Discussion
The incremental cost characteristics of the two plants are,
IC1 = 0.2P1 + 5 Rs/MWh
IC2 = 0.1P2 + 10 Rs/MWh
The total load is 40 MW, what is the optimal sharing of load ?
Answer: D
The optimal sharing is P1 = 30 MW and P2 = 10 MW.
Neglecting losses, the load is shared most economically when both plants run at the same incremental cost, with \(P_{1} + P_{2} = 40\).
\[ \begin{aligned} 0.2P_{1} + 5 &= 0.1P_{2} + 10 \\ 0.2P_{1} + 5 &= 0.1(40 - P_{1}) + 10 \\ 0.3P_{1} &= 9 \\ P_{1} &= 30,\ P_{2} = 10 \end{aligned} \]
Check: \(IC_{1} = 0.2(30) + 5 = 11\) and \(IC_{2} = 0.1(10) + 10 = 11\) Rs/MWh, equal as required. Any other split leaves the incremental costs unequal; for example 10 and 30 MW gives 7 and 13 Rs/MWh, so shifting load to plant 1 would cut the total cost.
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