Modélisation des systèmes électriques sous contraintes actives et passives combinées dans le cadre de l’électrification d’avions légers

Due to its predominantly decarbonised nature in France, electricity represents an increasingly part of the energy sources linked to individual or collective mobility systems: electric bicycles, electric cars, autonomous electric trains, more electric aircraft, etc. This energy transition is necessarily accompanied by a policy of designing energy-saving systems with maximised efficiency. This increase of efficiency involves, for example, the use of advanced electrical energy conversion structures that use magnetic coupling materials [1]. Magnetic structures are designed using precise local finite element methods. On the opposite, the models of these structures for systemic simulations are based on global characteristics such as impedance. The two previous approaches are not directly compatible.

Magnetic materials, whether hard to generate magnets or soft to create magnetic circuits, are widely used in electrical engineering systems, ranging from the rotating motor to the transformer present in static interleaved DC/DC converters for example. Magnetic materials involves multiphysical phenomena with temperature effects on magnetism (Curie temperature), magneto-mechanical effects such as magnetostriction [2], effects due to corrosion or effects due to the nature of the material itself [3].

The modelling of magnetic materials can usually be done macroscopically at the scale of the magnetic component with specific parameters such as the remanent field or the coercive excitation. This method does not always take into account the multiphysical phenomena.  Another approach consists in applying a local finite element modelling whose finesse allows to take into account the couplings but not the dynamic behaviour of the material. 

Many of works in our laboratory aim to model coupled phenomena within electrical engineering and power electronics systems (electrical, thermal, mechanical, etc.) [4] using the same tool for systemic representation of physical phenomena: the bond graph [5]. This tool then leads to a dynamic representation of multiphysical systems combining macroscopic and microscopic characteristics. It has also been shown that bond graphs can be adapted to systems governed by irreversible partial differential equations such as diffusion equations.

In addition, recent works at LGP have focused on identifying the characteristics of non-linear magnetic materials through the study of their hysteresis cycle [6] with the aim of including these models in a dynamic simulation of a more complex system.  The limitation of these models lies in their phenomenological aspects, from which time is often excluded as a variable. Thus, these models cannot be easily inserted into a temporal systemic simulation. Moreover, locally, the electromagnetic field responds to partial differential equations, thus allowing a temporal simulation of quantities on a microscopic scale relative to the magnetic component. Moreover, the electromagnetic field can be seen as a vector field carrying power and can therefore also be represented using the bond graph tool.

The objective of this research work is therefore to overcome the weaknesses initially mentioned by applying the energy methodology deployed at LGP on electromagnetic fields within magnetic materials and then to couple this local microscopic study with the previous results on the macroscopic characterisation of magnetic materials in order to produce, through a change of scale, a model that can be directly included in a systemic simulation.

The work of the thesis will thus be articulated around 2 main and complementary activities:

- Local energetic representation of electromagnetic phenomena governed by second order partial differential equations (Maxwell's equations) by bond graph,

- Taking into account the local intrinsic physical properties of the material in order to reproduce macroscopic behaviour such as hysteresis.

After a phase of understanding of the subject associated with a bibliographical study, the study of phenomena governed by Maxwell's equations will be tackled. This will be completed using the bond graph tool on the basis of work already carried out at LGP. The proposed approach will be applied to the circulation of the magnetic field in and around ferromagnetic materials.  The bond graph modelling will lead to the expression of dynamic equations that can be simulated with numerical software such as Matlab. A comparative study can then be conducted using classical finite element software such as Ansys. In addition, the LGP has tools for measuring local magnetic fields, which can be used to validate certain results [7]. Initially, the work will concern simple systems such as the study of the magnetic field of an air coil. It will then be possible to develop the models in the case of electromagnetic propagation in material media. The case of the core coil and magnetic couplers for interleaved converters will be developed.

The work will analyse if the bond graph, due to its properties, will be able to provide complementary analysis elements on the frequency behaviour of quantities but also on the characteristics of energy transfers through electromagnetic fields. It is expected that the work will highlight the possible limitations or advantages of this representation approach in relation to existing tools widely presented in literature.

The second phase of the work will focus on physical scaling methodologies that will allow to link local properties and behaviours of magnetic materials such as the state of the material to observable and quantifiable phenomena at the macroscopic scale. This crucial work could allow, via a unique approach, to insert the local multiphysical models developed into systemic time simulations. This would allow, for example, to study the global influence of temperature on the energy performance of static converters, thus allowing the optimisation of conversion efficiencies. As a consequence, this work could allow the macroscopic magnetic analysis of a material to be compared with its health condition or ageing.

In summary, the thesis work should enable the establishment of a generic approach for the implementation of a bond graph type representation for the modelling of electromagnetic phenomena in magnetic systems included in static conversion structures used for electric mobility. Thus, the interest of this work will be to link properties and multi-scale dynamic models of materials with the objective of revealing the limits and advantages at the scale of the global system.

1. L. Havez, E. Sarraute, and D. Flumian, « 3d Virtual Identification of a Power Inter Cell Transformer », in PCIM Europe 2015 ; International Exhibition and Conference for Power Electronics, Intelligent Motion, Renewable Energy and Energy Management ; Proceedings of, pp. 1-8, 2015.
2. V. Segouin, M. Domenjoud, Y. Bernard, L. Daniel, « Electro-mechanical behaviour of ferroelectrics: Insights into local contributions from macroscopic measurements », Acta Materialia, vol. 211, 2021.
3. I. Costa, M. C. L. Oliveira, H. G. de Melo , R. N. Faria, « The effect of the magnetic field on the corrosion behavior of Nd–Fe–B permanent magnets », Journal of magnetism and magnetic materials, vol. 278, 2004.
4. B. Trajin, P.-E. Vidal, « Bond graph multi-physics modeling of encapsulating materials in power electronic modules », European Physical Journal Applied Physics, vol. 89, no. 2, 2020.
5. W. Borutzky, « Bond graph methodology - Development and analysis of multidisciplinary dynamic system models », Springer, 2010.
6. S. Amirdehi, B. Trajin, P.-E. Vidal, J. Vally, D. Colin, « Power transformer model in railway applications based on bond graph and parameter identification », IEEE Transactions on Transportation Electrification, vol.6, no.2, 2020.
7. G. Viné, P.-E. Vidal, J.M. Dienot, « Electromagnetic antenna for power electronic modules: towards a real time electromagnetic characterization »,  19th Conference on Power Electronics and Applications (and Exhibition), 2017.

The Production Engineering Laboratory (Laboratoire Génie de Production or LGP) can trace its origins back to 1989.

It is housed at the Ecole Nationale d’Ingénieurs de Tarbes– French National Industrial and Mechanical Engineering School, located in the South-West of France. The LGP has had a strong track record since its early days and has been recognised by the French Ministry of Higher Education and Research since 1991.

As such, the LGP is part of the research Pole of the University of Technology of Tarbes and University of Toulouse.

Le (la) candidat(e) devra être issu d’une formation scientifique spécialisée dans un des domaines suivants : génie électrique et automatique / électronique de puissance. Outre des qualités techniques avérées, le (la) candidat(e) devra posséder une curiosité scientifique pour aborder les différentes étapes proposées mais aussi être force de proposition dans le déroulement de l’étude. Une bonne maîtrise des outils de simulation numérique ainsi qu’une compréhension des concepts de modélisation multiphysique sont demandées. Une expérience en test et validation de systèmes électriques constituerait un plus significatif. La maîtrise de logiciels Matlab et/ou Python est demandée. Le (la) candidat(e) devra également posséder un bon niveau de maîtrise de l’anglais et des qualités de communication et de synthèse écrites et orales en français comme en anglais.