Question

4.2 The input-output curve of a gas-fired generating unit is approximated by the following function: HUP) 120+9.3p +0.0025pa (MI/h) This unit has a minimum stable generation of 200 MW and a maximum output of 500 MW. The cost of gas is 1.20 $/MJ. Over a 6-h period, the output of this unit is sold on a market for electrical energy at the prices shown in Table 4.15. Assuming that this unit is optimally dispatched, is initially on-line, and cannot be shut down, calculate its operational profit or loss for this period. Table 4.15 Data for Problem 4.2. Period Price (S/MWh) 4 13.5 12.5 10 13 15

Answer 1

Solution:

Given an input output curve of a gas fired function.

calculations:

The above function is maximized when it is differentiated and output equates to zero.

I.e. dH / dP = 9.3 + 0.005P = 0

So P = 9.3/0.005 = 1860 MJ

Now cost of gas = 1.2 per $/MJ

Hence total cost of gas = 1.2*1860 = $2232

Now dividing this energy over a period of 6 hours.

Hence per hour energy distribution = 1860/6 = 310 MJ

Now total price of energy = (310*12.5) + (310*10) + (310*13) + (310*13.5) + (310*15) + (310*11)

= 3875+3100+4030+4185+4650+3410

= $23250

operational profit or loss for this period is:

Hence total profit = Total price - Total cost

= 23250 - 2232

= $ 21,018.00

Thus the profit is $ 21,018.00 .