Finding the rotor voltage for a 1.8 MVA generator 2

[spede]

I am simulating a 1.8 MVA doubly-fed generator with a FEM-software. My problem is that I need an iteration method for solving the rotor voltage, when we know the output power to the network and the stator voltage. The problem is complicated, because the system is nonlinear and the equivalent circuit parameters change on each time step. So, what I need is an iteration method which concerns the machine as a black box and iterates the complex rotor voltage from the resulting complex output voltage.

 

[electricpete]

#1 - What is a doubly-fed generator?

#2 - Rotor voltage is normally controlled by the control system / voltage regulator.

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[spede]

#1 - What is a doubly-fed generator?

The machine is fed through slip-rings in the rotor circuit with a frequency converter.

So we have a slip-ring machine and we want to know the right rotor voltage to get the 1.8 MVA to the network.

 

[electricpete]

You said MVA, I assume maybe you are looking to supply 1.8MVAR?

From an equivalent circuit standpoint using the decoupled approximation (active and reactive flows are approxiamtely decoupled, active depends on phase angle and reactive depends on voltage magnitude), we would use

Q = 1.8MVAR = sqrt(3) * (V2-V1) ^2 / XL

Where
V2 is internal open circuit voltage of the generator stator
V1 is system voltage at utility bus assumed to be constant / fixed.
XL is total inductance between V1 and V2.

If V1 is the generator terminal, then XL is the generator sync reactance.
If there is a transformer between V1 and V2 then that reactance needs to be included as well.

You need to convert rotor voltage to open circuit stator voltage V1 as well. Not sure off-hand what is a simple formula there.

In practice I believe in order to maintain a constant reactive power flow against varying system voltage, you will need a closed-loop control system which senses voltage and adjusts rotor excitation accordingly.

This is just what little I know about a complex problem. I apologize if I am telling you the basics and leaving out the good stuff (which I don’t know).


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[spede]

Thanks for the quick answer!

However the problem is bit more complicated. The nominal power of the doubly-fed induction generator (DFIG) is 1.8MW and it is designed for a wind power station. So what we need is an output power of 1.8 MW with power factor very close to 1. It is not possible to transfer a lot of reactive power in the network, because the power stations or wind parks are usually located in remote locations.

I managed to solve the rotor voltage analytically with typical DFIG parameters (S=1.8MVA, PF=0.8). The answer was u_r = -0,57 + i52,50. The real problem with FEM-software is that we can't use the equivalent circuit parameters. So we have to iterate the rotor voltage. The problem is basically this:

INPUT: u_r = a + i*b -> DFIG (modelled as a black box) -> OUTPUT: S = S_r + i*S_i

Maybe this problem should be in some other section, because what we need is an iteration method to model this system. The rotor voltage needs to be solved from the resulting output power.

 

[electricpete]

Real (mw) power when generator is paralleled to a power system with other sources is controlled by generator speed and speed droop setting which control prime mover (real power input to the generator).

Again from my simple way of thinking (decoupled approximation), real power is not controlled by voltage.

To check your approach, the electric power engineering forum forum238 is a good place to start.

If you're sure you have the right formulation, I think there is a numerical methods forum.



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[edison123]

Don't induction generators (wind generators) have squirrel cage rotor windings ? Where is the question of rotor voltage here when the rotor winding is shorted ?

 

[spede]

Electricpete,

The speed of the machine affects greatly on the behaviour of the machine. However, in a wind mill generator we want a very large operating area with slip values from s = -0.15 to s = 0.15. This is done possible by a large frequency converter connected to the slip rings in the rotor (edison123: we don't have a cage induction machine with shorted windings). The converter is capable of feeding 1/3 of the nominal power of the machine back to the rotor circuit from the power produced by the stator.

You can find more information about this interesting connection from the Finnish ABB site:

http://www.abb.fi/global/abbzh/abbz...e=us&m=9F2&c=2962145025D8FE29C1256D73002F08B0

select Generators -> Wind Turbine Generators -> Induction Generators ->
Doubly fed, semi-variable speed speed generators

 

[Mstrvb19]

Spede, along the lines of what electricpete was doing with the fast decoupled method, I think the numerical analysis you are looking for is this.
The best iterative method we have is newton-raphson. Becuase this involves matrices, I am having trouble writing in the basic equation (in here). You can search for Newton-Raphson on Google and get some good info on it. The fast-decoupled method is a derivation of newton-raphson that only works for transmission line systems where conductors are primarily reactive and the system can be approximated such that real power flow only responds to phase relationship and reactive power only responds to voltage magnitude. Since you are attempting to solve the internal network of the machine, this would not work well for your application. Additionally, NR has been adapted to bus-system solutions, while your application would probably be best suited to a more direct mathematial definition of it, so you might also talk to the numerical methods folks. If you treat the control system/freq. drive as a separate entity, then you can do a series of iterative solutions, where you manually adjust the input from the freq. drive as it would be..make sense? Its a little much for a post, so definitely check the web resources on it.

 

[Mstrvb19]

just occurred to me-could you solve backwards? Since the power you deliver to the grid from the generator must be transferred across the air gap- you could determine the rotor voltage based upon dy/dt of the flux in the air gap.

 

[spede]

Thanks Mstrvb19!

This was just what I was looking for. The NR-method might do the job, if I can make it work. The matrices concerning the problem are not very easy to solve. But I'll look for the numerical methods section, if I have problems.