Modelling the Transient Response of Windings, Laminated Steel Cores and Electromagnetic Power Devices by Means of Lumped Circuits

Holmberg, P. 2000. Modelling the transient response of windings, laminated steel cores and electromagnetic power devices by means of lumped circuits. With special reference to windings with a coaxial insulation system. Acta Universitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 592. 97 pp. Uppsala. ISBN 91-554-4877-1 Electromagnetic transients impinging on electromagnetic power devices — such as electric machines, transformers and reactors — can stress the design severely. Thus the magnitudes of the transients are often decisive for the design of the devices. Further, the operation of a device can be transient in itself. This is the case for the explosive magnetic flux compression generator (EMG) and a ferromagnetic actuator. Models are presented that are mainly intended for transients in the millisecond range and faster. Hence, eddy currents and the related skin and proximity effect become significant in windings, magnetic cores and in the armatures of the devices. These effects are important for, e.g., the damping of the transients. Further, the displacement current in the insulation of the winding is significant. It changes the response of the windings dramatically, as it manifests the finite velocity of propagation of the electromagnetic fields. Under such circumstances, reflections and excited resonances can make the transient voltage and current distribution highly irregular. Induced voltages are modelled with self and mutual inductances or reluctances combined with winding templates. The displacement currents are modelled with capacitances or coefficients of potential. Cauer circuits and their dual form are used to model eddy currents in laminated cores and in conductors. The Cauer circuit enables one to consider hysteresis and the non-linear response of a magnetic core. It is also used to model the eddy currents in the moving armature of an EMG. A set-up is presented that can be used to study the transient voltage and the current distribution along a coil. The transient response of coaxially insulated windings is analysed and modelled in detail. A lumped circuit model is developed for a coil, Dryformer — the new high-voltage transformer — and Powerformer, the new high-voltage generator. An alternative model, a combined lumped circuit and FEM model, is presented for a coaxially insulated winding in two slot cores.