Three units are on-line all 720h of a 30-day month. Their characteristics are as follows:
H1 = 225 + 8.47P1 + 0.0025P12, 50<=P1<=350
H2 = 729 + 6.20P2 + 0.0081P22, 50<=P2<=350
H3 = 400 + 7.20P3 + 0.0025P32, 50<=P3<=450
In these equations, the Hi are in MBtu/h and the Pi are in MW.
Fuel costs for units 2 and 3 are 0.60 $/MBtu. Unit 1, however, is operated under a take-or-pay fuel contract where 60,000 t of coal is to be burned and/or paid for in each 30-day period. This coal costs 12 $/t delivered and has an average heat content of 12,500 Btu/lb (1 t=2000 lb).
The system monthly load-duration curve may be approximated by three steps as follows.
|
Load (MW)
|
Duration(h)
|
Energy (MWh)
|
|
800
|
50
|
40,000
|
|
500
|
550
|
275,000
|
|
300
|
120
|
36,000
|
|
Total
|
720
|
351,000
|
a. Compute the economic schedule for the month assuming all three units are on-line all the time and that the coal must be consumed. Show the MW loading for each load period, the MWh of each unit, and the value of gamma (the pseudo-fuel cost).
b. What would be the schedule if unit 1 was burning the coal at 12 $/t with no constraint to use 60,000 t? Assume the coal may be purchased on the spot market for that price and compute all the data asked for in part a. In addition, calculate the amount of coal required for the unit.