Calculation of electromagnetic fields at low frequencies

Like any physical system, the study of electrotechnical devices generally requires the use of a mathematical model. This is often obtained on the basis of physical considerations and simplifying assumptions about geometric shapes, material behavior and so on. This model, an approximate image of reality, is generally based on equations of varying complexity and number. These equations link quantities that may be local, such as vector fields, or global, such as voltages or currents.

In the case of electrotechnical systems, their behavior can first be represented by equivalent electrical circuits. The parameters of these circuits generally have a physical meaning, and are often related to global quantities such as flux or current in the windings. Even if for the most complex circuits an analytical solution is often difficult, numerical resolution of the equations generally poses no major problems and very quickly leads to an approximate solution with very high accuracy. Although this solution differs from the mathematical model, it is generally very close to it. These simple, fast and numerically robust models greatly facilitate the study of systems.

Nevertheless, a reduced number of equations is often obtained at the cost of constraining simplifying assumptions which, for certain applications, may not be acceptable. For example, models based on equivalent rotating machine diagrams often assume a sinusoidal distribution of induction in the air gap. This assumption then leads to models that cannot accurately quantify torque ripples or local forces. However, for applications where vibratory discretion is an important criterion, it is essential to take account of such phenomena. Furthermore, the precise identification of certain model parameters (such as leakage inductances or air gap reluctances) is often virtually impossible based on the system geometry (dimensions, arrangement of the various mechanical parts) and the physical characteristics of the materials used. It is therefore necessary either to have access to the system itself, in which case identification is carried out on the basis of experimental measurements, or to use a more refined model requiring geometry and material characteristics as input parameters. In this context, if you want to study, improve or design a complex electrotechnical system in greater detail, you need to use a numerical model based on the calculation of electromagnetic fields. This is based on the numerical resolution of Maxwell's equations (see box). These equations are defined for a specific part of space, called the study domain. This must be specified, and the boundary conditions to be verified by the fields on its borders must be defined. Once the equations associated with the boundary conditions have been defined, it is necessary...