3 Unit Commitment (40 pts) Consider the utility has the following load profile: Hour 12AM - 8AM 8AM - 4PM 4PM - 8PM 8PM - 12AM Demand [MW] 345MW 525MW 565MW 425MW 1. Assume only Unit 1 is on at the start of the day. Solve the unit commitment. For each period, calculate the dispatch result, on/off status of each generator, and the marginal system cost. Also show the total system operating cost of the day. Hour Status Dispatch (MW) Marginal Cost Unit 1 Unit 2 Unit 3 Unit 1 Unit 2 Unit 3 (S/MWh) 12AM - 8AM 8AM - 4PM 4PM-8PM 8PM - 12AM Total operating cost: Table 2: Example Unit Commitment Schedule Table 2. Assume the utility conducted an upgrade for Unit 2 and its maximum generation capacity is increased from 200MW to 300MW. Calculate how much this utility could save from this upgrade in this operating day. Please list out the full optimization problem and explain your solution strategy. You can use any preferred solution method to solve the problem, including using optimization software. If you are using the piece-wise linear method to solve the economic dispatch, please re-calculate the actual marginal cost and total system cost using the dispatch result and the actual cost function (not the piece-wise linear ones). 3 Unit Commitment (40 pts) Consider the utility has the following load profile: Hour 12AM - 8AM 8AM - 4PM 4PM - 8PM 8PM - 12AM Demand [MW] 345MW 525MW 565MW 425MW 1. Assume only Unit 1 is on at the start of the day. Solve the unit commitment. For each period, calculate the dispatch result, on/off status of each generator, and the marginal system cost. Also show the total system operating cost of the day. Hour Status Dispatch (MW) Marginal Cost Unit 1 Unit 2 Unit 3 Unit 1 Unit 2 Unit 3 (S/MWh) 12AM - 8AM 8AM - 4PM 4PM-8PM 8PM - 12AM Total operating cost: Table 2: Example Unit Commitment Schedule Table 2. Assume the utility conducted an upgrade for Unit 2 and its maximum generation capacity is increased from 200MW to 300MW. Calculate how much this utility could save from this upgrade in this operating day. Please list out the full optimization problem and explain your solution strategy. You can use any preferred solution method to solve the problem, including using optimization software. If you are using the piece-wise linear method to solve the economic dispatch, please re-calculate the actual marginal cost and total system cost using the dispatch result and the actual cost function (not the piece-wise linear ones)