Question

A constant load of 300 MW is supplied by two 200 MW generators, unit 1 and unit 2, for which the respective incremental fuel costs are

dC1/dPg1 = 0.1 Pg1 +20.00 and dC2/dPg2 = 0.12 Pg2 + 15.00
with powers Pg in MW and costs C in $/h
The saving in $/day thereby obtained compared to equal sharing between the generators ?

Answer 1

The question involves economic dispatch in power generation, where we calculate the optimal load distribution between two generators to minimize fuel costs. The cost savings are determined by comparing the cost of the optimal load distribution to an equal distribution strategy.

Step-by-step explanation:

The question is asking for a calculation of cost savings achieved by using two power generators with different incremental fuel costs to supply a constant load rather than an equal share strategy. By applying principles of economic dispatch, we determine the most cost-effective distribution of load between the generators.

To find the optimal cost savings, we calculate the power output for each generator, where Pg1 + Pg2 = 300 MW. The incremental costs for generators 1 and 2 are given as dC1/dPg1 = 0.1 Pg1 + 20 and dC2/dPg2 = 0.12 Pg2 + 15. We want to set these equal to each other to find the most economical distribution of load.

By setting the incremental costs equal, we solve for the values of Pg1 and Pg2 that minimize the total fuel cost. The savings can then be calculated by comparing the cost with the optimal distribution to the cost of the equal distribution of load between the two generators (150 MW each). Finally, multiplying the hourly savings by 24 gives us the daily savings in dollars.