# Steady State AC Magnetic: presentation

## Presentation

The Steady state AC Magnetic application allows the study of devices in the harmonic state ( sinusoidal steady state) for a given frequency.

The complex image of Maxwell's equations considers all physical quantities are sinusoidally time-varying for a given frequency. The magnetic field is connected with the presence of the time varying electric currents, compulsory sinusoidal. (Magnet type regions are forbidden).

This application takes into account the currents induced in the conducting regions (eddy currents). It also considers the skin effects* and the proximity effects in the conducting regions.

Note: * There are 3D Steady state AC Magnetic applications where the skin effect can be significant ; which means a significantly smaller skin depth as compared to the eddy current region dimensions.

## Important results

The results obtainable with Steady state AC Magnetic applications are:

• the same as for a Magneto Static application
• the induced currents and the power losses by Joule effect in eddy current regions

The computed physical quantities are sinusoidally time-varying (for a given frequency). It is expressed using their complex images.

Starting from the time dependent quantities, we could compute global, time independent quantities, such as inductance…

## Utilization

The Steady state AC Magnetic application can be used to model devices in different domains such as: induction heating, electromagnetic compatibility in general and electromagnetic screening in particular (e.g. transformers tanks), rotating machines in steady state…

The Steady state AC Magnetic application can be of the field-circuit coupling* type, for the study of rotating machines, of transformers, etc. in steady state, when the numerical model must take into account the electric circuits associated to the device. This application cannot be used with a kinematics coupling.

Note: * See chapter Circuit coupling: principles.

## Restrictions related to complex images!!!

Attention!!! In the context of a Steady state AC Magnetic application, all the physical quantities are expressed using their complex images.

The representation by complex images is valid on the following hypotheses:

• all the materials are linear
• the sources are sinusoidal (the regions containing magnets are forbidden).

Nevertheless, many devices can be studied taking into consideration these hypotheses. Moreover, the utilization of complex images can be extended in some particular cases as in the case presented in the next block.

## Accepted approximations

The utilization of a complex image representation can be extended in some cases:

• First, when taking into account the materials with nonlinear characteristics. Although in this case the quantities are not sinusoidal any longer, a method based on an energetic equivalence allows one to define a B(H) relation called “equivalent”, which takes into account the fact that the quantities are sinusoidal time-varying. So, the result, which is an approximation, since it is expressed under a sinusoidal form, will still give a relatively precise view of the results.
• Moreover, in the case of linear materials you should note that in the case of non-sinusoidal field sources, the problem could be treated as the superposition of many harmonic problems using decomposition in Fourier series. Some authors extend this possibility to the case of nonlinear materials.