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Assume we have a very long cable whose ends are not visible or accessible. One end we know is a generator, and the other a load. Can we determine which end of the cable has the generator attached without cutting the cable?

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    \$\begingroup\$ Sure, measure the voltage at some point. Then measure again at another point some distance away. If the voltage is lower, you moved to the direction of the load. If the voltage is higher, you moved to the direction of the source. This assumes that everything else stays the same during those measurements and that the cable has enough resitance to have a measurable voltage drop. \$\endgroup\$ Oct 21 at 7:54
  • \$\begingroup\$ You might want to learn about smith charts... \$\endgroup\$ Oct 21 at 7:55
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    \$\begingroup\$ @Jonathan_the_seagull How do you propose to measure impedances and represent them in a Smith chart without cutting the cable? A Smith chart is one of several ways to represent an impedance over frequency. So the Smith Chart by itself doesn't tell you how the measurement was done. \$\endgroup\$ Oct 21 at 7:57
  • \$\begingroup\$ can you get a probe onto the cable itself at any point? to directly see the voltage with a scope or whatever? \$\endgroup\$
    – danmcb
    Oct 21 at 8:00
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    \$\begingroup\$ Is this a real situation or a theoretical question ? Is there a site engineer with site plans to consult? \$\endgroup\$
    – Criggie
    Oct 22 at 1:50
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A cable consists of two conductors, with a finite space between them. Let's assume they're insulated.

Use capacitive sensing to determine the polarity of the instaneous voltage between them as a function of time.

Use a Hall sensor to determine the polarity of the magnetic field in the space between them as a function of time.

Once you've get the left-hand/right-hand rule polarities right, the vector product will indicate the direction of power flow.

As you only wanted direction, polarities are sufficient. However, if you can get the indications to be more accurate, like a measurement, then you can estimate the magnitude of the power flow.

As Marcus points out in comments, this is just an application of the Poynting Vector, which is true for electromagnetic waves in all of space, and for DC as well, but here is nicely simplified by there being a waveguide (power guide?) present in the form of your conductors.

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    \$\begingroup\$ Poynting vectors ftw! \$\endgroup\$ Oct 21 at 9:22
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Since you can measure

  • the electric field (red arrows) between both lines of the cable and
  • the magnetic field (green arrows) around each line of the cable

without cutting it, you can determine the Poynting vector (blue arrows), which is the cross product of both vector quantities.

enter image description here

The Poynting vector always points into the direction of energy flow as illustrated in this image (from Wikipedia).
Note: in case of AC the direction of current (magnetic field) switches but also does the direction of voltage (electric field) so the direction of the Poynting vector (energy flow) stays alwyas the same.

If you just want to know the direction of energy flow (not the quantity) it would be sufficient also to measure only the direction of the electric and magnetic fields.

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  • \$\begingroup\$ How do I measure those fields (which are mostly inside the cable?) without opening the cable? \$\endgroup\$ Oct 21 at 23:54
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    \$\begingroup\$ @Paŭlo Ebermann I guess you measure the strength of the fields outside the cable? \$\endgroup\$
    – PyRulez
    Oct 22 at 2:36
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    \$\begingroup\$ @Paŭlo Ebermann: the fields are not only inside the cable. Measuring the fields outside the cable shouldn't be a problem as long as cable diameter is not much larger than the distance between both lines; probably satisfied in most real cables. \$\endgroup\$
    – Curd
    Oct 22 at 8:02
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    \$\begingroup\$ It would, indeed, not work if a coax cable is used; which would be rather unusual for this application. \$\endgroup\$
    – Curd
    Oct 22 at 8:14
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If you can access a relatively longer section of the cable and if you have a contactless meter (aka clamp type meter) :

There'll always be a voltage drop across the cable. Measure the voltages at both ends using a clamp meter. If your meter is "sensitive" enough and if the voltage drop across the cable is "noticeable" enough , you'll observe that the voltage at one end is higher than the other. So this end is connected to generator side.

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    \$\begingroup\$ with a suitably resonant load, you can defeat this measurement. \$\endgroup\$ Oct 21 at 13:03
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    \$\begingroup\$ Or Ferranti effect. \$\endgroup\$ Oct 21 at 19:59
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    \$\begingroup\$ Clamp meters measure current without contact. To measure voltage at the end of a cable you need a probe meter with contact. A measurement instrument for electric fields is not suitable for a precise measurement of the voltage at the end of a cable. \$\endgroup\$
    – Uwe
    Oct 21 at 22:34
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    \$\begingroup\$ The question states "a very long cable whose ends are not visible or accessible" \$\endgroup\$
    – Uwe
    Oct 21 at 22:37
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    \$\begingroup\$ @Uwe so it could be one of those cables that experiences the Ferranti effect \$\endgroup\$
    – user253751
    Oct 22 at 11:49
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Yes, if you measure the instantaneous power P=V*I you get a positive or a negative result.

To do this you need to measure the voltage and the current. Both can be done without cutting, with clamp current meters and needle probes to punch through the insulation.

You can do this with the math channel on your scope, then measure the mean value of the math channel.

This is basically how energy meters work.

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    \$\begingroup\$ "we won't cut the cable, we'll just make a few holes in it" seems to be walking a very fine linguistic line, though \$\endgroup\$ Oct 21 at 20:10
  • \$\begingroup\$ @MatijaNalis current flow is never interrupted ;-) needle probes are very fine, you won't notice. \$\endgroup\$
    – Jeroen3
    Oct 21 at 20:50
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    \$\begingroup\$ I guess it depends on what the goal of the question is. If it is to determine the direction of power without interrupting it, then this works fine. If it is to determine the direction without marring the cable at all (maybe this measurement is being done underwater?) then this answer wouldn't work. \$\endgroup\$
    – notloc
    Oct 21 at 21:09
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    \$\begingroup\$ Never try to use needle probes at a high voltage cable for many kV. \$\endgroup\$
    – Uwe
    Oct 21 at 22:45
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    \$\begingroup\$ @Uwe yeah, that would be bad. Nowhere is kV mentioned though.... It should be academically possible to obtain some phase information from capacitive detection, but it becomes a lot more complicated. \$\endgroup\$
    – Jeroen3
    Oct 22 at 10:17

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