Simulation of the electric field of a three phase cable using FEMM

Finding analytical solutions to physical problems is always nice and rewarding, however it can be a bit of a pain when the geometry of the problem (just to mention one possible hustle) becomes more complex than just a sphere, a cylinder or any other basic shape.
If you think of a simple cable, with a copper core and a PVC insulation, calculating the electric field generated in the insulation layer using pen and paper may still be feasible, however, using FEMM greatly improves your life when doing calculations as an engineer, student, or “just” curious person.
This simple cable can be modelled using FEMM as follows



The cable has a total diameter of 7 cm, with a first PVC insulation with a radius of 2.6 cm, a 0.05cm air gap and another PVC insulation layer.
The permittivity of air is 1 while PVC has a permittivity of 3. The inner copper conductor is assumed to be at a potential of 22 kV while the outer boundary condition is set to 0 V. By running the simulation this is the obtained result





As expected the voltage goes down as we approach the external boundary. What about the electric field? The electric field goes down as well, however, close when we approach the air gap it suddenly jumps up and then down again as soon as we re-enter the PVC insulation layer. This behaviour can be explained because air has a permittivity 3 times lower than PVC.
Enough games now. Let’s bring out the big guns: a three phase cable!



This is a more realistic three phase cable that can be described as follows:

• Each conductor is insulated using rubber as a primary insulator.
• The second insulation layer is made out of PVC.
• We are going to assume that the upper conductor is at a potential of 9.8 kV while the other two sit at –4.9 kV. The outer boundary is at 0 V as usual.

Let’s start the simulation. The results are portraied below



The absolute value of the electric field and of the potential on the outer edge of the primary insulator of the upper conductor, are represented below




The absolute value of the electric field and of the potential on the outer edge of the primary insulator of the conductor on the lower left side, are represented below.



As you can see, the three conductors are influenced by the presence of the other two and the electric field and the potential reflect these influences. I hope you enjoyed this quick simulation, if you’d like to take a closer look you can download the files here.
Thanks for reading this post.