# Effective Scheme for Inductive Wireless Power Coil Design Using Scan-and-Zoom Optimization
## 1 Introduction  
Wireless power transfer technology has recently become widely used in a variety of applications. Inductive power transfer (IPT) in Figure 1 utilizes electro-magnetic coupling that has a low coupling coefficient and thus a high leakage inductance [1; 2; 3]. For this reason, it is difficult to achieve a high power transfer efficiency (PTE) when the transmitter (\(Tx\)) and receiver (\(Rx\)) coils are directly connected to the circuit and compensation circuits are connected to each of the \(Tx\) and \(Rx\) coils to make an impedance compensation [4]. Therefore, it is important to design the \(Tx\) and \(Rx\) coils to maximize the PTE considering the compensation circuit along with the coil geometric parameters.  
One of the most popular coil design methods is to directly use the inductance formula. The optimal coil design using the Neumann formula is introduced in reference [5] to calculate the self-mutual inductance of the coil. However, it is too difficult to obtain the general inductance and mutual inductance equation for complex coil shapes such as DD, DDQ. Bi-polar, and Tri-polar [6; 7]. In reference [8], the coil is designed based on the ideal circuit parameter values from the Wheeler formula for the single-layer circular coil. However, mutual inductance should be obtained by trial and error. Another equation-based method in reference [9] utilizes the equation obtained by the curve fitting to the measurement data of the single-layer circular coil. In summary, the equation-based methods in [5; 8; 9] have the following common disadvantages:  
* If the coil shape is changed, the inductance equation should be reformulated.  
* If the ferrite plate is attached to the coil, the accuracy of the inductance formulas will be reduced.  
To solve these disadvantages, finite element analysis (FEA) is utilized for the coil design. In the FEA method, the inductance, resistance, and coupling coefficient of the coil can be obtained easily from any coil shape even with the ferrite plate. In reference [10], using the FEA program, the inner and outer radii of the coil are swept to find the high PTE of the coil. The coil is designed via the Pareto front considering the multi-objective function based on the efficiency and the power density [11; 12]. However, the FEA method usually requires a long simulation time because the coil or ferrite plate shape parameters should be swept. This disadvantage is also pointed out in reference [13] and a faster coil design method is presented by introducing a lumped-loop model for the FEA simulation instead of conventional brute-force parameter sweeping. However, lumped-loop modeling is difficult to apply to arbitrary shapes and thus lacks generality.  
To address the challenge of simultaneously achieving design accuracy, simulation time, and application flexibility in the FEA-based coil design, it is essential to consider the adoption of an optimization algorithm. By integrating an optimization algorithm into the coil design process, the objective is to efficiently mitigate the complexities associated with reducing design simulation speed and increasing accuracy. A crucial aspect of the optimization algorithm's ability is to minimize the number of unnecessary FEA executions, therefore streamlining the coil design process and enhancing its overall power transfer efficiency. In this paper, the scan-and-zoom algorithm, one of the search-based optimization algorithms, is applied to the coil design to achieve a high PTE. The optimization algorithm is implemented in MATLAB and is interfaced with ANSYS Maxwell, one of the most popular FEA programs, to realize the proposed coil design method.  
The structure of this article is as follows. In Section 2, a detailed explanation of the conventional FEA-based coil design process is provided. Section 3 presents the coil modeling in the FEA program, the scan-and-zoom algorithm, and the proposed coil design method. The hardware is built to demonstrate the validity of the proposed method in Section 4. Finally, Section 5 provides a conclusion.