N1 stator turns 1

[xj25]

Hi,

I have been messing with an self-made induction motor equivalent circuit model (just regular steady state circuit). I got some results using circuit data from a real motor datasheet but I had to guess the values for N1 (stator turns per phase) and N2(rotor bars) because I don´t know them.

I took N2 = 58 bars, from

http://www.reliance.com/mtr/pcrss.htm

from a 4 pole/125HP motor (similar power to selected)
I tweaked to get N1 = 4 turns, and with this value the model matches the nominal and maximun torques for the motor. Motor has 4 poles.

My question is about N1. It shall account for turns/phase but 4 seems to me quite low value ¿?.
I don´t know too much about windings as you may deduce.

Please correct my present understanding:
1) Each phase has a winding with a number of coils in series (for 4 poles I think that can be used 2 or 4 coils/phase depending on the winding design)
2) Each coil has a number of turns. Number of turns is key parameter in motor design due to they define the flux level in the airgap. More turns mean less flux (for constant E and f) as E=4.44 K f N1 flux.
3) N1(turns/phase)= a coils/phase * b turns/coil

So the possible windings for N1=4, would be 2 coils of 2 turns per phase, or 4 coils of just 1 turn. I doesn´t seem too sensible for me so few turns...

If I increase N1, then I have to increase N2 (rotor bars) quite a lot to get same torque-speed curve.
i.e. with N1=6 I must set N2 about 130 bars to get the same curve. Rotor diameter is about 300mm.

Regards

 

[electricpete]

N1 and N2 might refer to number of rotor bars and stator slots (as in the Reliance link)
N1 and N2 might refer to effective turns on stator and rotor.
I think maybe there is mixing and matching of two different meanings for these symbols.

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[electricpete]

By the way, are you trying to estimate the equivalent circuit parameters for a real motor based on nameplate or other available data?

That's something I've spent quite a bit of time on. If you post the available data on the motor I'll be glad to give you an estimate of the equivalent circuit parameters along with some discussion/spreadsheet of how I got there

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[Brad1979]

Generally, equivalent circuit models rely on measurements of resistance, power, etc. of the motor at no-load and at locked rotor. You generally don't need to know info like # of turns. What model are you using? Also, unless you are trying to model a Reliance motor, I wouldn't rely on their slot information. Regarding your 3 points:

1) This may or may not be true. The coils need not be in series. If you had, for example, 4 coils/phase, they could be in series or they could be arranged 2 series/2 parallel, or they could be arranged 4 parallel. Dual voltage motors often take advantage of this.
2) Again, this may or may not be true. What you think of as a "coil" may in fact be distributed over multiple slots and have different turns depending what slot it is in. This is done to produce a more sinusoidal MMF in the air gap.
3) That seems correct (assuming that N1 is in fact turns/phase).

 

[electricpete]

1) Each phase has a winding with a number of coils in series (for 4 poles I think that can be used 2 or 4 coils/phase depending on the winding design)

Yes, a number of coils in series. No, for 4-poles it can be a lot more than 4.
For 4-pole motor let's say the 1hp 4 pole "standard" motor from your Reliance link.
It has 28/36 28 rotor bars and 36 stator slots.
It could be 12 series coils per phase in single-circuit wye configuration or 6 series coils per phase in double-circuit wye, or other possibilities....

2) Each coil has a number of turns. Number of turns is key parameter in motor design due to they define the flux level in the airgap. More turns mean less flux (for constant E and f) as E=4.44 K f N1 flux.
3) N1(turns/phase)= a coils/phase * b turns/coil

Yes each coil has multiple turns. If you add up the total series turns per phase (series coils per phase times turns per coil), then you have series turns per phase. Higher series turns per phase generally means lower flux density.

So the possible windings for N1=4, would be 2 coils of 2 turns per phase, or 4 coils of just 1 turn. I doesn´t seem too sensible for me so few turns...

No, can be a lot more as discussed in #1.


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[xj25]

So first conclusion is that first I should study windings or change topic

I adjoint motor data. As you may see I have info of the steady state equivalent circuit per phase. R1 L1, R2, L2, Lm Rm, and three working points.

To work with the equivalent circuit data, I must first reduce the rotor values to stator. For this I use this formulae took from a electrical machine book:
voltage transformation ratio V.tr= K1 N1 / K2 N2
current transformation ratio I.tr= (m1/m2)* V.tr
impedance transf. ratio Z.tr= V.tr * I.tr <- This is the relation I use to transform the rotor impedances as
z2' = z2* Z.tr

where K1, K2 winding factor (near 1). (m1, m2) number of phases in stator and rotor,
(N1, N2) number of total turns per phase in rotor and stator.

To calculate the factors I took this formulae from same book:
m1 = 3. That was easy .

m2= B/(2p) where B is number of rotor bars and p: pole pairs. So there is 1 phase per each bar under 1 pole.
I understood that each bar has a different phase due to being in a different geometric position under the pole, so different flux linkage in a specific time -> different phases induced in the rotor (squirrel cage).

N2 = 1 (squirrel cage rotor, so 1 turn per phase says the book, without too much explanation).

One thing I don´t see: say rotor with 20 bars and 2 poles. So m2= 10 phases. As N2=1 there are 10 "turns" (go and return bar). OK
Same rotor with 4 poles. So m2=5 phases. I don´t see how this match with N2=1 or if it should match somehow.

Then I tweak with B and N1, to get a working points similar to the datasheet.
With B=58 bars and N1=4 turns/phase I get Z.tr = 3.3 and with the circuit figures transformed I can predict (with some 10-15% error) the max speed and max power working points.

With this values for 4 poles Z.tr = 12N1/58 so changes in N1 affect quite dramatically the rotor transformed impedance.

If you see any incorrect formulae or argument plese note.
First point that I want to assure is if Ztr. calculation is OK.

Regards

 

[Brad1979]

Phases are the number of phases in your power input. Almost certainly you will be dealing with 1 or 3 phases. This should be on the nameplate of the motor. You do not determine phases by dividing the rotor bars by the number of poles. m2 isn't really a "phase." It's really just the ratio of the number of rotor slots(bars) to poles pairs. Similarly, my guess is that m1 is the ratio of stator slots to pole pairs.

But, I repeat, I don't think any of this is necessary if all you are looking for is the equivalent circuit model. If you are using a text book, it sounds like this might just be part of the theoretical development of the equivalent circuit model and not something you'll actually need for the equivalent circuit model. I mean, really, the whole point of an equivalent circuit model is you don't need to know things like turns ratios and winding factors, right? Unless you are designing the motor, those things are difficult to find out.

 

[xj25]

Hi Brad, thanks for your reply.

m1=3 is number of input phases.
m2=bars/2p it is shown in the book, and it calls it "rotor phases", and gives an explanation in the sense described above. I don´t feel to confident with the concept as to discuss much about it.

It happens that I have the secondary (rotor) and primary (stator) component values for R1/2 L1/2, so in order to calculate anything with the circuit I must do the reduction from 2º to 1º of the impedances involved (R2/s and L2), and for that I need the "impedance transformation factor" that the book says that depends on m1 and m2.

Regards

 

[electricpete]

It happens that I have the secondary (rotor) and primary (stator) component values for R1/2 L1/2

It is very common in the motor world to refer rotor quantities to the stator (without even adding a prime to denote that fact).
I have often seen ratios R1/R2 and L1/L2 and it always means with the rotor quantity referred to the stator... it seems somewhat meaningless ratio otherwise.

Are you sure these aren't already referred to the primary?
Can you tell us the numbers? L2/L1~1 is in the ballpark when rotor inductance is referred to stator.

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[electricpete]

Looking at your data sheet, we have quantities
Stator leakage impedance X1s'
Rotor leakage impedance X2s'
These are clearly BOTH referred to the primary as indicated by the ('). I'm not sure what the s means... maybe indicates the same thign.

The ratio X1s' / Xs2' is 1.124380575

The ratio L2/L1 is also 1.124380575

Therefore L2 must also be referred to the primary (unless your turns ratio is 1.000000 in which case you don't have to wory about it anyway).

If L2 is referred to the primary, I see no reason to suspect that R2 is not also referred to the primary.


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[xj25]

Using the values as beign refered to primary I don´t need anymore to mess with N1/N2.

s=2% (datasheet) Rc'=R2'(1-s)/s = 1.67 Ohms

Then I get
I1=368A I0=134A I2'=234A

This gives internal power P= 3phase * Rc * I2^2=274kW
At 47Hz with 2% slip n=1382 rpm

so M= P / (n*2pi/60) = 1903 Nm, in datasheet the value is 675 Nm (x2.8)
at max speed point the result changes in (x2.2) factor, so this seem not to work well.

So something is wrong and I don´t get to find out where, just trying things:

- supposing just R2 is secondary refered:
Torque and power matches nominal and max speed points. Breakdown torque is x2 higher.
I must set impedance transform ratio to 3.3 between primary and secondary to tune it.

- supposing that R2 and L2 are secondary refered (forget abour X2' value):
Torque and power matches nominal and max speed points. Breakdown torque is x1.2 higher.
I must set impedance transform ratio to 3.3 between primary and secondary to tune it.
This is the nearer point I reached to the datahsheet torque curve values, althougth may not have too much sense unless I assume the datasheet secondary X2' value is wrong.

So as I don´t see a clear end to this, and to avoid boring you much more I just would to know, for a 70-100kW motor, cooper bars squirrel cage:
- what is a regular ratio or values for L1/L2, R1/R2.
- what is a regular, per phase turns ratio between rotor/stator.

Regards

 

[electricpete]

I think the equivalent circuit values listed are consistent when we interpret them as referred to the stator.

Example calculation attached using equivalent circuit parameters in the first colum (assuming rotor quantities referred to stator) gives power output of 110kw... reasonably close to 105kw listed in the first column.

You might want to bounce it off your calculation, I suspect you have a math error somewhere.

Aside - Also I noticed that to reconcile the listed value of L2 and X2s', there is an exact factor of 1000 error. It suggests to me that L2 should be 0.38H, not 0.38mH. The same for L1 (should be H, not mH).

- what is a regular ratio or values for L1/L2, R1/R2.

1 for both, as a rough starting point.

- what is a regular, per phase turns ratio between rotor/stator.

I don't know.


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[electricpete]

I assumed the 450vac listed in your spreadsheet represented line to line voltage.

Accordingly, I made my per-phase rms voltage 450/sqrt3

I noticed you made your per-phase peak voltage 450*sqrt(2). If I have understood correctly that VLL=450, then you should divide this by sqrt(3).


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[electricpete]

To summarize suggested changes to the SPICE circuit:
VLL => 450 * sqrt(2) / sqrt(3)
L1 => 0.43 (vs 0.43m)
L2 => 0.39 (vs 0.39m)


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[electricpete]

No, I'm not positive which way to reconcile the factor of 1000 error. Will look at that later.

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[electricpete]

Sorry, there is no 1000 error. Forget that part.

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[xj25]

OOOPs, now it works quite well, was the stupid sqrt(3) in the input voltage.

I calculated a rough stimate of N1 (turns/phase) from some formulae I found (spreadsheet adjoint, the formulae are verified from two different sources so it should be quite good)

Regards!