Direct drive superconducting wind generators - Wind Power Generation and Wind Turbine Design - page 307

machine is related to a magnetic shear stress in the airgap of the machine given by
the following equation:

t

(1 )

s =

g

2
rr

2 rl p

where s g is the airgap shear stress, t is the motor torque, r r is the rotor radius, and
l r is the rotor core length [7]. The shear stress is effectively the mean value of the
tangential component of the Maxwell stress tensor over the surface of the rotor,
which is dependant on the square of fl ux density, as shown in eqn (2). This defi nes
the Maxwell stress tensor in the cylindrical coordinate system for the magnetic
fi eld, assuming that the components due to electric fi elds can be ignored:

1 1

2

(2 )

s = BB − B d

rt r t rt

m 2 m

0 0

where r is the radial direction, t is the tangential direction, s rt is the Maxwell
stress tensor at a point, B is the magnetic fl ux density, µ 0 is the permeability of
free space and d is the Kronecker's delta. For this reason machines with a higher
airgap fl ux density are capable of higher shear stress. A comparison of the shear
stress obtainable in various types of electrical machine, including HTS, is given
in [ 13 ].
If the torque exceeds the maximum overload shear stress capability of the
generator then the machine will 'pull out' and cease to generate. The magnetic
fl ux density in the airgap is limited to approximately 1 T in conventional
machines by saturation in the iron magnetic circuit. Hence, for a given airgap
fl ux density, the size of any given type electrical machine is largely determined
by its torque rather than power. For this reason direct drive wind generators are
large compared to their high speed geared equivalents. For a given wind speed
and blade effi ciency, the power obtainable from a wind turbine is proportional to
the swept area of the rotor. Therefore, increasing the power of a wind turbine
means increasing the diameter of the rotor, and since the blade tip speed is main-
tained within a certain limit for either mechanical or environmental (noise) rea-
sons, this means a proportionally lower rotational speed and even higher torque
as turbine power increases.
Wind turbines are commercially available with direct drive conventional syn-
chronous generators, and turbines with direct drive permanent magnet genera-
tors (PMGs) are now beginning to appear, which have signifi cantly greater
torque density and hence smaller size and lower mass compared to conventional
generators.
In 2008, Converteam UK Ltd. delivered a prototype direct drive PMG to Siemens
Windpower in Denmark. This generator has been demonstrated on the Siemens
3.6 MW turbine at a test site in Denmark. Figure 2 shows this generator leaving
the Converteam factory in Rugby, UK.
Converteam UK Ltd. are also in the process of producing a 5 MW direct drive
PMG for the DarwinD offshore turbine.