EE8501 PSA

EE8501 PSA

1. EE8501
POWERSYSTEMANALYSIS
1

2. UNIT-1
INTRODUCTION

11. UNIT -2

12. 400MVA
15kV
400MVA
15/345kV
T1
T2
800MVA
345/15kV
800MVA
15kV
40Mvar 80MW
280MVAr 800MW
L
in
e
2
L
in
e
1345kV
100mi
345kV
200mi
50mi
3520MVA
Line 3
345kV
1 4
2
5
Single-line diagram
TheN-RPower Flow: 5-busExample
1
2

13. |V| θ P
G
Q
G
P
L
Q
L Q
Gmax
Q
Gmin
Table 2.
Line inputdata
TheN-RPower Flow: 5-busExample
1
3
Bus Type perdegrees
unit
per
unit
per
unit
per
unit
per
unit
per
unit
per
unit
Table1. 1 Slack 1.0 0   00  
Businput
data
2
3
Load
Constant
voltage

1.05


0
5.2
0

8.0
0.8
2.8
0.4

4.0

-2.8
4 Load   0 0 00  
5 Load   0 0 00  
R X G B Maximum
MVA
Bus-
to-Bus
perunitperunitperunitperunitperunit
2-4 0.0090 0.100 0 1.72 12.0
2-5 0.0045 0.050 0 0.88 12.0
4-5 0.00225 0.025 0 0.44 12.0

14. Table 3.
Transformer
inputdata
Bus
1
2
Input Data
|V
1 |= 1.0, θ
1= 0
P
2 = P
G2-P
L2 =-8
Q
2 =Q
G2-Q
L2 =-2.8
|V
3 |= 1.05
P
3 =P
G3-P
L3 = 4.4
P
4 =0, Q
4 =0
P
5 =0, Q
5 =0
Unknowns
P
1, Q
1
|V
2|, θ
2
3 Q
3, θ
3
4
5
|V
4|, θ
4
|V
5|, θ
5
Table 4. Input data
andunknowns
1
4
TheN-RPower Flow: 5-busExample
R X G
c B
m Maximum Maximum
TAP
per per perper MVA Setting
Bus-
to-Bus
unit unit unitunit perunit perunit
1-5 0.00150 0.02 0 0 6.0 —
3-4 0.00075 0.01 0 0 10.0 —

15. LettheComputerDotheCalculations!
(Ybus Shown)
1
5

16. YbusDetails
24
R
24 jX
24
1 1
0.89276j9.91964
0.009j0.1
Y perunit
25
R
25 jX
25
1 1
1.78552j19.83932
0.0045j0.05
Y perunit
j
B
24
j
B
25
2 2
22
R
24 jX
24R
25 jX
25
1 1
Y 
Elementsof Y
bus connected tobus2
Y
21 Y
23 0
1
6
2 2
2.67828j28.459028.584784.624per unit
(0.89276j9.91964)(1.78552j19.83932)j
1.72
j
0.88

17. EditMode
EunM
Network ...
Aggregation ...
Filters,Expressions,etc
Area/Zone
Filters...
Mode CaseInformation
liiill§I
CaseDescription•••
Case Summary•••
CustomCaseInfo...
PowerFlowList,••
QuickPowerFlowList,,,ft!
AUXExportFormatOesc...
I
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fill
E.lllll
2imulator
Options•••
lliSI
CaseData Views
BusReIandReactivePowerMismatches
••[email protected]
mm:mlllIF_xp_ln_r•· ------ '-"
miDCTransmissionLines 8,
1±1Generators
ImpedanceCorrection1
!IllLineShunts
Loads
!IllMismatches
Multi-TerminalDC
!IllSwitchedShunts
Three-WindingTransfor
TransformerControls
1±1
1±1
Bl:".:l Aggregations
!IllAreas
ii08 .;g,,.oImRecords... Geo... Set ... Columns ...·I;
HerearetheInitialBusMismatches
'-"i!rtiM!iiU!i.;•
CaseInformation .D_ra_w ToolsO'p-_tio_n_s AddOns Window _
Case: TD_2008_Five8usE><ample.PWB S t a t us :I ni t i a l i ze dISi mul ator 13
6T
Model
Explorer•••
C l x
...
1
&
1
,....TD... tl:mi IOptions ...
Number Name AreaName Type
2 Two I PQ
Misma:chMW
-800.00
Mismatch Mvar Mismatch MVT
-150.00 813.94
SearchNow Opticns ...
1.050pu
0.000Deg
Search
1.000pu
0.000Deg
8
ThemismatchoftheMvarpowerflowequation
4Four 11 JPQ 37.29 605.20 606.35
3 Three PV 400.85 0.00 400.85
5Five PQ 0.00 66.00 66.00
1One Slack 0.00 0.00 0.00
Bus Substation Open
View...View...Windows
...

18. AndtheInitialPowerFlowJacobian
Model
Explorer...
Case:E><ample6_9.pwb Status:I ni t i a l i ze dISi mul ator 13 -c:i
X
Aggregation ...
w
PowerFlowList...
QuickPowerFlowList...
AUXExportFormat Oesc•••
!t!
Bus
View...
I
I
lttl
Hi
Open
Windows ...
CaseSummary...
2imulator
Options•..
CustomCaseInfo•••
Substation
View..,
ViewsCaseData
Area/Zone
Filters...Filters, Expressions,etc
CaseInformation
Mi§@MIMl.!i§IQ.lili§iiMM§.MU
IExplore
Fields Explore OptionsI
1±1!Ji!!iLoads [!]
!IllMismatches
!IllSwitchedShunts
!IllThree-WindingTransfoo
TransformerControls
Aggregations
!IllAreas
1±1!Ji!!iInjectionGroups
1±1!Ji!!ilnterfaces
!IllIslands
!IllMulti-SectionLines
MWTransactions
B
!IllOwners
!IllSubstations
!IllSuperAreas
TielinesbetweenAreas
TielinesbetweenZones
TransferDirections
!IllZones
B SolutionDetails
PowerFlowJacobian
XVBus ,c : = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =,1
lO1ffi I<·
-·
-
·
+81iMi.I Records • Geo• S e t •
Columns•
·I·'i!.·T'-li·1t:miIOptions •
Number Name JacobianEquation Angle BusZ AngleBus3 AngleBus4 AngleBus5 •
volt MagBusZ VoltMa•
I 2 Two RealPower Z9.76 -9.9Z
-99.44
149.04
-39.6B
O.B9
-19.B4 Z.6B
z 3 Three RealPower 99.44
-99.443 4Four RealPower -9.9Z
-19.B4
-Z.6B
-39.6B
I09.Z4
1.79
-0.B9
-1.79
Z7.16
4 5Five RealPower
5 2 Two Reactivepower
6 3 Three VoltageMagnitude
7 4Four Reactivepower O.B9
1.79
7.46
-l l . 9 Z
3.57
3.57
-9.09
-9.9Z
-19.B4B 5Five Reactivepower
SearchNow Options •
JacobianEquation

19. FiveBus PowerSystemSolved
slack
One
Two
ThreeFourFive
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1.000 pu
0.000 Deg
0.974 pu
-4.548 Deg
0.834 pu
-22.406 Deg
1.019 pu
-2.834 Deg
1.050 pu
-0.597 Deg
395 MW
114 Mvar
520 MW
337 Mvar
19
800 MW
280 Mvar
80 MW
40 Mvar

20. 37BusExampleDesignCase
MetropolisLight and Power ElectricDesign Case 2
A
SLACK345
RAY138
RAY69
MVA FERNA69
A
DEMAR69
BLT69
BLT138
BOB138
BOB69
WOLEN69
SHIMKO69
7.4 Mvar
14 MW ROGER69
UIUC69
MVA
PETE69
H ISKY69
TIM69
TIM138
PAI69
GROSS69
HANNAH 69
60 MW
AMANDA69
HOMER69
LAUF69
MORO138
LAUF138
H ALE69
PATTEN69
WEBER69
BUCKY138
MVA
SAVOY69
1.02 pu
38 MW
SAVOY138
JO138 JO345
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
16 MW
-14 Mvar
A
MVA
A
MVA
A
MVA
A
MVA
A
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1.02 pu
A
MVA
MVA MVA
1.03 pu
1.02 pu
1.03 pu
1.01 pu
1.00 pu
1.01 pu
1.00 pu
1.02 pu
1.01 pu
1.00 pu
1.01 pu
1.01 pu
1.01 pu
1.01 pu
1.00 pu
1.00 pu
1.02 pu
0.99 pu
0.99 pu
1.00 pu
1.02 pu
20 MW
28 Mvar
1.00 pu
1.01 pu
1.01 pu
1.00 pu 1.00 pu
1.01 pu
1.02 pu
1.03 pu
A
MVA
1.02 pu
A
MVA
SLACK138 MVA
RAY345
TIM345
MVA
A
MVA
A A
1.03 pu
1.02 pu
A
LYNN138
A
MVA
1.02 pu
A
MVA
1.00 pu
A
MVA
System Losses:10.70 MW
220 MW
52 Mvar
12 MW
3 Mv ar
20 MW
12 Mvar
124 MW
45 Mvar
37 MW
13 Mvar
12 MW
5 Mvar
150 MW
0 Mvar
56 MW
13 Mvar
15 MW
5 Mvar
2 Mvar
3 Mvar
45 MW
0 Mvar
25 MW
36 Mvar
36 MW
10 Mvar
10 MW
5 Mvar
22 MW
15 Mvar
60 MW
12 Mvar
23 MW
7 Mvar
33 MW
13 Mvar
15.9 Mvar 18 MW
5 Mvar
58 MW
40 Mvar
19 Mvar
14.2 Mvar
25 MW
10 Mvar
20 MW
3 Mvar
23 MW
6 Mvar 14 MW
3 Mvar
4.9 Mvar
7.3 Mvar
12.8 Mvar
28.9 Mvar
0.0 Mvar
55 MW
25 Mvar
39 MW
13 Mvar
150 MW
0 Mvar
17 MW
3 Mvar
14 MW
4 Mvar
KYLE69
A
20
MVA

21. GoodPowerSystemOperation
•Goodpowersystemoperationrequiresthat
there be no“reliability”violations(needingto
shedload,have cascadingoutages, orother
unacceptable conditions)foreitherthecurrent
conditionorinthe eventofstatisticallylikely
contingencies:
•Reliabilityrequiresasa minimumthattherebe no
transmissionline/transformer limitviolationsand
thatbusvoltagesbe within acceptable limits
(perhaps0.95 to1.08)
•Examplecontingenciesare thelossof anysingle
device.Thisisknownasn-1reliability. 12

22. Lookingat theImpactofLine Outages
MetropolisLight and Power ElectricDesign Case 2
A
SLACK345
MVA FERNA69
A
DEMAR69
BLT69
BLT138
BOB138
BOB69
WOLEN69
SLACK138 MVA
RAY345
RAY138
RAY69
SHIMKO69
7.3 Mvar
14 MW ROGER69
UIUC69
MVA
PETE69
H ISKY69
TIM69
TIM138
TIM345
PAI69
GROSS69
H ANNAH 69
60 MW
AMANDA69
110%
MVA
H OMER69
LAUF69
MORO138
MVA
LAUF138
HALE69
PATTEN69
45 MW
0 MvarWEBER69
BUCKY138
MVA
SAVOY69
1.02 pu
38 MW
SAVOY138
JO138 JO345
A
MVA
A
MVA
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
16 MW
-14 Mv ar
A
MVA
A
MVA
A
MVA
A
MVA
A
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1.02 pu
A
MVA
A
MVA
A
MVA
1.03 pu
1.02 pu
1.03 pu
1.03 pu
1.01 pu
1.00 pu
1.01 pu
1.00 pu
1.02 pu
1.01 pu
1.00 pu
1.01 pu
1.01 pu
1.01 pu
1.01 pu
1.02 pu
1.01 pu
1.00 pu
1.02 pu
0.90 pu
A 0.90 pu
0.94 pu
1.01 pu
0.99 pu
1.00 pu
1.00 pu
1.00 pu 1.00 pu
1.01 pu
14 MW
3 Mvar
1.01 pu
1.03 pu
A
MVA
1.02 pu
A
MVA
A
LYNN138
A
MVA
1.02 pu
A
MVA
1.00 pu
A
MVA
Sy stemLosses:17.61 MW
227 MW
43 Mvar
12 MW
3 Mvar
20 MW
12 Mvar
124 MW
45 Mvar
37 MW
13 Mvar
12 MW
5 Mvar
150 MW
4 Mvar
56 MW
13 Mvar
15 MW
5 Mvar
2 Mvar
9 Mvar
25 MW
36 Mvar
36 MW
10 Mv ar
10 MW
5 Mvar
22 MW
15 Mvar
60 MW
12 Mvar
20 MW
40 Mvar
23 MW
7 Mvar
33 MW
13 Mvar
16.0 Mvar 18 MW
5 Mvar
58 MW
40 Mvar
19 Mvar
11.6 Mvar
25 MW
10 Mvar
20 MW
3 Mvar
23 MW
6 Mvar
4.9 Mvar
7.2 Mvar
12.8 Mvar
28.9 Mvar
0.0 Mvar
55 MW
32 Mvar
39 MW
13 Mvar
150 MW
4 Mvar
17 MW
3 Mvar
14 MW
4 Mvar
KYLE69
A
MVA
A
80%
135%
MVA
A
Opening
one line
(Tim69-
Hannah69)
causes
overloads.
Thiswould
notbe
Allowed.
22

23. ContingencyAnalysis
Contingency
analysisprovides
anautomatic
wayof looking
atallthe
statisticallylikely
contingencies. In
thisexample the
contingencyset
isallthe single
line/transformer
outages
23

24. PowerFlowAndDesign
•Onecommonusage ofthepowerflowisto
determine howthesystemshouldbe modified
to removecontingenciesproblemsorserve new
load
•Inanoperationalcontextthisrequiresworking with
theexistingelectricgrid, typicallyinvolving re-
dispatchofgeneration.
•Ina planningcontextadditionstothe gridcanbe
consideredaswell asre-dispatch.
•Inthenextexample we lookathowtoremove
theexistingcontingencyviolationswhile serving
newload.
16

25. AnUnreliableSolution:
somelineoutages resultinoverloads
BLT69
BLT138
MetropolisLight and Power ElectricDesign Case 2
A
SLACK345
SLACK138 MVA
RAY345
RAY138
RAY69
MVA FERNA69
A
DEMAR69
BOB138
BOB69
WOLEN69
SHIMKO69
7.4 Mvar
14 MW ROGER69
2Mvar
UIUC69
MVA
PETE69
H ISKY69
TIM69
TIM138
TIM345
PAI69
GROSS69
HANNAH 69
60 MW
AMANDA69
HOMER69
LAUF69
MORO138
LAUF138
HALE69
PATTEN69
45 MW
0 MvarWEBER69
BUCKY138
MVA
SAVOY69
1.02 pu
38 MW
SAVOY138
JO138 JO345
A
MVA
A
MVA
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
16 MW
-14 Mvar
A
MVA
A
MVA
A
MVA
A
MVA
A
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1.02 pu
A
MVA
A
MVA
A
MVA
1.02 pu
1.01 pu
1.02 pu
1.03 pu
1.01 pu
1.00 pu
1.01 pu
1.00 pu
1.02 pu
1.01 pu
1.00 pu
1.01 pu
1.01 pu
1.01 pu
1.01 pu
1.02 pu
0.99 pu
1.00 pu
1.02 pu
0.97 pu
0.97 pu
0.99 pu
1.02 pu
20 MW
40 Mvar
1.00 pu
1.01 pu
1.01 pu
1.00 pu 1.00 pu
1.01 pu
14 MW
3 Mvar
1.02 pu
1.03 pu
A
MVA
1.02 pu
A
MVA
A
LYNN138
A
MVA
1.02 pu
A
MVA
1.00 pu
A
MVA
System Losses:14.49 MW
269 MW
67 Mvar
12 MW
3 Mvar
20 MW
12 Mvar
124 MW
45 Mvar
37 MW
13 Mvar
12 MW
5 Mvar
150 MW
1 Mvar
56 MW
13 Mvar
15 MW
5 Mvar
4 Mvar
25 MW
36 Mvar
36 MW
10 Mvar
10 MW
5 Mvar
22 MW
15 Mvar
60 MW
12 Mvar
23 MW
7 Mvar
33 MW
13 Mvar
15.9 Mvar 18 MW
5 Mvar
58 MW
40 Mvar
19 Mvar
13.6 Mvar
25 MW
10 Mvar
20 MW
3 Mvar
23 MW
6 Mvar
4.9 Mvar
7.3 Mvar
12.8 Mvar
28.9 Mvar
0.0 Mvar
55 MW
28 Mvar
39 MW
13 Mvar
150 MW
1 Mvar
17 MW
3 Mvar
14 MW
4 Mvar
KYLE69
A
MVA
A
96%
MVA
25
Case now
hasnine
separate
contingencies
having
reliability
violations
(overloadsin
post-contingency
system).

26. AReliableSolution:
no line outagesresultinoverloads
BLT69
BLT138
MetropolisLight and Power ElectricDesign Case 2
A
SLACK345
RAY69
MVA FERNA69
A
DEMAR69
BOB138
BOB69
WOLEN69
SHIMKO69
7.4 Mvar
14 MW ROGER69
UIUC69
AMANDA69
H OMER69
LAUF69
LAUF138
H ALE69
MVA
PETE69
H ISKY69
TIM69
TIM138
PAI69
GROSS69
H ANNAH 69
60 MW
MORO138
PATTEN69
45 MW
0 MvarWEBER69
BUCKY138
MVA
SAVOY69
1.02 pu
38 MW
SAVOY138
JO138 JO345
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
16 MW
-14 Mvar
A
MVA
A
MVA
A
MVA
A
MVA
A
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1.02 pu
A
MVA
1.03 pu
1.03 pu
1.01 pu
1.00 pu
1.01 pu
1.00 pu
1.02 pu
1.01 pu
1.00 pu
1.01 pu
1.01 pu
1.01 pu
1.01 pu
1.00 pu
0.99 pu
1.02 pu
0.99 pu
0.99 pu
1.00 pu
1.02 pu
20 MW
38 Mvar
1.00 pu
1.01 pu
1.01 pu
1.00 pu 1.00 pu
1.01 pu
14 MW
3 Mvar
1.02 pu
1.03 pu
A
MVA
1.02 pu
A
MVA
SLACK138 MVA
26
RAY345
RAY138
TIM345
MVA
A
MVA
A
MVA
A
MVA
1.01 pu
1.02 pu
1.02 pu
A
LYNN138
A
MVA
1.02 pu
A
MVA
A
MVA
System Losses:11.66 MW
266 MW
59 Mvar
12 MW
3 Mvar
20 MW
12 Mvar
124 MW
45 Mvar
37 MW
13 Mvar
12 MW
5 Mvar
150 MW
1 Mvar
56 MW
13 Mvar
15 MW
5 Mvar
2 Mvar
4 Mvar
25 MW
36 Mvar
36 MW
10 Mvar
10 MW
5 Mvar
22 MW
15 Mvar
60 MW
12 Mvar
23 MW
7 Mvar
33 MW
13 Mvar
15.8 Mvar 18 MW
5 Mvar
58 MW
40 Mvar
19 Mvar
14.1 Mvar
25 MW
10 Mvar
20 MW
3 Mvar
23 MW
6 Mvar
4.9 Mvar
7.3 Mvar
12.8 Mvar
28.9 Mvar
0.0 Mvar
55 MW
29 Mvar
39 MW
13 Mvar
150 MW
1 Mvar
17 MW
3 Mvar
14 MW
4 Mvar
KYLE69
A
MVA
Kyle138
A
M V
A
Previous
case was
augmented
withthe
addition of a
138kV
Transmission
Line

27. 27
GenerationChangesandTheSlack
Bus
•Thepowerflowisa steady-stateanalysistool,
sotheassumptionistotalloadpluslossesis
alwaysequaltototalgeneration
•Generationmismatchismadeupatthe slack bus
•Whendoinggenerationchangepowerflow
studiesonealwaysneedstobecognizantof
wherethegenerationisbeingmadeup
•Commonoptionsinclude “distributedslack,” where
themismatchisdistributedacrossmultiple
generatorsbyparticipationfactorsorbyeconomics.

28. GenerationChange Example1
SLACK345
SLACK138
MVA
RAY345
RAY138
RAY69
MVA FERNA69
A
DEMAR69
BLT69
BLT138
BOB138
BOB69
WOLEN69
SHIMKO69
0.0 Mvar
ROGER69
UIUC69
PETE69
H ISKY69
TIM69
TIM138
TIM345
PAI69
GROSS69
H ANNAH 69
AMANDA69
H OMER69
LAUF69
MORO138
LAUF138
H ALE69
PATTEN69
WEBER69
BUCKY138
SAVOY69
SAVOY138
JO138 JO345
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
0 MW
0 Mv ar
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
-0.002 pu
MVA
0.00 pu
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
0.00 pu
A
MVA
A
MVA
A
MVA
0.00 pu
-0.01 pu
0.00 pu
0.00 pu
0.00 pu
-0.03 pu
-0.01 pu
0.00 pu
0.00 pu
0.00 pu
-0.03 pu
-0.01 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu 0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
A
MVA
MVA
-0.01 pu
A
A
LYNN138
A
MVA
0.00 pu
A
MVA
0.00 pu
A
MVA
162 MW
35 Mvar
0 MW
0 Mvar
0 MW
0 Mvar
-157 MW
-45Mvar
0 MW
0 Mvar
0 MW
0 Mvar
0 MW
2 Mvar
0 MW
0 Mvar
0 MW
0 Mvar
0 MW
0 Mvar
0 MW
3 Mvar
0 MW
0 Mvar
0 MW
0 Mvar
0 MW
0 Mvar
0 MW
0 Mvar
0 MW
0 Mvar
0 MW
0 Mvar
0 MW
4 Mvar
0 MW
0 Mvar
0 MW
0 Mvar
-0.1 Mvar 0 MW
0 Mvar
0 MW
0 Mvar0 MW
0 Mvar
-0.1 Mvar
0 MW
0 Mvar
0 MW
0 Mvar
0 MW
0 Mvar 0 MW
0 Mvar
-0.1 Mvar
0.0 Mvar
-0.1 Mvar
-0.2 Mvar
0.0 Mvar
0 MW
51 Mvar
0 MW
0 Mvar
0 MW
2 Mvar
28
0 MW
0 Mvar
0 MW
0 Mvar
Displayshows
“Difference
Flows”
between
original
37 buscase,
andcase with
aBLT138
generation
outage;
note allthe
power change
ispicked
up atthe slack
Slack bus

29. GenerationChange Example2
SLACK345
RAY69
MVA FERNA6
9
A
DEM AR69
BLT69
BLT 138
BOB138
BOB69
WOLEN69
SLACK138
MVA
RAY345
RAY138
SH IM KO69
-0.1 Mvar
ROGER69
UIUC69
PET E69
HISKY69
TIM69
TIM138
TIM 345
PAI69
GROSS69
H ANNAH 69
AMANDA69
0 MW
0 Mvar
H OM ER69
LAUF69
M ORO138
LAUF138
H ALE69
PAT TEN69
WEBER69
BUCKY138
SAVOY69 42 MW
SAVOY138
JO138 JO345
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
0 M W
0 Mvar
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
-0.003 pu
MVA
0.00 pu
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
0.00 pu
A
MVA
A
MVA
A
MVA
0.00 pu
-0.01 pu
0.00 pu
0.00 pu
0.00 pu
-0.03 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
-0.03 pu
-0.01 pu
-0.01 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu 0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
A
MVA
0.00 pu
A
MVA
A
LYNN138
A
MVA
0.00 pu
A
MVA
0.00 pu
A
MVA
0 M W
37 M v ar
0 MW
0 Mvar
0 MW
0 Mvar
-157 M W
-45 M var
0 M W
0 M var
0 M W
0 M var
0 MW
0 Mvar
0 M W
0 M var
0 M W
0 M var
0 MW
0 Mv ar
-14 M var
0 M W
0 M var
0 M W
0 M var
0 M W
0 M v ar
0 MW
0 M v ar
0 MW
0 Mvar
0 MW
0 Mvar
99 M W
-20 Mvar
0 M W
0 M v ar
0 MW
0 Mvar
-0.1 Mvar 0 M W
0 M var
0 MW
0 Mvar0 MW
0 Mvar
-0.1 M var
0 M W
0 M var
0 MW
0 Mvar 0 MW
0 Mvar
0.0 Mvar
0.0 M var
-0.1 M var
-0.2 Mvar
0.0 M var
19 MW
51 Mvar
0 MW
0 Mvar
0 MW
0 Mvar
29
0 M W
0 M var
0 M W
0 M var
Displayrepeatspreviouscaseexceptnowthe change in
generationispicked up byother generatorsusing a
“participationfactor”(changeisshared amongstgenerators)approach.

30. VoltageRegulationExample:37Buses
Displayshowsvoltage contour of the power system
SLACK345
LAUF138
BUCKY138
SLACK138
MVA
RAY345
RAY138
RAY69
MVA
FERNA6
9
A
DEM AR69
BLT69
BLT138
BOB138
BOB69
WOLEN69
SHIM KO69
7.4 M var
14 MW ROGER69
2M var
UIUC69
PETE69
HISKY69
TIM69
TIM138
TIM345
PAI69
GROSS69
HANNAH69
AM ANDA69
HOMER69
LAUF69
M ORO138
HALE69
PATTEN6
9 45 M W
0 MvarWEBER69
1.02 pu
SAVOY69 38 MW
SAVOY138
JO138 JO345
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
0 M W
0 M va
A
r
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1.02 pu
A
MVA
A
MVA
A
MVA
1.03 pu
1.01 pu
1.02 pu
1.03 pu
1.01 pu
1.00 pu
1.00 pu
0.99 pu
1.02 pu
1.01 pu
1.00 pu
1.01 pu
1.01 pu
1.01 pu
1.01 pu
1.02 pu
1.00 pu
1.00 pu
1.02 pu
0.997 pu
0.99 pu
33 M W
10 M var
1.00 pu
1.02 pu
1.00 pu
1.01 pu
1.00 pu
1.00 pu 1.00 pu
1.01 pu
1.02 pu
1.03 pu
A
MVA
1.02 pu
A
MVA
A
LYNN138
A
MVA
1.02 pu
A
MVA
1.00 pu
A
MVA
219 MW
52 M var
21 M W
7 Mvar
45 M W
12 M var
157 MW
45 Mvar
37 MW
13 Mvar
12 M W
5 Mvar
150 MW
0 Mvar
56 M W
13 M var
15 MW
5 M var
3 M var
58 MW
36 Mvar
36 MW
10 Mvar
0 MW
0 Mvar
22 M W
15 M var
60 MW
12 Mvar
20 MW
9 Mvar
23 M W
7 Mvar
33 M W
13 M var
15.9 M var 18 MW
5 M var
58 M W
40 M var51 M W
15 M var
14.3 M var
15 MW
3 M var
23 M W
6 Mvar 14 MW
3 M var
4.8 Mvar
7.2 Mvar
12.8 M var
29.0 M var
20.8 M var
92 MW
10 Mvar
20 MW
8 M var
150 MW
0 Mvar
17 M W
3 Mvar
14 M W
4 M var
1.010 pu
0.0 Mvar
System Losses:11.51 MW
Automaticvoltageregulationsystemcontrolsvoltages.
30

31. Real-sizedPowerFlowCases
•Realpowerflowstudies areusuallydone with
caseswithmany thousandsofbuses
•OutsideofERCOT,busesareusuallygroupedinto
variousbalancingauthorityareas,witheacharea
doingitsowninterchangecontrol.
•Casesalsomodela varietyofdifferent
automatic controldevices,suchasgenerator
reactive powerlimits,load tapchanging
transformers,phaseshiftingtransformers,
switchedcapacitors,HVDCtransmissionlines,
and (potentially)FACTS devices. 23

32. Sparse MatricesandLargeSystems
•Sinceforrealisticpowersystemsthemodel
sizesarequitelarge,thismeanstheY
busand
Jacobianmatricesarealsolarge.
•However, mostelementsinthesematricesare
zero,therefore specialtechniques,sparse
matrix/vectormethods,areusedtostore the
valuesandsolvethepowerflow:
•Withoutthese techniqueslargesystemswouldbe
essentiallyunsolvable.
24

33. 33
InterconnectedOperation
Power systems areinterconnectedacross
largedistances.
Forexample mostofNorth Americaeast of
theRockiesisone system,mostofNorth
AmericawestoftheRockiesisanother.
MostofTexasandQuebecare each
interconnectedsystems.

34. totalgen-totalload-totallosses=tie-line flow
28
Balancing AuthorityAreas
A“balancingauthorityarea”(previously calleda
“controlarea”)hastraditionallyrepresentedthe
portion oftheinterconnectedelectric grid
operatedbya single utilityortransmission
entity.
Transmissionlinesthatjointwoareasare
knownastie-lines.
T h enetpoweroutofanareaisthe sumof
theflowonitstie-lines.
T h eflowoutofanarea isequalto

35. controllingfrequency.
29
Area ControlError(ACE)
T h eareacontrolerrorisacombination
of:
the deviationof frequency fromnominal, and
the difference betweenthe actualflow outof an
areaandthescheduled (agreed)flow.
T h atis,theareacontrolerror(ACE)is
thedifference betweentheactualflowout
ofan areaminusthescheduledflow,plusa
frequencydeviationcomponent:
ACEprovidesa measureofwhetheranarea
isproducingmore orlessthanitshouldto
satisfy schedulesandtocontributeto
P
actual tie-lineflow P
sched 10fACE

36. otherareas.
30
Area ControlError(ACE)
T h eidealisforACEtobe zero.
Because theloadisconstantly changing,
eachareamustconstantlychangeits
generationtodrivetheACEtowardszero.
ForERCOT,thehistoricaltencontrolareas
were amalgamatedintoone in2001,sothe
actualandscheduledinterchange are
essentiallythe same (bothsmallcompared
tototaldemandinERCOT).
InERCOT,ACEispredominantly dueto
frequencydeviationsfromnominalsince
thereisverylittle scheduled flowtoorfrom

37. AutomaticGenerationControl
Mostsystemsuseautomatic generation
control(AGC)toautomaticallychange
generationtokeeptheirACE close tozero.
Usuallythecontrolcenter(eitherISO
orutility)calculatesACEbasedupontie-
lineflowsandfrequency; thentheAGC
modulesends controlsignalsouttothe
generators everyfoursecondsorso.
31

38. PowerTransactions
Powertransactionsare contractsbetween
generatorsand(representativesof)loads.
Contractscanbeforanyamountoftime at
anypriceforanyamountofpower.
Scheduledpowertransactionsbetween
balancingareasare called“interchange”and
implementedbysettingthevalueofP
schedused
intheACEcalculation:
ACE=P
actual tie-lineflow –P
sched +10βΔf
…andthencontrollingthe generationtobring
ACE towardszero.
32

39. 39
“Physical”powerTransactions
•ForERCOT,interchange isonlyrelevantover
asynchronousconnectionsbetweenERCOT
andEasternInterconnectionorMexico.
•InEasternandWesternInterconnection,
interchange occursbetweenareasconnected
by AClines.

40. ThreeBusCaseonAGC:
nointerchange.
Bus2 Bus1
1.00PU
78 MW
-21 MVR
Bus3
HomeArea
266 MW
133 MVR
150MWAGC ON
166MVR AVR ON
250 MWAGC ON
34 MVRAVR ON
133 MW
67 MVR
1.00PU
-40 MW
8 MVR
40MW
-8MVR
-77 MW
25 MVR
39 MW
-11 MVR
1.00 PU
-39MW
12 MVR
101 MW
5 MVR
100MW
Net tie-lineflowis
closetozero
Generation
40
isautomatically
changedtomatch
changeinload

41. 100MW Transactionbetween
areasinEasternorWestern
Bus2 Bus1
1.00PU
85MW
-23MVR
Bus3
HomeArea
ScheduledTransactions
100.0MW
225MW
113MVR
150MWAGCON
138MVRAVRON
291MWAGCON
8MVRAVRON
113MW
56MVR
1.00PU
8MW
-2MVR
-8MW
2MVR
-84MW
27MVR
93MW
-25MVR
1.00PU
-92MW
30MVR
0MW
32MVR
100MW
Scheduled
41
100MW
TransactionfromLeft toRight
Nettie-line
flow isnow
100MW

42. PTDFs
Powertransferdistributionfactors(PTDFs)
showthelinearizedimpactofatransferof
power.
P T D F scalculatedusingthefast
decoupled powerflowBmatrix:
θB
1
P
Onceweknowθwecan derivethechange in
thetransmission lineflowstoevaluatePTDFs.
Notethat wecan modifyseveral elementsin P,
in proportion tohowthespecified generatorswould
participatein thepowertransfer.
36

43. Nine Bus PTDFExample
10%
60%
55%
11%
64%
57%
A
G
B
C
D
EF
300.0MW
400.0MW 300.0MW
250.0MW
150.0MW
71%
0.00deg
71.1MW
92%
44% 32%250.0MW
74% 250.0MW
24%
I
H
200.0MW
150.0MW
37
Figureshowsinitialflowsfora ninebuspower system

44. Nine BusPTDFExample,cont'd
43%
57%
13%
35%
2%
20%
10%
A
G
B
C
D
EF
300.0MW
400.0MW 300.0MW
250.0MW
150.0MW
34% 32%250.0MW
34% 250.0MW
34%
I
H
200.0MW
150.0MW
38
30%
0.00deg
71.1MW
Figure nowshowspercentage PTDF flowsfora change in transaction from A to I

45. Nine BusPTDFExample,cont'd
6%
6%
12%
61%
19%
12%
6%
21%
21%
A
G
B
C
D
E
I
F
H
300.0MW
400.0MW 300.0MW
250.0MW
250.0MW
200.0MW
3
250.0MW
150.0MW
150.0MW
20%
18%
0.00deg
71.1MW
FigurenowshowspercentagePTDFflowsforachangein transactionfrom Gto F

46. 46
LineOutageDistributionFactors
(LODFs)
•LODFsare usedtoapproximatethechange in
theflowonone line causedbytheoutage of a
secondline
–typicallythey areonlyusedtodetermine the
changeinthe MWflow comparedtothe pre-
contingency flowif acontingency were tooccur,
–LODFsareusedextensivelyinreal-time
operations,
–LODFsareapproximatelyindependentof flowsbut
dodependonthe assumednetwork topology.

47. 47
LineOutageDistributionFactors
(LODFs)
P
lchangein flowonlinel,
duetooutageoflinek.
P
kpre-contingencyflowonlinek
P
lLODF
l,kP
k,
Estimates changeinflowonlinel
ifoutageon linekweretooccur.

48. 48
LineOutageDistributionFactors
(LODFs)
andthentherewasanoutageoflinek,
ifLODF
l,k=0.1 then theincreaseinflow
onlinelafteracontingencyoflinekwouldbe:
P
lLODF
l,kP
k0.1100 10MW
from50 MWto60 MW.
If linekinitiallyhadP
k100 MWofflowonit,
andlinelinitiallyhadP
l50MWflowon it,

49. UNIT 3 & UNIT 4
BALANCED AND UNBALANCED
FAULT ANALYSIS

50. INTRODUCTION
Afault calculationistheanalysisofthepowersystemelectricalbehaviourunder
fault conditions,withparticular referenceto theeffectsonthesystemcurrents
andvoltages. Accuratefault calculationsareessential forpropersystemdesign.
Theanalysisoffault conditionsandtheireffectsonthepowersystemisof
particularrelevance tosuch conditionsas:
SLID
E
5
0
a
.
thechoiceofasuitablepowersystemarrangement,withparticular
referenceto theconfigurationofthetransmissionordistribution
network.
thedeterminationoftherequiredloadandshort-circuitratingsofthe
powersystemplant.
thedeterminationofthebreakingcapacityrequiredofthepowersystem
b
.
c
.switchgearand
fusegear.d
.
thedesignandapplicationofequipmentforthecontrolandprotection
ofthepowersystem.
theoperationofthesystem,withparticularreference tosecurityof
supplyand economicconsiderations.
theinvestigationofunsatisfactoryperformanceofthepowersystemorof
e
.
f.
individualitemsofpowersystem
plant.

51. TypesofFault
Inthe contextof electrical fault calculations,apowersystemfault
may be definedasanyconditionor abnormalityofthe system
which involvesthe electrical failureof primaryequipment,i.e.
generators, transformers,busbars,overheadlinesandcablesand
all other items ofplant whichoperate at power systemvoltage.
SLID
E
5
1
Electrical failure generallyimpliesone oftwoconditionsortypes
of failure (sometimesboth), namelyinsulationfailure resultingin
a short-circuitconditionor aconductingpathfailure resultingin
an open-circuitcondition,the former beingbyfar the more
commontypeoffailure.

52. a) Short-circuitedphases
Faultsofthistypearecausedbyinsulationfailurebetweenphaseconductorsorbetween
phaseconductorsandearth, orboth. Figure1 givesdetails ofthevariousshort-
circuited-phasefaults.
SLID
E
5
2
Thethree-phasefault,whichmay ormaynotbeto earth, istheonly balancedshort-
circuit conditionandistheoneusedasthestandardindeterminingthesystemfault
levelsorratings.

53. c) Simultaneousfaults
Asimultaneousfault condition,or amultiple fault condition,is
definedasthe simultaneouspresence oftwoormorefaultswhich
may be ofsimilar ordissimilar typesandmaybe at the same or
different pointsinthe power system.
SLID
E
5
3
The mostcommonsimultaneousfault conditionisundoubtedly
thedouble-circuitoverheadlinefaultinwhichacommon
cause,i.e. lightningor clashingconductors,resultsinafaulton
eachof the two circuitsconcerned.
Anothersimultaneousfaultconditionisknownasthe cross-
country earth-fault,inwhichasingle-phase toearthfault atone
pointoccurs coincidentallywithasecondsuchfaultonanother
phase atsome otherpointinthe system.

54. d)
Windi
ngfaults
Thistypeoffault,whichcanoccurinmachineortransformerwindings, isdetailedin
Figure3,and consistsmainly ofshortcircuits,fromonephasetoearth,orfromphaseto
phase,orfromonepoint
toanotheronthesamephasewinding.Thelastfaultconditionisknownastheshort-
circuited
turnsfault.Thisconditioncanposespecialproblemsfromaprotectionpointofview
becausethecurrentintheshortedturnscanbeverylarge,whilethatintheremainderof
thewindingmaybequitesmall.
Short-circuited turns Open-circuitedwinding
The open-circuitedwindingconditionisquiterareinpracticeandisusuallytheresultof
damageto thewindingasa consequenceofa precedingwinding shortcircuitatornearthe
pointoffault. Opencircuitsintransformersmayalsooccurasa resultoffailureoftap-
changingequipment.
SLID
E
5
4
Phase-to-earth
fault
Phase-to-phase
fault
Figure3. Winding
faults

55. FactorsAffectingFaultSeverity
Theseverityofa powersystemfault conditionmaybeassessedinterms
ofthe disturbanceproducedandthefaultdamagecaused,themagnitude
ofthefaultcurrentanditsdurationbeingofparticularinterest,especially
inrelationtothedesign andapplicationofthepowersystemprotection.
Themainfactorswhich affect theseverityofafaultare:
a) Sourceconditions
These relatetotheamountandlocationofallconnectedgeneration
equipment-includingthetiesorinterconnectionswithothersystems,the
twoextremesof minimumandmaximumconnectedplantbeingof
particular interest. Theminimumandmaximumplantconditionsare
normallythosecorrespondingto the conditionsofminimumandmaximum
connectedload.
SLID
E
5
5

56. b) Powersystemconfiguration
Thisisdeterminedbytheitemsofplant,i.e.generators,transformers,
overheadlines andcablecircuits,etc.,assumedtobeinserviceforthe
particular condition beinginvestigatedandbyothersuchfactorsasmayhavea
bearingonthemake-upofthe equivalentcircuitofthesystem. Thesystem
configurationmaychangeduringthe courseofafaultwithconsequentchanges
inthemagnitudeanddistributionofthefault currents. Typicalcausesofthe
abovechangesbeingthesequentialtrippingof thecircuit-breakersatthetwo
endsofthefaultedtransmissionline andthesequentialclearanceofmultiple
faultconditions.
SLID
E
5
6

57. c) Neutralearthing
Faultswhichinvolvetheflowofearthcurrent,i.e.phasefaultsto
earth, maybeinfluencedconsiderablybythesystemneutral earthing
arrangements,particularlybythenumberofneutralearthingpoints
and thepresenceorabsenceofneutral earthingimpedance. The
powersystem maybesingle-pointormultiple-pointearthedandsuch
earthingmaybedirect,i.e.solidearthing,orviaaneutral impedance.
The132kV,275kV andthe400kVsystemsemploydirectmultiple
earthingwhilethe66kVand belowgenerallyemploysingle-point,
sometimesmultiple,resistance earthing.
SLID
E
5
7

58. d)Natureandtypeoffault
Fromwhathasbeensaidalready,itisevidentthatthe type
and locationof afault will have asignificanteffect onthe
magnitudeanddistributionof the systemfaultcurrents.
Likewise,the
effectof agivenfaultconditionmaybe considerablymodified
bythe simultaneouspresenceof one or more otherfault
conditions,forexample, the combinationof ashortcircuitand
anopen-circuited phase condition.
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59. The wide range ofpossible systemfaultconditionsandthe
many factorswhichinfluence themresult inawiderange of
possiblefault severity,rangingfromverylowlevelsuptothe
maximum level possiblefor the system.Itisofvalue to
consider astandard fault conditionwhendiscussingsystems
andthe three-phasefault level maybe expressedinamperes
but itisusuallyexpressedin MVA,correspondingtothe rated
systemvoltageandthe current for asymmetrical three-phase
fault. Thisthree-phase fault levelnormally
determinesthe requiredshort-circuit ratingofthe power
systemswitchgear.A factor whichmayalsohave tobe taken
into accountisthemaximumvalue ofthe one-phase toearth
fault currentwhich,inasolidlyearthedsystem,mayexceed
themaximumthree-phase fault current.
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60. MethodsofFault
Calculation
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♦ The informationnormallyrequiredfromafault calculationis
thatwhichgivesthevaluesofthe currentsandvoltagesatstatedpointsin
the power systemwhenagivenfault conditionisimposedonthe
s
ystem.
♦ Afaultcalculationistherefore, essentiallyamatter of
networkanalysisandcanbe achievedbyanumber ofmethods,i.e.
mesh-
current
ornodal-voltage methods,networkreduction
techniquesornetworkanalyser.
simulationusing
a
♦ The choice of methoddependsonthe size andcomplexity
of thecircuitmodel andthe availabilityofcomputing
facilities.

61. MethodsofFaultCalculation
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♦ Anessential partof power systemanalysisandfault
calculationis thatwhichconcernsthe determinationofthe
equivalent system networkfor the systemoperating
conditionsandthe faultconditionsunder
consideration.
♦ Asstatedearlier,faultscanbesubdividedintoeither
balanced(symmetrical)orunbalanced(unsymmetrical)
faultconditions,lattercasebeinganalysed,traditionally,
bythemethodof
thi
ssymmetrical
components.
♦ Bothclassesoffault are analysedbyreducingthe power
system, withitsfaultcondition,toanequivalentsingle-
phase network.

62. BalancedFaults
Thebalanced fault isoftentheseverestandisthesimplestto determine.
Hence,this istheonenormallyusedtodeterminethe'duty' ofthesystem
switchgear andbusbars
FaultCalculationProcedure
Theanalysisofa3-phasebalancedfaultcondition consists,ingeneral,ofthree
parts:
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a.
networ
k, b.
c.
thesystemwithitsfaultconditionisrepresented byitspositive
sequence
thenetworkissolvedintermsofper-unit quantities,
theresultingper-unit quantitiesareconvertedtoactual
values.
Component
Representation
Overheadlinesandcablesarenormallyrepresentedbytheirseriesimpedance
onthebasisthattheshuntimpedanceishigh.Transformersandsynchronous
machinesarenormallyrepresentedbytheirreactancesastheresistancevalues
arerelativelysmall.Loadimpedancesarenormallymuchlargerthantheother
networkimpedancesand
hence,theyarenormallyneglectedinfault
calculations.

63. THREEPHASEFAULTS
Thefollowingexampleispresentedto illustrate themethodsemployed
forthe casewhichinducespositivesequencecomponentsonly. The
systemshown representsapowerstationconnectedtothegrid,together
withitsauxiliary systems. Theprinciplecircuitandplantparameters
aregiveninTable1.
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64. G2/
3
G
Inf
bus
Bus
1
T2/T
3
G
1


T
1
T
4
T
5
M
2
Bus2
03
B
03
A
M
1
T
6
T
7
M
3
M
4
L L
MCC
2
Bus
3
Bus
4
MCC
1



 
Afaultisassumedto
occurfirstonbusbar
MCC1andsecondlyon
busbarMCC2. The
faultlevelquotedon
Bus1 is 2500MVA.
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Exampl
e

65. G2/
3
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71 MVA,X=263 pu on100
MVA
T2/T
3
71 MVA,X
l =
009pu
G (2500-147-
71)MVA
G
1
147MVA,X
d =1867
pu
T
1
150MVA,X
l=013
pu
T
4
16 MVA,X
l =01
pu
T
5
16 MVA,X
l =009
pu
T
6
2 MVA,X
l =006
pu
T
7
4 MVA,X
l -006
pu
M
1
88
MVA
M
2
806
MVA
M
3
1247
MVA
M
4
0977
MVA
S
L
0918MW,09
p.f.
Table
1

66. grid
infeed
10
0(2500147
71)
=
·438
Base100
MVA
71MVA
generation
2·63
(given)
100
0971

127
147
MVA
generator
1001
86714
7
1
27
100
13
150

08
100
1
16

625
03
B
03
A
100
09
16

5625
MCC
2
MCC
1
10006
3
2
10006

15
4
N.B. 2x2 MVA
Transformersin
parallel
3
1
2
Normalised systemreactances
on equivalentcircuit
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67. Theresolution oftheproblemintosequencecomponentsresultsin
considerablesimplificationofallproblemsinvolvingasymmetrysuchasthat
introducedbyshort-circuitingconductorsofasystemeithertogetherorto
earth,singlyorinpairs,orby theopencircuitingofa conductor. The
resolutionoftheproblemintosequence componentshasthefurtheradvantage
inthatitisolatesthequantitiesinto componentswhichrepresentabetter
criteria ofthecontrollingfactororfactorsin certainphenomena.
Consider thefollowingsystemofvectorsshownbelow.
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78. Rewriting equation(1),andforconvenienceneglecting thebardenotingvector
quantities
V
a = V
a1 +V
a2 +V
a0
V
b =λ
2
V
a1 +λV
a2 +
V
a0V
c =λV
a1 +λ
2
V
a2
+V
a0
(2
)
andV
a0,V
a1 andV
a2 maynowbewrittenasV
0,V
1 and V
2
whereλisanoperator which movesavector120°
anticlockwise,i.e.
λ = 0.5+
0.886jλ
2
= -0.5
–0.886j λ
3
= 1
(3
)
Otherusefulidentitiesinaregiveninthefollowing
Table1.
Table1
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79. Thetransformationof phasequantitiestosequenceandreverseis
givenby [V
ph]=[T][V
seq]
an
d
[V
seq]=[T]
-1
[V
ph]
wher
e
[T]
=
(4
)
an
d
[T]
-1
=
(5
)
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80. Anuntransposedtransmissionlinegivesriseto3percentnegativesequence
voltage.Showapproximatelyhowthisaffectsthemagnitudesoftheterminal
voltagesofthegeneratorsupplyingthesystem.
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Nozerosequencesvoltage;letV2=003V1
Va =V1+003V1 =(1+003)V1
Vb =
2
V1 +003V1 =(
2
+
003)V1Vc =V1 +
2
003V1 =
(+003
2
)V1

81. Componentsof
voltage
V
A =0andsincethegeneratorisonlyableto generatepositivesequence
components, E
0 = E
2 =0
Also,sinceI
B =I
C =0,I
0 =I
2 =0
0
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1
Z
1Z
2
Z
E
1
1
I


82. PRACTICALFAULT
STUDIES
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Aspreviouslystated,powersystemsaresubjectto excessive damagewhen
high magnitudecurrentsareflowingduetosystemshortcircuit. The
analysissofarhasbeenconfinedtosteady-stateconditionsarising
subsequentto faultincidence.Theinitialtransientconditionhasbeen
neglectedwhich,formanypracticalsituations,isconsideredto be
satisfactory. However,theinstantofinitiationoftheshortcircuit relativeto
thevoltagewaveform,hasamarkedeffectuponthe maximumpeakvalueof
theshort-circuitcurrentwhichmaybeimportantfromthepointofviewof
fastactingfaultclearancedevices,i.e.doesthecircuit breakeroperateprior
tothedecayofthetransientcomponentofthecurrent.

83. The total currentisobtainedbyaddingthesteady-stateandthetransient
components.
SLIDE 83

84. Inpractice,thetimevariationoftheshortcircuit currentisdependent
onthe actualcharacteristicofthegenerator. Toa closeapproximation,
theshort circuitcurrentcanbeallocatedtothefollowingcategories:
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1
.
2
.
3
.
thecontinuous
component thetransient
component the
subtransientcomponent
Thesecategoriesaredeterminedbytheelectromagneticprocessthat
occurs inthegenerator. Formostfaultstudies,therepresentationand
calculationof theshortcircuitcharacteristicsarebasedona constant
voltageandontheassumptionthatthedecayoftheacshort-circuit
currentisdueto anincrease inthegeneratorreactancesfrom
(1) thesubtransient
reactance
Xd
"
to (2) thetransientreactanceXd'
andfinally (3) thesynchronous
reactance
Xd

85. SynchronousandInductionMotorLoads
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Forashort-circuitperiodofT≤ 0·2s,synchronousmotorscanbe
treatedin thesamemannerassynchronousgenerators. Ina larger
short-circuit period,themachine issubjectedtoaspeeddropandis
thenoperatinginan assynchronousmode. Highandlowvoltage
motorssimilarlymakea contributiontotheshort-circuitcurrent.
However,duetodifferencesintheirconstruction,thiscontribution
decaysveryrapidly.
Short-circuitanalysisisgenerallypreceded bydatacollectionand
the preparationofa one-linediagram,followedbythe
determinationofthe exact objectivesofthestudy. Table2gives
anindicationofparameter valuestobeusedundercertain
circumstances.

86. Table
2
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