Roth's method for the solution of boundary-value problems in electrical engineering

Abstract

Between the years 1927 and 1938 the French engineer E. Roth developed a powerful method for the solution of boundary-value problems in electrical engineering. He applied the method to problems in heat conduction and magnetic-field problems in electrical machines and transformers, although the application of the method is not necessarily limited to such devices. In spite of its possibilities, the method has been omitted from the standard treatises on electromagnetic problems, because there are certain difficulties associated with it. The paper gives a critical account of the method, listing both advantages and disadvantages and relating these to the physical and mathematical basis of Roth's work. List of symbols A = magnetic vector potential B-magnetic flux density H = magnetic field strength / = current density V = electric scalar potential V* = magnetic scalar potential a, b, c, d, e,f = slot dimensions m, n = parameters C m n = coefficient x, y = rectangular coordinates X = function of x only Y = function of y only J

FEM-Based Statistical Data-Driven Modeling Approach for MFT Design Optimization

“…3, all of the available methods (e.g. FEM, Roth [11] etc.) resort to some type of computationally intensive numeric techniques.…”

Planar Magnetic Components in More Electric Aircraft: Review of Technology and Key Parameters for DC–DC Power Electronic Converter

“…With n the number of turns in a layer, a the conductor width and b the core window width Some other semi-analytical computational models based on the resolution of Poisson's equation such as PEEC formulation [44] or Roth's method [45] can be used for 2-D transformer's winding cross section. These methods are efficient only when material in rectangular region is homogeneous.…”

Leakage Inductance Analytical Calculation for Planar Components With Leakage Layers

“…Multiply the two sides of the second equation of (32) by cos(knx), and integrate it on [0, L]: 35, (36) and the first equation of (32), the following matrix system are obtained:…”

“…To be more general, the method of Roth can be applied for 2D transformer's winding cross section. This method consists in using double Fourier series to solve the Poisson's equations in a rectangular region [36]. However, double Fourier series exhibit a low convergence rate so that they are computationally expensive.…”