# How do utilities calculate transmission lines impedance?

I'm an electrical engineering student getting into Transmission Circuit Analysis, and a question came out to me: How do utilities measure their transmission lines impedance?

Do they use special meters? Or just mathematical calculations?

Similarly, I'm studying Distance Relays, where knowing the impedance of a specific transmission line is essential to set them up.

So, what do you think, people?

Regards!

F. Alvarez.

• Unfortunately there's only one or two power engineers who regularly answer here. My non-expert answer is that when you have a wavelength of several thousand km, you can probably get away with tuning the effective impedance to be nearly exactly what you want using discrete loads placed at occasional intervals on the line (like every few km). – The Photon Mar 17 '15 at 16:44
• I assume you're asking about characteristic impedance and not just R, L and C of a short line. Without knowing much about power systems, I can tell you it's fairly easy to measure the impedance of a line by measuring Zin for a few load conditions. Zin can be calculated from Vin and Iin (and phase), which any power meter will measure. So I could have a go at measuring Z0. Calculations could be pretty accurate too though. – tomnexus Mar 17 '15 at 16:52
• I think they can use the open circuit and short circuit experiment to measure it. You can google for it. – T.Nhan Mar 17 '15 at 17:03
• @T.Nhan, again I'm not an expert, but I don't think you want to short-circuit a 300 kV line. – The Photon Mar 17 '15 at 17:35
• @ThePhoton: You are allowed to short circuit a 300 kV line (we do it regularly during testing and maintenance.) You just aren't allowed to short circuit it while it's on. – Li-aung Yip Mar 20 '15 at 9:00

Some confusion seems to have arisen between the electronics engineer use of 'impedance' to mean 'characteristic impedance', and the electrical engineer use of 'impedance' to mean 'inductance and resistance of a lumped element'.

Rest assured that it does make sense to calculate 'the impedance' of a 300 kV, 1,000 km transmission line, it's just that the electrical engineers are talking about a different kind of impedance.

I learned how to do distance relay settings calculations in a training course (though I haven't done it for real, yet.) Apart from that, I do power system analysis for a living, so I am familiar with the transmission line impedance calculations.

For overhead transmission lines, we can calculate the impedance (per kilometre) if we know the following:

• The type of conductor, i.e. '30/3.00/7/3.00 ACSR/GZ', used for the main circuits and the earthwires (if any). This lets us look up the AC resistance/km and the physical outer diameter of the conductor, which is needed for the calculation.
• The spacing of the conductors at the pole top, which determines mutual inductance effects.
• The spacing of the conductors above the ground, and the ground volume resistivity, which determines capacitance to ground.

The calculation method can be found in either of the following well-known books:

• Westinghouse Electrical Transmission and Distribution Reference Book (now published by ABB). Chapter 3, Characteristics of Aerial Lines.

• Areva Network Protection and Automation Guide (freely available online) - section 5.18 Equivalent Circuits and Parameters of Power System Plant - Overhead Lines and Cables.

A lot of useful data is given here, including typical OHL configurations. This book was formerly known as the GEC Protective Relays Application Guide, and is considered the "bible" for British and Commonwealth electrical protection engineers.

The simple answer is that they don't. As tomnexus partially indicated, you are confusing two kinds of transmission lines.

A transmission line, in the general sense, has a characteristic impedance, which can be calculated in various ways, or which can be measured. It is important when transmitting power or signals at high frequencies.

What the utility companies deal in are 50 or 60 Hz power transmission lines, and at these frequencies characteristic impedances simply don't matter. Not only that, but when such impedances do matter, the load impedances must be carefully matched to the transmission line impedances. This is obviously not the case when plugging appliances into the wall. The power used by household devices varies over a range of ~100 to one, so no fixed characteristic impedance will match the expected loads.

It sounds like you may have made the assumption that the impedance measurement has to be done by a special procedure. While this is possible, it is impractical as the power required from a test unit would be pretty massive for a transmission line in the grid.

The neat thing about those relays you're studying is that they can resolve all voltages and currents as phasors, and determine all other parameters mathematically, on the fly.

Characteristic impedance does have to be assumed prior to actual installation, but this is tested at the factory and is highly reliable. So, a high impedance fault is either a tree limb to ground, or very distant. A low impedance fault current is very near, or so catastrophic that the instantaneous function has to trip anyway, without delay. Substation engineering then consists of laying out current transformers and potential transformers so that the math makes sense, and all parameters can be provided to the functions that require them. Well, besides sizing all the components, selecting trip times, installing communication for carrier signals etc, etc.

Edit: to be clear, voltage and current waveforms are known at both ends of every major conductor, and modern relays timestamp it by GPS. Getting the characteristic impedance of the line is pretty much what these relays do, and when it changes, something is wrong.