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Question 3 A plant has two generators $G_1$ and $G_2$ supplying the plant bus. Their costs of generation are given by: $C_1 = 0.01P_{G1}^2 + 45P_{G1} + 900$ $/h$ $C_2 = 0.02P_{G2}^2 + 43P_{G2} + 2500$ $/h$ $G_1$ cannot operate below 50 MW or above 600 MW while $G_2$ cannot operate below 50 MW or above 800 MW. Calculate: (a) the optimum values of $P_{G1}$ and $P_{G2}$ such that the system load demand of 500 MW is met; and (7 marks) (b) the increase in the overall generation cost of the plant due to the generation limits when the system load demand is 1200 MW. (18 marks) (Total: 25 marks)

          Question 3
A plant has two generators $G_1$ and $G_2$ supplying the plant bus. Their costs of generation are given by:
$C_1 = 0.01P_{G1}^2 + 45P_{G1} + 900$ $/h$
$C_2 = 0.02P_{G2}^2 + 43P_{G2} + 2500$ $/h$
$G_1$ cannot operate below 50 MW or above 600 MW while $G_2$ cannot operate below 50 MW or above 800 MW. Calculate:
(a) the optimum values of $P_{G1}$ and $P_{G2}$ such that the system load demand of 500 MW is met; and
(7 marks)
(b) the increase in the overall generation cost of the plant due to the generation limits when the system load demand is 1200 MW.
(18 marks)
(Total: 25 marks)

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question 3 a plant has two generators g1 and g2 supplying the plant bus their costs of generation are given by c1 001pg12 45pg1 900 h c2 002pg22 43pg2 2500 h g1 cannot operate below 12009

Added by Jose Miguel S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Supreeta N

11/16/2023

Step 1

First, we find the incremental cost functions: $\frac{dC_1}{dP_{G1}} = 0.02P_{G1} + 45$ $\frac{dC_2}{dP_{G2}} = 0.04P_{G2} + 43$ For optimal operation, the incremental costs must be equal: $0.02P_{G1} + 45 = 0.04P_{G2} + 43$ $0.02P_{G1} - 0.04P_{G2} = -2$ $P_{G1} Show more…

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Question 3 A plant has two generators $G_1$ and $G_2$ supplying the plant bus. Their costs of generation are given by: $C_1 = 0.01P_{G1}^2 + 45P_{G1} + 900$ $/h$ $C_2 = 0.02P_{G2}^2 + 43P_{G2} + 2500$ $/h$ $G_1$ cannot operate below 50 MW or above 600 MW while $G_2$ cannot operate below 50 MW or above 800 MW. Calculate: (a) the optimum values of $P_{G1}$ and $P_{G2}$ such that the system load demand of 500 MW is met; and (7 marks) (b) the increase in the overall generation cost of the plant due to the generation limits when the system load demand is 1200 MW. (18 marks) (Total: 25 marks)

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