The fuel$-$cost functions in $$/$h for two $800$ MW thermal plants are given by

$=400+6\mathrm{.}0+0\mathrm{.}004$

$=500++$

Where $$ and $$ are in MW$.$

$($a$)$ The incremental cost of power is $$8/$MWh when the total power demand is $550$ MW$.$

Neglecting losses, determine the optimal generation of each plant

$($b$)$ The incremental cost of power is $$10/$MWh when the total power demand is $1300$ MW$.$

Neglecting losses determine the optimal generation of each plant.

$($c$)$ From the results of $($a$)$ and $($b$)$ find the fuel$-$cost coefficients $$ and $$ of the second plant.

Problem $5$:

The fuel$-$cost functions in $$/$h for three thermal plants are given by

$=350+7\mathrm{.}20+0\mathrm{.}0040$

$=500+7\mathrm{.}30+0\mathrm{.}0025$

$=600+6\mathrm{.}74+0\mathrm{.}0030$

Where $,,$ and $$ are in MW$.$ The governors are set such that generators share the load

equally. Neglecting line losses and generator limits$,$ ind the total cost in $$/$h when the total

load is

$($i$)=450$

$($ii$)=745$

$($iii$)=1335$

Problem $6$:

Neglecting line losses and generator limits$,$ determine the optimal scheduling of generation for

each loading condition in Problem $5.$

$($a$)$ By analytical technique

$($b$)$ Find the savings in $$/$h for each case compared to the costs in Problem $5$ when the

generators shared load equally.