Abstract
| The paper proposes the determination of the inductance of a Superconducting Magnetic Energy Storage (SMES) device with modular toroid coil based on a new 2-D FEM modeling using the response surface methodology (RSM) applied on 3-D FEM modeling. An earlier 2-D FEM modeling of a SMES device created in FEMM software is based on the assumption of the equality between the inductances of the complete circular cross section toroid and of the rectangular cross section toroid, providing an approximationfor the depth of planar model which does not take into account the leakage magnetic flux. Therefore a 3-D model of real geometry was realized using ANSYS software to improve this approximation. Imposing the equality of the magnetic field energies in 2-D and 3-D simulations, a new value for depth of 2-D FEM planar modeling is derived as polynomial regression of second order of the 3-D results, based on two factors characterizing the geometric torus shape: the coil inner diameter ratio and the coil thickness ratio. The application of analysis of variance (ANOVA) and the computation of some adjusting coefficients prove the descriptive and predictive power of this model. The inductances of different configurations of SMES device derived from the new 2-D FEM modeling are compared to those based on the earlier 2-D FEM modeling and on the 3-D FEM modeling. The results indicate an underestimation of the depth of the earlier 2-D FEM planar modeling and consequently, of the magnetic field energy and of the inductance for SMES devices with large inner diameter, when the leakage magnetic flux increases. The proposed model can improve the results of optimizations of the SMES device performed in previous papers. |
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