Plot the input-output characteristics for each unit

Question

The system to be studied consists of two units as described in Problem. Assume a daily load cycle as follows.

Time Band	Load (MW)
0000-0600	50
0600-1800	150
1800-0000	50

Also, assume that a cost of 180$ is incurred in taking either unit off-line and returning it to service after 12 h. Consider the 24-h period from 0600 one morning to 0600 the next morning.

a. Would it be more economical to keep both units in service for this 24-h period or to remove one of the units from service for the 12-h period from 1800 one evening to 0600 the next morning?

b. What is the economic schedule for the period of time from 0600 to 1800 (load=150 MW)?

c. What is the economic schedule for the period of time from 1800 to 0600 (load=50 MW)?

Problem
Assume that the fuel inputs in MBtu per hour for units 1 and 2, which are both on-line, are given by

H₁ = 8P₁ + 0.024P₁² + 80
H₂ = 6P₂ + 0.04P₂² + 120

where
H = fuel input to unit n in MBtu per hour (Millions of Btu per hour)
P = unit output in megawatts

a. Plot the input-output characteristics for each unit expressing input in MBtu per hour and output in megawatts. Assume that the minimum loading of each unit is 20 MW and that the maximum loading is 100 MW.

b. Calculate the net heat rate in Btu per kilowatt-hour, and plot against output in megawatts.

c. Assume that the cost of fuel is 1.5 / $ MBtu. Calculate the incremental production cost in $ / MWh of each unit, and plot against output in megawatts.