Question

Two generating units have the following characteristic :

Unit 1 (Gas) : H₁(P₁) = 100 + 4*P₁ + 0.002*P₁² 50 MW < P₁ < 500 MW
Unit 2 (Coal): H₂(P₂) = 300 + 6*P₂ + 0.0025*P₂² 50 MW < P₂ < 400 MW

The fuel costs for the units are as follows:
. Gas : 0.6 $/MBtu
. The coal costs 14 $/ton and has an average heat content 125-- Btu/lb (1 ton = 2000 lb)
Unit 2 is on a take-or-pay supply contract and must burn 500 tons of coal during the 8-h time period.
Assume both units are on-line and they should meet the following load :
Period Duration Load (MW)
1 4 hours 400
2 4 hours 650

For a starting value of y = 12 $/ton, in iteration 1, the power output of Unit 2 during time period 1 is equal to :

a. 100 MW
b. 200 MW
c. None of thses
d. 300 MW

Answer 1

Without a clear methodology or additional data to recalculate Unit 2's output based on the new coal cost, we cannot accurately determine the power output of Unit 2 during time period 1; thus, the answer is 'None of these'.

Step-by-step explanation:

To determine the power output of Unit 2 (Coal) during time period 1 given that the fuel costs for coal have changed to $12/ton, we first need to understand the operating constraints of the unit under the 'take-or-pay' contract, which requires the burning of 500 tons of coal during the 8-hour time period.

Therefore, regardless of the demand, Unit 2 must operate at a level to consume this quantity of coal. Looking at the given fuel cost of coal and its average heat content, the computations would involve finding the fuel cost per megawatt-hour (MWh) of electricity produced and then determining the economic dispatch for both units to meet the load demand at minimum cost.

However, since the problem asks for an iteration based on a new coal cost but does not provide a methodology or additional data to recompute the dispatch, we cannot give an exact value for the power output of Unit 2 during time period 1, hence the answer is 'c. None of these'. Additionally, Unit 1 (Gas) operates within its given capacity constraints (50 MW < P1 < 500 MW).