A New Multiconductor Cell Three-Dimension Matrix-Based Analysis Applied to a Three-Core Armoured Cable

In this paper, a procedure based on three-dimension matrices is presented: it is the generalization of multiconductor cell analysis to any transmission line where the positions of all the active and passive conductors may change with continuity along their length. A meaningful example of this is given by a three-core single lead-screened armoured cable where cores and armour wires are wound helically with different lay lengths. Therefore, this generalization is presented with reference to these cables but it can be applied to any transmission line. The proposed matrix procedures can be implemented in any standard computer by means of a mathematical software (e.g., MATLAB). The computational complexity of this novel method is shown in comparison with the finite element method commercial software FLUX 3D, which takes 70 h for meshing and solving a 3-m long model. On the contrary, the present matrix algorithms take from minute fractions to maximum 2 min (depending on subconductor number) to obtain results having negligible differences with respect to FEM FLUX 3D ones if paramagnetic materials are involved and differences up to maximum 7% with ferromagnetic ones (which imply, for submarine cable installations, a current rating computation difference lower than 3%).