VArs flowing into Tx line at both ends - why?

[andrewward]

Hi everyone,

I've been running power flow models and can't explain what I am observing and how to stop it. Can anyone help me understand what is going on?

This is a real life situation. I have a transmission circuit of 100km with a power station at each end.

At one end the voltage is set to 1.045pu and 258MVAr are flowing into the transmission line. At the other end the other power station is holding the voltage at 1.055pu and 136MVAr are flowing into the transmission circuit.

Why does the reactive power flow into the circuit at both ends? Nb positive seq. impedance of the circuit is R1=18.96ohms, X1=113.37ohms.

Of equal importance, is there a way of reducing the amount of reactive power flowing into the circuit? The generators around the system are exceeding their var limits. I've tried raising the voltage from 1.045 to 1.055. This reduces the difference between the two var flows. But, there are still approx. 150MVAr flowing into the line at each end.

Thanks for the help.
Andrew

 

[alehman]

Is your line connected to anything else at either end? I suspect your VAR's are escaping though some path not being considered or there is a measurement error.

 

[andrewward]

The circuit is connected to a bus at each end with other circuits coming off each bus. But, the flows that I stated in the previous post come directly from the powerflow software and are the flows at each end of that circuit.

The power flow solution did converge properly as well. I note that there are a number of other circuits in the system doing the same thing.

 

[davidbeach]

Something to look at: The program may be assigning an arbitrary direction at each end of the line, both into the line in this case, and then also including an angle. If the program says into the line at an angle of 90 to 270 it isn't really into the line.

 

[electricpete]

Do a var balance.

Vars in at each end plus vars produced in the power line plus vars consumed by power line should equal zero.

Vars produced would be by the capacitors in the pi model of the transm line.

Vars consumed would be something like I^2 * X where X is reactance.

In your situation everything except the last one is putting vars in. The vars consumed by the power line series reactance must equal the sum of all the other stuff. Either that or you have made an error.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[jghrist]

What is the real power flow through the line?

 

[jstickley]

andrew...

I find it hard to believe you'd see such behavior physically, so I'm assuming that you're describing the behavior of a powerflow model.

As such, I think you've answered your own question... the powerflow did not converge well. Sometimes you'll see odd solutions like that in poorly conditioned loadflow cases.

If you're dealing with one of those "everything but the kitchen sink" type of regional loadflow models we see nowadays, it often helps to condense your case by equivalizing portions of the system external to you area of study. Re-solving the case using flat start conditions can also help.

Best of luck, these things can be difficult to correct from time to time.

 

[electricpete]

I need to make an obvious correction to my statement above:
"Vars in at each end plus vars produced in the power line minus vars consumed by power line should equal zero."

It seems like an improbably occurence but possible from a theoretical standpoint. As jghrist may be pointing towards - if you have a ridiculously high real power flow through the line might explain it (remembering vars absorbed go as current squared). Ridiculously high series impedance doesn't wrok because you would very quickly be violating stability limits.

Anyway you said X=113 ohms.
I assume that is ohms at transmission voltage.

Assume reactive power Q = sqrt(3)*I^2 * X ~ 300E6
I = sqrt(Q/X/sqrt(3)) = sqrt(300E6/113/sqrt(3)) ~ 1240A

Is that in the ballpark of your system?

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[electricpete]

To get a feel for how real and reactive components fit together we need to know your voltage.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[electricpete]

I don't know typical numbers but I'm thinking maybe 113 ohms is a ridiculously high impedance? What do you guys think.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[electricpete]

Stike that. Replace my message above with corrected version:

"I don't know typical numbers but I'm thinking maybe 113 ohms is a ridiculously high reactance? What do you guys think."

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[electricpete]

I see from Bergen Power System Analysis p77 that typical XL for 138kv lines is in the range 0.8 ohms / mile. So 113 ohms may not be an unrealistic impedance.

Still interested to know the voltage and the real power flow in the line.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[mersin33]

I dont know what you are using as software, but try to check the var balance in the overall system after the solution (convergence).

You may want to check the line parameter as well. B may be very small or X may be very large (could have entered pu values instead of actual values, etc).

good luck

 

[andrewward]

Sorry for such a long silence. I've had to give attention to a few other things at work at the moment.

Thanks for all the responses.

jstickley it IS an "all but the kitchen sink" problem. New generation is expected in a region of the grid and most of the power exported from this region flows into the grid via a single 220kV bus. The transmission line we've been talking about is one of only three lines between this bus and the rest of the grid. I have been asked to see how much power I can export from this bus under n-1 contingency. The large MW MVAr flows on the line in question occur as the export MW increase and when one of the other lines is out of service.

How does a flat start possibly help in a powerflow such as this? Also, any other tips for helping the convergence of difficult powerflow models (and reason why they work) would be really helpful.

To answer all the other questions:

Nominal voltage: 220kV
Real power flow (from sending end at V=1.055pu): 354.5MW
Rating: 492.7MVA
% Loading of the line: 86.3%
Capacitance: 2.50934uF
Length: 280.347km
Mutual reactance because double circuit line (X0m): 207ohms
There is a power station at each end of the transmission line.

A correction to my original post: this is a real power system network, BUT the power flow values come from an extreme powerflow solution. Sorry about that.

I am using DigSILENT. I'll have a look at the var balance in order to learn how to use it. Thanks for that.

Thanks guys.

P.s. here are some comments from a work colleague:

"The reason I can think of without looking into details is the high reactive power loss on the remaining circuit. If you saw 150 MVar flow into the line from both ends, the line MVAr loss must be 300 MVar. This would occur when you try to transfer a large amount of MW across the line.
If there are plenty of Var resources at both ends, then it is very likely that Var will be supplied from both ends. In other cases, it must be Var rich at one end, and Var poor at the other end, so Var would be sent from the rich end all the way through."

"As you have found out, an increase in operating voltage (i.e. 1.04pu to 1.05pu) can reduce the MVar loss. I can not think of any other way to reduce the MVAr loss if you still want to transfer the same amount of MW across the line."

 

[dpc]

I'd try doing a simplified model with another power flow program if possible to see if you get anything close to the result you now are seeing.

100km is a long line, but 300 MVar is a lot of vars.

Do you have any actual metering data on the line? If so, I would use it to test the power flow model at the metered load, just as a point of comparison.

I would also run simulations at load greater and less than this case and see what the sensitivity is to load and, more importantly, sending end voltage. I've found that very small changes in voltage at the swing bus can really have a big impact on the power flow convergence.

Good luck, and let us know what you figure out..

 

[jghrist]

From simplified calculations at the sending end, it seems that a reactive loss of 394 Mvar (258 + 135) seems unreasonable. Sending end apparent power is sqrt(354.5²+135²) = 379.3 MVA. At 1.055 pu voltage (232.1 kV), this is 943.5 A. Assuming this current stays the same throughout the line (actually it wouldn't because of charging current), would mean a reactive loss of I²·X = 101 Mvar.

 

[jstickley]

andrew...

It really just sounds to me like you have a poorly conditioned powerflow model (which isn't entirely uncommon in large regional models nowadays). Does it have problems solving even with small (or no) disturbances? I've seen cases that, even from a solved state, when re-solved, take 10-15 iterations to settle to convergence again. Of course, I have not used digSILENT, either... it may behave differently than other packages (they all have their quirks).

Anyway, the reason I suggested a flat start is that often times, it's necessary to disturb the model's initial conditions quite a bit in order to see correct convergence. If you can condense the model by equivalizing large areas that are of no interest, you can often re-solve the entire case from a flat start and obtain a reasonable convergence.

As I stated earlier (and you're observing), it's not an easy problem to correct. Correcting poorly conditioned powerflow cases has always seemed to me more art than science.

 

[bacon4life]

jghist

Is the there a factor of 3 included in your calculations? I would have thought it was:

379.3/(1.732*232.1*1000)=943.5A

(943.5*1.732)^2 * 113 = 302 MVAR

andrewward

Using approximations from Bergen for a short lossless line, the angle can be calculated, and then the reactive power in the line calculated.

Psend=-Preceive = |Vreceive| * |Vsend|*sin(theta)/X
Q sending = |Vsend|^2/X - |Vsend|*|Vreceive|*cos theta /X
Q receiving = |Vreceive|^2/X - |Vsend|*|Vreceive|*cos theta /X

thus for the case where the voltages are both 1.055pu

theta = arcsin((353.5*113)/(232.1*232.1)) = 47.9 degrees
Q sending = Qreceiving = 232.1^2/113 - 232.1*232.1 * cos 47.9 / 113 = 157 MVA

Qtotal = 314 MVA

For the case of one terminal at 1.045 and the other at 1.055, the approximation doesn't match as well to your results, but it still predicts that over 300 MVARS are needed.

Have you tried taking the voltages, currents and angles from the two buses then checking by hand the if they are self-consistent to the the long line model with hyperbolic correction factors?

 

[jghrist]

bacon4life,

Right you are - I forgot the 3.

Perhaps with the mutual reactance taken into account, the 394 Mvar is not out of line.