# Motor/Generator Analysis

I have measured the DC resistance of a split-phase capacitor run induction motor's two windings. They are 53 and 35 ohms. The motor is
impedance protected. Using the nameplate voltage and current, I have calculated the total impedance at 60 Hz to be 110 ohms. This total impedance is larger than the DC resistance, and so I have algebraically subtracted the resistance from the total impedance to get the inductive impedance, but I don't know if I did that step right:
http://users.aol.com/DGoncz/Publications/Drafts/MotorAnalysis.bmp
I am pretty sure about R1/R2 = X1/X2 although the winding *are* different colors and could be different gages, but I am not sure about
1/(1/(R1+X1) + 1/(R2+X2)) = 110 ohms
I don't know if you can add a resistance and an inductive impedance arithmetically this way. I have seen things like
R1 at angle 0 degrees + X1 at angle 90 degrees sqrt(R1^2 + X1^2)
I have invested hundreds of dollars into this motor/generator and while I would like to avoid a rewind, these high resistances make a rewind look inevitable. If I can get a good model, though, I may find a Q>1 for some capacitance, and that would indicate, I think, that self-excitation could commence.
What is not shown in MotorAnalyis.bmp is R1 in series with L1 and so X1, and R2 in series with L2 and so X2, and R1/L1/X1 in parallel with R2/L2/X2 and the capacitor C.
Yours,
Doug Goncz Replikon Research Falls Church, VA 22044-0394
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On 1 Jun 2005 12:02:57 -0700, snipped-for-privacy@aol.com wrote:

Reactance is at a right angle to resistance so it is incorrect to add them arithmetically. This is easy to accomodate in MathCAD since it can do arithmetic with complex variables. Just multiply your X terms by i which MathCAD understands to be the complex operator sqrt(-1). You can direct MathCAD to use j instead of i since j is more commonly used in electrical engineering. Using the j convention, an R in series with an X has impedance R + j*X. In polar notation, this would be a Z with an angle theta. Z is the magnitude, volts/amps and theta is the phase angle between voltage and current.
Sample MCad sheet available if you'd like. Email me -- and tell me which version of MCad you're running.
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Doug, you don't simply add reactance and resistance, since they are orthogonal quanities (at right angles to one another)..
To compute Impedance, Z, simply use the same formula as you would use for computing the hypotenuse of a right triangle (The Pythagorean Thorem). In this case:
Z = SQRT(Resistance Squared + Reactance Squared).
A simple empirical method of determining the impedance is simply to connect a variable resistor (potentiometer) in series with the generator, apply a 60-Hz AC voltage (say 24-Volts), then adjust the variable resistor until the AC voltage across it is equal to the AC voltage across the generator windings. You can then measure the resistance of the adjustable resistor with a simple ohm meter and its value will be numerically equal to the impedance of the generator, since the voltage drop across each will be equal.
E = IZ = IR, where the AC current passing though both the generator and the variable resistor (when connected in series) are of course equal.
Harry C.
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Harry C. wrote:

Thanks, Harry, that was what I meant when I wrote
sqrt( R1^2 + X1^2)
You've confirmed that these are vector quantities.
I have a calibrator output on my 'scope that is a 60 Hz *square wave* but I'd need a sine wave to use the potentiometer method, right?
Doug
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Doug, since reactance varies with frequency you really need a 60-hz sinewave source (something like a doorbell transformer or toy train transformer should do nicely).
A pulse or square wave contains many higher frequency harmonics which would confuse the measurement.
Hope this helps, Harry C.
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Doug, as a follow on, it is important to note that the current draw of a motor is typicallly stated for its maximum horsepower load, hence tells you almost nothing about its impedance/reactance.
Harry C.
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I have ordered two 10-1134 motors and eleven 5 mfd capacitors from Surplus Center. I have ordered an 11.1111 mfd 50 VDC cap sub box from Electronic Parts. I intend to mate the hanger threads on the end bells of the motors with a close nipple and install a threaded rod and cap nuts to join the shafts. One motor will be the prime mover, and the other will be the test generator.
I have written to Terry Given to see if he will recruit me into the IEEE.
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I have ordered an LCR meter and a less expensive cap sub box that should be rated 200 VDC instead of 50 VDC.
Doug
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I wrote:

The LCR meter is on the way from a private ebay seller overseas by air mail. The cap sub box has not been shipped yet. The motors are on their way by Parcel Post.
Doug
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snipped-for-privacy@aol.com wrote in sci.electronics.design and rec.crafts.metalworking:

The LCR meter has arrived from Hong Kong.
The inductance of the motor coils in parallel is 112 microhenries.
The resonant capacitance is (confirm?) 62 microfarads.
There are 36 poles on this split-capacitor motor.
The synchronous speed would be (confirm?) 400 rpm.
The motor runs at 225 (rated) rpm.
The motor runs with 175/400 = 44% slip.
I need to run the motor at 400+44% = 576 rpm.
I have to do that because of the impedance protection, right?
So the efficiency will indeed be low.
At 90 pedal rpm, with my existing cog, I will need a
x * 90 / 8 = 576; x = 576 * 8 / 90 = 51 tooth cog, which is just what I have.
However, if I splice two motors together at 225 rpm, I will have to recompute.
I recall that damping reduces the apparent frequency of an impulse driven resonant system, and wonder if the substantial resistance of this impedance protected motor will reduce the continuously driven resonant frequency, or whether my recollection only applies to impulse driven resonant systems.
Yours,
Doug Goncz Replikon Research Seven Corners, VA 22044-0394
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snipped-for-privacy@aol.com wrote:

No. 112 millihenries.
Doug
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On 10 Jun 2005 15:00:48 -0700, snipped-for-privacy@aol.com wrote:

I've picked up this thread late so I've probably missed important bits. However the following comments may be useful.
If I've understood the post correctly you are aiming to use an impedance protected 36 pole motor as a self excited induction generator.
Self excited induction generators rely on the tiny residual pattern of magnetisation of the rotor being reinforced by the current flowing in the near resonant stator winding circuit. It has to be operating close to resonance for the current build up to be large enough to reinforce the rotor field pattern. It has to be on the capacitative side of resonance to permit the phase angle of the stator current to reinforce the rotor field pattern.
It is a positive feedback regenerative system and on a large efficient motor the output can build up to far beyond its rated motor power until limited by magnetic saturation. This effect is sometimes used for regenerative braking of single and three phase motors and can result in a spectacularly short stopping time.
With a care and control of speed, self excited induction generator systems are possible but they're pretty touchy devices. If you're unlucky with the the rotor iron they may not retain enough initial magnetism to enable the output to build up (manufacturers strive to reduce this because it degrades the efficiency when used as a motor) Also it must use a reasonably efficient motor for the magnetic feedback to exceed the system losses.
Efficiency is your major problem. An impedance protected motor means a motor with deliberately large leakage inductance so that the impedance of this inductance limits the current that flows when the motor is stalled or overloaded. With limited stalled current the starting torque (already poor because it is a capacitor run machine) has to be boosted by the use of a high resistance rotor and this results in your observed very high slip speed. Even if there were no other losses of any kind the motor efficiency could not be any better than the % synchronous speed - 56%. With other losses taken into account the motor efficiency is probably no better than 40%.
With the uH to mH correction your sums are OK but this level of efficiency is too low for a succesful induction generator.
Jim
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snipped-for-privacy@yahoo.com wrote:

Many thanks to Jim and other contributors to the thread "Motor Generator Analysis".
I have put a lot of money and time into this, and I want to give it my best shot, but I don't want to whip a dead horse, so to say.
Frankly, I don't understand magnetics. At least not as I understand resonance. I'm an amateur musician; I understand resonance and know a little about phase shifts near the peak. I do understand that because the slope of the curve is negative on the high-frequency (capacitative) side of resonance, loading of the generator, within limits, will result in additional power to meet the load.
But B x I makes my head spin. I'm fine in 3 dimensions. So I get some of it. And I get that in the cylindrical coordinate system, B and I can be locally orthogonal, and can vary in time, with phase shifts, while being wrapped into a connected topology. I just don't feel that the way I feel resonances. It's not intuitive.
Would replacing the rotor "windings" with copper wire or bus bar (easy), and rewinding the stator with bigger wire (hard) have any chance at all of working together by lowering the leakage inductance and rotor resistance to allow resonance?
That's my best question; is there any hope at all?
This is a one-off demo, not a production prototype!
Yours,
Doug Goncz Replikon Research Falls Church, VA 22044-0394
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On Tue, 21 Jun 2005 18:57:47 -0700, DGoncz wrote:

Well, let's touch base with reality here.
What do you actually have? A bicycle with a generator?
Let's get to the basics. Don't pull theory on these frat boys, they'll tear you to ribbons.
What do you have now, and what are you trying to accomplish?
Thanks, Rich
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There have been a few different configurations on road.
There was a motor, glued to the V in the bottom bracket on the mountain bike. An EROS bike motor, with an adapter to the custom cogs Jensen made. And a chain to a right hand crank and cogs, with the pedal tending to unscrew. And a Bicycle Lighting Systems PAR 35 6VDC light. This rig didn't work real well, so I made a motor mount, and got a bigger motor.
The Ametek servo motor is 4" OD and 5" L. See ftp://users.aol.com/DGoncz for photos of the trapezoidal mount with hose clamps, low in the V near the bottom bracket. Not bad. Rode up hill at night with the B.L.S. light.
Then there was the big round disk covering the main triangle. Of 3/4 inch LDF. This allowed for chain drive from the pedals or the rear wheel. The rear gear on the mountain bike was brazed from a steel BMX spider and had a bottom bracket lock ring on it. It mounted to the flip flop hub, relaced to the rim.
With that rig, I added ultracapacitors. Eight PC 2500 2700 F 2.5 V caps from Maxwell, surplus. And a digital dashboard.
The caps were never used on the recumbent. The Ametek motor mounts under the seat back bag on the Thunderbolt. The mount was made of plastic drain pipe. Eventually it became clear that an idler was needed to keep the chain on the rear cog, which was made from a Big Cheese BMX chain ring holder, mounted on a mountain bike disc hub, relaced to the rear rim.
That was the rig in the videos at ftp://users.aol.com/DGoncz . New Year's Eve. 24 watts of Christmas lights on the bike, driven by the Ametek and an inverter.
There was also the AC generator, subject of this thread, painstakingly mounted to the front derailer post. One day, the Ametek drove the inverter which drove the front motor/generaor in motor mode. It was a shakedown.
What I am trying to accomplish is to provide all the electrical needs of an infantry soldier, with reasonable mobility and load carrying ability, on dirt roads, whether riding or stopped, such that the only resupply will be ammunition and food. Currently we resupply a lot of primary and secondary batteries to our infantry. An awful lot. A mobility and operational capability restricting large quantity, in fact.
Doug
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snipped-for-privacy@aol.com wrote:

If you posted all that in English u might get more feedback.

I would start at this point if I were you, because I think your idea of a way to do it is fundamentally flawed.
Using a soldier to manually generate electricity will impose substantial extra physical demands on him. This means healthy soldiers will cover less miles, do less work, arrive more tired, and generally make them an inferior fighting force. Hardly what you want in your military!
The whole idea with power is to have the power help the user, rather than the user slave away to produce the power. One helps, the other hinders.
This issue makes your whole approach a dead duck in most situations. It may have its apps, but will be deprecated in most situations.
More logical would be a solar panel on the bike. Even supplying endless batteries is better that pedal power, when you can provide those supplies.
NT
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I believe a bicycle coasting down a hill normally travels faster than a walking soldier. If generator output allows power capture on coasts, reducing speed to walking speed, then as far as mobility goes, on dirt roads, it's a dead heat for speed, with the bicycle/generator out ahead in terms of independence from supply.
Doug
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On Sat, 02 Jul 2005 17:49:23 -0700, DGoncz wrote:

Yabbut, who gets volunteered to push the damn thing back up the hill?
Thanks, Rich
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Yabbut, which is easier, backpacking 1000 feet vertical with 70 pounds on you, or pedaling a 100 pound bicycle up the equivalent road? I admit bikes can't go everywhere, but anywhere they go they are more efficient than porting a load.
Doug
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snipped-for-privacy@aol.com wrote:

If you actually work out how much energy you can capture that way, I think youll find it disappointing.
NT