Environmental Engineering Reference
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Δ
C
Δ
P
P (MW)
Figure 7.5
Typical input-output curve for a thermal generating unit
O A
O B
Figure 7.6 Demonstration of the equal incremental cost solution. (Based on fi gure in Neuenswander,
J.R., Modern Power Systems , Intertext Books, 1973)
unit B is placed at a distance from O A equal to the total demand P d = P A + P B . Any vertical
line intersecting the curves will therefore represent the cost of a given operating condition.
As before a sharing of the demand by the two generators is sought such that the cost is
minimum.
Let the vertical line C 1 represent the operating point at which the slopes of the two curves
are equal. The length of C 1 represents the total cost per hour of operating both units. Any
other operating points (such as the ones represented by lines C 2 or C 3 ) result in higher cost.
Hence the most economic operating point is the one at which the slopes of the cost lines (i.e.
the incremental costs ) of the two units are equal. This result is valid no matter how many
generators are feeding power to the system. The same conclusion can be proven using the
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