Recall that the \"system lambda\" is the cost to the system owner of producing t
ID: 1801319 • Letter: R
Question
Recall that the "system lambda" is the cost to the system owner of producing the next MW over the next hour; it is equal to the incremental cost of an individual unit when the system is economically dispatched for minimum cost and the unit is not at an upper or lower generation limit. A two-unit system is given by the following data. C1(Pg1) = 0.015 middot (Pg1)2 + 2 middot (Pg1) + 6 C2(Pg2) = 0.020 middot (Pg2)2 + 6 middot (Pg1) + 4 The demand is 300MW Write the KKT conditions that must be satisfied at the optimal solution to this problem, assuming that both units are operating between their respective upper and lower limits. Set up the linear matrix equation to solve the economic dispatch problem for this system, assuming that both units are operating between their respective upper and lower limits. Do NOT solve the system of equations. The solution to the problem in (2) is Pg1 = 228.57MW, Pg2 = 71.43MW. Assuming that each unit has a minimum generation capability of 80 MW. Indicate why the given solution is not feasible. Identify the optimal feasible solution Identify the incremental costs of each unit at the optimal feasible solution Identify the system lambda at the optimal feasible solution Would the total cost of supplying the 300MW increase or decrease (relative to the total cost corresponding to the optimal feasible solution) if the minimum generation capabilities on both units were changed to 79MW?Explanation / Answer
1. ?L/?Pg1 = 0.03P1 + 2 - ? =0 ?L/?Pg 2 = 0.04 P2 + 6 - ? = 0 ?L/?? = P1 + P2 - 300 = 0 3. (a) Because Generator 2 is below its minimum capability (b) Pg2 = 80 MW , Pg1 = 300 - 80 ? 220 MW - Pg1 (c) ?C1/?Pg1 = 0.03 Pg1 + 2 = 0.03 · (220 )+ 2 = 8.6$ / MW - hr = IC1 ?C2/?Pg 2 = 0.04 Pg 2 + 6 = 0.04 · (80 )+ 6 = 9.2$ / MW - hr = IC2 (d) lambda = 8.6$/MW-hr ( Since unit 1 would supply the next MW-hr) (e) Total cost would decrease
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