Brain Teaser:

[rattus]

Consider an ideal single phase alternator driving an ideal inductor.

How much torque is required to drive the alternator shaft in the steady state??

 

[winnie]

The problem with 'ideal' is that different people will define various aspects of the inductor as part of 'ideal' and others will call them flaws.

For 'ideal' I would ignore resistance, and ignore core saturation. I would also ignore bearing friction and windage of the rotor. However I would not ignore things like the speed of light nor the permeability of free space.

With this in mind, the average torque would be slightly greater than zero. The torque would pulse positive and negative at twice the AC frequency, as energy was stored and retrieved from the inductor magnetic field, and a very small amount of average torque would be required to make up for the electromagnetic radiation produced by the changing inductor magnetic field.

-Jon

 

[bcorbin]

Maybe you should stipulate "the alternator and the inductor occupy their own, infinte and otherwise empty universe." Then the answer would be zero. :grin:

 

[rattus]

I mean Ideal:

I mean Ideal:

The problem with 'ideal' is that different people will define various aspects of the inductor as part of 'ideal' and others will call them flaws.

For 'ideal' I would ignore resistance, and ignore core saturation. I would also ignore bearing friction and windage of the rotor. However I would not ignore things like the speed of light nor the permeability of free space.

With this in mind, the average torque would be slightly greater than zero. The torque would pulse positive and negative at twice the AC frequency, as energy was stored and retrieved from the inductor magnetic field, and a very small amount of average torque would be required to make up for the electromagnetic radiation produced by the changing inductor magnetic field.

-Jon

Winnie, "ideal" means exactly that, no resistance, no hysteresis, no eddy currents, no friction, no windage, no radiation. In other words, it behaves exactly like the math says.

Then, the average torque would be zero.

Now what if we had an ideal three-phase alternator driving three identical ideal inductors?

 

[bcorbin]

Hmmm.....I still say zero, since the three identical inductors could be expressed as a single inductor three times the size. I think the key here is "steady state".

 

[rattus]

Hmmm.....I still say zero, since the three identical inductors could be expressed as a single inductor three times the size. I think the key here is "steady state".

You are missing a key point here.

 

[winnie]

Not only will the _average_ torque be zero, but the instantaneous torque will also be zero at all times.

In the single phase example, sometimes power would flow from the alternator to the inductor, and sometimes from inductor to alternator, so the alternator will sometimes have positive torque and sometimes negative torque. In the three phase example, the different phases will source or sink power at different times, so that the net torque for all three phases is always zero.

Note I still have a terminology quibble on the term 'ideal inductor'. You are saying that an ideal inductor is something that follows the math of V = di/dt. I agree that this is a very common use of the term. However I believe that since inductance is based in the magnetic properties of current flow, one could reasonably include the magnetic field of the inductor, and the mathematics of that magnetic field, as part of an ideal inductor.

-Jon

 

[rattus]

I believe he has got it!

I believe he has got it!

Yep, instantaneous power in a balanced three phase system is zero, therefore the instantaneous torque would be zero as well.

Winnie, the teaser said "ideal", not "almost ideal". And, I am the teaser today.

The concept of an ideal circuit element is quite useful in describing basic concepts. Of course such elements do not exist, but that is not the point. The point is that we wish to simplify the example to get a point across without getting mired in messy details.