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