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# Generator Power/Torque Angle

## Generator Power/Torque Angle

(OP)
Hello,

I am looking for some clarification on generator power/torque angle. I am asking for an explanation on how exactly kW output is increased/decreased. I am slightly confused as when you are synched to the grid how can you put out more/less power but still maintain constant 3600 RPM? I have a slight understanding of it being tied to operation of the steam valve but don't understand exactly what's going on behind the scenes.

-Thanks

### RE: Generator Power/Torque Angle

The rotor is held to the magnetic field by the magnetic flux.
Think of the flux as a rubber band.
As the load on the generator increases the rubber band stretches a little bit.
As more steam is admitted to the turbine, the rotor position advances a few electrical degrees in relation to the rotating magnetic field.
Too much load and the rubber band nay break.
In a generator the torque exceeds the strength of the magnetic field.
In a generator this is called "pole slip".
Torque transients, current transients, voltage transients.
Circuit breakers may be opening.
The grid sets the frequency or speed.
The rotor stays locked to the rotating field matched to the grid within a couple of degrees.
Induction generators are different.

Bill
--------------------
"Why not the best?"
Jimmy Carter

### RE: Generator Power/Torque Angle

waross pretty much nailed the intuitive explanation.

The definition of "rotor angle" is the electrical angle between the machine quadrature axis and the synchronous reference.

### RE: Generator Power/Torque Angle

Bill (waross) described it as a rubber band. We can flesh out why it acts that way...

Imagine you have a permanent magnet in an external uniform magnetic field. The torque on the magnet is
T ~ |Bmag| * |Bext| * sin(delta) where delta is the angle between them
when delta is 0, the torque is zero. As you increase delta, the torque increase. But only up to a maximum where delta=pi/2... at that point the torque suddenly reverses. That's like pulling on a rubber band, the further you pull the more the tension, until suddenly the band snaps.

Above is an experiment was set up in a stationary reference frame (other than slow change in delta).
Now consider it was only stationary relative to a synchronous rotating reference frame associtaed with the external field (everything moving together at that sync speed). You can substitute power for torque since P=T*w. The external field plays the role of the stator field, the PM plays the role of the rotor field. So now we see the physical interpretation of delta as an angle between rotor field and stator field.

Let's come at it from a completely different viewpoint. Setting aside machine theory for the moment, if you study the fast decoupled load flow approximation for power transmission accross an inductive branch in a network, then you can come up with something like:

P = |V1| * |V2| *sin(delta) / |XL|

where delta is the angle between vectors V1 and V2 and XL is the inductive reactance in the series branch between nodes 1 and 2.
(actually I think the FDLF may simplify sin(delta)~delta but that simplification is not needed here).

Apply this result to a steady state 2-element model of a sync generator as an internal ideal voltage with a series synchronous reactance. Then the angle between the internal voltage source and the terminal voltage is delta which is the power angle you're talking about. The angle between the voltages is the same as the angle in the fields in the previous analogy. This may be the roundabout way of looking at it, but sometimes it helps to look from multiple angles (no pun intended).

=====================================
(2B)+(2B)' ?

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