Physics of motor startup 3

[VermontPE]

I am trying to come up with a satisfactory description of the physics involved with a typical full-voltage induction motor startup. Assume the motor is a typical induction motor driving a constant torque load that is full load at rated RPM. Basically, what happens with the voltage, stator current and flux, rotor current and flux, rotor RPM, etc.

Something like this: (Please correct and add to this...)

1. Contactor closes

1. Applied voltage tries to drive current into stator windings

3. Rising flux in stator windings results in current opposing applied voltage, with no net current flowing.

4. Rising stator flux induces current in rotor

5. Rising current in rotor produces flux opposing stator flux

6. Opposing fluxes produce torque - if the torque is high enough to overcome load inertia, rotor rotates.

7. As flux continues to build in the stator and rotor, motor accelerates.

8. System reaches steady state.


I'm trying to get down into the details of this, so if you want to be technical, please do so. I'm trying to understand those first few critical cycles. If it depends on motor parameters, assume typical values. Where does the inrush fit into this? I would love to see a graph of the values listed above for the first 10 cycles of a start, and then another for the first 10 seconds until the motor reaches steady state.

One of the things I have been trying to get at is the answer to this question:
Why, when resistance is added to the rotor, does the starting torque increase? I know it increases the power factor, but does this somehow change the angle of the flux in the rotor (physical angle or phase angle?) thus producing more directly opposing fields and therefore more force?

For the record I think this stuff is fun.

Tom

 

[DickDV]

Thanks alot, guys! I've learned more in this short thread about motor rotor behavior than in the last several years of questioning around.

The only part I still don't have an understanding of now is why a NEMA B torque curve, for example, shows decreasing torque from locked rotor to pull-up torque. If I've picked up correctly on the above discussion, then I don't see any explanation for that part of the curve.

Anyone care to comment on that.

And, thanks again to all who posted.

 

[electricpete]

I believe my post of 5 Oct 05 17:32 adddressed that (2nd paragraph) among other things.

Let me know if you don't agree.

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[electricpete]

Maybe I should add (if it's not obvious) that as speed increases in this region, the decrease in reactance (caused by decrease in frequency seen by rotor) causes an increase in power factor.

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[DickDV]

electricpete, if I read your post of 5Oct05 correctly, you say that with slight increases in speed away from locked rotor, the torque goes up.

The NEMA B curve goes down in that region. Am I missing something here?

 

[electricpete]

The curve I'm describing would increase continuously from 0 speed until breakdown torque speed, then decrease continously from breakdown-torque-speed to syncronous speed at which point it is 0.

This is pretty typical of most of the motor curves I have seen. I have seen in textbooks the kind of curve you describe... necessary to show the "minimum pullup torque". I'm not sure offhand exactly what would drive that behavior.

One thought - the torque speed curve can be 100% defined by the equivalent circuit parameters. You can find the speed of breakdown torque by solving dT/ds=0 and d^T/ds^2 <0. That always happens. If there is also a combination of parameters to give another point dT/ds=0, this time with d^T/ds^2 >0, that would be your minimum between start and breakdown torque...again usually doesn’t happen. If I get a chance I may check the equation to see what characteristics drive that particular unusual behavior.


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[electricpete]

The type of curve you are talking about is here:

http://tristate.apogee.net/mnd/mfcttor.asp

(different than what I described).

I think there may be a couple of effects at work in that initial dip.

The discussion so far focused really on power aspects. I said in this speed range, the dominant effect was reactance was going down. Based on this you do expect to see an monotonic increase in power output within this range. But power output is the product of torque times speed. When we go from 5% speed to 10% speed that is a dramatic increase in speed, so even with power output increasing within this range we might see some decrease in torque. Maybe there is a more direct way to get disussion of torque without going through power as an intermediate...still thinking.

A minor effect may also be deep bar effect which tends to increase rotor resistance and therefore increase torque at high slip frequencies.

I'll think some more but welcome any other comments.

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[electricpete]

If you use the linear equivalent circuit and neglect the magnetizing reactance, the torque-speed curve will have torque increasing continuously as speed increases from 0 speed to breakdown-torque-speed.

The proof:
Z:=R1+R2/s + I*(X1 + X2);

All the remaining quantities represent magnitudes:
I1:= V/((R1+R2/s)^2+(X1+X2)^2)^(1/2)



P_SHP:=I1^2*R2*(1-s)/s
P_SHP := V^2/((R1+R2/s)^2+(X1+X2)^2)*R2*(1-s)/s

T:=P_SHP/w
where w = wsync*(1-s)
T := V^2/((R1+R2/s)^2+(X1+X2)^2)*R2/s/wsync

dT_ds := 2*V^2/((R1+R2/s)^2+(X1+X2)^2)^2*R2^2/s^3/wsync*(R1+R2/s)-V^2/((R1+R2/s)^2+(X1+X2)^2)*R2/s^2/wsync

simplify:
dT_ds := Numerator / Denominator
Numerator = -V^2*R2*(-R2^2+R1^2*s^2+s^2*X1^2+2*s^2*X1*X2+s^2*X2^2)
Denominator = (R1^2*s^2+2*R1*s*R2+R2^2+s^2*X1^2+2*s^2*X1*X2+s^2*X2^2)^2*wsync

Solve for numerator = 0
s_Tmax := (+/-) R2 / sqrt(R1^2+X1^2+2*X1*X2+X2^2)*R2

If anyone is really interested I can post these equations in graphics format (a little easier to read).

Exclusing the negative value, there is only one point where dT/ds=0 and that is at breakdown torque (under the assumptions given at the beginning).

There are motors that act differently than this, with an initial dip in torque and then increase as shown here:

http://tristate.apogee.net/mnd/mfcttor.asp

I did notice after my previous posts that our power plant circulating water motor acts that way. It is a large slow speed motor.

I conclude it must be one of the two factors not included in the above model:
1 - non-linearity associated with the fact that rotor resistance is higher at high slip.
2 - the existence of magnetizing branch in the equivalent circuit which was not modeled above.

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[electricpete]

Typo Correction:
"s_Tmax := (+/-) R2 / sqrt(R1^2+X1^2+2*X1*X2+X2^2)*R2"
should have been
"s_Tmax := (+/-) R2 / sqrt(R1^2+X1^2+2*X1*X2+X2^2)"


I jumped over the fact that there is only one positive value where dT/ds=0. That means only one maximum or minimum of the T vs s curve. Since we know there is a maximum, there can be no minimum for positive s.


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[electricpete]

If the math above is to tedious, just follow it to the point of

T := V^2/((R1+R2/s)^2+(X1+X2)^2)*R2/s/wsync

Plot this function in excel using positive values for all the paramters. You will find that no matter what values you choose, this function T will never have a minimum for positive values of s.

(Once again there are two items not included in this model mentioned above)

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[DickDV]

electricpete, I surely appreciate the thought and effort you've been willing to put into these questions.

If you check out the NEMA A, B, C, & E torque speed characteristics, all of them have a minimum point somewhere around 20-25% of base speed.

As I believe you have concluded, the equivalent circuit that you have analysed doesn't provide any explanation for this behavior and is therefore not entirely valid for operation in this range of high slip.

The reasons for this behavior remain a mystery to me.

Thanks again for your work on this difficult subject

 

[waross]

Hello
A couple of points on your original post. Maybe semantics or possibly I have misunderstood something.
But;
3. Rising flux in stator windings results in current opposing applied voltage, with no net current flowing.

"Rising flux in stator windings results in current opposing applied voltage,"
Possibly more accurate if stated as <Rising flux in stator windings results in voltage opposing applied voltage,>
"net current flowing"
Possibly more accurate if stated as <back EMF (voltage opposing applied voltage) acts to reduce line current.

6. Opposing fluxes produce torque - if the torque is high enough to overcome load inertia, rotor rotates.
At standstill the opposing fluxes produce force not torque. The torque is produced when the flux rises in the adjacent coil fed from another phase. This also explains electricpetes statment that the torque is zero at standstill.
if the torque is high enough to overcome load inertia, rotor rotates.
Possibly more accurate if stated as <if the torque is high enough to overcome static friction, rotor rotates.>
respectfully

 

[electricpete]

On the subject of the possible "dip" (minimum) in torque speed curve between locked rotor and breakdwon torque:

I scavenged around and found 4 manufacturer's torque speed curves for specific motors. Two had the dip and two didn't.

The discussion above is not flawed by the assumptions. It is a proof by contradiction. If assuming A and B leads to C, then experimental observation of not(C) leads us to conclude the cause is either not(A) or not(B).

So my conclusion as stated , the cause of the dip is either:
1 - non-linearity associated with the deep bar effect which causes the rotor resistance to be higher at high slip.
2 - the existence of magnetizing branch in the equivalent circuit causes voltage drop across X1.

#2 may be a little weak in terms of a cause... you have to view it in terms of the model...doesn't lend much undestanding. I tend to think a thorough analysis would rule out #2 and leave us only with #1. If I have time (probably not in the near future), I'll study it a little closer.

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[electricpete]

Does anyone else have thoughts on the cause of the "dip" in the torque speed curve discussed above?

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[cswilson]

I can't make any of my equations produce the "dip" either, analytically or numerically. Still looking, trying to see if there are any higher-order effects.

 

[waross]

I have a couple of thoughts. Thinking about the torque curves of wound rotor motors, low slip motors and high slip motors such as are used on punch presses and shears. Would a crossover effect from the high resistance cage and the low resistance cage in a dual squirrel cage motor explain a torque dip?
respectfully

 

[DickDV]

I sure appreciate your efforts to try to bring understanding to this.

I, for no apparent reason, have always just passed it off as magnetic saturation occurring probably in the rotor but why it would get worse as the speed goes up from zero would beg an explanation that I certainly don't have.

Thanks again guys. If nothing further comes from this thread, I've still learned a lot.

 

[electricpete]

You are right Dick. The high currents during starting cause high leakage flux which can cause saturation in some parts of the motor such as the core teeth. As current decreases during the start, the saturation decreases and the effective leakage reactance would tend to decrease the current and the power factor. This tends to decrease the torque (depending on how it compares with the other effects which tend to oincrease torque with speed).

I think the other big effect is the deep bar effect. Just to elaborate a little more, the torque equation has R2 as a factor in the numerator and as one of several terms in teh denominator. T := V^2/((R1+R2/s)^2+(X1+X2)^2)*R2/s/wsync
For large slip, the R2/s term in the denominotor is much smaller than the X1+X2 terms in the denominator, so the denominator dependence on R2 is small and the torque for a given value of s is roughly proportional to R2 (based on the numberator. So with R2 decreasing as deep bar effect lessens during startup, this provides another effect which may tend to decrease the torque.

The magnetizing reactance neglected above I don't think has any big role. I don't have any proof but I don't think so.

There can surely be a lot more things that the designers do to shape the torque speed curve that I don't know about. At least I'm learning something here.

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[electricpete]

A correction to my first paragraph (in bold):
"...The high currents during starting cause high leakage flux which can cause saturation in some parts of the motor such as the core teeth. As current decreases during the start, the saturation decreases and the effective leakage reactance increases which would tend to decrease the current and the power factor. This tends to decrease the torque (depending on how it compares with the other effects which tend to increase torque with speed).

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[amptramp]

Just for fun!

An old standby from Allen-Bradley:

http://literature.rockwellautomation.com/idc/groups/literature/documents/br/150-br008_-en-p.pdf

On Wye-Delta starting but does a good job explaining starting current components and residual flux:

http://www.mastercontrols.com/EngInfo/Articles/Wooddall/TA_RWood.htm

 

[electricpete]

On page 2-16 page of amptrap's Allen-Bradley link, we see the following:

"As the motor begins to accelerate [from locked rotor], the torque drops off, reaching a minimum value called pullup torque. Pullup torque is caused by harmonics which result from windings being concentrated in the slots. If the windings are uniformly distributed around the periphery pull-up torque is greatlyl reduced. Some motor design curves show no pull-up torque and follow the dashed line [continuously increase from locked-rotor to breakdown torque]"

So apparently another possible cause of the dip is harmonic effects. That rings true to me although I don't understand it.

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