# Retractable Wireless Charging Windings for Inspection Robots
## 2 Principle and Modeling of WPT System
### Modeling of WPT System  
The amount of output power and the energy efficiency of the system are the main concerns in designing the WPT system. The energy flow is represented by using Poynting vectors [27]. Using the Poynting vectors, the actual energy flow among coils can be shown, and the direction of the energy flow can be justified. The line-type coil can be generated from a series of lines with connections interpolated with lines or curves using the splines in the 3D space [28]. \(L\) and \(M\) values can be calculated once all the segments of the coils are available and can be calculated using Neumann's formula numerically [29].  
A specialist WPT simulation tool, IPTVisual [21], is used to model the electrical parameters of the system. IPTVisual (v1.0) is a custom-developed, open-format software platform implemented in TypeScript and executed via the Node.js runtime. It provides a flexible and lightweight interface for defining arbitrary winding geometries, calculating impedance matrices, and visualizing spatial energy transfer using Poynting vector fields rendered in 3D WebGL. The tool enables script-based coil generation, supports both current- and voltage-driven excitation, and allows for fast parametric analysis through batch simulations.  
The visualization layer provides interactive field maps to aid in the identification of regions with strong coupling or energy loss.  
Unlike commercial finite element method (FEM) tools such as ANSYS Maxwell or field solvers like FastHenry [30], IPTVisual is tailored specifically for rapid conceptual design and education rather than high-fidelity analysis. ANSYS offers detailed electromagnetic and multiphysics modeling capabilities with precise meshing control but at the cost of significant computational time and complexity. For example, a typical simulation of a simple circular coil with a fine mesh can take over an hour and consume several gigabytes of memory. FastHenry, while efficient for computing inductance matrices, lacks integrated 3D visualization and circuit interaction features [31]. IPTVisual, in contrast, computes mutual and self-inductance with segment-level resolution, and its solver retains amplitude and phase information, enabling the direct computation of reactive and real power distribution.  
Validation studies have shown that IPTVisual can match the analytical accuracy of [PERSON]'s [32] and [PERSON]'s [33] formulations, and outperform FastHenry in certain complex misaligned configurations. Moreover, compared to ANSYS, IPTVisual demonstrates close inductance values within acceptable error margins but at a fraction of the execution time and memory usage. Despite its strengths, IPTVisual has limitations. It assumes filamentary conductors, does not model frequency-dependent losses like skin or proximity effects, and lacks thermal and mechanical solvers. As such, it should be used in conjunction with FEM tools for final validation and when complex material or spatial interactions must be considered. While IPTVisual is not yet publicly released, the core solver module is being prepared for distribution via a GitHub repository and the MathWorks File Exchange. This will enable other researchers to replicate and adapt the modeling framework for use in related studies.