|San José State University|
& Tornado Alley
of the Generation of Electrical Power from Wind Turbines
Electric power generation from wind turbines is intermittent and uncertain. It must be complemented by natural gas power generation which can be switched on and off as wind varies. Or, more precisely expressed, wind power makes economic sense, if at all, as a supplement to a natural gas power generating system. Thus the design of a power generation system would start with the required investment in the natural gas generating system required to satisfy a given schedule of demand. This would involve an initial investment in the facilities for natural gas power generation and its periodic replacement. The operating costs would involve the cost of the natural gas over time. There could also be maintenance costs over time. The benefit is the value of the power generated. This is the base case.
The alternate system is the same natural gas power system plus the initial investment in wind power equipment and its periodic replacement. The benefit of the combined natural gas and wind power system is value of the power generated, which is the same as the base case.
The value of the windpower system is the difference in the benefits and costs for the alternate system and the base case. The output of electricity is the same for both systems. The benefit of the windpower system is thus the savings in natural gas use made possible by the operation of that windpower system.
The difference in costs is essentially the costs of the windpower generation system.
Reducing the operation of the natural gas generating system might possibly extend the life of the system and hence reduce costs. However some investigators believe that the wear on the natural gas generators involved in cutting their operations back and then later starting them up again offsets any benefits of their downtimes while the wind turbines are generating electrical power. One study found that the reduced efficiency of the intermittent use of the natural gas generators entirely offset the savings on natural gas during the operation of the windpower generators. Here the saving on natural gas fuel will be accepted but there is no change in the timing of the replacement of the natural gas power generators.
Thus the benefit of the windpower system is the value of the natural gas saved during its operation. The question then is, "How much wind power capacity is needed to generate one kilowatt-hour of electricity?" This is usually expressed in the relation
The load factor for wind generators is very low, on the order of 0.2. This means that to get one kilowatt-hour of power generated the wind system needs 5 kilowatts of capacity.
The Energy Information Administration in its Annual Energy Outlook for December of 2010 gives the operating and maintenance (O&M) Cost for a conventional combined cycle natural gas electrical power generating system as $45.60 per megawatt-hour. The O&M cost includes the fuel costs. The O&M cost is then $0.0456 per kilowatt-hour (kwhr). So 5 kilowatts of generating capacity would be saving $0.0456 per kilowatt-hour of electricity or $0.0091 per hour per kilowatt of generating capacity. Per day that is 21.9 cents and $80 per year.
That $80 per year per kilowatt of generating capacity would go on year after year. The present value of a perpetuity of Y per year is Y/r, where r is the interest rate. In order to take into account the general increase in prices the interest rate should be a long term interest corrected for inflation; i.e., the real rate of interest. The long term interest rate in the U.S. is about 2.75 percent. Thus the present value of $80 per year forever is 80/0.0275, which is $2907.
Now the question is what is the cost of one kilowatt of generating capacity for wind power. The construction cost for the Sheringham Shoal offshore wind farm in the United Kingdom was about $5000 per kilowatt of generating capacity. Some of the equipment in the wind farm has a finite life but with a discrepancy between $2907 worth of benefits and $5000 as part of the capital cost it is hardly worthwhile to bother with refining the cost figure to take into account the finite life of the equipment. The wind generators are expected to last twenty to thirty years. If the equipment were to last for thirty years the discounted construction cost would be increased to about $9000 per kilowatt of capacity. The benefit cost ratio for the wind power is then 0.323, roughly speaking an insignificant one third. If the life span is twenty years then the discounted value of the construction cost would be $11940, in which case the benefit cost ratio is the even more insignificant 0.24.
The offshore construction cost would be higher than onshore construction but the cost of onshore wind farm have to include the value of the land occupied.
The investment in wind power is a very poor use of a country's resources. Roughly seven out of every ten dollars invested are never to be returned.
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