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# Capacitive coupling loss in AC Transmission line

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#### usmanyousaf

##### Junior Member level 2
Hi,

I want to ask about capacitive coupling loss in AC transmission cable. The cable would be travelling underwater (may be seawater or fresh water), with 50Hz 220VAC/5A (MAX) . The cable gauge is locally available 40/76 which is somewhere between 18AWG and 20AWG with PVC insulation. i need to know about formula/table for calculating capacitive loss in transmission line. Any reference will be highly acknowledged.

thank you

I don't have any specific references, but in principle it shouldn't be difficult to model or compute in a 2D way. You need to know either the conductivity or complex permittivity of the medium (at your specific frequency), along with the geometry of the cable. If you can model the cross section of the cable as a couple of point sources, then that makes things easier. Just calculate the electric field from the cable, use that to find the displacement current and then the power loss in the conductive medium. That should give you a number in terms of power loss per meter (or whatever unit) of cable.

since this is just a part of my final year project, capacitive loss was an objection raised by a faculty member. and i couldn't find any calculation or modelling anywhere on the internet. can you give me a link or literature which would help me model the exact system. or if you have any such experience, what would be estimated loss in the system i mentioned above ? an Electrical engineer told me there is a formula for such calculation, but i couldn't find one.

I don't think there is any one formula for the problem, unless you simplify it greatly. Any rigorous method is going to involve doing area/volume integrals of electric fields, the shape of which depends on your geometry. Doing the calculations by hand would be painful, but with the assistance of a computer (using MATLAB or something similar) it shouldn't be too hard.

Here's a page I found which gives the basic math. The second half of that page deals with dielectric heating, which is what you want. Equation 20 in particular relates power dissipation to electric field, via complex permittivity (which is directly related to conductivity and frequency). What you want to do is calculate your E field from your cable geometry, then put it into formula 20, and integrate over volume.

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