A Novel Reluctance Network Analysis Applicable for Open Magnetic Circuits

Abstract

A finite element method (FEM) is widely used in electromagnetic design and analysis, though a long calculation time and a large computer capacity are generally required. To overcome this issue, the authors proposed a reluctance network analysis (RNA) [1], which is suitable for fast calculation of various electric machines’ characteristics, including transformers and motors. However, previous researches on the RNA were limited to closed magnetic circuits. To expand the application scope of the RNA for a wireless power transfer (WPT) and a particle accelerator, which have open magnetic circuits, this paper presents a novel RNA model for open magnetic circuits with the concept of the Kelvin transformation [2], [3], which has been utilized in the open boundary problems in the FEM.Fig. 1(a) – (c) show the proposed RNA model for open magnetic circuits in case of 2-D and 3-D axisymmetric analysis. As shown in Fig. 1(a), an analytical region including the point at infinity is separated into interior and exterior regions. Then, both regions are divided into multiple elements represented by unit magnetic circuits as shown in Fig. 1(b) and (c). Each reluctance can be determined by dimensions of the element and permeability of the material. In the quadrant regions, dimensions of an element lr, lq, lz, lj, lr’, lq’, lz’, and lj’ can be expressed by the following equations:lr = |r1-r2| (1)lq = r1|q1-q3| = r3|q1-q3| (2)lz = const. (3)lj = p(r1+ r2)sin(|q1+q3|/2) (4)lr’ = |a2/r1’- a2/r2’| (5)lq’ = a2/r1’|q1’-q3’| = a2/r3’|q1’-q3’| (6)lz’ = const. (7)lj’ = p(r1’ + r2’)sin(|q1’+q3’|/2) (8)On the other hand, in the rectangular regions, dimensions of an element are lx, ly, lz, lj, lx’, ly’, lz’, and lj’. Among them, lx and lx’ can be expressed by the following equations:lx = |x1-x2| = |r1-r2| (9)lx’ = |x1’-x2’| = |a2/r1’- a2/r2’| (10)Fig. 2(a) - (c) show specifications of an analytical object and simulation results, respectively. Here, flowing flux density on a red solid line is compared. It is understood that calculated values of the RNA and FEM are in good agreement. Also, the RNA results hardly change even if the value of a changes within the range of the necessary and sufficient spatial resolution.