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Power Generation

A number of power stations are committed to meeting the following electricity load demands over a day:

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Time of Day

Electricity Load (in Megawatts)

00:00 – 06:00

15,000

06:00 – 09:00

30,000

09:00 – 15:00

25,000

15:00 – 18:00

40,000

18:00 – 24:00

27,000

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Power Generation

There are three types of generating unit available. Each generator has to work between a minimum and a maximum level (in Megawatts).

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2

Generator Type

No. of Generators

Min. Level (Megawatts)

Max. Level (Megawatts)

1

12

850

2,000

2

10

1,250

1,750

3

5

1,500

4,000

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Power Generation

Starting up a generator involves a cost. There is also an hourly cost of running each generator at its minimum level. In addition, there is an extra hourly cost for each megawatt at which a unit is operated above its minimum level. All this information is given in the table below

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Generator Type

Starting Cost

Cost/ hour at Min. Generation Level

Cost/hour/megawatt above Min. Generation Level

1

2000

1000

2.0

2

1000

2600

1.30

3

500

3000

3.0

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Power Generation

In addition to meeting the estimated load demands, there must be sufficient generators working at any time to make it possible to meet an increase in load of up to 15%. This increase would have to be accomplished by adjusting the output of generators already operating within their permitted limits.

Which generators should be working in which periods of the day to minimize total costs?

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Mathematical Model

 

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Mathematical Model

 

6

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Mathematical Model

 

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Mathematical Model

 

8

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Mathematical Model

 

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Optimal Solution

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Cost = 1,015,150.0

Start [*,*] (tr)

: 1 2 3:=

1 12.0 2.0 0.0

2 0.0 6.0 0.0

3 0.0 0.0 0.0

4 0.0 1.0 2.0

5 0.0 0.0 0.0;

Operate [*,*] (tr)

: 1 2 3:=

1 12.0 2.0 0.0

2 12.0 8.0 0.0

3 12.0 8.0 0.0

4 12.0 9.0 2.0

5 12.0 9.0 0.0;

Output [*,*] (tr)

: 1 2 3:=

1 11500.0 3500.0 0.0

2 16000.0 14000.0 0.0

3 11000.0 14000.0 0.0

4 21250.0 15750.0 3000.0

5 11250.0 15750.0 0.0;

Stop [*,*] (tr)

: 1 2 3:=

1 0.0 0.0 0.0

2 0.0 0.0 0.0

3 0.0 0.0 0.0

4 0.0 0.0 0.0

5 0.0 0.0 2.0;