GATE Electrical Engineering (EE) 2023 Solved Paper

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 ) = 0.1 $\mathit{a}{\mathit{P}}_{\mathit{G}1}^2$ + 40 𝑃_𝐺1 + 120 𝑅𝑠/ℎ𝑜𝑢𝑟 0 𝑀𝑊 ≤ 𝑃_𝐺1 ≤ 350 MW
𝐹₂ (𝑃_𝐺2) = 0.2 ${\mathit{P}}_{\mathit{G}2}^2$ + 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. With 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