## 3 WPT Model Decomposition Approach Validation and Optimization
Figure 11: The absolute values of resonant cavity-based WPT system scattering parameters (TEM mode parameters) (**a**) and their phases (**b**) against frequency, calculated using the decomposition approach and directly using Ansys HFSS. are fast but applicable only in the case of a simple objective function landscape, which is not the case in the present study since the objective function must control the shape of the curve of interest. Such complicated optimization tasks typically give objective functions with multiple local minima. Also, constrained optimization requires introducing penalty functions, significantly increasing the floating-point operation count [38]. The global optimization algorithms also require a large number of objective function evaluations to find the global minimum [39; 40]. If the number of parameter value combinations examined per algorithm's iteration is insufficient, there is a high risk of finding a local minimum rather than a global one. Applying a global optimization method to the entire model involving both antennas would lead to a prohibitively large CPU time. To find the optimal parameters of the WPT system under study for each sub-model, the generalized S matrix is calculated using different combinations of parameters. Once the sub-model S parameters are found (precomputed for different combinations of sub-model parameters), the overall WPT system's S parameters can be quickly calculated using a simple MATLAB code--the calculation takes just a few seconds on modern computers. The MATLAB routine combines the precomputed S parameters for different sub-model parameter combinations. As the sub-model parameter space dimensions (the number of parameters varied by the optimization algorithm) are smaller than those of the entire model, the number of combinations for which the S parameters need to be calculated with Ansys HFSS 2023 R1 is considerably reduced, leading to a substantial reduction in the CPU time. This is a distinct advantage of the decomposition method. Also, the decomposition method allows us to divide the WPT system model into smaller sub-models, which allows the S parameters to be computed much faster due to the smaller model size. Thus, using the decomposition method, the exhaustive search-based optimization takes just a few minutes instead of hours or even days. Thus, there is no need for more sophisticated optimization methods. It is worth noting that only those sub-model's parameters are varied that significantly affect the S matrix element values. For instance, in the sub-model involving the dipole antenna, only the feed-line length, dipole length, and reflector length are varied to generate different parameter combinations to be examined. The feed-line width is kept fixed at a value that gives 50 \(\Omega\) characteristic impedance to ensure impedance matching with the generator and the load (an RF-DC converter or RF power meter, depending on the measurement scenario). The width of the dipole is found to have little effect on the curve shape as long as it is not too small or too large. The same applies to the reflector width. Regarding the sub-model containing the Tx antenna director, only the director length is varied, while the width is kept fixed as it does not significantly affect the results. Additionally, the WPT parameters ensuring the strongest coupling between the waveguide and the antennas, as described in the previous section, are used as an initial guess for the optimization process. These parameters minimize the power reflected back to the generator. An exhaustive search is performed across all the precomputed sub-model parameter values and all values of the optimization parameters that are not associated with the sub-model S parameters. The parameters are optimized one at a time; only values corresponding to the precomputed combinations are used. Once all parameters have been changed, the process is repeated. The algorithm executes until no further improvements are obtained by varying the parameter values.