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# Line impedance calculation verification

## Line impedance calculation verification

(OP)
Anyone have any experience with transmission line impedance calculations using OPGW static wires (ones with fiber optic cable in the center) and how the impedance differs from standard EHS or HSS static wires (steel static wires)?

Just curious, as we've got a debate here over whether our calculations are correct.  The ratio of zero-sequence reactance to positive-sequence reactance using a standard EHS or HSS static wire is typically around 3 to 3.5.  With the OPGW wires, we're getting ratios of around 2 to 2.5.

I think what we're getting is right, as the OPGW static wires have larger diameters and lower inductive reactances than standard static wires, but wondered if someone could give a sanity check.

### RE: Line impedance calculation verification

I think it depends a lot on the particulars.  I calculated the pos- and zero-seq impedances of a vertical 115 kV line with Drake conductor, 7' spacing to the shield wire and 10' spacings between phases and got:

z1=0.074+j0.439 ohm/km
z0=0.323+j2.178 ohm/km with 3/8" EHS-AG shield
z0=0.331+j1.797 ohm/km with Alcoa 34/57/551 OPGW

x0/x1 = 4.96 for EHS and 4.09 for OPGW

ra=4.865, xa=1.289 ohm/km for EHS
ra=0.436, xa=0.363 ohm/km for OPGW

rho=100 ohm-m

In this case, neither shield wire reduced the zero-sequence reactance a whole lot from the conductors with earth return only (2.233 ohm/km).  If you had 2 shield wires, your figures might be closer, but would both be OPGW?

### RE: Line impedance calculation verification

(OP)
jghrist --

You're definitely right -- the x0/x1 ratio is highly dependent on particulars:  structure configuration, spacings, conductor types, etc.  Most of our lines are H-frame structures (giving horizontal conductor arrangements), which obviously will give different results than vertical arrangements from single-pole structures.

Given that your calculations gave the reduction in x0/x1 ratio that ours gave when using OPWG (even with different specific details), I've got more confidence that my line constants program is correct, and can safely say "I told you so" to my co-workers now.

BTW, do you use a commercially available line constants package, or is yours a "do-it-yourself" job (as is ours)?

### RE: Line impedance calculation verification

We use Aspen (in another office), but my calculations were done with Mathcad using equations from the Westinghouse T&D Manual and shield wire self-impedances from our CDEGS grounding program database.

### RE: Line impedance calculation verification

(OP)
I've seen a demo of Aspen's line constants program, and thought it looked pretty nice.  So far, we've been able to do everything we need with our own custom job -- it's wonderful the things you can do with visual basic and Access (our line constants program is part of our transmission database).

Just was curious to know what others are doing, maybe as info I can use if I ever decide to approach management with a proposal for something new.

Thanks again.

### RE: Line impedance calculation verification

There is an interesting paper by Edmund O. Schweitzer, III, "Evaluation and Development of Transmission Line Fault-Locating Techniques which use Sinusoidal Steady State Information", Ninth Annual Western Protective Relay Conference, October 26-28, 1982, Spokane, Washington.
Unfortunately it is not available on "SEL Literature" in Internet but surely you can get it directly from SEL.
The author's own two-end algorithm is used to verify the calculated positive- and zero-sequence line impedances from SEL relays event reports generated at both ends of the line for faults involving ground. I personally have used this method and I have found it quite helpful.

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