# Pelton turbine model when hydroelectric station works on grid

1. Apr 3, 2013

### vampslayer

Hi!
When my Hydroelectric station is not connected to a GRID (islanded mode)
I control the frequency or the speed, and here are the equations for my turbine:
http://oi46.tinypic.com/3127ixe.jpg
Look the third equation.
I built that in Matlab Simulink, and my out put is turbine speed n[o/min]
http://oi48.tinypic.com/1zqc3o5.jpg

That's all good. But now I want to make simulation model when my hydroelectric station is connected to the GRID.
In that case I control the Power and my speed is constant, f=50Hz so n=const.
So I need equations for that case, and If I look my third equation
dw/dt=(1/J)*(Mv-Mtr-Mt)
dw/dt=0(because speed is const) -> Mt=Mtr-Mv
So my equation in this case is Mt=Mtr-Mv ?
Mt is load torque and I think it should be my output if I want to control the power
Mv- is Torque developed on turbine blades(Torque of water)
Mtr - friction torque

I just want to check am I right about this guys?

2. Apr 3, 2013

### jim hardy

Your equation looks right to me, steady state output is equal to input minus friction losses.
Any torque imbalance goes into accelerating the machine, and you've locked ω at synchronous which is close to how they work in real world.

But I don't pretend to know a thing about Matlab.

Is your Matlab model stable?
Real generators have something called "Amortisseur Windings" to prevent small oscillations about synchronous speed, which are called "hunting".
They'd add to your torque equations a term proportional to ω-ωn , making Mt a function of ω.

But that's a refinement for quite a bit later on when you unlock ω to make your modelling more rigorous.

Have fun with this - it looks real interesting. I hope you'll continue the thread.

It is refreshing to see your progress and increasing confidence.
I look forward to learning from you !

old jim

3. Apr 3, 2013

### vampslayer

Ty Jim and I will continue threading, but I don't think you can learn a lot from me, I am just a student with no experience(just a lil bit in Matlab)
I'm not sure what do you mean about "Is your matlab model stable", but for beginning I will model my generator very simple Pgen=η*Mt*ω
and I will make feedback Pgen(that's when I control the power).

This is my turbine model when I control the power(based on the equations in the first post)
http://oi45.tinypic.com/fkqz2s.jpg

So let's see what should happen in a moment when I switch from OFF GRID mode to ON GRID mode and vice versa.
Right now, when I switch from OFF Grid to ON Grid Mode, the speed is const and Mt is rising until some value(I still don't have PID power governor, but I think here comes his functionality, power governor must keep this Mt or Pgen close to (Pref-reference value of Pgen)), but when I switch from ON Grid to OFF Grid, speed is rising and my PID speed governor must act.

4. Apr 3, 2013

### vampslayer

And Jim, what do you think about how I simulate the affect of generator in OFF GRID mode.
I did it as a load torque, Mt=P/ω(Turbine see Generator through load torque)
P- power which turbine gives to generator., and that Power should be equal to the power of what load is connected to the generator.
http://oi46.tinypic.com/3127ixe.jpg
look third equation.

What do you think about this at all?

5. Apr 3, 2013

### jim hardy

I said earlier I think it makes sense - you summed torques and calculated acceleration.
And I think it's correct for both ONGRID and OFFGRID.
Ahh, physics from first principles is beautiful !

I just meant is it hunting or oscillating...

Not quite sure I followed all that. If power(Mt ?) is settling out at some value it sounds like you're close.
If it's continuing to rise , that doesn't sound right.

Regarding your PID controller -

Our governor was not Integral, just P with some D.
It sensed speed by a shaft mounted centrifugal pump.
Pump discharge pressure was opposed by a spring and through hydraulic amplifiers controlled the steam inlet valves to maintain constant speed.
Spring force was the speed setpoint.
The spring was adjusted remotely by a knob in control room..
To control power you just adjusted the speed setpoint by compressing or releasing the spring a little bit.

It had gain of about 33% valve travel(steamflow) per % speed error.
So at synchronous speed and no load, speed setpoint was 100% of synchronous.
At synchronous speed and 100% load, speed setpoint was 103% synchronous.
......3% speed error X gain of 33 = valves wide open, full power at synchronous speed.
If you lose load, turbine accelerates, governor closes valves at rate of 33% valve travel per % speed error, so turbine would settle to 103% of 1800 RPM = 1854 RPM with valves (almost completely)closed.
That type governor control scheme is often called "Droop Control", ie power droops when turbine speeds up.

PID governors do exist and they'll hold speed at exactly synchronous due to their integral term. They are useful when islanded (off grid) to keep customers' electric clocks correct. In fact our switchboard had two wall clocks - one from a 60hz outlet and one a battery powered quartz. Integration to keep clocks correct would be done manually... But that's just a boring anecdote...
Point was - your PID governor will probably have to have limits else it'll call for more power than your source (water pipes) can deliver. Start with a simple proportional one.

I think the proper term for PID governor is "Isochronous", as in 'same time' as with the clocks. I never worked on one of those.

See if this helps you with governors, if not ignore it.

http://www.control.com/thread/1026221805

I hope i'm not just muddying things for you.

Your model looks like a lot of fun. I'm afraid to look into Matlab - I might get hooked.

6. Apr 3, 2013

### vampslayer

Actually this is what i get
Mt=Mv-Mtr=-Mtr
And why?, I think that's because Mv(torque of water is only acting when I use water to change speed)
When I switch to ON Grid mode(I still dont have power governor so its open feedback)
my speed feedback is not acting so Mv=0.

Of course when I add PID power governor Mv won't be 0

I will post my whole hydroelectric model Jim if you wish.
Matlab is good, and it should be very easy for someone like you, with experience

7. Apr 3, 2013

### jim hardy

I envy you, for your math is still fresh !

I don't understand... water acts on the wheel whenever it's admitted, even if the only opposing torque is friction - your Mtr.

So you need a minimum water flow just to overcome friction.
Any leftover torque goes into either load Mt, or acceleration dω/dt.

Now - if you shut off all water, the generator will spin the turbine by drawing power from grid. In which case yes, "load" becomes negative and equal to friction losses.

I guess I was thinking too much of normal operation and envisioning the machine. You never stood next to it and marveled at how that huge steel shaft can twist... and I never worked Matlab.

I think in pictures. So let me change my mental image for a moment and look harder at your equations forgetting the machinery.
Hmmm ( scratches head icon)
So I think now you are right, if water admission Mv is zero, then power Mt is equal and opposite to friction Mtr.
The computer has no idea whether there's a source for that power, it just reports the number to satisfy the equation. . . Of course - how silly of me ! That there's no grid from which to draw power is immaterial to that equation . This is a calculating engine not a steam engine !

Keep on please - i'll get the hang of this yet !

Sorry for so many words, but I am a plodder.

Seems you're doing fine.

old jim

8. Apr 4, 2013

### vampslayer

That's exactlly what I need, someone with real life experiences, and I hope one day I will work on a real stuffs and stand next to huge steel shaft and work on it.

No, no it's ok, you are explaining me a lot of things, and with this stuffs(power engineering) you must be ample.

So here is my whole model. I still didn't find the parameters for governors but I will. I learned in college year ago something about that, but we would have the transfer function of process, and it was in "s-domain(Laplace transform)"
http://tinypic.com/view.php?pic=35d50rl&s=6

I want to ask you now a lil bit more about this Pref(you can see on image). Who determines the amount of Pref? We are connected to the grid, so grid maybe? If grid needs X amount of power, to compensate its own needs(grid needs), then my Pref must be equal to X

Is this right?

Last edited: Apr 4, 2013
9. Apr 4, 2013

### SirAskalot

In a true system, Pref is set by the power company. That is, the amount of power the generator owner has bid into the pool for that hour/day etc. This amount depends on the market price (merit order).

First of all, what is the purpose of your simulations? Is it transient stability, steady state analysis, is it a generic or specific system you have in mind?

What your value of Pref should be depends on the purpose of the analysis. But true for most analysis the system should be in steady state at time=-0. So the input should equal the output.

As for the turbine governor controller, in most power plants connected to a regular grid, as mentioned, only proportional controlled (Kp) is used. Multiple integral controllers controlling the same system(grid) would make the system unstable. (every controller, hundreds of them, would try to oppose each other when a error/deviation occurs). The controller measures speed/frequency and acts on the error/deviation between the setpoint and measurement. That is Kp is the slope of the "droop" in a "house diagram". See this link:
http://www.ece.ualberta.ca/~knight/electrical_machines/synchronous/parallel/house.html [Broken]

When your system islands this will happen:
- First stage; Load torque will change causing a acceleration in the rotation, torque angle will oscillate and in response the power "produced" by the generator. This may cause the system to become unstable and trip the protection. Time duration: seconds to minutes.
- second stage; Turbine governor starts to react to the speed change trying to counteract the dropping/increasing frequency. Speed will settle to steady state with a lower or higher frequency than 50/60 Hz. Due to the lack of integral action. Time: several minutes. (water flow in a large hydro power plant(kaplan, francis turbine) cant change so fast due to momentum of the water in the piping. With pelton turbine this action can be faster due to the ability to shift the nozzle away from the turbine)
-third stage; System operator will change the setpoint (manually) to restore the correct frequency. Time:several minutes after the fault.

Last edited by a moderator: May 6, 2017
10. Apr 4, 2013

### SirAskalot

In your model:
The feedback/control of the output power to Pref is not a parameter that is usually controlled. The negative feedback should come from the speed/frequency of the system and subtract from the setpoint(50/60 Hz or xxxx rpm)

11. Apr 4, 2013

### jim hardy

Islanded (or "Off Grid") : You and your load ARE the grid. It's a local grid. So when you control frequency you are matching power generation to power consumption, if any. If none you're just supplying your internal losses.

"On Grid" : Much of your customer load is rotating motors which have inertia and a speed/power curve of their own. If total grid generation and use are mismatched speed will change just as with any other machine. Power mismatch will accelerate every rotating mass on the grid.
Normally one plant is not large enough to affect grid frequency, though. That's why we call it "Infinite Bus" and treat it math-wise as an immovable object..

------------------ some miscellaneous thoughts ----

as SirAskalot said, a central dispatch office tells you how much power he wants you to pump into the grid. That becomes your Pref. In my plant we set that Pref with the governor speed control knob that adjusts that spring I mentioned.

Here's a real world example of islanded:
My site had a fossil generator adjacent the nuclear plant. They shared a switchyard.
One foggy morning we lost all transmission lines out of the switchyard. There'd been a dry spell and insulators were loaded up with salt(the lines ran near the ocean), when the fog rolled in it moistened the salt and insulators started flashing over.

The nuke was shut down, I don't remember anymore if it tripped or we were in process of heating up.... But its internal consumption was forty megawatts.

The operators in the fossil control room saw load decrease to forty megawatts and thought something was awry upstate, so they raised their governor to try and send more power upstate.
Well - megawatts stayed at just about forty but frequency went up to 61 hz.
So they tried again. At 62 hz with generation still ~ forty megawatts, they realized what had happened and held frequency there. I was in the nuke plant and noticed our reactor flow was up to nearly 103%. All the pumps had sped up, of course.

So we were a small grid unto ourselves, one plant generating and one consuming, where obviously the one and only generator WAS large enough to change grid frequency.

Boring anecdote I know, I relate it only for the purpose of helping you visualize this machinery.
When you can work it 'in your head' you will have more faith in your equations.
At least that's what I have to do. When I can resolve the math with a mental model I feel more confident.

The governor on a steam turbine is fast - the steam inlet valves can travel full stroke in ~ one tenth of a second.
I would think a hydro plant must have turbine bypass valves so a sudden load rejection and inlet valve closure doesn't cause a hydraulic ram effect that'd wreck the inlet pipes..

I hope you become interested in power systems, they're interesting.
I was just a curious plant instrument guy who looked into the power system through a very small window. I don't have power system expertise, just worked around some folks who did.

old jim

12. Apr 4, 2013

### dlgoff

If I can jump into this very interesting and informative thread for a minute, ...

The North American Electric Reliability Corporation (NERC) has a publication that fits into this thread that's "intended to explain the concepts and issues of balancing and frequency control." BALANCING AND FREQUENCY CONTROL to ensure the reliability of the bulk power system

Here are a few visuals/pages.

https://docs.google.com/viewer?pid=bl&srcid=ADGEESiI-TizqsV0cRjlLirKA_z0t7Sg1hsteOk29JX1Wu0LfXIVlhJpJXOHR3xtC-FcAieRSp3uPaWhZbrgB2wXGtf-CIHmzaHG9olSaaRKDfbNbS1tk97WA-HtdGK_7DVaZBw_hV9j&q=cache%3A_-4EPn3Ba8kJ%3Awww.nerc.com%2Fdocs%2Foc%2Frs%2FNERC%2520Balancing%2520and%2520Frequency%2520Control%2520040520111.pdf%20&docid=b11d8c36a8eae7b4e95faf80431fd2a9&a=bi&pagenumber=7&w=891

https://docs.google.com/viewer?pid=bl&srcid=ADGEESiI-TizqsV0cRjlLirKA_z0t7Sg1hsteOk29JX1Wu0LfXIVlhJpJXOHR3xtC-FcAieRSp3uPaWhZbrgB2wXGtf-CIHmzaHG9olSaaRKDfbNbS1tk97WA-HtdGK_7DVaZBw_hV9j&q=cache%3A_-4EPn3Ba8kJ%3Awww.nerc.com%2Fdocs%2Foc%2Frs%2FNERC%2520Balancing%2520and%2520Frequency%2520Control%2520040520111.pdf%20&docid=b11d8c36a8eae7b4e95faf80431fd2a9&a=bi&pagenumber=8&w=891

https://docs.google.com/viewer?pid=bl&srcid=ADGEESiI-TizqsV0cRjlLirKA_z0t7Sg1hsteOk29JX1Wu0LfXIVlhJpJXOHR3xtC-FcAieRSp3uPaWhZbrgB2wXGtf-CIHmzaHG9olSaaRKDfbNbS1tk97WA-HtdGK_7DVaZBw_hV9j&q=cache%3A_-4EPn3Ba8kJ%3Awww.nerc.com%2Fdocs%2Foc%2Frs%2FNERC%2520Balancing%2520and%2520Frequency%2520Control%2520040520111.pdf%20&docid=b11d8c36a8eae7b4e95faf80431fd2a9&a=bi&pagenumber=9&w=891

https://docs.google.com/viewer?pid=bl&srcid=ADGEESiI-TizqsV0cRjlLirKA_z0t7Sg1hsteOk29JX1Wu0LfXIVlhJpJXOHR3xtC-FcAieRSp3uPaWhZbrgB2wXGtf-CIHmzaHG9olSaaRKDfbNbS1tk97WA-HtdGK_7DVaZBw_hV9j&q=cache%3A_-4EPn3Ba8kJ%3Awww.nerc.com%2Fdocs%2Foc%2Frs%2FNERC%2520Balancing%2520and%2520Frequency%2520Control%2520040520111.pdf%20&docid=b11d8c36a8eae7b4e95faf80431fd2a9&a=bi&pagenumber=15&w=891

You can get the pdf here: http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&sqi=2&ved=0CC8QFjAA&url=http%3A%2F%2Fwww.nerc.com%2Fdocs%2Foc%2Frs%2FNERC%2520Balancing%2520and%2520Frequency%2520Control%2520040520111.pdf&ei=vwVeUeuRGKbz0gHHnIGwBQ&usg=AFQjCNFNovutwDN31cNKZd1hFc-Hk5H_sQ&bvm=bv.44770516,d.aWc

Okay. I'm done. Thanks.

13. Apr 4, 2013

### jim hardy

You seem to have a knack for finding just right graphics for any concept. They added immensely to every discussion you've joined.

So I really hope you're NOT done.

Thanks, old jim

14. Apr 7, 2013

### vampslayer

Thank you all on your posts, I've read them all, and they are helping me to understand this matter.
Now I will say a bit bit closer what I am trying to do. I want to simulate situation when my hydroelectric power station is connected to the grid, and for some unknown reason link between GRID and my Hydroelectric power plant breaks suddenly. This can be caused by I don't know, some power system lines breaks or what so ever. At that situation my hydroelectric power plant works in islanded mode and my hydroelectric power plant must supply the consumers, it must compensate the GRID as much as possible. In that scenario the Load would increase a lot, and that's where I want to act. Speed would drop a lot and that's exactly what's going on in my matlab simulation.
When I change Load for example from 150kW to the 450kW my speed of course suddenly drops, from 1000 r/min to the 900 r/min and then governor acts and in a few seconds speed is back to 1000 r/min again. Ok, so what do I want? This drop is huge, 1000->900, that's 10% which means frequency drops from 50Hz to the 45Hz. I would like to somehow limit my speed drop to the let's say 4% or so. Do you guys have any Idea how this stuffs works and what should I do, and even if you don't I would like to read other opinions.

One more important stuff. While hydroelectric power plant is on GRID , the turbine needle is opened 100% and jet shifter is opened about 50-60%.Why? Well because jet shifter is faster than
turbine needle, and we use him to react fast. So when load increases from 150kW to 450kW jet shifter opens to the 80% or so.

jet shifter is pelton turbine deflector

Last edited: Apr 7, 2013
15. Apr 7, 2013

### jim hardy

In my utility there were relays scattered about the grid that disconnect feeders, knocking out whole neighborhoods, at various stages of underfrequency. It was called "Load Shedding" , an attempt to quickly match load to available generation.

I saw this mentioned in a paper dlgoff linked. It gave typical mw/hz load shedding.

Our steam turbine would allow 2 minutes below 58 hz, then it disconnected itself to protect against blade resonance. So system had that long to get itself back in shape, ie load matched to available generation.

At 56.1 hz our reactor shut down to protect itself against low flow and that tripped the turbine.

Once upon a time we had a system disturbance that left a big metropolitan area way short of generation. One of our turbines failed to disconnect on underfrequency signal. When it tried to supply the whole city by itself, its shaft snapped.

Hope that's some help.

You're getting the hang of this !

You'll have to match load to available generation. Add some load shedding relays.
The dynamics will be fascinating - you have an inertia term so you'll see a rate of frequency decay proportional to generation shortfall, you can shed load in chunks according to that rate.

surely somebody with genuine power system experience can give you proper terminology and real world algorithms.

old jim

Last edited: Apr 7, 2013
16. Apr 7, 2013

### vampslayer

So one of the solutions of this problem is cutting off feeders/consumers or like you call it "Load Shedding"? In that case, if you look my example(Load jumps from 150kW to 450kW), you want me to shed load with load shedding relays to prevent large frequency fall. Price of this is that some areas stay out of electricity.

Can you explain me what is the blade resonance and what it causes. What bad can happen if frequency is below 58Hz for over 2 minutes. I know that the frequency should be 50/60Hz to keep balance between resources and customer demand but I thought that condition must be "true" just to avoid additional costs. Why would I produce more than customers need, that's waste of money. Is there any other reason for this beside the money?

That's what I need, I need to prevent frequency to fall that low, but to be honest I don't know what bad that can cause. If turbine don't disconnect at low frequency it's possible that its shaft would snap?

17. Apr 7, 2013

### dlgoff

18. Apr 7, 2013

### jim hardy

http://www.basler.com/downloads/loadshed.pdf

http://store.gedigitalenergy.com/FAQ/Documents/SFF/GET-6449.pdf section 3 is background info.

http://www.midwestreliability.org/01_about_mro/overview/mro_manual/MRO_UFLS_Program_06-03-10.pdf [Broken]

a lot has happened after I retired ; http://www.publicpower.org/Media/magazine/ArticleDetail.cfm?ItemNumber=19303

.......................

The turbine blades are very large and under tremendous centrigugal force.
So the metal in them sees tremendous tension at speed.
Designers do not want the turbine operated at a frequency that can excite vibration at one of a blade's natural frequencies. Fatigue can set in quickly.
Our turbine had that limit on underfrequency operation, 2 minutes at 58hz or lower.
If a blade fatigues and breaks off, it makes quite a mess of other blades as it works its way out of the turbine. It is not uncommon for them to enter the condenser at considerable speed and shear some tubes, then you have both a turbine and a condenser to repair.

One must also be sure nothing is connected to the generator that could excite the natural torsional frequency of the shaft, around 7hz for ours. Generator's voltage regulator should be kept relatively slow.
I would think numbers for a waterwheel are different than a steam turbine.
You dont need to model that for anything you've asked - just be aware such things exist.
Search on "sub synchronous resonance" when you have some spare time.

Power systems are an interesting machine.

Last edited by a moderator: May 6, 2017
19. Apr 7, 2013

### jim hardy

That is the standard frequency. As machines got larger their design became more refined and less tolerant of off-frequency operation.

my reference to 58 hz was for our 60 hz system.
At 58 hz we are making less not more than customers need..

Maybe i'm confusing you with these extras.
Sorry, i Just wanted to make it interesting, if instead i'm causing you pain i'll stop.

I guess i'm enthusiastic to see somebody else interested in power systems.

Keep us posted about your simulation.
You can refine it as much as you want to, one step at a time.
Unlike a real one your simulated generator wont be hurt by what would amount to mechanical abuse.
So have fun with it!

old jim

20. Apr 7, 2013

### dlgoff

Loadshed, SCADA, retired :surprised...

Gets me to thinking what I worked on for the power utility.

with a little Economic Dispatch thrown in

using a custom designed Harris Controls system.

I think you'll enjoy this Jim.

"scadahistory.com/resources/SCADA+History.docx" [Broken]

Last edited by a moderator: May 6, 2017
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