excel tool for calculating axial flux generators

[Menelaos]

Hi Fieldliners,

As I am working on my 6 KW on grid axial flux generator I was creating an excel tool to make Things a little easier. I don't know if you guys over here already have a tool similar to this one...but in case you don't I would like to introduce the one I made. It may not be too easy to understand when looking at it for the first time but I am looking forward to your comments on it. I tried to translate it from German to English...so please don't mind spelling mistakes. Some things are still to be added and the tool will be updated on a regular basis.

Max

PS. I tried to post before...hope i didn't double post...

[Menelaos]

hm...ok...so nobody seems to be interested...

[dlenox]

Menelaos,

why not put up the .xls so others can play with it, only then would they be able to provide feed back.

dan lenox

[fabricator]

It looks pretty cool to me.

[WindJuggler]

First of nice program.

There was someone else looking for some formulas you should have used.
http://fieldlines.com/board/index.php/topic,141270.0.html

Have you tested the program with a real generator? If you do let us know how the numbers are compared to the calculations.
I have played around with it. It is pretty much self explanatory.
I work the other way around when I'm designing my rotor and stator. Start with a diameter and see if the coils would fit.

[WindJuggler]

Hi,

I found a mistake in your program. You didn't take the speed at which the magnets pass the coils into account.
If the rotor is larger, the speed of the magnets will be more compared to smaller rotors.
When I change some variables that influence the disk size the number of windings doesn't change.

Go to the link I provided earlier. There is a formula with dA/dt in it.

[Menelaos]

Thanx for your comments,

In the meantime we added some features to the programm. I will make an english version so that u guys can handle it as well...

The mistake u discovered actually is not a mistake. The speed of the magnets at different Diameters does not matter at all. It also took me a while to understand the reasons an dit is not so easy for me to explain in a foreign language but I give it a try:

Usually the coils in the stator are placed directly next to each other, without much space between them. If u now move them to a greater radius, I agree that the magnets pass them with more speed and thus also the output is supposed to be higher...but this is not the case. If the number and dimensions of the coils remanis the same, there will then be some space between the coils. The magnets are "faster" but they still strike the same amount of copper in the same time span. The sine wave would be higher as the speed is higer, I agree. The maximum voltage will also be higer BUT the sine wave will be shorter in length because there is space between the coils. When rectifying, the output voltage will remain the same. If u fill the gaps between the coils with more coils, of course the output will be higher but as long as this is not done, there will be no change at all.

in order to understand this, u hae to ask your self: What happens at the time when the magnets go oder the gap between the coils...
Nothing at all!!!

If you move the coils together and thus bring them on a smaller circumference so that they are directly next to each other, then the flux between the magnets is "used" all the time which is not the case in the example i stated before. In the end it will all be the same due to rectifying process. SO it is a bad idea to habe space between the coils. It doesent change anything but making the generator bigger in size.

I filled in the numbers of my last generator. The programm gave me charging voltage at 142 RPM. In real life it is 136 to 140 RPM. I find this close enough.

I also filled in the numbers fpr my 6 KW Generator. Also here the numbers match very well so far. I plan to reach 250 volts at 55 RPM. I will report if this will be the case when i have finished the machine. The resistance of the coils is 5.1 Ohms. The tool calculated 5.03...also quite close.

In the new version the weight of copper is calculated and the design is changed a little. Now fileds for hight of coils turn red if it is too much and one can set numbers for the airgap between magnets an stator as well as for the thickness of Material over the coils after casting. That makes thinx a lot easier.

The latest (german) version can be downloaded on the website of a friend with who i made the tool together:

http://www.nadaparasiempre.com/hobbies/wind-energy/generator/index.html

What i discoverd on this new design of the bord is that the file I uploaded in my first post can only be seen and downloaded if one is logged in. For users not logged in it is invisible...

Max

[ChrisOlson]

It may not be too easy to understand when looking at it for the first time but I am looking forward to your comments on it

Hi Max,

It was easy to understand and it seemed to accurately reflect the mistakes I made in (over)winding my generator in my 13 footer.  I entered the data for my 10 foot star-wired machine it it hit the number of turns and generator size right on.  Looks pretty good, actually.
--
Chris

[Menelaos]

Thats nice to hear :-)

OK, here we go with the english version of the improved tool...see attached...

The main improvement are:
1. the approximation of wire weight which makes it easier to order the right amount
2. changes in the area for coil hight: the blue fields turn red if the stator does not fit between the air gap. It is now easy to countercheck with the airgap section where the flux is calculated. Always try to use as little space as possible. It will reduce the resistance of the generator and also the amount of wire needed.

SOme more changes will be applied to the section where power is calculated. Those numbers are interpolated from the tables u can see on the other sheets. I will make those calculations more precise. Anyway those numbers are only based on Ohm law. It does not considder stalling of Rotor and so on. In practise the numbers will change more or less but for a first approximation it is enough I think.

Also the determination of diameters for the rotor and stator size is an approximation only. Big generators tend to be smaller in practise. Very small generators tend to be a little bigger...but for roughly checking it is fine.

[fabricator]

Yeah that looks good but, although they have tried several times American English still uses inches and fractions of an inch and thousandths of an inch and feet per second, stuff like that, also the spelling for how high something is is height, maybe a better word would be thickness.

[Menelaos]

Im sorry for not beeing a native speaker...

Maybe there is somebody here who takes 2 minutes of time and corrects my spelling and replaces some words with ones that fit better. Also the change from metric units to "inch" system :-) can be done in a few minutes by applying some factors in the formulas- should not take long...feel free to edit or improve the tool to ur desires

Then simply upload the corrected files to share with others...

Max

[ChrisOlson]

Maybe there is somebody here who takes 2 minutes of time and corrects my spelling and replaces some words with ones that fit better. Also the change from metric units to "inch" system :-) can be done in a few minutes by applying some factors in the formulas

Although some would like to see it in inches, feet, mph, etc., I actually prefer to work with the metric version because it's more universal.  Some extra fields could be put in the spreadsheet to display both at once, however, that would be merely a convenience for non-metric users.  Otherwise I'd leave it SI because when you work with English units you have to apply factors to arrive back at watts (if it was completely in English units we'd be using horsepower instead of watts).  The English units of measurement are long obsolete in engineering so I'd leave it as is and force those who still use English units of measurement to conform   

Calculating those power curves is very hard to do with any degree of accuracy.  You have to take into account the resistance in the tower drop and wire run too, and that varies by each installation.  I entered the data for my little 8 foot 12 volt machine, and once again it hit it right on.  I think the total weight of wire is off a bit, perhaps because of the lengths used in coil interconnects, etc..  But as we say here in the US, it's "close enough for government work".

Overall, I find little wrong with it except for the part in graphing the power curve not taking into account resistance in the wire run.  Otherwise it's a very excellent tool, nice attractive interface, easy to understand, and reasonably accurate.  I would consider putting protection on the sheet to prevent accidentally changing a formula - except leave the data entry cells and other non-critical cells unprotected.  That way people can change the wording to whatever they want without risking rendering the sheet useless by accidentally overwriting a formula.
--
Chris

[ChrisOlson]

Thats nice to hear :-)

OK, here we go with the english version of the improved tool...see attached..

Max,

I used wedge magnets in one of my 10 footers and I had to "fudge" the dimensions in the entry fields for the magnets  because the sheet doesn't take that into account.  I used the actual length of the wedge magnet, then "fudged" the width of the magnet to get the area to come out right.  That seemed to work fine.  I wouldn't factor that into the sheet because of the complexity of it, but if other people use wedge magnets instead of bars I just wanted to note that you can "fudge" the width to make the area of the magnet agree with what it actually is, and the sheet seems to accurately then predict the number of turns of wire required.
--
Chris

[Menelaos]

Yes, the power calculation is a tough task. Even Battery capacity and state of charge make a big difference. It is nearly impossible to take everything into account. My Turbine will be grid tied anyway so there will be completely different results again...
I my self hardly ever look at those numbers. It is only to give a rough idea especially for low winds. In high winds everything will be different again...

I am happy u like the tool and i hope it can help some people find the right setup for their machine more easy.

The calculation of wire weigt might be a littlebit off but it should be about 10% right....enough to get an idea on how much money one has to spend on wire and to check the differences in corellation with airgap,size of statoor --> resin (money), flux--> magnets (money) and resistance --> power loss.
This way it is quite easy to find an economical construction that is effective on material and efficiancy. Especially for big generators this sometimes can make a big difference...

[Menelaos]

By the way...

why not put up the .xls

I tried but the attachment manager didn't let me upload a file larger than 150 Kb...so I had to zip it...

Max

[ChrisOlson]

SO it is a bad idea to habe space between the coils. It doesent change anything but making the generator bigger in size.

I concur on this.  On both of the last two generators I built I went to great pains to pack the coils into the smallest diameter they would fit in instead of selecting the diameter for easy fit.  Both generators ended up more powerful than what I figured they would.  When you build that way the magnets never stop working at their full power - there's no gaps between the coils to give the magnets a "rest".  Therefore it takes more shaft power to turn the generator, it's more efficient, and it puts out more power.

The hard part is matching the prop to that.  I haven't done so well with prop/generator matching on either of the last two machines I built.
--
Chris

[WoodSpinner]

From what I can see it looks pretty neat, but I dont have excell, just ms works and it wont load the whole thing and claims there are errors. 
John

[Menelaos]

It works fine with open office as well which you can download for free...

Why should the magnets need a "rest"?

If you move the coils more apart from each other then you have la larger circumferance. SInce the same amount of magnet still strikes the same amount of copper in the same time, there should not be any change in power output.

The magnet that is between 2 coils has a "rest"...ok...but at the same time other magnets then pass other coil legs with more speed due to greater circuferace and make more "power" at the same time...

There is no mathematical explaination for this. there must be other aspects to be the reason for what u observed..i think...  

[ChrisOlson]

There is no mathematical explaination for this. there must be other aspects to be the reason for what u observed..i think...  

Perhaps it was because I overwound both.  But one thing I do know is that keeping those magnets busy makes a much smoother-running generator.

I corrected the spelling in your spreadsheet and added a English <-> SI converter to it for the "metric challenged"  
--
Chris

[Flux]

I haven't tried the calculator yet but it looks interesting. I will try when I have some spare time.

Just a few comments on the general discussion.

The emf generated depends on the flux per pole and the rate of change. The rate of change depends on the number of poles ( magnets) and rotational speed.  If you like this is frequency. it comes down to angular velocity if you like, don;t confuse it with the passing surface velocity in ft/sec.

In one rotation the magnets will link the flux a certain number of times, placing them on a larger radius will not change this but they will have to go faster to do those flux reversals in the same time.

This and a lot of other confusion seems to come from early text book equations for the emf generated in a wire moving through a uniform magnetic field. This e = Blv equation is a starting point and best forgotten, it doesn't work in real life as a single wire can't exist, if you connect the ends to measure the volts you create a loop. Also you are not moving the conductor through a uniform field, it keeps changing polarity.

Forget that stupid thing and you will then not be considering other stupid things like active sides and dead sides of coils and worrying about keeping coil ides at right angles to the magnet path.

It all comes down to flux linking loops, if all the flux links the loop then linear speed is irrelevant

Also the basic emf equation assumes that each turn will link the same flux at the same instant. This works with single turns or when the turns are all in the same place on top of each other but when you get turns side by side then the linkage will be progressive as the magnet sweeps over sections of the coil.  If the hole in the coil is magnet size or bigger then all turns will link all flux at some time but not at the same time.

When you crowd things in even more and the inner turns are smaller than the magnet you will still keep increasing emf even though some turns now never link the total flux. These contribute less and in radial machines there comes a time when they mainly contribute resistance and little more emf and are best avoided.

For axial machines these inner turns become very short and contribute little in the way of resistance and you can go on adding them to a greater extent and still get some useful gain.

I have not done any experiments to see how much this helps or hinders, but certainly making the coils elliptical or near triangular instead of following the magnet shape seems to still give good results.

As you do this crowding you certainly need more turns for the same voltage but you also have extra winding space for more copper, these factors seem to work together to a large extent. In the end the heating will depend on the wire size and the coil resistance, so if you don't have to drop wire size and you can end up with less resistance you must gain.

There is another factor that I don't have an answer for and this will also affect the result, even if you end up with more loss and more resistance you may still have better cooling if you distribute the wire over the entire surface rather than having holes in it. The heat dissipation of the resin is virtually zero so having effectively useless copper ( electrically) in these areas, dissipating heat may still give a lower temperature rise from a greater total heat input. Another area to investigate.

Magnets couldn't care less whether they have idle periods or are working all the time, in a polyphase machine they are working all the time anyway, the holes in coils don't affect this issue. in the end it comes down to heat loss and heat dissipation.

Where the best compromise is I really don't know, I don't have the time or patience to jam in high density windings in a tiny space when having a bit bigger disc makes the whole thing so much easier but each to his own preferences.

Flux

[WindJuggler]

Hi,

You are correct I figured it out already. It is not the speed that matters but the change in Webers. Larger diameter equals more speed but the magnetic field changes slower due to the fact that space between the magnets is larger.

[GWatPE]

Hi Max,

do you have plans to allow for round magnets, and coils?  I had to fudge things a fair bit to model my own mill, with 9coils, and 12 mags per rotor. 

Gordon.

.

[ChrisOlson]

Magnets couldn't care less whether they have idle periods or are working all the time, in a polyphase machine they are working all the time anyway, the holes in coils don't affect this issue. in the end it comes down to heat loss and heat dissipation.

Flux, I base most of my observations on things I've tried.

Some months ago I built a 40 turn stator for my 8 foot turbine using AWG 14 wire and 10" generator rotors.  The thing was a vibrator and I wasn't too happy with it's performance.  I got about 450 watts out of it, peak.  It finally burned up so I built a new one for it, except this time I wound two-in-hand AWG 15, 38 turns and it was a really tight fit.  Had to do a little hammering on the coils to get them to fit in the space.  I used wedge magnets and wedge-shaped coils.

The new stator ran MUCH smoother and it put out the same volts at the same rpm, and more watts.  I could get close to 700 watts out of that one.  That one finally burned up too and it wrecked my rotors - tore a bunch of magnets off it.

I peeled all the remaining magnets off the rotors and built a new 11" generator, this time winding with two-in-hand AWG 14, 36 turns.  Again, it was an extremely tight fit - so tight that I reverted to using the hydraulic press to smash everything into place, which flattens the coils a bit and expands them at the same time to the outside so they're very tightly packed into the circumference of the stator.  Still didn't lose any volts/rpm, but this generator was too powerful for the blades.  I ended up opening the air gap so the blades could drive it.  I've since closed the air gap on this machine and converted it to a 24 volt.

My observations in the three stators were that I kept increasing the wire size every time, which reduced resistance and gave me more power.  But I ultimately ended up with 4 less turns than I started with on the first one, got more power, packed the coils into the tightest space they would fit in, and so far haven't been able to destroy the dual-wound AWG 14 generator.  At 24 volts it cuts in about 8 mph wind speed and puts out 900 watts in a good stiff wind without even really working it.

In 12 volt configuration it kept burning out rectifiers all the time and it would start to vibrate.  But otherwise it runs totally smooth with just a slight humming noise.

So which changes made the improvements in performance that I got from this machine thru its evolution of burned up generators?  You're saying I could've just went to 14" rotors for an easy fit and I'd get the same performance as I got by packing those coils under 11" rotors?
--
Chris

[joestue]

Magnets couldn't care less whether they have idle periods or are working all the time, in a polyphase machine they are working all the time anyway, the holes in coils don't affect this issue. in the end it comes down to heat loss and heat dissipation.

Flux, I base most of my observations on things I've tried.
{details removed}
In 12 volt configuration it kept burning out rectifiers all the time and it would start to vibrate.  But otherwise it runs totally smooth with just a slight humming noise.

So which changes made the improvements in performance that I got from this machine thru its evolution of burned up generators?  You're saying I could've just went to 14" rotors for an easy fit and I'd get the same performance as I got by packing those coils under 11" rotors?
--
Chris

Too many variables and no real benchmarks.
You can wind your coils for trapezoidal waveforms, sine or your choice of harmonics, but do you know how much the difference was contributing to your three cases? how about line and rectifier losses?

Sticking the magnets too close together introduces a third dimension due to flux leakage, this isn't easy to generalize with a spreadsheet, unless you want to resort to 1960's era fluid dynamics and its "variable constants"

someone said "If you move the coils more apart from each other then you have larger circumference. Since the same amount of magnet still strikes the same amount of copper in the same time, there should not be any change in power output."

this might be partly true for a machine where the coils are individually rectified, but in practice with WYE connected 3 phase this results in very high losses, it won't even turn with delta.

as magnets are expensive and copper is cheap, it would be good to stick the magnets as far apart as is possible.

[ChrisOlson]

Too many variables and no real benchmarks.
You can wind your coils for trapezoidal waveforms, sine or your choice of harmonics, but do you know how much the difference was contributing to your three cases? how about line and rectifier losses?

I base my observations on what Doc Wattson says I got going into the batteries, which takes into account line and rectifier losses because I measure the actual wattage where it counts.  And I've been satisfied with the performance of the last three generators I've built even though I overwound the last two so they don't perform exceptionally in high winds.

My observation has been, despite theory and 25 pages of mathematical calculations, that having no gaps between the coils makes for a more efficient and smoother-running generator.
--
Chris

[dlenox]

Max,

Thanks for being a bit patient with getting replies.  Sometimes life gets in the way and it takes a while before people can respond to the postings.

Also thanks for the work you did on the .xls spreadsheet.

Dan Lenox

[Beaufort]

Very, very nice!  I have a spreadsheet for this kind of work too and I've not been able to clean it up enough like yours to put it up here.    I still have to crawl through all the formulas to check them with mine but I see a few areas for suggestion:

• The bottom section lists power and efficiency as the windspeed is changed.  In practice the efficiency at lower windspeeds near cutin is very far off from theoretical.  So I have a correction factor for certain sized machines where eddy currents are a bigger factor at low speeds, so the efficiency turns out nearer to 35% than 70%.  I spent a lot of time trying to figure out why my model didn't match what I built, and it turned out that's just the way they work at lower speeds.
  
  It looks like the power curve assumes a constant TSR and therefore Cp from the blades?  In reality TSR drops much lower after cutin and gives very different results, however I've had good results to model the Cp/Lambda parabola and to iterate solving for RPM.  I think your blade efficiency number is where this calculation is wrapped up right now.  That parabola is very important because it shows where the peak power is produced, and how machines can end up on either side of the curve if certain things are changed (resistance, furling effects, etc.).
  
  Again, very very nice. 
  

[ChrisOlson]

It looks like the power curve assumes a constant TSR and therefore Cp from the blades?  In reality TSR drops much lower after cutin and gives very different results

Yes, this is an important factor that's hard to put into Max's spreadsheet.  I know from experience with the blades I use that they run at a very low 4 TSR at cut-in speed of 7 mph wind and they pick up to about 6 TSR at 18-20 mph wind, then start dropping again to where they finally reach stall/furl at about 4.5 TSR in the mid-20's wind speed.  It's a parabolic power curve but I don't know how it would be incorporated into a spreadsheet like this without some very complicated formulas.

Using Max's sheet, I enter the max 6 TSR, and compensate by using a ridiculously low cut-in wind speed, then in the power calculation section use the 10 m/sec wind speed where my blades peak - and it comes out very, very close to actual.  To double check, in the start of charging section I entered the actual cut-in TSR of 4, and 3.1 m/sec wind speed,  to see if the number of turns is correct - and again it jived with actual.

So that should be a warning to somebody who would use the sheet verbatim without understanding the power curve of your turbine blades - if you use the sheet verbatim you will end up with a machine that cuts in late and has good top end performance and not so good low wind performance.
--
Chris

[Beaufort]

I know from experience with the blades I use that they run at a very low 4 TSR at cut-in speed of 7 mph wind and they pick up to about 6 TSR at 18-20 mph wind, then start dropping again to where they finally reach stall/furl at about 4.5 TSR in the mid-20's wind speed. 

What you're describing is a bit different from how I build them and from what others here describe, but I think it's just a matter of where you want your power.  Most here seem to have a TSR slightly higher than the "design" TSR at cutin and it falls off as wind speed increases.  The logic is that you get maximum power out at your site's average wind speed, and live with the inefficiency at higher wind speeds.  So in a sense, you design it to sit at the top of the parabola at cutin and then slide off one side.  I think you're describing starting off on the high side of the parabola and hitting the peak at 18-20, and then sliding down the curve. 

Yeah, to get this into Excel I had to break down the TSR/Lambda curve into a 4th-order polynomial.  Then I used a macro to goal seek on each point of the power curve to find where the alternator load matches the wind power input...and this spits out a TSR for each wind speed on the curve.  This all assumes you have the TSR curve to begin with, which is only possible with known airfoils (Oh, I really like the S809 airfoil...I've been working with this one after reading about your experience here.  Way more torque on the low end than the flat-face carved planks and it self-limits at higher speeds).

[Flux]

Yes the type of blades and how they perform at various tip speeds does affect the results. I don't know how you deal with this in a spread sheet.

The performance is much more dependent on the match between alternator and blades than on the alternator itself.

Chris seems to know his blade characteristics which is more than most of us can hope for. Most will have to get the cut in right with an assumed tsr then take what comes higher up the range.

We have a reasonable idea what Dan's type blades behave like and also Hugh's which tend to be a little faster, if you choose your own profile or buy commercial blades you will have less information to base things on.

I suspect there is not a lot of difference in the maximum power out at peak point with different blades but the tsr at which it happens may be quite different.

Flux

[ChrisOlson]

What you're describing is a bit different from how I build them and from what others here describe, but I think it's just a matter of where you want your power.  Most here seem to have a TSR slightly higher than the "design" TSR at cutin and it falls off as wind speed increases.

Yes, when you use these S809 blades, they're a completely different animal than the flat-face blades.  The S809's simply refuse to spin at high TSR in low winds - but at the same time you can load them and they'd don't lose speed (rpm) in low winds.  So I've found the generator has to be wound to match this characteristic.

The flat-faced blades are light weight and they spin like crazy at first, lose speed right after cut-in, then have a gradual drop-off in efficiency to where they finally stall/furl.  This requires a generator with less turns of wire to prevent heavy stalling in the mid-range wind speeds.  Or the other problem you can run into with high-speed flat-face - having the batteries hammered down to a low voltage and they'll run in heavy stall trying to bring the batteries back up.  The S809's will just pull like a locomotive with hammered batteries and put out more power under that situation - if the generator is matched for it.

If you use S809 blades on a generator wound for flat-face you'll stand there and scratch your head going, "Those blades are worthless - they don't put out any power."

But putting all this in an Excel spreadsheet is a daunting task.
--
Chris

[ChrisOlson]

It looks like the power curve assumes a constant TSR and therefore Cp from the blades?  In reality TSR drops much lower after cutin and gives very different results

I used to have a little 6.8 foot (7 footer I called it) turbine and over several weeks I hand charted what I got out of it for actual ouput, using my little home weather station anemometer to measure wind speed.  I entered the charted data into Excel and had the software graph it.  That graph is attached below.  I also calculated the theoretical shaft power and entered that in a different column, so I had it graph that too.

But the generator output (red line) is not done by any calculations or formulas - this is an actual graph of what it used to make for power.  Where the power drops off at the top end is where the machine used to furl.  To my way of thinking, this is what a realistic power graph for a turbine should look like.  If somebody could develop one of these spreadsheets that would accurately predict this, they'd win the prize - I don't know what the prize is but they'd win it.
--
Chris

[SparWeb]

...they'd win the prize - I don't know what the prize is but they'd win it. 

Nobody's claimed Volvo Farmer's 100/100/100 prize yet...

I just started experimenting with the spreadsheet - I will agree, it's a great quick reference, but I wouldn't stake money on it.  The CP is always a slippery figure.  In my measurements (flawed as they are) I see TSR go up and down, CP go up and down, and plotting TSR versus CP makes a wild scatter of points through which no line may pass.

It's in my toolbox, now, thank you!  You don't happen to be good at calculus, by any chance, Menelaos?