Line Constants Calculations

[davidbeach]

I am trying to refine our line constants calculations to account for differences between the calculations and actual faults. Our Z1 values seem pretty close, but it is quite clear that our Z0 values could be improved. Historically the line constants have been calculated considering only the three conductors of the transmission line (and mutual impedance with other adjacent transmission lines). As a first step I have added the under built distribution neutral into the calculations where present, and that makes a significant difference. There are a few other things that I'd like to be able to look at, but need a bit more information. Documented references would be great.

1. Does the presence of 750 VDC lines (light rail traction power) parallel to our AC lines need to be accounted for? If so, how?

2. Are there any good references for calculation of the affect of rails as ground conductors, such as electrical properties of the rail and how the grounding of the rail (typically impedance grounded) should be accounted for?

3. In the development of the calculations in Anderson (Analysis of Faulted Power Systems) he makes the assumption that any ground conductors are grounded at both ends; does the presence of multiple grounds alter the results?

4. The calculations for the transformation from phase impedances to sequence impedances (Anderson) makes the assumption that there are three phases. What affect on the results would there be if instead of two circuits in phase with each other the lines in question have a mutual 30 degree phase shift?

Thanks.

 

[Eleceng01]

davidbeach,

I seem to remember seeing a great book by Turan Gonen on modelling of transmission lines. I used it as an example when I was developing line constant caalculations in Mathcad given line geometry. I seem to remember an example with 2 static wires and how they affected the Z0 of the lines. Hope this helps.

 

[davidbeach]

Eleceng01, I've whipped up a nifty MathCad calculation based on Anderson that will take any number of circuits and any number of ground wires (so far I've tried as many as nine circuits). So, for conventional phase wire and ground wire (shield or distribution neutral) I think I'm covered. It's the weirder stuff, not covered in Anderson or Blackburn, that I'm interested in at this point.

 

[JensenDrive]

CAPE and ASPEN have a line constants analysis software package, but I believe they eventually go back to some form of the same equations as seen in Anderson. I do not know if they really could handle strange ground wires, such as railways or pipes. From what I hear, the unusual cases you are looking into are beyond the typical formulas. Sounds like some finite element analysis is needed. Way out of my experience level. It might be neat if you could take the lines out of service long enough to measure Zo and the mutuals. Measuring Z0 should not be too hard conceptually, but I bet it would take quite a bit of manhours. I am not sure how you would measure mutuals, now that I think about. You inject current in one line, and measuring voltage at both ends of the other line, where the line ends are far apart. It seems you need two extremely well synchronized voltage measurements that will be miles apart. That will be tricky. Am I correct on that?

Also, since you are going so far with the calcs, it might be interesting to calculate the effect of non-uniformity of the lines arrangement on the sequence impedances. I know of no program that calculates how Z1 and Z0 and Z2 cross couple on non-uniform and non-transposed lines. As non of the fault analysis software on the market can make use of the coupling coefficients, I guess it does not matter.

 

[JensenDrive]

It occurs to me that I think Milsoft also has a line impedance analysis package (and again, I think it uses equations similar to those listed by Anderson; the author of "Distribution System Modeling and Analysis," William Kersting, is somehow associated with Milsoft).

Who else makes line impedance analysis software?

 

[jghrist]

David,

This subject was covered in a paper presented this year at the Georgia Power Relay Conference, Why We Should Measure Line Impedance?, by U. Klapper, B. Vandiver, D. Welton, and A. Apostolov. A nearly identical paper with some references is at

http://www.omicron.at/fileadmin/user_upload/files/pdf/en/2006-TransmissionLineImped.pdf.

Detailed calculations may require a more sophisticated electromagnetic fields analysis. SES has two programs that might help, see

http://www.sestech.com/Products/SoftPackages/ROW.htm

and

http://www.sestech.com/Products/SoftPackages/SESTLC.htm.

 

[davidbeach]

jghrist,

I saw the presentation of that paper at Georgia Tech and am very interested in getting lines tested, but testing requires the line be out of service and for critical lines that can be a major undertaking. The testing can't calculate mutual coupling between lines unless both/all lines can be taken out of service for the testing. Not likely that both circuits on a pair of 230kV circuits can be taken out of service and absolutely no way that all circuits in a multi-circuit right-of-way can be taken out of service simultaneously. Testing will be a good tool, but it won't solve everything. I'll look at the sestech stuff when I have a bit more time.

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JensenDrive,

My calculations do include all couplings, both in the phase domain and in the sequence domain. I can tell you how the negative sequence of one line couples to the zero sequence of another line in the same right-of-way, but I know of no practical use for that information, the matrix calculations provide it whether I can use it or not.

-----------

I figure that if including the under built distribution neutral drops Z0 by 20% then four steel rails will have a non-negligible affect.

Some of it is also a matter of curiosity and may not have much impact on the calculations but it would be interesting to see if anybody has previously addressed these things.

 

[rcw retired EE]

David - we recently had to verify Zo impedances on two 230 kV transmission lines and look at fault current distribution in overhead static wires, gas pipleines and distribution neutrals during power plant ground faults.

A local company (Toronto) specializes in this testing, using a 55 Hz generator and spectrum analyzers. The generator injects a pseudo fault current in the system while CT and VT inputs to the spectrum analyzer record the currents and voltages at critical points. Multiple analyzers that are time synchronized via GPS can be used for large systems. The data is analyzed at 55 hZ and adjusted back to 60 to minimize the interference from load currents and system voltages. The result was calculated, measured and verified data for Zo and current splits.

They claimed they could do the same test to measure line constants, and have done it on several 230 kv substaions with all lines in service.

 

[ePOWEReng]

If you have some recorded SLG fault data from the lines in question, where the fault location was known and the fault resistance can be approximated, then you can back calculate the Z0. If nothing else this would be a good check from your present calcs.

 

[cuky2000]

The responses below are the first impression assessment that may require further analysis to be confirmed.

1. Since the DC line does not create mutual inductance, there is not effect on the positive and negative impedance on the AC line. However, the zero sequence may be considered if the neutral conductor of the DC line is grounded. This could be modeled as similar underbuilt AC grounded neutral conductor.

2. See the enclose paper and references at the end of this publication.

http://www.arema.org/eseries/script...library/2001_Conference_Proceedings/00004.pdf

3. Multigrounded line could be modeled as several short lengths of lumped parameters in Pi configuration. For short line, this model may be expected to have close approximation.

4. Since the line impedance is consider as a linear transfer function, the effect of the phase shift may not have significant impact in the linear range of the impedance.

 

[davidbeach]

Thanks cuky2000, I've printed out the paper and will give it a read through.