Page 356 - Wind Energy Handbook

330 CONCEPTUAL DESIGN OF HORIZONTAL-AXIS TURBINES

6.2.1 Cost modelling

The sensitivity of the cost of energy to changes in the values of parameters
governing turbine design can be examined with the aid of a model of the way
component costs vary in response. The normal procedure is to start with a baseline
design, for which the costs of the various components are known. In a rigorous
analysis, the chosen parameter is then assigned a different value and a fresh design
developed, leading to revised component weights, based on which new component
costs can be assigned.
In general, the cost of a component will not simply increase pro rata with its mass,
but will contain elements that increase more slowly. An example is the tower
surface protective coating , the cost of which increases approximately as the square
of the tower height, if all dimensions are proportional to this height. If the design
parameter variation considered is only about þ/ 50 percent, it is usually suffi-
ciently accurate to represent the relationship between component cost and mass as
a linear one with a fixed component:

m(x)
C(x) ¼ C B ì þ (1 ì) (6:1)
m B

where C(x) and m(x) are the cost and mass of the component respectively when the
design parameter takes the value x, and C B and m B are the baseline values; ì is the
proportion of the cost that varies with mass, which will obviously differ for differ-
ent baseline machine sizes.
The choice of the value of ì inevitably requires considerable expertise as regards
the way manufacturing costs vary with scale, which may be limited in the case of
products at the early stage of development. In view of this, the effort of developing
fresh designs for different design parameter values may well not be justified, so
resort is often made to scaling ratios based on similarity relationships. This
approach is adopted in the investigation of optimum machine size which follows.

6.2.2 Simplified cost model for machine size optimization—an
illustration

The baseline machine design is taken as a 60 m diameter, 1.5 MW turbine, with the
costs of the various components taken from Fuglsang and Thomsen (1998). These
are given in Table 6.1 as a percentage of the total.
Machine designs for other diameters are obtained by scaling all dimensions of all
components in the same proportion, except in the case of the gearbox, generator,
grid connection and controller. Rotational speed is kept inversely proportional to
rotor diameter to maintain constant tip speed, and hence constant tip speed ratio at
a given wind speed. As a result, all machine designs reach rated power at the same
wind speed, so that rated power is proportional to diameter squared. Consequently
the low-speed shaft torque increases as diameter cubed, which is the basis for
assuming the gearbox mass increases as the cube of rotor diameter, even though the
gearbox ratio changes. Hence, if a blanket value of ì of 0.9 is adopted for simplicity,