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Sheik480
13 April 2015, 0013
Lately I've been having some difficulty wrapping my mind around the interplay of voltage and its limitations on induction motor speeds. I understand very well the behavior of dc motors and the relationships between magnetic field strength, amperage, voltage, and motor speed in our straightforward friends, but obviously there are some significant differences between dc motors and ac motors, especially ac motors of the nonsynchronous variety.

Here's how I understand induction motors make speed and torque:

1) Multi-phase ac voltage is applied to the stator windings in a motor, creating a rotating magnetic field.

2) This rotating magnetic field moves past the rotor bars, cutting them with varying flux and inducing current and a magnetic field.

3) These two rotating magnetic fields oppose eachother and create a torque between the stator and rotor, giving us our motor.

Now, from my understanding, the torque the motor produces is a product of stator voltage and slip speed; if the slip is greater at the same voltage, the rotor is more strongly magnetized and creates greater torque, or if the voltage is greater and slip is the same, the rotor is also more strongly magnetized and the same effect is achieved. Thus, if there is very little slip, there is very little torque, nearly regardless of voltage.

So here is my question: aside from controller frequency limitations, what limits induction motor speed at upper limits and no load? With very little slip, the magnetic field of the rotor is weak and creates minimal bemf. I've heard discussion of voltage limiting maximum induction motor rpm, but this doesn't make any sense to me without specific discussion of a torque component: there is very little rotor magnetiziation to create limiting back voltage. What gives? Please let me know if my question is vague or needs any clarification.

podolefsky
13 April 2015, 0809
One way to think about variable frequency drive is that it is a series of single frequency curves. Torque is proportional to magnetic flux and current. Flux is proportional to the ratio V/f (voltage / frequency). Generally with variable frequency drive, V/f is kept constant up to base speed (about 1000 rpm in the picture below). With V/f constant, torque is limited by current, which is limited by the controller (and, of course, what the motor can take).

V is maximum at base speed (full pack voltage). Above base speed, V is constant while f keeps increasing, which reduces flux, which reduces torque. This is the "field weakening" region.

Torque reduces asymptotically to zero, so you can keep increasing speed by increasing frequency. The limit is where the power equals frictional losses, or the rotor speed is high enough that is breaks apart (or induction limits as Spoonman said below).

http://lh6.ggpht.com/_X6JnoL0U4BY/S1huqYNgsAI/AAAAAAAAINw/Fo55efK7w8s/tmp32315_thumb1_thumb.png?imgmax=800

It's explained pretty well here:

http://ecatalog.weg.net/files/wegnet/WEG-induction-motors-fed-by-pwm-frequency-converters-technical-guide-028-technical-article-english.pdf

Spoonman
13 April 2015, 0816
Now, from my understanding, the torque the motor produces is a product of stator voltage and slip speed;

Stator current and slip - the voltage is a function of the BEMF and reactive impedance (which, granted, are influenced by the slip).



if the slip is greater at the same voltage, the rotor is more strongly magnetized and creates greater torque, or if the voltage is greater and slip is the same, the rotor is also more strongly magnetized and the same effect is achieved. Thus, if there is very little slip, there is very little torque, nearly regardless of voltage.


...and the above illustrates why my initial comment is important - the voltage is not the deciding factor in the magnetic field strength. Low torque motors have greater winding numbers and hence higher impedances at any given frequency, meaning that you will see greater voltage variation for any given change in current, but less current overall than a higher torque motor and therefore more slip under load. Higher torque motors have far lower winding counts and so far less impedance, this means more current for any given voltage, resulting in a far more powerful magnetic field and far less slip under load.

In either circumstance as the slip approaches zero, so too does the torque. This is because the torque comes from the phase mismatch between the stator and rotor fields - ie: the regularity with which the stator field swaps the poles on any given bar in the rotor - if they're in phase, then the poles don't swap and so there's no magnetic field produced in the rotor and, consequently, no torque.



So here is my question: aside from controller frequency limitations, what limits induction motor speed at upper limits and no load? With very little slip, the magnetic field of the rotor is weak and creates minimal bemf. I've heard discussion of voltage limiting maximum induction motor rpm, but this doesn't make any sense to me without specific discussion of a torque component: there is very little rotor magnetiziation to create limiting back voltage. What gives? Please let me know if my question is vague or needs any clarification.

well... assuming you mean aside from the centrifugal force trying to tear the rotor apart... then the next big issue is the inductance of the stator itself.

Even if you take the rotor out of the rotor entirely, you're still left with a bunch of wirewound inductors which, put simply, resist change in current. The voltage required to persuade them to permit the current flowing to change is a function of the magnitude of the current and the rate of change required.

If you look at your RC motors for battery powered planes and helicopters etc... (these are usually BLDC rather than AC but the principles are similar enough for this discussion) you have lots of windings producing high impedance which means relatively low current, and similarly low inductances permitting high stator frequencies at modest voltages.

Looking towards traction motors then, you have circuits carrying vastly more current through very large, heavy wires - very low impedance but far higher inductance circuits. These do not change direction so willingly and although they can be made to do so, the voltages associated with such efforts lead to considerable additional complexity in the power electronics required.

Throw the rotor back into the equation now at this point and take into account the BEMF produced at any given speed and your voltage requirement for any desired operation increases dramatically - the former becomes a motor with low torque but which can run extremely fast and so produce decent power for its size; the latter then results in a motor which generates far higher torque at far lower speed.

In theory if you could spin an RC motor fast enough you could match the power output of a traction motor - but that little motor would have to spin awefully damned fast. :p

Add to this then the dynamic nature of the reactance or the system due to variation in slip on account of a variable load (wind turbulance or gravel for example) and you can see why things would become a little complicated.

Sheik480
13 April 2015, 0958
One way to think about variable frequency drive is that it is a series of single frequency curves. Torque is proportional to magnetic flux and current. Flux is proportional to the ratio V/f (voltage / frequency). Generally with variable frequency drive, V/f is kept constant up to base speed (about 1000 rpm in the picture below). With V/f constant, torque is limited by current, which is limited by the controller (and, of course, what the motor can take).

V is maximum at base speed (full pack voltage). Above base speed, V is constant while f keeps increasing, which reduces flux, which reduces torque. This is the "field weakening" region.

Torque reduces asymptotically to zero, so you can keep increasing speed by increasing frequency. The limit is where the power equals frictional losses, or the rotor speed is high enough that is breaks apart (or induction limits as Spoonman said below).

http://lh6.ggpht.com/_X6JnoL0U4BY/S1huqYNgsAI/AAAAAAAAINw/Fo55efK7w8s/tmp32315_thumb1_thumb.png?imgmax=800

It's explained pretty well here:

http://ecatalog.weg.net/files/wegnet/WEG-induction-motors-fed-by-pwm-frequency-converters-technical-guide-028-technical-article-english.pdf

Ah, this is a key I have been missing! This means the effective torque constant of the motor changes with the voltage/frequency ratio, right?



Stator current and slip - the voltage is a function of the BEMF and reactive impedance (which, granted, are influenced by the slip).



...and the above illustrates why my initial comment is important - the voltage is not the deciding factor in the magnetic field strength. Low torque motors have greater winding numbers and hence higher impedances at any given frequency, meaning that you will see greater voltage variation for any given change in current, but less current overall than a higher torque motor and therefore more slip under load. Higher torque motors have far lower winding counts and so far less impedance, this means more current for any given voltage, resulting in a far more powerful magnetic field and far less slip under load.

I specified voltage as that's what is applied to the phase windings; amps produce torque, but voltage (and it induction motors, slip) is what causes amps. How is bemf modeled with slip and flux? Is it similar to permanent magnet motors and rpm?


In either circumstance as the slip approaches zero, so too does the torque. This is because the torque comes from the phase mismatch between the stator and rotor fields - ie: the regularity with which the stator field swaps the poles on any given bar in the rotor - if they're in phase, then the poles don't swap and so there's no magnetic field produced in the rotor and, consequently, no torque.

This is exactly what I described in what I understand is happening in an induction motor to create torque. I'm glad I have that part right.


well... assuming you mean aside from the centrifugal force trying to tear the rotor apart... then the next big issue is the inductance of the stator itself.

Even if you take the rotor out of the rotor entirely, you're still left with a bunch of wirewound inductors which, put simply, resist change in current. The voltage required to persuade them to permit the current flowing to change is a function of the magnitude of the current and the rate of change required.

If you look at your RC motors for battery powered planes and helicopters etc... (these are usually BLDC rather than AC but the principles are similar enough for this discussion) you have lots of windings producing high impedance which means relatively low current, and similarly low inductances permitting high stator frequencies at modest voltages.

Looking towards traction motors then, you have circuits carrying vastly more current through very large, heavy wires - very low impedance but far higher inductance circuits. These do not change direction so willingly and although they can be made to do so, the voltages associated with such efforts lead to considerable additional complexity in the power electronics required.

Throw the rotor back into the equation now at this point and take into account the BEMF produced at any given speed and your voltage requirement for any desired operation increases dramatically - the former becomes a motor with low torque but which can run extremely fast and so produce decent power for its size; the latter then results in a motor which generates far higher torque at far lower speed.

In theory if you could spin an RC motor fast enough you could match the power output of a traction motor - but that little motor would have to spin awefully damned fast. :p

Add to this then the dynamic nature of the reactance or the system due to variation in slip on account of a variable load (wind turbulance or gravel for example) and you can see why things would become a little complicated.

Ironically, I come from the world of rc and am very familiar with the ridiculous qualities of those little screamers :D what I'm understanding from this statement is that iron losses are a large limiter at high frequency?


Thank you very much, both of you! I'm sorry if I seem impertinent, I'm trying to reconcile my current understanding with what's actually happening. I really appreciate you taking your time to help me out!

Spoonman
14 April 2015, 0130
I specified voltage as that's what is applied to the phase windings; amps produce torque, but voltage (and it induction motors, slip) is what causes amps. How is bemf modeled with slip and flux? Is it similar to permanent magnet motors and rpm?


The underlined bit requires a little more refinement - you're correct in so far as you require a potential difference in order for a current to flow, however voltage is no indication on it's own of the amount of current flowing and it's the amount of current flowing that determines the rigidity/torque of the system and hence the degree of slip which you can expect to see. Higher peak current means less slip under any given circumstance.

You can illustrate this to yourself very easily by setting up a motor and idling it with a controller set for constant speed (speed being dictated, as it is, by voltage), monitor the current flowing at idle and then load the motor. You'll notice, assuming you don't reach the current limits of the power supply or the controller, or the stall torque of the motor, that the voltage applied/rotor speed remains relatively constant whilst the current requirement rises proportionally to the load.

Neither are voltage and slip synonymous - the absolute amount of slip is a function of the impedance of the motor, and the amount at any given time is a function of the load - the greater the load, the greater the degree of slip, hence the greater the frequency with which the stator and rotor fields are out of phase, and consequently, the more current flows. Therefore, as slip increases you'll see a very small change in either the rotor speed or the voltage applied depending on how your control is carried out, but also a correspondingly large change in current.



...iron losses are a large limiter at high frequency?


Iron losses are a limiting factor with regard to the heat that can be dissipated and the voltage that can be applied, but they're a seperate issue to those I mentioned earlier.

Sheik480
14 April 2015, 1418
The underlined bit requires a little more refinement - you're correct in so far as you require a potential difference in order for a current to flow, however voltage is no indication on it's own of the amount of current flowing and it's the amount of current flowing that determines the rigidity/torque of the system and hence the degree of slip which you can expect to see. Higher peak current means less slip under any given circumstance.

I don't remember saying volts on their own cause torque, but that volts and slip cause amps and torque. Is it incorrect that if volts and frequency are kept the same (although I would think the rotor can't actually tell what the stator frequency is, only what it is relative to the rotor ie. slip), then increasing load causes slip which causes amps and thus torque? Haha, I'm all twisted around about whether amps cause slip or slip causes amps :confused:


You can illustrate this to yourself very easily by setting up a motor and idling it with a controller set for constant speed (speed being dictated, as it is, by voltage), monitor the current flowing at idle and then load the motor. You'll notice, assuming you don't reach the current limits of the power supply or the controller, or the stall torque of the motor, that the voltage applied/rotor speed remains relatively constant whilst the current requirement rises proportionally to the load.

Neither are voltage and slip synonymous - the absolute amount of slip is a function of the impedance of the motor, and the amount at any given time is a function of the load - the greater the load, the greater the degree of slip, hence the greater the frequency with which the stator and rotor fields are out of phase, and consequently, the more current flows. Therefore, as slip increases you'll see a very small change in either the rotor speed or the voltage applied depending on how your control is carried out, but also a correspondingly large change in current.

This I already understand well. I think you answered my original question at the end of your first post. And now after rereading that post, I better understand you statment about inductance limiting frequency.

podolefsky
14 April 2015, 1457
You're both right :)

The governing equation for torque is:

torque = k * V/f * I_rotor

k is a constant, I_rotor depends on the load. It could go either way - keep the rotating field frequency constant, increase load > slows rotor > increases slip > increases I_rotor > increases torque (would be like going from flats to a hill). Or, increase the frequency of the rotating field > increases slip > increases I_rotor > increases torque (accelerating on flat ground).

Of course, ultimately, currents create the magnetetic fields (if you had voltage but no current, you would have no field). But you can write B = k V/f, so you can think of the flux as being proportional to voltage.

Hugues
14 April 2015, 1834
Gee, i thought i knew what was happening when I twist my throttle :confused:

Is there an "elevator speech" version of how induction motors work ? There is no way I can explain this to someone else in 2 min.

podolefsky
14 April 2015, 1955
10 second version: First you need to know Faraday's law: a changing magnetic field creates a voltage (or EMF) in a conductor. EMF creates a current, which creates a magnetic field. Basically, the stator produces a changing magnetic field that "induces" a field in the rotor. The two fields interact and the stator's field "drags" the rotor around by it's field.


2 min version: In order to induce a field in the rotor, and make torque, the stator field has to be turning faster than the rotor. If they were turning the same speed, it would look to the rotor like the field wasn't changing, so you wouldn't get any induction. The difference in speeds is called "slip", and slip determines torque. This is totally different from DC motors or "synchronous" AC motors, where the stator field turns at the same speed as the rotor.

In single frequency drives, like industrial equipment that runs from 50 or 60Hz, the stator field turns at a single frequency, and the slip changes as the rotor changes speed due to the load. In the diagram I posted, each of those individual lines is torque vs slip for a single frequency. With variable frequency drive, like you have with your AC-20, you can change the frequency. There is sort of an optimal amount of slip that is most efficient, so with variable frequency the controller is trying to stay at that optimal slip. It is hugging the right edge of those torque/slip curves, creating a smooth curve like you see in dyno plots.

Your AC-20 has a speed sensor on it, which tells the controller the speed of the rotor. When you twist your throttle, you are telling the controller to try to get a certain amount of torque (assuming you are in torque control mode). The controller takes the rotor speed and does a calculation to figure out the voltage and frequency it needs to apply to the stator to get that amount of torque with the optimal amount of slip.

Here's a nice animation of what's going on:


https://www.youtube.com/watch?v=WDr9lhxDssk

Sheik480
14 April 2015, 2000
Given that, what causes horsepower to fall off so quickly in the dynomometer charts I've seen for ac systems?

podolefsky
14 April 2015, 2204
Given that, what causes horsepower to fall off so quickly in the dynomometer charts I've seen for ac systems?

Someone could verify this, but I think it's because there isn't perfect coupling between stator and rotor fields. If the stator and rotor were ideal, you would have perfect coupling and true constant power. In a real motor, you end up with leakage reactance (http://electrical4u.com/resistance-leakage-reactance-or-impedance-of-transformer/), causing a voltage drop that increases with frequency.

Spoonman
15 April 2015, 0252
Cheers podelofsky - we were kinda going around in circles to an extent there. :p

The power tail off is certainly contributed to by the nonideal complex impedance of both the rotor and that stator - the latter half of which (your leakage reactance; the first half being plain old resistance), of course, increases with frequency on account of the inductive nature of each, meaning that you wind up requiring more voltage in order to switch the fields at higher frequency. There may also be an increase in the first half of the equation if the temperature of the unit rises, any such increase being a function of the power flowing through the motor in the first place, and the reduction in efficiency (and hence tendancy towards heat generation), on account of the increase of the frequency dependent variable - the reactance. ... this of course then becomes a comounded effect as voltage increases farther etc...

Now when you consider then that you're already operating with significant BEMF at these RPM then it's easy to see why you may not have the required voltage overhead to keep the current constant as the RPM increases - so this is where field weakening occurs. We can't push the same amount of current so we can't generate as much torque, but we can generate, for a while at least, enough torque to continue to accelerate the motor although there will be lower power transfer overall.

If you refer to any of HPEV's graphs you'll see that the torque begins to drop off at exactly the same time as peak power is achieved - this is on account of not being able , at any given voltage, to generate enough relative potential difference to continue to deliver the current that had been delivered up to that point. As the voltage of the pack is increased, you will see that this point shifts to the right accordingly.

Beyond this point, both BEMF and complex impedance continue to build, and so no matter what voltage your pack, you will always see the power tail off - higher voltages merely mean that it happens at higher revs.

Another point of note WRT the HPEV's graphs is that they report battery voltage and current, so in the chart, you see the voltage remain constant as the current rises - on the other side of the controller of course, the opposite is true.

Spoonman
15 April 2015, 0305
Is it incorrect that if volts and frequency are kept the same then increasing load causes slip which causes amps and thus torque? Haha, I'm all twisted around about whether amps cause slip or slip causes amps :confused:


It's exactly correct - and yes, I see where you're getting twisted around.

Current acts to prevent slip so:
- more slip -> more current
but
- more current -> less slip.

This is where the rigidity I mentioned earlier comes in - if you have a higher current rated motor, then you will have a lower slip range on account of a greater ability to generate torque, ie: the rotor only get's so far away before it gets tugged back into line. If you have a lower current rated motor, then you have less rigidity, and so the slip range is greater for the same relative load.
For example, if I have a traction motor loaded at 50%, I might experience a slip of (arbitrary numbers) about 0.7% between the stator and rotor speeds. On the other hand, if I load an RC motor to 50% I could see slip of 3-5% between the two.

The fundamental reason for this is that the former motor derives its power primarily from torque and as a result is an incredibly rigid system, whereas the latter derives its power from speed, and so is far more compliant.

Hugues
15 April 2015, 0335
Interesting, you got me on board with your 10 sec version and the video is quite clear.

I thought the stator would have been pushing the rotor rather than dragging it, interesting.

On a related topic: torque is quite constant for such motor, and this from 0 rpm. But I do feel I have more acceleration power on my bike after, say 50 km/h than I have between 0 and 50. Do you experience the same ? And if so, why ?

I've tripled checked my controller settings incl throttle and they are maximizing acceleration.

I would like to put some data on this, just need to find a quiet piece of track somewhere.

Spoonman
15 April 2015, 0535
On a related topic: torque is quite constant for such motor, and this from 0 rpm. But I do feel I have more acceleration power on my bike after, say 50 km/h than I have between 0 and 50. Do you experience the same ? And if so, why ?

I've tripled checked my controller settings incl throttle and they are maximizing acceleration.


There are many things that could cause that sensation - if could be something physical but I expect that it's more likely your perception, there's a lul in excitement between the instant surge off the line and the point at which you begin to develop enough speed to get some wind roar going.

If it were to be something physical then it could be in the controller programming in order to make low speed response more managable; it could be to do with an overlap in the impendance of the motor above a certain RPM, and the effective impedance of the output stage of the motor controller, meaning that you get a jump in the power delivery to the drivetrain; or it could be related to the efficiency curve of the motor.

You'd need to log the battery and motor voltage and current delivery, and the accompanying wheelspeed in order to know for sure.

podolefsky
15 April 2015, 0644
Hugues, I get the same feeling with my AC-20. I think it's purely psychological. The dyno chart says torque is actually a little higher at low RPM, so acceleration should be greater. It's just more of a rush going 30-60 than 0-30. You've got more wind, more chain noise, more excitement.

If you put in a 10:1 gear reduction, you could probably wheelie and that would be a different story. But then you would top out at 50 mph. You'd have a very badass scooter.

Hugues
15 April 2015, 0956
ok all clear, i'll need to put some data on this, probably just an impression.
i wish it would be easier to log data out of the Curtis/AC-20 combo using Torque app,

Sheik480
15 April 2015, 1150
It's exactly correct - and yes, I see where you're getting twisted around.

Current acts to prevent slip so:
- more slip -> more current
but
- more current -> less slip.

This is where the rigidity I mentioned earlier comes in - if you have a higher current rated motor, then you will have a lower slip range on account of a greater ability to generate torque, ie: the rotor only get's so far away before it gets tugged back into line. If you have a lower current rated motor, then you have less rigidity, and so the slip range is greater for the same relative load.
For example, if I have a traction motor loaded at 50%, I might experience a slip of (arbitrary numbers) about 0.7% between the stator and rotor speeds. On the other hand, if I load an RC motor to 50% I could see slip of 3-5% between the two.

The fundamental reason for this is that the former motor derives its power primarily from torque and as a result is an incredibly rigid system, whereas the latter derives its power from speed, and so is far more compliant.

Alright, I think I'm starting to wrap my head around it. For the rc motors, which are permanent magnet machines, I know the actual coupling between the stator's magnet field and the rotor's magnetic field is 100%: if there isn't coupling, you get cogging, which is very apparent and loved by nobody. I would think that in the induction machine, the actual magnetic field of the rotor is perfectly aligned with the stator's magnetic field even if it's rotating relative to the rotor, is that right? As for the induction motor, why can't you simply increase slip to increase torque at a given voltage and frequency? It seems like it would be similar to increasing the rotor magnet strength, creating a motor with an effectively lower voltage constant and greater bemf for the magnetic fields rpm. Is this right?

podolefsky
15 April 2015, 1319
I don't think the coupling can ever be 100%. There will always be some stray fields that don't interact with the rotor.

Induction motors are definitely hard to get your head around.

The rotor *field* rotates at the same rate as the stator field, while the rotor itself rotates slower. Here's a nice animation:

http://www.ece.umn.edu/users/riaz/animations/sqmovies.html

You can't increase slip at will the way I think you're saying. You either have to increase the frequency so the stator field rotates faster, or load the motor so the rotor slows down. Slip is defined as (stator field speed - rotor speed) / stator field speed. To change slip, you have to change one of those speeds.

You are right that increasing slip is like increasing the rotor magnetic field strength - in fact, it is exactly that. With more slip, you get more induced current in the rotor and thus stronger field.

Spoonman
16 April 2015, 0339
I would think that in the induction machine, the actual magnetic field of the rotor is perfectly aligned with the stator's magnetic field even if it's rotating relative to the rotor, is that right?

Almost, but not quite. As podelofsky has pointed out, the two do rotate at the same frequency, so to that extent they are aligned, however there is a phase shift between them on account of the inductive nature of the system - this is illustrated in the animation he's provided where you can observe that the peak flux density in the airgap leads the peak response in the squirrel cage bars by a few degrees.


As for the induction motor, why can't you simply increase slip to increase torque at a given voltage and frequency? It seems like it would be similar to increasing the rotor magnet strength, creating a motor with an effectively lower voltage constant and greater bemf for the magnetic fields rpm. Is this right?


You can't increase slip at will the way I think you're saying. You either have to increase the frequency so the stator field rotates faster, or load the motor so the rotor slows down. Slip is defined as (stator field speed - rotor speed) / stator field speed. To change slip, you have to change one of those speeds.

You are right that increasing slip is like increasing the rotor magnetic field strength - in fact, it is exactly that. With more slip, you get more induced current in the rotor and thus stronger field.

the above pretty much nails it - slip is an inherent characteristic of any given system, it's not something that you control and it's not something that you can utilise. Knowledge of it allows you to correlate voltage, current and loading with RPM; you can then feed this information back into your control loop if you so wish, in order to stabilise rotor RPM under dynamic loading, or track an optimal efficiency curve for power transfer applications.

Now having said that - torque follows demand for acceleration and is entirely self regulating, so it's not something you need to worry about to begin with. Any motor will develop sufficient slip, hence draw enough current and create enough torque (up to it's stall torque limit) in order to achieve any given RPM target as defined by the voltage applied to the stator - hence the fabled V/hz relationship. The torque limits are defined then by the maximum current and voltage which can be provided by the controller and handled by the motor. There's a stall torque rating on all motors as well but that's largely a function of the voltage handling limitations of the system.

Stevo
17 April 2015, 0616
This thread is good reading.
So can a comparison be made to a pmac motor with similar power output? Which is more efficient?

podolefsky
17 April 2015, 0632
This thread is good reading.
So can a comparison be made to a pmac motor with similar power output? Which is more efficient?

They are both 3-phase and the stator design is nearly identical. But almost completely different operating principles. PMAC uses permanent magnets to create the rotor field, no induction. PMAC is a synchronous motor - the rotor turns at the same speed as the stator field. No slip, torque depends only on stator current.

PMAC and induction of the same continuous power will be similar size.

Generally speaking PMAC is more efficient since no energy is required to create the rotor field, but induction has advantages at certain speeds and loads. Good explanation here:

http://www.teslamotors.com/blog/induction-versus-dc-brushless-motors