J.C. Sabonnadiere

Performance derivative calculations and optimization process

The calculation of the sensitivity versus a geometric or physical parameter and its use in an optimization process are presented. The 2-D finite-element method is used in the magnetic field calculation. The quasiNewton method is used to determine the direction of minimization, and the constraints of upper and lower bounds of parameters are treated by the penalty function. A cubic approximation method is used in the unidimensional minimization. Minimization of the current density (J/sub c/) while keeping the force desired for a relay model is presented as an example. >

Inverse problem methodology and finite elements in the identification of cracks, sources, materials, and their geometry in inaccessible locations

Inverse problem methodology is extended, through the more difficult geometric differentiation of finite-element matrices, to identify the location, material, and value of unknown sources within an inaccessible region using exterior measurements. This is done through the definition of an object function that vanishes at its minimum when the externally measured electric field matches the electric field given by an assumed configuration that is optimized to match measurements. The method is demonstrated by identifying the shape, permittivity, charge, and location of an electrostatic source through exterior measurement. The procedure is then extended to eddy current problems for the identification of the location and shape of cracks in metallic structures. An example demonstrates that when dealing with eddy current problems the least squares object function used by others has multiple local minima so that gradient methods have to be combined with search methods to identify the one absolute minimum. Procedures are also given for handling situations with no cracks and overdescribed cracks. >

Solution of magnetic fields and electrical circuits combined problems

A finite element formulation is developed to analyse the magnetic fields in constrained electrical circuits by combining field and circuit equations. The terminal voltages are specified and the corresponding magnetizing currents assumed as unknown. This method takes into account the eddy currents and it has a symmetric coefficient matrix with respect to the ones mentioned in the literature. This approach makes it possible the computation of the characteristics of induction motor, specially squirrel cage induction motor, excited by constant voltage power sources. It is verified using a magnetic relay and a 4-pole shaded-pole motor.

Energy methods for the evaluation of global quantities and integral parameters in a finite elements analysis of electromagnetic devices

For almost all finite element analysis of electromagnetic devices the engineer or the designer is much more interested in the knowledge of the global quantities (flux, active and reactive powers, forces, torques ...) and the electric or magnetic design parameters (reluctances, inductances, capacitances...) than the display of fields map. In many current software these quantities are generally computed by numerical quadrature formulae over the values of fields or flux densities. For instance the computation of forces and torques is usually made by quadrature of the Maxwell stress tensor along an arbitrary integration path. The results depend in fact strongly of the choice of the path and may in specific cases be very inaccurate. An other reason of this lack of accuracy is the fact that quadrature formulae are applied to quadratic expressions of fields, wich are themselves obtained from scalar or vector potential interpolated values by a numerical derivation scheme. But it is well known that numerical differentiation is source of a lot of inaccuracy although the subsequent integration procedure smoothes the results. The paper will introduce methods based on the property of optimization of an energy functional. These methods suit particularly well the finite element method which is based on the same principle.

Magnetic fields in nonlinear anisotropic grain-oriented iron-sheet

The authors propose a 2-D magnetic field calculation method that takes into account the nonlinear anisotropic property in the grain-oriented steel. An elliptical model is used; the magnetic permeability is represented by a tensor with field-dependent components. This model is applied to a finite-element method using a scalar potential. The iron nonlinearity is considered and a Newton-Raphson method is applied to a family of B-H curves to improve convergence. To minimize variation of flux density between elements, an auto-adaptive process has been used. This modelling of nonlinear anisotropic magnetic fields is applied to a three-phase transformer core. >

A dual method for constrained optimization design in magnetostatic problems

In recent years, many modern optimization techniques have been developed in the field of mathematical programming. The feasibility of applying these techniques to the magnetostatic design problems such as a permanent magnet synchronous machine and a magnetic actuator is discussed, and an improvement in the optimization method of the moving asymptotes (MMA) is suggested. The improvement of the latter consists in using an active constraint set strategy, in order to make it possible to find feasible points during the process. Theoretical aspects are considered, and numerical results of some problems are discussed. >

The finite element post-processor of FLUX3D (field computation package)

The FLUX3D software is a package for three-dimensional analysis of electric and magnetic fields based on the classical components, including pre- and post-processor, mesh generator, and solver. FLUX3D is built on a database management system which allows several possibilities of connection of each component with external packages. Each component includes specific capabilities which enhance the use of FLUX3D. The main aspects of the architecture, entities, domain of computation, facilities and the various commands are described, and some illustrative examples are presented. >

Prediction of transient electromagnetic environment in power networks

In this paper the authors suggest exact analytic formulations which allow numerical characterization of the transient electromagnetic environment, during operation of circuit breakers or disconnecters, of an electric power transmission network. In this work, an exact method for calculating the transient field radiated by an air insulation substation (AIS) together with the strictest formalism which enables the same calculation to be made for a power transmission line are paid particular attention. Results of simulations for different examples together with results of measurements complete the study. >

An ellipsoid algorithm for the optimum design of magnetostatic problems

An ellipsoid algorithm for solving nonlinear programming problems is described whose objective and constraint functions are convex and are not assumed to be differentiable. The authors suggest some modifications to the basic ellipsoid algorithm to adapt it to magnetostatic applications. One way to do this is to control the new ellipsoid at each iteration to generate small ellipsoids and to speed up the basic algorithm. Illustrative examples show the applicability of the method to solving constrained nonlinear optimization problems in magnetostatics. >

3D anisotropic magnetic field calculation in transformer joints

One three dimensional anisotropic nonlinear magnetic field computation has been performed. The comprehensive understanding of flux distribution in a complex transformer corner joint is obtained and used in its design. Three anisotropic models, corresponding with actual cases in engineering computation, are investigated and their general forms in the Jacobian matrix are developped.