Really quick Droop control question

[tim9000]

Hi,
I just want to double check my understanding of Power angle.
Say you have a large network, and you have a bus with a small generator and a larger load on it.
For power to be going into that bus from the rest of the network there has to be power angle between the bus and a bus(s) which power is flowing from. The implication for the small generator being that it's speed has drooped down lower/slower then synchronisation? So that means that for that generator the angle between the stator electromagnetic field (which is presumably still grid synchronous frequency) and the rotor mechanical angle, is greater than 90 degrees? So if this was a isolated generator and load then I presume that it would be slipping poles etc? But because this is part of a network that is that not the case and it just droops slower a bit and power flows?
Cheers!

 

[jim hardy]

For power to be going into that bus from the rest of the network there has to be power angle between the bus and a bus(s) which power is flowing from.

at steady state it's a constant angle, just like twist in the drive shaft of your pickup truck or rear drive car.

The implication for the small generator being that it's speed has drooped down lower/slower then synchronisation?

only long enough to establish that angle.

So that means that for that generator the angle between the stator electromagnetic field (which is presumably still grid synchronous frequency) and the rotor mechanical angle, is greater than 90 degrees?

Whatever gave you that idea ? Re-ead Lavoisier

So if this was a isolated generator and load then I presume that it would be slipping poles etc?

Slipping poles ? There's nothing to slip against, the isolated generator completely determines voltage. You flipped from generator in a network to generator isolated and tried to apply the same words. Think about the machinery not the prose.

But because this is part of a network that is that not the case and it just droops slower a bit and power flows?
Cheers!

not slower, runs same speed just lagging behind.
That's the same mistake James Fenimore Cooper made in "Last of the Mohicans", chapter 'Adam Helmer's Run' (from hostile Indians)
Author wrote that the Indians chasing Adam took turns running right behind him while the others kept some constant distance behind, allowing them to run slower yet keep up. Mark Twain lambasted him mercilessly for that basic physics error.

 

[anorlunda]

I think it is easiest to visualize when you think about rates of change rather than absolute quantities.

1. The rate of change of generator speed (and thus frequency) is proportional to the mismatch between mechanical power and electrical power.
2. The rate of change of angle is proportional to the mismatch between frequency and grid frequency. In the USA think of grid frequency fixed at 60 hertz.
3. Electrical power is proportional to angle. Feed this back to step 1)

The absolute quantities the OP asked about come from solving these equations when all rates of change are zero.

The double integration with a feedback creates an oscillator. Indeed, when you make any change, the frequency, angle, and power all swing a lot before settling down. That is why we call these the swing equations.

Does anyone agree with me that expressing it this way makes it easier to understand?

 

[jim hardy]

Does anyone agree with me that expressing it this way makes it easier to understand?

Yes.

Any system with a displacing force and a restoring force is capable of simple harmonic motion

Grid is a multi node torsional spring-mass system rotating at synchronous speed.
When we add to it automatic voltage regulators that change the megawatts per degree coefficient of the generators , well,,,, that has to be added to the equations of motion.

 

[tim9000]

Whatever gave you that idea ?

Slipping poles ? There's nothing to slip against, the isolated generator completely determines voltage. You flipped from generator in a network to generator isolated and tried to apply the same words. Think about the machinery not the prose.

The premise in my mind which I am struggling to move on from is: the torque angle in the generator is what changes depending on how much the load is, not the speed/frequency. I didn't think I was thinking in Prose, but maybe I am. Maybe a mistake that I'm making is that I'm imagining that running a synchronous motor with a torque load is the same as running a synchronous generator with an electrical load, maybe they're not the same thing? So in that case as the torque required of the motor gets bigger the torque angle gets bigger. Similarly, I was imagining that as the load on the synchronous generator gets bigger (more current drawn). For example imagine a network of generators and loads on buses and focus on one bus in particular that has a generator and load on it. As that electrical load gets bigger the generator would have it's torque angle grow (and slow the prime mover down as it does) also the electromagnetic synchronous rotary speed in the winding would stay the same as the rest of the network...but are you both implying that it doesn't? That in fact when the electrical load on the synchronous generators grows and the torque required to maintain the same frequency grows, that it isn't the torque angle that grows, it stays in lock-step with the electromagnetic speed which slows down (changing the frequency)?
@anorlunda Because I was imagining that when the frequency is slower than synchronous or changing to slow down, then the torque angle is growing inside the generator, and as the frequency is mismatched that the torque angle would just keep growing, until it started slipping poles.Otherwise what I was saying last time which @jim hardy , I didn't articulate correctly, was that it decelerates (for a short time) creating greater torque angle, then stops decelerating and continues at the synchronous speed. So to create the a brief frequency droop which creates the voltage angle? So in this case the voltage angle and the torque angle would be the same thing?Thanks for the helpful replies, I'll keep deceleration in mind, I just re-looked at the Swing equation to refresh myself a little bit.P.S.
Jim, have you had a chance to look at that email yet? Cheers

 

[jim hardy]

Otherwise what I was saying last time which @jim hardy , I didn't articulate correctly, was that it decelerates (for a short time) creating greater torque angle, then stops decelerating and continues at the synchronous speed.

That's exactly right.

What confuses me is terms voltage angle and torque angle.
I am accustomed to watching a stroboscope shine on the turbine shaft , strobe plugged into a wall outlet so it's synched to machine terminal volts. The rust spots and keyway stand nearly still , shifting about slightly as the system "breathes" ( as you know i consider it a living thing) .
What you described is exactly what you see. The machine pulls ahead or drops behind when load changes, also when excitation changes, and I always called it "Power Angle" . It'll hunt a bit at ~1hz as amortisseur windings damp out a change in power angle.
So those two terms are undefined to me and the mental picture I'm trying to paint from your words falls apart.

 

[jim hardy]

synchronous motor with a torque load is the same as running a synchronous generator with an electrical load, maybe they're not the same thing?

motor can get out of step with terminal volts.
Generator connected to a robust voltage source like a big bus can get out of step with it.

Generator connected to just a load like lamps has complete control of the voltage so there's nothing for it to get out of step with. It can slow down, speed up, and that determines frequency . It'll have a power angle but since synchronous impedance between internal voltage and terminals is reactive it can't exceed 90 degrees. X_Lshifts voltage 90 degrees no more.

 

[tim9000]

Rather than saying too much I'll keep it simple at this stage.
As far as I'm aware: the torque angle is between the synchronous stator winding magnetic field and the magnetic field of the rotor.
And the voltage angle is the difference between voltage peaks between buses, which I think is the same thing as the power angle.

I don't know exactly how long it takes for the torque angle to reach 90 degrees, but I wouldn't think long at all, so that means that you'll never have a situation (under normal operation) where one bus frequency is 4% slower than the rest of the network for more than a few fractions of a second (that order of magnitude), that 4% slow down is a very brief thing?

So mathematically (measurably in practice) the torque angle of the generator (on the imaginary bus) and the power angle of the (imaginary) bus to the rest of the network, is/are the same value?

P.S.
Jim, have you had a chance to look at that email yet? Cheers

I'm pretty eager to hear if you think it's a good idea or not.

 

[jim hardy]

don't know exactly how long it takes for the torque angle to reach 90 degrees, but I wouldn't think long at all, so that means that you'll never have a situation (under normal operation) where one bus frequency is 4% slower than the rest of the network for more than a few fractions of a second (that order of magnitude), that 4% slow down is a very brief thing?

It's brief. generator protection relays will disconnect it on "out of step" to prevent slipping a pole. That torque reversal is violent.

So mathematically (measurably in practice) the torque angle of the generator (on the imaginary bus) and the power angle of the (imaginary) bus to the rest of the network, is/are the same value?

Power angle of a generator is between its rotor and its terminals due to Z_synchronous.. If you connect its terminals directly to a stout bus that's one angle.

If there's angular displacement between that bus and "the rest of the network" , that's another angle dependent on impedance . between them.
Are the impedances equal ?