12. 400 MVA
15 kV
400 MVA
15/345 kV
T1
T2
800 MVA
345/15 kV
800 MVA
15 kV
40 Mvar 80 MW
280 MVAr 800 MW
Line2
Line1
345 kV
100 mi
345 kV
200 mi
50 mi
3 520 MVALine 3
345 kV
1 4
2
5
Single-line diagram
The N-R Power Flow: 5-bus Example
1
2
13. |V| θ PG QG PL QL QGmax QGmin
Table 2.
Line input data
The N-R Power Flow: 5-bus Example
1
3
Bus Type per degrees
unit
per
unit
per
unit
per
unit
per
unit
per
unit
per
unit
Table 1. 1 Slack 1.0 0 0 0
Bus input
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 0 0
5 Load 0 0 0 0
R X G B Maximum
MVA
Bus-
to- Bus
per unit per unit per unit per unit per unit
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
input data
Bus
1
2
Input Data
|V1 |= 1.0, θ1 = 0
P2 = PG2-PL2 = -8
Q2 = QG2-QL2 = -2.8
|V3 |= 1.05
P3 = PG3-PL3 = 4.4
P4 = 0, Q4 = 0
P5 = 0, Q5 = 0
Unknowns
P1, Q1
|V2|, θ2
3 Q3, θ3
4
5
|V4|, θ4
|V5|, θ5
Table 4. Input data
and unknowns
1
4
The N-R Power Flow: 5-bus Example
R X Gc Bm Maximum Maximum
TAP
per per per per MVA Setting
Bus-
to- Bus
unit unit unit unit per unit per unit
1-5 0.00150 0.02 0 0 6.0 —
3-4 0.00075 0.01 0 0 10.0 —
16. Ybus Details
24
R24 jX24
1 1
0.89276 j9.91964
0.009 j0.1
Y per unit
25
R25 jX25
1 1
1.78552 j19.83932
0.0045 j0.05
Y per unit
j
B24
j
B25
2 222
R24 jX24 R25 jX25
1 1
Y
Elements of Ybus connected to bus 2
Y21 Y23 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. Edit Mode
EunM
Network ...
Aggregation ...
Filters, Expressions, etc
Area/Zone
Filters...
Mode Case Information
liiill§I Case Description•••
Case Summary•••
Custom Case Info...
Power Flow List,••
QuickPower Flow List,,, ft!
AUX Export Format Oesc...
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fill
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Case Data Views
BusRe Iand Reactive Power Mismatches
• •1@m1m1.114a31pnmnnt
mm:mlll IF_xp_ln_r •· - - - - - - ' - "
mi DC Transmission Lines 8,
1±1 Generators
Impedance Correction1
!IllLine Shunts
Loads
!IllMismatches
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!IllSwitched Shunts
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Transformer Controls
1±1
1±1
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Here are the Initial Bus Mismatches
'-"i ! rti M!iiU!i .;•
Case Information . D_ra_w Tools O'p-_tio_n_s Add Ons Window _
Case: TD_2008_Five8usE><ample.PWB Status: Initialized I Simulator 13
6 TModel
Explorer•••
Cl x
...1&1,.... T D...tl: miIOptions ...
Number Name Area Name Type
2 Two I PQ
Misma:chMW
-800.00
MismatchMvar Mismatch MVT
-150.00 813.94
Search Now Opticns ...
1.050 pu
0.000 Deg
Search
1.000 pu
0.000 Deg
8
The mismatch of the Mvar power flow equation
4 Four 11 JPQ 37.29 605.20 606.35
3 Three PV 400.85 0.00 400.85
5 Five PQ 0.00 66.00 66.00
1One Slack 0.00 0.00 0.00
Bus Substation Open
View... View... Windows
...
18. And the Initial Power Flow Jacobian
Model
Explorer...
Case: E><ample6_9.pwb Status: Initialized I Simulator 13 - c:i
X
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w
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Area/Zone
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Case Information
Mi§@MIMl.!i§IQ.lili§iiMM§.MU
IExplore
Fields Explore Options I
1±1!Ji!!iLoads [!]
!IllMismatches
!IllSwitched Shunts
!Ill Three-Winding Transfoo
Transformer Controls
Aggregations
!IllAreas
1±1!Ji!!iInjectionGroups
1±1!Ji!!ilnterfaces
!IllIslands
!IllMulti-Section Lines
MW Transactions
B
!IllOwners
!IllSubstations
!IllSuper Areas
Tielines between Areas
Tielines between Zones
Transfer Directions
!IllZones
B SolutionDetails
Power Flow Jacobian
X VBus ,c : = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = ,1
l O 1ffi I< ·-·-·+81iMi .I Records • Geo• Set•
Columns•
· I · 'i!. · T '-li· 1t:mi IOptions •
Number Name Jacobian Equation Angle BusZ Angle Bus3 Angle Bus4 Angle Bus 5
• volt MagBus Z Volt Ma•
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 4 Four RealPower -9.9Z
-19.B4
-Z.6B
-39.6B
I09.Z4
1.79
-0.B9
-1.79
Z7.16
4 5 Five RealPower
5 2 Two Reactive power
6 3 Three Voltage Magnitude
7 4 Four Reactive power O.B9
1.79
7.46 -ll.9Z
3.57
3.57
-9.09
-9.9Z
-19.B4B 5 Five Reactive power
Search Now Options •
Jacobian Equation
19. Five Bus Power System Solved
slack
One
Tw o
ThreeFourFive
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1.000 pu
0.000 Deg
0.97 4 pu
-4.548 Deg
0.834 pu
-22.406 Deg
1.019 pu
-2.834 Deg
1.050 pu
-0.5 97 Deg
395 M W
114 M v ar
52 0 M W
33 7 M var
19
800 M W
280 M var
80 M W
40 M var
20. 37 Bus Example Design Case
Metropolis Light and Pow er Electric Design Case 2
A
SL A C K 3 4 5
RA Y 1 3 8
RA Y 6 9
MVA FERN A 6 9
A
DEM A R 6 9
B L T 6 9
B L T 1 3 8
B O B 1 3 8
B O B 6 9
WO L EN6 9
SH I M K O 6 9
7 .4 M v a r
1 4 M W RO GER6 9
UI UC6 9
MVA
P ET E6 9
H I SK Y 6 9
T I M 6 9
T I M 1 3 8
P A I 6 9
GRO SS6 9
H A NNA H 6 9
6 0 M W
A M A N DA 6 9
H O M ER6 9
L A U F6 9
M O R O 1 3 8
L A U F1 3 8
H A L E6 9
P A T T EN6 9
WEB ER6 9
B U CK Y 1 3 8
MVA
SA V O Y 6 9
1 .0 2 p u
3 8 M W
SA V O Y 1 3 8
JO 1 3 8 JO 3 4 5
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1 6 M W
- 1 4 M v a r
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 .0 2 p u A
MVA
MVA MVA
1 .0 3 p u
1 .0 2 p u
1 .0 3 p u
1 .0 1 p u
1 .0 0 p u
1 .0 1 p u
1 .0 0 p u
1 .0 2 p u
1 .0 1 p u
1 .0 0 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 0 p u
1 .0 0 p u
1 .0 2 p u
0 .9 9 p u
0 .9 9 p u
1 .0 0 p u
1 .0 2 p u
2 0 M W
2 8 M v a r
1 .0 0 p u
1 .0 1 p u
1 .0 1 p u
1 .0 0 p u 1 .0 0 p u
1 .0 1 p u
1 .0 2 p u
1 .0 3 p u
A
MVA
1 .0 2 p u
A
MVA
SL A C K 1 3 8 MVA
RA Y 3 4 5
T I M 3 4 5
MVA
A
MVA
A A
1 .0 3 p u
1 .0 2 p u
A
L Y NN 1 3 8
A
MVA
1 .0 2 p u
A
MVA
1 .0 0 p u
A
MVA
Syst em Losses: 10.70 MW
2 2 0 M W
5 2 M v a r
1 2 M W
3 M v a r
2 0 M W
1 2 M v a r
1 2 4 M W
4 5 M v a r
3 7 M W
1 3 M v a r
1 2 M W
5 M v a r
1 5 0 M W
0 M v a r
5 6 M W
1 3 M v a r
1 5 M W
5 M v a r
2 M v a r
3 M v a r
4 5 M W
0 M v a r
2 5 M W
3 6 M v a r
3 6 M W
1 0 M v a r
1 0 M W
5 M v a r
2 2 M W
1 5 M v a r
6 0 M W
1 2 M v a r
2 3 M W
7 M v a r
3 3 M W
1 3 M v a r
1 5 .9 M v a r 1 8 M W
5 M v a r
5 8 M W
4 0 M v a r
1 9 M v a r
1 4 .2 M v a r
2 5 M W
1 0 M v a r
2 0 M W
3 M v a r
2 3 M W
6 M v a r 1 4 M W
3 M v a r
4 .9 M v a r
7 .3 M v a r
1 2 .8 M v a r
2 8 .9 M v a r
0 .0 M v a r
5 5 M W
2 5 M v a r
3 9 M W
1 3 M v a r
1 5 0 M W
0 M v a r
1 7 M W
3 M v a r
1 4 M W
4 M v a r
KYLE6 9
A
20
MVA
21. Good Power System Operation
• Good power system operation requires that
there be no “reliability” violations (needing to
shed load, have cascading outages, or other
unacceptable conditions) for either the current
condition or in the event of statistically likely
contingencies:
• Reliability requires as a minimum that there be no
transmission line/transformer limit violations and
that bus voltages be within acceptable limits
(perhaps 0.95 to 1.08)
• Example contingencies are the loss of any single
device. This is known as n-1 reliability. 12
22. Looking at the Impact of Line Outages
Metropolis Light and Power Electric Design Case 2
A
SL A C K 3 4 5
MVA FERN A 6 9
A
DEM A R6 9
B L T 6 9
B L T 1 3 8
B O B 1 3 8
B O B 6 9
WO L EN6 9
SL A C K 1 3 8 MVA
RA Y 3 4 5
RA Y 1 3 8
RA Y 6 9
SH I M K O 6 9
7 .3 M v a r
1 4 M W RO GER6 9
UI UC6 9
MVA
P ET E6 9
H I SK Y 6 9
T I M 6 9
T I M 1 3 8
T I M 3 4 5
P A I 6 9
GRO SS6 9
H A NN A H 6 9
6 0 M W
A M A N DA 6 9
11 0 %
MVA
H O M ER6 9
L A U F6 9
M O R O 1 3 8
MVA
L A U F1 3 8
H A L E6 9
P A T T EN6 9
4 5 M W
0 M v a rWEB ER6 9
B U CK Y 1 3 8
MVA
SA V O Y 6 9
1 .0 2 p u
3 8 M W
SA V O Y 1 3 8
JO 1 3 8 JO 3 4 5
A
MVA
A
MVA
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1 6 M W
- 1 4 M v a r
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 .0 2 p u A
MVA
A
MVA
A
MVA
1 .0 3 p u
1 .0 2 p u
1 .0 3 p u
1 .0 3 p u
1 .0 1 p u
1 .0 0 p u
1 .0 1 p u
1 .0 0 p u
1 .0 2 p u
1 .0 1 p u
1 .0 0 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 2 p u
1 .0 1 p u
1 .0 0 p u
1 .0 2 p u
0 .9 0 p u
A 0 .9 0 p u
0 .9 4 p u
1 .0 1 p u
0 .9 9 p u
1 .0 0 p u
1 .0 0 p u
1 .0 0 p u 1 .0 0 p u
1 .0 1 p u
1 4 M W
3 M v a r
1 .0 1 p u
1 .0 3 p u
A
MVA
1 .0 2 p u
A
MVA
A
L Y NN 1 3 8
A
MVA
1 .0 2 p u
A
MVA
1 .0 0 p u
A
MVA
Syst em Losses: 17.61 MW
2 2 7 M W
4 3 M v a r
1 2 M W
3 M v a r
2 0 M W
1 2 M v a r
1 2 4 M W
4 5 M v a r
3 7 M W
1 3 M v a r
1 2 M W
5 M v a r
1 5 0 M W
4 M v a r
5 6 M W
1 3 M v a r
1 5 M W
5 M v a r
2 M v a r
9 M v a r
2 5 M W
3 6 M v a r
3 6 M W
1 0 M v a r
1 0 M W
5 M v a r
2 2 M W
1 5 M v a r
6 0 M W
1 2 M v a r
2 0 M W
4 0 M v a r
2 3 M W
7 M v a r
3 3 M W
1 3 M v a r
1 6 .0 M v a r 1 8 M W
5 M v a r
5 8 M W
4 0 M v a r
1 9 M v a r
1 1 .6 M v a r
2 5 M W
1 0 M v a r
2 0 M W
3 M v a r
2 3 M W
6 M v a r
4 .9 M v a r
7 .2 M v a r
1 2 .8 M v a r
2 8 .9 M v a r
0 .0 M v a r
5 5 M W
3 2 M v a r
3 9 M W
1 3 M v a r
1 5 0 M W
4 M v a r
1 7 M W
3 M v a r
1 4 M W
4 M v a r
KYLE6 9
A
MVA
A
8 0 %
135%
M VA
A
Opening
one line
(Tim69-
Hannah69)
causes
overloads.
This would
not be
Allowed.
22
24. Power Flow And Design
• One common usage of the power flow is to
determine how the system should be modified
to remove contingencies problems or serve new
load
• In an operational context this requires working with
the existing electric grid, typically involving re-
dispatch of generation.
• In a planning context additions to the grid can be
considered as well as re-dispatch.
• In the next example we look at how to remove
the existing contingency violations while serving
new load. 16
25. An Unreliable Solution:
some line outages result in overloads
B L T 6 9
B L T 1 3 8
Metropolis Light and Pow er Electric Design Case 2
A
SL A C K 3 4 5
SL A C K 1 3 8 MVA
RA Y 3 4 5
RA Y 1 3 8
RA Y 6 9
MVA FER N A 6 9
A
DEM A R 6 9
B O B 1 3 8
B O B 6 9
WO L EN 6 9
SH I M K O 6 9
7 .4 M v a r
1 4 M W RO GER 6 9
2 M v a r
UI U C 6 9
MVA
P ET E6 9
H I SK Y 6 9
T I M 6 9
T I M 1 3 8
T I M 3 4 5
P A I 6 9
GR O SS6 9
H A N N A H 6 9
6 0 M W
A M A N DA 6 9
H O M ER 6 9
L A U F6 9
M O R O 1 3 8
L A U F1 3 8
H A L E6 9
P A T T EN 6 9
4 5 M W
0 M v a rWEB ER 6 9
B U CK Y 1 3 8
MVA
SA V O Y 6 9
1 .0 2 p u
3 8 M W
SA V O Y 1 3 8
JO 1 3 8 JO 3 4 5
A
MVA
A
MVA
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1 6 M W
- 1 4 M v a r
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 .0 2 p u A
MVA
A
MVA
A
MVA
1 .0 2 p u
1 .0 1 p u
1 .0 2 p u
1 .0 3 p u
1 .0 1 p u
1 .0 0 p u
1 .0 1 p u
1 .0 0 p u
1 .0 2 p u
1 .0 1 p u
1 .0 0 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 2 p u
0 .9 9 p u
1 .0 0 p u
1 .0 2 p u
0 .9 7 p u
0 .9 7 p u
0 .9 9 p u
1 .0 2 p u
2 0 M W
4 0 M v a r
1 .0 0 p u
1 .0 1 p u
1 .0 1 p u
1 .0 0 p u 1 .0 0 p u
1 .0 1 p u
1 4 M W
3 M v a r
1 .0 2 p u
1 .0 3 p u
A
MVA
1 .0 2 p u
A
MVA
A
LY N N1 3 8
A
MVA
1 .0 2 p u
A
MVA
1 .0 0 p u
A
MVA
Syst em Losses: 14.49 MW
2 6 9 M W
6 7 M v a r
1 2 M W
3 M v a r
2 0 M W
1 2 M v a r
1 2 4 M W
4 5 M v a r
3 7 M W
1 3 M v a r
1 2 M W
5 M v a r
1 5 0 M W
1 M v a r
5 6 M W
1 3 M v a r
1 5 M W
5 M v a r
4 M v a r
2 5 M W
3 6 M v a r
3 6 M W
1 0 M v a r
1 0 M W
5 M v a r
2 2 M W
1 5 M v a r
6 0 M W
1 2 M v a r
2 3 M W
7 M v a r
3 3 M W
1 3 M v a r
1 5 .9 M v a r 1 8 M W
5 M v a r
5 8 M W
4 0 M v a r
1 9 M v a r
1 3 .6 M v a r
2 5 M W
1 0 M v a r
2 0 M W
3 M v a r
2 3 M W
6 M v a r
4 .9 M v a r
7 .3 M v a r
1 2 .8 M v a r
2 8 .9 M v a r
0 .0 M v a r
5 5 M W
2 8 M v a r
3 9 M W
1 3 M v a r
1 5 0 M W
1 M v a r
1 7 M W
3 M v a r
1 4 M W
4 M v a r
KYLE6 9
A
MVA
A
9 6 %
MVA
25
Case now
has nine
separate
contingencies
having
reliability
violations
(overloads in
post-contingency
system).
26. A Reliable Solution:
no line outages result in overloads
B L T 6 9
B L T 1 3 8
Metropolis Light and Power Electric Design Case 2
A
SL A C K 3 4 5
RA Y 6 9
MVA FERN A 6 9
A
DEM A R6 9
B O B 1 3 8
B O B 6 9
WO L EN6 9
SH I M K O 6 9
7 .4 M v a r
1 4 M W RO GER6 9
UI UC6 9
A M A N DA 6 9
H O M ER6 9
L A U F6 9
L A U F1 3 8
H A L E6 9
MVA
P ET E6 9
H I SK Y 6 9
T I M 6 9
T I M 1 3 8
P A I 6 9
GRO SS6 9
H A NN A H 6 9
6 0 M W
M O R O 1 3 8
P A T T EN6 9
4 5 M W
0 M v a rWEB ER6 9
B U CK Y 1 3 8
MVA
SA V O Y 6 9
1 .0 2 p u
3 8 M W
SA V O Y 1 3 8
JO 1 3 8 JO 3 4 5
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1 6 M W
- 1 4 M v a r
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 .0 2 p u A
MVA
1 .0 3 p u
1 .0 3 p u
1 .0 1 p u
1 .0 0 p u
1 .0 1 p u
1 .0 0 p u
1 .0 2 p u
1 .0 1 p u
1 .0 0 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 0 p u
0 .9 9 p u
1 .0 2 p u
0 .9 9 p u
0 .9 9 p u
1 .0 0 p u
1 .0 2 p u
2 0 M W
3 8 M v a r
1 .0 0 p u
1 .0 1 p u
1 .0 1 p u
1 .0 0 p u 1 .0 0 p u
1 .0 1 p u
1 4 M W
3 M v a r
1 .0 2 p u
1 .0 3 p u
A
MVA
1 .0 2 p u
A
MVA
SL A C K 1 3 8 MVA
26
RA Y 3 4 5
RA Y 1 3 8
T I M 3 4 5
MVA
A
MVA
A
MVA
A
MVA
1 .0 1 p u
1 .0 2 p u
1 .0 2 p u
A
L Y NN 1 3 8
A
MVA
1 .0 2 p u
A
MVA
A
MVA
Syst em Losses: 11.66 MW
2 6 6 M W
5 9 M v a r
1 2 M W
3 M v a r
2 0 M W
1 2 M v a r
1 2 4 M W
4 5 M v a r
3 7 M W
1 3 M v a r
1 2 M W
5 M v a r
1 5 0 M W
1 M v a r
5 6 M W
1 3 M v a r
1 5 M W
5 M v a r
2 M v a r
4 M v a r
2 5 M W
3 6 M v a r
3 6 M W
1 0 M v a r
1 0 M W
5 M v a r
2 2 M W
1 5 M v a r
6 0 M W
1 2 M v a r
2 3 M W
7 M v a r
3 3 M W
1 3 M v a r
1 5 .8 M v a r 1 8 M W
5 M v a r
5 8 M W
4 0 M v a r
1 9 M v a r
1 4 .1 M v a r
2 5 M W
1 0 M v a r
2 0 M W
3 M v a r
2 3 M W
6 M v a r
4 .9 M v a r
7 .3 M v a r
1 2 .8 M v a r
2 8 .9 M v a r
0 .0 M v a r
5 5 M W
2 9 M v a r
3 9 M W
1 3 M v a r
1 5 0 M W
1 M v a r
1 7 M W
3 M v a r
1 4 M W
4 M v a r
KYLE6 9
A
MVA
Ky le1 3 8
A
M V
A
Previous
case was
augmented
with the
addition of a
138 kV
Transmission
Line
27. 27
Generation Changes and The Slack
Bus
• The power flow is a steady-state analysis tool,
so the assumption is total load plus losses is
always equal to total generation
• Generation mismatch is made up at the slack bus
• When doing generation change power flow
studies one always needs to be cognizant of
where the generation is being made up
• Common options include “distributed slack,” where
the mismatch is distributed across multiple
generators by participation factors or by economics.
28. Generation Change Example 1
SL A C K 3 4 5
SL A C K 1 3 8 MVA
RA Y 3 4 5
RA Y 1 3 8
RA Y 6 9
MVA FERNA 6 9
A
DEM A R 6 9
B L T 6 9
B L T 1 3 8
B O B 1 3 8
B O B 6 9
WO L EN 6 9
SH I M K O 6 9
0 .0 M v a r
RO GER6 9
UI UC6 9
P ET E6 9
H I SK Y 6 9
T I M 6 9
T I M 1 3 8
T I M 3 4 5
P A I 6 9
GRO SS6 9
H A NN A H 6 9
A M A N DA 6 9
H O M ER6 9
L A U F6 9
M O R O 1 3 8
L A U F1 3 8
H A L E6 9
P A T T EN6 9
W EB ER6 9
B U CK Y 1 3 8
SA V O Y 6 9
SA V O Y 1 3 8
JO 1 3 8 JO 3 4 5
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 v a r
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 .0 0 2 p u MVA
0 .0 0 p u
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
0 .0 0 p u A
MVA
A
MVA
A
MVA
0 .0 0 p u
- 0 .0 1 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
- 0 .0 3 p u
- 0 .0 1 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
- 0 .0 3 p u
- 0 .0 1 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u 0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
A
MVA
MVA
- 0 .0 1 p u
A
A
L Y NN 1 3 8
A
MVA
0 .0 0 p u
A
MVA
0 .0 0 p u
A
MVA
1 6 2 M W
3 5 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
- 1 5 7 M W
- 4 5 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
2 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
3 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
4 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
- 0 .1 M v a r 0 M W
0 M v a r
0 M W
0 M v a r0 M W
0 M v a r
- 0 .1 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r 0 M W
0 M v a r
- 0 .1 M v a r
0 .0 M v a r
- 0 .1 M v a r
- 0 .2 M v a r
0 .0 M v a r
0 M W
5 1 M v a r
0 M W
0 M v a r
0 M W
2 M v a r
28
0 M W
0 M v a r
0 M W
0 M v a r
Display shows
“Difference
Flows”
between
original
37 bus case,
and case with
a BLT138
generation
outage;
note all the
power change
is picked
up at the slack
Slack bus
29. Generation Change Example 2
SL A C K 3 4 5
RA Y 6 9
MVA
FER NA 6
9
A
DEM A R6 9
B L T 6 9
B L T 1 3 8
B O B 1 3 8
B O B 6 9
WO L EN 6 9
SL A CK 1 3 8 MVA
RA Y 3 4 5
R A Y 1 3 8
SH I M K O 6 9
-0 .1 M v a r
RO G ER 6 9
UI U C6 9
P ET E6 9
H I SK Y 6 9
T I M 6 9
T I M 1 3 8
T I M 3 4 5
P A I 6 9
GR O SS 6 9
H A N NA H 6 9
A M A N DA 6 9
0 M W
0 M v a r
H O M ER 6 9
L A U F6 9
M O RO 1 3 8
L A U F1 3 8
H A L E6 9
P A T T EN 6 9
WEB ER 6 9
B U CK Y 1 3 8
SA V O Y 6 9 4 2 M W
SA V O Y 1 3 8
JO 1 3 8 JO 3 4 5
A
MVA
A
M VA
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 v a r
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 .0 0 3 p u M VA
0 .0 0 p u
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
M VA
A
MVA
A
MVA
A
MVA
0 .0 0 p u A
MVA
A
MVA
A
MVA
0 .0 0 p u
-0 .0 1 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
-0 .0 3 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
-0 .0 3 p u
-0 .0 1 p u
-0 .0 1 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u 0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
A
MVA
0 .0 0 p u
A
MVA
A
L Y N N 1 3 8
A
MVA
0 .0 0 p u
A
MVA
0 .0 0 p u
A
MVA
0 M W
3 7 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
- 1 5 7 M W
- 4 5 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
-1 4 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
9 9 M W
-2 0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
-0 .1 M v a r 0 M W
0 M v a r
0 M W
0 M v a r0 M W
0 M v a r
-0 .1 M v a r
0 M W
0 M v a r
0 M W
0 M v a r 0 M W
0 M v a r
0 .0 M v a r
0 .0 M v a r
-0 .1 M v a r
-0 .2 M v a r
0 .0 M v a r
1 9 M W
5 1 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
29
0 M W
0 M v a r
0 M W
0 M v a r
Display repeats previous case except now the change in
generation is picked up by other generators using a
“participation factor” (change is shared amongst generators) approach.
30. Voltage Regulation Example: 37 Buses
Display shows voltage contour of the power system
SL A C K 3 4 5
L A U F1 3 8
B U CK Y 1 3 8
SL A C K 1 3 8 MVA
RA Y 3 4 5
RA Y 1 3 8
RA Y 6 9
MVA
FERN A 6
9
A
DEM A R6 9
B L T 6 9
B L T 1 3 8
B O B 1 3 8
B O B 6 9
W O L EN6 9
SH I M K O 6 9
7 .4 M v a r
1 4 M W RO GER 6 9
2 M v a r
UI UC6 9
P ET E6 9
H I SK Y 6 9
T I M 6 9
T I M 1 3 8
T I M 3 4 5
P A I 6 9
GRO SS6 9
H A NNA H 6 9
A M A ND A 6 9
H O M ER 6 9
L A U F6 9
M O RO 1 3 8
H A L E6 9
P A T T EN 6
9 4 5 M W
0 M v a rW EB ER 6 9
1 .0 2 p u
SA V O Y 6 9 3 8 M W
SA V O Y 1 3 8
JO 1 3 8 JO 3 4 5
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 v aA
r
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
M VA
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
M VA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1 .0 2 p u A
MVA
A
MVA
A
MVA
1 .0 3 p u
1 .0 1 p u
1 .0 2 p u
1 .0 3 p u
1 .0 1 p u
1 .0 0 p u
1 .0 0 p u
0 .9 9 p u
1 .0 2 p u
1 .0 1 p u
1 .0 0 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 2 p u
1 .0 0 p u
1 .0 0 p u
1 .0 2 p u
0 .9 9 7 p u
0 .9 9 p u
3 3 M W
1 0 M v a r
1 .0 0 p u
1 .0 2 p u
1 .0 0 p u
1 .0 1 p u
1 .0 0 p u
1 .0 0 p u 1 .0 0 p u
1 .0 1 p u
1 .0 2 p u
1 .0 3 p u
A
M VA
1 .0 2 p u
A
MVA
A
L Y N N1 3 8
A
MVA
1 .0 2 p u
A
MVA
1 .0 0 p u
A
MVA
2 1 9 M W
5 2 M v a r
2 1 M W
7 M v a r
4 5 M W
1 2 M v a r
1 5 7 M W
4 5 M v a r
3 7 M W
1 3 M v a r
1 2 M W
5 M v a r
1 5 0 M W
0 M v a r
5 6 M W
1 3 M v a r
1 5 M W
5 M v a r
3 M v a r
5 8 M W
3 6 M v a r
3 6 M W
1 0 M v a r
0 M W
0 M v a r
2 2 M W
1 5 M v a r
6 0 M W
1 2 M v a r
2 0 M W
9 M v a r
2 3 M W
7 M v a r
3 3 M W
1 3 M v a r 1 5 .9 M v a r 1 8 M W
5 M v a r
5 8 M W
4 0 M v a r5 1 M W
1 5 M v a r
1 4 .3 M v a r
1 5 M W
3 M v a r
2 3 M W
6 M v a r 1 4 M W
3 M v a r
4 .8 M v a r
7 .2 M v a r
1 2 .8 M v a r
2 9 .0 M v a r
2 0 .8 M v a r
9 2 M W
1 0 M v a r
2 0 M W
8 M v a r
1 5 0 M W
0 M v a r
1 7 M W
3 M v a r
1 4 M W
4 M v a r
1 .0 1 0 p u
0.0 M va r
Syst em Lo sses: 11.5 1 MW
Automatic voltage regulation system controls voltages.
30
31. Real-sized Power Flow Cases
• Real power flow studies are usually done with
cases with many thousands of buses
• Outside of ERCOT, buses are usually grouped into
various balancing authority areas, with each area
doing its own interchange control.
• Cases also model a variety of different
automatic control devices, such as generator
reactive power limits, load tap changing
transformers, phase shifting transformers,
switched capacitors, HVDC transmission lines,
and (potentially) FACTS devices. 23
32. Sparse Matrices and Large Systems
• Since for realistic power systems the model
sizes are quite large, this means the Ybusand
Jacobian matrices are also large.
• However, most elements in these matrices are
zero, therefore special techniques, sparse
matrix/vector methods, are used to store the
values and solve the power flow:
• Without these techniques large systems would be
essentially unsolvable.
24
33. 33
Interconnected Operation
Power systems are interconnected across
large distances.
For example most of North America east of
the Rockies is one system, most of North
America west of the Rockies is another.
Most of Texas and Quebec are each
interconnected systems.
34. total gen - total load - total losses = tie-line flow28
Balancing Authority Areas
A “balancing authority area” (previously called a
“control area”) has traditionally represented the
portion of the interconnected electric grid
operated by a single utility or transmission
entity.
Transmission lines that join two areas are
known as tie-lines.
T h e net power out of an area is the sum of
the flow on its tie-lines.
T h e flow out of an area is equal to
35. controlling frequency. 29
Area Control Error (ACE)
T h e area control error is a combination
of:
the deviation of frequency from nominal, and
the difference between the actual flow out of an
area and the scheduled (agreed) flow.
T h a t is, the area control error (ACE) is
the difference between the actual flow out
of an area minus the scheduled flow, plus a
frequency deviation component:
ACE provides a measure of whether an area
is producing more or less than it should to
satisfy schedules and to contribute to
Pactual tie-line flow Psched 10fACE
36. other areas. 30
Area Control Error (ACE)
T h e ideal is for ACE to be zero.
Because the load is constantly changing,
each area must constantly change its
generation to drive the ACE towards zero.
For ERCOT, the historical ten control areas
were amalgamated into one in 2001, so the
actual and scheduled interchange are
essentially the same (both small compared
to total demand in ERCOT).
In ERCOT, ACE is predominantly due to
frequency deviations from nominal since
there is very little scheduled flow to or from
37. Automatic Generation Control
Most systems use automatic generation
control (AGC) to automatically change
generation to keep their ACE close to zero.
U s u ally the control center (either ISO
or utility) calculates ACE based upon tie-
line flows and frequency; then the AGC
module sends control signals out to the
generators every four seconds or so.
31
38. Power Transactions
Power transactions are contracts between
generators and (representatives of) loads.
Contracts can be for any amount of time at
any price for any amount of power.
S c heduled power transactions between
balancing areas are called “interchange” and
implemented by setting the value of Pschedused
in the ACE calculation:
ACE = Pactualtie-lineflow– Psched+ 10β Δf
…and then controlling the generation to bring
ACE towards zero.
32
39. 39
“Physical” power Transactions
• For ERCOT, interchange is only relevant over
asynchronous connections between ERCOT
and Eastern Interconnection or Mexico.
• In Eastern and Western Interconnection,
interchange occurs between areas connected
by AC lines.
40. Three Bus Case on AGC:
no interchange.
Bus 2 Bus 1
1.00 PU
78 MW
-21 MVR
Bus 3Home Area
266 MW
133 MVR
150 MW AGC ON
166 MVR AVR ON
250 MW AGC ON
34 MVR AVR ON
133 MW
67 MVR
1.00 PU
-40 MW
8 MVR
40 MW
-8 MVR
-77 MW
25 MVR
39 MW
-11 MVR
1.00 PU
-39 MW
12 MVR
101 MW
5 MVR
100 MW
Net tie-line flow is
close to zero
Generation
40
is automatically
changed to match
change in load
41. 100 MW Transaction between
areas in Eastern or Western
Bus 2 Bus 1
1.00 PU
85 MW
-23 MVR
Bus 3Home Area
Scheduled Transactions
100.0 MW
225 MW
113 MVR
150 MW AGC ON
138 MVR AVR ON
291 MW AGC ON
8 MVR AVR ON
113 MW
56 MVR
1.00 PU
8 MW
-2 MVR
-8 MW
2 MVR
-84 MW
27 MVR
93 MW
-25 MVR
1.00 PU
-92 MW
30 MVR
0 MW
32 MVR
100 MW
Scheduled
41
100 MW
Transaction from Left to Right
Net tie-line
flow is now
100 MW
42. PTDFs
Power transfer distribution factors (PTDFs)
show the linearized impact of a transfer of
power.
P T D F s calculated using the fast
decoupled power flow B matrix:
θ B1
P
Once we know θ we can derive the change in
the transmission line flows to evaluate PTDFs.
Note that we can modify several elements in P,
in proportion to how the specified generators would
participate in the power transfer. 36
43. Nine Bus PTDF Example
10%
60%
55%
11%
64%
57%
A
G
B
C
D
EF
300.0 MW
400.0 MW 300.0 MW
250.0 MW
150.0 MW
71%
0.00 deg
71.1 MW
92%
44% 32%250.0 MW74% 250.0 MW
24%
IH
200.0 MW
150.0 MW
37
Figure shows initial flows for a nine bus power system
44. Nine Bus PTDF Example, cont'd
43%
57%
13%
35%
2%
20%
10%
A
G
B
C
D
EF
300.0 MW
400.0 MW 300.0 MW
250.0 MW
150.0 MW
34% 32%250.0 MW34% 250.0 MW
34%
IH
200.0 MW
150.0 MW
38
30%
0.00 deg
71.1 MW
Figure now shows percentage PTDF flows for a change in transaction from A to I
45. Nine Bus PTDF Example, cont'd
6%
6%
12%
61%
19%
12%
6%
21%
21%
A
G
B
C
D
E
I
F
H
300.0 MW
400.0 MW 300.0 MW
250.0 MW
250.0 MW
200.0 MW
3
250.0 MW
150.0 MW
150.0 MW
20%
18%
0.00 deg
71.1 MW
Figure now shows percentage PTDF flows for a change in transaction from G to F
46. 46
Line Outage Distribution Factors
(LODFs)
• LODFs are used to approximate the change in
the flow on one line caused by the outage of a
second line
– typically they are only used to determine the
change in the MW flow compared to the pre-
contingency flow if a contingency were to occur,
– LODFs are used extensively in real-time
operations,
– LODFs are approximately independent of flows but
do depend on the assumed network topology.
47. 47
Line Outage Distribution Factors
(LODFs)
Pl change in flow on line l,
due to outage of line k.
Pk pre-contingency flow on line k
Pl LODFl,k Pk ,
Estimates change in flow on line l
if outage on line k were to occur.
48. 48
Line Outage Distribution Factors
(LODFs)
and then there was an outage of line k,
if LODFl,k =0.1 then the increase in flow
on line l after a contingency of line k would be:
Pl LODFl,k Pk 0.1 100 10 MW
from 50 MW to 60 MW.
If line k initially had Pk 100 MW of flow on it,
and line l initially had Pl 50 MW flow on it,
49. UNIT 3 & UNIT 4
BALANCED AND UNBALANCED
FAULT ANALYSIS
50. INTRODUCTION
A fault calculation is the analysis of the power system electrical behaviour under
fault conditions, with particular reference to the effects on the system currents
and voltages. Accurate fault calculations are essential for proper system design.
The analysis of fault conditions and their effects on the power system is of
particular relevance to such conditions as:
SLID 5
a
.
the choice of a suitable power system arrangement, with particular
reference to the configuration of the transmission or distribution
network.
the determination of the required load and short-circuit ratings of the
power system plant.
the determination of the breaking capacity required of the power system
b
.
c
.switchgear and
fusegear.d
.
the design and application of equipment for the control and protection
of the power system.
the operation of the system, with particular reference to security of
supply and economic considerations.
the investigation of unsatisfactory performance of the power system or of
e
.
f.
individual items of power system
plant.
51. TypesofFault
In the context of electrical fault calculations, a power system fault
may be defined as any condition or abnormality of the system
which involves the electrical failure of primary equipment, i.e.
generators, transformers, busbars, overhead lines and cables and
all other items of plant which operate at power system voltage.
SLID 5
Electrical failure generally implies one of two conditions or types
of failure (sometimes both), namely insulation failure resulting in
a short-circuit condition or a conducting path failure resulting in
an open-circuit condition, the former being by far the more
common type of failure.
52. a) Short-circuitedphases
Faults of this type are caused by insulation failure between phase conductors or between
phase conductors and earth, or both. Figure 1 gives details of the various short-
circuited-phase faults.
SLID 5
The three-phase fault, which may or may not be to earth, is the only balanced short-
circuit condition and is the one used as the standard in determining the system fault
levels or ratings.
53. c) Simultaneousfaults
A simultaneous fault condition, or a multiple fault condition, is
defined as the simultaneous presence of two or more faults which
may be of similar or dissimilar types and may be at the same or
different points in the power system.
SLID 5
The most common simultaneous fault condition is undoubtedly
the double-circuit overhead line fault in which a common
cause, i.e. lightning or clashing conductors, results in a fault on
each of the two circuits concerned.
Another simultaneous fault condition is known as the cross-
country earth-fault, in which a single-phase to earth fault at one
point occurs coincidentally with a second such fault on another
phase at some other point in the system.
54. d)
Windi
ngfaults
This type of fault, which can occur in machine or transformer windings, is detailed in
Figure 3, and consists mainly of short circuits, from one phase to earth, or from phase to
phase, or from one point
to another on the same phase winding. The last fault condition is known as the short-
circuited
turns fault. This condition can pose special problems from a protection point of view
because the current in the shorted turns can be very large, while that in the remainder of
the winding may be quite small.
Short-circuited turns Open-circuited winding
The open-circuited winding condition is quite rare in practice and is usually the result of
damage to the winding as a consequence of a preceding winding short circuit at or near the
point of fault. Open circuits in transformers may also occur as a result of failure of tap-
changing equipment.
SLID 5
Phase-to-earth
fault
Phase-to-phase
fault
Figure 3. Winding
faults
55. FactorsAffectingFaultSeverity
The severity of a power system fault condition may be assessed in terms
of the disturbance produced and the fault damage caused, the magnitude
of the fault current and its duration being of particular interest, especially
in relation to the design and application of the power system protection.
The main factors which affect the severity of a fault are:
a) Sourceconditions
These relate to the amount and location of all connected generation
equipment - including the ties or interconnections with other systems, the
two extremes of minimum and maximum connected plant being of
particular interest. The minimum and maximum plant conditions are
normally those corresponding to the conditions of minimum and maximum
connected load.
SLID 5
56. b) Powersystemconfiguration
This is determined by the items of plant, i.e. generators, transformers,
overhead lines and cable circuits, etc., assumed to be in service for the
particular condition being investigated and by other such factors as may have a
bearing on the make-up of the equivalent circuit of the system. The system
configuration may change during the course of a fault with consequent changes
in the magnitude and distribution of the fault currents. Typical causes of the
above changes being the sequential tripping of the circuit-breakers at the two
ends of the faulted transmission line and the sequential clearance of multiple
fault conditions.
SLID 5
57. c) Neutralearthing
Faults which involve the flow of earth current, i.e. phase faults to
earth, may be influenced considerably by the system neutral earthing
arrangements, particularly by the number of neutral earthing points
and the presence or absence of neutral earthing impedance. The
power system may be single-point or multiple-point earthed and such
earthing may be direct, i.e. solid earthing, or via a neutral impedance.
The 132kV, 275kV and the 400kV systems employ direct multiple
earthing while the 66kV and below generally employ single-point,
sometimes multiple, resistance earthing.
SLID 5
58. d) Natureandtypeoffault
From what has been said already, it is evident that the type
and location of a fault will have a significant effect on the
magnitude and distribution of the system fault currents.
Likewise, the
effect of a given fault condition may be considerably modified
by the simultaneous presence of one or more other fault
conditions, for example, the combination of a short circuit and
an open-circuited phase condition.
SLID 5
59. The wide range of possible system fault conditions and the
many factors which influence them result in a wide range of
possible fault severity, ranging from very low levels up to the
maximum level possible for the system. It is of value to
consider a standard fault condition when discussing systems
and the three-phase fault level may be expressed in amperes
but it is usually expressed in MVA, corresponding to the rated
system voltage and the current for a symmetrical three-phase
fault. This three-phase fault level normally
determines the required short-circuit rating of the power
system switchgear. A factor which may also have to be taken
into account is the maximum value of the one-phase to earth
fault current which, in a solidly earthed system, may exceed
the maximum three-phase fault current.
SLID 5
60. MethodsofFault
Calculation
SLID 6
♦ The information normally required from a fault calculation is
thatwhich gives the values of the currents and voltages at stated points in
the power system when a given fault condition is imposed on the
s
ystem.♦ A fault calculation is therefore, essentially a matter of
networkanalysis and can be achieved by a number of methods, i.e.
mesh-
current
ornodal-voltage methods, network reduction
techniques or network analyser.
simulation using
a
♦ The choice of method depends on the size and complexity
of thecircuit model and the availability of computing
facilities.
61. MethodsofFaultCalculation
SLID 6
♦ An essential part of power system analysis and fault
calculation is that which concerns the determination of the
equivalent system network for the system operating
conditions and the faultconditions under
consideration.
♦ As stated earlier, faults can be subdivided into either
balanced (symmetrical) or unbalanced (unsymmetrical)
fault conditions, latter case being analysed, traditionally,
by the method of
thi
ssymmetrical
components.
♦ Both classes of fault are analysed by reducing the power
system, with its fault condition, to an equivalent single-
phase network.
62. BalancedFaults
The balanced fault is often the severest and is the simplest to determine.
Hence, this is the one normally used to determine the 'duty' of the system
switchgear and busbars
FaultCalculationProcedure
The analysis of a 3-phase balanced fault condition consists, in general, of three
parts:
SLID 6
a.
networ
k, b.
c.
the system with its fault condition is represented by its positive
sequence
the network is solved in terms of per-unit quantities,
the resulting per-unit quantities are converted to actual
values.
Component
Representation
Overhead lines and cables are normally represented by their series impedance
on the basis that the shunt impedance is high. Transformers and synchronous
machines are normally represented by their reactances as the resistance values
are relatively small. Load impedances are normally much larger than the other
network impedances and
hence, they are normally neglected in fault
calculations.
63. THREEPHASEFAULTS
The following example is presented to illustrate the methods employed
for the case which induces positive sequence components only. The
system shown represents a power station connected to the grid, together
with its auxiliary systems. The principle circuit and plant parameters
are given in Table 1.
SLID 6
65. G2/
3
SLID 6
71 MVA, X = 263 pu on 100
MVA
T2/T
3
71 MVA, Xl =
009pu
G (2500-147-
71)MVA
G
1
147 MVA, Xd = 1867
pu
T
1
150 MVA, Xl = 013
pu
T
4
16 MVA, Xl = 01
pu
T
5
16 MVA, Xl = 009
pu
T
6
2 MVA, Xl = 006
pu
T
7
4 MVA, Xl - 006
pu
M
1
88
MVA
M
2
806
MVA
M
3
1247
MVA
M
4
0977
MVA
S
L
0918 MW, 09
p.f.
Table
1
67. The resolution of the problem into sequence components results in
considerable simplification of all problems involving asymmetry such as that
introduced by short- circuiting conductors of a system either together or to
earth, singly or in pairs, or by the open circuiting of a conductor. The
resolution of the problem into sequence components has the further advantage
in that it isolates the quantities into components which represent a better
criteria of the controlling factor or factors in certain phenomena.
Consider the following system of vectors shown below.
SLID 6
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78. Rewriting equation (1), and for convenience neglecting the bar denoting vector
quantities
Va = Va1 + Va2 + Va0
Vb = λ2Va1 + λVa2 +
Va0 Vc = λVa1 + λ2Va2
+ Va0
(2
)
and Va0, Va1 and Va2 may now be written as V0, V1 and V2
where λ is an operator which moves a vector 120°
anticlockwise, i.e.
λ = 0.5 +
0.886j λ2 = - 0.5
– 0.886j λ3 = 1
(3
)
Other useful identities in are given in the following
Table 1.
Table 1
SLID 7
79. The transformation of phase quantities to sequence and reverse is
given by [Vph] = [T] [Vseq]
an
d
[Vseq] = [T] -1
[Vph]
wher
e
[T]
=
(4
)
an
d
[T] -1
=
(5
)
SLID 7
80. An untransposed transmission line gives rise to 3 per cent negative sequence
voltage. Show approximately how this affects the magnitudes of the terminal
voltages of the generator supplying the system.
SLID 8
No zero sequences voltage; let V2 = 003 V1
Va = V1 + 003V1 = (1 + 003)V1
Vb = 2
V1 + 003V1 = (2
+
003)V1 Vc = V1 + 2
003V1 =
( + 0032
)V1
81. Components of
voltage
VA = 0 and since the generator is only able to generate positive sequence
components, E0 = E2 = 0
Also, since IB = IC = 0, I0 = I2 = 0
0
SLID 8
Z1 Z2
Z
E
11I
82. PRACTICALFAULT
STUDIES
SLID 8
As previously stated, power systems are subject to excessive damage when
high magnitude currents are flowing due to system short circuit. The
analysis so far has been confined to steady-state conditions arising
subsequent to fault incidence. The initial transient condition has been
neglected which, for many practical situations, is considered to be
satisfactory. However, the instant of initiation of the short circuit relative to
the voltage waveform, has a marked effect upon the maximum peak value of
the short-circuit current which may be important from the point of view of
fast acting fault clearance devices, i.e. does the circuit breaker operate prior
to the decay of the transient component of the current.
83. The total current is obtained by adding the steady-state and the transient
components.
SLIDE 83
84. In practice, the time variation of the short circuit current is dependent
on the actual characteristic of the generator. To a close approximation,
the short circuit current can be allocated to the following categories:
SLID 8
1
.
2
.
3
.
the continuous
component the transient
component the
subtransient component
These categories are determined by the electromagnetic process that
occurs in the generator. For most fault studies, the representation and
calculation of the short circuit characteristics are based on a constant
voltage and on the assumption that the decay of the ac short-circuit
current is due to an increase in the generator reactances from
(1) the subtransient
reactance
Xd
"
to (2) the transient reactance Xd'
and finally (3) the synchronous
reactance
Xd
85. SynchronousandInductionMotorLoads
SLID 8
For a short-circuit period of T ≤ 0·2s, synchronous motors can be
treated in the same manner as synchronous generators. In a larger
short-circuit period, the machine is subjected to a speed drop and is
then operating in an assynchronous mode. High and low voltage
motors similarly make a contribution to the short-circuit current.
However, due to differences in their construction, this contribution
decays very rapidly.
Short-circuit analysis is generally preceded by data collection and
the preparation of a one-line diagram, followed by the
determination of the exact objectives of the study. Table 2 gives
an indication of parameter values to be used under certain
circumstances.
