#### EBF 483

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EBF 483 Homework 4 Due: Beginning of class on Thursday, Instructions: Please answer all questions clearly and completely. If you use graphs or tables in your answers, they must be clear enough that the graders can understand them (this means labeling axes, variables, and so forth). If a question requires you to make calculations, you must show your work. Your homework must be typed up and pages must be stapled together — the instructors will not accept homework that is handwritten or unstapled. See the syllabus for other formatting details. Each question is worth ten (10) points. The following questions refer to the three-node network below. 1. The total cost functions and maximum outputs for the two generators in the network are: TC(G1) = 8 + 2G1 G1_max = 40MW TC(G2) = 5 + 6G2 G2_max = 20MW where G1 and G2 represent energy output (MWh) at Generators 1 and 2, and TC is the total cost function. Solve the economic dispatch problem for the system, assuming that the customer at Node 3 demands 50 MWh of energy. Assume that demand is completely price-inelastic. Please provide the following information in your solution: a. The amount of electricity (MWh) produced by each generator; b. The system lambda, in $/MWh; c. Power flow on each of the three transmission lines; d. The total system cost of serving the 50 MWh of electricity demand 2. Repeat question 1, but assume that demand falls to 25 MWh. G1# L# G2# Node#1# Node#2# Node#3# R# 2R# R# 3. The total cost functions for the two generators in the network are: TC(G1) = 10 + 5G1 + 2G12 TC(G2) = 5 + 7G2 + G22 where G1 and G2 represent energy output (MWh) at Generators 1 and 2, and TC is the total cost function. Assume that there are no limits on how much electricity each generator can produce. Solve the economic dispatch problem for the system, assuming that the customer at Node 3 demands 60 MWh of energy. Assume that demand is completely price-inelastic. Please provide the following information in your solution: a. The amount of electricity (MWh) produced by each generator; b. The system lambda, in $/MWh; c. Power flow on each of the three transmission lines; d. The total system cost of serving the 60 MWh of electricity demand. 4. Now assume that Generator 2 can produce a maximum of 30 MWh (assume that there is no constraint on how much electricity Generator 1 could produce). How does this change the total system cost of serving the 60 MWh of electricity demand, and the power flows on each transmission line? (Hint: If you found in Question 3 that Generator 2 would optimally produce more than 30 MWh, you will need to reduce output on Generator 2 and increase output on Generator 1, then re-calculate the total system cost and power flows.)

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