Study of Current Distribution over a Power Cable Presenting Non-Uniform Geometry using the Partial Differential Equations Approach

Abstract

This   paper   presents   a   theoretical   study   of   the currents  and  voltages  characteristics  transmission  over  an  energy cable  (Power  Line  Transmission  PLT).  The  geometry  of  line  is non-uniform.  The  proposed  approach  is  based  on  the  Distributed Network  model,  where  the  lumped  parameters  vary  as  the  line's geometry. Most of the numerical methods applied use a frequency approach. However,  other  techniques  are  available  in  the  time  domain  that are  more  applicable  when  the  perturbation  is  transitory  or  an impulse.  The  partial  differential  equations  (PDE)  of  telegraphers  with variable  coefficients  are  used  in  order  to  model  the  transmission over non-uniform lines.  This  paper  presents  the  adaptation  and  application  of  the  FDTD method  to  solve  the  problem  of  transmission  of  an  electric  wave over  a  transmission  line  whose  electromagnetic  topology  is  non-uniform. As an  example, the final  part of  the paper proposes  the  modeling of    the  transmission  of  a  transitory  wave  over  an  electric  power cable. We present an application in the case of the propagation of lightning on an energy cable composed of three twisted wires. The validation  of  the  proposed  method  will  be  set  by  comparing  the obtained  results  with  those  obtained  from  a  simulation  in  the frequency domain followed by an IFFT.