High Resolution Modeling of Magnetic Field Exposure Scenarios in the Vicinity of Inductive Wireless Power Transfer Systems

The increasing development and commercialization of electric and hybrid electric vehicles includes the challenge of enabling an efficient and comfortable charging process of a car‘s battery. A promising solution for this purpose is provided by the use of inductive power transfer (IPT) technologies for a contactless charging with an electric power in the order of several kW [1]. A current driven charging coil (primary coil) is positioned on the floor below the car and coupled via an airgap with a secondary coil attached to the bottom of the car. IPT systems generate magneto-quasistatic fields with frequencies from 80 up to 140 kHz. A person positioned inside or near the car, however, will also be exposed to these magnetic fields. Exposure related changes of the electric field strength inside the human body can lead to stimulations of nerve and muscle tissues. Therefore, limits for the volume-averaged body-internal electric strength are proposed by the International Commission on Non-Ionizing Radiation Protection (ICNIRP) [2]. Investigations of the human exposure to magneto-quasistatic fields require the use of high-resolution numerical simulation techniques such as the Finite-Difference Time Domain (FDTD) method. Complex geometries of conductive and/or permeable sheets contained in the IPT system and the car body as well as anatomical body phantoms have to be considered in exposure simulations. Also, potential misalignments between the IPT system’s coils might have an influence on the exposure and need to be taken into account. A high-resolution discretization of such scenarios within commercially available eddy current solvers is often unfeasible as it requires the solution of very high-dimensional and extremely ill-conditioned algebraic systems of equations. As an alternative, three two-step methods have been introduced in [3] and [4] making use of domain decomposition approaches enabling a division of the exposure scenario into two domains: the source area including the influence of shielding geometries and the area occupied by the exposed body. These three two-step methods – the Coupled Scaled-Frequency (SF-)FDTD method, the Co-Simulation SF-FDTD method and the Co-Simulation Scalar-Potential Finite Difference (SPFD) method – are used here for a high-resolution modeling of magneto-quasistatic exposure scenarios including realistic models of various IPT systems, the car and the human body. With the application of the two-step methods a reduction of the memory demands and the simulation time is achieved in comparison to a monolithic application of the SF-FDTD method and the simulations can be performed on a standard computer workstation. Figure 1 a) shows an exposure scenario where a human body model (body phantom Duke [5]) is positioned beside a car model with an IPT system positioned below the car. For an improvement of the coupling between the IPT’s coils, optimization analyses are conducted using an FEM-based magneto-quasistatic field solver included in the software ANSYS Maxwell 3D [6]. Here, different geometry designs are compared to each other regarding an optimization of the coupling coefficient and a reduction of the magnetic leakage fields, coincidentally. The optimized model geometries of different IPT systems are used in exposure analyses carried out with the abovementioned two-step methods. In a first step, the magnetic source field simulation is performed with the software CST Microwave Studio (MWS) [7]. The simulation model includes the IPT system and the car body sheets, but not the human body model, since its interaction with the magnetic source field is negligible. Source field simulations are also carried out considering lateral misalignment of the IPT system’s coils and different values for the thickness of the car body sheets for an analysis of a consequential variation of the leakage fields – and thus the exposure of the human body. Figure 1 b) shows the magnetic flux density in a cross section of the car and in the center of the IPT system with the designated position of the human body model indicated. In a second step, the exposure of the human body is calculated, i.e., the exposure-related distribution of the body-internal electric field strengths, using the previously calculated source fields. Within the two-step SF-FDTD methods this second step is also carried out using CST MWS or, alternatively, using the software Sim4Life [8], whereas within the Co-Simulation SPFD method a discrete Poisson equation is solved using a preconditioned conjugate gradient solver. A high flexibility is achieved by the use of the Co-Simulation SPFD method (as well as with the Co-Sim SF-FDTD method), since the magnetic source field simulation can be computed using any magnetic field simulation tool. Figure 1 c) shows the electric field strength in the median plane of the human body voxel model. The maximum voxel-averaged electric field strength is evaluated for each scenario to analyze the influence of each configuration (different IPT systems, coil misalignments and car body sheet thicknesses) on the exposure and for an exposure assessment according to the ICNIRP guidelines.