Simplified power transformer models for environmental magnetic impact analysis

In the paper a comparison among different analytical integral models to the simulation of the outer magnetic field generated by power transformer is presented. The proposed models are adopted for cast resin transformer where the contribution of the winding become significant compared to the contribution of the low voltage (LV) terminals and connection; in the case of oil transformer the metallic tank shield the field produced by the windings. An analytical integral approach is useful in order to insert the proposed model in a simulation environment that discretize only the sources by the Biot-Savart law. The two proposed models are based on the main assumption to neglect the presence of the magnetic core and consider the contributions of the two windings, primary and secondary, supplied with the same amperturns but with opposite directions. The models differ from the formula adopted in the calculation of the magnetic field generated by the coils that compose the windings of the transformer. A first model is described by an easy closed formula based on the hypothesis that the field point is far from the source and the distance is much greater than the coil dimensions; this model is less accurate close to the transformer. A second model integrate the magnetic field generated by two solid solenoids that represent the primary and secondary winding without introducing any hypothesis. The integration process requires the integration of first and second kind Bessel function. Such model can provide the magnetic field also really “near” the transformer windings. In the paper a full comparison among the models and with numerical simulation provided by FEM code is provided. Moreover a comparison with experimental results on a 630 kVA put in evidence the validity of the proposed analytical approach.