Line Constants Calculations
Line Constants Calculations
(OP)
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.
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.






RE: Line Constants Calculations
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.
RE: Line Constants Calculations
RE: Line Constants Calculations
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.
RE: Line Constants Calculations
Who else makes line impedance analysis software?
RE: Line Constants Calculations
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://
RE: Line Constants Calculations
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.
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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.
RE: Line Constants Calculations
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.
RE: Line Constants Calculations
RE: Line Constants Calculations
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. htt
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.
RE: Line Constants Calculations