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A least-squares algorithm has been implemented using the three-dimensional finite element method and tested on the unipolar ion-flow field problem in HVDC systems with unstructured mesh. The two-dimensional extruded example shows promising results for more complex three-dimensional modeling. Indeed, the close agreement between the 3D and 2D simulation results for both the charge density distribution and the electric field on the exterior boundary demonstrates the robustness of the algorithm.

The electromagnetic modeling of Printed Circuit boards (PCB) is often carried out with the analytic formula or two dimensional simulation, which can not take into account the three dimensional effect. In this paper, the PCB is simulated using full maxwell equation discretized finite element methods. The result is compared with experimental measurement.

Real time models of electrical machines are mainly based on equivalent electrical circuits to calculate the global quantities like current, voltage or torque. Other quantity of interest like iron or joules losses in the permanent magnets can be also obtained by means of lookup tables filled from experimental results or offline simulation based on a finite element model for example. Technics are now available to derive reduced models from solutions set of finite element model calculated for different values of parameters. With these reduced models any quantity of interest can be calculated for any values of parameters. Besides, boards embedded very powerful Field-Programmable Gate Array (FPGA) are available making it possible to expect that the reduced models can run in real time. In this communication, we describe how real time model derived from a 3D finite element model is implemented on an FPGA. The example of application is a single-phase transformer considering the primary and secondary currents as parameters and we show that we can calculate global quantities as the magnetic linkage flux in the windings or local quantities like the value of the magnetic flux density in any point with a computational time lower than 1 microsecond. Using the fiber optic link, the model can be coupled with other real time simulator or power amplifier. The co-simulation with the Opal-RT simulator has been done to validate the model. Within the project MAXIMA, this work will contribute to the development of a real time model derived from a FE model, which is a brick to construct a digital twin of an axial flux machine.

The Cauer Ladder Networks (CLN) method has been already applied to reduce a Finite Element (FE) model of an electro-quasistatic problem. The obtained reduced model is based on two equivalent electrical circuits. In this communication, we modify the FE model in order to obtain a reduced model based on only one equivalent electrical circuit when applying the CLN method. The proposed approach is applied on a bushing of a high voltage transformer.