optimal transmission...
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Optimal Transmission SwitchingOptimal Transmission Switching
Emily Bartholomew Fisher, Johns Hopkins UniversityRi h d P O’N ill F d l E R l t C i iRichard P. O’Neill, Federal Energy Regulatory Commission
Michael C. Ferris, University of Wisconsin, Madison
Energy, Natural Resources & the EnvironmentINFORMS Annual MeetingINFORMS Annual Meeting
October 12-15, 2008Washington D CWashington D.C.
**Views in this presentation are solely those of the authors, and do not reflect official positions of their institutions.
OutlineOutlineOutlineOutline
Bulk Power/Transmission systemy◦ Capacity◦ Power flow characteristics
Optimal Power Flow Optimal Power Flow with Transmission Optimal Power Flow with Transmission
Switching Test system results Test system results
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Bulk Power SystemBulk Power SystemBulk Power SystemBulk Power System
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Power Networks have CapacityPower Networks have Capacity
Load: 80 MW
Power Networks have CapacityPower Networks have Capacity
80 MW generated 80 MWLoad: 80 MWg
Example: Transmission line has capacity of 100 MWcapacity of 100 MW
80 MW generated Load: 120 MW80 MW generated
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Flow in Power Networks is SpecialFlow in Power Networks is SpecialPower flows on all lines in proportion to the electrical characteristics f the lines
Flow in Power Networks is SpecialFlow in Power Networks is Special
electrical characteristics of the lines3 MW generated
Example: 2 MW
Example: Lines are identical
1 MW
3 MW load
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Putting it TogetherPutting it TogetherPutting it TogetherPutting it Together
200 MW generated Capacity limit: 100 MW
133 MW
200 MW l d
67 MW
200 MW load
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Optimal DispatchOptimal Dispatchtypical formulationtypical formulation
pCMing ngng pCMin
maxmin PngpP s t
Minimize cost of gen
Gen capacity constraintsngngpng
maxminnk
Pnkpnk
P
s.t. p y
Trans capacity constraints
maxmin
0 dgk ndPngpnkp Power balance
nnn
0 nkpmnkB
Network flow constraints
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Ideally, want to serve all load from Ideally, want to serve all load from cheaper generatorcheaper generator
Total Cost: $20/MWh x 200 MWh = $4 000/h
$20/MWh200 MW generated
Total Cost: $20/MWh x 200 MWh = $4,000/h
Capacity limit: 100 MW$20/MWh
200 MW load
$40/MWh
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But that is infeasibleBut that is infeasibleBut that is infeasible…But that is infeasible…
Capacity limit: 100 MW$20/MWh
200 MW generated
133 MW
200 MW load
67 MW
200 MW load
$40/MWh
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A feasible dispatchA feasible dispatchA feasible dispatchA feasible dispatchTotal Cost: $20/MWh x 100 MWh
+$40/MWh x 100 = $6 000/h
Capacity limit: 100 MW$20/MWh
100 MW generated+$40/MWh x 100 $6,000/h
67 MW
200 MW l d33MW
100 MW generated
33MW
200 MW load
$40/MWh
g
67 MW$40/MWh 67 MW
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However, if you open the However, if you open the constrained line….constrained line….
Total Cost: $20/MWh x 200 MWh = $4,000/h
$20/MWh200 MW generated
$ $ ,
$20/MWh
200 MW
200 MW load
$40/MWh
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Optimal Dispatch formulationOptimal Dispatch formulationwith Transmission Switchingwith Transmission Switching
pCMing ngng pCMin
maxmin PngpP s t
Minimize cost of gen
Gen capacity constraintsngngpngs.t. p y
Trans capacity constraintsknknkknk zPpzP maxmin
maxminnnn
0 dgk ndPngpnkp Power balance
nnn 0 nkpmnkB Network flow constraints
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Why do we have to change the Why do we have to change the Network Flow Constraints?Network Flow Constraints?
3 MW generated Capacity limit: 100 MW
0 MW
2 MW
0 MW
3 MW l d
1 MW
3 MW load
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Optimal Dispatch formulationOptimal Dispatch formulationwith Transmission Switchingwith Transmission Switching
pCMing ngng pCMin
maxmin PngpP s t
Minimize cost of gen
Gen capacity constraintsngngpngs.t. p y
Trans capacity constraintsknknkknk zPpzP maxmin
maxminnnn
0 dgk ndPngpnkp Power balance
nnn 0 nkpmnkB Network flow constraints
01 MzkpB
01 MkznkpmnkB
01 MkznkpmnkB
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IEEE 118IEEE 118--bus Systembus SystemIEEE 118IEEE 118 bus Systembus System
Commonly-used test case represents a subset of the actual AEP transmission network as of December, 1962.
Case Summary19 Generators99 Loads, total demand: 3,668 MW186 Transmission lines
Source of image: PowerWorld 15
Results from IEEE 118Results from IEEE 118--bus systembus systemResults from IEEE 118Results from IEEE 118 bus systembus system
O LiSystem Dispatch
C tPercent S iOpen Lines Cost Savings
none –$2,054 -
38 lines open –$1,543 24.9%
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Does this mean the network was Does this mean the network was not well planned?not well planned?1400
"Off Peak-Optimal" Lines open
1300
1350
t [$]
“Original Load-Optimal" Lines open
Off Peak Optimal Lines open
1200
1250
patc
h C
ost
1100
1150
yste
m D
isp
1000
1050
Sy
0 1 2 3 4Number of Lines Allowed Open
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Thanks!Thanks!Thanks!Thanks!
Questions?
hi hsource: www.whitehouse.gov
Reference:Fisher Emily Bartholomew Richard P O’Neill MichaelFisher, Emily Bartholomew, Richard P. O’Neill, Michael C. Ferris. “Optimal Transmission Switching,” IEEE Transactions on Power Systems, vol. 23, no. 3, 2008, pp 1346 – 1355.
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