Turbine design: tip-speed, cut-in, and # turns

[wired1]

I am part of a group that is currently trying to complete a wind turbine project that started a while ago. The blades have already been built and are 10 feet (about 3 meters) in diameter. We'll be using a PM generator with two rotors, 12 magnets on each rotor. My question involves calculating the number of turns we will need per coil for our stator.

1) From my understanding I can make the design based on what I want my cut-in RPM to be. I found some data and the average wind speed here is 5-6 meters per second. When calculating my cut-in RPM, should I use the average speed for my wind velocity or something else.

Also, I need to know the tip-speed ratio to calculate the cut-in RPM. I wasn't a part of designing the blades, but it is a three blade system. How can I go about determining the tip-speed ratio?

2) We are planning to use the turbine to charge a 12 V battery. I intend to use 9 coils, 3-phase (so 3 coils per phase). The magnets are sized 2"x1"x1/2". They are rated 14,500 Gauss which equals 1.45 Tesla. I am planning on using a star wiring configuration. I have tried using Faraday's law to calculate the number of turns, but for the area term, do I use the area of one magnet, or total area of all magnets?

Basically if someone could give me a step by step run down on how to use all this info to calculate the number of turns I need per coil, I would greatly appreciate it.

[Flux]

"1) From my understanding I can make the design based on what I want my cut-in RPM to be. I found some data and the average wind speed here is 5-6 meters per second. When calculating my cut-in RPM, should I use the average speed for my wind velocity or something else."

Something else. You need to be cut in at something like 3m/s to get power in light winds.

"Also, I need to know the tip-speed ratio to calculate the cut-in RPM. I wasn't a part of designing the blades, but it is a three blade system. How can I go about determining the tip-speed ratio?"

Ask the person who designed it! 3 blades could have a tsr of somewhere between 4 and 8.

If you can't get at it that way then try putting some of your blade dimensions into one of the many blade calculators. That should give you some general figure.

"I have tried using Faraday's law to calculate the number of turns, but for the area term, do I use the area of one magnet, or total area of all magnets?"

Depends on the formula you use. Some use flux per pole and some use total flux which would include total magnet area.

You will find various formulae here and if they are any use they will specify which you need to use. If not don't use them.

I work from flux per pole but my strange equations use frequency which you have to determine from speed and number of poles. Many formulae will give the answer directly from number of magnets.

For what it's worth this is my method.

Volts per phase are given by 4.4x flux per pole x f x N

N is number of turns per phase ( 3 times coil turns in your case).

Flux per pole is gap flux density x area of magnet.

Your gap density will be dependent on the distance between magnets ( stator thickness + clearances). Typically it might be half of your Br figure say 7000 gauss.

Having got the volts per phase your line voltage will be 1.7 x this and the dc figure will be x 1.4.

You will probably find it far easier to look for a formula from someone else ( preferably Hugh Piggot or someone you can trust) and work from that.

Unless you know your gap flux density you will have to make an inspired guess or resort to a test coil like most other people.

For a 12v machine you will have quite a small number of turns and it will need lots of strands in hand, the wire you come up with will be too thick to use directly as it will have eddy current problems if you can handle it.

If you look at the Otherpower 10ft machine with rectangular magnets you will probably find your turns are very similar unless the blade designer has gone crazy.

If you take the 24v coil figures you will need half the turns and twice as many wires in parallel.

I think you would do better to jerry connect it or wind in 3 separate star circuits. Either method will need lots of rectifiers and you may find it easier to mount them up the tower. I really think you will struggle with a star winding with 3 coils in series.

Flux

[wired1]

Hey, thanks for the help. I just wanted to clarify some of those numbers in the equation you wrote. The 1.7 times phase voltage gives you the RMS line voltage for star wiring, and then multiplying by 1.4 gives me the max line voltage?

Also, what are the disadvantages for using series-star winding for a 12 V system? For the 10 foot otherpower project I've been following they used a delta configuration instead of star, and I think I've read that Hugh Piggott doesn't recommend series-star for 12 V systems. Why is this? Won't using a star configuration as opposed to a delta allow the system to begin charging at lower wind speeds?

[Flux]

"I just wanted to clarify some of those numbers in the equation you wrote. The 1.7 times phase voltage gives you the RMS line voltage for star wiring, and then multiplying by 1.4 gives me the max line voltage?"

The equation gave you the rms voltage of 0ne phase. If it is star connected you have 2 phases feeding the line terminals with a phase displacement of 120 deg. The voltage between the line terminals ( any two output terminals) will be root 3 x phase volts or 1.7 x the line volts. This is still rms.

If you feed the ac output to a rectifier then the resultant dc volts will be another 1.4 times the rectifier input rms volts. It is just under the PEAK ac voltage but don't get bogged down with peak ac voltages. What you have is the mean dc voltage which is just slightly under the peak ac. It is the mean of the 6 superimposed peaks from the rectifier and the slight ripple that is left means that it is nearer 1.4 than the peak of root 2 ( 1.414 x ac rms). Hope this clears up that one.

Now the star bit. The objection to star in this case is a purely practical one. At 12v you are looking at only a few turns of extremely thick wire that can carry something like 100A. You are virtually into copper strip and the cross sectional area will be so large that the magnets rotating past this thick strip will introduce eddy currents in it. The only way to avoid this is to use multiple strands in hand of thinner wire. I wouldn't use anything thicker than #12 so you have several strands of thick and awkward wire to wind together and you have many ends to clean and join.

It's not impossible but tricky.

For a given set of coils star connection will indeed give you a lower cut in speed but there is no reason why you can't get the same cut in with more turns of thinner wire. If you delta connect then you use 1.7 times the turns of 48% csa to get the same cut in and current rating.

For this particular type of alternator delta does have problems with circulating currents and all delta machines have problems when connected to rectifier loads. it is not so bad that it won't work and in fact it probably may be as good as a badly wound multi strand star winding although it may drag at cut in.

I wouldn't even consider delta as it is far better to bring out the 6 phase ends and rectify each phase separately and this is generally called Jerry connection here after the person who proposed it.

Hugh tends to favour a star winding with individual coils connected to a star point and you bring out 9 leads to a multi phase rectifier. this leaves you with coils of 3 times the number of turns of a 3 phase star and it is much easier to deal with the thinner wire.

All these methods require more leads and a different rectifier arrangement. You can bring lots of leads down the tower and fit the rectifier in a box at the bottom or you can mount it at the top. Either way you just run a pair of wires to the battery.

I suggested making 3 star windings each using one coil of the three and you would have 3 rectifiers in parallel. This is in fact Hugh,s method with the three star points joined.

The truth is that 12v is just about on the limit of practicality for a 10ft machine, you are dealing with very high currents and the resistance of the circuits has to be so incredibly low that you are struggling, the line cables alone will defeat you with bigger than a 10ft machine unless you pay a fortune.

Flux