ee 369 power system analysis lecture 14 power flow tom overbye and ross baldick 1
Post on 16-Dec-2015
251 Views
Preview:
TRANSCRIPT
EE 369POWER SYSTEM ANALYSIS
Lecture 14Power Flow
Tom Overbye and Ross Baldick
1
AnnouncementsRead Chapter 12, concentrating on sections
12.4 and 12.5. Homework 12 is 6.43, 6.48, 6.59, 6.61,
12.19, 12.22, 12.20, 12.24, 12.26, 12.28, 12.29; due Tuesday Nov. 25.
2
400 MVA15 kV
400 MVA15/345 kV
T1
T2800 MVA345/15 kV
800 MVA15 kV
520 MVA
80 MW40 Mvar
280 MVAr 800 MW
Line 3 345 kV
Line
2
Line
1345 kV 100 mi
345 kV 200 mi
50 mi
1 4 3
2
5
Single-line diagram
The N-R Power Flow: 5-bus Example
3
Bus Type
|V|
per unit
θ
degrees
PG
per
unit
QG
per
unit
PL
per
unit
QL
per
unit
QGmax
per
unit
QGmin
per
unit
1 Slack 1.0 0 0 0
2 Load 0 0 8.0 2.8
3 Constant voltage
1.05 5.2 0.8 0.4 4.0 -2.8
4 Load 0 0 0 0
5 Load 0 0 0 0
Table 1. Bus input data
Bus-to-Bus
R
per unit
X
per unit
G
per unit
B
per unit
Maximum
MVA
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
Table 2. Line input data
The N-R Power Flow: 5-bus Example
4
Bus-to-Bus
R
per
unit
X
per
unit
Gc
per
unit
Bm
per
unit
Maximum
MVA
per unit
Maximum
TAP
Setting
per unit
1-5 0.00150 0.02 0 0 6.0 —
3-4 0.00075 0.01 0 0 10.0 —
Table 3. Transformer input data
Bus Input Data Unknowns
1 |V1 |= 1.0, θ1 = 0 P1, Q1
2 P2 = PG2-PL2 = -8
Q2 = QG2-QL2 = -2.8
|V2|, θ2
3 |V3 |= 1.05
P3 = PG3-PL3 = 4.4
Q3, θ3
4 P4 = 0, Q4 = 0 |V4|, θ4
5 P5 = 0, Q5 = 0 |V5|, θ5
Table 4. Input data and unknowns
The N-R Power Flow: 5-bus Example
5
Let the Computer Do the Calculations! (Ybus Shown)
6
Ybus Details
02321 YY
2424 24
1 10.89276 9.91964
0.009 0.1Y j per unit
R jX j
2525 25
1 11.78552 19.83932
0.0045 0.05Y j per unit
R jX j
24 2522
24 24 25 25
1 1
2 2
B BY j j
R jX R jX
2
88.0
2
72.1)83932.1978552.1()91964.989276.0( jjjj
unitperj 624.845847.284590.2867828.2
Elements of Ybus connected to bus 2
7
Here are the Initial Bus Mismatches
8
And the Initial Power Flow Jacobian
9
Five Bus Power System Solved
slack
One
Two
ThreeFourFiveA
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1.000 pu 0.974 pu
0.834 pu
1.019 pu
1.050 pu 0.000 Deg -4.548 Deg
-22.406 Deg
-2.834 Deg
-0.597 Deg
395 MW
114 Mvar
520 MW
337 Mvar
800 MW 280 Mvar
80 MW 40 Mvar
10
37 Bus Example Design Case
slack
Metropolis Light and Power Electric Design Case 2SLACK345
SLACK138
RAY345
RAY138
RAY69
FERNA69
A
MVA
DEMAR69
BLT69
BLT138
BOB138
BOB69
WOLEN69
SHI MKO69
ROGER69
UI UC69
PETE69HI SKY69
TI M69
TI M138
TI M345
PAI 69
GROSS69
HANNAH69
AMANDA69
HOMER69
LAUF69
MORO138
LAUF138
HALE69
PATTEN69
WEBER69
BUCKY138
SAVOY69
SAVOY138
J O138 J O345
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
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
1.03 pu
1.02 pu
1.03 pu
1.03 pu
1.01 pu
1.00 pu1.01 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
1.00 pu
1.00 pu
1.02 pu
0.99 pu
0.99 pu
1.00 pu
1.02 pu
1.00 pu1.01 pu
1.01 pu
1.00 pu 1.00 pu
1.01 pu
1.02 pu 1.02 pu
1.02 pu 1.03 pu
A
MVA
1.02 pu
A
MVA
A
MVA
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 Mvar
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
14 MW
2 Mvar
38 MW 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
20 MW 28 Mvar
23 MW 7 Mvar
33 MW 13 Mvar
15.9 Mvar 18 MW 5 Mvar
58 MW 40 Mvar
60 MW 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
7.4 Mvar
0.0 Mvar
55 MW 25 Mvar
39 MW 13 Mvar
150 MW 0 Mvar
17 MW 3 Mvar
16 MW -14 Mvar
14 MW 4 Mvar
KYLE69A
MVA
11
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
Good Power System Operation
• North American Electric Reliability Corporation now has legal authority to enforce reliability standards (and there are now lots of them).
• See http://www.nerc.com for details (click on Standards)
13
Looking at the Impact of Line Outages
slack
Metropolis Light and Power Electric Design Case 2SLACK345
SLACK138
RAY345
RAY138
RAY69
FERNA69
A
MVA
DEMAR69
BLT69
BLT138
BOB138
BOB69
WOLEN69
SHI MKO69
ROGER69
UI UC69
PETE69HI SKY69
TI M69
TI M138
TI M345
PAI 69
GROSS69
HANNAH69
AMANDA69
HOMER69
LAUF69
MORO138
LAUF138
HALE69
PATTEN69
WEBER69
BUCKY138
SAVOY69
SAVOY138
J O138 J O345
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
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1.03 pu
1.02 pu
1.03 pu
1.03 pu
1.01 pu
1.00 pu1.01 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
0.90 pu
0.94 pu
1.01 pu
0.99 pu1.00 pu
1.00 pu
1.00 pu 1.00 pu
1.01 pu
1.01 pu 1.02 pu
1.02 pu 1.03 pu
A
MVA
1.02 pu
A
MVA
A
MVA
LYNN138
A
MVA
1.02 pu
A
MVA
1.00 pu
A
MVA
System Losses: 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
14 MW
2 Mvar
38 MW 9 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
20 MW 40 Mvar
23 MW 7 Mvar
33 MW 13 Mvar
16.0 Mvar 18 MW 5 Mvar
58 MW 40 Mvar
60 MW 19 Mvar
11.6 Mvar
25 MW 10 Mvar
20 MW 3 Mvar
23 MW 6 Mvar 14 MW
3 Mvar
4.9 Mvar
7.2 Mvar
12.8 Mvar
28.9 Mvar
7.3 Mvar
0.0 Mvar
55 MW 32 Mvar
39 MW 13 Mvar
150 MW 4 Mvar
17 MW 3 Mvar
16 MW -14 Mvar
14 MW 4 Mvar
KYLE69A
MVA
80%A
MVA
135%A
MVA
110%A
MVA
Opening one line (Tim69-Hannah69) causes overloads. This would not be Allowed.
14
Contingency Analysis
Contingencyanalysis providesan automaticway of lookingat all the statisticallylikely contingencies. Inthis example thecontingency setis all the single line/transformeroutages
15
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
An Unreliable Solution:some line outages result in overloads
slack
Metropolis Light and Power Electric Design Case 2SLACK345
SLACK138
RAY345
RAY138
RAY69
FERNA69
A
MVA
DEMAR69
BLT69
BLT138
BOB138
BOB69
WOLEN69
SHI MKO69
ROGER69
UI UC69
PETE69HI SKY69
TI M69
TI M138
TI M345
PAI 69
GROSS69
HANNAH69
AMANDA69
HOMER69
LAUF69
MORO138
LAUF138
HALE69
PATTEN69
WEBER69
BUCKY138
SAVOY69
SAVOY138
J O138 J O345
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
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
1.01 pu
1.02 pu
1.03 pu
1.01 pu
1.00 pu1.01 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
1.00 pu1.01 pu
1.01 pu
1.00 pu 1.00 pu
1.01 pu
1.02 pu 1.02 pu
1.02 pu 1.03 pu
A
MVA
1.02 pu
A
MVA
A
MVA
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
14 MW
2 Mvar
38 MW 4 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
20 MW 40 Mvar
23 MW 7 Mvar
33 MW 13 Mvar
15.9 Mvar 18 MW 5 Mvar
58 MW 40 Mvar
60 MW 19 Mvar
13.6 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
7.4 Mvar
0.0 Mvar
55 MW 28 Mvar
39 MW 13 Mvar
150 MW 1 Mvar
17 MW 3 Mvar
16 MW -14 Mvar
14 MW 4 Mvar
KYLE69A
MVA
96%A
MVA
Case now has nine separate contingencies having reliability violations(overloads in post-contingency system).
17
A Reliable Solution:no line outages result in overloads
slack
Metropolis Light and Power Electric Design Case 2SLACK345
SLACK138
RAY345
RAY138
RAY69
FERNA69
A
MVA
DEMAR69
BLT69
BLT138
BOB138
BOB69
WOLEN69
SHI MKO69
ROGER69
UI UC69
PETE69HI SKY69
TI M69
TI M138
TI M345
PAI 69
GROSS69
HANNAH69
AMANDA69
HOMER69
LAUF69
MORO138
LAUF138
HALE69
PATTEN69
WEBER69
BUCKY138
SAVOY69
SAVOY138
J O138 J O345
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
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
1.03 pu
1.01 pu
1.02 pu
1.03 pu
1.01 pu
1.00 pu1.01 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
1.00 pu
0.99 pu
1.02 pu
0.99 pu
0.99 pu
1.00 pu
1.02 pu
1.00 pu1.01 pu
1.01 pu
1.00 pu 1.00 pu
1.01 pu
1.02 pu 1.02 pu
1.02 pu 1.03 pu
A
MVA
1.02 pu
A
MVA
A
MVA
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
14 MW
2 Mvar
38 MW 4 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
20 MW 38 Mvar
23 MW 7 Mvar
33 MW 13 Mvar
15.8 Mvar 18 MW 5 Mvar
58 MW 40 Mvar
60 MW 19 Mvar
14.1 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
7.4 Mvar
0.0 Mvar
55 MW 29 Mvar
39 MW 13 Mvar
150 MW 1 Mvar
17 MW 3 Mvar
16 MW -14 Mvar
14 MW 4 Mvar
KYLE69A
MVA
Kyle138A
MVA
Previous case was augmented with the addition of a 138 kV Transmission Line
18
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.
19
Generation Change Example 1
slack
SLACK345
SLACK138
RAY345
RAY138
RAY69
FERNA69
A
MVA
DEMAR69
BLT69
BLT138
BOB138
BOB69
WOLEN69
SHI MKO69
ROGER69
UI UC69
PETE69
HI SKY69
TI M69
TI M138
TI M345
PAI 69
GROSS69
HANNAH69
AMANDA69
HOMER69
LAUF69
MORO138
LAUF138
HALE69
PATTEN69
WEBER69
BUCKY138
SAVOY69
SAVOY138
J O138 J O345
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
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
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 pu0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu
-0.002 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu0.00 pu
0.00 pu
0.00 pu 0.00 pu
0.00 pu
0.00 pu0.00 pu
0.00 pu0.00 pu
A
MVA
-0.01 pu
A
MVA
A
MVA
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 -45 Mvar
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 Mvar 0 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
0.0 Mvar
0 MW 51 Mvar
0 MW 0 Mvar
0 MW 2 Mvar
0 MW 0 Mvar
0 MW 0 Mvar
0 MW 0 Mvar
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
20
Generation Change Example 2
slack
SLACK345
SLACK138
RAY345
RAY138
RAY69
FERNA69
A
MVA
DEMAR69
BLT69
BLT138
BOB138
BOB69
WOLEN69
SHI MKO69
ROGER69
UI UC69
PETE69
HI SKY69
TI M69
TI M138
TI M345
PAI 69
GROSS69
HANNAH69
AMANDA69
HOMER69
LAUF69
MORO138
LAUF138
HALE69
PATTEN69
WEBER69
BUCKY138
SAVOY69
SAVOY138
J O138 J O345
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
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
0.00 pu
-0.01 pu
0.00 pu
0.00 pu
0.00 pu
-0.03 pu0.00 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
-0.003 pu
0.00 pu
0.00 pu
0.00 pu
0.00 pu0.00 pu
0.00 pu
0.00 pu 0.00 pu
0.00 pu
0.00 pu0.00 pu
0.00 pu0.00 pu
A
MVA
0.00 pu
A
MVA
A
MVA
LYNN138
A
MVA
0.00 pu
A
MVA
0.00 pu
A
MVA
0 MW 37 Mvar
0 MW 0 Mvar
0 MW 0 Mvar
-157 MW -45 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
42 MW -14 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
99 MW -20 Mvar
0 MW 0 Mvar
0 MW 0 Mvar
-0.1 Mvar 0 MW 0 Mvar
0 MW 0 Mvar 0 MW
0 Mvar
-0.1 Mvar
0 MW 0 Mvar
0 MW 0 Mvar
0 MW 0 Mvar 0 MW
0 Mvar
0.0 Mvar
0.0 Mvar
-0.1 Mvar
-0.2 Mvar
-0.1 Mvar
0.0 Mvar
19 MW 51 Mvar
0 MW 0 Mvar
0 MW 0 Mvar
0 MW 0 Mvar
0 MW 0 Mvar
0 MW 0 Mvar
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.
21
Voltage Regulation Example: 37 Buses
Display shows voltage contour of the power system
slack
SLACK345
SLACK138
RAY345
RAY138
RAY69
FERNA69
A
MVA
DEMAR69
BLT69
BLT138
BOB138
BOB69
WOLEN69
SHI MKO69
ROGER69
UI UC69
PETE69
HI SKY69
TI M69
TI M138
TI M345
PAI 69
GROSS69
HANNAH69
AMANDA69
HOMER69
LAUF69
MORO138
LAUF138
HALE69
PATTEN69
WEBER69
BUCKY138
SAVOY69
SAVOY138
J O138 J O345
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
MVAA
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
A
MVA
A
MVA
1.03 pu
1.01 pu
1.02 pu
1.03 pu
1.01 pu
1.00 pu1.00 pu
0.99 pu
1.02 pu
1.01 pu
1.00 pu
1.01 pu1.01 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
1.00 pu
1.02 pu
1.00 pu1.01 pu
1.00 pu
1.00 pu 1.00 pu
1.01 pu
1.02 pu1.02 pu
1.02 pu 1.03 pu
A
MVA
1.02 pu
A
MVA
A
MVA
LYNN138
A
MVA
1.02 pu
A
MVA
1.00 pu
A
MVA
219 MW 52 Mvar
21 MW 7 Mvar
45 MW 12 Mvar
157 MW 45 Mvar
37 MW
13 Mvar
12 MW 5 Mvar
150 MW 0 Mvar
56 MW
13 Mvar
15 MW 5 Mvar
14 MW
2 Mvar
38 MW 3 Mvar
45 MW 0 Mvar
58 MW 36 Mvar
36 MW 10 Mvar
0 MW 0 Mvar
22 MW 15 Mvar
60 MW 12 Mvar
20 MW 9 Mvar
23 MW 7 Mvar
33 MW 13 Mvar 15.9 Mvar 18 MW
5 Mvar
58 MW 40 Mvar 51 MW
15 Mvar
14.3 Mvar
33 MW
10 Mvar
15 MW 3 Mvar
23 MW 6 Mvar 14 MW
3 Mvar
4.8 Mvar
7.2 Mvar
12.8 Mvar
29.0 Mvar
7.4 Mvar
20.8 Mvar
92 MW 10 Mvar
20 MW 8 Mvar
150 MW 0 Mvar
17 MW 3 Mvar
0 MW 0 Mvar
14 MW 4 Mvar
1.010 pu 0.0 Mvar
System Losses: 11.51 MW
22
Automatic voltage regulation system controls voltages.
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
Sparse Matrices and Large Systems
• Since for realistic power systems the model sizes are quite large, this means the Ybus and 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
Eastern Interconnect Example
Peoria
Rockford
Nort h Chi cago
Abbot t Labs ParkU. S. N Trai ni ng
O l d El m
Deerf i el d
Nort hbrook
Lakehurst
Waukegan
Zi on
G urnee
Ant i och
Pl easant
Round Lake
Zi on (138 kV)
Lake Zur i ch
Lest hon
Apt aki si c
Buf f al o G roove
Wheel i ng
Prospect Hei ght s
Pal at i ne
Ar l i ngt on
M ount Prospect
Prospect
G ol f M i l l
Des Pl ai nes
El mhurst
I t asca
Garfi eld
Tol l w ay
W407 ( Ferm i )
Wi l son
Barr i ngt on
D undee
Si l ver Lake
Cherry Val l ey
Wempleton
N elson
H -471 (N W Steel )
Paddock
Ponti ac Midpoi nt
Brai dw ood
State Li ne
Shefi eld
Chiave
Munster
St. John
El ect r i c Junct i on
Pl ano
La Sal l e
Lombard
Li sle
Col l i ns
D resden
Lockport
East Frankfort
Goodi ngs Grove
Li ber t yvi l l e345 kV
Li ber t yvi l l e138 kV
Lake George
D unacr
Green Acres
Schahfer
Tower Rd
Babcock
Hei ght s
Prai ri e
Racine
Michigan Ci ty
El wood
D equine
Louisa
East Mol ine
Sub 91
Walcott
D avenport
Sub 92
Rock Crk.
Salem
GILMAN
WATSEKA 17GO D LN D
ELPASO T
MIN ON K T
O GLESBY
1556A TPO TTAWA T
O GLSBY M
O GLES; T
H EN N EPIN
ESK TAP
LTV TP NLTV TP E
H EN N E; T
LTV STL
PRIN C TP
PRIN CTN
RICH LAN D
KEWAN IP
S ST TAP
GALESBRG
N ORMA; BN ORMA; R
R FAL; R
MON MOUTH
GALESBR5
KEWAN ;
H ALLOCK
CAT MO SSFARGO
SPN G BAY
E PEO RIA
RSW EAST
PION EERC
RAD N O R
CAT TAP
CAT SUB1
SB 18 5
E MO LIN E
SB 43 5
SB 112 5
KPECKTP5
SO .SUB 5
SB 85 5
SB 31T 5
SB 28 5
SB 17 5
SB 49 5
SB 53 5
SB 47 5SB 48 5
SB A 5
SB 70 5
SB 79 5
SB 88 5
SB 71 5
BVR CH 65 BVR CH 5 ALBAN Y 5
YO RK 5
SAVAN N A5
GALEN A 5
8TH ST.5
LO RE 5
SO .GVW.5
SALEM N 5
ALBAN Y 6
GARD E;
H 71 ;BT
H 71 ; B
H 71 ; R
R FAL; B
N ELSO; R
N ELSO;RT
STERL; B
D IXO N ;BT
MECCORD 3
CO RD O ;
Q uad Ci ti es
LEECO ;BP
Byron
MARYL; B
MEN D O ; T
STILL;RT
B427 ;1T
LAN CA; R
PECAT; B
FREEP;
ELERO ;BT ELERO ;RT
LEN A ; RLEN A ; B
H 440 ;RT
H 440 ; R
STEWA; B
H 445 ;3B
Roscoe
Pi erpont
S PEC; R
FO RD A; R
H arl em
Sand Park
N WT 138
BLK 138
RO R 138
JAN 138
ALB 138
N OM 138
D AR 138
H LM 138
PO T 138 MRE 138
CO R 138 D IK 138
BCH 138
Sabrooke
Bl awkhawk
Al pine
E. Rockford
Charl es
Belvi dere
B465
Marengo
WIB 138
WBT 138ELK 138
N LG 138
N LK GV T
SGR CK5
BRLGTN 1
BRLGTN 2
SGR CK4
UN IVRSTY
UN IV N EU
WH TWTR5
WH TWTR4
WH TWTR3
SUN 138
VIK 138
LBT 138
TICH IGNPARIS WE
ALBERS-2
C434
El mw ood
Ni l es
Evanst on
Devon
Rose Hi l l
Skoki e
Nort hw est
Dr i ver
Ford Ci ty
H ayford
Sawyer
Nort hr i dge
Hi ggi nsDes Pl ai nes
Frankl i n Park
O ak Park
Ri dgel and
D799
G al ew ood
Y450
Congress
Rockw el lCl ybourn
Q uarry
Lasal l e
State
Crosby
Ki ngsbury
Jeff erson
O hio
Taylor
Cl int
D ekov
Fi sk
Crawford
Universi ty
Ri ver
Z-494
Washington Park
H arbor
Calumet
H egewi sch
Z-715
South H ol l and
Evergreen
D amen
Wal l ace
Beverly
G3851
Z-524
G3852
Wi ldwood
H arvey
Green Lake
Sand Ridge
Chicago H ei ghts
Burnham
Lansi ng
F-575
F-503
Gl enwood
Bl oom
Park ForestMatteson
Country Club H i l l s
Al t G E
Nat om a
Woodhi l lU. Park
Moken
M cHenry
Cryst al Lake
Al gonqui n
Hunt l ey
P Val
Woodstock
Bl ue Isl and
G394
Al sip
Crestwood
K-319 # 1
K-319 # 2
Bradl ey
Kankakee
D avi s Creek
Wi lmington
Wi l ton Center
Frankfort
N Len
Brigg
O akbrook
D owners Groove
Woodridge
W604
W603
Bol ingbrook
Sugar Grove
W. De Kal b G l i dden
N Aurora
El gi n
Hanover
Spaul di ngBart l et t
Hof f m an Est at es
S. Schaumberg
Tonne
LandmBusse
Schaumberg
How ard
Berkel ey
Bel l w ood
La G range
Church
Addi son
NordiG l endal e
G l en El l yn
But t e
York Cent er
D775
Bedford Park
Cl earning
Sayre
Bridgevi ew
Ti nley Park
Roberts
Palos
Romeo
Wi l l ow
Burr Ri dge
Jo456
J322
Sout h El gi n Wayne
West Chi cago
Aurora
Warrenvi l l e
W507
Montgomery
O swego
Wol f Creek
Frontenac
W600 ( Napervi l l e)
W602
W601J307
Sandwich
Wat erm an
J323
Mason
J-371
J-375
J-339
Streator
Marsei l l esLasal l e
N LASAL
Mendota
J370
Shore
Goose Lake
J-305
J-390
J-326
Pl ainfi eld
J -332
Archer
Bel l Road
Wi l l Co.
H i l l crest Rockdale
Jol i et
Kendra
Crete
Upnor
LAKEVIEW
BAIN 4
Kenosha
SO MERS
ST RITA
BIG BEN D
MUKWO N GO
N ED 138
N ED 161
LAN 138
EEN 138
CASVILL5
TRK RIV5
LIBERTY5
ASBURY 5
CN TRGRV5
JULIAN 5
MQO KETA5
E CALMS5
GR MN D 5
D EWITT 5
SBH YC5
SUB 77 5
SB 74 5SB 90 5
SB 78 5
D AVN PRT5
SB 76 5
SB 58 5
SB 52 5
SB 89 5
IPSCO 5
IPSCO 3
N EWPO RT5
H WY61 5
WEST 5
9 SUB 5
TRIPP
Z-100
O rlan
Kenda
MPWSPLIT
WYO MIN G5
MT VERN 5
BERTRAM5
PCI 5
SB J IC 5
SB UIC 5
-0.40 deg
2.35 deg
-13.3 deg -13.4 deg
McCook
-1.1 deg
1.9 deg
0.6 deg
93%B
MVA
105%B
MVA
Example, which models the Eastern Interconnectcontains about 43,000 buses. 25
Solution Log for 1200 MW OutageIn this example thelosss of a 1200 MWgenerator in NorthernIllinois was simulated. This caused a generation imbalancein the associated balancing authorityarea, which wascorrected by a redispatch of localgeneration.
26
Interconnected OperationPower 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.
27
Balancing Authority AreasA “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.
The net power out of an area is the sum of the flow on its tie-lines.
The flow out of an area is equal to
total gen - total load - total losses = tie-line flow28
Area Control Error (ACE)The 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.That 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 controlling frequency.
29
actual tie-line flow schedACE 10P P f
Area Control Error (ACE)The 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 other areas.
30
Automatic Generation Control
Most systems use automatic generation control (AGC) to automatically change generation to keep their ACE close to zero.
Usually 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
Power TransactionsPower 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. Scheduled power transactions between balancing
areas are called “interchange” and implemented by setting the value of Psched used in the ACE calculation:ACE = Pactual tie-line flow – Psched + 10β Δf…and then controlling the generation to bring ACE
towards zero.32
“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.
33
Three Bus Case on AGC:no interchange.Bus 2 Bus 1
Bus 3Home Area
266 MW
133 MVR
150 MW
250 MW 34 MVR
166 MVR
133 MW 67 MVR
1.00 PU
-40 MW 8 MVR
40 MW -8 MVR
-77 MW 25 MVR
78 MW-21 MVR
39 MW-11 MVR
-39 MW
12 MVR
1.00 PU
1.00 PU
101 MW 5 MVR
100 MWAGC ONAVR ON
AGC ONAVR ON
Net tie-line flow is close to zero
Generationis automaticallychanged to matchchange in load
34
100 MW Transaction between areas in Eastern or Western
Bus 2 Bus 1
Bus 3Home Area
Scheduled Transactions
225 MW
113 MVR
150 MW
291 MW 8 MVR
138 MVR
113 MW 56 MVR
1.00 PU
8 MW -2 MVR
-8 MW 2 MVR
-84 MW 27 MVR
85 MW-23 MVR
93 MW-25 MVR
-92 MW
30 MVR
1.00 PU
1.00 PU
0 MW 32 MVR
100 MWAGC ONAVR ON
AGC ONAVR ON
100.0 MW
Scheduled100 MWTransaction from Left to Right
Net tie-lineflow is now100 MW
35
PTDFsPower transfer distribution factors (PTDFs) show
the linearized impact of a transfer of power.PTDFs calculated using the fast decoupled
power flow B matrix:
1
Once we know we can derive the change in
the transmission line flows to evaluate PTDFs.
Note that we can modify several elements in ,
in proportion to how the specified generators would
par
θ B P
θ
P
ticipate in the power transfer. 36
Nine Bus PTDF Example
10%
60%
55%
64%
57%
11%
74%
24%
32%
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
250.0 MW
150.0 MW
150.0 MW
44%
71%
0.00 deg
71.1 MW
92%
Figure shows initial flows for a nine bus power system
37
Nine Bus PTDF Example, cont'd
43%
57% 13%
35%
20%
10%
2%
34%
34%
32%
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
250.0 MW
150.0 MW
150.0 MW
34%
30%
0.00 deg
71.1 MW
Figure now shows percentage PTDF flows for a change in transaction from A to I
38
Nine Bus PTDF Example, cont'd
6%
6% 12%
61%
12%
6%
19%
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
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
39
WE to TVA PTDFs
40
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.
41
Line Outage Distribution Factors (LODFs)
42
,
change in flow on line ,
due to outage of line .
pre-contingency flow on line
,
Estimates change in flow on line
if outage on line were to occur.
l
k
l l k k
P l
k
P k
P LODF P
l
k
Line Outage Distribution Factors (LODFs)
43
,
If line initially had 100 MW of flow on it,
and line initially had 50 MW flow on it,
and then there was an outage of line ,
if =0.1 then the increase in flow
on line after a continge
k
l
l k
k P
l P
k
LODF
l
,
ncy of line would be:
0.1 100 10 MW
from 50 MW to 60 MW.
l l k k
k
P LODF P
Flowgates
• The real-time loading of the power grid can be assessed via “flowgates.”
• A flowgate “flow” is the real power flow on one or more transmission elements for either base case conditions or a single contingency– Flows in the event of a contingency are approximated
in terms of pre-contingency flows using LODFs.
• Elements are chosen so that total flow has a relation to an underlying physical limit.
44
Flowgates
• Limits due to voltage or stability limits are often represented by effective flowgate limits, which are acting as “proxies” for these other types of limits.
• Flowgate limits are also often used to represent thermal constraints on corridors of multiple lines between zones or areas.
• The inter-zonal constraints that were used in ERCOT until December 2010 are flowgates that represent inter-zonal corridors of lines.
45
top related