This is a solution to a three unit-commitment problem for different scenarios, 1- three hours UC with no constraints, 2- Three hours UC with constraint of Reserve of 7% of the load, 3- Three hours UC with constraint of Ramp rate of 55MW/h for all units, 4- Four Hours UC with no constraint Excel File is available upon request

1. Part1
Initial
State
Hour
1 0 0
Demand
(MW)
A B C Pmin (MW) Pmax (MW)
1 1 1 170 475 1 1 1 0 1 1
1 1 0 150 400 1 1 0 1 1 1
1 0 1 120 325 1 0 1 1 1 1
1 0 0 100 250 1 0 0 1 0 1
0 1 1 70 225 0 1 1 1 0 1
0 1 0 50 150 0 1 0 1 0 0
0 0 1 20 75 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0
Unit
Pmin
(MW)
Pmax
(MW)
Min Up
(TD)
(h)
Min Down
(TU)
(h)
No Load
Cost
($)
Marginal
Cost
($MWh)
A 100 250 4 3 300 8
B 50 150 2 1 200 15
C 20 75 1 1 0 18
Unit
Status
00
01
10
11
All Cheapest
A B C
1 0 1 1 0 500 Green 150 100 0 0 2,550 2,550 1 1 0
2 0 1 0 1 200 Green 150 130 20 0 1,900 1,900 1 0 1
3 0 1 0 0 0 Green 150 150 0 0 1,500 1,500 1 0 0
1 200 Green 1 6,200 5,850
2 500 Green 2 5,850 5,650
3 700 Orang 3 5,650
1 0 Green 1 5,800 5,800
2 500 Orang 2 5,650
3 500 Orang 3 5,250 5,250
2 0 Green 2 5,100
3 200 Green 3 4,900 4900
4 0 Green 4 8,300
5 200 Green 5 8,100
6 500 Green 6 8,050 8,050
4 0 Green 4 8,100
5 0 Green 5 7,700
6 500 Green 6 7,850
4 0 Orang 4 7,950
5 200 Orang 5 8,100
6 0 Green 6 7,000
4 0 Orang 4 7,750
5 0 Orang 5 7,700
6 0 Green 6 6,800
4 0 Green 4 9,000
5 200 Green 5 8,800
6 500 Green 6 8,750
The cheapest path from analysing above table is to arrive at State 10 in Hour 3, with total cost of $ 6,800. Tracing back the path, below is the UC plan
Cost with Predecessor statesLowest
Transition
plus State
Cost
2,550
1,900
1,500
First Three Hours No Ramp Rate Nor Spinning Reserve were considered
1,000 11
500 01
200
Unit Data
Start Up Cost
($)
Initial Status
Units Possible Operating Scenarios
System
State 1 2 3
150 300
Colour Coding: at most one Orange can be in the UC plan
Hourly Demand
Unit has been OFF for time ˂ TD
Unit has been OFF for time ≥ TD
Unit has been ON for time ˂ TU
200 01
Description Action
Can NOT start unit
Can start unit
Can NOT Shut Down Unit
11 0 1 1
1 0 1
1 1 1
1 1 0
1 0 19
8
7
6
Can Shut Down Unit
Unit Status Description
Unit has been ON for time ≥ TU
To
State
From
State
250 50
250
5
4
1 1 0
Operating Cost
Start-up
Shutdown
Cost
Colour Code
Demand PA PC
1 1 1
System
State
Transition Costs
0300
300
10
State CostPB
300
2050
1700
1500
0
0
50
3450
3250
1 0 0
230 50 20
200
200
200
150
0
130
3,650
3,950
50 3200
2,100
2,300
2,100
50 0 2450
3,200
3,400
50 20 2650200
0 1 10 150 50 3350
1
1 0 0200 0 0 1900
180 0 20 2100
200 3,550
3,850
3,350
1,900
Unit Status
1 1
1
4,150
3,250
3,750
3,750
From State
1 1 0
1
1 1
01
1
1
2,650
2,850
3,150
1 0
2,450
2,450
2,950
1 0
1,900
1,900
7
8
9
1
2
3
4
5
6
11
100
6
100 3$ 0
$ 1500
$ 3,200
$ 1,900
TOTAL { 0, 3, 6, 10}
is $ 6,800
$ 6,800
$ 4,900
$ 1,500

2. Part 2
Initial
State
Hour
1 0 0
Demand
(MW)
A B C Pmin (MW) Pmax (MW)
1 1 1 170 475 1 1 1 0 1 1
## # 0
1 1 0 150 400 1 1 0 1 1 1
## # #
1 0 1 120 325 1 0 1 1 1 1
## #
1 0 0 100 250 1 0 0 1 0 1
## #
0 1 1 70 225 0 1 1 1 0 1
## #
0 1 0 50 150 0 1 0 0 0 0
## #
0 0 1 20 75 0 0 1 0 0 0
## #
0 0 0 0 0 0 0 0 0 0 0
Unit
Pmin
(MW)
Pmax
(MW)
Min Up
(TD)
(h)
Min Down
(TU)
(h)
No Load
Cost
($)
Marginal
Cost
($MWh)
A 100 250 4 3 300 8
B 50 150 2 1 200 15
C 20 75 1 1 0 18
Unit
Status
00
01
10
11
all
Cheapest
A B C
1 0 1 1 0 500 Green 150 100 0 0 2,550 2,550 1 1 0
2 0 1 0 1 200 Green 150 130 20 0 1,900 1,900 1 0 1
3 0 1 0 0 0 Green 150 150 0 0 1,500 1,500 1 0 0
1 200 Green 1 5,700 5650
2 500 Green 2 5,650 5650
3 700 Orang 3 5,650
1 0 Green 1 5,300 5300
2 500 Orang 2 5,450
3 500 Orang 3 5,250 5250
2 0 Green 2 5,100
3 200 Green 3 4,900 4900
4 0 Green 4 8,300 8,300
5 200 Green 5 8,100 8,150
6 500 Green 6 8,050 8,050
4 0 Green 4 8,100 8,100
5 0 Green 5 7,700 7,750
6 500 Green 6 7,850
4 0 Orang 4 7,750
5 200 Orang 5 7,600
6 0 Green 6 7,000
4 0 Orang 4 7,550
5 0 Orang 5 7,200
6 0 Green 6 6,800
4 0 Green 4 9,000 9,000
5 200 Green 5 8,800
6 500 Green 6 8,950
The cheapest path from analysing above table is to arrive at State 10, with total cost of $ 6,800. Tracing back the path, below is the UC plan
Observations:
> Operating Scenario 0 1 0 could not supply the 7% Reserve Demand since Pmax is 150MW which is the
lowest hour demand during the three hour period, however this did not affect at all since it was not
viable scenario in the original case
> The Base case scenarios are capable of supporting 7% load reserve, hint, the overall UC plan and
cost did not change
0 01,900
1,900
11 0 1 1 200 0 150 50 3350
3,350
0 1 13,550
3,850
10 1 0 0 200 200 0 0 1900
1,900
1
02,450
2,950
9 1 0 1 200 180 0 20 2100
2,100
1 0 12,300
2,100
8 1 1 0 200 150 50 0 2450
2,450
1
0250 0 50 3200
3,200
1
1
1
3,400
7 1 1 1 200 130 50 20 2650
2,650
1 1 12,850
3,150
6 1 0 1 300
1 1 13,950
4,150
5 1 1 0 300 250 50 0 3250
3,250
1 1 03,750
3,750
0 1700 1,900
0 1500 1,500
4 1 1 1 300 230 50 20 3450
3,650
State Cost
Lowest
Transition
plus State
Cost
From State
Cost with Predecessor states
Unit Status
50 2050 2,550
To
State
From
State
System
State
Start-up
Shutdown
Cost
Colour Code
Demand PA PB PC
Unit has been OFF for time ≥ TD Can start unit
Unit has been ON for time ˂ TU Can NOT Shut Down Unit
Unit has been ON for time ≥ TU Can Shut Down Unit
Transition Costs Operating Cost
200 01
Unit Status Description
Description Action
Unit has been OFF for time ˂ TD Can NOT start unit
Colour Coding: at most one Orange can be in the UC plan
Unit Data
Start Up Cost
($)
Initial Status
1,000 11
500 01
First Three Hours UC considering 7% Reserve of the hour demand and ignoring Ramp Rate
Units Possible Operating Scenarios
System
State
Hourly Demand
1 2 3
150 300 200
7
8
9
1
2
3
4
5
6
11
100
6
100 3
$ 200
$ 0
$ 1500
$ 3,200 $ 0
TOTAL { 0, 3, 6, 10}
is $ 6,800
$ 1,900
$ 6,800
$ 4,900
$ 1,500

3. Part 3
Initial
State
Hour
1 0 0
Demand
(MW)
A B C Pmin (MW) Pmax (MW)
1 1 1 170 475 1 1 1 0 1 1
## # 0
1 1 0 150 400 1 1 0 1 1 1
## # #
1 0 1 120 325 1 0 1 1 0 1
## #
1 0 0 100 250 1 0 0 1 0 1
## #
0 1 1 70 225 0 1 1 1 0 1
## #
0 1 0 50 150 0 1 0 1 0 0
## #
0 0 1 20 75 0 0 1 0 0 0
## #
0 0 0 0 0 0 0 0 0 0 0
Colour Coding:
Unit
Pmin
(MW)
Pmax
(MW)
Min Up
(TD)
(h)
Min Down
(TU)
(h)
No Load
Cost
($)
Marginal
Cost
($MWh)
A 100 250 4 3 300 8
B 50 150 2 1 200 15
C 20 75 1 1 0 18
Unit
Status
00
01
10
11
all Cheapest
A B C
1 0 1 1 0 500 Green 150 100 0 0 2,550 2,550 1 1 0
2 0 1 0 1 200 Green 150 130 20 0 1,900 1,900 1 0 1
3 0 1 0 0 0 Green 150 150 0 0 1,500 1,500 1 0 0
1 200 Green 155 40 1 6,785 6,165
2 500 Green 185 20 2 6,165 5,825
3 700 Orang 205 20 3 5,825
1 0 Green 1
2 500 Orang 185 0 2 6,105
3 500 Orang 205 0 3 5,565 5,565
2 0 Green 2
3 200 Green 3
4 0 Green 130 20 4 8,475
5 200 Green 5
4 0 Green 150 0 4 8,275
5 0 Green 150 0 5 8,015
9 4 1 0 1 0 Orang 200 180 20 4 8,265 1 0 1
10 4 1 0 0 0 Orang 200 200 0 4 8,065 1 0 0
4 0 Green 0 50 4 9,175
5 200 Green 0 50 5 9,115
The cheapest path from analysing above table is to arrive at State 8 with total cost of $ 8,015. Tracing back the path, below is the UC plan
Observations:
> Considering the Ramp rate of 5 MW/hr did affect the UC. Many transitions were not possible and
state 6 from the base case is not visible anymore.
> The cost of UC increase by $ 1,215 from the Base case UC
0 1 1
150 3350 3,550
0 2100 2,100
0 1900 1,900
11 0 1 1 200
150 3350 3,350
Ramp Constraints
8 1 1 0 200
50 2450 2,450
1 1 0
50 2450 2,450
7 1 1 1 200
50 2650 2,650
1 1 1
6 1 0 1 300
Ramp Constraints
1 0 1
Ramp Constraints
5 1 1 0 300
Ramp Constraints
1 1 0115 3705 4,205
95 3565 4,065
1 1 195 3765 4,265
75 3625 4,325
0 1500 1,500
4 1 1 1 300
105 4035 4,235
State + Start
up cost
From State
Cost with Predecessor states
Unit Status
50 2050 2,550
0 1700 1,900
Transition Costs Operating Cost
To
State
From
State
System
State
Start-up
Shutdown
Cost
Colour Code
Demand PA PB PC
State Cost
( Marginal +
No load)
Unit has been OFF for time ˂ TD Can NOT start unit
Unit has been OFF for time ≥ TD Can start unit
Unit has been ON for time ˂ TU Can NOT Shut Down Unit
Unit has been ON for time ≥ TU Can Shut Down Unit
500 01
200 01
Unit Status Description
Description Action
at most one Orange can be in the UC plan
Dashed Gray transitions are not possible due to TD Constraints
Red Transitions are not possible due to Ramp Rate constraints
Unit Data
Start Up Cost
($)
Initial Status
1,000 11
Units Possible Operating Scenarios
System
State
Hourly Demand
1 2 3
150 300 200
First Three Hours UC considering Ramp Rate and ignoring Reserve Requirement
7
8
9
1
2
3
4
5
11
100
5
8
0 3$ 0
$ 1500
$ 5,565
$ 0
TOTAL { 0, 3, 5, 8} is
$ 8,015
$ 8,015
6
$ 3,565
$ 2,450
$ 1,500

4. Part4
Initial
State
Hour
1 0 0
Demand
(MW)
A B C Pmin (MW) Pmax (MW)
1 1 1 170 475 1 1 1 0 1 1 1 1
1 1 0 150 400 1 1 0 1 1 1 1 1
1 0 1 120 325 1 0 1 1 1 1 1 0
1 0 0 100 250 1 0 0 1 0 1 0 0
0 1 1 70 225 0 1 1 1 0 1 0 0
0 1 0 50 150 0 1 0 1 0 0 0 0
0 0 1 20 75 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
Unit
Pmin
(MW)
Pmax
(MW)
Min Up
(TD)
(h)
Min Down
(TU)
(h)
No Load
Cost
($)
Marginal
Cost
($MWh)
A 100 250 4 3 300 8
B 50 150 2 1 200 15
C 20 75 1 1 0 18
Unit
Status
00
01
10
11
All Cheapest
A B C
1 0 1 1 0 500 Green 150 100 0 0 2,550 2,550 1 1 0
2 0 1 0 1 200 Green 150 130 20 0 1,900 1,900 1 0 1
3 0 1 0 0 0 Green 150 150 0 0 1,500 1,500 1 0 0
1 200 Green 1 6,200 5,850
2 500 Green 2 5,850 5650
3 700 Orang 3 5,650
1 0 Green 1 5,800 5,800
2 500 Orang 2 5,650
3 500 Orang 3 5,250 5,250
2 0 Green 2 5,100
3 200 Green 3 4,900 4,900
4 0 Green 4 8,300 8,500 8,500
5 200 Green 5 8,100 8,650
6 500 Orang 6 8,050 8,050
4 0 Green 4 8,100 8,300
5 0 Green 5 7,700 8,250
6 500 Orang 6 7,850
4 0 Orang 4 7,950
5 200 Orang 5 8,100
6 0 Green 6 7,000
4 0 Orang 4 7,750 6,800
5 0 Orang 5 7,700
6 0 Green 6 6,800
4 0 Gray 4 9,000 9,200
5 200 Gray 5 8,800 9,350
6 500 Gray 6 8,750
7 0 Green 7 11,500
8 200 Green 8 11,350
9 500 Green 9 10,950
10 700 Green 10 10,950
7 0 Green 7 11,300
8 0 Green 8 10,950
9 500 Green 9 10,750
10 500 Green 10 10,550
7 0 Green 7 11,700
8 200 Green 8 11,250
9 0 Green 9 10,200
10 200 Green 10 10,200
12 0 Green 12 15,760
13 200 Green 13 15,560
14 500 Green 14 15,510
12 0 Green 12 13,700
13 0 Green 13 13,300
14 500 Green 14 13,450
The cheapest path from analysing above table is to arrive at State 16 with total cost of $ 13,300. Tracing back the path, below is the UC plan
1 15,010
5,310
16 1 1 0 400 0 150 50 2750
2,750
1 1 02,750
3,250
15 1 1 1 400 250 130 20 4810
4,810
1
1 0 1
3,400
3,200
3,400
3,750
14 1 0 1 300 250 0 50 3200
3,200
1 1
3,650
3,950
4,150
13 1 1 0 300 250 50 0 3250
3,250
1 1 0
3,250
3,750
12 1 1 1 300 230 50 20 3450
3,450
1
01,900
1,900
11 0 1 1 200 0 150 50 3350
3,350
0 1 13,550
3,850
10 1 0 0 200 200 0 0 1900
1,900
1
1200 150 50 0 2450
2,450
1
0
02,450
2,950
9 1 0 1 200 180 0 20 2100
2,100
1 0 12,300
2,100
8 1 1 0
1
3,400
7 1 1 1 200 130 50 20 2650
2,650
1 1 12,850
3,150
6 1 0 1 300 250 0 50 3200
3,200
1
1 1
0
13,950
4,150
5 1 1 0 300 250 50 0 3250
3,250
1 1 03,750
3,750
0 1500 1,500
4 1 1 1 300 230 50 20 3450
3,650
State + Start
up cost
From State
Cost with Predecessor states
Unit Status
50 2050 2,550
0 1700 1,900
Transition Costs Operating Cost
To
State
From
State
System
State
Start-up
Shutdown
Cost
Colour Code
Demand PA PB PC
State Cost
( Marginal +
No load)
Unit has been OFF for time ˂ TD Can NOT start unit
Unit has been OFF for time ≥ TD Can start unit
Unit has been ON for time ˂ TU Can NOT Shut Down Unit
Unit has been ON for time ≥ TU Can Shut Down Unit
500 01
200 01
Unit Status Description
Description Action
Colour Coding: at most one Orange can be in the UC plan
Dashed Gray transitions are not possible due to TD Constraints
Unit Data
Start Up Cost
($)
Initial Status
1,000 11
First Five Hours No Ramp Rate Nor Spinning Reserve were considered
Units Possible Operating Scenarios
System
State
Hourly Demand
1 2 3 4 5
150 300 200 300 400
7
8
9
1
2
3
4
5
6
11
100
6
100 3$ 0
$ 1500
$ 3,200 $ 6,800
TOTAL { 0, 3, 6, 10, 13, 16}
is $ 13,300
12
13
14
15
16
$ 1,500
$ 4,900
$ 1,900
13
$ 10,550
$ 3,250
16
$ 13,300
$ 2,750
$ 0