SED3: The Generator Theory

This is a sub-section of my posts describing the Sustainable Energy Design 3 course group project to Design and Build a Micro Wind Turbine – for more information see here

Identifying a methodology to design the generator was difficult. Our only restricting variables of power left a lot of variation, and the scale of wind turbine being relatively uncommonly studied (it’s so much more efficient to build much larger turbines that few waste money on the guaranteed financial loss that is this tiny scale we were working with), gave us very little guidance.

Type of Generator

Single-sided Axial Flux Permanent Magnet Generator

Number of Magnets and Coils

Turbine calculations provide the turbine radius 0.38m = 380mm for a power of 100W, with an optimum TSR of 3.5. We are assuming a cut-in wind speed, when the wind is sufficient to generate power for to initially start the blades moving, of 3m/s and an optimum wind speed as chosen/suggested by Stein (the lecturer) of 12m/s.

We can use these values to calculate the RPM for cutin and optimum wind speeds using Equation 1 from Latouflis et al (K.C. Latouflis, 2012).

If we were directly charging the battery then the load that the generator sees is purely a result of the battery – this means that as the battery charges, the load decreases. We are going to be using a Maximum Power Point Tracker (MPPT) system which allows us to control what load the generator sees and thus control the power output created so as to maximise efficiency.

We therefore need to know what the V_DC load is going to be at cutin and whilst running at optimum TSR, so we will assume that these are the limits of the battery for our initial calculations but this will be developed later when discussing the MPPT system.

As we are using a 12V leisure battery, we can therefore assume that the VDC limits are 3V to 13.5V and as our diameter is 720mm this suggests a power rating of around 100W although this is actually also dependent upon the feedback from the MPPT.

This allows us to calculate approximately the ElectroMotive Force (EMF) – the V_AC the generator needs to generate at cut-in and at optimum using the above equations at 32.79V and 7.03V respectively.

This allows us to calculate the RPM at cutin using Equation 4 shown above at about 5000RPM.

We have then chosen the nominal frequency of the generator as 50Hz as this is the British Grid standard and thus allows potential grid connection if this was wanted. This then allows us to use the Equation 5 to calculate the ideal number of pole pairs.

However, for the purpose of maintaining a higher efficiency, smoother output without the introduction of additional components, and potential grid connection, we are using 3 phase. In order for this to happen we therefore need to have a multiple of 3 number of coils. Additionally, according to the literature, the ideal ratio is coils to pole pairs for maximum efficiency is 3 coils to 4 pole pairs (as shown in Equation 6).

Therefore although the ideal number of magnets was calculated at 6 this suggests either: 4 pole pairs for 3 coils or 8 pole pairs for 6 coils

So we therefore chose to have:

8 pole pairs and 6 coils.

 

Stator and Rotor Geometry

Inner diameters D_si and D_ri of the stator and rotor are largely dictated by the axle and bearings sizes as they have to fit around or on this with minimal mechanical losses. Values of 30mm for the stator and 50mm for the rotor are currently sufficient to cover a variety of axles. The literature for homemade generators suggested reuse of car and van hubs “loose stub axles”, and obviously the better the bearings, the less mechanical losses.

The outer diameters of the stator and rotor R_so and R_ro are ideally minimal around the requirements of the coil and magnet placement so as to minimise the weight.

Therefore we need to decide on the magnet dimensions – the magnets are the most expensive component of a micro turbine design so ideally the dimensions should be minimised where possible to stay within budget.

As shown in Figure 1 the magnet length l_m is approximately equal to the effective length of the generator l_a. The larger this is, the stronger the magnetic field.

The magnet width affects two main factors:

• the strength of the magnetic fields interacting with the coils which increases generally with increased width
• the flux leakage losses between magnets which increases the closer together the magnets are i.e. with larger values of pole pitch ratio a₁ as shown in Equation 7.

Both of these are to be compromised with the increased cost and weight that comes with this.

This ratio could be decreased by either:

• decreasing magnet width or
• by increasing the radius R_m that the magnets are at

The minimum R_m of course being the distance at which the magnets are back to back around the perimeter. It is recommended to keep the value of the pole pitch around 0.6 for rectangular magnets to create a more sinusoidal waveform, generally between 0.4 and 0.7 across the literature.

The thickness of the magnets are often standard sizes provided by the manufacturer or supplier – in our case for N42 magnets from Eclipse Magnets that’s multiples of 5mm.

The chosen value of R_m decides the placement of the coils and so R_sc because for minimal current harmonics, the losses due to noise and vibration in the AC waveform, the magnets and coils should be laid out as shown in Figure 1.

This also helps us choose our coil dimensions. Because the coils are often shaped trapezoidally, the dimensions are often defined in terms of the radii to the ends of the coils and similarly to the magnets, increasing the size of the coils generally improves its properties but adds weight and cost. However, the bigger limit of these are keeping the coils matching to the magnets, both because disproportionately large coils create losses in terms of harmonics but also gain less improved properties the more mismatching to the magnet.

According to Latouflis et al (K.C. Latouflis, 2012) there is a rule of thumb that the thickness of the rotor is approximately equal to thickness of magnets so that it can structurally hold them in place.

So despite the general guidelines and some manufacturing limitations, this still leaves a lot of room for choice and variables to account for in the geometry of the rotors and stators. In the literature, it was apparent that many of the dimensions choices were made around what other people had previously used as the complexity of the problem requires more full analysis to optimise further and as of yet, very little of this has been done and as in our case, the costs (time and money) to carry out such an investigation puts that beyond the scope of our assignment.

Therefore we looked at the values chosen for dimensions of various literature – this was difficult as there were not many examples of turbines of our scale, due to the limited resources (3D printer sizes for example) that we have an so we had to choose turbines with similarly small scales to compare and to try and account for how our differences would affect those values. For example, although Piggott provides a variety of recommended values across his book, we have only considered those given for his “1200 machine” i.e. a HAWT with turbine diameter of 1200mm.

Although better values could be chosen to more finely optimise the current harmonics and minimise the losses from noise and vibration, as we are ultimately passing the AC sine wave through a sub-optimal DC rectifier, the losses are comparably insignificant. Therefore we considered that the benefits of the modelling required to optimise this could not justify the time required within our timescales and resources available to us on this assignment.

Magnet and Coil Properties

Ultimately you want to maximise the effective length and magnet width to increase the magnetic strength however you are limited by both magnet costs and minimising flux leakage. Most of the calculations from the literature assumed no flux leakage but the closer together the magnets are then the less accurate this assumption and therefore the resulting calculations are.

In terms of choosing magnet and coil properties and dimensions, there are a lot of variables to choose from and how this is allocated varies largely across the literature. As the magnets are the most expensive single cost involved the construction of the generator, this limits the grade that can be afforded to N42 Neodymium at most. The datasheets (as shown in Figure 2) for this grade provide us with values of B_r and H_c.

Then using the natural constant of the permittivity of a vacuum, we can then calculate the achievable recoil permittivity as shown in Equation 10, and this allows us to calculate the properties of the magnetic fields at the surface of the magnet i.e. when it will ideally interact with the coils using Equation 11. The value of K_sat is 1 because the generator is coreless.

The gap ideally needs to be minimised so as to maximise B_mg and this is made of the gap from the resin layer over magnets, resin layer over coils, and air gap thickness. In practice when manufacturing, it is difficult to create a resin layer less than 1mm that consistently covers for corrosion resistance, and although the air gap is ideally minimised, if it is too close then there is a possibility that the rotor and stator will touch and create friction which would dramatically reduce the efficiency of the generator as well as damage and heat that would need to be managed.

Therefore it is recommended that an air gap of 1mm would allow for any potential uneven resin surface and still avoid contact. Thus g = 3mm in total, approximately 1mm for each section.

With this value of B_mg and the dimensions chosen earlier, we can calculate the magnetic flux per pole in Equation 13

This then allows us to calculate the number of coil turns ideally required with Equation 14. If number of turns is too low for the battery then blades will rotate too quickly while trying to reach cutin RPM but if there are too many turns then generator will charge the battery at very low speed, it will exert too much torque which makes it inefficient and can cause stalling.

There is lot of optimisation achievable through variations in the actual type of winding done for example to maximise the efficiency of the space used or to improve harmonics, using features like overlapping winding, or layered winding but this adds a lot of complication to manufacturing for minimal gain on our scale of generator so we are using simple single layer winding. Current calculations suggest N_c = 6.12559.

The value of the fill factor k_f as shown in Equation 15, needs to be calculated. Generally it can be assumed to be around 0.55 for single layer winding but it needs to be measured after manufacturing and adjusted to the actual value, as miscalculation from relying on the estimation can cause problems. If it is a lower value than assumed, the coils will not fit in the stator mould and so the generator won’t work or at least will have to be redesigned and recalculated. If it is higher than assumed then it will increase g which will make it a less effective generator, although this is preferred to being lower.

Assume efficiency of generator to be 0.8 as many similar generators are assumed to be around 0.9 but these have been refined and manufactured by more experienced people (thus will contain less error to cause losses).

With this assumption we can calculate I_ACmax using Equation 16 to get a value of 4.712.

Then can use this calculate the ideal coil leg width using Equation 17 to get 5.2mm.

The heating coefficient, and resistivity of wire are generally derived from natural properties and from the copper wire data sheets. Grade 2 magnet wire is ideal but lower quality can be used so assuming Grade 2 we get 6mm.

Using the stator axial thickness chosen earlier of 10mm we can also use Equation 18 to calculate the number of coils per phase.

For a small wind turbine you can assume a current density of 6000kA/m² (according to Latouflis et al this is a reasonable value for a small wind turbine (K.C. Latouflis, 2012) ) and so calculate from Equation 19 instead.

To calculate the ideal coil wire diameter therefore required we can use Equation 20.

Ideally we have the largest wire size to fit available space as this minimises loss of power and heating of stator however there are standard wire thicknesses so we have to choose the closest approximation from the following information.

This just leaves the decision of wiring the stator coils in star or delta formation? Star formation is the most common method for micro wind turbines with axial flux permanent magnet generators as Delta creates parasitic currents.

However Piggott (Piggott, 2010) suggests that “for 12 volts series connected the wires become very clumsy. I therefore propose a parallel connection for these stators” which requires an alternative rectifier to accommodate for the resulting parasitic currents. This is based on the fact that 12V battery charging needs very thick wires to reduce losses inherent in high currents required and so it is ‘clumsy’ handling such thick wires in star formation.

Table of Final Properties

References

Brusca, S., R. Lanzafame, and M. Messina. . (2014). Design of a Vertical-axis Wind Turbine: How the Aspect Ratio Affects the Turbine’s Performance. Retrieved from Int J Energy Environ Eng International Journal of Energy and Environmental Engineering 5.4 333-40. Web. 2.

Garrison F. Price, T. D. (2008). Design and Testing of a Permanent Magnet Axial Flux Wind Power Generator. Proceedings of The 2008 IAJC-IJME International Conference.

K.C. Latouflis, G. M. (2012). Axial Flux Permanent Magnet Generator Design for Low Cost Manufacturing of Small Wind Turbines. Wind Engineering, 36(4), 411-442.

Mihai CHIRCA, S. B. (2014). Design Analysis of a Novel Double-Sided Axial-Flux Permanent-Magnet Generator for Micro-Wind Power Applications. 472 – 476.

Piggott, H. (2010). A Wind Turbine Recipe Book.

Wind Energy Overview. (n.d.). (Belarusian Portal on Renewable Energy) Retrieved 2016

http://www.magnet2buy.com. (n.d.). Retrieved February 2016

 

Next: The Charging Circuit

This is a sub-section of my posts describing the Sustainable Energy Design 3 course group project to Design and Build a Micro Wind Turbine – for more information see here