Optimal Transmission Switching Optimal Transmission Switching Emily - - PowerPoint PPT Presentation

Optimal Transmission Switching Optimal Transmission Switching

Emily Bartholomew Fisher, Johns Hopkins University Ri h d P O’N ill F d l E R l t C i i Richard P . O’Neill, Federal Energy Regulatory Commission Michael C. Ferris, University of Wisconsin, Madison Energy, Natural Resources & the Environment INFORMS Annual Meeting INFORMS Annual Meeting October 12-15, 2008 Washington DC Washington D.C.

**Views in this presentation are solely those of the authors, and do not reflect

• fficial positions of their institutions.

Outline Outline Outline Outline

 Bulk Power/Transmission system

y

• Capacity
• Power flow characteristics

 Optimal Power Flow  Optimal Power Flow with Transmission  Optimal Power Flow with Transmission

Switching

 T

est system results

 T

est system results

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Bulk Power System Bulk Power System Bulk Power System Bulk Power System

3

Power Networks have Capacity Power Networks have Capacity

Load: 80 MW

Power Networks have Capacity Power Networks have Capacity

80 MW generated 80 MW Load: 80 MW g

Example: Transmission line has capacity of 100 MW capacity of 100 MW

80 MW generated Load: 120 MW 80 MW generated

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Flow in Power Networks is Special Flow in Power Networks is Special

Power flows on all lines in proportion to the electrical characteristics f the lines

Flow in Power Networks is Special Flow in Power Networks is Special

electrical characteristics of the lines

3 MW generated

Example:

2 MW

Example: Lines are identical

1 MW

3 MW load

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Putting it Together Putting it Together Putting it Together Putting 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 Dispatch Optimal Dispatch typical formulation typical formulation



p C Ming

ng ng p

C Min

max min P ng p P  

s t

Minimize cost of gen Gen capacity constraints

ng ng p ng

max min nk P nk p nk P  

s.t.

p y Trans capacity constraints

max min     

      

d g k

nd P ng p nk p

Power balance

n n n     

 

   nk p m n k B  

Network flow constraints

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Ideally, want to serve all load from Ideally, want to serve all load from cheaper generator cheaper generator

Total Cost: $20/MWh x 200 MWh = $4 000/h

$20/MWh

200 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 infeasible But that is infeasible But 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 dispatch A feasible dispatch A feasible dispatch A feasible dispatch

Total 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 d

33MW

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/MWh

200 MW generated

$ $ ,

$20/MWh 200 MW

200 MW load

$40/MWh

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Optimal Dispatch formulation Optimal Dispatch formulation with Transmission Switching with Transmission Switching



p C Ming

ng ng p

C Min

max min P ng p P  

s t

Minimize cost of gen Gen capacity constraints

ng ng p ng

s.t.

p y Trans capacity constraints

k nk nk k nk

z P p z P

max min

 

max min n n n     

      

d g k

nd P ng p nk p

Power balance

n n n



   nk p m n k B  

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 formulation Optimal Dispatch formulation with Transmission Switching with Transmission Switching



p C Ming

ng ng p

C Min

max min P ng p P  

s t

Minimize cost of gen Gen capacity constraints

ng ng p ng

s.t.

p y Trans capacity constraints

k nk nk k nk

z P p z P

max min

 

max min n n n     

      

d g k

nd P ng p nk p

Power balance

n n n



   nk p m n k B  

Network flow constraints

   

1      M z k p B  

   

1      M k z nk p m n k B  

   

1  M k z nk p m n k B  

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IEEE 118 IEEE 118-bus System bus System IEEE 118 IEEE 118 bus System bus System

Commonly-used test case represents a subset of the actual AEP transmission network as of December, 1962. Case Summary 19 Generators 99 Loads, total demand: 3,668 MW 186 Transmission lines

Source of image: PowerWorld

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Results from IEEE 118 Results from IEEE 118-bus system bus system Results from IEEE 118 Results from IEEE 118 bus system bus system

O Li System Dispatch C t Percent S i Open 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 patch Cost 1100 1150 ystem Disp 1000 1050 Sy 1 2 3 4 Number of Lines Allowed Open

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Thanks! Thanks! Thanks! Thanks!

 Questions?

hi h

source: www.whitehouse.gov

Reference: Fisher Emily Bartholomew Richard P O’Neill Michael Fisher, 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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