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The expressions of fuel cost of two thermal generating units as a function of the respective power generation P_G1 and P_G2 are given as F1(P_G1) = 0.1aP_G1² + 40 P_G1 + 120 Rs/hour 0 MW ≤ P_G1 ≤ 350 MW F2(P_G2) = 0.2P_G2² + 30 P_G2 + 100 Rs/hour 0 MW ≤ P_G2 ≤ 300 MW where a is a constant. For a given value of a, optimal dispatch requires the total load of 290 MW to be shared as P_G1 = 175 MW and P_G2 = 115 MW. If the load remaining unchanged, the value of a is increased by 10% and optimal dispatch is carried out. The changes in P_G1 and the total cost of generation, F (= F1 + F2) in Rs/hour will be as follows

1. P_G1 will decrease and F will increase
2. Both P_G1 and F will increase
3. P_G1 will increase and F will decrease
4. Both P_G1 and F will decrease

Correct answer: P_G1 will decrease and F will increase

Solution

Increasing the value of 'a' in the fuel cost function F1(P_G1) raises the quadratic coefficient, making the cost of generating power at P_G1 more expensive. As a result, to minimize costs while maintaining the total load of 290 MW, P_G1 must decrease, leading to an overall increase in the total generation cost F.

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