ECG 740 Basic Economic Dispatch of

Power Generation

G1 G2 G3

System

Incremental cost curves

975 $9.163/MWh

9.16

9.16

9.16

975 = 450 + 315 + 210

483 MW

305 MW

187 MW

Upper limit violated: → P1= 450 MW → solve the dispatch problem with two generators: P2 + P3 = 525 MW → λ = $9.4/MWh → P2 = 315 MW → P3 = 210 MW

Base Point and Participation Factors

Composite Generation Production Cost Function

lossPPPP

PP

PP

PP

150

),014.8.6)(000358.1

1(

)018.3.6)(000456.1

1()016.7(

)000436.1

1(

321

3

3

2

2

1

1

Results (obtained numerically):

• P1 = 35.1 MW • P2 = 64.1 MW • P3 = 52.5 MW • Ploss = 1.7 MW • Pdemand = 150 MW

Locational Marginal Price (LMP)

• Transmission line load carrying capability (power flow limit) may result in different LMP at different locations.

• See example on pages 92-95.

Economic Dispatch Including Losses and Voltage Constraints

• This is referred to as “Optimal Power Flow” or OPF (to be seen in Chapter 8)

Lambda Iteration Method

L H

1 1

H L

M H L

H M

1

L M

Pick and such that

( ) 0 ( ) 0

While Do

( ) / 2

If ( ) 0 Then

Else

End While

m mL H

Gi D Gi Di i

mM

Gi Di

P P P P

P P

Linear Programming (LP) Method

• http://www.ece.iastate.edu/~rkumar/EE458/PWL_CostCurves

2005.pdf

Dynamic Programming (DP) Method

• Applied in case of non-convex input-output generator curves.

• Generator outputs are generated at discrete points of the entire set load values (rather than a specific load).

Assignment

• Solve the following problems from Chapter 3:

– 3.1 through 3.8

– 3.13 through 3-.17