Motor / transformer variable frequency control

[artis]

few questions

1) is it true that for a 50 or 60hz induction motor maximum torque is achieved from 0hz up to design hz and if an VFD is used and frequency is increased above 50 or 60hz like 100hz the rpm will increase but the available torque will decrease?
Is the reason behind this the fact that the motor stator coils are wound with the number of turns that are fixed for a fixed frequency so going beyond this frequency decreases the current that can flow through the coils and so the B field is weaker and results in less torque?

The same rule must apply to all inductors, so my next question is this

2) the same must apply to transformers as if a transformer has a fixed winding ratio then increasing the primary frequency above certain point would result in lowered current in the primary and lower B flux in the core resulting in lower secondary voltage/current?

 

[essenmein]

1) It is not quite true, torque is more or less current dependent assuming you can get the rotor excited properly. Then like most electric machines, once you enter field weakening region you are essentially in a constant power mode (at which speed this happens is BEMF dependent, ie directly related to available driving voltage and stator turns), then since power remains constant, speed increases, torque must go down.

2) a transformer at different frequencies with the same applied voltage will generate the same output, within the magnetic limits of the core material (more on this in a bit). What changing the frequency does is increase or reduce the magnetizing current (higher frequency reduces magnetizing current), this in turn affects the core hysteresis losses. As frequency gets too high eddy current losses in the core will limit the applied voltage or frequency. Note that these magnetizing losses are present regardless of load (assuming applied voltage is always the same). Conversely as frequency goes down, you will eventually saturate the magnetic core, and it will cease being a very good transformer. So a transformer will operate identically, independent of frequency, assuming you are within the operational range of the core material. Skin effect also plays a part if freq is high enough.

 

[artis]

1) ok I guess I needed to specify some details more , assume the rotor is either locked or with a very high load on it (at the point where induction motor is most efficient) so at this point it should have torque that is high and the highest as we go from zero hz up to rated hz , then above rated hz the torque would decrease , at least this is how I see it.2) ok I see the point about the transformer, sure core losses will impact electrical performance but leaving them out for the moment , assuming we are talking about an air core inductor where core losses or limitations don't apply, isn't here also the case that increasing frequency lowers the current given we have a constant voltage/current supply ? In theory.
Or have I got this wrong and in theory frequency increase doesn't decrease current and this only happens due to real physical limitations surrounding the coil, like core losses, skin effect on coil itself , inductive , capacitive etc?

So I guess I have to ask whether a ideal air core coil doesn't have this limitation of current vs frequency?

 

[essenmein]

1) ok I guess I needed to specify some details more , assume the rotor is either locked or with a very high load on it (at the point where induction motor is most efficient) so at this point it should have torque that is high and the highest as we go from zero hz up to rated hz , then above rated hz the torque would decrease , at least this is how I see it.2) ok I see the point about the transformer, sure core losses will impact electrical performance but leaving them out for the moment , assuming we are talking about an air core inductor where core losses or limitations don't apply, isn't here also the case that increasing frequency lowers the current given we have a constant voltage/current supply ? In theory.
Or have I got this wrong and in theory frequency increase doesn't decrease current and this only happens due to real physical limitations surrounding the coil, like core losses, skin effect on coil itself , inductive , capacitive etc?

So I guess I have to ask whether a ideal air core coil doesn't have this limitation of current vs frequency?

1) Well as an assumption, there is quite a difference between locked rotor and heavily loaded where its most efficient! I think "rated speed" is only really useful for line operated machines at line frequency, as soon as you control it with a VFD you would use a speed torque curve to describe the useful operating range.

As far as induction machines go, they are asynchronous, so at locked rotor, they still require AC on the stator otherwise the rotor field is not created, ie not zero Hz at 0rpm. All machines follow a speed torque curve not too dissimilar from the above. There are other considerations, but essentially below the knee speed, system phase current limit is what limits torque, above the knee, system voltage limits how much torque producing current you can drive into the machine. If the available current is the same, but you increase the bus voltage on the inverter, the knee simply moves up in speed proportionally to the increase in voltage. Field weakening allows effective high speed operation, torque tails off as speed increases but mechanical power more or less remains constant.

2) As far as I know, ignoring material limitations and with limitless current, an air core transformer follows the equations with no apparent limit to frequency (high or low) until you get into short enough wavelengths where other effects come into play.

Where are you going with this?

 

[artis]

quite frankly nowhere, I was just reading some related physics and wanted to be sure I'm thinking correctly.

Yes as for the ac induction motor , sorry should have said at least 1hz instead of 0, surely without induction taking place the rotor doesn't feel any force at all.
I think I get the picture , from few hz up to rated hz the torque increases rapidly and so does rpm , then above rated hz rpm continue to increase but torque falls off due to the fact that increasing frequency but having constant voltage results in less current through the stator coils.

I assume you say that mechanical power expressed in kW or HP stay almost constant because those are calculated from the product of torque times RPM so when one falls the other increases and the result stays about the same ?
Although I would assume that torque falls faster than RPM increases above a certain frequency.?

 

[essenmein]

quite frankly nowhere, I was just reading some related physics and wanted to be sure I'm thinking correctly.

Yes as for the ac induction motor , sorry should have said at least 1hz instead of 0, surely without induction taking place the rotor doesn't feel any force at all.
I think I get the picture , from few hz up to rated hz the torque increases rapidly and so does rpm , then above rated hz rpm continue to increase but torque falls off due to the fact that increasing frequency but having constant voltage results in less current through the stator coils.

I assume you say that mechanical power expressed in kW or HP stay almost constant because those are calculated from the product of torque times RPM so when one falls the other increases and the result stays about the same ?
Although I would assume that torque falls faster than RPM increases above a certain frequency.?

From zero rpm, or a few Hz, to the knee speed, the torque is constant and dependent on current, mechanical power increases from zero to maximum at the knee speed.

The knee speed to me is when you demand 100% Iq and the machine will not spin faster, you have "run out of voltage" at this point, increase you bus voltage, this speed moves up. If you want to run above this knee speed, you have to apply Id, or field weakening current, now some of your phase current is used to reduce the net back EMF (ie cancel some of the rotor flux), since you are still phase current limited, this means you have less Iq available for making torque. Rated Hz doesn't make sense in this context, the machine will happily run from zero Hz (in case of synchronous machine) to a maximum frequency determined by the pole count and mechanical rpm limit of the machine (bearings etc).

There are other things that come into play and as speed goes up really high you do stop being in "constant power", and enter a voltage limited area. Frequency does affect your voltages, iwL vector (produced by the stator inductance) is taking voltage without producing torque. However fundamentally these speed limits come about not because of Hz, but because of Volts, the main one is back EMF.

 

[artis]

I remember seeing this clearly how the back EMF works to limit current is when I was on an older electric train as a kid , a DC train runs from 3kV overhead line and it had an ammeter in the electric utility box near the waiting area , I watched the meter and everytime from a complete stop as the DC motors were switched on the meter went to something like 600A and then as the speed of the train increased as the motors spun up the amperage decreased to the point where at near max speed the amps were some 50A maybe , surely those were series synchronous motors and the max speed of the train wasn't probably their max speed and if uncoupled with a lighter load they would probably spin even faster and the amps would go even lower probably to the point where the commutator would self destruct due to arcing over or else.

 

[essenmein]

Ahem, DC motors are not synchronous machines.

 

[artis]

yup my bad in DC there is nothing to be synchronous about, I guess the correct term for them is series universal motor as they all have commutators and can run on both AC and DC.

 

[essenmein]

yup my bad in DC there is nothing to be synchronous about, I guess the correct term for them is series universal motor as they all have commutators and can run on both AC and DC.

Heh, and universal motors are the odd ball wrt to speed torque curve as well, they are hilariously non linear, and everything about voltage, speed and current you thought you knew with "normal" machines goes out the window.

 

[artis]

well one thing I know in the midst of the night about them is that they have IIRC the highest starting torque of all electric motors , and they are dirt cheap and simple in design so all power tools use them.
Now that I think about it I am not sure how and what changes in this type of motor if used on AC and again voltage/current is kept constant but frequency is increased, given they are series wound I would say that the rpm can only be influenced by strength of the B field which is itself proportional to current through the motor which is then determined by voltage applied, as far as I know these motors are in the simplest case controlled by voltage.
but then again the commutator at high rpm's is like a switch mode supply of sorts right? so the back emf becomes larger the higher the rpm's go so torque should decrease with increased rpm

 

[essenmein]

well one thing I know in the midst of the night about them is that they have IIRC the highest starting torque of all electric motors , and they are dirt cheap and simple in design so all power tools use them.
Now that I think about it I am not sure how and what changes in this type of motor if used on AC and again voltage/current is kept constant but frequency is increased, given they are series wound I would say that the rpm can only be influenced by strength of the B field which is itself proportional to current through the motor which is then determined by voltage applied, as far as I know these motors are in the simplest case controlled by voltage.
but then again the commutator at high rpm's is like a switch mode supply of sorts right? so the back emf becomes larger the higher the rpm's go so torque should decrease with increased rpm

Yup, since these motors are series machines they do behave quite differently. Since both the excitation and torque producing currents are the same (being connected in series) means that at any speed everything is dependent on everything... lol

If you look at the one extreme, locked rotor (ie starting torque), zero BEMF, current is only limited by DC resistance of field and armature winding => large currents in both the field and armature = many torques.

As speed increases, BEMF rises, current for both the field and armature go down, now your field is weaker and armature currents are lower meaning less torque.

So as speed increases, these machines reduce their field naturally, creating less BEMF, therefore allowing more speed.

The theoretical upper speed is actually only limited by friction and windage, well, and mechanical integrity, but basically independent of voltage, due to their self field weakening property.

So at a fixed voltage, speed will change dramatically with load...