Question

Consider two generating units with input-output curves
Unit 1: coal-red steam unit: H1 (P1) = 500 + 8P1
Unit 2: gas turbine: H2 (P2) = 210 + 7P2
and operating limits
Unit 1: 150< P1 < 500 MW
Unit 2: 100 < P2 < 250 MW
Suppose the fuel costs are
Coal: $3.50/MBtu
Gas: $2.50/MBtu
and the load is L = P1 + P2 = 600 MW.
Both units are on so that unit 1 must supply at least 150 MW and unit 2
must supply at least 100 MW.
(a) Determine the P1 and P2 Such that the total generation cost
c (P1; P2) = 3:50 H1 (P1) + 2:50 H2 (P2)
to supply 600 MW is minimized. Calculate the generation cost. (Hint: write
c (P1; P2) in the form c (P1; P2) = a0 + a1P1 + a2P2 and the solution should be
obvious.)

(b) Suppose the load is increased to 601 MW. What is the change in generation
cost?

Answer 1