The Black Swan Power company owns a generator that runs on LNG fuel. The fuel
costs are relatively expensive, but it is economic to turn on the generator when
electricity prices are high enough. However the operation of the generator is subject to
‘ramp rate’ constraints. The capacity of the generator is 180 MW, but the power
supplied can increase by at most 50 MW in any half hour period. Moreover the
generator cannot be shut down too quickly, so that the power supplied can be reduced
by at most 90 MW in any half hour period. So if, for example, the generator is off for
the period 3.30pm to 4pm, then it cannot reach full capacity till the period 5.30pm to
6.00pm.
Assume that LNG costs are relatively stable and the cost per MWh (one megawatt for
one hour) of generation from this source is $37.50. So that when electricity prices are
above $37.50 per MWh the generator can make money and it will lose money if
prices are below $37.50 per MWh.


Question： The managers need to decide a schedule of operation on a half hourly
basis over the course of a winter afternoon/evening from 4 pm till midnight.
Suppose that the schedule of operation has to be set in advance and the operators
wish to maximize expected profit. Show how this problem can be formulated as a
(linear) optimization problem assuming that there are representative scenarios
available.