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Despite its well-founded criticism and lack of proper justification under core saturation conditions, the T-equivalent transformer model (Steinmetz scheme) is obviously championing in the literature. This educational paper aims to explain in a simple manner the limitations of the T-model of a low-frequency transformer and critically analyses some attempts to improve it.

Using a simplified examination of magnetic fluxes in the core and windings and using the modeling in ATPDraw, it is shown that transient transformer models with the indivisible leakage inductance allow circumventing the drawbacks of the T-model.

The authors show the absence of valid grounds for subdividing the leakage inductance of a transformer between its primary and secondary windings. The connection between the use of individual leakage inductances and inaccurate prediction of inrush current peaks is outlined as an important example.

The presented models can be used either as independent tools or serve as a reference for subsequent developments.

Over generations, the habitual transformer T-equivalent is widely used by engineers and Electromagnetic Transients Program experts with no attention to its inadequacy under core saturation conditions. Having studied typical winding configurations, the authors have shown that neither of them has any relation to the T-equivalent.

This educational paper will contribute to the correct understanding of the transients occurring in a transformer under abnormal conditions such as inrush current or ferroresonance events, as well as during an out-of-phase synchronization of step-up generator transformers.

To demonstrate the improvement of three‐axial magnetic sensors systems for magnetocardiography when using minimum norm solutions (MNS).

The thesis is proved by using figures of merit and by means of repeated numerical simulations, starting from a BEM model for forward calculations.

We found out that both for under‐determined and over‐determined problems two figures of merit show better performance of a three‐axial sensor system when compared with two mono‐axial sensor systems. We also showed the positive impact of three component magnetic field data on MNS by means of repeated simulations.

The analysis is limited to theoretical sensor systems and can be applied also to realistic measurement set‐ups. Noise is considered uncorrelated. The analysis could be carried out with the help of other figures of merit. More refined models for the human body could be adopted.

The use of three axial sensor systems is encouraged in the field of magnetocardiography.

Numerical analysis of inversion algorithms using three‐dimensional magnetic field data in magnetocardiography have been never carried out.

To provide a time domain formulation for reconstruction of transient currents flowing in massive parallel conductors from magnetic data collected in the dielectric space surrounding the conductors.

A boundary integral equation (BIE) formulation involving Mitzner's and Rytov's high order surface impedance boundary conditions (SIBCs) is used. Input data of the inverse problem are the magnetic fields at given locations near the conductors. In order to validate the inversion algorithm, the magnetic field data are computed solving the direct problem with FEM for given current waveforms.

The improvement in reconstruction accuracy of the new time domain BIE formulation employing high order SIBCs has been demonstrated numerically in a simple test case. The range of validity of the technique has been extended to current pulses of longer duration and the computational burden has shown to increase only by a factor of 4.

The proposed formulation can be compared with other possible formulations, both in the time and in the frequency domain.

Based on this formulation a new current sensing technique is proposed for realization of low cost current sensors based on magnetic sensor arrays.

The inverse problem addressed in the paper has been solved for the first time.