WIND ENERGY SYSTEMS - Cd3wd
WIND ENERGY SYSTEMS - Cd3wd WIND ENERGY SYSTEMS - Cd3wd
Chapter 8—Economics 8–5 results with similar results for small machines, to see if there are any effects of size. Results of a study on small machines[6, 2] are given in Table 8.2. Column one gives the cost percentages for machines currently available in 1980 and column two gives the cost percentages predicted for second and third generation machines in 1990. TABLE 8.2 Construction Costs for Small Wind Turbines(%) 1980 1990 Rotor and hub 12.0 20.5 Controls 6.0 6.6 Transmission 11.0 14.5 Generator/power conversion 7.0 11.6 Frame 8.0 2.4 Tower 18.0 7.5 Installation 20.0 25.6 Distribution 16.0 9.5 Shipping 2.0 1.8 100.0 100.0 We see in this table that the frame and tower are two components which have a good potential for cost reduction, from 26 percent to 10 percent of total cost. The cost of distribution (dealerships, service groups, etc.) would appear to have some potential for cost reduction. As the percentage of these cost components is reduced, then other components become relatively more expensive. We see installation increasing from 20 to 25 percent of the total cost, indicating a need for considerable innovation in this area. There are no major differences between projected percentage costs for the large and small turbines. Major cost components are blades, transmission, tower, and installation for all turbines, indicating that these components need to be carefully studied for possible cost reductions. One of the challenges of economic studies is to estimate the cost of the installed wind turbine when it is being produced in large quantities. The cost of the initial few machines is quite high because of many specially made parts and substantial amounts of hand labor while later machines are able to take advantage of higher volume production. A decrease in cost per unit of product with increase in volume has been found to occur in a wide variety of areas, including Model-T Fords, aircraft, steel production, petroleum refining, and electric power generation. The classic example in recent times has been the hand-held calculator, along with other integrated circuit components. This decrease in cost has been formalized by learning curves. These are widely used in many different industries. They are developed from the following mathematical model. If y represents the cost of an object while x represents the cumulative volume, then the normalized incremental cost dy/y is assumed to be related to the normalized incremental volume dx/x Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
Chapter 8—Economics 8–6 by the differential equation dy y = −mdx (1) x The parameter m is a constant of proportionality and the sign is negative because the cost decreases while the volume increases. We integrate this equation from the cumulative volume x to the volume x(2 n ). The cost is decreasing from y 1 to y 2 while the cumulative volume is doubling n times. The result is Solving for y 2 yields ln y 2 y 1 = −(mn)ln2 (2) The slope s of the cost curve is defined as y 2 = y 1 e −(mn)ln2 (3) The cost y 2 after n doublings of volume is then s = e −m ln 2 (4) y 2 = y 1 s n (5) The plot of y 2 versus n is a straight line on log-log paper. Figure 2 shows plots of normalized y 2 (for y 1 = 1) for slopes of 0.95, 0.9, 0.85, and 0.8. Given the cost of the first unit and the slope of the learning curve, one can estimate the cost of the tenth or hundredth unit of production, as well as all intermediate values. We normally think in terms of the cumulative production volume x rather than the number of volume doublings n, so we need a relationship between n and x. It can be shown that the value of n for an increase in volume from x 1 to x 2 is n = ln(x 2/x 1 ) ln 2 (6) The choice of slope s is critical to economic studies. This requires information about other learning curves from the past as well as careful estimates about how manufacturing costs should go in the future. Historical research has shown[5] slopes of 0.86 for Model-T Fords, 0.8 for aircraft assembly, 0.95 for electric power generation, 0.79 for steel production, and 0.74 for hand-held calculators. Various parts of the wind turbine would be expected to show different learning curves. Components such as blades, hubs, and gearboxes that are essentially unique to wind turbines would have smaller values of s. Electrical generators, on the other Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
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Chapter 8—Economics 8–5<br />
results with similar results for small machines, to see if there are any effects of size. Results of<br />
a study on small machines[6, 2] are given in Table 8.2. Column one gives the cost percentages<br />
for machines currently available in 1980 and column two gives the cost percentages predicted<br />
for second and third generation machines in 1990.<br />
TABLE 8.2 Construction Costs for Small Wind Turbines(%)<br />
1980 1990<br />
Rotor and hub 12.0 20.5<br />
Controls 6.0 6.6<br />
Transmission 11.0 14.5<br />
Generator/power conversion 7.0 11.6<br />
Frame 8.0 2.4<br />
Tower 18.0 7.5<br />
Installation 20.0 25.6<br />
Distribution 16.0 9.5<br />
Shipping 2.0 1.8<br />
100.0 100.0<br />
We see in this table that the frame and tower are two components which have a good potential<br />
for cost reduction, from 26 percent to 10 percent of total cost. The cost of distribution<br />
(dealerships, service groups, etc.) would appear to have some potential for cost reduction.<br />
As the percentage of these cost components is reduced, then other components become relatively<br />
more expensive. We see installation increasing from 20 to 25 percent of the total cost,<br />
indicating a need for considerable innovation in this area.<br />
There are no major differences between projected percentage costs for the large and small<br />
turbines. Major cost components are blades, transmission, tower, and installation for all<br />
turbines, indicating that these components need to be carefully studied for possible cost<br />
reductions.<br />
One of the challenges of economic studies is to estimate the cost of the installed wind<br />
turbine when it is being produced in large quantities. The cost of the initial few machines is<br />
quite high because of many specially made parts and substantial amounts of hand labor while<br />
later machines are able to take advantage of higher volume production. A decrease in cost per<br />
unit of product with increase in volume has been found to occur in a wide variety of areas,<br />
including Model-T Fords, aircraft, steel production, petroleum refining, and electric power<br />
generation. The classic example in recent times has been the hand-held calculator, along with<br />
other integrated circuit components.<br />
This decrease in cost has been formalized by learning curves. These are widely used in<br />
many different industries. They are developed from the following mathematical model. If y<br />
represents the cost of an object while x represents the cumulative volume, then the normalized<br />
incremental cost dy/y is assumed to be related to the normalized incremental volume dx/x<br />
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001