Coils modeling

Foreword: physical aspects

A coil is a two-terminal circuit component formed from a conductor wound to a certain number of turns on a supporting structure. The coil support may be composed of either a magnetic or a non-magnetic core, and most frequently, the conductors employed are single-stranded or multi-stranded wires. Coils may also be constructed by winding conductors with non-circular cross-sections and even metallic sheets or any other shape.

When a power supply is connected to the terminals of a coil, an electrical current traverses the winding and generates a magnetic flux density field in the surrounding media. The resulting field is governed by the Biot-Savart law and stores magnetic energy drawn from the supply. On the other hand, if a time-varying magnetic flux links the coil turns, an electromotive force is induced between its terminals as predicted by Faraday and Lenz laws.

Other secondary physical phenomena also take place, depending on materials and on the time rate of change of the current flowing in the coil. These include Joule losses, which may be augmented by an uneven current density distribution arising from skin and proximity effects at higher frequencies. Coils also tend to resonate at sufficiently high frequencies due to parasitic inter-turn capacitive effects.

The coils in SimLab

The two categorizations will be explained in next paragraphs.

Here is a table showing the categorization of the SimLab coils features:

Multi-stranded coil

The simple representation multi-stranded coil allow to simulate multi-stranded wires in a simplified representation: There is no represention of each strand. As it is a simplified representation, some physical phenomena such as skin effect and proximity effects are not taken into account.

Solid conductor

The solid conductor allow to simulate conducting medium in its real representation. For the winding, each strand must be represented. it takes into account precise local physical phenomena such as skin effect and proximity effects.

Meshed coil

The meshed coils correspond to coils which are meshed bodies and are fully integrated into the finite element domain.

Non-Meshed coil

The non-meshed coil is a 3D coil representation which is not linked to any meshed body (do not belong to the finite element domain). The non-meshed coils should be regarded instead as being superposed to the domain. Analytic Biot-Savart equation is solved to compute the generated magnetic field.

This page explains the main differences between the five possibilities in SimLab to facilitate the choice.

Meshed coils: Coil vs Solid conductor components (Circuit)

The Circuit Designer is available in Magnetic Transient 2D and 3D solutions.

Coil Conductor

The Coil allows to simulate multi-stranded wires in a simplified representation: There is no representation of each strand. Meshed multi-stranded coil are well suited to represent windings composed by a large number of turns of a wire with a relatively small cross-section. Consequently, they are generally assigned to surface bodies (in 2D) or volume bodies (in 3D) representing slots or compartments enclosing the coil turns. Moreover, meshed multi-stranded coil manage all relevant parameters describing the winding configuration inside their enclosure, such as the number of turns and the fill factor. As it is a simplified representation, some physical phenomena such as skin effect and proximity effects are not taken into account. Typical applications: Motor winding, actuator coil etc. Here is an example of meshed multi-stranded coil representation:

Solid Conductor

The Solid Conductor allows to simulate individual conductors with arbitrary cross-section shapes. For the winding, each strand must be represented. it takes into account precise local physical phenomena such as skin effect and proximity effects. Typical applications: Induction heating inductor, winding with a small number of turns with a need of a precise modeling. Here is solid conductor representation for the same example:

Comparison

Here is a comparative table:

Table 1. Comparison of meshed coil modeling approaches in SimLab

Meshed Coil region type	Current density	Mesh	Description of the coupled electric circuit	Frequency behavior of Joule losses
Solid Conductor	Flux evaluates a non-uniform current density distribution reflecting the skin and proximity effects.	Complex meshes required.	Potentially elaborate. One FE coupling component required for each Solid Conductor region.	Skin and proximity effects fully taken into account, leading to augmented Joule losses at higher frequencies.
Coil	Flux evaluates an equivalent uniform current density distribution.	Coarser meshes are possible.	Straightforward. Only one FE coupling component required.	If optional inputs are defined - Coil fill factor value entered and Material with Resistivity value assigned to Coil bodies: Joule losses are non-zero and constant at any frequency. Results are accurate for direct current and low-frequency excitations.
				If optional inputs are not defined: Joule losses are constant and equal to zero at any frequency.

Connection

Meshed coil: Imposed Current Coil LBC (No Circuit)

The Imposed Current Coil LBC is available in Analysis ribbon:

The LBC is available in Magneto Static 2D and 3D and Magnetic Transient 2D and 3D solutions.

This is a particular case of multi-stranded coil with simplified representation, suitable for simple use cases: The coil bodies are not connected to a circuit. All the physical inputs, including an imposed current value, are entered in the LBC dialog box.

Please refer to the previous paragraph to understand the multi-stranded coil with simplified representation.

In this case, the Joule losses are not computed.

Meshed coil: Passive Solid Conductor LBC (No Circuit)

The Passive Solid Conductor LBC is available in Analysis ribbon:

The LBC is available in Magnetic Transient 2D and 3D solutions.

This is a particular case of solid conductor: The solid conductor is not supplied and not connected to a circuit. The solid conductor is "Passive" which means that the only flowing current is an induced current (or eddy current). One typical application is the induction heating, the heated part is modeled as a passive solid conductor.

Meshed coils vs Non-Meshed coils

The meshed coils correspond to coils which are meshed bodies and are fully integrated into the finite element domain.

Solid conductors are well adapted to the modeling of individual conductors with arbitrary cross-section shapes in 2D or 3D simulation. An example is provided in the next image which represents an induction heating coil:

Meshed multi-stranded coils are well suited to represent windings composed by a large number of turns of a wire with a relatively small cross-section. Consequently, they are assigned to surface bodies (in 2D) or volume bodies (in 3D) representing slots or compartments enclosing the coil turns. Moreover, multi-stranded coils manage all relevant parameters describing the winding configuration inside their enclosure, such as the number of turns and the fill factor. The rotating electric machine in the following image illustrates the use of three meshed multi-stranded coil to model a stator winding in 2D:

From a finite element method point of view, the face or volume bodies assigned to a meshed coil belongs to the computational domain and is discretized by finite elements. In consequence, it is possible to evaluate and display local quantities such as the current density, the magnetic induction, and the power loss density inside these bodies.

In 3D applications, however, the description of a coil with an arbitrary shape through a meshed coil may become too complicated, and meshing the associated volume may lead to an excessively large numerical problem. Therefore, 3D Magneto Static and Magnetic Transient solutions provide the user with an alternate way of specifying a coil in 3D: the non-meshed coil magnetic source LBC.

This variety of magnetic source is an entity superposed to the 3D domain and independent from any meshed surface or volume bodies. In a simulation containing a non-meshed coil, the magnetic induction that it generates analytically with the Biot-Savart law is evaluated. Moreover, the finite element formulation implemented in the software takes this additional field contribution into account in the meshed parts of the domain.

However, and in contrast with the case of meshed coils, post-processing local quantities inside a non-meshed coil is impossible.

Non-meshed coils usage is often necessary in 3D, especially on large and complex devices, but also for simple devices containing large coils or many coils (motors, transformers, etc.). The definition becomes easier and the meshing and the solving are faster. In such use cases, the local precise computation on the winding is usually not necessary. Here is an exemple of a transformer with non-meshed coils:

Several predefined templates of non-meshed coils are conveniently available for the user, with geometries ranging like Toric coils. A composed coil type exists as well, allowing the user to create a 3D non-meshed coil of arbitrary shape.

The non-meshed coils are current supplied through the circuit Coil component in Magnetic Transient 3D solution and through an imposed current value in the Non-Meshed Coil LBC dialog box in Magneto Static 3D solution.

For an extended discussion on the use of meshed and non-meshed coils LBC in SimLab, please refer to the Non-Meshed coil page.

Summary comparative table