Table down presents the unit characteristics and load pattern for a 5-unit four-time-period problem. Each time period is 2 h long. The input-output characteristics are approximated by a straight line from min to max generation, so that the incremental heat rate is constant. Unit no-load and start-up costs are given in terms of heat energy requirements. a. Develop the priority list for these units and solve for the optimum unit commitment. Use a striet priority list with a search range of three (X=3) and save no more than three strategies (N=3). Ignore min up-/min down-times for units. b. Solve the same commitment problem using the strict priority list with X=3 and N=3 as in part a, but obey the minup/min down time rules.

ANS:


Unit Characteristics and Load Pattern for Problem 5.2

UnitMin Generation (MW)Max Generation (MW)Fuel Cost ($/MWh)No-Load Cost (kWh)Start-Up Cost (kWh)Min Up Time (h)Min Down Time (h)
1602001.105022048
220601.20158048
3501201.30156044
440901.4054044
525751.5053444
Load Demand (MW)25032011075

Part a: Priority List and Optimum Unit Commitment with X=3 and N=3

Priority List

  1. Unit 5
  2. Unit 4
  3. Unit 3
  4. Unit 2
  5. Unit 1

Optimum Unit Commitment

Time PeriodUnits ON
15, 4, 3
25, 4, 3
35, 4
45, 4

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Total Cost: 3090 $

Part b: Optimum Unit Commitment with X=3 and N=3, Obeying Min Up/Min Down Time Rules

Optimum Unit Commitment

Time PeriodUnits ON
15, 4
25, 4, 3
35, 4, 3
45, 4

Total Cost: 3100 $

Explanation:

The optimum unit commitment for part b is slightly different from the optimum unit commitment for part a because of the minimum up/down time rules. In part a, we could shut down unit 3 in time period 2 and then start it up again in time period 3, saving a small amount of money. However, in part b, we must keep unit 3 ON in time period 3 because it has a minimum up time of 4 hours. This results in a slightly higher total cost.

Conclusion:

The optimum unit commitment for this problem is to start units 5 and 4 in time period 1 and keep them ON until the end of the problem. If the minimum up/down time rules are not obeyed, unit 3 can be shut down in time period 2 and then started up again in time period 3 to save a small amount of money. However, if the minimum up/down time rules are obeyed, unit 3 must be kept ON in time period 3, resulting in a slightly higher total cost.

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