The weight of wind turbine generators is a significant issue because weight translates to costs. The structural weight of a direct-drive generator, for example, can exceed 80% of the total weight on the tower. The structure is needed to overcome the force of magnetic attraction between stationary and moving parts. The attraction force, a result of the normal component of Maxwell stress, can be 10 times the torque producing shear stress. The function of the generator structure is to maintain an airgap between the rotor and stator.
Ideally, a directly-driven generator should produce moderate to high shear stress while negating the effect of the magnetic attraction. A new topology has potential to meet that challenge, without resorting to exotic structural or magnetic materials such as superconductors. The concept takes the active materials in the machine – copper, magnets and steel – and changes their relative positions to minimize the normal-force effects. The result is a structure that need only support the weight of the active components, leading to a reduction of about 55% compared to conventional permanent magnet (PM) machines. Results show the weight reduction while maintaining high efficiency at all loads. Experimental results from a 20kW, 100 rpm prototype verify the expected performance.
The new design is air-cored, meaning there is no iron in the stator so there is little attraction between rotor and stator. In two-sided axial-flux air-cored machines, the two rotors attract each other. Because the airgap-flux density, B, is lower than for an iron-cored machine, the shear stress, σ, is lower as shown by
σ ∝ BJ (1)
where J = current density, A/mm2. The current density in the generator coils is limited by copper losses and cooling requirements. To produce the same torque, T, the outer radius, ro, of an axial-flux machine must increase to accommodate the lower shear stress because
where kr = ratio of inner to outer radii.
The increase in machine radius, when moving from iron-cored to air-cored designs can cancel the expected reductions in structural weight. One wind turbine design from Goliath Wind OU, Estonia, proposes an ironless radial-flux generator which has no airgap closing force. This is accomplished with an ironless outer stator. Its generator has a large radius, R, held in place by a lightweight spoked structure. The ironless stator produces a large airgap, so its flux density and shear stresses are small. A large air-gap radius is needed because of the low shear stress. Equation 3 is the radial-flux equivalent of Equation 2,
where L = axial length. A previous simple study showed that air-cored machines are potentially lighter for a range of power ratings.
Developing a C-core machine
A logical development of such axial-flux disc machines is to increase the rotor-shaft radius. Because airgap normal forces act near the junction of shaft and discs, the discs can be made thinner and therefore lighter. Taking this further leaves a C-shaped cross section, where the limbs carry magnets and the stator winding is held independently between them. A further step lets flux cross the web of the C and makes the rotor out of modules each carrying a pair of magnets. Rotating the C-core modules 90° produces a radial flux machine. Increasing the axial length allow increasing the radial-flux generator’s torque rating without increasing the outer diameter.
This topology has advantages over existing ironless designs. A radial-flux ironless permanent magnet machine has a large effective airgap. This C core machine, however, has a smaller airgap length making possible higher flux densities and shear stresses. A corollary is that less permanent-magnet material is needed to produce the same flux density, so the design will be cheaper. This machine also has the advantage of two main flux paths, longitudinal and transversal, not just one. Because the amount of magnetically active steel depends on its non-saturation, this should be a lighter design than an axial-flux, two-disc machine.
Active and inactive material
The new topology is structurally superior to an iron-cored machine. In a conventional radial-flux machine, large airgap normal forces can act at distances of several meters from points where these forces can be reacted against. This implies that the rotor and stator structures must be stiff, large, and heavy. In contrast the new machine has no forces on the stator. Although the two limbs of the C-core are attracted to each other, normal stresses are reacted at points within the C-core – close to their point of application. This topology means that the steel in the C-core fulfills both active and inactive roles.
To test the ideas, a 20kW, 100rpm generator was designed at the University of Edinburgh and built by Fountain Design Ltd. (fountaindesign.co.uk) It is instructive to describe the build sequence and highlight topology’s manufacturing advantages. The rotor of the prototype C-core machine was made of 32 modules, each carrying a pair of permanent magnets similarly oriented. In this small machine, the C-core module was assembled from three trapezoidal pieces of mild steel, with magnets sliding onto the inner and outer pieces. For larger machines, magnetic material could be glued in place and magnetized later.
This would ease the problems of handling large magnets. Modularity allows the cheap and efficient production of large volumes. An assembled module is quite benign and safe to handle, because there is relatively little leakage flux outside the confines of the C core. The modules can be brought together and fixed to a common rotor structure. The prototype uses an aluminum disc.
Bringing together a rotor and stator can be a difficult and dangerous task in a conventional permanent-magnet machine because of the large magnetic attractions. Doing so is liable to pull either the rotor or stator off center and produce an unbalanced magnetic pull, thereby closing the airgap clearance even further.
A feature of the C core machine is that because there is no iron in the stator, there is no force of attraction between rotor and stator. This makes a straightforward task of threading the stator winding into the rotor. The stator in the prototype is made of 24 pseudo arc shaped concentrated coils, clamped between two rings. The coil’s discrete nature means they will be easy to replace. This will be a significant advantage in larger machines, as electrical faults are one of the more common causes of failure in direct-drive wind-turbine generators.
The 20kW prototype machine generated a perfectly sinusoidal no-load voltage waveform of 26.7 Hz frequency at 100 rpm. A power-versus-efficiency chart gives the mechanical-to-electrical efficiency of the prototype generator over a range of speeds for a range of loads, typical for this size machine. Results show that the design matches the performance of conventional PM synchronous generators.
Conventional PM machines tend to have optimal aspect ratios (axial length to airgap diameter). In terms of electromagnetically active material, less of it is needed with a small aspect ratio and large airgap radius, R. This is because the active weight is almost proportional to the airgap surface area (2πRL) whereas the torque, according to Equation (3), is proportional to R2L. Increasing the radius therefore increases the specific torque (with respect to the active weight).
There are two limits to how small the aspect ratio can be. There is a practical limit to how big the airgap diameter can be so that the generator can be transported and fit into a nacelle. The second limit is the structural material: the structural weight of a radial-flux machine is proportional to the square of the airgap radius (for a constant axial length and for a deflection fixed in relation to the airgap clearance). The C-core machine follows the same scaling laws for active weight, but has a different law for the structural material.
In C-core modules, limbs deflect into the airgap by:
where y = deflection, w = uniformly distributed load and a product of the normal component of Maxwell stress and the width of the limb. l = length of the cantilevered beam, and A = the second moment of area.
For a fixed axial length and a trapezoidal cross section, the weight of structural material, wstr (needed to limit y to a fixed proportion of the airgap clearance) is related to the airgap radius by:
This means the specific torque with respect to structural weight also rises with increased airgap radius.
The Generator weight and airgap charts show the generator weight based on the C core concept for 100 kW to 2 MW wind turbines. The electromagnetic design used the same basic pole pitch layout as the 20kW machine, with the number of poles and coils varied proportionately to the airgap radius.
The airgap clearance above and below the coil was taken as 0.1% of the airgap diameter. The magnetic flux was modeled using a simple lumped parameter magnetic circuit and the iron was not allowed to saturate.
For structural modeling, the maximum deflection of a C-core limb was restricted to 10% of the airgap clearance. Generator mass versus power show results for five different axial active lengths. As expected, designs with an active length of 0.4m are lightest because they reduce the active and structural weight. At larger ratings, these axially short machines may not be practical because of their large airgap diameters. Even the axially longest have great promise because these designs are not yet optimized for minimum weight.
Filed Under: Nacelle