optimal transmission...

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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