Color Plate Section
498 Artifi cial Intelligence in Power System Optimization
Cost ($/hr)
Incremental
Cost ($/MWh)
MW
MW
Chapter 2
Cost ($/hr)
Incremental
Cost ($/MWh)
MW
MW
P
1
P
2
P
1
P
4
P
3
P
2
P
4
P
3
Fig. 2.2 Quadratic approximation cost function.
Fig. 2.3 Piecewise linear approximation cost function.
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Cost ($/h)
Power (MW)
15000
10000
5000
0
0 50 100 150 200 250
PG3
PG2
PG1
0 50 100 150 200 250
150
100
50
0
Incremental Cost ($/MWh)
Power (MW)
PG3
PG2
PG1
Fig. 2.6 Generation costs of three units in example 2.1.
Fig. 2.7 Incremental costs of the three units in example 2.1.
500 Artifi cial Intelligence in Power System Optimization
Incremental Cost ($/MWh)
Power (MW)
PG3
PG2
PG1
0 50 100 150 200 250
150
100
50
0
56.00 $/MWh
76.667 MW
90.000 MW
153.333 MW
Power (MW)
PG3
PG2
0 50 100 150 200 250
150
100
50
0
56.000 $/MWh
Incremental Cost ($/MWh)
PG1
Max 100 MW
Unit 1 is not in it limit
Fig. 2.8 Graphical representation of the dispatch result in the example 2.1.
Fig. 2.9 Graphical representation of the dispatch result in example 2.2 when unit 1 is exceeding
its limit.
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Power (MW)
PG2
0 50 100 150 200 250
150
100
50
0
Incremental Cost ($/MWh)
PG3
PG1
122 MW
98 MW
100 MW
68.8 $/MWh
Fig. 2.11 Graphical representation of the dispatch result in example 2.2 with all units within
their limits.
Fig. 2.23 Convergence properties of the IEEE 30 bus test system.
PSO-ED
PSO-QP-ED
Iteration
Total Generator Fuel Cost ($/h)
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