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Small Wind Energy Systems 163

proportional to their operating speed. In accordance with Figure 7.2, the gearbox efficiency can be
calculated as given by the following equation:

η
P gear = P gear rated, (7.6)
η rated
where
is the loss in the gearbox at rated speed (in the order of 3% at rated power)
P gear rated,
η is the rotor speed (r/min)
η rated is the rated rotor speed (r/min)

The losses in the gearbox dominate the efficiency on most wind turbines, and a simple calculation
shows that small wind turbine systems, with low wind velocity range, have roughly 70% of their
annual energy dissipation because of the mechanical various losses plus the gearbox efficiency [13].
The design of an electrical machine is often considered from the point of view of obtaining the
maximum torque. Usually, the external volume (or the weight) of the machine is sized by their
maximum torque for the considered application, but for a generator application, the designer should
consider the shaft power production profile. The wind turbine power has a performance coefficient
C p , which considers the turbine mechanical design together with their aerodynamic efficiency. The
tip-speed ratio (TSR) λ is a function of ω r the generator rotational speed, the radius of the blade, and
the linear wind velocity as given by Equation 7.7. One can design a generator by maximizing the C p
(
coefficient at the minimum speed v min) in order to obtain a given turbine power, for example, for a
very small system such as P turbine = 5kW.

ω ⋅r
λ = (7.7)
v
T ) is calculated. Figure 7.3 shows that
Then, for such a 5 kW generator, the maximum torque ( max
v ), the power is limited to a maxi-
for a minimum wind speed up to the maximum wind speed ( max
P ), the wind
mum power ( max ), and also when the wind velocity is less than a certain limit speed (v lim
generator will stop.
Three wind power generator designs have been compared—one with ferrite, another with
bounded NdFeB, and a third one with sintered NdFeB as discussed in [13]. The active length is
calculated from their required torque for a given operating range and simulated by 2D finite element
analysis. Both copper ()P c and iron ()P i losses are calculated by
c (
v (
2
Pv min) = σ c JV v min) (7.8)
where
σ is the copper resistivity
c
J is the current density (in this case, equal to 5 A/mm )
2
v )
V c is the copper volume, which depends on the minimum wind velocity ( min
k Bv Mv min )
i (
PB fv min ) = ( s ) ( v , (7.9)
,
,
,
v ,
s s i
where
k is an iron loss coefficient determined by the iron flux density ()B s and the frequency (in this
case, which is determined by the wind velocity)
M i is the iron mass, which depends on the minimum and actual wind velocity
Copper and iron losses are represented in Figure 7.8 and compared for the increasing power level.
The generator has a certain operating region around the power and velocity curves; the integral of