To design a good working PM-generator for a wind turbine isn't simple. One has to make a lot of choices and find good arguments for every choice. Several different choices can result in an acceptable design. It depends on the available materials, on the skills of the maker, on the required electrical power at a certain rotational speed and on the amount of money one wants to spend which design is optimal for a certain situation. I have designed, built and tested several different PM-generators in the past forty years. All my experiences are described shortly in public report KD 341: "Development of the PM-generators of the VIRYA windmills" from May 2007 but the last review is of June 2021. For almost every configuration of armature and stator there is a separate KD-report which can be found in the reference of KD 341. The AC current coming out of the generator is normally rectified. Rectification of a 1-phase winding, a 3-phase winding and a 2-phase winding is explained for star and for delta in public report KD 340. All public reports can be copied for free from my website:
www.kdwindturbines.nl at the menu KD-reports.
Next I will give a short description of which choices one has to make.
The first choice is axial flux or radial flux. Axial flux means that the direction of the magnetic field lines in the air gap is in parallel to the armature axis. Radial flux means that the direction of the magnetic flux in the air gap is perpendicular to the armature axis. The armature contains the magnets. The stator contains the coils. Most radial flux generators are made from asynchronous motors and have a stator with an iron stamping. The air gap of these generators is the distance in between the armature and the stator. Most axial flux generators have two iron armature disks with magnets on the inside and a stator with coils and no iron in it in between the magnets. The air gap for these generators is the distance in between the inner side of the magnets at both armature disks. However, it is also possible to design an axial flux generator with only one armature disk. These generators are simpler because the stator is not enclosed in between two armature disks. I have designed several 8-pole axial flux generators with only one armature disk. As most people on this forum work with axial flux generators I now assume that one has made this choice and that one uses two armature disks.
The second choice is the kind of magnets. I assume that neodymium magnets are used as these magnets give the strongest flux density. One can chose for rectangular or for circular magnets. Both types of magnets are possible but I prefer circular magnets for different reasons. One reason is that positioning is easier. The other reason has to do with the shape of the wave which is generated in one phase but this also has to do with the forth choice.
The third choice is the number of magnets in one armature so this determines the number of poles. As there must be the same number of north and south poles, the number of poles must be even. However, a one layer, 3-phase winding is only possible if the number of armature poles is dividable by four. So for this reason the number of armature poles can only be 4, 8, 12, 16, 20 and so on. The bigger the magnets and the more poles, the larger the maximum torque level of the generator and the higher the maximum electrical power at a certain rotational speed.
The forth choice is the distance in between the magnets on the same armature disk. The generation of a voltage in a coil is explained in chapter 9 of report KD 341. The second way of explanation is best for axial flux generators with no iron in the coils. This explanation shows that a voltage is only generated in the two legs of a coil and only as long as these legs are moving through the magnetic flux in the air gap in between the magnets on both armature disks. There must be a certain distance in between the sides of adjacent magnets on the same armature disk. For rectangular magnets this distance is smallest at the inside of the magnets and largest on the outside. The difference depends on the number of armature poles and on the radial length of the magnets. For circular magnets the distance is minimal about on the pitch circle. If the distance is chosen small, there will be a rather large magnetic flux flowing from one magnet to its neighbour and so this magnetic flux won't flow through the coils. If the distance is taken large, there will be a large part of the time for which no voltage is generated in the legs of the coil. I have found for circular magnets that optimum the distance in between the sides of the magnets is about half the magnet diameter. In report KD 340 it is shown that a coil of the 3-phase winding is only used during 2/3 of the time if the winding is rectified in star. So for a distance of half the magnet diameter, the part of the time for which no voltage is generated coincides with the part of the time for which the coil isn't used. If the distance is take larger than half the magnet diameter you will get a very fluctuating rectified current.
The fifth choice is the distance in between the magnets at both armature disk. The larger the distance, the more space there is for the stator coils. However, the larger the distance, the lower the flux density in the air gap and so the lower the voltage which is generated in a coil with a certain number of turns per coil and for an armature which is running at a certain rotational speed. The flux density in the air gap can be calculated if the remanence Br of the magnets is known. The most general magnet quality gives a remanence of about 1.2 Tesla (T). The magnetic resistance of an air gap is about the same as the magnetic resistance of the magnet itself. The flux density called remanence is gained when the magnet is short-circuited by an iron disk which is far from saturation. The magnetic resistance is very similar to the Ohmic resistance. Assume that the magnet thickness is t1 and that the thickness of the air gap is t2. So the magnetic resistance with an air gap increases by a factor (t1 + t2) / t1. This means that the flux density in the air cap decreases by a factor Br * t1 / (t1 + t2). So if the thickness of the air gap is taken the same as the thickness of the magnet, the magnetic flux in the air gap is only half Br. If we follow a magnetic loop for an axial flux generator with two armature disks you see that in one magnetic loop there are four magnets and two air gaps. So there are two magnets for one air gap. So if the thickness of the air gap is taken twice the thickness of a magnet, the flux density in the air gap is about 0.6 T. My advice is to take the air gap not larger than twice the magnet thickness. The fact that thicker and so more expensive coils with more copper in it can be used in larger air gaps is finally neutralized by the reduction of the flux density.
The sixth choice is the kind of stator winding. A 3-phase winding is preferred above a 1-phase winding because the number of coils which can be laid for a 1-layer, 3-phase winding is a factor 1.5 larger than for a 1-phase winding. The number of coils for a 3-phase, 1-layer winding is 3/4 of the number of armature poles. The coil sequence for an 8-pole generator is U1, V1, W1, U2, V2 and W2.
The seventh choice is the wire thickness and the number of turns per coil. This is the most difficult choice of all. Three different coil shapes are given in figure 5 and 6 of KD 341 for an 8-pole generator with rectangular magnets. The lowest picture of figure 5 gives the shape for which there is maximum place for the wires of the legs of a coil and for which the average pitch in between the left leg and the right leg of a coils is almost the same as the armature pole pitch. So assume that this shape is chosen. This means that in one leg of a coils there is place for a certain total cross sectional copper area. For a certain total cross sectional copper area one can chose many turns per coil for a thin wire ore less turns per coil for a thick wire. The open voltage generated at a certain rotational speed is proportional with the number of turn per coil. However, the wire resistance and so the copper losses increases strongly if the number of turns per coil is increased and if the wire thickness is reduced. The optimum number of turns per coil is realized for the optimum matching in between rotor and generator. Matching is explained in chapter 8 of my public report KD 35. Optimum matching means that the Pmech-n curve of the generator for the wanted load is lying close to the optimum parabola of the rotor. So to check the matching one needs the optimum parabola of the rotor. The formula for the optimum parabola is given as formula 8.1 of KD 35. One also needs the Pmech-n curve of the generator for the given load. For battery charging, this means the Pmech-n curve for the average charging voltage. However, this curve depends on the number of turns per coil and this number is unknown for a new generator. This problem is solved as follows.
One simply makes a choice for a certain wire thickness and lays as many turns per coil as possible within the available space. Assume 100 turns per coil are possible. Next this prototype is measured on an accurate test rig for different voltages. Every voltage gives a certain Pmech-n curve. For every curve the matching is checked with the optimum cubic line of the chosen windmill rotor. Assume that the matching is optimal for a voltage of 16 V. Assume that the generator is used for 24 V battery charging. This gives an average charging voltage of about 26 V. So the voltage is a factor 26 / 16 too low. This means that the number of turns per coil has to be increased by a factor 26 / 16 = 1.63. So the final number of turns per coil has to be 1.63 * 100 = 163. The wire thickness has to be reduced such that the cross sectional copper area is the same as for the test winding. The generator with the final winding is now measured again and it should be that the Pmech-n curve for the final winding for 26 V is the same as for the test winding for 16 V. You see that this is a rather complicated procedure which requires an accurate test rig with which it is possible to measure the mechanical power and this requires measuring of the torque and the rotational speed. Most people don't have such a test rig therefore can't find the optimum winding for a certain rotor and a certain load.
There is another conclusion which can be drawn from the measurements. It is assumed that the windmill is provided with a safety system which limits the rotational speed, the thrust and the power for a certain rated wind speed. So the optimum cubic line ends at the P-n curve of the rotor for this rated wind speed which is about 10 m/s. One has made a certain choice for the size and the number of magnets and this means that the Q-n curve of the generator bends to the right at high rotational speeds and it will have a certain maximum value. The Pmech-n curve will therefore also bend to the right at high powers. So it might be that the matching is only good at low wind speeds. This means that the generator is too small for the chosen rotor. The generator can be made bigger by using bigger magnets or by using more poles.
Many more choices have to be made about the mechanical construction and the bearings but I think that what I have explained up to now is enough for this post.