4 ms·

> A major missing detail is accounting for the other phase conductors in the transmission line. Good point. So for the customary 3-phase power lines the UNC ex

> A major missing detail is accounting for the other phase conductors in the transmission line. Good point. So for the customary 3-phase power lines the UNC exam is confusing and the given sample solution wrong. In reality you could steal much less than the already ridiculous amount in the exam. The German railways operate a 1-phase power grid. (After all 3-phase transmission makes only sense if you are able to balance the consumption of the 3 phases at a single place (small area in real life). With relatively few trains using 1 phase at uncoordinated locations that's not the case. And they cannot use the public grid because for historical reasons they operate on a different frequency. A 1-phase transmission line needs 2 conductors. With my high school physics, I can't tell what that means. Isn't it so that when the max current flows in one direction in one conductor it will flow in the opposite direction in the other one? So what you can steal is determined by d1^2 - d2^2 where dn is your stealing coil's distance from conductor n? Orders of magnitudes worse than in the exam once again.

hilbert42 6y ago
"A 1-phase transmission line needs 2 conductors" Right, but for many single phase installations a ground/earth return is often employed. This often simplifies things and saves a lot of infrastructure costs. Whether it's single or 3-phase, calculating the coupling efficiency will, at best, only be a rough guesstimate unless great care is taken to accurately collect and collate all physical and electrical parameters. Not only will interline coupling be relevant so will the fact that three phases are involved and we'd have to take into account standing waves etc. (mind you at 50/60Hz the wavelength is enormous (thousands of kms) so the transmission line effect is likely be trivial at the local level - see note). I reckon this article deliberately avoided the transmission line/multiphase effect to avoid that controversy or complicatlation. __ PS: ignoring the transmission line velocity factor and ground effects, the wavelength at 60Hz is 5000km and it's 6000km at 50Hz; therefore the first voltage maxima (lambda/4) will, in both instances, only ocurr at over a thousand km from the source. Standing wave effects due to the presence of three phase will reduce this but it's still a big distance - too big to have much of an effect to vary much over a single farmer's land. The solution therefore would be to calculate the various vectors for any given point on the line (here, at any area on the farmer's land and take that as constant for calculating the coupling to the secondary (pickup) inductor). It seems to me the most practical way would be to just measure the field strength empirically or to look up the various tables and monographs readily available in power engineering.
- usr1106 6y ago
  > Right, but for many single phase installations a ground/earth return is often employed Often? Not what I as a complete laymen in power transmission have observed. The mentioned power grid of the German railways uses 2 conductors. Why they would pay nearly 100% more in infrastructure cost than just using ground as conductor for return current I have no idea. There must be a reason. The Finnish railways don't have their own power grid, with the frequency being the same as the general grid they can get power from there. However, they have another way of seemingly wasting metal for a return conductor. Normally trains use the rails as return conductor. That seems "free" metal to use, because the train needs more than enough for it for mechanical reasons. However, Finnish railway lines have a second overhead wire next to the railway line and autotransformers or booster transformers (I don't understand the difference) to make sure the current is directed from the rails to the much thinner overhead return wire instead. The overhead wire being insulated from earth in contrast to the rails. https://en.m.wikipedia.org/wiki/Split-phase_electric_power https://en.m.wikipedia.org/wiki/Split-phase_electric_power mentions the same (?) for British railways. As a reason for the extra effort they mention reducing transmission losses and reducing electro-magnetic interference to the environment. I guess reducing electro-magnetic interference means that the "stealing" scenario from the original posting does really only work for 1-phase single wire power lines where the return current goes via earth. And even there not really well, as the article has shown. The only place where I have seen single wire power lines is Iceland. 20 kV lines I guessed when I saw them. > I reckon this article deliberately avoided the transmission line/multiphase effect to avoid that controversy or complicatlation. I agree. But I would have expected that the assumptions/simplifications had been mentioned as part of the task description.
  - hilbert42 6y ago
    "Often? Not what I as a complete laymen in power transmission have observed." First, it depends on the country and its rules (some permit it others don't); second, it depends on the application. The balanced system in your Wiki link is common too and it has advantages over the single system. For starters, it's a balanced power feed from a center-tapped transformer, and thus they are often used in sound studios and laboratories to reduce hum. noise and ground currents. Sometimes in the US you'll see the three-wire 110/220V systems. As they use three-wire feeds, they're more expensive than single-wire ones such as here: https://en.m.wikipedia.org/wiki/Single-wire_earth_return https://en.m.wikipedia.org/wiki/Single-wire_earth_return Earth return is mostly used in rural areas to feed small communities and such. This is to save cost. It is usually only employed on medium voltage feeds (6,600, 11,000 Volt lines). Rather than terminating in a substation, lines generally terminate in a single stepdown transformer. I would imagine it wouldn't be very common in Europe as it's pretty built up/has a large population (when I was living there I never saw any - but then, I was mostly in large cities, so I wouldn't have expected to see them). I've not been to Iceland but with its smallish population I wouldn't be surprised if single lines with earth return are used there - it would make sense to use them there. You are also unlikely to see single line feeds if the current is high or the line voltage is very high (intercity transmission lines, etc.) as ground eddies are potentially dangerous. Nor will you see it used where high current without sufficient voltage would lead to excessive I^2R losses. That said, many railways effectively use ground return. As you mentioned, many electricified lines use the rail tracks as a return and they're effectively earthed. In lines where the rails aren't welded together but only joined by fishplates you'll see multi-strand copper wire connecting each rail to ensure that the return also doesn't suffer excessive I^2R losses. I've lived in Europe but it's not my usual home so I'm not overly conversant with railway power systems there. However, I do know there are three common European electrification standards for normal railway services (i.e.: standard and Iberian guages - not specialized ones, narrow guage etc.). And roughly by country they are 25kV (Fr & Eastern EU), 15kV (De), and 3kV (Es & It). France, I think, still has some of the older 1.5kV standard. Not sure what Scandinavian countries use but I think it's 15kV and or possibly 25kV (so Finnish railways are likely to be 15kV or 25kV but I'm guessing here). Therefore, the max/min ratio of voltages in use is 25/1.5 or 16.67 : 1. This is very significant, for what engineering calls for at 1.5kV DC is very different to that at 25kV. AC Both 1.5 and 3kV will nearly always use a single overhead line with earth/rail return. The higher voltages will more likely use two lines (this is likely both an enginering matter and a safety requirement). So this would mostly account for the differences you mention. Note: 1.5 and 3kV are DC and the 15 & 25kV are AC. (Note: trams and small/light rail often use 750VDC.) The mixture of different voltages in use across Europe and the fact that they have this high ratio of 16.6 : 1 has called for some innovative solutions. For instance, there are classes of locomotives that now use all three common voltages (3kV, 15kV & 25kV) and they automatically switch between them when moving from one county to another.
amluto 6y ago
> Isn't it so that when the max current flows in one direction in one conductor it will flow in the opposite direction in the other one? So what you can steal is determined by d1^2 - d2^2 where dn is your stealing coil's distance from conductor n? There are two wires because of Kirchoff's current law -- if the current goes out in one direction, it has to come back somehow. There are "single wire earth return" systems that use the ground as the return wire, for better or for worse. If you replace d^2 by d^-2 in your equation, you'll be closer. Although, as noted in the OP, the magnetic field around a wire is proportional to distance^-1.
- usr1106 6y ago
  Yes, of course the field does not grow by the square of the distance.

hilbert42 6y ago

"A 1-phase transmission line needs 2 conductors" Right, but for many single phase installations a ground/earth return is often employed. This often simplifies things and saves a lot of infrastructure costs. Whether it's single or 3-phase, calculating the coupling efficiency will, at best, only be a rough guesstimate unless great care is taken to accurately collect and collate all physical and electrical parameters. Not only will interline coupling be relevant so will the fact that three phases are involved and we'd have to take into account standing waves etc. (mind you at 50/60Hz the wavelength is enormous (thousands of kms) so the transmission line effect is likely be trivial at the local level - see note). I reckon this article deliberately avoided the transmission line/multiphase effect to avoid that controversy or complicatlation. __ PS: ignoring the transmission line velocity factor and ground effects, the wavelength at 60Hz is 5000km and it's 6000km at 50Hz; therefore the first voltage maxima (lambda/4) will, in both instances, only ocurr at over a thousand km from the source. Standing wave effects due to the presence of three phase will reduce this but it's still a big distance - too big to have much of an effect to vary much over a single farmer's land. The solution therefore would be to calculate the various vectors for any given point on the line (here, at any area on the farmer's land and take that as constant for calculating the coupling to the secondary (pickup) inductor). It seems to me the most practical way would be to just measure the field strength empirically or to look up the various tables and monographs readily available in power engineering.

usr1106 6y ago
> Right, but for many single phase installations a ground/earth return is often employed Often? Not what I as a complete laymen in power transmission have observed. The mentioned power grid of the German railways uses 2 conductors. Why they would pay nearly 100% more in infrastructure cost than just using ground as conductor for return current I have no idea. There must be a reason. The Finnish railways don't have their own power grid, with the frequency being the same as the general grid they can get power from there. However, they have another way of seemingly wasting metal for a return conductor. Normally trains use the rails as return conductor. That seems "free" metal to use, because the train needs more than enough for it for mechanical reasons. However, Finnish railway lines have a second overhead wire next to the railway line and autotransformers or booster transformers (I don't understand the difference) to make sure the current is directed from the rails to the much thinner overhead return wire instead. The overhead wire being insulated from earth in contrast to the rails. https://en.m.wikipedia.org/wiki/Split-phase_electric_power https://en.m.wikipedia.org/wiki/Split-phase_electric_power mentions the same (?) for British railways. As a reason for the extra effort they mention reducing transmission losses and reducing electro-magnetic interference to the environment. I guess reducing electro-magnetic interference means that the "stealing" scenario from the original posting does really only work for 1-phase single wire power lines where the return current goes via earth. And even there not really well, as the article has shown. The only place where I have seen single wire power lines is Iceland. 20 kV lines I guessed when I saw them. > I reckon this article deliberately avoided the transmission line/multiphase effect to avoid that controversy or complicatlation. I agree. But I would have expected that the assumptions/simplifications had been mentioned as part of the task description.
- hilbert42 6y ago
  "Often? Not what I as a complete laymen in power transmission have observed." First, it depends on the country and its rules (some permit it others don't); second, it depends on the application. The balanced system in your Wiki link is common too and it has advantages over the single system. For starters, it's a balanced power feed from a center-tapped transformer, and thus they are often used in sound studios and laboratories to reduce hum. noise and ground currents. Sometimes in the US you'll see the three-wire 110/220V systems. As they use three-wire feeds, they're more expensive than single-wire ones such as here: https://en.m.wikipedia.org/wiki/Single-wire_earth_return https://en.m.wikipedia.org/wiki/Single-wire_earth_return Earth return is mostly used in rural areas to feed small communities and such. This is to save cost. It is usually only employed on medium voltage feeds (6,600, 11,000 Volt lines). Rather than terminating in a substation, lines generally terminate in a single stepdown transformer. I would imagine it wouldn't be very common in Europe as it's pretty built up/has a large population (when I was living there I never saw any - but then, I was mostly in large cities, so I wouldn't have expected to see them). I've not been to Iceland but with its smallish population I wouldn't be surprised if single lines with earth return are used there - it would make sense to use them there. You are also unlikely to see single line feeds if the current is high or the line voltage is very high (intercity transmission lines, etc.) as ground eddies are potentially dangerous. Nor will you see it used where high current without sufficient voltage would lead to excessive I^2R losses. That said, many railways effectively use ground return. As you mentioned, many electricified lines use the rail tracks as a return and they're effectively earthed. In lines where the rails aren't welded together but only joined by fishplates you'll see multi-strand copper wire connecting each rail to ensure that the return also doesn't suffer excessive I^2R losses. I've lived in Europe but it's not my usual home so I'm not overly conversant with railway power systems there. However, I do know there are three common European electrification standards for normal railway services (i.e.: standard and Iberian guages - not specialized ones, narrow guage etc.). And roughly by country they are 25kV (Fr & Eastern EU), 15kV (De), and 3kV (Es & It). France, I think, still has some of the older 1.5kV standard. Not sure what Scandinavian countries use but I think it's 15kV and or possibly 25kV (so Finnish railways are likely to be 15kV or 25kV but I'm guessing here). Therefore, the max/min ratio of voltages in use is 25/1.5 or 16.67 : 1. This is very significant, for what engineering calls for at 1.5kV DC is very different to that at 25kV. AC Both 1.5 and 3kV will nearly always use a single overhead line with earth/rail return. The higher voltages will more likely use two lines (this is likely both an enginering matter and a safety requirement). So this would mostly account for the differences you mention. Note: 1.5 and 3kV are DC and the 15 & 25kV are AC. (Note: trams and small/light rail often use 750VDC.) The mixture of different voltages in use across Europe and the fact that they have this high ratio of 16.6 : 1 has called for some innovative solutions. For instance, there are classes of locomotives that now use all three common voltages (3kV, 15kV & 25kV) and they automatically switch between them when moving from one county to another.

amluto 6y ago

> Isn't it so that when the max current flows in one direction in one conductor it will flow in the opposite direction in the other one? So what you can steal is determined by d1^2 - d2^2 where dn is your stealing coil's distance from conductor n? There are two wires because of Kirchoff's current law -- if the current goes out in one direction, it has to come back somehow. There are "single wire earth return" systems that use the ground as the return wire, for better or for worse. If you replace d^2 by d^-2 in your equation, you'll be closer. Although, as noted in the OP, the magnetic field around a wire is proportional to distance^-1.

usr1106 6y ago
Yes, of course the field does not grow by the square of the distance.