|San José State University|
& Tornado Alley
of the Generation of Electrical Power from Solar Devices
Electric power generation from from solar devices is intermittent and uncertain. At best it is available only during the daylight hours and then at variable intensity. On cloudy days it is reduced, even to zero. It must be complemented by natural gas power generation which can be switched on and off daily and as sunlight varies. Or, more precisely expressed, solar 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 solar power equipment and its periodic replacement. The benefit of the combined natural gas and solar power system is value of the power generated, which is the same as the base case. The value of the solarpower system is the difference in the benefit and costs for alternate system and the base case. That difference reduces the savings in natural gas use made possible by the operation of the solarpower system. The difference in costs is essentially the costs of the solarpower 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 which the solar 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 a windpower generation system. 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 solarpower system is the value of the natural gas saved during its operation. The question then is, "How much solar power capacity is needed to generate one kilowatt-hour of electricity?" This is usually expressed in the relation
The load factor for solar generators is very low, on the order of 0.23. This is the value estimated by officials at Austin Energy, the electric power provider for Austin, Texas. This means that to get one kilowatt-hour of power generated the solar system needs 4.35 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 4.35 kilowatts of generating capacity would be saving $0.0456 per kilowatt-hour of power generated, or $0.0105 per hour per kilowatt of capacity. Per day that is 21 cents per day and $76.70 per year.
That $76.70 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 real interest rate in the U.S. is about 2.75 percent. Thus the present value of $76.70 per year forever is 76.70/0.0275, which is $2789.
Now the question is what is the cost of one kilowatt of generating capacity for solar power. The construction cost for the 30 megawatt solar facility Austin Energy of Austin, Texas was $180 million. This is $6000 per kilowatt of capacity. Likewise a 25-megawatt photovoltaic facility for Florida Power & Light in South Florida cost $152 million, which is $6080 per kilowatt of capacity. solar farm in the United Kingdom was about $5000 per kilowatt of generating capacity. Some of the
The equipment in the solar power facility has a finite life but with a discrepancy between $2789 worth of benefits and $6000 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 solar pwoer generation equipment is expected to last thirty years. If the equipment were to last for thirty years the discounted construction cost would be increased to about $10800 per kilowatt of capacity. The benefit cost ratio for the solar power is then 0.258, roughly speaking an insignificant one fourth.
The investment in solar power is a very poor use of a country's resources. Roughly three out of every four dollars invested will never be returned. This is under the best of circumstances. If the life of the equipment is only twenty years instead of thirty then the benefit cost ratio drops to 0.2.
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