Pelton turbine model when hydroelectric station works on grid

[jim hardy]

In a steam plant -

The turbine of course begins to accelerate so its governor drives the steam inlet valves closed.
Other valves open to bypass steam around the turbine straight to the condenser.
That's because the the boiler cannot be immediately driven from full power to near zero power.
As fuel to boiler cuts back to match power demand, the bypass valves modulate shut.

Your hydro plant probably has analogous equipment.
The water in the inlet pipes cannot be immediately decelerated, so something must allow it to go around the turbine instead.

That's the basic concept. Others here are obviously better versed in hydro plant equipment and terminology than I am.

 

[vampslayer]

Your hydro plant probably has analogous equipment.
The water in the inlet pipes cannot be immediately decelerated, so something must allow it to go around the turbine instead.

Yeah, that would be deflector in hydro plant

 

[vampslayer]

I found that terms isochronous and droop speed control are closely related to this topic. I've just read some free ebooks. Would be good if someone of you would explain main differences isochronous and droop mode.

Also one more questions. What would be huge load change? For example if my nominal turbine Power is Pn=1734kW, what it would be huge load disturbance? How many percentage of nominal power?
And if my the load changes for 30%, how much I should let the frequency to be changed?
What are some normal borders. I'm asking for relation between load change and frequency change.

 

[Localise]

Microgrid with dump load

Hello everybody,

with interest I read the threads on this topic so far. I really enjoyed having found this! I am not sure whether it's ok to post into this thread, as the last post is already two months old. But I will let the admins decide.

Me, too, I want to simulate a little grid in Matlab/Simulink. I am studying Renewable Energies and this might become my thesis. I am at the very, very, very beginning at the moment and my questions are very silly compared to the stuff that has already been discussed here... I am thankful for every hint, though!

The grid consists of two small hydro turbines (combined output is about 3 kW), two permanent magnet synchronous generators, a PI controller, a dump load (that controls the speed) and a consumer.

The following data will be given: the turbine characteristics, the consumer characteristics and the torque.

The input signal will be rpm, the output signal will be the speed deviation that goes to the dump load and the disturbance is the consumer. I think so anyway, does that make sense?

How will the two parallel turbines behave with the PI controller? I do not know how they would react to a sudden load variation in reality – so I do not know what to bear in mind while doing the simulation.

And than I am not sure which equations I will need to describe and simulate this system.

So far only these came to my mind:

(1) $P = ρgHQη$

(2) $\frac{dω}{dt} = \frac{1}{J} (M_t + M_l)$

η = efficiency of turbine and generator
M_t= turbine torque
M_l= load torque
J=rotating mass

I think my problem is that I do not really know how to start systematically. Would it be better to start “drawing” the system in Matlab/Simulink?

Thank you very much for taking the time to read all of this and thank you in advance for any hints you might think of!

Lise

 

[SirAskalot]

I will try to share some of my experiences when it comes to matlab/simulink, as I have scratched my head to many times trying to get it to work, and I hope you don't have to.

First you need to have a opinion and goal on what your model is to describe. What is the output variables you are interested in. In power system analysis one can distinguish between stationary and transient behavior. The first can be described by algebraic equations, the latter with differential equations.

As far as modelling goes, one would "always" try to simplify the model as much as possible without the result being invalid. Thus one can try to make a statement and a assumption regarding the system, and model accordingly. However one should always verify that the assumptions are correct in some way. Either by incorporating the more complex phenomena and notice no change in the output variable in the two models. Or based on earlier research.

You should always acquire the equations you need to describe the system before you start modeling. Most advanced power system analysis books describe these in dept. Trying to make a model in matlab/simuling without equations, I would say is a bad approach.

Simulink incorporates several toolboxes, one popular in power system is the "power system toolbox". It operates with currents and conductors like in pspice etc. and not the usual transfer functions in ordinary simulink. Making it easier to start with. I am not a big fan of this because I have seen many students "drawing" huge systems only by dragging and dropping components. When its time to run the simulation it either displays many warnings or errors or shows unexpected results. They then spend most of their time trying to resolve these problems. And this takes a lot of time since one now needs to figure out how each block/component work.

I believe the problem lies in the how easy it is to build a large network, and one neglects the mathematical equations and misses the true understanding of how the system works.

Just think back to your course in ordinary differential equations. A RL or circuit is governed by a simple 1.st order ODE. Taking the laplace transform and modelling in simulink is simple once one has mastered it. On the other hand, drawing the electrical circuit in pspice or "sim power systems" is also easy, but one only gets the results and not the physical/mathematical behavior of a inductor.

Doing all the calculations and laplace transforms in a large network, like a 3 phase inverter is hard and time consuming. But here is where the simplifications comes into play. In the simplest form a converter is only a controlled voltage or current source. Why not use such a simplification instead of modelling all the switches?

Anyhow I could ramble on for hours about this, but to make it short:

Start small, verify the behavior of the model, and expand it as you go, always having full control on how each "block" behaves and what the expected output should be.

In power systems, start with the mechanical system. Depending on the simplicity, the flow in the turbine could be constant at first. Then you got Newtons 2nd law of rotation. (1 order ODE). Output variable is speed.

Speed is linear related to frequency. Amplitude of the voltage is controlled by the excitation system controlled by something (proportional controller with a setpoint maybe?).

Then you got your load. Is it constant or dependent on voltage or frequency? Constant may be the easiest to start with ( you can change it manually to see the response)

The load (power) and speed is proportional to the (counter) electromagnetic torque(M_t) produced by the generator. Which is the input to your 1. order ODE you started with.

Run the simulation, using proper initial values if you like ( initial speed of rotation). Change the load and observe the speed. If it behaves as you expect continue to expand the model. Expectation comes from experience, and in this simple example you probably know how Newton laws works with acceleration etc.

Next step would be to implement a turbine governor (input power) to make the system stable. (Start with a simple proportional controller.)

Just ask if something is unclear. A photo (print screen) of the network is always helpful.

PS: There are many software's dedicated to power system analysis like; Simpow, DIgSILENT PowerFactory etc. If your university has a license you might want to look into these.

 

[Localise]

Thank you so much for your quick reply! Your explanations clarified a lot for me. Or at least I think so ;) I have been mulling over a few things and here indeed are some more questions...

Am these assumptions correct:

1) In a stationary system there are no oscillations after a sudden change in the circuit (e.g. a load step), but a steady state is assumed directly after the change. As opposed to a transient system.
2) Every system could be described as transient or stationary, assuming a stationary state is just a simplification.
→ Is there an advantage in simulating a transient system? Or what indicates that I should assume a transient state?

I had a go at drawing a block diagram of what I want to draw in Simulink: http://tinypic.com/r/533hn4/5

The corresponding equations would be:

1)$ΔM = M_t + M_l$
2)$ΔM \frac{1}{J} = n_{eff}$
3)$Δn = n_{ref} + n_{eff}$

and about the part around the PI controller I am not yet sure. Does this make any sense somehow?

And then I have two questions on Matlab/Simulink itself:
Is it correct that it would be possible to do the simulation without Simulink?
Is it simpler to do it with Simulink?

Thank you so much again for any hints.

 

[jim hardy]

and about the part around the PI controller I am not yet sure. Does this make any sense somehow?

in my steam plant that would have been just a P controller, with gain perhaps 25.
..


The dynamic system will be much more informative
but probably difficult to keep stable - the computer is perfectly happy to extend your linear equations well past the physical limits of the machinery.
For example it sees nothing wrong with a valve's being 10000% open and it may oscillate your system between huge negative and positive numbers if the math says it'd happen.
So one must address limitations on travel and rate of travel (slew rate) of the parts he is modelling. And order of execution becomes important - program must flow in agreement with cause-effect else you have a paradox- something gets calculated from a value that follows not precedes it..

As suggested - start simple and build. Add plenty of 'meters' for debugging.

Welcome to simulation !

old jim

 

[dlgoff]

To add a little to old jim's "dynamic system" and "simulation welcome", here's a little online PID Control animation. Kind of fun, albeit it's not a Pelton turbine.

 

[Localise]

Thank you for your warm welcome!

So I will go with a stationary system...
The PID controller animation was very nice to see, thank you for that dlgoff.

I tried a more detailed diagram of what I want to simulate: http://tinypic.com/r/2e4esqt/5

Is this what you described, Sir Askalot? Did I forget anything?

For the transfer to Simulink: To “draw” this in Simulink I have to find the functions for the PI controller and the rest to press it into the form shown in the following diagram, correct? :
http://tinypic.com/r/nwymg6/5

I am sorry, if these are stupid questions. I have been fiddling around with this so long and even after a break I feel that I am unable to think straight about Simulink at the moment... Thank you all for your patience. It always takes me a while to get used to stuff that is very new to me.

 

[Localise]

I have been fumbling around for a bit more with the equations and that is how far I have come:

$1.\ P_a(t)=P_T-P_L$
$2.\ P_T(t)=M_a(t)ω(t)=M_a(t)2πf(t)$
$3.\ M_a(t)=\frac{P_a(t)}{ω(t)}$
$4.\ M_a(t)=J_T\frac{dω}{dt}=J_T2π\frac{df}{dt}$
$5.\ \frac{df}{dt}=\frac{1}{2πJ_T}\frac{P_a(t)}{2πf_0}=\frac{1}{T_A}\frac{df_0}{P_0}P_a(t)$
$6.\ T_A=\frac{J_Tω_0^2}{P_0}$
$7.\ ΔP\frac{1}{sT_a}=Δf$
$8.\ ΔP_L(t)=V_LΔf(t)$
$9.\ ΔP_T(t)=V_PΔf(t)$
$10.\ s=\frac{1}{V_P}\frac{P_N}{f_N}$

These are the equations that lead to the following block diagrams in Simulink:

The inertia of the grid itself: http://tinypic.com/r/1zmh0r5/5

The grid's self-regulation: http://tinypic.com/r/2d10fn4/5

Implemented P-controller: http://tinypic.com/r/9zowoh/5

Implemented PI-controller: http://tinypic.com/r/28aqeeh/5

All values are example values, so I can check whether it actually is possible to run the simulation.

So far I think this makes some sense to me. I just do not really know how to work in the data that are given. It's just the turbine characteristics (P-n-curve). For now I am supposed to assume constant speed. Where does that come in? How do I get the transfer function for the turbine?

For the moment I “modelled” the turbine as a lag element, as I have seen this in examples. Is a turbine always a lag element? Or approximated as a lag element?

Is it the Laplace transform of the second equation?

Am I totally wrong here? Thank you for any hints.

 

[SirAskalot]

Sorry for the late answer, but during the vacation I forgot this thread.

I re-read your first post, and you mentioned a "dump load". Can you clarify what you mean by that? I have yet to encounter such a "object" in a normal power system. But it may be possible to incorporate such a object with the pros and cons that follows.

1) In a stationary system there are no oscillations after a sudden change in the circuit (e.g. a load step), but a steady state is assumed directly after the change. As opposed to a transient system.
2) Every system could be described as transient or stationary, assuming a stationary state is just a simplification.
→ Is there an advantage in simulating a transient system? Or what indicates that I should assume a transient state?

In a stationary system you normally use the (simplified) algebraic equations. Eg. a http://www.ece.uAlberta.ca/~knight/electrical_machines/synchronous/parallel/house.html or load flow analysis
And as such, the time variable is neglected, as opposed to transient system analysis where one uses differential equations where time is a important variable.

There are pros and cons to using both methods. As an example, a experienced engineer could get the result and give an answer to a problem using stationary (or simple transient analysis) analysis, because of his experience on what is the governing factors. Where as a novice (as myself) would have to build experience from scratch, starting simple and increasing complexity, backtracking and noting the difference (or lack of difference) in the results. So on the next project one use this experience and uses the appropriate model, with regard to complexity. Saving project time.

In your case, even though its a thesis, you should gain experience with power systems and modelling. Not only produce "cutting edge research" which could have been obtained with a simpler model. You should either way justify the validity of your model and results.

Is it correct that it would be possible to do the simulation without Simulink?
Is it simpler to do it with Simulink?

Stationary analysis could be done with pen, paper and a slide rule. Transient simulation could be done with pen, paper and a plotting tool for single ordinary differential equation (ODE). For system of differential equations such as advanced transient analysis, numerical ODE solvers are a "must". Remember that Simulink is only a graphical interface to the ODE solvers in Matlab. You could always solve the same problem by using the ODE solver in Matlab by writing the system of equations in a function/script file.

Generally Simulink is gaining popularity because of its simple interface and reduced project time and expenses.

I tried a more detailed diagram of what I want to simulate: http://tinypic.com/r/2e4esqt/5

Doing stationary analysis, using eq. (2) in your initial post: dw/dt=0. In other words, in stationary state (steady state) nothing is changing ( no change in speed/frequency ). Solving eq. (2) (or similar equation) with dw/dt=0 renders inertia (J) to be omitted. Hence inertia has no effect on the system, with the right assumptions. Otherwise it looks ok. I did not have in mind the dump load object. And one might want to omit it to start with, in order to build the system on known facts and equations.

A normal system controls the frequency / speed with a proportional (P) controller which adjusts the input power (P_turbine).
In normalized values (p.u):
Δn * K_p = P_turbine
Δn = n_ref - n_shaft

where K_p is the gain (multiplier) in the controller. This is the equations in the "house diagram".

I have been fumbling around for a bit more with the equations and that is how far I have come:

Now you have started doing transient analysis.

The inertia of the grid itself: http://tinypic.com/r/1zmh0r5/5

Where is the inertia (or equivalent)? w=ΔT * (1/J) * (1/s) <-- integrator
You may also set the initial value of the integrator to 2*pi*f_0.

Implemented P-controller: http://tinypic.com/r/9zowoh/5

What is V_L? Remember what ΔM (ΔP) is. Its the turbine power _minus_ the load power. So your summation sign must change.

For the moment I “modelled” the turbine as a lag element, as I have seen this in examples. Is a turbine always a lag element? Or approximated as a lag element?

Yes, its mostly is, at least for hydro power. The physical explanation is that the flow in the pipes cannot change instantly. And closing the turbine valve has a built in time constant due to safety reasons.

Is it the Laplace transform of the second equation?

No, to model it correctly one needs to take into account the physical dimensions of the water pipe, flow equations etc.

For now I am supposed to assume constant speed. Where does that come in?

What do you mean? With the model you now have the speed does change.

As a last advice/question. Have you run the simulation ? Is the starting values correct? Are the steady state values correct? Speed frequency etc.? Compare with the steady state calculations.
As a example:
Intial: P_turbine = 1kW, P_load=1 kW. f_0=50 Hz. Kp= 1 kW/Hz.
Step change in load: P_load = 2 kW
Results: f = 49 Hz

 

[Localise]

Thank you so much for this massive answer, SirAskalot. I hope I can clarify a few things, that I had not described properly:

I re-read your first post, and you mentioned a "dump load". Can you clarify what you mean by that?

A dump load is a ballast that absorbs the excess output of the generator. So there is always a fixed total load on the generator at all times. So not the flow through the turbine is controlled, but the load on the generator. If the demand falls to zero then the ballast or dump load must be capable of absorbing the full output power of the turbine. The turbine can therefore run continuously at full flow and there is no longer a need for a flow-regulating mechanism.

Remember that Simulink is only a graphical interface to the ODE solvers in Matlab.

By inertia I meant to describe the response time of the system. I am not sure about the correct English term here, sorry. Does “response time” help? I mean the fact that there is a time delay between a load change and a response in frequency.

You may also set the initial value of the integrator to 2*pi*f_0.

How did you see that I had not done that? Engineer's magic?!

What is V_L?

In contrast to the grid-”inertia”-diagram, I wanted to take into account the frequency dependency of the load (V'L) in the grid-self-regulation-diagram. With frequency dependency I mean the frequency response resulting from inductive and capacitive components in the load impedance caused, for example, by lines, transformers and motors, that draw less power when the frequency decreases. The frequency decreases and a permanent deviation
builds up. If a higher amplification factor of the self-regulating effect is chosen, this deviation is smaller. A smaller amplification factor is results in an almost linear decrease in frequency.

Does this make sense? Do I need to take this into account?

Is it the Laplace transform of the second equation?

No, to model it correctly one needs to take into account the physical dimensions of the water pipe, flow equations etc.

I do not have these dimensions and I won't get them. But I thought I do not need those as the system is “governed” by a dump load instead.

For now I am supposed to assume constant speed. Where does that come in?

What do you mean? With the model you now have the speed does change.

Ok, it took me a bit to get my head round that. Matlab is quite massive and something very new to me.

Now you have started doing transient analysis.

I now realized that I had not fully understood the difference between transient and stationary. Your explanations helped a lot. So indeed, I am working on a transient system.

The inertia of the grid itself: http://tinypic.com/r/1zmh0r5/5

Where is the inertia (or equivalent)? w=ΔT * (1/J) * (1/s) <-- integrator

By inertia I meant to describe the response time of the system. I am not sure about the correct English term here, sorry. Does “response time” help? I mean the fact that there is a time delay between a load change and a response in frequency.

You may also set the initial value of the integrator to 2*pi*f_0.

How did you see that I had not done that? Engineer's magic?!

What is V_L?

In contrast to the grid-”inertia”-diagram, I wanted to take into account the frequency dependency of the load (V'L) in the grid-self-regulation-diagram. With frequency dependency I mean the frequency response resulting from inductive and capacitive components in the load impedance caused, for example, by lines, transformers and motors, that draw less power when the frequency decreases. The frequency decreases and a permanent deviation
builds up. If a higher amplification factor of the self-regulating effect is chosen, this deviation is smaller. A smaller amplification factor is results in an almost linear decrease in frequency.

Does this make sense? Do I need to take this into account?

Is it the Laplace transform of the second equation?

No, to model it correctly one needs to take into account the physical dimensions of the water pipe, flow equations etc.

I do not have these dimensions and I won't get them. But I thought I do not need those as the system is “governed” by a dump load instead.

For now I am supposed to assume constant speed. Where does that come in?

What do you mean? With the model you now have the speed does change.

Is this explained by what I said regarding the dump load?

As a last advice/question. Have you run the simulation ? Is the starting values correct? Are the steady state values correct? Speed frequency etc.? Compare with the steady state calculations.

As a example:
Intial: P_turbine = 1kW, P_load=1 kW. f_0=50 Hz. Kp= 1 kW/Hz.
Step change in load: P_load = 2 kW
Results: f = 49 Hz

This again raises the question about the transfer function of the turbine and the input of the turbine characteristics (P-n-curve). Where do I enter P_turbine? And P_dump_load…

 

[SirAskalot]

How did you see that I had not done that? Engineer's magic?!

I didn´t, just a guess based on own experiences.

Does this make sense? Do I need to take this into account?

Ok, it makes sense. But the extent depends on how large the grid is and what load sinks there are. Have you done some research and found a proper value?

I do not have these dimensions and I won't get them. But I thought I do not need those as the system is “governed” by a dump load instead.

Ok, I have misunderstood your system. I was talking about the whole system. I think you may talk about the "efficiency" of the turbine. If you want the generator and turbine to produce a constant amount of power the governor and turbine models may not be necessary.

This again raises the question about the transfer function of the turbine and the input of the turbine characteristics (P-n-curve). Where do I enter P_turbine? And P_dump_load…

By P-n curve you mean power vs. speed on the turbine? Do you have this data?
If its a linear equation you can use a gain or other math expression where speed is the input and turbine power is the output. If its data points, you can use a "look up table". n is the speed and is related to frequency and the pole pair number of the generator. ( n / w / f is the output of the integrator).

So to clearify:
- Do you want to regulate the input to the turbine/generator?
- How is the dump load controlled? Only w.r.t. frequency to start with?
- Does the dump load have some time constants? (What type of element is it? Switched resistors?)

As a last advice, you should use the equations known and implement them into a diagram (like the one you have made) making sure to name all the signal ('wires', outputs, etc.). This will help a lot in the understanding.

 

[Localise]

By P-n curve you mean power vs. speed on the turbine? Do you have this data?

Yes, I will get this data. And as far as I know it is not data points but a curve.

So to clearify:
- Do you want to regulate the input to the turbine/generator?

No, the input to the turbine will be constant. I want to regulate the load on the generator, or rather as the input to the turbine is constant, the load on the turbine/generator has to be constant: If there is less demand by the consumer, the dump load “provides the additional demand”.

- Does the dump load have some time constants? (What type of element is it? Switched resistors?)

Most probably ceramic heating resistances will be used. I am sorry, for this lack of information. Also, I do not yet have any info about time constants or any other parameters of the dump load.

As a last advice, you should use the equations known and implement them into a diagram (like the one you have made) making sure to name all the signal ('wires', outputs, etc.). This will help a lot in the understanding.

I will do this and hopefully have more information asap. You have already helped me a lot in understanding what I want to do here, SirAskalot.