Droop control (load sharing in AC Mains distribution networks)

[tim9000]

Hi,

I have quite a superficial understanding of Droop control:

http://www.openelectrical.org/wiki/index.php?title=Droop_Control

https://en.wikipedia.org/wiki/Droop_speed_control

I'm not after a super technically detailed explanation, but if anyone has any more detailed sources for how it is actually implemented then I'd be interested.

On a side note/question, is it fair to say that the swing equation describes transient stability:

https://en.wikipedia.org/wiki/Swing_Equation

But that droop control is used to govern dynamic stability?

Cheers

 

[jim hardy]

On a side note/question, is it fair to say that the swing equation describes transient stability:

https://en.wikipedia.org/wiki/Swing_Equation

But that droop control is used to govern dynamic stability?

Cheers

To fully answer that question is a very nontrivial undertaking .

Briefly
no, the droop is to control steady state load sharing between all the machines on the system .
So long as your system has enough inertia and the interconnections are 'stiff' stability happens naturally.
'Stiffness' is a function of impedance in the interconnections, megawatts per degree of power angle as explained in @anorlunda's insights article.
When its electrical 'stiffness' gets low enough damping comes down and low frequency oscillations commence. I've seen them at 2/3 hz.
Droop likely actually will make them worse.

There exists a device called "power system stabilizer" that detects mechanical rotor speed changes at power system natural frequency and tweaks excitation to damp them out. So far as i know they're below 1 hz.

try
http://www.e2psi.com/index.php?s=135
http://www.meppi.com/Products/GeneratorExcitationProducts/Static%20Excitation%20System/Power%20System%20Stabilizer.pdf
http://ethesis.nitrkl.ac.in/3683/1/DESIGN_OF_POWER_SYSTEM_STABILIZER.pdf

This is different subject than "sub synchronous resonance" . Anything that affects power is dangerous if it approaches natural frequency of turbine rotor or blades. Our turbine rotor's fundamental for torsional oscillation was 7 hz and very lightly damped. It is important that the excitation system be incapable of participating in a closed loop at those frequencies which so far as i know are in the 'several hz' region. A Westinghouse generator guru once told me "Nothing above 1 hz ever."

This book has a good reputation in the power systems community
https://www.amazon.com/dp/0471862061/?tag=pfamazon01-20

 

[tim9000]

Yeah steady-state, that's sort of what I meant. As far as I know it goes:
sub-transient, transient, dynamic, steady-state. So that end of the time scale.

I got a chance to take a quick look at the e2psi and Mitsubishi papers, I found the Mitsubishi one very interesting, unfortunately I don't remember Control theory that well so I didn't absorb as much as I would have liked to. I'm going to try to read through the third one (the thesis one) tomorrow.

This is different subject than "sub synchronous resonance" . Anything that affects power is dangerous if it approaches natural frequency of turbine rotor or blades. Our turbine rotor's fundamental for torsional oscillation was 7 hz and very lightly damped. It is important that the excitation system be incapable of participating in a closed loop at those frequencies which so far as i know are in the 'several hz' region. A Westinghouse generator guru once told me "Nothing above 1 hz ever."

This book has a good reputation in the power systems community
https://www.amazon.com/dp/0471862061/?tag=pfamazon01-20

I'll try to get access to the book, was there any specific excerpt you could upload? I'm quite interested but I have no idea how you would determine the natural frequency of a turbine blade. (So what it wobbles bigger and bigger until it breaks?) What was he referring to never being above 1 Hz?
What about the linear 'frequency Vs power' and 'voltage Vs reactive power', how is that implementation done in control measurement/feedback?

Thanks!

 

[jim hardy]

I'll try to get access to the book, was there any specific excerpt you could upload?

I'm not aware of its being online . My copy is buried in a box in the barn someplace.

I have no idea how you would determine the natural frequency of a turbine blade.

i don't either. It's a column in tension, stress is highest of course at the root where its entire mass is pulling away from the shaft. That's where they fail i think from fatigue as they wobble and after a surprisingly short time.
Of course a loosed blade wrecks the others as it exits the turbine. If it gets slung into the condenser it shears the tubes letting seawater into the system.

What was he referring to never being above 1 Hz?

Never allow any periodic change to excitation at > 1 hz.

What about the linear 'frequency Vs power

Governor measures speed and moves steam valves proportional to offset from 60 hz. All governors in a region have same %power vs frequency slope. Ours was around 3% Δ speed = 100% change in power. Most governors are electronic nowadays, ours was a hydraulic analog using a centrifugal oil pump as speed sensor..
That's local.

'voltage Vs reactive power', how is that implementation done in control measurement/feedback?

System wide , dispatch office sends raise-lower commands to the individual plants to control power flow around the system.
Since that would place a nuke plant under control of a computer instead of a licensed operator, dispatch of nukes is by voice over the radio.

What about the linear 'frequency Vs power' and 'voltage Vs reactive power', how is that implementation done in control measurement/feedback?

Locally the voltage regulator measures machine current and adjusts terminal volts .
Our system guys wanted machine voltage at high side of transformer to change 6% for 100% change in megavars. That's 6% droop.
Since the main transformer is something like 17% impedance, the var correction actually raises voltage instead of lowering it when lagging vars increase , so as to cancel out 11 of those 17% dropped across transformer.
Observe that makes it positive instead of negative feedback which changes the closed loop response of the machine. It becomes a lot more lively .

When studying excitation keep in mind that everything interacts and you have to consider them individually. It's a closed loop system and my alleged brain can only handle changing one thing at a time. old jim

 

[tim9000]

Hey Jim, thanks again

Yeah I was imagining the blades wobbling and snapping if they spun at some sort of harmonic that was destructive to them. But I really didn't envision the shaft being under tension, but I suppose it really would be.

System wide , dispatch office sends raise-lower commands to the individual plants to control power flow around the system.

I think I understand looking at the speed of the generator to determine how much more to increase the prime-mover, and so increase real power. H'mm, I've thought about this a little bit but due to my lack of experience with generation I don't see the connection between reactive power droop in one plant and the rest of the network. I was thinking they'd just change the excitation current on the rotor of the generator. However from that picture with Volts on the y-axis and Q on the x-axis (http://www.openelectrical.org/wiki/index.php?title=Droop_Control) I don't actually know which they mean to be the independent variable for the 'droop control' anyway...

Locally the voltage regulator measures machine current and adjusts terminal volts .
Our system guys wanted machine voltage at high side of transformer to change 6% for 100% change in megavars. That's 6% droop.
Since the main transformer is something like 17% impedance, the var correction actually raises voltage instead of lowering it when lagging vars increase , so as to cancel out 11 of those 17% dropped across transformer.
Observe that makes it positive instead of negative feedback which changes the closed loop response of the machine. It becomes a lot more lively .

I'd better start my line of inquiry by just coming clean: '17% impedance', really daft question, but 17% of what? (I'm interested in pursuing the meaning of that paragraph deeper)

It is important that the excitation system be incapable of participating in a closed loop at those frequencies which so far as i know are in the 'several hz' region. A Westinghouse generator guru once told me "Nothing above 1 hz ever."

Never allow any periodic change to excitation at > 1 hz.

My 'Automatic Control' is pretty rusty, I remember a tiny-wee bit about closed loop transfer functions/ poles & zeros...negative feedback is 'like the error on the output...or something'. So positive feedback tells how to react 'where you want to go' rather than the error? (so there is larger amplification of response? I remember like integrating could cause over-shoot, but I assume this is not related to a specific function) I don't ever remember seeing a positive feedback loop.
Could you maybe elaborate on what the difference is and why it is so important the excitation system be incapable of participating in a closed loop at those frequencies? (If you have the time)

As always, cheers!

 

[jim hardy]

I really didn't envision the shaft being under tension, but I suppose it really would be.

torsion ?

I don't see the connection between reactive power droop in one plant and the rest of the network. I was thinking they'd just change the excitation current on the rotor of the generator. However from that picture with Volts on the y-axis and Q on the x-axis (http://www.openelectrical.org/wiki/index.php?title=Droop_Control) I don't actually know which they mean to be the independent variable for the 'droop control' anyway...

Yes you control vars by excitation which is field current. There's droop in the voltage regulator just as in the governor to the end of making machines share reactive load, megavars.

I don't actually know which they mean to be the independent variable for the 'droop control' anyway...

Per the graph in your link, for voltage control, voltage is independent and for power it's speed setting.

17% impedance', really daft question, but 17% of what? (I'm interested in pursuing the meaning of that paragraph deeper

You remember Per Unit method
17% Per unit . It's the transformer impedance. 100% load change causes 17% voltage change .

why it is so important the excitation system be incapable of participating in a closed loop at those frequencies? (If you have the time)

If you get a sustained oscillation a natural frequency of blade wobble or at natural frequency of shaft torsional oscillation you are into mechanical engineering's cyclic fatigue territory.

 

[tim9000]

torsion ?

yes, apologies; thanks. Although I suppose there would also be a little bit of tension too :p

Yes you control vars by excitation which is field current. There's droop in the voltage regulator just as in the governor to the end of making machines share reactive load, megavars.

I need to research why V&Q and P&f are related, I can't remember; Similarly I remember that PV was a generator bus, PQ was a load bus and V&angle was the swing bus, but I can't remember the significance.

You remember Per Unit method
17% Per unit . It's the transformer impedance. 100% load change causes 17% voltage change .

Ah yeah, I did that a fair bit once upon a time, like Z_base=V_base²/S_base, V_{pu_old}*V_{base_old} = V_{pu_new}*V_{base_new} sort of thing.
Putting that back into real-world quantities, so the transformer has real inductance and pri&sec coil resistances, is this just a conversion of those?

If you get a sustained oscillation a natural frequency of blade wobble or at natural frequency of shaft torsional oscillation you are into mechanical engineering's cyclic fatigue territory.

I have no trouble imagining so, but I never considered that you'd have to take that into account when designing your feedback system for power stability, how enlightening. So it's got a frequency on which if it...spins at? Then it can fatigue? And you need to make sure the PSS avoids that?

 

[jim hardy]

is this just a conversion of those?

yes.

So it's got a frequency on which if it...spins at? Then it can fatigue? And you need to make sure the PSS avoids that?

imagine two flywheels connected by a limber shaft. Stationary. Lock one in a vise and rotate the other one so it turns a couple degrees as the shaft twists. Now release it and shaft will untwist , overshoot the other way, go into a damped torsional oscillation.
Same thing could happen if it were rotating at synchronous speed, one end rocks ahead and behind with respect to the other..

In early seventies as a favor to Westinghouse we built a shaft torsion meter to measure steady state angular displacement between the ends of our turbine shaft.
It twists 3.2 degrees from no load to full load as turbine applies torque an generator absorbs it.
Our meter had a big dial indicating degrees, -2 to +6 i think, and it turned the DC displacement signal into an FM frequency tone . We hooked that tone to a tape recorder in the plant that captures electrical transients (this was maybe 1974 or 5.)
We waited for an electrical trip and within a few months captured one.
The shaft unwrapped from +3.2degrees to quite a bit negative and decayed with a prominent 7hz fundamental and some other frequencies visible.
We made a trace of the event on the recording equipment of the day, a Honeywell Visicorder light beam galvanometer oscillograph (if anybody remembers those monsters ...)
We sent that trace to Westinghouse who phoned to thank us , it verified their calculations.
One stage of very big blades also had a fundamental of 7 hz.

So 7 hz is a deadly frequency for that turbogenerator.

You need to make sure it doesn't happen.
Early attempts at some sort of capacitive compensation for long transmission lines made the generator and line resonant at shaft natural frequency and snapped the turbine shafts. Look up Sub Synchronous Resonance. You might find papers by Chester Raczkowski who figured that one out.

old jim

 

[jim hardy]

see also https://www.physicsforums.com/threads/damping-in-generators.741644/

 

[tim9000]

yes. imagine two flywheels connected by a limber shaft. Stationary. Lock one in a vise and rotate the other one so it turns a couple degrees as the shaft twists. Now release it and shaft will untwist , overshoot the other way, go into a damped torsional oscillation.
Same thing could happen if it were rotating at synchronous speed, one end rocks ahead and behind with respect to the other..

In early seventies as a favor to Westinghouse we built a shaft torsion meter to measure steady state angular displacement between the ends of our turbine shaft.
It twists 3.2 degrees from no load to full load as turbine applies torque an generator absorbs it.
Our meter had a big dial indicating degrees, -2 to +6 i think, and it turned the DC displacement signal into an FM frequency tone . We hooked that tone to a tape recorder in the plant that captures electrical transients (this was maybe 1974 or 5.)
We waited for an electrical trip and within a few months captured one.
The shaft unwrapped from +3.2degrees to quite a bit negative and decayed with a prominent 7hz fundamental and some other frequencies visible.
We made a trace of the event on the recording equipment of the day, a Honeywell Visicorder light beam galvanometer oscillograph (if anybody remembers those monsters ...)
We sent that trace to Westinghouse who phoned to thank us , it verified their calculations.
One stage of very big blades also had a fundamental of 7 hz.

So 7 hz is a deadly frequency for that turbogenerator.

You need to make sure it doesn't happen.
Early attempts at some sort of capacitive compensation for long transmission lines made the generator and line resonant at shaft natural frequency and snapped the turbine shafts. Look up Sub Synchronous Resonance. You might find papers by Chester Raczkowski who figured that one out.

old jim

fascinating story.
When you said it decayed with a 7hz fundamental, what sort of electrical trip? Staying with the two fly-wheel analogy I'm trying to picture what was actually 7 hz in the torsion of the shaft. (I'm trying to understand what between prime-mover and load could cause a torsion oscillation)
So any multiple of 7 Hz variation between the two fly-wheels was the like being at natural frequency?
Thanks

 

[jim hardy]

you're very kind. I know my anecdotes are boring. Just trying to help you visualize it with same thought process that led me into it..

The turbine blades apply torque in direction of rotation to the shaft along its length perhaps eighty feet

generator applies opposing torque and it's perhaps fifty feet long

there's your two major moments of inertia distributed along the shaft and the natural frequency was 7 hz.

what sort of electrical trip?

a generator trip opens the high side circuit breakers immediately zeroing generator torque so the shaft unwraps immediately. (Of course the steam valves get snapped shut to remove turbine torque so it won't overspeed.)

A turbine trip snaps the steam valves shut but torque falls off over a few seconds as steam that's already in the turbine makes its way on through turbine to condenser. Turbine trip waits thirty seconds before opening generator breakers so machine won't speed up at all.
So the shaft unwraps slowly.

Generator trip is a step change to torsion, turbine trip is gradual. That's why Westinghouse asked us if we would capture an electrical trip for them.

So any multiple of 7 Hz variation between the two fly-wheels was the like being at natural frequency?

A sympathetic vibration at a shaft or blade natural frequency can hurt a machine.

 

[tim9000]

Don't put your anecdotes down.

there's your two major moments of inertia distributed along the shaft and the natural frequency was 7 hz.

I'm clear with everything up to that. Because isn't a moment of inertia a value, not a periodic function?

a generator trip opens the high side circuit breakers immediately zeroing generator torque so the shaft unwraps immediately.

Ah okay, so the generator output almost stops drawing current as a step-function. But I've never heard the term 'unwrap'ped in that context, what do you mean by it? So the turbine trip is gradual, so there is torque being put on the on the shaft as the generator instantly removes it. So does this make like a decaying 7hz oscillation on the shaft? My hypothesis: So the shaft at the generator end slows down, the shaft goes into some some torsion, maxes at some slower speed, then starts speeding up back the other way and overshoots, speeding up to be faster than the turbine end, then maxes and starts spinning back the other way relative to the turbine end (still rotating but now slower then the turbine end), and repeat, as it decays?

P.S; Jim: I take it the data results I send you in the last email was satisfactory (what I would expect to happen in a working design for my idea)?

Thanks

 

[jim hardy]

P.S; Jim: I take it the data results I send you in the last email was satisfactory (what I would expect to happen in a working design for my idea)?

i'm still trying to sort that out

but it looks like you're right, phasor addition is as expected and i don't see drastic amplitude mismatch. The small mismatch is curious though.

Now in a generator there's no primary, excitation is of course from the rotor
you can rewire it zigzag and get single phase, as you're doing with transformers
each winding has same current and VA all right but total kva out becomes VlineX Iline not Vline X Iline X √3 .

Glad to see you tinkering with 3 phase. It's kinda fun. I'm looking forward to learning about my wound rotor with 3 slip rings. Hoping that hurricane headed for Florida doesn't flood it with seawater.

old jim