23- Economic Dispatch
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Transcript of 23- Economic Dispatch
![Page 1: 23- Economic Dispatch](https://reader034.fdocuments.in/reader034/viewer/2022050723/55cf8efe550346703b97d600/html5/thumbnails/1.jpg)
OBJECTIVE: To supply power to power to our
customers at minimum fuel cost
PROBLEM STATEMENT: Given a power system with m generating units and a total demand of PTD
, how much power should each unit generate so that the total demand is supplied at minimum fuel cost.
ECONOMIC OPERATION OF
POWER SYSTEMS
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![Page 3: 23- Economic Dispatch](https://reader034.fdocuments.in/reader034/viewer/2022050723/55cf8efe550346703b97d600/html5/thumbnails/3.jpg)
Mathematical Formulation
Minimize { CT = Ci(PGi) }i=1,2..,m
Such that:• PGi = PTD +PLoss (Power Balance)i=1,2,,m
• PGimax ≤ PGi ≤ PGi
min i=1,2,3,…,m
• Power flow constraints
Where: Ci(PGi) is the cost curve for the generator i
(in $/HR)
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Question
• How do we solve the optimizationproblem?
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Optimization
Without any constraints
With equality constraints
With inequality constraints
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Minimize { CT = Ci(PGi) }i=1,2..,m
Such that:• PGi = PTD +PLoss (Power Balance)i=1,2,,m
• PGimax ≤ PGi ≤ PGi
min i=1,2,3,…,m
• Power flow constraints
Where: Ci(PGi) is the cost curve for the generator i
Economic Dispatch without transmission losses and generator limits
1)
![Page 7: 23- Economic Dispatch](https://reader034.fdocuments.in/reader034/viewer/2022050723/55cf8efe550346703b97d600/html5/thumbnails/7.jpg)
Rule: Operate all generators at the same incremental cost value.
λ = ICi for i=1,2,3,….,m
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![Page 10: 23- Economic Dispatch](https://reader034.fdocuments.in/reader034/viewer/2022050723/55cf8efe550346703b97d600/html5/thumbnails/10.jpg)
Minimize { CT = Ci(PGi) }i=1,2..,m
Such that:• PGi = PTD +PLoss (Power Balance)i=1,2,,m
• PGimax ≤ PGi ≤ PGi
min i=1,2,3,…,m
• Power flow constraints
Where: Ci(PGi) is the cost curve for the generator i
Economic Dispatch without transmission losses but including generator limits
2)
![Page 11: 23- Economic Dispatch](https://reader034.fdocuments.in/reader034/viewer/2022050723/55cf8efe550346703b97d600/html5/thumbnails/11.jpg)
Rule: Operate all generators that are NOT at their limits at the same incremental cost value.
λ = ICi for those units that are NOT
at their limits
![Page 12: 23- Economic Dispatch](https://reader034.fdocuments.in/reader034/viewer/2022050723/55cf8efe550346703b97d600/html5/thumbnails/12.jpg)
![Page 13: 23- Economic Dispatch](https://reader034.fdocuments.in/reader034/viewer/2022050723/55cf8efe550346703b97d600/html5/thumbnails/13.jpg)
Minimize { CT = Ci(PGi) }i=1,2..,m
Such that:• PGi = PTD +PLoss (Power Balance)i=1,2,,m
• PGimax ≤ PGi ≤ PGi
min i=1,2,3,…,m
• Power flow constraints
Where: Ci(PGi) is the cost curve for the generator i
Economic Dispatch including transmission losses and generator limits
3)
![Page 14: 23- Economic Dispatch](https://reader034.fdocuments.in/reader034/viewer/2022050723/55cf8efe550346703b97d600/html5/thumbnails/14.jpg)
Rule : Operate all generators that are NOT at their limits at the same system lambda.
λ = Li * ICi for those units that are
NOT at their limits
Where: Li is the penalty factor for generator i
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