Analysis of Pipe-Type Cable Impedance Formulations at Low Frequencies

This paper analyzes series impedances of screenless cables enclosed by a common conducting pipe. Established analytical formulas for pipe-type cables parameters are analyzed by taking finite pipe thickness and proximity effect into account. Analytical low-frequency approximations are developed and analyzed. The analysis shows that a classical formulation by mixing infinite and finite pipe thickness can result in incorrect inductance and even negative self-resistance at low frequency. This paper analyzes corrections to take a finite pipe thickness into account. Finite-element simulations reveal that the core-to-core proximity effect is substantial for the analyzed cable design with much lower high-frequency inductance than that obtained from analytical formulas. This paper also analyzes given proximity-effect formulations and proposes corrections based on analytical low-frequency approximations. The proposed proximity effect corrections improve resistance and inductance in common and differential mode.