This is an extension of the Tariff Rates (Power Generation) problem of Section 12.15 [Chapter 15].[17] In addition to the thermal generators a reservoir powers two hydro generators: one of type A and one of type B. When a hydro generator is running, it operates at a fixed level and the depth of the reservoir decreases. The costs associated with each hydro generator are a fixed start-up cost and a running cost per hour. The characteristics of each type of generator are shown in Table 16.1.
Table 16.1:
|
Operating |
|
Reservoir depth |
|
|
|---|---|---|---|---|
|
level |
Cost per hour |
reduction per hour |
Start-up cost |
|
|
Hydro A |
900 MW |
£90 |
0.31 metres |
£1500 |
|
Hydro B |
1400 MW |
£150 |
0.47 metres |
£1200 |
For environmental reasons, the reservoir must be maintained at a depth of between 15 and 20 metres. Also, at midnight each night, the reservoir must be 16 metres deep. Thermal generators can be used to pump water into the reservoir. To increase the level of the reservoir by 1 metre requires 3000 MWh of electricity. You may assume that rainfall does not affect the reservoir level.
At any time it must be possible to meet an increase in demand for electricity of up to 15%. This can be achieved by any combination of the following: switching on a hydro generator (even if this would cause the reservoir depth to fall below 15 metres); using the output of a thermal generator which is used for pumping water into the reservoir; and increasing the operating level of a thermal generator to its maximum. Thermal generators cannot be switched on instantaneously to meet increased demand (although hydro generators can be).
Which generators should be working in which periods of the day, and how should the reservoir be maintained to minimize the total cost?