Rework Problem 6.62, except assume the \(1000 \mathrm{MW}\) value also includes losses, and the penalty factor for the first unit is 1.0 and for the second unit 0.95.

Problem 6.62

The fuel-cost curves for two generators are given as follows:

\[
\begin{aligned}
& \mathrm{C}_{1}\left(\mathrm{P}_{1}ight)=600+18 \cdot \mathrm{P}_{1}+0.04 \cdot\left(\mathrm{P}_{1}ight)^{2} \\
& \mathrm{C}_{2}\left(\mathrm{P}_{2}ight)=700+20 \cdot \mathrm{P}_{2}+0.03 \cdot\left(\mathrm{P}_{2}ight)^{2}
\end{aligned}
\]

Assuming the system is lossless, calculate the optimal dispatch values of \(P_{1}\) and \(P_{2}\) for a total load of \(1000 \mathrm{MW}\), the incremental operating cost, and the total operating cost.