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

 

[electricpete]

There are a large number of ways to explain it.

One way is the motor equivalent circuit which can be derived from an understanding of essential principles of an induction motor.

Once you know the motor equivalent circuit, circuit analysis can predict for you current as a function of speed and torque as a function of speed. Reviewing these results with a firm understanding of the basis of the equivalent circuit reveals the relative importance of all the underlying factors.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[electricpete]

On the subject of “inrush”. I don’t want to get locked up in terminology but there are two different components of starting current.

One is the locked rotor current which we can determine from the equivalent circuit assuming zero speed. AC current starts at locked rotor current and then begins to decrease toward FLA as motor gets close to operating speed.

Another is the exponentially-decaying dc offset which occurs whenever we suddenly apply a voltage to an inductive/resistive circuit. It results in a maximum possible peak total current (ac plus dc) of 2*sqrt(2) times the rms locked rotor current. This component decays away within the first few cycles.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[electricpete]

I will attempt a rough discussion of starting characteristics without resorting to the equivalent circuit.

At low speed the slip is very high. This creates a high voltage in the rotor at high frequency. The high votlage is responsible for the relatively high current. The high frequency increases the impedance of the rotor leakage reactance so that rotor appears to have a very low power factor. Therefore even though the current is ~5x FLA, the torque is lower than 5x FLT due to the low power factor. As we increase speed just a little within this low-speed range, the dominant effect is reduction of that rotor leakage reactance which generally slightly increase torque and decreases current with increasing speed (but still very low speed <0.5*sync speed).

At very high speed (approx operating speed) the slip is very low. This creates a much lower voltage in the rotor and much less significant role of the rotor leakage reactance now close to zero so rotor resistance is a dominant impedance. If we increase speed just a little the dominant effect is decrease in induced voltage so torque decreases and current decrease.

So at low speed the dominant feature (with changes in speed) is leakage reactance, which explains the shape of current and torque vs speed curves in this region.

At high speed the dominant feature (with changes in speed) is change in rotor induced votlage, which explains the shape of current and torque vs speed curves in this region.

In between, there is a mixture and the curve slowly changes from one shape to the other.

Once you understand torque vs speed and current vs speed characteristics for motor, you can combine it with torque vs speed curve of your load to predict how the motor acts during startup.

If you want details on how to predict torque and current from equivalent circuit let me know, it can be solved analytically.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[subtech]

VermontPE
Here is what you are looking for. Don't let the title put you off. Chapter 32 will answer in detail any and all questions you have about 3 ph. motors.

Delmars Standard Textbook of Electricity-Second Edition by Stephen L. Herman

Can be had in used/good cond. from just about any used bookseller on the web for about 25 or 30 bucks and you will use it 'till you wear the cover off.(I own 2 copies)

Regards
Mike

 

[jraef]

E-pete is so wonderfully thorough, I can't possibly improve on that. There is another part of your question however that bothers me.

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?

The problem I see with your question is that you may not be aware that slip-ring motors come in 2 flavors, Wound Rotor Induction Motors (WRIM), and Synchronous Motors (SM).

Changing the rotor resistance in a WRIM can be worked into the description that e-pete posted, especially the part where he describes the change in rotor induced voltage affecting the torque speed curve. His description was generalized for all Induction Motors. Synchronous motors are close, but not the same. By the way, when external resistance is added, torque is reduced, not increased.

When you mentioned "increasing power factor", you were referring to the characteristics of a Synchronous Motor. DC voltage is applied to the SM rotor (through the slip rings) to alter the field strength, which can be used to manipulate the power factor one way or the other. That action is not the same as what is happening in a WRIM.

"Our virtues and our failings are inseparable, like force and matter. When they separate, man is no more." Nikola Tesla
Read the Eng-Tips Site Policies at faq731-376
Member, [blue]P³[/blue]

 

[VermontPE]

jraef,

Every graph I look at for wound rotor induction motors shows the torque peak moving from high speed to low speed with increasing rotor resistance. If the resistance is low, the startup torque is low. If the resistance is high, the startup torque is high. What is the physics of this? By physics I mean, where does the charge move? What fields are caused in the stator and rotor and how do they behave? Increasing R in the rotor offsets the inductance and pushes the phase of the current closer to the phase of the voltage for more delivered power. I think. At least at startup. Once the motor is running if the resistance is left connected to the rotor coils it will result in reduced torque, probably because when the rotor is moving it gets itself back in phase with the rotating field and then the resistance just limits the current in the rotor.

 

[CJCPE]

In "Electric Machinery" (Fitzgerald, Kingsley, Umans), torque is determined by analyzing a motor's equivalent circuit. Torque is maximum when the power delivered to (rotor resistance)/slip is maximum. Using the impedance matching principle, that occurs when Rres/s is equal to the other impedance in the equivalent circuit (all in series). For Rres/s = Zs as Rres increases, s must also increases. That is why the peak torque occurs at higher values of slip as the rotor resistance increases. The analysis also shows that the actual value of peak torque remains constant as the torque -speed curve is stretched towards the left in the figure that you posted.

The maximum locked rotor torque occurs when the peak torque point occurs at 100% slip. Further increasing the rotor resistance puts the peak torque point in the negative speed (braking) region and reduces the locked rotor torque.

"Circuits Devices and Systems" (Ralph Smith), a more general text, discusses the increase in starting torque in terms of increasing power factor using a similar equivalent circuit. Increasing power factor also moves the angle between the rotor field and the stator field closer to 90 degrees.

 

[VermontPE]

Here are some more possible mechanisms...ignore the wound rotor and imagine different designs of bars in a squirrel cage motor.

Some of the rotor bars are in regions where the effective field is very nearly zero. Increasing the resistance of the bars can force more of the total current to flow in the bars in higher regions of field, producing more emf and therefore more torque. This may be a load of...I'm not sure.

There are 2 components to moving charges in a rotor. The changing magnetic field places forces on the charges. One is the motion of the charge in the wire (in this case a rotor bar), the second is the motion of the wire (bar) itself (which conatins the charge). Higher resistance in the bars means that the charges cannot move through the bars as easily, meaning that of the total forces more is applied to moving the rotor, thus more torque.

Not sure the validity of these concepts.

Tom

 

[CJCPE]

Tom

I think that your first proposed mechanism is invalid because the rotor conductors are distributed uniformly and any increase in rotor resistance would effect the current proportionally everywhere.

With regard to your second proposed mechanism: The magnetic field produced by the stator does not change. A field of constant amplitude rotates at the synchronous speed, RPM = 120 X frequency / poles. The field is stronger at its center and weaker at the leading and trailing edges. Rotor current is caused to flow by the relative motion of the rotor conductors moving backwards through the field because of slip. The frequency of the rotor current is rotorfreq = slip x poles / 120. The rotor current causes a magnetic field that rotates forward with respect to the rotor at RPM = 120 x rotorfreq / poles. To determine the speed of the rotor field with respect to the stator, you add the speed with respect to the rotor to the rotor speed. That gives you a magnetic field in the rotor that rotates at exactly the same speed as the stator field but at about a 90 degree angle. The torque is produced by the force between the stator field and the rotor field. It is the relative magnitudes of the two fields and the angle between them that determines the torque.

Chuck

 

[davidbeach]

CJCPE, your first statement only applies to single cage designs. In dual cage designs different bars can have different properties, and carry differing currents dependent on the operating conditions.

 

[VermontPE]

A concept not yet discussed is the idea of resonance. Does changing the rotor resistance change the resonant frequency of the rotor's impedance, matching (or unmatching as the case may be) the frequency of the rotating field with the resonant frequency of the rotor?

 

[jraef]

Every graph I look at for wound rotor induction motors shows the torque peak moving from high speed to low speed with increasing rotor resistance. If the resistance is low, the startup torque is low.

You are right, I missed the word "starting" when I read your question. Oops

 

[electricpete]

Regarding the comment on resonance - there are no significant capacitive elements in an induction motor equivalent circuit model at power frequency or below, so I don't see any possibility of circuit resonance unless there is an external connected capacitance.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[cswilson]

I'm late to the thread, as I've been traveling, but I think I can contribute some insight going back to my days of trying to figure out how these darned things worked...

The current (and hence flux-linkage) response of the rotor to the stator voltage is just that of a first-order low-pass filter with an L/R time constant. Sketch out both the gain and phase bode plots as a function of slip frequency for this. On the gain plot, the magnitude is a roughly constant 1/R at low frequencies, then above the "break frequency" (R/L in rad/sec), it falls off with a slope of -1 on a log/log plot.

The phase plot shows near 0 degree lag at low frequency, passing through -45 at the break frequency, and asymptotically approaching -90 at higher frequencies.

Next, you may want to redo the Bode plots with the axes plotted linearly, not as log plots. You may also want to mirror the plot so that slip frequency increases to the left, because in the way we are used to looking at these motor plots, with a constant-frequency input, the slip is higher at lower speeds.

The torque generated is simply proportional to the magnitude of the rotor response multiplied by the sine of the lag angle. That's really all there is to it. Sure, there are some minor higher-order effects, but this catches the fundamental issues. I used a simple Excel spreadsheet, and could create the classic induction motor curves very easily.

At low slip frequencies, the lag angle and its sine increase faster than the magnitude decreases, so torque increases with slip. However, as you continue to increase slip frequency, the angle, and especially its sine, start levelling off, while the magnitude continues to decrease. The frequency of the torque peak is directly related to the R/L break frequency.

Therefore, as you increase the rotor resistance, you increase the (slip) frequency of the torque peak. Each of the torque/speed plots you show is fundamentally the same -- the ones with higher resistance are just "stretched out". Their magnitude would also fall off with increasing slip if that were plotted (this would get you into negative velocities).

Curt

 

[VermontPE]

cswilson

Finally what I have been trying to get to. Thanks!

Tom

 

[Marke]

Hello VermontPE

Increasing the resistance of the bars can force more of the total current to flow in the bars in higher regions of field,

Sort of correct, if you take a square bar and position it at the surface of the rotor, it will have a fixed value of resistance and inductance. If you position the same bar deeper into the rotor, it will have the same resistance (provided that the material and crossectional area are the same) but it will have a higher reactance.
Now take two bars of the same square cross section and position one at the surface of the rotor, and the other deeper down into the rotor, and connect them in parallel. During start, the freqeuncy of the rotor current is dependent on the slip. At high slip, the effect of the rhigh reactance of the inner bar, is to concentrate most of the current in the outer bar. The effective resistance is higher than under almost zero slip conditions where the current is more evenly distributed.
If we take a single thin rotor bar positioned on the radius of the rotor with the outer edge near to the surface and the inner edge towards the shaft, and we compare this bar with a square bare at the rotor surface with equal cross sectional area, both bars will exhibit the same DC resistance and perform with similar full load slip characteristics. The start characteristics will be markedly different however because the current distribution in the bar during start, will be a concentration towards the outer edge resulting in a higher power dissipation in the bar and a resulting higher start torque.

Mark Empson

http://www.lmphotonics.com

 

[bam55]

Does all this mean that at no load starting for an say 100HP induction squirral cage motor -the inrush is going to be low or negligable( Won't dim the lights)?

 

[electricpete]

No. Locked rotor current magnitude (and also any dc offset) are indepdent of load. Load can affect the duration of the starting current (not the magnitude).

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[bam55]

Just to deviate a little further to get to it: Is there any point in putting a soft start for this motor which only starts at no load? (The application is a magnetic coupled adjustable speed drive controlled fan which starts it at no load) Is there not a spike whether I have a soft start or not?