Capacitance plays a crucial role in high dv/dt situations, making the accurate estimation of parasitic capacitance essential. This paper introduces an improved method of moments (MoM) for calculating the capacitance of round conductors, with or without insulation layers. The proposed method combines MoM with an analytical solution based on Laplace's equation. Compared to the original MoM, the proposed method does not require consideration of polarization charges on the surface of the insulation layer, which reduces the matrix size. Additionally, the proposed method can provide asymptotic formulas for capacitance calculation. The proposed method is compared with the 2D finite-element method (FEM), MoM and measurements. The results demonstrate that the proposed method aligns well with both the FEM simulations and the actual measurements. The proposed method uses less than half the time to calculate the same cases compared to the original MoM.

This paper presents a comprehensive model for power transformers, by considering eddy current losses in both the core and conductors. This is achieved through a meticulous analytical approach that ensures high fidelity in representing the transformer's electromagnetic properties. The consideration of magnetic flux effects on inductance and resistance values significantly enhances the model's accuracy and validity. Traditional analytical methods often resort to simplified approaches due to the complexity of these calculations. The paper addresses these limitations by evaluating the eddy current losses in the core and conductors, and by providing a detailed understanding of each component's impact on transformer behavior. Furthermore, by considering the core and conductor effects on the magnetic field distribution, the model handles a wide range of frequencies, making it suitable for conducting comprehensive transient analysis. To validate the model, comparisons with the finite element method and empirical measurements are conducted. Additionally, a reduced-order transformer model is developed using admittance matrix reduction. This approach focuses on the nodes of interest, effectively eliminating not-observed nodes and reducing computational complexity without compromising accuracy. In this way, voltages at specific points of interest are computed efficiently, maintaining the accuracy of the original model.

This article summarizes the main results and contributions of the MagNet Challenge 2023, an open-source research initiative for data-driven modeling of power magnetic materials. The MagNet Challenge has (1) advanced the state-of-the-art in power magnetics modeling; (2) set up examples for fostering an open-source and transparent research community; (3) developed useful guidelines and practical rules for conducting data-driven research in power electronics; and (4) provided a fair performance benchmark leading to insights on the most promising future research directions. The competition yielded a collection of publicly disclosed software algorithms and tools designed to capture the distinct loss characteristics of power magnetic materials, which are mostly open-sourced. We have attempted to bridge power electronics domain knowledge with state-of-the-art advancements in artificial intelligence, machine learning, pattern recognition, and signal processing. The MagNet Challenge has greatly improved the accuracy and reduced the size of data-driven power magnetic material models. The models and tools created for various materials were meticulously documented and shared within the broader power electronics community.

Litz wires, which are utilized to suppress eddy current, often have complex structures. This paper presents a partial element equivalent circuit (PEEC)-based 3D model for Litz wires with round conductor. The model accounts for both transverse and longitudinal magnetic fields. The discretization of the Litz wire is based on cylindrical elements resulting in a reduced number of elements. Cylindrical element analysis is based on a 2D analytical method. The proposed model is compared with 3D FEM, which shows the model has good accuracy and fast computational speed. It is promising to facilitate Litz wires optimization.

This article presents a 3-D numerical impedance calculation method based on cylindrical elements. It can be used to model the Litz wire and further air-core coil wound by the Litz wire. The discretization is based on cylindrical elements, resulting in a small amount of elements. Cylindrical element analysis is based on a 2-D analysis and its analog to 3-D. The analysis considers both transverse and longitudinal magnetic fields applied to elements. The proposed method is applied to several Litz wires and compared with 3-D finite element method (FEM), which validates that the method has good accuracy and fast computational speed. The effectiveness of the method for the air-core coil is validated by measurements. The proposed method is promising in facilitating coil optimization.

Magnetic components are essential parts in many power electronic applications. Their characteristics deeply impact the performances of the applications. This article proposed a 2-D calculation method for frequency-dependent winding losses and leakage inductance of magnetic components of round conductors. The method does not have any limitations on the winding arrangement and considers the impact of magnetic cores and air gaps. The method is compared with several analytical methods and the 2-D finite-element method (FEM). Measurements and 3-D FEM are also used to validate the method. The results show that the proposed method generally has more than ten times shorter computational time than 2-D FEM and comparable accuracy, which can speed up the magnetic component design.

In this article, an approach combining semi-empirical equations and the method of images is proposed for round conductor layer windings with un-gapped core. The new equation for proximity effect can convert the constant field strength from the magneto-motive force (MMF) across the core window into a frequency-dependent uniform background magnetic field strength, which can take partly the interaction between conductors into account. Geometric factors are introduced by fitting the finite element method (FEM) results to improve the accuracy. The method of images is used to calculate the field strength in order to counteract the impact of the 2-D edge effect. The new method is compared with the 2-D FEM, analytical methods, and is also validated by measurements with EE core transformers. The proposed method shows good accuracy (< 10% error) compared with 2-D FEM for both high and low porosity factor windings. Therefore, it can handle more winding configurations than other 1-D analytical methods.

Litz wire, which is used to suppress eddy current, always have complex structure. Solving its 3-D finite element model (FEM) requires high computational resources. This article presents a 2.5-D loss calculation method for round Litz wires, which do not need mesh. One pitch of Litz wire is set as an object. The exact structure is constructed by a recursive method and then is sliced into several sections per pitch. Each section is represented by a cross section area. Two-dimensional problems are solved based on an analytical method, which is based on magnetic vector potentials in quasi magneto-statics situation. One pitch of the Litz wire is approximately represented by the summation of 2-D problems. The proposed method is compared with 3-D FEM results, which shows the proposed method has good accuracy and fast computational speed.

Winding loss calculation is essential for inductor and transformer design. In this article, a revised 1-D Ferreira's formula is proposed, which considers the interaction between conductors. Then, a 2-D loss calculation approach is proposed based on the analytical solution of round conductors under a uniform external field. An equivalent external magnetic field is calculated to estimate the winding losses, considering the impact of eddy current. The proposed approach is compared with the 2-D FEM with three types of windings and shows good accuracy with less than 10% error. 3-D FEMs and samples are built based on two simulated windings to validate the loss calculation.