SOLUTION: Optimal Unit Commitment Schedule Problems

PROBLEM 1
Part a) You are given the three generating units and asked to find the optimal unit
commitment schedule for the units to supply load over a 4 hour time period.
The generators have input output functions, H (P) which have a mathematical form of
H (P) = a +bP+cP in MBTU/h
The parameters for the three generators are:
a
b
C
Pmax
Unit
1
2
0.02
Fuel
Cost
$/MBTU
2.0
1.0
1000
800
12
Pmin
MW
20
30
10
10
10
MW
250
300
200
0.06
3
10
0.07
2.5
The hourly load is:
Hour
1
2
3
4
MW Load
220
400
600
350
Each generator has a start up cost that must be factored in when the unit starts. You
should assume that this start up cost is incurred even if the unit was on then off for only
one or two hours and than gets turned back on.
Generating Unit
1
2
3
Start Up cost
2400
3600
2000
You have been provided with a worksheet on the page 3 which has the unit combinations
ordered by capacity and for each hour the economic dispatch total cost to supply that load
is given for each feasible combination. If a combination is infeasible for a given load than
there is an X shown.
Find the optimal unit commitment schedule.
Part b) For the problem in part a, what is the optimal schedule if unit 1, once it is started
must stay on for 2 hours.
The table below shows the production cost for the units to supply the hourly load given in the bottom row.
This table’s numbers do not include start up cost or accumulated cost from previous hours. Start up costs
are given in the small table at the bottom.
Row No
Unit 1 2 3
1
combination 111
MW Capacity
750
10236
15659
23374
14014
2
combination 1 10
MW Capacity
550
7232
12790
х
11090
3
combination 0 11
MW Capacity
500
8766
16450
х
13874
4
combination 101
MW Capacity
450
11151
20188
х
16750
5
combination 0 1 0
MW Capacity
300
5904
х
X
х
6
combination 100
MW Capacity
250
8336
х
х
х
7
combination 001
MW Capacity
200
х
х
х
х
8
combination 000
MW Capacity
0
start
х
х
х
х
Hour
1
2
3
4
Load
220
400
600
350
X
is an infeasible state
Unit
1
2
3
Start up cost
2400
3600
2000

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