The functions of two power plants, of a lossless system, are as follows:

a. Write the LaGrange function
b. Write KKT conditions
c. Assume that the demand is PD. Express the incremental cost of the system as a function of PD when economic dispatch is optimal.
d. Assume that the demand is PD. Express the incremental cost of the system as a function of PD when economic dispatch is optimal, and when unit 2 operates at the maximum limit.
 

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F₁ (P₁) = C₁ = 900 +45P₁ + 0.01P² F₂ (P₂) = C₂: = 2500+ 43P₂ +0.003P² [$/h] [$/h] 50 P₁ ≤ 200 MW 50 P₂ ≤ 600 MW F₁ (P₁) = C₁ = 900 +45P₁ + 0.01P² F₂ (P₂) = C₂: = 2500+ 43P₂ +0.003P² [$/h] [$/h] 50 P₁ ≤ 200 MW 50 P₂ ≤ 600 MW