Optimal Transmission Switching Optimal Transmission Switching Emily - PowerPoint PPT Presentation

Optimal Transmission Switching Optimal Transmission Switching Emily Bartholomew Fisher, Johns Hopkins University Richard P Ri h d P O’N ill F d . O’Neill, Federal Energy Regulatory Commission l E R l t C i i 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 official 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  T est system results est system results 2

Bulk Power System Bulk Power System Bulk Power System Bulk Power System 3

Power Networks have Capacity Power Networks have Capacity Power Networks have Capacity Power Networks have Capacity 80 MW 80 MW generated g Load: 80 MW Load: 80 MW Example: Transmission line has capacity of 100 MW capacity of 100 MW 80 MW generated 80 MW generated Load: 120 MW 4

Flow in Power Networks is Special Flow in Power Networks is Special 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 electrical characteristics of the lines 3 MW generated 2 MW Example: Example: Lines are identical 1 MW 3 MW load 5

Putting it Together Putting it Together Putting it Together Putting it Together Capacity limit: 100 MW 200 MW generated 133 MW 67 MW 200 MW l 200 MW load d 6

Optimal Dispatch Optimal Dispatch typical formulation typical formulation Min  g  Min C C ng p p Minimize cost of gen ng min max s t s.t. Gen capacity constraints p y   P p p P ng ng ng ng min max Trans capacity constraints   P p P nk nk nk        Power balance 0 p p P ng k g d nk nd min max           n n n   Network flow constraints      0 B p nk n m k 7

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 Total Cost: $20/MWh x 200 MWh = $4,000/h 200 MW generated $20/MWh $20/MWh Capacity limit: 100 MW 200 MW load $40/MWh 8

But that is infeasible But that is infeasible But that is infeasible… But that is infeasible… 200 MW generated Capacity limit: 100 MW $20/MWh 133 MW 67 MW 200 MW load 200 MW load $40/MWh 9

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 +$40/MWh x 100 = $6 000/h 100 MW generated Capacity limit: 100 MW $20/MWh 67 MW 33MW 100 MW 33MW g generated 200 MW l 200 MW load d $40/MWh $40/MWh 67 MW 67 MW 10

However, if you open the However, if you open the constrained line…. constrained line…. Total Cost: $20/MWh x 200 MWh = $4,000/h $ $ , 200 MW generated $20/MWh $20/MWh 200 MW 200 MW load $40/MWh 11

Optimal Dispatch formulation Optimal Dispatch formulation with Transmission Switching with Transmission Switching Min  g  Min C C ng p p Minimize cost of gen ng min max s t s.t. Gen capacity constraints p y   P p p P ng ng ng ng   Trans capacity constraints min max P z p P z nk k nk nk k        Power balance 0 p p P ng k g d nk nd min max      n   n n n n n Network flow constraints      0 B p nk n m k 12

Why do we have to change the Why do we have to change the Network Flow Constraints? Network Flow Constraints? Capacity limit: 100 MW 3 MW generated 0 MW 0 MW 2 MW 1 MW 3 MW l 3 MW load d 13

Optimal Dispatch formulation Optimal Dispatch formulation with Transmission Switching with Transmission Switching Min  g  Min C C ng p p Minimize cost of gen ng min max s t s.t. Gen capacity constraints p y   P p p P ng ng ng ng   Trans capacity constraints min max P z p P z nk k nk nk k        Power balance 0 p p P ng k g d nk nd min max      n   n n n n n Network flow constraints      0 B p nk         n m k           1 1 0 0 B B p p z z M M     nk k n m k k        1 0 B p z M nk n m k k 14

IEEE 118 IEEE 118-bus System IEEE 118 IEEE 118 bus System 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 15

Results from IEEE 118 Results from IEEE 118 Results from IEEE 118 bus system Results from IEEE 118-bus system bus system bus system System Dispatch Percent O Open Lines Li Cost C t Savings S i none –$2,054 - 38 lines open –$1,543 24.9% 16

Does this mean the network was Does this mean the network was not well planned? not well planned? 1400 "Off Peak-Optimal" Lines open Off Peak Optimal Lines open 1350 “Original Load-Optimal" Lines open 1300 t [$] patch Cost 1250 1200 ystem Disp 1150 1100 Sy 1050 1000 0 1 2 3 4 Number of Lines Allowed Open 17

Thanks! Thanks! Thanks! Thanks!  Questions? source: www.whitehouse.gov hi h 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. 18