Coil Conductor region with losses and simplified geometrical description

Introduction

This chapter discusses the creation of coil conductor regions with losses and a simplified geometric description. This type of coil region adds basic information to a coil conductor region without losses, allowing Flux to evaluate the Joule losses in the winding.

The following topics are covered in this documentation:

What this type of region models.
How to create a coil conductor region with losses and simplified geometrical description in a Flux project.
Limitations.
Example of application.

What this type of region models

The coil conductor region with simplified geometrical description allows the user to represent a coil in the Finite Element domain. The region behaves as a magnetic field source and may be driven either by a coupled circuit or have its current imposed by the user.

When compared to the coil conductor region without losses, this type of coil region requires the user to provide only two additional parameters: the material of the coil and its filling factor.

This extra information allows Flux to evaluate the Joule losses in the winding, but is insufficient for a complete consideration of skin and proximity effects through homogenization. On the other hand, the losses evaluated in this region are considered in Flux magneto-thermal applications (AC Steady State Magnetic - Transient Thermal).

Consequently, this coil region type is well adapted to the modeling of devices in which the Joule loss distribution is not relevant nor frequency dependent. Under such circumstances, Flux will accurately evaluate the losses based upon a description of the winding that remains compact and straightforward.

The coil conductor region with simplified description also supports an additional resistance, which is provided as a lumped resistance value while creating its associated FE coupling component.

For further details on extending the capabilities of a coil conductor region with simplified description to account for the skin and proximity effects, the user is referred to the following documentation topic:

Coil Conductor region with losses and detailed geometrical description.

How to create it in a Flux project

In Flux 2D and in Flux Skew, the coil conductor region with simplified description is a surface region, while in Flux 3D it becomes a volume region. The availability of these regions in Flux FEM applications is discussed in the following documentation topic: Coil models and their availability in Flux projects.

In any case, this region may be created as follows:

while creating a new region, select Coil Conductor Region in the drop-down menu Type of region;
then, in the Basic Definition tab, proceed in the same manner as in the case of a coil conductor region without losses.
in the Coil Loss Models tab, check the option Compute coil losses (winding geometry details required) and then:
- Provide a material for the coil conductor.
- Select Simplified description (neglects proximity and skin effects) in the drop-down menu.
- Provide the coil fill factor.

Note: The provided material must have a defined electrical property; that is, it must contain a model for the constitutive relation J(E) relating the current density J to the electric field E. The simplest approach would be using a material with a constant, isotropic resistivity ρ = 1/σ in such a way that J = σE. Other resistivity models are available in Flux, and the user could also rely on Flux Material Manager to import predefined materials in the Flux project.

Note: The coil fill factor is a real-valued formula or a number in the range ]0,1] . It measures the ratio between the conductor volume and the volume needed to house the winding (including an insulator or dielectric). A tightly-packed winding has a fill factor close to 1, while loosely-wound coils will exhibit lower fill factor values.

Limitations

Differently from the coil conductor region without losses, this region includes a material in its description. Consequently, the user may post-process quantities related to the material resistivity in the surface (in 2D) or volume (in 3D) regions representing the coil (e.g., the power loss density in the winding or the total dissipated power). In the case of a coil conductor region without losses, the user was constrained to use the FE coupling component as a computation support.

Consequently, the Joule losses dissipated by the coil may be evaluated in the following ways:

Using the Computation menu, followed by the following choices: On physical entity → Compute → Region.
Using the Computation menu, followed by the following choices: On physical entity → Compute → Circuit.
With a sensor (Predefined type: Losses by Joule effect) on a Volumer region or in Surface region.
With a sensor (Predefined type: Losses by Joule effect) on a Stranded Coil Conductor component.

Keep in mind, however, that only approaches 2 and 4 above (i.e., those employing the FE coupling component as a computation support) will directly evaluate the total Joule losses in projects containing symmetries or periodicities. Under such circumstances, approaches 1 and 3 (which use the region as a computation support) yield losses values that must be multiplied by a factor k, in which k equals the number of "copies" of the region generated by the symmetry or periodicity.

Moreover, it should be remarked that approaches 1 and 2 do not account for the power dissipated in the additional resistance of the FE coupling component.

The coil conductor region does not take the skin and proximity effects into account. Consequently, its use is not recommended in projects requiring a detailed evaluation of the current and loss density distributions in a winding.

Example of application

Let's consider the modeling of a solenoid in Flux 3D. A similar coil has already been analyzed in the documentation chapter presenting the coil conductor region without losses, in which the solenoid inductances were evaluated with the help of sensors and compared to an analytical formula.

In that example, the user could create a coil conductor region without losses by providing only the number of turns N = 500 and without assigning a material to the region. Furthermore, let's suppose in what follows that:

the solenoid is made from a copper (which is a material promptly available in Flux Material Manager) and
its fill factor is 0,747.

This additional information permits enhancing the previous model by choosing the coil conductor region with simplified geometrical to represent the solenoid in Flux 3D.

The recompense from using this more elaborate type of region is that Flux becomes capable of evaluating additional quantities in the post-processing stage. Figure 1 shows a few examples that were obtained in a Steady State AC project representing the solenoid, for a sinusoidal current of 1/√(2) A RMS.

Figure 1. While post-processing current density distribution (a) was already possible with a coil conductor region without losses, using a coil conductor region with losses allows post-processing additional quantities such as the Joule loss density (b) and the magnetic energy density (c).

Note, however, that the coil conductor region with simplified geometrical description still does not account for current concentration effects such as the skin and proximity effects. Consequently, in the Steady State AC application considered in this example, quantities related to the current distribution in the winding result uniformly distributed in the coil (e.g., current density, Joule losses density) and remain constant at higher frequencies (e.g. coil resistance, inductance, current density and Joule losses density).

This behavior is highlighted in Table 1, which compares a few relevant quantities evaluated with the same AC Steady State application representing the solenoid. The values in that table were evaluated with the help of sensors and I/O parameters in Flux 3D for two different frequencies.

Table 1. Evaluation of AC Steady State quantities in Flux 3D with a coil conductor region with simplified geometrical description at two frequencies. The current and voltage phasors correspond to peak values.
Frequency (Hz)	Current (A)	Voltage (V)	Resistance (Ω)	Inductance (mH)	Reactance (Ω)	Active Power (W)	Reactive Power (VA)
150	1+ j 0	1.50 + j 1.48	1.5	1.568	1.48	0.75	0.74
400	1 + j 0	1.50 + j 3.94	1.5	1.568	3.94	0.75	1.97

The complex values of current, voltage and power evaluated by Flux and available in Table 1 are represented in the time domain in Figure 2. The plots in that figure show that the behavior of the coil conductor region with losses and simplified geometrical description in this example is similar to the one of a series RL network with fixed resistance and inductance.

Figure 2. Time domain representation of the voltage, current and power in the solenoid