Why are high RPMs needed for any useful PMA output?

[brandnewb]

I just can't do the math. even if I knew which formula is relevant.

I mean what is the difference between a PMA with coils (narrow mm2) that generate lets say 180VAC(rms) at low velocity
and the same PMA with coils with thicker coils and a higher velocity of magnets running over them?

Which formula is there in pysics that explains all this?

[joestue]

take a mangnet and drag it across a copper sheet.

you'll find there is a minimum velocity needed to make the copper sheet move, due to its own weight and friction. lets say that velocity is 5 miles an hour.

so if you drag the sheet at 5mph you'll find the magnet has to travel 10mph. the efficiency of dragging the copper sheet is 50%, and you're doing say, 1 watt worth of work on the copper due to friction, and 2 watts of work to move the magnet

now understand that if you drag the copper sheet at 1000 miles an hour, the magnet needs to travel 1005 miles an hour.

now the magnet is doing 200 watts of work on the copper sheet, and you're doing 201 watts of work to move the magnet.

now you're at 99.5% efficiency. same magnet, same copper sheet.

[kitestrings]

joe,

Thank you for this explanation.  It's one I never would have thought or expected.  In part I guess I just associate the idea that the copper moves at all with a vague understanding of eddy currents - something we're usually trying to avoid - and in part that I regrettably just don't have the background in theory.

I tend to look at this type of question in much simpler terms.  There's no such thing as a free lunch, right, and we can vary some material choices & design elements, but in the end we're doing work.  You can pedal the bike faster in a lower gear, or harder in a higher gear... that sort of thing.

brandnewb,

There was a fellow here for many years named Flux.  He was brilliant, and experienced and kind and patient... and had a knack for explaining things.  Unfortunately he passed away a few years ago.  I still miss him, as others do, I'm sure.  I looked quickly through a few of my bookmarks, and prints of discussion he contributed to - this was one:

"Increasing magnet strength, disc diameter and number of magnets does effectively increase power.

Cut in voltage depends on the rate of change of flux and the number of turns. You can get any cut in you want by altering the number of turns if all else stays the same.

Power eventually depends on the voltage and circuit resistance. you can only get more power by lowering the circuit resistance once you fix the cut in.

The way to lower resistance is to use thick wire, which restricts the number of turns. Stronger magnets, more of them and increased frequency are the things that let you get more volts with less turns.

Larger discs let you get more nagnet area in, you can do it with few magnets of large area or lots of smaller magnets but by adopting lots of smaller magnets you keep the turn length short and it is easier to get the same result.

Flux"

You can break it down to relevant the formulas... from Flux, or Adriaan, or Ed, or Hugh or the Dan's, but I think a lot of it comes back to these type of concepts, and much hinges on the goal(s) and available materials and skills/limitations to build.

Best, ~ks

[Adriaan Kragten]

The relation in between the mechanical power P (in W), the torque Q (in Nm) and the rotational speed (in rpm) is given by:

P = pi * Q * n / 30       (W)

So if you have a certain torque Q, the mechanical power P increases proportional to the rotational speed n. The electrical power of a PM-generator depends on the efficiency. The efficiency is reduced by copper losses in the winding and by iron losses if the stator has iron in the coils. But for a certain efficiency, a higher mechanical power results in a higher electrical power. So generally the electrical power also increases proportional to the rotational speed. However, if you have a certain efficiency, the heat losses also increase proportional to the rotational speed and at high rotational speeds, the generator can become too hot. Very high rotational speeds are therefore only allowed for generators with very high efficiencies of for generators with very good cooling.

Any PM-generator with a certain winding has a certain maximum torque level Qmax but the rotational speed at which Qmax is reached, depends on the voltage. The higher the voltage, the higher the rotational speed for which the maximum torque is reached. The voltage is zero if the winding is short-circuited directly after the generator. The Q-n curve for short-circuit is first rising linear to the rotational speed but then it bends to the right and it has its maximum torque at a rather low rotational speed. The Q-n curve for a certain loaded voltage has the same shape as the Q-n curve for short-circuit but it lays more to the right as the voltage is higher.

I have measured a PM-generator for short-circuit and for different constant voltages and the Q-n, P-n and Pel-n curves are given in my public report KD 78. The efficiency curves are also given. If you look at these curves, you see that the electrical power increases for higher loaded voltages but a higher loaded voltage needs a higher rotational speed. If you study the figures as given in KD 78, you will get a good feeling for what a PM-generator can do without any theoretical knowledge.

All measurements are given for the standard 230/400 V winding. If you modify the winding, for instance by connecting the first and the second layer in parallel instead of in series, you halve the voltage but you double the current. You will find the same chararacteristics for half the voltage because the internal copper losses will be the same.

KD 78 also contains measurements for different constant load resistances. A constant voltage has only a high efficiency for a small rpm range. A constant resistance has a high efficiency for a large rpm range but a constant load resistance results in increase of the voltage at increasing rotational speed.

[brandnewb]

thanks gang!! interesting reading all.

But somehow I failed to get interesting amps out of my test setup when going low speed even though at very large diam!! (1.3m something like that)

It made me completly abandon that avenue and am now focusing on lesser diams. greater rpms.

Adriaan, Please can you try and explain once more from my ignorant point of view?

[topspeed]

I also woke up to these high RPMs...as my VAwt WAS SLOWER AND SLOWER WHEN i INCREASED THE SIZE.

So I made 40% thinner wings with insanely thin wing tips ( 10% or less )...and lenngthtened the blades to get better aerodynamical effect and more capture area.

Still not ready but all the pieces have been worked out.

[Adriaan Kragten]

thanks gang!! interesting reading all.

But somehow I failed to get interesting amps out of my test setup when going low speed even though at very large diam!! (1.3m something like that)

It made me completly abandon that avenue and am now focusing on lesser diams. greater rpms.

Adriaan, Please can you try and explain once more from my ignorant point of view?

The main reason why the power at high rpm is higher than at low rpm follows directly from the formula for P as given in my previous post. But there is another effect which has to do with the shape of the Q-n curve for a constant voltage. Lets look at the measured Q-n curves for star connection as given in report KD 78. Figure 4 give the Q-n curves for short-circuit in star and delta. The curve for star is about straight up to 100 rpm and the Q-value at n = 100 rpm is about 20 Nm. The peak torque is about 30 Nm at n = 300 rpm. Short-cuircuit means that the external voltage is zero. In figure 1 it can be seen that the open DC voltage at n = 100 rpm is about 35 V. So this voltage is used to overcome the internal resistance of the winding. As the short-circuit voltage is zero, no external electrical power is produced and all generated power is used for heating of the generator winding. In figure 5 it can be seen that this power is about 200 W for n = 100 rpm.

Figure 8 gives the Q-n curves for DC voltages of 26 V, 52 V and 76 V. These curves have about the same shape as the Q-n curve for short-circuit in star but are lying more to the right as the voltage is higher. Figure 10 gives the efficiency curves. It can be seen that the peak efficiency is higher as the voltage is higher. Figure 9 gives the Pmech-n and Pel-n curves. This figure clearly shows that the highest Pel-n curve is gained for the highest voltage. However, the Pel-n curve for 76 V only starts at a rather high rotational speed of about 235 rpm.

It will be clear that it is impossible to generate a torque at low rpm which is lying left from the Q-n curve for short circuit in star. If the voltage is in between 0 V and 26 V, the Q-n curve will lay in between the Q-n curve for short-circuit in star and the Q-n curve for 26 V. But for very low voltages, the efficiency will be very low because almost all generated energy will be used to heat the winding. As the voltage is higher, the fraction of the energy which is used for heating of the winding will be smaller and so the efficiency will be higher. This is another reason why you should not use very low rotation speeds and very low voltages.

The measured generator was made from an asynchronous motor so it has a stator with iron in the coils. So apart from copper losses, you also have iron losses. There are also losses because of the friction of the bearings and the seal on the shaft. The combined iron losses and friction losses have been measured for an unloaded generator. In figure 2 it can be seen that this power loss is about 4 W at n = 100 rpm. The iron losses at short-circuit will be smaller than at open clamps because the short-circuit current creates a magnetric field opposed to the magnetic field of the magnets. So in the 200 W as given in figure 5 for n = 100 rpm, some W are for the friction and iron losses but the main part are copper losses. For an axial flux generator with no iron in the coils, there are no iron losses and the peak efficiency can therefore be somewhat higher. But the magnet costs are much higher as rather thick magnets are needed to get an acceptable strenght of the magnetic field in the air gap.

[DanB]

In a PMA Voltage is directly related to overall flux coupled by the coils, number of turns in the stator, and rpm (rate of change of the magnetic field).  Double the rpm and you double the voltage.
Resistance goes up with the square of the number of turns.  (double the number of turns 4 x the resistance).  If you double the number of windings you double the voltage but you have to use wire with half the cross sectional area and it'll be twice the length so 4 x resistance.
Power (V*A) is related to the square of rpm, if you double rpm you double voltage and current.

An axial flux turbine can make loads of power at very low rpm.  I've built several that are good for 3kW or more at or below 200 rpm.
But with all the above considerations, roughly speaking ~ power output at any given rpm is related to the square of the weight of the alternator.  (if you want twice the power at x rpm plan on about 4x the alternator)
And I always figure (roughly speaking) ~ alternator weight is related to the cube of blade diameter.  (double blade diameter, 4x the swept area and 4x the power so 8x the alternator)

[brandnewb]

rather than having me reinvent the wheel, both figuratively and literally, I'd like to recreate this 3KW axial flux design.

Can it be done with 192 x n45 neodymium at 10mm width, 60mm length and 5mm height?

All my calculations point at no more than 1.2 to 2KW at best before the coils start to melt when having an S32Lifep04 bank attached.

Calculations also suggested that increasing RPM and doubling cell count (64S) will show reduced return on investment. There is a sweet spot though that I have yet to discover. Maybe like 50 cells or something.

[Adriaan Kragten]

rather than having me reinvent the wheel, both figuratively and literally, I'd like to recreate this 3KW axial flux design.

Can it be done with 192 x n45 neodymium at 10mm width, 60mm length and 5mm height?

All my calculations point at no more than 1.2 to 2KW at best before the coils start to melt when having an S32Lifep04 bank attached.

Calculations also suggested that increasing RPM and doubling cell count (64S) will show reduced return on investment. There is a sweet spot though that I have yet to discover. Maybe like 50 cells or something.

A magnet thicknes of only 5 mm is very thin for an axial flux generator. Assume that you glue two magnets together. Assume that you use two steel sheets with the magnets glued to the inside and the stator in between. So now in one magnetic loop, there are eight magnets and two air gaps and so four magnets per air gap. So you have a total magnet thickness of 4 * 5 = 20 mm per air gap. Assume that the thickness of the air gap is chosen 20 mm too. Now it can be calculated that the flux density in the air gap is half the remanence Br. The remanence for N45 is about 1.34 T and so the calculated flux density in the air gap is about 0.67 T which seems acceptable. If two magnets are glued together, you need four magnets per pole. If you have 192 magnets, you can make a 48-pole generator. So the angle in between adjacent magnets is 360 / 48 = 7.5°.

There must be a certain distance in between adjacent magnets otherwise you will loose too much magnetic flux because of magnetic short-circuit in between adjacent magnets. Assume that the pitch in between adjacent magnets at the pitch circle is twice the magnet width and so 20 mm. So the cicumference of the pitch circle becomes 20 * 48 = 960 mm. So the diameter of the pitch circle becomes 980 / pi = 306 mm. You should make a composite drawing for this diameter of the pitch circle and see what distance in between the magnets you get at the inside of the magnets. I have calculated that this distance is about 8 mm which seems okay. As the magnets have a lenght of 60 mm, the outside diameter of the steel sheets must be at least 306 + 60 = 366 mm but I would take about 380 mm. If you make a 3-phase, 1-layer winding you will get 48 * 3/4 = 36 coils and so 12 coils per phase. I can't predict the power at a certain rotational speed but this generator will be rather strong.

The number of turns per coil for a certaint open DC voltage at a certain rotational speed can be found by try and error. So you take a certain wire thickness and make the most dense coil possible for this wire thickness. Then you measure the open AC-voltage for only one coil at a certain rotational speed. So the open AC-voltage for twelve coils in series will be twelve times the measured value for one coil. The open DC-voltage for rectification in star or delta can be calculated with the formulas which are given in my report KD 340. If the voltage is too low or too high, you have to modify the wire thickness and the number of turns per coil. Once you know which combination of wire thickness and number of turns per coil gives the wanted open DC-voltage at the wanted rotational speed, you have to make a complete 3-phase winding and measure the generator on a heavy test rig for a range of loaded voltages. One loaded voltage will give the best matching with the chosen wind turbine rotor. Best matching means that the Pmech-n curve of the generator for that voltage lays as close as possible to the optimum cubic line of the rotor.

The explanation of voltage generation is given in chapter 9 of my report KD 341. Figure 4 out of this chapter gives the coil configuration for an 8-pole axial flux generator with a 3-phase winding with six coils.