Post on 16-Jan-2016
description
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
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)
Question
• How do we solve the optimizationproblem?
Optimization
Without any constraints
With equality constraints
With inequality constraints
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)
Rule: Operate all generators at the same incremental cost value.
λ = ICi for i=1,2,3,….,m
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)
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
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)
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