N D B c :V S C -V S E N D C 0 .000 0 .026 0 .052 0 .078 0 .104 0 .130[s ]
-2000
-1500
-1000
-500
0
500
1000
1500
2000[A ]
Sending end currents:
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ECE 524: Transients in Power Systems
Session 27; Page 6/28 Spring 2018
(f ile lect25.pl4; x-v ar t) c:VRECA - c:VRECB - c:VRECC - 0.095 0.100 0.105 0.110 0.115 0.120 0.125 0.130[s]
-2000
-1500
-1000
-500
0
500
1000
1500
2000[A]
Receiving end currents
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ECE 524: Transients in Power Systems
Session 27; Page 7/28 Spring 2018
EMTDC ImplementationBreaker set for single pole operation (eachphase can operate independently)
Now need three trip inputs, see in circuit diagram below
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ECE 524: Transients in Power Systems
Session 27; Page 8/28 Spring 2018
R=0
T im e dB re a k e r
L o g icO p e n @ t0B R K A
TL in eT
TER
M
T im e dB re a k e r
L o g icO p e n @ t0T E R M
VS E N D VR E C
VS E N D
VR E C
IB R E AK A
IB R E AK B
IB R E AK C
Ire c A
Ire c B
Ire c C
T im e dB re a k e r
L o g icO p e n @ t0B R K B
T im e dB re a k e r
L o g icO p e n @ t0B R K C Need a seperate control for each
phase of the breaker now
Main : Graphs
0.100
-250 -200 -150 -100 -50
0 50
100 150 200 250
y (k
V)
VSEND VREC
Voltages for 3 pole close, withterminal open
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ECE 524: Transients in Power Systems
Session 27; Page 9/28 Spring 2018
Main : Graphs
0.100
-0.50
0.00
0.50
y (k
A)
IBREAKA IBREAKB IBREAKCCurrents for 3 pole close to opencircuited line
Main : Graphs
0.100
-250 -200 -150 -100
-50 0
50 100 150 200 250
y (k
V)
VSEND VRECSingle phase close:
Voltage (open circuited line)
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ECE 524: Transients in Power Systems
Session 27; Page 10/28 Spring 2018
Main : Graphs
0.100
-0.50
0.00
0.50
y (k
A)
IBREAKA IBREAKB IBREAKC
Current (open circuited line)
Main : Graphs
0.100
-250 -200 -150 -100
-50 0
50 100 150 200 250
y (k
V)
VSEND VRECClose 1 phase, with load 3 phaseshort.....
Sending end voltage (note reflections onsending end)
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ECE 524: Transients in Power Systems
Session 27; Page 11/28 Spring 2018
Main : Graphs
0.100 0.150
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
y (k
A)
IBREAKA IBREAKB IBREAKC
Sending end currents:
Main : Graphs
0.100 0.150
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
y (k
A)
IrecA IrecB IrecC
Receiving end currents
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ECE 524: Transients in Power Systems
Session 27; Page 12/28 Spring 2018
Trapped Charge and Inrush Current
When clearing a line, breakers open at natural current zeroIf line is unloaded this is a capacitive current, so clear at voltage peakPotential for inrush currentsNote that emt-programs exaggerate this effect since don't allow for self-dischargeMismatch in voltage between source side of breaker and line side of breaker determines:
Inrush current1.Magnitude of worst case overvoltage at receiving end of line if that is open2.
Won't see same on all three phase with 3 pole closing
1 Zc Zc
132kV LL
VS
I
SWITI
10 uOhm
V1
100km line
V2VV
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ECE 524: Transients in Power Systems
Session 27; Page 13/28 Spring 2018
( f i l e R E C L O S E . p l 4 ; x - v a r t ) v : V 1 A v : V 1 B v : V 1 C 0 . 0 0 0 0 . 0 2 6 0 . 0 5 2 0 . 0 7 8 0 . 1 0 4 0 . 1 3 0[ s ]
- 1 2 0
- 8 0
- 4 0
0
4 0
8 0
1 2 0
[ k V ]
Voltages at sending end of the linewhen energize open circuited line:
Energize lineThen clear it Then reclose
The transient voltages in the trappedcharge are largely due to residualeffects of the initial closing transient.
( f i le R E C L O S E .p l4 ; x - v a r t ) v :V 2 A v :V 2 B v :V 2 C 0 . 0 0 0 0 . 0 2 6 0 . 0 5 2 0 . 0 7 8 0 . 1 0 4 0 . 1 3 0[ s ]
- 3 0 0
- 2 0 0
- 1 0 0
0
1 0 0
2 0 0
3 0 0
[ k V ]And a receiving end
Note the larger transientsfor the reclose
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ECE 524: Transients in Power Systems
Session 27; Page 14/28 Spring 2018
Sending end currents (combine the two switches)
( f i le R E C L O S E . p l4 ; x - v a r t ) c : V S A - V 1 A c : V S B - V 1 B c : V S C - V 1 C c : V S A - S W IT A c : V S B - S W IT B c : V S C - S W IT C
0 . 0 0 0 0 . 0 2 6 0 . 0 5 2 0 . 0 7 8 0 . 1 0 4 0 . 1 3 0[ s ]- 6 0 0
- 4 0 0
- 2 0 0
0
2 0 0
4 0 0
6 0 0
[ A ]Bigger current on reclose due to largervoltage across the charactersitic impedance
Repeat with the system in steady-state before open the breakers.
( f i l e R E C L O S E . p l 4 ; x - v a r t ) v : V 1 A v : V 1 B v : V 1 C 0 . 0 0 0 0 . 0 2 6 0 . 0 5 2 0 . 0 7 8 0 . 1 0 4 0 . 1 3 0[ s ]
- 1 2 0
- 6 8
- 1 6
3 6
8 8
1 4 0
[ k V ]
Sending end voltages:note that trappedcharge changedsince voltage atpoint on wave forbreaker clearinghas changed
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ECE 524: Transients in Power Systems
Session 27; Page 15/28 Spring 2018
( f i l e R E C L O S E . p l4 ; x - v a r t ) v : V 2 A v : V 2 B v : V 2 C 0 . 0 0 0 0 . 0 2 6 0 . 0 5 2 0 . 0 7 8 0 . 1 0 4 0 . 1 3 0[ s ]
- 3 0 0
- 2 0 0
- 1 0 0
0
1 0 0
2 0 0
3 0 0
[ k V ]
Receiving end voltages
R=0
T im e dB re a k e r
L o g icO p e n @ t0B R K 1
B R K 1
R E S IS T
T im e dB re a k e r
L o g icO p e n @ t0R E S IS T
1 E -5 [o h m ]
1 E -5 [o h m ]
1 E -5 [o h m ]TL in e
T
TER
M
T im e dB re a k e r
L o g icO p e n @ t0T E R M
VS E N D VR E C
VS E N D
VR E C
IB R E AK A IR A
IB R E AK B
IB R E AK C
IR B
IR C
EMTDC implementation:
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ECE 524: Transients in Power Systems
Session 27; Page 16/28 Spring 2018
Ma in : G ra p h s
0 .0 0 0 0 .0 5 0 0 .1 0 0 0 .1 5 0 0 .2 0 0 0 .2 5 0 0 .3 0 0
-1 2 5 -1 0 0
-7 5 -5 0 -2 5
0 2 5 5 0 7 5
1 0 0 1 2 5
y (k
V)
V S ENDSending end voltageswith two transients
Some differencefrom ATP
Main : Graphs
0 .000 0 .050 0 .100 0 .150 0 .200 0 .250 0 .300
-300
-200
-100
0
100
200
300
y (k
V)
V RECReceiving end voltages
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ECE 524: Transients in Power Systems
Session 27; Page 17/28 Spring 2018
Ma in : G raphs
0 .100 0 .120 0 .140 0 .160 0 .180 0 .200 0 .220 0 .240 0 .260
-0 .80
-0 .60
-0 .40
-0 .20
0 .00
0 .20
0 .40
0 .60
0 .80
y (k
A)
IB REA K A IB REA K B IB REA K C IRA IRB IRC
Sending end currents
Main : Graphs
0.000 0.050 0.100 0.150 0.200 0.250 0.300
-125 -100
-75 -50 -25
0 25 50 75
100 125
y (k
V)
VSENDRepeat without firstenergization transient
Sending end voltage
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ECE 524: Transients in Power Systems
Session 27; Page 18/28 Spring 2018
Main : Graphs
0.000 0.050 0.100 0.150 0.200 0.250 0.300
-250 -200 -150 -100
-50 0
50 100 150 200 250
y (k
V)
VRECReceiving end voltages
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ECE 524: Transients in Power Systems
Session 27; Page 19/28 Spring 2018
Options to Reduce Inrush
Controlled breaker pole closingPre-insertion resistor, bypass after a few travel timesSecondary transient (small) when bypassSingle phase case: size R = ZcNo reflection for return waves
Voltage divider - apply 50% of voltage to the1.input of the lineReduces voltage and current2.
Resistor sized for current loading and dissipationHow about three phase line:
Ideally size for the first line mode,1.Some mismatch if do single pole reclosing2.Many utilities just use one standard size3.resistor, rather than optimize for each line. Not ideal, but eliminates most of the transient4.
2 Zc
1 R
Zc
132kV LL
VS
I
SWITI
632 Ohm
V1
100km line
V2VVV
132kV LL
VSALT
I
SWITAI
269.8 Ohm
V1A
100km line
V2AVVV
Rpre = Zc1
Rpre = Zc0
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ECE 524: Transients in Power Systems
Session 27; Page 20/28 Spring 2018
132kV LL
VS
I
SWITI
632 Ohm
V1
100km line
V2VVV
132kV LL
VSALT
I
SWITAI
269.8 Ohm
V1A
100km line
V2AVVV
Rpre = Zc1
Rpre = Zc0
( f i le P R E IN S . p l4 ; x - v a r t ) v : V 1 A A v : V 2 A A v : V S A 0 . 0 9 8 0 . 0 9 9 0 . 1 0 0 0 . 1 0 1 0 . 1 0 2 0 . 1 0 3 0 . 1 0 4[ s ]
- 2 0
0
2 0
4 0
6 0
8 0
1 0 0
1 2 0
[ k V ]
Initial close with R = Zc1
No overvoltageatthe receiving endSending end voltage increases whenafter 2 travel times
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ECE 524: Transients in Power Systems
Session 27; Page 21/28 Spring 2018
( f i le P R E IN S . p l4 ; x - v a r t ) c : V S A L T A - S W IT A A c : V S A L T B - S W IT A B c : V S A L T C - S W IT A C 0 . 0 9 6 0 . 0 9 8 0 . 1 0 0 0 . 1 0 2 0 . 1 0 4 0 . 1 0 6 0 . 1 0 8 0 . 1 1 0 0 . 1 1 2[ s ]
- 1 5 0
- 1 0 0
- 5 0
0
5 0
1 0 0
1 5 0
2 0 0
[ A ]
Sending end current
No longer have repeatedreflections, transient lasts2 travel times.
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ECE 524: Transients in Power Systems
Session 27; Page 22/28 Spring 2018
( f i le P R E IN S .p l4 ; x - v a r t ) v :V 1 A A v :V 2 A A v :V S A 0 . 1 0 0 0 . 1 0 4 0 . 1 0 8 0 . 1 1 2 0 . 1 1 6 0 . 1 2 0[ s ]
- 1 2 0
- 8 0
- 4 0
0
4 0
8 0
1 2 0
[ k V ]
Bypass the resistor after 1 cycle:
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ECE 524: Transients in Power Systems
Session 27; Page 23/28 Spring 2018
( f i le P R E IN S .p l4 ; x - v a r t ) v :V 1 A v :V 2 A v :V S A 0 . 0 9 5 0 . 0 9 9 0 . 1 0 3 0 . 1 0 7 0 . 1 1 1 0 . 1 1 5[ s ]
- 1 2 0
- 8 0
- 4 0
0
4 0
8 0
1 2 0
[ k V ]
Repeat with R = Zc0
Actually reducevoltages further
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ECE 524: Transients in Power Systems
Session 27; Page 24/28 Spring 2018
( fi le P R E IN S .p l4 ; x -va r t) v :V 2 A v :V 2 B v :V 2 C 0 . 0 0 0 0 .0 2 6 0 . 0 5 2 0 .0 7 8 0 .1 0 4 0 . 1 3 0[s ]
- 2 5 0 .0
- 1 8 7 .5
- 1 2 5 .0
- 6 2 .5
0 .0
6 2 .5
1 2 5 .0
1 8 7 .5
2 5 0 .0[ k V ]Reclose with R=Zc0
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ECE 524: Transients in Power Systems
Session 27; Page 25/28 Spring 2018
R=0
Tim edBreaker
LogicOpen@t0BRK1
BRK1
RESIST 269.8[ohm ]
269.8[ohm ]
269.8[ohm ]TLine
T
TER
M
Tim edBreaker
LogicOpen@t0TERM
VSEND VREC
EMTDC implementation(with Rpre = Zc1)
Main : Graphs
0.2020 0.2030 0.2040 0.2050 0.2060 0.2070 0.2080 0.2090
-150
-100
-50
0
50
100
150
y (k
V)
VSEND VRECPhase sending andreceiving endvoltage with Rpre = Zc1
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ECE 524: Transients in Power Systems
Session 27; Page 26/28 Spring 2018
Main : Graphs
0.2000 0.2020 0.2040 0.2060 0.2080 0.2100 0.2120 0.2140
-0.200
-0.150
-0.100
-0.050
0.000
0.050
0.100
0.150
0.200
y (k
A)
IRA IRB IRC
Sending end currents
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ECE 524: Transients in Power Systems
Session 27; Page 27/28 Spring 2018
Main : Graphs
0.1990 0.2000 0.2010 0.2020 0.2030 0.2040 0.2050 0.2060 0.2070 0.2080 0.2090
-150
-100
-50
0
50
100
150
y (k
V)
VSEND VRECRepeat with Rpre=Zc0
Main : Graphs
0.180 0.190 0.200 0.210 0.220
-0.125 -0.100 -0.075 -0.050 -0.025 0.000 0.025 0.050 0.075 0.100 0.125
y (k
A)
IRA IRB IRC
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ECE 524: Transients in Power Systems
Session 27; Page 28/28 Spring 2018
Main : Graphs
0.000 0.050 0.100 0.150 0.200 0.250 0.300
-250
-200
-150
-100
-50
0
50
100
150
200
y (k
V)
VRECReclose intotrapped charge with Rpre=Zc0