# A Novel Magnetic Equivalent Circuit Model for the Corner of Inductor Core
## 5 Conclusions  
In this work, in order to improve the inductance accuracy and describe the flux density distribution of the corner, a novel local corner MEC model is proposed. In this model, a corner is divided into \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & \(e_{max}\) & \(e_{avg}\) \\ \hline Local corner model & 6.0\% & 3.6\% \\ IEC corner model & 14.7\% & 8.6\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Relative error statistics of inductance. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & \(e_{avg}\) & **Time** \\ \hline Two branches & 3.4\% & \(26^{\prime}30^{\prime\prime}\) \\ Three branches & 3.3\% & \(30^{\prime}44^{\prime\prime}\) \\ Four branches & 3.3\% & \(46^{\prime}48^{\prime\prime}\) \\ Five branches & 3.2\% & \(66^{\prime}47^{\prime\prime}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Inductance Comparison of different corner branch numbers. three branches to make the corner flux density different from the inner corner to the outer corner, and automatic calculation of the reluctance and flux of each branch by iterative calculation. The uneven flux distribution of the joint part between the corner and the limb surrounded by winding is discussed. Based on this, the joint part is innovatively divided into several branches in series with the corner branches. In addition, a branch reluctance of leakage in the inner corner of the core window is modeled and added in parallel with the corner branches, contributing to the accuracy of the inductance calculation especially when the core is under saturation. The local corner MEC model fully describes the flux path and flux density distribution of the corner, which has a high accuracy of corner branch flux density \(\mathbf{B}\) calculation and provides a ground for judging the magnetic core saturation. In general practice, the core loss is calculated by the Steinmetz equation for sinusoidal current waveform or the improved Steinmetz equation and general Steinmetz equation for other current waveforms, which are a function of flux density amplitude. The power loss of the corner accounts for a considerable portion of the total core loss because the flux density is uniformly distributed, and the inner corner flux density is high. Through the local MEC model, the flux density distribution of the corner is described, and the flux density can be accurately calculated, which can improve the accuracy of the core corner loss calculation. Furthermore, the core hotspot calculation depends on the loss dissipation and can benefit from the accurate core loss. Furthermore, the accurate flux calculation improves the inductance accuracy. A wide range from 20 A to 1000 A inductance of the local MEC model is compared to the measured inductance of the prototype square inductor, and the average relative error is less than 4%. Considering the measurement error of the test equipment, the average relative error upper limit of the local MEC corner model and the real value is less than 6%, which shows a highly accurate inductance calculation of this model. By analyzing the number of corner branches, at least two parallel corner branches can be used to model the local corner MEC model and ensure calculation accuracy. In addition, compared with the MEC models with the fixed single reluctance branch of the corner, the local corner MEC model can describe the flux distribution of the corner and improve the inductance calculation accuracy. Compared with the finite element method, the local corner MEC model is simple and does not need to mesh or regenerate the model after the geometry is modified. The local corner MEC model has great advantages of rapid parametric modeling and high computational efficiency with an acceptable calculation accuracy and flux density description, which makes it ideal for performing inductance curve calculations, optimizing design, and as an online digital twin lumped parameter model.