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Problem 1:
A unit has a minimum ON time of 4 hours and a minimum OFF time of 3 hours. Assume that the unit is initially ON for 2 hours and the total number of scheduling periods is 24.
Model the minimum ON/OFF time constraints of the unit using startup indicators, shutdown indicators, only unit status variables, and ON/OFF time for the first 10 hours. Note that all variables used in the model should be defined.
Problem 2:
Unit G1’s minimum capacity is 200MW and its maximum capacity is 800MW. When G1 is OFF, its output is 0. When G1 is ON, there is a so-called prohibited zone constraint: G1 cannot operate between 300MW and 400MW, or between 600MW and 700MW.
List the MILP-based model for the above constraints on G1’s output considering its prohibited zone constraint. Note that all variables used in the model should be defined.
Problem 3:
A unit has the following parameters.
Min ON Time Min OFF Time Cold Start Hour Cold Start Cost ($) Warm Start Hour Warm Start Cost ($) Hot Start Hour Hot Start Cost ($)
4 hours 2 hours >=6 1000 4 to 5 500 <=3 300
List the MILP formulation for modeling the variable startup cost for the unit in an 8-hour unit commitment problem.
Problem 4:
A unit has the following fuel contract.
The unit has to pay a cost of $30,000 for up to 200 tons of fuel. Above 200 tons and below 300 tons, the fuel price is $120/ton. Beyond 300 tons, the fuel price is $100/ton.
List the MILP formulation that models the unit’s fuel contract.
Problem 5:
There are eight generating units in a power system. To ensure the security of the system operation, the following constraint has to be enforced.
If one or two of the three units in the west (G1, G2, and G3) is committed, at most three of the five units in the east (G4, G5, G6, G7, and G8) can be committed.
List the MILP formulation that can enforce the above constraint.
Sample Solution
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