# Wavelength on power transmission lines

#### terahertz

At the power-line frequency (50Hz), the wavelength of electromagnetic waves in free space is 6,000 km. Similarly, the phase velocity of voltage/current waves is about 4,000 km at this frequency. The question is, why do we bother about the wavelength at all at the power-line frequency, when the longest transmission line in the world is no longer than 1,100 km.

In other words, why do engineers working in the field of power transmission use transmission-line theory to analyse power transmission lines when circuit theory would be quite adequate (given that the length of a typical power transmission line is much smaller than the wavelength).

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#### meBigGuy

Gold Member
I suppose they don't need transmission line theory in terms of simplistic 50Hz wave propagation, but load transients, faults and other impulse related things would certainly need analysis in a rigorus way. Here is an abstract from a paper that kind of illustrates the complexity. (and we haven't even begun on load balancing, corona losses and the such)

"The present work gives a model for ‘real-world’ high voltage transmission lines. The formulation of line parameters as a function of frequency takes into account the tower configuration, effect of earth conductivity and skin effect. The general transmission line problem is formulated in terms of partial differential equations. The Laplace transform offers a complete solution and has the advantage of reduced time requirements. Both switching and lightning surges can be simulated based on lines step response. The simulation is based on MATLAB software package, version 4.2b. Comparisons between field tests from Romanian 400 kV and computer results are presented."

#### HowlerMonkey

Maybe certain lengths are susceptible to harmonic ringing?

#### AlephZero

Homework Helper
In other words, why do engineers working in the field of power transmission use transmission-line theory to analyse power transmission lines when circuit theory would be quite adequate (given that the length of a typical power transmission line is much smaller than the wavelength).
Maybe the OP can explain what he/she thinks is the different between "transmission line theory" and "circuit theory". Unless you want to model the complete line as a single resistor, or something equally (over-)simplistic, there is no fundamental difference IMO. Transmission line theory is just what you get by modeling the line as a set of identical finite sized chunks joined end to end, with each chunk modeled with resistors, inductors, and capacitors, and then taking the limiting situation of an "infinite" number of "infinitely short" chunks.

Of course for radio frequency transmission lines you would most likely start from Maxwell's equations rather than chunks of line modeled with Rs Cs and Ls, but that is no different in principle.

Actually a good question - if you are referring to what I think you are - understanding of line impedance is used to set up protective relaying. If there is a fault on the transmission line the event is more of a unit step and trans line theory is used to evaluate the distance and impedance of the fault. REF : http://www.gedigitalenergy.com/multilin/notes/artsci/art14.pdf.

However there is not any standing wave or other tuned phenomena considered, eg. it is not about the 60 hz, but about the length and consistency of the line itself.

Back in the day they built multi-step impedance sensing relays with electromagnetic relays - doing this digitally now is much easier. The old relays - or I should say the engineering in them, were true works of art.

#### terahertz

AlephZero, the difference between transmission line theory and circuit theory is that the former takes into account the difference in the phase of the signal as a function of the distance along the line whereas the latter ignores it and considers the phase to constant along the line.

#### sophiecentaur

Gold Member
The question is, why do we bother about the wavelength at all at the power-line frequency, when the longest transmission line in the world is no longer than 1,100 km.

In other words, why do engineers working in the field of power transmission use transmission-line theory to analyse power transmission lines when circuit theory would be quite adequate (given that the length of a typical power transmission line is much smaller than the wavelength).
So a quarter wavelength is less than 300km. Put an open circuit at the end of a quarter wave of transmission line and it will look like a short circuit at the driven end. That is surely worth taking into account as there are plenty of lines which are that long.

#### gerbi

Gold Member
So a quarter wavelength is less than 300km.
Huh ? At system frequency (50-60 Hz) wavelength is 5000 or 6000 km. So quarter of it is 1250 or 1500 km.

λ = c/f = (300*10^6 m/s) / 50 Hz

#### sophiecentaur

Gold Member
Oh yes. Of course, you're right. I didn't do the sums - durr. But there are plenty of situations where the total line length is 1000k+. (Even the UK is that long!) A sudden removal of a load will cause a significantly awkward load. Also, with more than two alternators connected to a loop of lines (not as much as a quarter wavelength involved), it can be impossible to sync them all without high reactive currents.

#### terahertz

Huh ? At system frequency (50-60 Hz) wavelength is 5000 or 6000 km. So quarter of it is 1250 or 1500 km.
I think what was meant was that at the power-line frequency, a 1,100 km long transmission line is about one quarter wavelength long. If this length of line is terminated in an open circuit, its input impedance is zero.

#### sophiecentaur

Gold Member
I think what was meant was that at the power-line frequency, a 1,100 km long transmission line is about one quarter wavelength long. If this length of line is terminated in an open circuit, its input impedance is zero.
I was just being incredibly sloppy. Sorry. Right idea but my wrong figures!

#### gerbi

Gold Member
I think what was meant was that at the power-line frequency, a 1,100 km long transmission line is about one quarter wavelength long. If this length of line is terminated in an open circuit, its input impedance is zero.
I know, this was just a clarification (not 300km but 1250 km).

Oh yes. Of course, you're right. I didn't do the sums - durr. But there are plenty of situations where the total line length is 1000k+. (Even the UK is that long!) A sudden removal of a load will cause a significantly awkward load. Also, with more than two alternators connected to a loop of lines (not as much as a quarter wavelength involved), it can be impossible to sync them all without high reactive currents.
I think this is the case. Getting close to 1/4 of wavelenght can be dangerous and systems are still getting bigger. Power capacity is increasing rather fast and this creates a lot of problems (increased short-circuit current, power flow between systems etc.). With this all in mind - a proper study case requires an accurate mathematical model (I doubt that simple circuit theory would be accurate enough in those all system stability calculations).

#### sophiecentaur

Gold Member
It's a very good case for using DC for long links. I believe the conversion losses AC-DC-AC are less with new technology.

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