Design of a PM-generator for a wind turbine

[Adriaan Kragten]

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.

[Astro]

Very good write up.
I would only add the plates used on the rotor have an affect as well. You are going to want something high in iron and thick enough to provide for saturation of the magnetic flux from the mags you are sticking on it. This along with if you are going to use a dual axial with a steel plate or a steel plate with more mags on it plays a part in how the flux is going to flow, not only across the gap where your coils are going to be but to the sides of the mags as well.
 My advice is to not cut corners here and do everything possible to get as much flux flowing across the coil gap as possible and not to the sides, or because the plate is to thin, or not of enough iron content to absorb the flux on the back side of the mag that is stuck to the plate.
 In short, design it so that you are giving the flux it's easiest path to pass through your coil gap and no where else.
Because of that I think you are being very generous with your gap between magnets on opposite rotors. The flux drops off very rapidly as you move out away from the mags and 1/4in can make a huge difference.
For example the gauss of a 2 x 1 x 1/2 n52 mag at 1in is 685 but at 3/4 of an inch it is 1,063. That 1/4in difference just cost you or gained you about 1/3rds of your total gauss. If 200 degree 14 awg is .067 diameter, that 1/4 inch is only less then 4 winds on the coil. Plus if you are going to pour the mags in epoxy, plus if the stator is not perfectly flat......... my point is it is rather easy to end up with a gap from mag to mag on opposite discs that can easily equal 1/4 inch more then you wanted and as I said that 1/4 inch just cost you 1/3 rds of your gauss. So again from plate material to coil thickness to total gap between opposite mags on a dual axial, try and make it so the flux's easiest path is across the coil gap.
 In the end a well designed genny with cheaper less expensive mags can perform just as well or better then  a not as well designed genny with more expensive N52's. So each component must work to it's maximum, but also must work together. That applies to design anything that is of good quality and efficiency.

[Adriaan Kragten]

Very good write up.
I would only add the plates used on the rotor have an affect as well. You are going to want something high in iron and thick enough to provide for saturation of the magnetic flux from the mags you are sticking on it. This along with if you are going to use a dual axial with a steel plate or a steel plate with more mags on it plays a part in how the flux is going to flow, not only across the gap where your coils are going to be but to the sides of the mags as well.
 My advice is to not cut corners here and do everything possible to get as much flux flowing across the coil gap as possible and not to the sides, or because the plate is to thin, or not of enough iron content to absorb the flux on the back side of the mag that is stuck to the plate.
 In short, design it so that you are giving the flux it's easiest path to pass through your coil gap and no where else.
Because of that I think you are being very generous with your gap between magnets on opposite rotors. The flux drops off very rapidly as you move out away from the mags and 1/4in can make a huge difference.
For example the gauss of a 2 x 1 x 1/2 n52 mag at 1in is 685 but at 3/4 of an inch it is 1,063. So again from plate material to coil thickness to total gap between opposite mags on a dual axial, try and make it so the flux's easiest path is across the coil gap.
 In the end a well designed genny with cheaper less expensive mags can perform just as well or better then  a not as well designed genny with more expensive N52's. So each component must work to it's maximum, but also must work together. That applies to design anything that is of good quality and efficiency.

You are right. The steel plates to which the magnets are glued must be that thick that the iron in the sheets isn't saturated. First you calculate the effective flux density Br eff in the air gap. Assume you find that Br eff = 0.6 T. Assume that you have a circular magnet with a diameter of 40 mm. So the magnet area is 1257 mm^2. Assume that the armature disk is that large that the magnetic flux can flow to the armature disk from all directions. Assume that the thickness of the sheet is 6 mm. So the magnetic flux has to flow through an area of pi * 40 * 6 = 754 mm^2. So the concentration factor in between both areas is 1257 / 754 = 1.67 just at the edge of the magnet. This means that the flux density in the iron is 1.67 * 0.6 = 1.00 T. Mild steel iron is saturated at about 1.6 T so a thickness of 6 mm is certainly enough and it might even be chosen 5 mm. However, the sheets should also be strong and stiff enough because both sheets are pulled to each other by a strong force. For some rotors, the blades are directly connected to the front sheet and this certainly requires strong sheets. So the thickness of the sheet can also be determined by the mechanical load on the sheet.
Half of the magnetic flux coming out of one magnet flows in the iron to its left neighbour and the other half flows to its right neighbour. One must also check if there is no saturation just in between two magnets especially when there is a central hole in one sheet. So it might be that the sheets must have a certain outside diameter to prevent saturation at this point.

[MattM]

If only there was a way to cross-breed axial and radial, like using a conical magnet holder and a stick coil to move along the cone to adjust coils alignment to tangential velocity, which would allow you to adjust voltage.

[Astro]

If only there was a way to cross-breed axial and radial, like using a conical magnet holder and a stick coil to move along the cone to adjust coils alignment to tangential velocity, which would allow you to adjust voltage.

 Not a bad idea.
Above I mention gap between magnets on opposite plates and how fast gauss drops off as you move away from the magnet. Something to think about is those field lines do not just disappear, they are still going somewhere, just not across your coil gap. That is maybe something to think about when designing a generator.

[Astro]

Very good write up.
I would only add the plates used on the rotor have an affect as well. You are going to want something high in iron and thick enough to provide for saturation of the magnetic flux from the mags you are sticking on it. This along with if you are going to use a dual axial with a steel plate or a steel plate with more mags on it plays a part in how the flux is going to flow, not only across the gap where your coils are going to be but to the sides of the mags as well.
 My advice is to not cut corners here and do everything possible to get as much flux flowing across the coil gap as possible and not to the sides, or because the plate is to thin, or not of enough iron content to absorb the flux on the back side of the mag that is stuck to the plate.
 In short, design it so that you are giving the flux it's easiest path to pass through your coil gap and no where else.
Because of that I think you are being very generous with your gap between magnets on opposite rotors. The flux drops off very rapidly as you move out away from the mags and 1/4in can make a huge difference.
For example the gauss of a 2 x 1 x 1/2 n52 mag at 1in is 685 but at 3/4 of an inch it is 1,063. So again from plate material to coil thickness to total gap between opposite mags on a dual axial, try and make it so the flux's easiest path is across the coil gap.
 In the end a well designed genny with cheaper less expensive mags can perform just as well or better then  a not as well designed genny with more expensive N52's. So each component must work to it's maximum, but also must work together. That applies to design anything that is of good quality and efficiency.

You are right. The steel plates to which the magnets are glued must be that thick that the iron in the sheets isn't saturated. First you calculate the effective flux density Br eff in the air gap. Assume you find that Br eff = 0.6 T. Assume that you have a circular magnet with a diameter of 40 mm. So the magnet area is 1257 mm^2. Assume that the armature disk is that large that the magnetic flux can flow to the armature disk from all directions. Assume that the thickness of the sheet is 6 mm. So the magnetic flux has to flow through an area of pi * 40 * 6 = 754 mm^2. So the concentration factor in between both areas is 1257 / 754 = 1.67 just at the edge of the magnet. This means that the flux density in the iron is 1.67 * 0.6 = 1.00 T. Mild steel iron is saturated at about 1.6 T so a thickness of 6 mm is certainly enough and it might even be chosen 5 mm. However, the sheets should also be strong and stiff enough because both sheets are pulled to each other by a strong force. For some rotors, the blades are directly connected to the front sheet and this certainly requires strong sheets. So the thickness of the sheet can also be determined by the mechanical load on the sheet.
Half of the magnetic flux coming out of one magnet flows in the iron to its left neighbour and the other half flows to its right neighbour. One must also check if there is no saturation just in between two magnets especially when there is a central hole in one sheet. So it might be that the sheets must have a certain outside diameter to prevent saturation at this point.

Easiest way to think about it is that the plates are your ground. I understand we are alternating poles, but if you do not absorb all the field lines from the side of the magnet you are sticking to the plate, it is basically like having a bad ground. The voltage is still going to go somewhere (to the easiest path) just not to where you want it to go.

[Adriaan Kragten]

Very good write up.
I would only add the plates used on the rotor have an affect as well. You are going to want something high in iron and thick enough to provide for saturation of the magnetic flux from the mags you are sticking on it. This along with if you are going to use a dual axial with a steel plate or a steel plate with more mags on it plays a part in how the flux is going to flow, not only across the gap where your coils are going to be but to the sides of the mags as well.
 My advice is to not cut corners here and do everything possible to get as much flux flowing across the coil gap as possible and not to the sides, or because the plate is to thin, or not of enough iron content to absorb the flux on the back side of the mag that is stuck to the plate.
 In short, design it so that you are giving the flux it's easiest path to pass through your coil gap and no where else.
Because of that I think you are being very generous with your gap between magnets on opposite rotors. The flux drops off very rapidly as you move out away from the mags and 1/4in can make a huge difference.
For example the gauss of a 2 x 1 x 1/2 n52 mag at 1in is 685 but at 3/4 of an inch it is 1,063. So again from plate material to coil thickness to total gap between opposite mags on a dual axial, try and make it so the flux's easiest path is across the coil gap.
 In the end a well designed genny with cheaper less expensive mags can perform just as well or better then  a not as well designed genny with more expensive N52's. So each component must work to it's maximum, but also must work together. That applies to design anything that is of good quality and efficiency.

You are right. The steel plates to which the magnets are glued must be that thick that the iron in the sheets isn't saturated. First you calculate the effective flux density Br eff in the air gap. Assume you find that Br eff = 0.6 T. Assume that you have a circular magnet with a diameter of 40 mm. So the magnet area is 1257 mm^2. Assume that the armature disk is that large that the magnetic flux can flow to the armature disk from all directions. Assume that the thickness of the sheet is 6 mm. So the magnetic flux has to flow through an area of pi * 40 * 6 = 754 mm^2. So the concentration factor in between both areas is 1257 / 754 = 1.67 just at the edge of the magnet. This means that the flux density in the iron is 1.67 * 0.6 = 1.00 T. Mild steel iron is saturated at about 1.6 T so a thickness of 6 mm is certainly enough and it might even be chosen 5 mm. However, the sheets should also be strong and stiff enough because both sheets are pulled to each other by a strong force. For some rotors, the blades are directly connected to the front sheet and this certainly requires strong sheets. So the thickness of the sheet can also be determined by the mechanical load on the sheet.
Half of the magnetic flux coming out of one magnet flows in the iron to its left neighbour and the other half flows to its right neighbour. One must also check if there is no saturation just in between two magnets especially when there is a central hole in one sheet. So it might be that the sheets must have a certain outside diameter to prevent saturation at this point.

Easiest way to think about it is that the plates are your ground. I understand we are alternating poles, but if you do not absorb all the field lines from the side of the magnet you are sticking to the plate, it is basically like having a bad ground. The voltage is still going to go somewhere (to the easiest path) just not to where you want it to go.

It is not so that there are a certain number of field lines in the magnet which always have the same strength and that they are only guided differently by the steel plate. The idea of field lines is created by man to show the direction of the magnetic field. If you take a single magnet without any iron around it, all outside field lines are flowing through air. So you have the longest air gap possible and so the highest magnetic resistance outside the magnet resulting in a low flux density outside the magnet. This means that you also have only a low flux density in the magnet itself. If the north and the south pole are short-circuited by an iron arc which is far from saturation, the magnetic resistance for the field lines outside the magnet becomes almost zero which means that flux density outside the magnet becomes much stronger and so the flux density in the magnet itself also becomes much stronger. This maximum possible flux density in the magnet is called the remanence Br. An air gap in the arc results in increase of the magnetic resistance and so in decrease of the flux density from Br to Br eff. But the flux density in the air gap is only the same as Br eff if the field lines are flowing through the same area as the magnet area.

[Adriaan Kragten]

Matching in between rotor and generator can be checked in the P-n graph or in the Q-n graph. The advantage of using the P-n graph is that the electrical Pel-n curve can be drawn in the same graph and this makes it possible to derive the Pel-V curve. The advantage of using the Q-n graph is that it is easy to see that the measured Q-n curve of the generator for a certain load has a maximum value for a certain rotational speed and that it even decreases for higher rotational speeds (see my report KD 78). The optimum line of the rotor through the points of maximum Cp is a parabola in the Q-n graph. If the windmill is provided with a safety system which limits the rotational speed, this parabola will have an end for the rated wind speed. So then it is possible to design a PM-generator which matches well for all wind speeds.

If the windmill has no safety system, the optimum parabola will have no maximum. The torque is proportional to V^2. So the rotor torque at V = 20 m/s is four times larger than at V = 10 m/s. At V = 30 m/s, it is nine times larger than at V = 10 m/s. Assume that one has designed a PM-generator which is large enough to give an acceptable matching at V = 10 m/s. This requires an already rather large generator and the generator torque will lie close to the maximum torque at V = 10 m/s. If the wind speed rises up to 20 m/s, the generator will be much too small as it will never be able to give a torque which is four times higher. If the load is maintained at the same level, the generator will become very hot. At a wind speed of 30 m/s, the situation will even be much worse and the generator will certainly burn. This means that it can provide no torque at all and so at a wind speed of 30 m/s, the rotor will turn unloaded. This results in increase of the tip speed ratio by about a factor 8/5 and the rotational speed at 30 m/s will therefore be almost five times higher than at 10 m/s. The centrifugal forces increase with the square of the rotational speed and will therefore be about 25 times higher than at 10 m/s. This will certainly result in complete destruction of the rotor.

The rotational speed of a HAWT can be limited by turning the rotor out of the wind or by pitch control. There is no way to limit the rotational speed of a VAWT by aerodynamics so especially a Darrieus like rotor can spin extremely fast at very high wind speeds. This is one of the main disadvantages of this kind of wind turbine. The only way to stop a Darrieus rotor is a very large brake directly on the shaft but this brake can become very hot if it maintains the rotational speed at a certain value. If it stops the rotor completely, you have the inherent starting problem because of the negative starting torque coefficient at low tip speed ratios (see my report KD 601). So a Darrieus rotor is very dangerous at very high wind speeds and this is one of the reasons why I will always discourage people to start with this kind of wind turbine. Don't think that very high wind speeds will not occur at your site. I have measured a maximum wind speed of 25 m/s at my site which is lying far from the sea. Buildings in The Netherlands have to be calculated for a wind speed of 35 m/s and there are countries for which gusts with a maximum wind speed of 60 m/s are not unusual.

In my public report KD 215, I give thirteen disadvantages of Darrieus rotors. In my public report KD 601, I have tried to solve disadvantage no 3 and no 13, so I found a way to get a positive starting torque coefficient at low values of lambda and I found an aerodynamic theory for the optimum tip speed ratio and the chord. But for every solution of a certain problem, you create a new problem. For instance, my new system requires that the center of gravity of the airfoil coincides with the aerodynamic center and this requires a hollow blade. But still eleven disadvantages remain and some of these disadvantages are that severe that they destroy the wind turbine at high wind speeds. I have seen a Darrieus rotor built by Vestas shaking like hell and Vestas has certainly people with aerodynamic knowledge. So you can't solve all the problems. This is the reason why none of the commercial Darrieus rotors which have ever been built have become a success. The Dutch company which built the Turby, a very nice 3-bladed H-Darrieus rotor with twisted blades, finally went bankrupt, mainly because starting of the rotor took that much energy that the yearly output was much too low (see test of the Dutch test field of Schoondijke). So I don't understand why people start with Darrieus rotors if they have read my report KD 215.

[Astro]

 To me the whole thing is rather poetic.
Just like two people in love that want nothing more then to be together. Same could be said about gauss lines around a magnet. Same thing could be said about putting a turbine up into the air to be with the wind. Or how electrons just want to complete the circuit. Actually the same thing could be said about how a fuel cell works.
 But what do I know. I just know it is easier to get some work done, ponder things, play my drums, or sit and watch the game on tv if my wife has something else to do. I know that if I try and make things more to her liking and things she likes to do, the smoother things go and the more she is attracted to me.

[SparWeb]

Hi Adriaan,

Reading your first post, this seems like a suitable contribution to the FAQ section of Fieldlines.  Would you like to add a few illustrations to make your post more readable?  In the FAQ it would be easier to find, and more people would read and refer to it.  I've seen in some of your reports the kinds of illustrations that would really work well with your write-up.

No obligations, just a suggestion.

[Adriaan Kragten]

Hi Adriaan,

Reading your first post, this seems like a suitable contribution to the FAQ section of Fieldlines.  Would you like to add a few illustrations to make your post more readable?  In the FAQ it would be easier to find, and more people would read and refer to it.  I've seen in some of your reports the kinds of illustrations that would really work well with your write-up.

No obligations, just a suggestion.

Making correct pictures for some of the points is too much work. You find some essential pictures of magnet and coil configuration in chapter 9 of my public report KD 341. Detailed information about a certain generator principle is given in the reports mentioned in the reference of KD 341. I have even made complete technical drawings of several generators which you find in the public manuals or design reports of certain small VIRYA windmills. All VIRYA windmills which are made public are described in three folders which you can find at the menu VIRYA folders on my website. In these folders, it is described in detail where certain drawings can be found. So people who really want to know how a generator can be built, can find the information if they visit my website and look at the correct place.

[MattM]

I've seen all sorts of ways to collect electrons using magnets and wire on YouTube.

Bifilar coils are intruging.  Using them in series across alternating magnets sounds like it has potential.

[joestue]

I've seen all sorts of ways to collect electrons using magnets and wire on YouTube.

Bifilar coils are intruging.  Using them in series across alternating magnets sounds like it has potential.

Bifilar coils take up more space and there is no point to use them in a low frequency machine.

Winding 2 or 3 or 4 wires in hand is not the same as a bifilar coil.

[MattM]

Have you tried bifilar or is that your opinion?  Because from people doing tests with them on YouTube - with direct comparisons to conventional coils of the same mass - they are not exactly what you describe.  Nor would I bring up multiple wires in hand and confuse them with bifilar.

[Mary B]

I remember when bifilar coils were all the rage in ham radio receiving antennas... the typical 3db better receive claims etc...

Until it was tested in a lab and the difference was negligible over a standard coil. Still see claims by small hand made antenna manufactures using it but it is considered snake oil at this point.

In a switch mode power supply is that .02db difference worth it? Yes when it translates to less heat in the design. But they are running at 100++khz where it will make a difference, under 200 hz? Nah don't bother with the expense.

[joestue]

I did run some numbers on how thin the insulation has to be in order to try and pack in more copper using copper sheet metal.. pretty thin..

in theory you can pack round wire about 95% fill factor, but the plastic insulation is the biggest hit. maybe 80% is practical on wind turbines.

now take two wires or three wires and twist them together and then wind a coil out of them. maybe 60% fill factor max.

[Adriaan Kragten]

For the calculation of the flux density in the air gap and the armature sheets you need the remanece Br in Tesla for the chosen magnet quality. Most suppliers of neodymium magnets give the quality and the price depending on the quantity for a magnet of certain dimensions but they don't give the remanence. However, the supplier Supermagnete gives a list with the remanence as a function of the quality. This (Dutch) list is given on: www.supermagnete.nl/physical-magnet-data.

Transport of magnets isn't allowed by normal post except if the magnets are covered in an iron shell or if a very big box is used to prevent that a magnet field is felt outside the box. So most magnet suppliers have their own shipping company. I have tried different suppliers and finally I found that the Polish supplier ENES website: www.enesmagnets.pl had a very large range of standard rectangular and circular magnets at a rather low price. But they only supply metric magnets of low or medium quality. It might be that this company only supplies magnets in Europe and that for inch magnets you need an American supplier.

[kitestrings]

I'm late here, but yes, thank you Adriaan, this is a very interesting read and summary of the key decisions.  Of course this assumes that you've already asked yourself some turn-point questions before the alternator build, like:

Why build a wind turbine, wouldn't solar be simpler, less maintenance, less cost, ...;>] ?
What's the goal?  How much power do I need?
Are we storing power in batteries, or grid-tied?
If so, what is the nominal voltage?
Will we be tied to this voltage, or using some sort of MPPT, configuration switching, or buck/boost converter?
What will be our means of control?  for charge control, and for overspeed protection?

We assume we are here, because we have already answered most of these decision points.  Accepting that, you mentioned a couple of times the challenge of matching the alternator to the prop.  It seems this is clearly one of the harder nuts to crack.  In my minds eye, I picture the parabolic curve of the available power from the rotor.  If we could, we would follow it exactly for a given rotor size.  This proves harder than it sounds, because we are trying as best as possible to match a very linear output relative to speeds from our alternator to this curve.  If we start too low or too high, or if the line is too steep we have some inherent compromise; something gained on one end, may result in sacrifice on the other.

Still, as I understand it, we do have some levers we can pull, if you will.  I wonder if you can speak to the potential influences of adding line resistance, or changing (slightly) the air-gap.  My understanding is that we can change where we start (higher or lower cut-in), and we can increase or decrease the voltage by how many turns in our coils, but if we want to change the slope of our line, there are not many choices.

[Adriaan Kragten]

The optimum rotor curve is a cubic line in the P-n graph and a parabolic line in the Q-n graph. Mostly I use the cubic line and this line is increasing very strongly at increasing rotational speed. This line can't be followed if the generator load is a battery. The number of turns per coil determines at what rotational speed, the rectified open DC voltage coming out of the rectifier becomes equal to the open battery voltage. So the Pmech-n curve starts at this rotational speed (if the little power needed for the unloaded iron losses and for the bearing friction is neglected). The shape of the Pmech-n curve is about a straight line for the first part of the curve but the curve bends to the right if you come closer to the maximum generator torque. The steepness of this line is stronger as the generator is bigger and as the rotational speed at which the Pmech-n curve starts, is higher. So the Pmech-n curve of the generator can never cover the optimum cubic line completely. But the best matching is realized if the Pmech-n curve of the generator has a point of intersection with the optimum cubic line at a wind speed of about 4 m/s and at a wind speed of about 7 m/s. If this is realized, the matching is good enough in between wind speeds of about 3 m/s and 8 m/s.

If the windmill is grid connected by an inverter and if the inverter accepts a large variation of the input voltage, theoretically the inverter can be programmed such that the optimum cubic line is followed for wind speeds above about 2 m/s. But not all inverters have this option. Certain inverters vary the input voltage such that the output power is maximal but this doesn't guarantee that the optimum cubic line of the rotor is followed. It might be that at high wind speeds, the rotor runs at a too high tip speed ratio because the increase of the generator efficiency because of a higher voltage is larger than the decrease of the Cp because of a tip speed ratio larger than the optimum value.

I have only checked the matching for battery charging windmills and I have measured several radial flux PM-generators on a very accurate test rig of the University of Technology Eindhoven. But for small generators, I have built my own test rig (see report KD 595). So without measured generator characteristics, it isn't possible to check the matching and then only try and error can give you an idea if you have made the correct choice for the wire thickness and the number of turns per coil and for the chosen magnet size and number of magnets.

The choice in between solar and wind is mainly determined by the wind regime. Solar has become much cheaper but that is not the case for good quality small wind turbines. If you need only a small amount of energy, solar might be the best choice. But if you need a lot of energy in the winter to power your heat pump, wind can be a much better choice as in December, solar generates only about 2 % of the total yearly output.

[Adriaan Kragten]

The easiest way is to design, build and test the generator first and to design the windmill rotor afterwards. This is especially the case if the generator is made from an asynchronous motor using the standard 230/400 V winding, so one can't change the number of turns per coil. The generator should be measured for 26 V and 52 V for star and for delta (13 V is too low for a standard winding) so the generator measurements can be used for 24 V or 48 V battery charging. So four different Pmech-n curves are available. The highest voltage gives the highest power and efficiency. It is possible to modify a standard 230/400 V winding into a 115/200 V winding by connecting the coils in the first layer in parallel to the coils in the second layer. This procedure is explained in report KD 341. The measurements for 52 V can now be used for 26 V. The advantage of star rectification is that the unloaded Pmech-n curve is lying lower which reduces the starting wind speed. Assume one choses 48 V battery charging for the standard winding so one can use the curves for 52 V star. So now the Pmech-n curve of the generator is known.

Next one choses a windmill rotor which matches best with the given Pmech-n curve of the generator. The formula for the optimum cubic line is given as formula 8.1 in report KD 35. In this formula it can be seen that R is given to the power of 5. So a little change in the rotor diameter gives already a strong change in the position of the optimum cubic line. So one makes a choice for Cp, R and lambda and draws the curve in the same graph as the measured Pmech-n curve of the generator. If the matching isn't optimal, one changes R or lambda till the optimum matching is gained.

This procedure is followed in all my KD-reports in which I give the rotor calculations of a certain rotor. Report KD 484 gives the rotor calculations for the VIRYA-3B3 rotor. This windmill makes use of the generator for which the measurements are given in report KD 78. However, the standard 230/400 V winding is modified into a 115/200 V winding. Figure 4 shows the matching for 26 V star. The Pmech-n curve has no point of intersection with the optimum cubic line but lays very close to it and so the matching is acceptable. Figure 6 shows the matching for 13 V delta. Now the matching is perfect. However, if the Pel-V curves as given in figure 5 and 7 are compared, it can be seen that the Pel-V curve for 26 V star is better above a wind speed of 4 m/s. In figure 8 it can be seen that the starting behaviour is slightly better for star rectification.

[MattM]

I did run some numbers on how thin the insulation has to be in order to try and pack in more copper using copper sheet metal.. pretty thin..

in theory you can pack round wire about 95% fill factor, but the plastic insulation is the biggest hit. maybe 80% is practical on wind turbines.

now take two wires or three wires and twist them together and then wind a coil out of them. maybe 60% fill factor max.

I did try 1/2" x 10' strips of 16 ounce copper to make coils.  Very tightly packed single-axis spirals were easy to wind up and they came in at 6.7 ounces with wire leads soldered on each end and a thin paper insulator separating the rows.  They were not very productive at that 1/2" width and made more heat than conventional enamel wire.  I suspect eddy currents made them a poor choice.  Changing insulators to electrical tape did nothing to improve it.  Maybe if they had been more like flat wire which is usually more like 3/16" or less.  But, hey, they were extremely easy to make, take apart, and to rewind.

When I was speaking of bifilars I was thinking more along the lines of Fermat's spiral shapes for the bifilar coils, keeping them flat and building them serially 3/4'ers or more around the radius of the stator.  The key to Fermat's spirals is each coil is able to operate in the opposite polarity without disturbing their neighboring coil.  Bifilars have less drag by their nature - flux has simultaneous relief in both flow directions.  So the idea is not really any different than a conventional design as it will still have an odd number of phases to account for the odd phase that is swapping polarity.  As the magnets move around like in a conventional design, there is always one of the phases involved in switching directions, while the remaining phases are under the influence of the alternating magnetic poles.  Fermat's coils may be a bit harder to make, but it shouldn't care as much how things are wired directionally when creating the serial arrays.  I'm using ferrous magnets where the flat coil designs, which are stacked overlapping other phases, won't have anywhere near the field line strength of those rare earth magnets.  Making the coils is a little trickier to keep them flat.  But it should be harder to screw things up when wiring up the phases.

[bigrockcandymountain]

Adriaan, could you share your thoughts on deciding between an asynchronous motor based generator with 230v/400v winding vs building from scratch an axial with potted coils.  That was the biggest decision for me when designing a turbine.  I know you have exprience with both, and not many here do. 


Great writeup and I think it better go in FAQ for sure.  Thanks for doing this. 

[kitestrings]

I was hoping to see someone comment(s) on the effect of adding line resistance, as that has been talked about a lot here in the past, and I think it ties in to some of the choices that Adriaan is walking us through on this post.  Dan, Flux, and others I believe have used it as a means of altering, with some limitations the slope of the line for battery-tied systems - the bulk of systems here.  Similarly altering the air-gap, with limits, has been used to tweak a turbine that say is heavy stall limited.

Regarding your comment, "The easiest way is to design, build and test the generator first and to design the windmill rotor afterwards."

I'll politely disagree.  While this may be the easiest, from a design perspective, to me it seems backwards.  I would not purchase an auxiliary generator at a random kVA, then fit a motor to it (LP, gas, diesel), without first calculating the load requirement.  Of all the things discussed, no single element has more influence on output than the rotor size.  To me the design should start with the load requirements, the size of the rotor to meet that requirement, and you work your way in from there...

[Mary B]

For the calculation of the flux density in the air gap and the armature sheets you need the remanece Br in Tesla for the chosen magnet quality. Most suppliers of neodymium magnets give the quality and the price depending on the quantity for a magnet of certain dimensions but they don't give the remanence. However, the supplier Supermagnete gives a list with the remanence as a function of the quality. This (Dutch) list is given on: www.supermagnete.nl/physical-magnet-data.

Transport of magnets isn't allowed by normal post except if the magnets are covered in an iron shell or if a very big box is used to prevent that a magnet field is felt outside the box. So most magnet suppliers have their own shipping company. I have tried different suppliers and finally I found that the Polish supplier ENES website: www.enesmagnets.pl had a very large range of standard rectangular and circular magnets at a rather low price. But they only supply metric magnets of low or medium quality. It might be that this company only supplies magnets in Europe and that for inch magnets you need an American supplier.

I got in a box of magnets for a different project(building a driveway sweeper fora friend) and I saw the delivered but it wasn't sitting outside the door... then I looked up... it was hanging off the front of a door with a nasty note that it stuck to everything in his truck LOL

[Mary B]

I did run some numbers on how thin the insulation has to be in order to try and pack in more copper using copper sheet metal.. pretty thin..

in theory you can pack round wire about 95% fill factor, but the plastic insulation is the biggest hit. maybe 80% is practical on wind turbines.

now take two wires or three wires and twist them together and then wind a coil out of them. maybe 60% fill factor max.

I did try 1/2" x 10' strips of 16 ounce copper to make coils.  Very tightly packed single-axis spirals were easy to wind up and they came in at 6.7 ounces with wire leads soldered on each end and a thin paper insulator separating the rows.  They were not very productive at that 1/2" width and made more heat than conventional enamel wire.  I suspect eddy currents made them a poor choice.  Changing insulators to electrical tape did nothing to improve it.  Maybe if they had been more like flat wire which is usually more like 3/16" or less.  But, hey, they were extremely easy to make, take apart, and to rewind.

When I was speaking of bifilars I was thinking more along the lines of Fermat's spiral shapes for the bifilar coils, keeping them flat and building them serially 3/4'ers or more around the radius of the stator.  The key to Fermat's spirals is each coil is able to operate in the opposite polarity without disturbing their neighboring coil.  Bifilars have less drag by their nature - flux has simultaneous relief in both flow directions.  So the idea is not really any different than a conventional design as it will still have an odd number of phases to account for the odd phase that is swapping polarity.  As the magnets move around like in a conventional design, there is always one of the phases involved in switching directions, while the remaining phases are under the influence of the alternating magnetic poles.  Fermat's coils may be a bit harder to make, but it shouldn't care as much how things are wired directionally when creating the serial arrays.  I'm using ferrous magnets where the flat coil designs, which are stacked overlapping other phases, won't have anywhere near the field line strength of those rare earth magnets.  Making the coils is a little trickier to keep them flat.  But it should be harder to screw things up when wiring up the phases.

There was a long discussion on this way back when... and eddy currents are the problem. Some even tried printed circuit board coils but to get the current carrying needed the traces ended up to wide and yup, eddy currents.

[Adriaan Kragten]

Adriaan, could you share your thoughts on deciding between an asynchronous motor based generator with 230v/400v winding vs building from scratch an axial with potted coils.  That was the biggest decision for me when designing a turbine.  I know you have exprience with both, and not many here do. 


Great writeup and I think it better go in FAQ for sure.  Thanks for doing this.

In KD 341 you find the more than forty years long history of the development of PM-generators for the VIRYA windmills. I started with a modified car generator but the required rotational speed was much too high for 12 V battery charging. Next I designed a 12-pole PM-generator using ferroxdure magnets and a special winding. Later neodymium magnets came available and with neodymium you can make a 4-pole armature which is strong enough to get saturation of the stator stamping. Using the housing of an asynchronous motor has the following advantages:
1) It is possible to use the standard 230/400 V winding or to modify this winding to a 115/200 V winding without rewinding.
2) The air gap is very small, so rather thin and cheap magnets can be used. But the generator can still have a large maximum torque level for a relatively small outside diameter.
3) Asynchronous motors are made in a large range so there is always a housing available with a maximum torque level which is high enough for the chosen windmill rotor.
4) Asynchronous motors are also made in large quantities and therefore they are relatively cheap.
5) The housing is water tight which gives a good protection of the winding and the front bearing (if a good seal is used). The back bearing cover can be closed.
6) The bearings are mounted at a large distance from each other. So a moment in the shaft gives rather low radial bearing loads.
7) For some generators, it is even possible to use the original motor shaft. But for my first generators I have used a special stainless steel shaft with a tapered shaft end. The generator hub was connected to this shaft by one heavy central bolt.
8 ) The housing is provided with cooling fins so even without a fan, a lot of heat can be dissipated. This makes it possible to use the generator as a brake (if the windmill has a proper safety system).
9) It is also possible to design a PM-generator with a high pole number if a high frequency is wanted.
10) I have tested several 4-pole PM-generators and the measuring reports are public available for three different frame sizes being 90, 112 and 132 (report KD 78, KD 200 and KD 82). So from these measurements, one can get a very fast impressing of the maximum torque level for a certain frame size. The maximum torque level is proportional to the armature volume. So if one designs a generator with another frame size, one can estimate the maximum torque level if the armature volume is compared to one of my tested generators (at least if the armature construction and the flux density in the air gap are the same).
11) An extensive description of the armature construction and the calculation of the flux density in the air gap is given in public report KD 503 for a generator using frame size 100. This generator is an alternative for the generator frame size 90 (with lengthened stator stamping) which is used for the VIRYA-3B3.

The disadvantages are:
1) As the stator contains iron, you can get a large peak on the sticking torque if the armature isn't designed well. But there are ways to flatten this peak almost completely.
2) The original motor is designed for a rather high voltage so if the generator is used at very low voltages it can't have a high efficiency or it can become too hot at high rotational speeds. But if the original winding is used for 52 V star or for 26 V delta, the efficiency is acceptable.
3) Mounting of the magnets in the armature might be tricky if big magnets are used. Mounting of the armature in the stator requires a big force as the armature is always pulled against the stator.

I have designed some axial flux generators but I don't like the construction with a stator in between two armature disks. So I have designed several 8-pole PM-generators with only one armature disk. In chapter 7 of KD 341, I have compared a 26-pole radial flux generator with an iron stator with such an 8-pole axial flux generator with no iron in the coils and with about the same torque level. Much more magnetic material is needed for the axial flux generator. Other disadvantages of an axial flux generator are that all components have to be manufactured and that it is difficult to protect the magnets from rain or dust. One has to develop skills to cast the coils in epoxy or polyester.

[joestue]

I suspect eddy currents made them a poor choice.

There are a lot of flux lines running at weird angles relative to the coils, because there is no magnetic core for them to preferentially flow through, and so winding the coils from full width copper strip will force all the flux lines to be parallel to the axis of the coil, otherwise they generate eddy currents in the copper.

I wouldn't expect this wasted eddy current to dominate, when it comes to approaching rotor burn out conditions. but if the additional drag exceeds the total KWH increase from decreasing resistance losses at high loads, then it isn't worth it. also if making the alternator stiffer makes the whole system generate even less power then again there is no point.

[Generator]

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.

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.

Adriaan, thanks for sharing this great info. Have you considered design using iterative method for generators? Simulation software can make design changes automatically in given range and come up with most optimized design for various parameters.

Also curious about the Name you have used e.g. Virya, does it mean anything in your language?

[DamonHD]

From Wikipedia:

Vīrya (Sanskrit; Pāli: viriya) is a Buddhist term commonly translated as "energy" ...

Rgds

Damon

[Adriaan Kragten]

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.

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.

Adriaan, thanks for sharing this great info. Have you considered design using iterative method for generators? Simulation software can make design changes automatically in given range and come up with most optimized design for various parameters.

Also curious about the Name you have used e.g. Virya, does it mean anything in your language?

Virya is not a Dutch but a Sanskrit word. There has been a time when I was rather active with Indian knowledge and I practiced Transcendental Meditation and the TM-Siddhi Program. The siddhis are described by Patanjali. I have a book about the Yoga-Sutras of Patanjali commented by Dr. I. K. Taimni. In the end of this book there is a list with Sanskrit words. Virya is translated into Dutch as ontembare energy which I translate in English as energy which can't be tamed. So it is something like renewable energy and I found this a nice name for my wind turbines.