Work arrangement of generator set

some Electric power The system uses four different types of generators to meet the power demand . The known power demand of each time of day is shown in table 1.

surface 1： Daily electricity demand （ mw ,MW）

time interval （0-24）	0-5	5-7	7-10	10-13	13-17	17-20	20-22	22-24
demand	10000	20000	24000	32000	25000	26000	15000	12000

Each generator has a maximum generating capacity , When connected to the power grid , Its output power should not be lower than a certain minimum output power . All generators have a starting cost , And the fixed hourly cost of working in the minimum power state , And if the power is higher than the minimum power , Then there is a cost per megawatt per hour for the excess power , Marginal cost . These data are listed in table 2 in .

surface 2： Generator condition

	Quantity available	Minimum output power （MW）	Maximum output （MW）	fixed cost （ element / Hours ）	Marginal cost per megawatt （ element / Hours ）	start-up cost
model 1	10	800	1800	2200	2.7	4000
model 2	5	1000	1500	1800	2.2	1600
model 3	8	1200	2000	3800	1.8	2400
model 4	4	1800	3500	4600	3.6	1200

It is only allowed to start or shut down the generator at the beginning of each period . Different from starting the generator , It doesn't cost anything to shut down the generator .

problem （1） Which generators should be used in each period to minimize the total cost per day , What is the minimum total cost ？

problem （2） If at any time , The generator set in operation must be reserved 20% Generating capacity margin , In case of a sudden rise in electricity consumption . Then which generators should be used in each period to minimize the total cost per day , At this time, what is the minimum total cost ？

Choose to do ：（ Finished the question （1） And questions （2） And students who have spare power to learn, please continue ）

problem （3） If the power demand in each period of the day is in the table 1 On the basis of 30% Left and right fluctuations , And the system has no energy storage . At this time, according to problem （1） Power generation plan , There are two possible situations ：

1） System loss of load （ That is, the power demand is greater than the power generation ）,

2） Power generation is greater than demand , Cause power waste .

Assume that the loss of load loss is q（ Company ： element / mw ）, hypothesis q Value respectively q=600 and  q=5000 Then how should the generator set be arranged to generate electricity in each period ？

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