Analytical solutions for the electric field of high-voltage direct current submarine cable

Analytical solutions are derived using image theory for the electric field of submarine high voltage direct current (HVDC) bipolar cable. The derived formulas are validated by ensuring their compliance with both the tangential and normal boundary conditions at material interfaces. To show the applicability and usefulness of this formulation, a MATLAB computer program is written to apply the equations, and various electric field solutions above and below the sea surface are presented for different depths and separation distances between the conductors. This study provides easy-to-use equations in order to be able to evaluate the electric field emitted by a submarine cable. It is important to highlight that the formulation is general and can be applied to any similar cable configuration.