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This paper aims to present a fast and modular framework implementation for the thermal analyses of foreign metal objects in the context of wireless power transfer (WPT) to evaluate whether they pose a hazard to the system. This framework serves as a decision-making tool for determining the necessity of foreign object detection in certain applications and at certain transmitted power levels.

To assess the necessity of implementing foreign object detection, the considered WPT system is modeled, and Arnoldi-Krylov-based model order reduction is applied to generate separate reduced models of the ground and vehicle modules of the WPT system. This enables interoperable evaluations to be conducted. Further discussion on the implementation details of the system-level simulations used to evaluate the electrical and thermal characteristics is provided. The resulting modular implementation allows for efficient evaluation of the thermal behavior of the wireless charging system at various transferred power levels and under various boundary conditions.

Based on the transferred power level, the WPT model, the relative positioning between the vehicle and the charging pad and the charging time, it may be necessary to divide the area of the charging pad into multiple regions for the purpose of implementing foreign object detection.

While the tools and fundamentals of thermal analysis are widely known and used, their application to high-power WPT systems for electric vehicles has not yet been thoroughly discussed in this form in the literature. The approach presented in this paper is not limited to the specific WPT model discussed but rather is directly applicable to other WPT models as well.

In this paper, the authors study the nonlinear matrix equation Xp=Q±A(X-1+B)-1AT, that occurs in many applications such as in filtering, network systems, optimal control and control theory.

The authors present some theoretical results for the existence of the solution of this nonlinear matrix equation. Then the authors propose two iterative schemes without inversion to find the solution to the nonlinear matrix equation based on Newton's method and fixed-point iteration. Also the authors show that the proposed iterative schemes converge to the solution of the nonlinear matrix equation, under situations.

The efficiency indices of the proposed schemes are presented, and since the initial guesses of the proposed iterative schemes have a high cost, the authors reduce their cost by changing them. Therefore, compared to the previous scheme, the proposed schemes have superior efficiency indices.

Finally, the accuracy and effectiveness of the proposed schemes in comparison to an existing scheme are demonstrated by various numerical examples. Moreover, as an application, by using the proposed schemes, the authors can get the optimal controller state feedback of $x(t+1) = A x(t) + C v(t)$.