|Jan26-12, 06:52 PM||#1|
Synchronous Generator ( again )
So I decided to take a brake from electronics, and get back to physics of synchronous machines, or alternators if you will.
A great deal of help was mr. jim hardy, trying to explain the alternator in the intuitive way. And so he succeed. I got the basics right. Now I want to tackle some more physics about it.
So we have a stator and a rotor.
all flux or mmf
I believe that this represents the rotor, but "unwrapped"?
I want to talk about torque angle.
The picture shows the case where we have a resistive load. This means current will produce a field exactly pi/2 ahead of the rotor field, am I correct?
This means that the field of the rotor is always perpendicular to the field of the stator?
Does this mean that the δ=pi/2? Or the torque angle?
is the torque angle, the angle between, rotor field and the RESULTING field?
I have tons of more questions, but lets settle this for now.
|Jan26-12, 08:50 PM||#2|
i hope i understand the question -
and i think it stems from the derivative relationship between flux and voltage.
well, start your thinking from open circuit
in which case your sketch shows machine at instant of voltage zero crossing.
in absence of armature reaction (no armature current)
there's no armature MMF
the stator field IS the rotor field;
so torque angle is zero.
when resistive current begins to flow
there appears a MMF component due to armature reaction
which is perpendicular to rotor field
(remember voltage is derivative of flux and d[itex]\Phi[/itex]/dt is zero at the poles, max between poles);;
so instant of max voltage is 90 deg from your sketch and so will be resistive load current peak,
so armature reaction MMF will be 90 deg from rotor MMF
so armature reaction adding in a perpendicular MMF rotates total field relative to rotor
so we begin to develop a torque angle between rotor and total field.
you can watch this with a stroboscope synched to terminal volts(total field) and shined on the shaft keway..
now, were armature current 90deg out of phase with terminal volts
the armature MMF would be aligned with rotor not perpendicular
so there'd be no rotation of total field
hence no torque angle
which meshes up nicely with observations that reactive current neither transfers electric power nor produces torque..
here's another writeup
|Jan27-12, 04:21 AM||#3|
When do we say that the machine is in synchronism? When the torque angle is 0, I assume nothing happens then.
But I was told that when mechanical torque equals electrical torque, we are in synchronism?
Is this correct?
And isn't this dangerous? If we have a very big torque angle, don't we have big torque?
Lets say that the prime mover is spinning the machine clockwise. Mechanical torque would be then clockwise.
But we have a electric torque, which is in opposite direction. Doesn't this tend to twist the shaft of the rotor?
|Jan27-12, 08:14 AM||#4|
Synchronous Generator ( again )
i'm embarassed, made a mental mistake unwrapping the machine to match your drawing will correct that.
re your question ""Doesn't this tend to twist the shaft of the rotor?""
quick answer -
yes the torque twists the shaft that's why it is stout steel
the torque is in proportion to electrical power generated
in my English units it is:
horsepower = 2 X pi X torque X rpm / 33,000
and it's pretty apparrent that the 33000 units converter term comes from 60 sec/min (accounts for rpm ) X 550 ft-lbs/sec (one hp=550ftlbs/sec)
now the generator rotor is pretty stout
on our big turbine we measured the twist.
going from zero to full power , about one million horsepower, it twisted 3.2 degrees , mostly in the steam turbine.
whole thing probably 150 feet long
as i said in another post, torsional oscillation is possible
turbine shaft had a resonant point at 7 hz and the damping was very light
so that is a frequency to be avoided in any electrical load connected to generator.
if you google "subsynchronous resonance" you can find tales of broken turbine shafts.
there's also a torsional resonance of the whole machine's inertia against the electric grid, 1 hz typical for steam turbines
i dont know what windmills would be. Hopefully not close to any blade or tower natural frequency.
|Jan27-12, 09:44 AM||#5|
Any thoughts here mr. jim?
|Jan27-12, 09:51 AM||#6|
no power out, torque equal zero (well there's windage but we are thinking of torque from magnetic effects).
Electrical power out and it's a generator torque opposes rotation;;
electrical power in and it's a motor torque aids rotation.
that agrees with the fellow's formula torque = K sin (torque angle) - zero at zero, + for positive angle and - for negative angle , unlike cosine.
note for an isolated machine there's nothing for it to be in synch with so the term is meaniingless then
when there's an external voltage like the grid which is far more powerful than our prime mover, we are locked into synch with the stator field by the magnetic torque.
we are not big enough to change the grid speed much, can only pump energy into it or extract energy from it at fixed speed of the grid.
so all the generators on a grid are spinning in unison with only small differences in their torque angle.
IF a machine ever gets past the 90 degree torque angle, note torque drops off again (sin function) and it will accelerate. When sine goes negative it becomes a motor and tries to pull back into synch, toward zero torque angle.
this is a very violent maneuver both electrically and mechanically and breaks things.
were torques unequal their difference wouldn't their difference accelerate machine , torque/moment of inertia?
these torques are very real and well behaved betwen -90 and +90 degrees.
what makes it click for me is this thoought experiment:
stop everythiing in your mind and de-energize the machine..
remove the rotor from the machine so you have a hollow cylinder with 3 phase windings surrounding it. You're looking down the axis of the cylinder.
place a child's compass in the center of the cylinder.
Apply some DC current through one phase of the stator. Will the compass align with that phase?
Now swap your DC current to the next phase. The compass will follow.
And so on.
You could make the compass spin by switching currents in sequence phase A, B, C.
Tesla figured out that by applying sinewaves to phases A, B, C he'd get a resultant magnetic field that rotated and didn't pulsate,
which was very handy for a motor.
If he put a strong electromagnet in the cylinder it would follow the rotating field
just like the child's compass
and if he put a squirrel cage rotor in there it would get currents induced in it that made it follow the rotating field albeit at slightly slower speed. Hence slip of induction motors.
SO if you took an induction mtor and placed inside its rotor a strong permanent magnet,
it would start and accelerate to near synchronous speed on the induction principle and when slip got low enough the permanent magnet would grab the rotating field and follow it driving slip to zero.
might you remember the old Garrard Synchro-Lab turntables of late 1950's ? (oops probably not)
look up "amortisseur windings on alternator"
|Jan27-12, 10:02 AM||#7|
Take 1 bicycle. Put it upside down. Spin the front wheel very hard. The wheel would continue spinning for a long time, due to low friction and in ideal world it would spin indefinitely Right?
This would represent, in my analogy a generator, operating with no load. So you have a prime mover turning the shaft, turning the rotor but its doesn't have any load, so no torque.
Now put your hand gently at the tire, and try to slow it down. Your hand would represent the load, and you would need POWER to continue spinning that wheel at the same speed it was spinning before.
So my load would be my hand. I would need power that comes from my prime mover, to overcome that torque.
This is something I came up with, to get me a little better navigation through all those powers and modes of alternator.
Is my analogy valid? Or am I completely off?
|Jan27-12, 10:04 AM||#8|
just saw your new post.
want to think on it so i dont embarass myself again.
When you get your two alternators try this
connect their stator windings in parallel
connect their fields in parallel and apply maybe 12 or 24 volts AC to the fields
now they think they're rotating in synchronism although they're standing still.
turn one and watch the other follow
turn one and hold the other, feel them transmit torque
if you do that experiment you've built something called a "Selsyn" , a widely used as position transmitter.
that should help your brain accept it. Tactile information takes a different neuron route into our cerebrum than does spoken or reading.
|Jan27-12, 10:09 AM||#10|
I think I just had an "aha" moment when you explained those rotor and stator currents.
There is a lot going on in this synchronous machine :(
But, nevertheless I am getting there.
|Jan27-12, 10:10 AM||#11|
|Jan28-12, 03:04 AM||#12|
in post #2
""in which case your sketch shows machine at instant of voltage zero crossing.""
should have said
"in which case your sketch shows machine at instant of voltage peak"
my bad, as noted earlier...
sorry about that.
haste makes waste.
|Jan28-12, 07:00 AM||#13|
|Jan28-12, 12:36 PM||#14|
when you can work the machine in your head, the equations are sure easier to remember.
Trouble is our mind can believe things that aren't physically possible
i have to keep on cross-checking my thought processes against each other, eliminating the ones that lead to impossible conclusions.
i have seen your fluency with equations and admire it.
you'll have success at whatever you choose to do.
The ability to swap back and forth between the math and the mechanics of something is a real valuable skill in industry. It allows you to communicate successfuly with audiences of vastly different educational levels.
|Jan28-12, 12:40 PM||#15|
I will on my final exam, ask from my professor, to draw me ANY situation of mentioned 6 (phasors) and I will have to tell if it is generator, motor, no load, under excitation, over excitation. I am getting very comfortable with synchronous machine.
Needless to say, without your guidance, I would be nowhere. Thank you.
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