This article presents a new analytical approach for the calculation of mutual inductance based on magnetic vector potential (MVP). To demonstrate the proposed mutual inductance calculation method, planar spiral coils of polygonal shape with an arbitrary number of sides are discussed. The coils considered in this work are coaxial and assumed to be composed of concentric filaments. The flux produced by the primary and linking the secondary is calculated by the line integral of the MVP. In order to simplify the calculation strategy, the MVP contribution of only one side of each single-turn filament of the primary is considered due to the symmetry of the coils’ shapes. Accordingly, coupling flux across the surface surrounded by each turn of the secondary is calculated by the line integral of the MVP over half path of the filament’s turn. The accuracy of the new analytical approach is confirmed by examining coil systems with a different primary and secondary in terms of the number of sides, the number of turns, and size. Results of the new approach are compared with those obtained from Ansys Maxwell, analytical studies in the literature, and experimental to demonstrate the validity of the proposed method. Results from this work are in good agreement with those obtained from simulation, studies in the literature, and experiment that proves the feasibility of formulas used in this work.

Mutual inductance (MI) calculation is of great importance, because there are many systems that operate on the principle of inductive coupling. This article presents a novel analytical model that calculates the MI between two nonidentical n-sided polygonal planar coils located in an arbitrary position in 3-D space. The model depends upon the misalignment of both the primary and the secondary coils of a wireless power transfer system operating based on inductive coupling. The polygonal coils used in this model may differ from each other in terms of size, shape, and turns number. The misalignment cases considered in the proposed model include lateral, angular, lateral–angular, and vertical distance variation between the primary and secondary coils. Based on Stokes theorem, instead of using the magnetic flux density vector, the magnetic vector potential (MVP) is used to reach the required magnetic flux in the calculation of the MI. A single analytical solution function that can calculate the MI between two planar polygonal coils of any shape in a simple manner and short time duration is obtained by performing difficult mathematical operations through MVP. Results obtained from the developed new model are compared with finite element analysis, and experimental and other studies in the literature. The good agreement of the results of this study with the other results has proved the accuracy and validity of the proposed new analytical model.

Accurate calculation of mutual inductance (MI) between solenoid coils is essential for system design, but complex geometries and spatial arrangements make it challenging. This paper presents a modified analytical method for calculating the MI between two circular-wound air-core solenoid coils arbitrarily oriented in three-dimensional (3D) space. The analytical model used to calculate the MI between two solenoid coils is based on the use of magnetic vector potential (MVP). The helical structure of the solenoid coils is represented by successive coaxial circular filaments arranged along their central axes. Each filament is represented by an equivalent regular polygon with a sufficient number of sides. The proposed approach allows the MI between two solenoid coils to be calculated using a single analytical formula, without imposing restrictions on the relative positions of the coils, while taking lateral and angular misalignments into account. The modified analytical model is validated for accuracy and applicability by comparing its results with experimental measurements and FEM-based simulation results for coil systems with different diameters, turn numbers, and turn pitches. The MI results for various angular and lateral misalignments are in good agreement with experimental measurements and FEM results. The MI calculation model proposed in this work provides a fast and reliable tool for analyzing the electromagnetic behavior of coupled coil systems, designing inductive power transfer systems, and assessing electromagnetic compatibility.

Bu çalışmada, Tek Fazlı Matris Dönüştürücünün (TFMD) frekans değiştirici olarak çalışması incelenmiştir. TFMD’nin devre topolojisi ve çalışması ele alınmış ve frekans değiştirici olarak çalışması için güvenli komutasyon anahtarlama stratejisi verilmiştir. Bu çalışmanın modellenmesi ve simülasyonu MATLAB/Simulink de yapılarak belirtilen çıkış frekansı değerleri için çıkış gerilimi dalga şekilleri elde edilmiştir.  

Bu çalışmada, Tek Fazlı Matris Dönüştürücünün (TFMD) frekans değiştirici olarak çalışması incelenmiştir. TFMD’nin devre topolojisi ve çalışması ele alınmış ve frekans değiştirici olarak çalışması için güvenli komutasyon anahtarlama stratejisi verilmiştir. Bu çalışmanın modellenmesi ve simülasyonu MATLAB/Simulink de yapılarak belirtilen çıkış frekansı değerleri için çıkış gerilimi dalga şekilleri elde edilmiştir.