Electrical Power Systems

410 Electrical Power Systems
or
where dC
dP
as:
i
gi
dC
dP
i
gi
= l, i = 1, 2, ..., m ...(16.13)
= IC i is the incremental cost of the i-th generator. Equation (16.13) can be written
dC
dP
1
g1
= dC
dP
2
g2
= ....... = dC
dP
m
gm
= l ...(16.14)
Therefore, optimal loading of generators occurs corresponding to the equal incremental cost
point of all the generators. Equation (16.14) called the Coordination Equation and m number of
equation is solved simultaneously with the generation-load balance eqn. (16.10), to give a
solution for the Lagrange multiplier l and the optimal generation of m generators.
urther explanations are given below regarding optimal loading of generators at equal
incremental cost.
Intuitively, it is clear why it cannot possibly be optimal to operate generators at different ICs.
ig. 16.3: Two generators at different incremental costs (ICs).
In ig. 16.3, say P g1 = 200 MW and P g2 = 100 MW and the corresponding IC i (i.e., slope of
the cost curves) are not equal. As shown in ig. 16.3, IC 1 is greater than IC 2 . Since IC 1 > IC 2 ,
if we reduce P g1 by (say) 20 MW, we can save quite a lot of cost per hour because the slope of the
cost curve is large. If we add the 20 MW to P g2 , the cost goes up less because the slope is smaller.
Thus, we can deliver the same total power 300 MW at less cost. In general, it pays to reduce the
power output of the generator with higher incremental cost. A continuation of this process
ultimately leads to equal incremental costs.
A systematic procedure is required for obtaining the value of l-in eqn. (16.14). If the fuel
cost curves are quadratic, then the incremental cost curves are linear. However, ICs may not be
linear and l can be obtained iteratively by considering the ICs as shown in ig. 16.4.
ig. 16.4: Incremental cost curves.