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9 coils / 12 magnets.
According to the Bavaria Winding Diagram Table, 9 coils / 10 magnets would be a better combination.
If nine coils and ten magnets is better a better choice than nine coils and twelve magnets depends on, if the coils have an iron core in the coils or not. I will explain this for four different options A, B, C and D.
A) Assume we have nine coils and twelve magnets (so a ratio 3/4) and no iron in the coils. This means that the coil sequence must be U1, V1, W1, U2, V2, W2, U3, V3, W3. This means that if the north pole N1 is opposite to U1, the north pole N3 will be opposite to U2 and the north pole N5 will be opposite to U3. So the voiltage generated in the three coils of one phase are exactly in phase to each other and this gives the maximum total voltage. It can be proven that the phase angle in between coils of phase U and coils of phase V is 120° and that the phase angle in between coils of phase V and coils of phase W is also 120° and so a 3-phase current is generated. As there is no iron in the coils, the armature will have no preference positions and so the generator will not suffer from cogging. So this is a good choice
B) Assume we have nine coils and twelve magnets and iron cores in the coils. Now four of the twelve magnets are just opposite to four iron cores at the same time and this gives a strong preference position. The armature pole angle is 360 / 12 = 30°. The stator pole angle is 360 / 9 = 40°. So the difference is 10°. This means that the armature will have a preference position every 10° and so it will have 36 preference positions per revolution. This results and a very strong fluctuation of the cogging torque. So this is a bad choice.
C) Assume we have nine coils and ten magnets (so a ratio 9/10) and no iron in the coils. This means that the coil sequence must be U1, U2, U3, V1, V2, V3, W1, W2, W3. This means that if the north pole N1 is opposite to coil U2, the south pole S6 will be almost opposite to U1 and the south pole S1 will be almost opposite to U3. So the voiltage generated in the three coils of one phase are not exactly in phase to each other and if coil U2 is wound right hand, coils U1 and U3 must be wound left hand. It can be proven that the difference in phase angle is 20° and this results in some reduction of the total voltage if the three coils U1, U2 and U3 are connected in series. As there is no iron in the coils, the armature will have no preference positions. So this option works but is not as good as option A because using ten in stead of 12 magnets results in a frequency which is a factor 10/12 lower. The total voltage will therefore also be lower than for option A if the same magnets are used.
D) Assume we have nine coils and ten magnets and iron cores in the coils. This means that the coil sequence must be U1, U2, U3, V1, V2, V3, W1, W2, W3. This means that if the north pole N1 is opposite to coil U2, the south pole S6 will be almost opposite to U1 and the south pole S1 will be almost opposite to U3. So the voiltage generated in the three coils of one phase are not exactly in phase to each other and if coil U2 is wound right hand, coils U1 and U3 must be wound left hand. It can be proven that the difference in phase angle is 20° and this results in some reduction of the total voltage if the three coils U1, U2 and U3 are connected in series. However, as now the coils contain iron cores, the armature will have a preference position if a magnet is just opposite to a core. But for a ratio 9/10 this happens only for one magnet and one core at the same time. The armature pole angle is 360 / 10 = 36°. The stator pole angle is 360 / 9 = 40°. So the difference is 4°. This means that the armature will have a preference position every 4° and so it will have 90 preference positions per revolution. This is much more than for option B and the peak on the cogging torque will therefore much lower than for option B but it wiil be bigger than for option A and C. The advantage of using iron core in the coils is that the air gap is much smaller which results in a much larger flux density in the coils and therefore in a much higher voltage at a certain rotational speed. Option D is a good choice if iron cores are used. But compared to option A and C, it will suffer from cogging and so one needs a windmill rotor with a rather high starting torque coefficient to get a sufficiently low starting wind speed.
