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Regarding standards, it is well established that common mode currents are the main source of far field emitted by variable frequency drive (VFD)-cable-motor associations. These currents are generated by the combination of floating potentials with stray capacitances between these floating potential tracks and the mechanical parts connected to the earth (the heatsink or cables are usual examples). Nowadays, due to frequency and power increases, the systematic compliance to EMC (ElectroMagnetic Compatibility) becomes increasingly difficult and costly for industrials. As a consequence, there is a well-identified need to investigate practical and low cost solutions to reduce the radiated fields of VFD-cable-motor associations. A well-adapted solution is the shielding of wound components well known as the major source of near magnetic field. However, this solution is not convenient, it is expensive and may not be efficient regarding far field reduction. Optimizing the components placement could be a better and cheaper solution. As a consequence, dedicated tools have to be developed to efficiently investigate not easy comprehendible phenomena and finally to control EMC disturbances using component placement, layout geometry, shielding design if needed. However, none of the modeling methods usually used in industry complies with large frequency range and far field models including magnetic materials, multilayer PCBs, and shielding. The contribution of this paper is to show that alternatives regarding modeling solutions exist and can be used to get in-deep analysis of such complex structures. It is shown in this paper that near field investigations can give information on far field behavior. It is illustrated by an investigation of near field interactions and shielding influence using a FE-PEEC hybrid method. The test case combining a common mode filter with the floating potentials tracks of an inverter is based on an industrial and commercialized VFD. The near field interactions between the common mode inductance and the tracks with floating potentials are revealed. Then, the influence of the common mode inductance shielding is analyzed.

Many studies have been carried out on EMC (ElectroMagnetic Compatibility) modeling of power electronic devices. Indeed, this field of research is closely linked to industrial constraints and needs, inherited from standards. Considering EMC purpose, developing reliable models in the early phase of the design of power electronics devices is a suitable solution. Several Computer Aided Design (CAD) tools have been developed as such [

These CAD tools must give quite complete models with parametric descriptions, so that industrial solutions can be improved. That is why layout techniques with a placement of components limiting EMC disturbances have been investigated [

To simplify the problem a near field analysis is developed in this paper. Shielding, layout complexity and component placement are taken into account. Moreover, from this analysis the behavior in far field can be deduced. The modeling method is presented in [

In a first part, the mechanisms linked to the generation of EMC perturbations in power converters are presented in order to explain how near field interactions can impact far field levels. In a second part, the usual modeling methods are presented and their limitations are highlighted. Regarding the complexity of required models these classical approaches need to be improved. A FE-PEEC coupling solution is used and presented [

The increase of power and frequency amplifies the disturbance level. Moreover, for marketing considerations, an increase of performance must not be threatened by the level of pollution of new structures. The means of disturbance reduction depend on the frequency range, which extends from some Hertz to a few Gigahertzes. Electromagnetic disturbances can be separated into two bands: Below 30MHz, the conducted ones are preponderant, beyond is the domain of radiated disturbances. In our case, the studied power electronics structure is a VFD. Multilayer printed circuits are often used because of thermal constraints. As a consequence, a full modeling of the geometries can be complex. Moreover, depending on the applications and the power range, the switching frequency is usually comprised between 10 kHz and 100 kHz. Conducted band studies show that the spectrum shapes are closely linked to the driver configurations. Indeed, EMC perturbations of a static converter are due to the differential and common mode currents [

Considering the static converter as an antenna, the semi-conductor component is the source and the cabling is the path. While switching, a semi-conductor component generates a high d

These phenomenons can be measured. As an example,

A useful solution is to shield the main near magnetic sources, here the common mode inductance. However, this drastically increases the weight and cost of the final product. In order to quantify the impact of the couplings and shielding on floating potentials, models need to be developed.

Voltage driven mechanism of common mode current generation.

Correlation between far field and common mode.

Electrical equivalent models are necessary to take into account EMC constraints during the design process. According to the studied component, the modeling method that will be used to evaluate EMC performances will be different, depending on its nature, the required accuracy and the level of the model. Models have to consider heterogeneity of media (Magnetic components, copper tracks, substrates such as FR4 for example and air) and multilayer topologies.

On the one hand, Method of Moments (MoM) and method of Partial Element Equivalent Circuits (PEEC) are useful because they are not expensive in computational time. Indeed, they do not require meshing the whole considered space [

A complex system such as motor drivers is made of many thin conductors and ferromagnetic materials. Modeling them using FEM requires a lot of meshes, which becomes too problematic to find a solution. For power electronics applications, this step has to answer two very strict conditions:

Close to the conductors, variations of magnetic field is very important [

Geometry of conductors is very hard to mesh with a good quality since it can be constituted by very this planes like DBC (Direct Copper Board).

Indeed, a good quality meshing requires two meshes into the skin depth for the skin effect to take into account.

On the other hand, because of three dimensional ferromagnetic materials, it is very complicated to solve this problem by PEEC method. Hence a hybrid method dealing with this type of problem was developed [

PEEC method easily takes into account interactions between complex 3D massive conductors;

FEM takes the interaction between conductors and ferromagnetic materials into account.

One of the advantages of PEEC method is a simple meshing of conductors since assumptions on their current density can be applied. Skin and induced effects can be easily modeled. Each element of FEM meshing is considered as an inductor with a uniform current density. In other words, a conductor is represented by a set of inductors using this hybrid method. Air around conductors and magnetic regions are still meshed using finite elements.

A general problem with inductors and ferromagnetic material is shown in

General description of FEM-PEEC coupled method.

To adapt FEM to the coupling, the magnetic scalar potential formulation is used. With this formulation, the magnetic field is calculated by a total scalar potential _{0} due to all inductors as Equation (1).

Ω_{0} is the region with air including the conductors. Ω_{1} is the ferromagnetic region. _{0} can be expressed with _{0k} representing the source of 1 A in the inductor k and its current _{k} (2).

Because curl _{0} where _{0} =

If _{0k} is the current density of inductor k fed by a current of 1 A, _{0k} has to satisfy (3) and (4).

Equation (4) is imposed because of _{t} continuity on the interface Γ_{01}. _{0k} is expressed by (5).

In Equation (5), _{0k} is the Biot and Savart magnetic field and δϕ_{k} is the jump between scalar and reduced potentials [

Note that this formulation does not require any meshing of the inductors but the source field t_{0k} has to be estimated before the finite element resolution. The weak form of T_{0}-ϕ formulation leads to the finite element matrix system (6).

In Equation (6), terms of matrices A and C are defined by (7).

Where α_{i} and α_{j} are the nodal finite element interpolation functions approximating _{k}, the current _{k} is unknown and a circuit relation must be added [

The magnetic induction in Ω_{0} (air) can be written using (9).

Combining (6) and (8) gives (10).

In equation (10), terms of matrices D and R are defined by (11).

Computations of D_{kl} require a fine meshing around inductors because the variation of _{0k} and _{0l} is very strong around them. To avoid this problem, a coupling of this formulation with PEEC method was proposed. D_{kl} is calculated by the mutual inductance M_{kl} that can be exactly determined by PEEC method. Substituting (5) into (11) gives (12).

The first term of right part of (12) represents the mutual inductance in vacuum between inductor

Note that the terms C_{ik} in (7) can be transformed as follow (14).

This avoids estimating t_{0} in entire domain. t_{0} is computed only on the interface Γ_{01} and on a layer of elements (Ω_{01}, _{0} in entire domain and relaxes the meshing around conductors. This was validated and gives stable results [

The chosen case of study is a simplified structure extracted from the geometry of an industrial variable speed drive. It is composed of a three-phase common mode filter with the floating potential tracks (U, V, W) of an inverter (

Description of the studied layout.

Electrical topology to model interactions.

The toroidal core inductance material is the FT-1KM nanocrystalline, manufactured by Hitachi.

This material has a higher permeability than ferrite; it is first-rated for common mode filtering applications. The initial permeability µr is equal to 16,000 at 20 °C and for a frequency equal to 100 kHz. Each winding is composed of five turns. The theoretical value of the inductance is 1.2 mH. Due to the winding turns, the inductance is the main source in near field. Moreover, because of mutual couplings with the other parts of the structure, additional perturbations can occur.

Regarding the PCB, it is composed of two layers. Phase 1 and 2 are crossed. Phase 3 and the floating potentials U, V and W are routed on the top layer. The copper width is equal to 70 µm. The resolution frequency is chosen equal to the switching frequency (10.6 kHz).

Using the hybrid method that is described in the previous section, the cabling is modeled using PEEC approach and the magnetic material of the inductance using the FE method.

The aim of the study is to evaluate the interactions between the filter and the floating potentials tracks which are the most influent part regarding common mode current generation (ic = C.d

The currents of floating potentials tracks are computed with and without the common mode filter. Hence the influence of the couplings between the floating potential tracks U, V, W, and the common mode filter can be analyzed. In addition,

Coupling and shielding influences on the currents of floating potentials tracks.

Currents without filter (A) | U | V | W |

328.628 | 373.487 | 403.316 | |

Currents with filter (A) | U | V | W |

Without shielding (A) | 465.60 | 527.09 | 570.53 |

With shielding (A) | 465.59 | 527.04 | 570.48 |

Usually, for industrial devices, a well adapted solution is the shielding of wound components well known as the major source of near magnetic. Using the modeling process, a shielding has been easily added on the common mode inductance to evaluate its influence on the currents (

Common mode inductance shielding.

Since the shielding is made of thin plates of conducting material, the classical FE description is not the best way since the low thickness can lead to numerical errors during the solving stage. So an adapted meshing strategy with specific type of mesh has been applied. Its use and the associated formulations are detailed in [

As shown in

Shielding influence repartition.

Shielding influence decreasing.

Regarding the performances of such a modeling process using this hybrid method, its solving time as well as the necessary memory space have been compared with the case of the use of only FE method. With the proposed method, they have been divided by three. Therefore, it is faster for a same problem and is able to solve more complicated structures with higher number of unknowns.

The influence of couplings has been verified by measuring the far field of variable speed drives according to the studied configuration. The emitted field is compared with a topology where the inductance is placed closer to the floating potential tracks (

The geometry is influent and routing process with component placement need to take into account these elements in order to reduce the possible increase of the common mode current.

Two positions of the common mode inductance.

Far field measurement showing the influence of the interactions.

The couplings cannot be neglected in a near field computation. However, is it also the case in a far field context? As a consequence, it is now necessary to compare modeling methods in order to transpose the study in the far field domain. Works are in progress to compare FEM, PEEC and multipole expansion models in far field. For example, a static study of the inductor using FEM and multipole approach is presented on

Magnetic field decrease (modulus)

In this part, the use of the proposed hybrid method on a test case has been detailed in order to underline its advantages and the real help it can bring to designers.

Nevertheless, it can be useful for very various types of applications where both magnetic and non-magnetic components and conductors are in the same structure such as power converters.

The possible parametric description, which is not detailed here, is a real advantage when designers want to evaluate the impact of geometrical but also physical parameters on the EMC performances of the studied structure.

Several conclusions can be made from this analysis focusing on the far field extrapolation from near field interactions. First, these interactions cannot be neglected during the modeling stage of power electronics devices. This is demonstrated thanks to an original modeling method based on the coupling between FEM and PEEC methods. A second conclusion is that the shielding of most polluting sources is not always the most suitable solution. An adequate placement of the components, and more particularly of the floating potential tracks, is a priority. Finally, this kind of modeling approach is very useful to test some improvements on the structure, in order to satisfy the standards and to improve the EMC and EMI performances of power electronic devices. New investigations will be carried out in order to improve the approach by using multipolar expansion for the far field studies.