This paper presents a model based technique to estimate the complex valued permeability of cable armour steel. An efficient analytical model is derived for the linearized mutual impedance of a transformer coil built on a core of magnetic armour steel. A numerical residue calculation is used to solve the related inverse problem based on impedance data. The analytical model is validated using commercial finite element (FEM) software to establish that edge effects can be neglected. The numerical residue calculation is investigated by studying its convergence based on a simple rectangular quadrature rule in comparison to the composite Simpson's rule. When there are no measurement errors, both methods converge with an unexpected high order (superconvergence). However, in practice the estimation performance will be governed by measurement and model errors. Assuming that there are Gaussian measurement errors, the present performance of the estimation technique is quantified and investigated by means of the Crame?r-Rao lower bound. In future, the proposed method will be useful as an input to general calculations of power losses in three-phase power cables.
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