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Paul Alciatore
03-09-2017, 02:57 PM
As some of you may have noticed, I have been trying for some time now to learn more about the various AC motors and their use. In this effort I have purchased several books and am presently reading "Three-Phase Conversion" by Graham Astbury. It is Number 47 in the "Workshop Practice Series" published by Special Interest Model Books. It is one of the later books in this excellent series, first published in 2011 and appears to be be fairly up to date.

I first have a caution for anyone who may also read this book. I am really trying to get the most from it so I am carefully working the Questions that the author has included at the end of the chapters. Unfortunately, the author's answer to the first question at the end of the first chapter as shown in the back of the book is in error. In that question he states that the value of a choke is 10 mH (milliHenry). But in showing how it is solved, in the back of the book, he enters that value as 0.1 meaning 0.1 Henry. He has clearly multiplied the value of that choke by a factor of ten. That value is squared, then added to another value and then a square root is taken, so it took me several passes through the math to finally realize that the error was his, not mine. If you do work through that problem you can either use the 100mH value and you will get his answers or, if you use the stated value of 10mH, then the correct answers are I = 0.372 A and Power Factor = 0.707.

OK, my question. So far I have read half way through Chapter 5, "The Steinmetz Connection". For those who are not familiar with this terminology, the Steinmetz connection refers to the use of a single capacitor to power the third phase of a three phase motor when it is connected to a single phase supply. This is perhaps the simplest and least expensive way for running a three phase motor with single phase power. Anyway, I was very interested in how this capacitor's value was determined and as far as I can see, his method is simply stated as "... the capacitor has to provide the full load current at the supply voltage, so ...". That is his sole basis for calculating the value of this capacitor. He uses Ohms law to find the capacitive reactance needed using the rated Voltage and rated maximum current of the motor. Then from that capacitive reactance, he uses the frequency of the power line with that capacitive reactance in the standard equation for capacitive reactance to fine the value of the capacitor in Farads. My question is, is this really all there is to it? Maximum current and rated Voltage of the three phase motor and the line frequency frequency? Has anyone seen a better derivation of the value of this capacitor?

In the book the author dismisses the rule of thumb used by some: 70 uF per KW. He claims that his calculation is more accurate. Of course, he also admits that this value is only good at full load and if the motor is not operated at the full load condition, then the size of the capacitor could/should be adjusted. But I am interested in the logic behind that primary calculation. The justification for doing it that way. How, with all the other impedances in the circuit (motor coils) does that value insure a proper Voltage and phase angle for that third motor connection point? It would seem to me that the calculation would be a lot more complicated.

Anybody have any real insight into this? Or know of a good reference work that does?

Lew Hartswick
03-09-2017, 04:48 PM
Well I suspect with the single cap. You'll never be able to get both the correct phase and voltage for the third phase. And as you pointed out the optimum value will be dependent on the load. So IMO it a "crap shoot" . :-) Especially on most machines the "load" will not be the same for any length of time.
It becomes a project suitable for a "dissertation" lots of scope pictures and pages of calculations. :-)
...lew...

Paul Alciatore
03-09-2017, 05:01 PM
Yea Lew, I guess I am looking for something between the "just do it this way" and the pages and pages of advanced math.

I am deliberately reading the book carefully and that means slowly, but looking ahead for a few pages and assuming that the author is correct, it appears that this Steinmetz Connection is capable of producing a fair match to the Voltages and phase angles of true three phase power when the motor is at the full load. To my mind, that just seems very surprising for a single capacitor. I would think a much more complicated network of parts would be needed. I will be reading these pages very carefully.

J Tiers
03-09-2017, 05:48 PM
The problem is with phase angle.

A capacitor can only affect the phase angle by a maximum of 90 deg. And that is when it's X(c) is much larger than the load impedance. In that case the voltage is quite low.

When the capacitor is much larger, so the X(c) is much less than the load impedance, then the voltage on the load is nearly the same as the applied voltage, but the phase shift is small.

Remember, the mechanical phasing in the motor is 120 deg. With the electrical phasing also at 120 deg, a very constant rotating field is produced. The sum of the magnetic fields in each phase coil (of a 2 pole motor) sums up to a single net field, which changes angle as the amplitude of the three phases changes.

That field also induces current in the rotor bars, which produces a field in the rotor which is again, a single N-S pair (for a 2 pole motor), which is dragged around by the rotating field.

The torque produced depends on the intensity of that rotating field, and the rotating field affects the rotor magnetic field, so there is a squared effect. With a constant rotating field, as with good 3 phase, the torque is also constant.

If for some reason, one phase is weak, then the torque will NOT be constant, and the motor will be overall weaker.

The Steinmetz circuit "kinda works", but it is very dependent on the load on the motor. The motor equivalent impedance looking into its terminals is composed of a series circuit, the resistance and leakage inductance is in series with a parallel circuit composed of the magnetizing inductance in parallel with a resistance dependent on the load applied to the motor. That "load equivalent" absorbs the actual power supplied via the output shaft to the mechanical load.

As the mechanical load changes, the value of the load equivalent resistance changes also. That obviously changes the optimal capacitor.

Looking at the phase angle, you need to have a definite phase difference between the single phase wires and the third wire. Without that, there is no "rotating magnetic field", and so no torque. The motor will act as if it has been "single phased", so if it were already running, it might continue, but would not start from stop. The current in the third wire would not be helpful, and probably would provide a drag.

This is somewhat related to the Scott-T connection. If you had a delta winding, with a center tap in one winding of the delta, and could create a 90 degree phase shift of the third phase wire voltage vs the center tap, at 86% of the phase voltage, then you would have a perfect equivalent of 3 phase.

You do not really need the center tap, if the voltages and phases are right, it would work as well with a wye.

Well, that looks encouraging, since a capacitor ca produce a 90 deg shift.

The first problem is that the 90 deg is not with reference to another phase wire, but rather to the center tap. The phase with reference to the other two wires remains 120 deg.

Another problem is that you cannot easily get BOTH the phase shift and the current flow, and it is highly dependent on the load. Splitting the difference gives a 45 deg shift, but it might be that some modification of that is actually best when considering torque, which is dependent on both shift and current. The 45 deg would be when the capacitive reactance is equal to the load resistance of the motor, which is in turn dependent on mechanical load.

If you could use a smaller capacitor from a higher voltage source, then you could get more phase shift, as X(c) could be larger and still give good current, potentially with less dependence on exact motor load. I think this is actually done in some "static converters" which are used in situations like irrigation pumping, where the load is pretty constant. A transformer is used to drive the capacitor from a higher voltage.

I once developed a system similar to this, but in reverse, where the fll energy of a 3 phase source was wanted to be applied to a single phase load. The har DID work.dest part of it was changing capacitors to keep the angle correct as the load changed. It DID work, but I would not have called it overly practical.

lakeside53
03-09-2017, 07:15 PM
Even though it doesn't work "well" you see it... within certain limits it has to be a bit better than a static converter (which as we all know in its common form doesn't convert squat).

I've seen it in several "smaller" motor implementations:

- Pumps for lathes and mills - singe phase conversion of the pump. One I remember had like an 8mfd cap across two legs.
- Emco mill for V10P etc. Some 50hz implementations use capacitor to run on single phase.
- Baldor buffers did this for decades. Factory single phase units used 3 phase motors with a capacitor across two legs.

The Artful Bodger
03-09-2017, 09:23 PM
Even though it doesn't work "well" you see it... within certain limits it has to be a bit better than a static converter (which as we all know in its common form doesn't convert squat).

I have difficulty understand that.

J Tiers
03-09-2017, 09:29 PM
Even though it doesn't work "well" you see it... within certain limits it has to be a bit better than a static converter (which as we all know in its common form doesn't convert squat).

I've seen it in several "smaller" motor implementations:

- Pumps for lathes and mills - singe phase conversion of the pump. One I remember had like an 8mfd cap across two legs.
- Emco mill for V10P etc. Some 50hz implementations use capacitor to run on single phase.
- Baldor buffers did this for decades. Factory single phase units used 3 phase motors with a capacitor across two legs.

A number of "static converters" DO have run capacitors. I don't recall which brands and models, but likely not the lowest end versions.....

I'd challenge the assertion that they "don;t convert squat". They clearly "convert" or "adapt" a 3 phase motor to no-hassle operation on single phase. Whinging about there not being real 3 phase rather misses the point, I'd suggest.

Most of the Baldor single phase units seem to be PSC motors, but I suppose they could be 3 phase in the higher voltage models. Not as likely for the 115/230 V types. A 3 phase with a capacitor is "effectively" just a crappy PSC motor anyway.

You do not get full power using the capacitor unless you do the full implementation with transformer etc. In that version, I suspect it can be done for a constant load application quite nicely.

Transformer with a center-tapped primary, across the input lines. Secondary with one end connected to the center tap, the other to the capacitor, other terminal of the capacitor to the third phase wire. With the proper values for capacitor and secondary voltage (could be tapped) it should be possible to get close to ideal 3 phase.

Paul Alciatore
03-09-2017, 09:49 PM
J, You and I both seem to be prone to these long explanations. In this case, I do not see how any of your comments answer or even shine any light on my questions.

The problem is with phase angle.

A capacitor can only affect the phase angle by a maximum of 90 deg. And that is when it's X(c) is much larger than the load impedance. In that case the voltage is quite low.

When the capacitor is much larger, so the X(c) is much less than the load impedance, then the voltage on the load is nearly the same as the applied voltage, but the phase shift is small.

Remember, the mechanical phasing in the motor is 120 deg. With the electrical phasing also at 120 deg, a very constant rotating field is produced. The sum of the magnetic fields in each phase coil (of a 2 pole motor) sums up to a single net field, which changes angle as the amplitude of the three phases changes.

That field also induces current in the rotor bars, which produces a field in the rotor which is again, a single N-S pair (for a 2 pole motor), which is dragged around by the rotating field.

The torque produced depends on the intensity of that rotating field, and the rotating field affects the rotor magnetic field, so there is a squared effect. With a constant rotating field, as with good 3 phase, the torque is also constant.

If for some reason, one phase is weak, then the torque will NOT be constant, and the motor will be overall weaker.

The Steinmetz circuit "kinda works", but it is very dependent on the load on the motor. The motor equivalent impedance looking into its terminals is composed of a series circuit, the resistance and leakage inductance is in series with a parallel circuit composed of the magnetizing inductance in parallel with a resistance dependent on the load applied to the motor. That "load equivalent" absorbs the actual power supplied via the output shaft to the mechanical load.

As the mechanical load changes, the value of the load equivalent resistance changes also. That obviously changes the optimal capacitor.

Looking at the phase angle, you need to have a definite phase difference between the single phase wires and the third wire. Without that, there is no "rotating magnetic field", and so no torque. The motor will act as if it has been "single phased", so if it were already running, it might continue, but would not start from stop. The current in the third wire would not be helpful, and probably would provide a drag.

This is somewhat related to the Scott-T connection. If you had a delta winding, with a center tap in one winding of the delta, and could create a 90 degree phase shift of the third phase wire voltage vs the center tap, at 86% of the phase voltage, then you would have a perfect equivalent of 3 phase.

You do not really need the center tap, if the voltages and phases are right, it would work as well with a wye.

Well, that looks encouraging, since a capacitor ca produce a 90 deg shift.

The first problem is that the 90 deg is not with reference to another phase wire, but rather to the center tap. The phase with reference to the other two wires remains 120 deg.

Another problem is that you cannot easily get BOTH the phase shift and the current flow, and it is highly dependent on the load. Splitting the difference gives a 45 deg shift, but it might be that some modification of that is actually best when considering torque, which is dependent on both shift and current. The 45 deg would be when the capacitive reactance is equal to the load resistance of the motor, which is in turn dependent on mechanical load.

If you could use a smaller capacitor from a higher voltage source, then you could get more phase shift, as X(c) could be larger and still give good current, potentially with less dependence on exact motor load. I think this is actually done in some "static converters" which are used in situations like irrigation pumping, where the load is pretty constant. A transformer is used to drive the capacitor from a higher voltage.

I once developed a system similar to this, but in reverse, where the fll energy of a 3 phase source was wanted to be applied to a single phase load. The har DID work.dest part of it was changing capacitors to keep the angle correct as the load changed. It DID work, but I would not have called it overly practical.

lakeside53
03-09-2017, 10:28 PM
I have difficulty understand that.

Most cheapo static converters are really just "starters" that drop out the third leg once running. Sure.. there a many variations on this, but not at the most common types. With the capacitor connection type (which has serious limitations for "general purpose use" ) the motor starts and runs without the potential relay etc. At least "some" power is supplied to the third leg via the capacitor.

J Tiers
03-09-2017, 11:09 PM
J, You and I both seem to be prone to these long explanations. In this case, I do not see how any of your comments answer or even shine any light on my questions.

You are under no obligation to read it. Feel free to put me on ignore :D

Your question was , boiled down, "do I follow this guy's instructions and just figure the capacitor for motor FLA?".

And, that answer is "not really but maybe" depending on what the guy means.

I may have left out a part, I had some of my stuff disappear partway through writing, and I thought I got it all back. Looks like a chunk of it is still gone...... naturally in the important part

Anyhow, the first bit was supposed to set the background of the situation, giving the "extreme cases" for the capacitor and showig that both lead to poor results, in opposite ways. That shows that the best condition is likely to be between them

Then, if you look at the part where I mention the 45 degree shift...... The deal there is that at that point, you have a situation where you have more or less maximized the combination of phase shift and current. It's LESS current than it should be and it is less VOLTAGE than it should be, and it is LESS phase shift than it should be, but it is the best condition for the combination.

That happens when the impedance of the capacitor is the same as the impedance of the motor (hopefully mostly resistance due to the mechanical load.

What THAT means is that IF you set the capacitor value to draw current equal to the motor current (with the motor load you have) when connected across a phase, you will have set the capacitor impedance to equal the motor impedance at that loading. Then when you put that capacitor in from one of the input wires to the third phase, you should have a 45 degree phase shift, and about 70% of the actual motor current.

That MAY NOT be absolutely optimum, but it's a good place to start.

So, if the guy you cite means to do THAT procedure, I suspect you can do it and be close to a good result. He may have set it as FLA simply because that is easy to read off the label.

You could estimate the motor current if you have some idea of the load. The base current will be about 40% of FLA, that is the idle current. The loading will draw more current. So half power you could estimate as 40% of FLA plus half of the remainder, or 40% plus 30% of FLA, or a net of 70% of FLA.

Likewise 25% power you can estimate motor current as 40% + 15%, or 55% of FLA, ans so forth. It's not exact, but nothing in this scenario is exact or correct, so..... (Ideally you could measure the current the motor draw when single phased at the load you want, and estimate the desired phase current as about 30% less than that. Or to measure what a 3 phase motor draws when driving the load. But either of those presumes you have already gotten the motor to run and drive the load, which is what this is all about to begin with.)

As for adjusting from there..... Per the first part of what I wrote, if you REDUCE the capacitor value, the PHASE SHIFT increases, but the current decreases. And if you INCREASE the capacitor value the reverse happens. I do not know if either of those variations will be better than the straight 45 degree setting.

My suspicion is that if you move in the direction of more phase shift you will get better results. That will be less capacitance.

With any more ideal calculations etc than this, you probably need to know more about the motor than you will actually be able to easily find out.

PStechPaul
03-09-2017, 11:25 PM
I did some calculations for a 208 VAC 1 HP motor, and I got 32 uF or 43 uF / kW. Here is what I did:

1 HP = 746 W = 249 W/Phase

120 V / Phase => 2.07 A / Phase

Z = 120 / 2.07 = 57.9 ohms

For 208 V across two input phases, the highest voltage at 90 degrees is 104 V with 45 degree phase angle

The capacitor voltage is 104 * sqrt(2) = 147 V

104 V into 57.9 ohms is 1.80 A

Capacitor reactance is 147 / 1.80 = 81.8 ohms

At 60 Hz, C = 1 / (2 * PI * 60 * 81.8) = 32.4 uF

I'm not 100% sure of this but it seems to be "in the ballpark". I might try a simulation.

J Tiers
03-09-2017, 11:44 PM
For a 230V motor...

NEC table amps for the motor is 3.6A. This is not necessarily a good number , but use it anyway.

The capacitor from the 45 degree shift is then supposed to draw 3.6A at 230V. So 230/3.6 = 64 ohms reversing the formula for X(c), (1/64)/(6.28 * 60) = 41 uF, for the motor operating at full current. Less for lower power output.

I'd suspect that the best value is possibly a bit less than that.

For a 208 motor, the current is a bit higher, and I come up with 50 uF. You would use the actual motor current on the tag as your starting point, these are based on the NEC value, which tends to be high. For instance I have an old 230V Crocker-Wheeler 1 HP 3 phase motor. It is rated at 3.4 A, and is a type that would be expected to have higher current than others.

PStechPaul
03-10-2017, 12:20 AM
I tried a simulation:

http://enginuitysystems.com/pix/electronics/Single_Phase_to_3_Phase_Motor.png

I'm not sure how helpful this is, but I found it hard to get any more than 3.25 mSec phase difference, which is about 70 degrees. And the shifted voltage is about half that of the other phases. The voltages are 40.3, 99.0, and 122.3.

The Artful Bodger
03-10-2017, 12:36 AM
Although theory tells us that the maximum phase shift to be had from a capacitive circuit is 90 degrees it is rather difficult to find any practical circuit without inductance.

wombat2go
03-10-2017, 09:44 AM
The imbalance in phase and magnitude causes negative sequence currents.
In the rotor, these cause torque in the opposite direction to the wanted, so higher input currents are needed for a given torque.
and also heat the rotor bars and rotor iron with the neg sequence currents at frequency |(f) + (f*(1-s)|

I see Paul is using LTSpice and I only have QUCS here.
I searched but could not find a symetrical components analsis in QUCS.
There are a few hits showing where attempts have been made to model it in LTSpice.

I am so old that I had to learn to do it with a slide rule solving the 3rd order matrices!.
Those calculations were tedious and error prone.

J Tiers
03-10-2017, 10:00 AM
What Paul found is in line with what I said above. You can get a maximum phase shift, OR you can get a higher current, pick one.

If you use a boost transformer as I described above, then with a higher voltage to work with, you can get closer to an ideal situation.

When it comes to negative sequence currents, phase is somewhat more important than amplitude. A smaller "pull" than normal is not ideal. But if it comes at the generally right time, it is better than if it is at the wrong time. A wrongly timed phase may tend to be actually a pull in the reverse direction, slowing rotation of the motor.

That is the general meaning of "negative sequence currents", they are currents that correspond to a reverse rotation, and subtract from the "positive sequence currents", reducing torque.

PStechPaul
03-10-2017, 11:18 PM
Here is a much better-looking waveform using a 2:1 boost (auto)transformer:

http://enginuitysystems.com/pix/electronics/Single_Phase_to_3_Phase_Motor_Boost.png

J Tiers
03-10-2017, 11:38 PM
Doing something along this line should actually be able to get very good indeed. It emulates a Scott-T, the capacitor provides the 90 deg phase shift for the winding between the center tap and L3. With the proper combination of a capacitor and a voltage ratio, it should do quite well. The output voltage should be made 86% of the phase to phase voltage, from center tap to L3, at the same time the phase shift is as close to 90 deg as possible and the motor current in L3 equal to that in the other lines..

This (in reverse) was the basis of the 3 phase to single phase converter I made. It was a demo for a potential client, but they never went further with it. They had wanted to avoid using an inverter system, and had a 3 phase wind source which they really wanted to get a single phase output from.

because of the step-up ratio that will be needed, the secondary current will always be lower than the primary, reducing issues of balance in the transformer.

http://img.photobucket.com/albums/0803/jstanley/wiring/Static%20Scott%20converter_zpstl9ini4y.jpg (http://smg.photobucket.com/user/jstanley/media/wiring/Static%20Scott%20converter_zpstl9ini4y.jpg.html)