This paper presents a novel strategy to model the full three-dimensional structures of end region of huge turbine-generators with power level up to 1000MW. The 3-D nonlinear anisotropic magnetic field including the eddy current losses is calculated by utilizing the reduced magnetic vector potential formulation. With the help of Biot-Savart's law, the magnetic field caused by currents in the stator and rotor windings, which are very complex in geometric shapes, can be calculated in a far easy way. The flux density distribution in the end region and the eddy current distribution in the structural parts under different operating conditions are presented

3-D eddy current analysis in the end region of a turbogenerator by using reduced magnetic vector potential

The use of boundary integral equation methods for the solution of some electromagnetic field problems are discussed. Boundary integral formulations using simple-layer potentials, and Green's formula, are explained. Readers are drawn to the similarity of discretization methods in use. Some salient features of the boundary element method are presented in review fashion. References are made to sample applications in a few problem areas. The paper concludes with a discussion that attempts to relate boundary integrals to partial differential methods.

Application of boundary integral equation methods to electromagnetics

An integral equation method is described for solving three-dimensional magnetostatic problems involving linear permeability interfaces and current sources. The interface is replaced by magnetic charges in free space to provide an equivalent interface condition. Application has been made to leakage field calculations in transformers. Numerical methods are combinations of analytical formulas and numerical integration; basis functions approximate the charge distribution.

Computation of magnetostatic fields in three-dimensions based on Fredholm integral equations

Aiming at the complexity of the structure in the end region of large turbogenerators, 3-D mathematical and physical models of nonlinear transient eddy current field are given by taking a 330-MW water-hydrogen-hydrogen-cooled turbogenerator for example. Both nonlinearity of B-H curve and noncontact structure between the copper screen and press plate, as well as the evolvent of stator end windings, were taken into consideration. When the copper screen thickness is different in the end region of the generator, 3-D transient electromagnetic field and losses of metal parts were calculated under no-load and rated-load conditions by finite-element method. The metal part losses, which were obtained from transient electromagnetic field, were applied to the thermal field as heat sources. Temperatures of copper screen were gained after the thermal field was calculated in the end region. The calculated results coincide well with the measured data.

Influence of Copper Screen Thickness on Three-Dimensional Electromagnetic Field and Eddy Current Losses of Metal Parts in End Region of Large Water-Hydrogen–Hydrogen-Cooled Turbogenerator

A mathematical model using an integral-equation/singularity-method approach is derived for determining the magnetic field and electromagnetic forces induced by current-carrying conductors in a region bounded by 3-D material-body surfaces which have complex configurations. Special analytical and numerical techniques that eliminate near-field computational difficulties and bypass the cumbersome matrix manipulations required by other integral-equation approaches are described. A comprehensive computer program package has been developed using this approach for obtaining the 3-D solutions in the end region of a turbine-generator due to armature end windings. Special computational techniques for handling the complex end-winding and surface geometry are described and detailed numerical results are presented for the 3-D field solution and the forces acting on the conductors.

An integral-equation/singularity-method approach for 3-D electromagnetic field determination in the end region of a turbine-generator

The method of singularities and special techniques for solving Fredholm integral equations are applied to the calculation of the axial flux in a simplified two-dimensional problem simulating the end-region of a turbogenerator including an air gap and several convex and concave corners. In this method the magnetic field is generated according to the Biot-Savart Law, the boundary conditions are satisfied by using singularities distributed on the boundary surfaces, and the strengths of the singularities are determined by solving a Fredholm integral equation of the second kind. Special techniques are developed which analytically remove mathematical singularities encountered in the governing equation which is solved by an iterative procedure. Current sheet strengths, magnetic flux distributions and their intensities on the boundary surfaces are obtained.

Electromagnetic field computations using the method of singularities

A new integral equation formulation for solving general 3-D electromagnetic field problems using the method of singularities is briefly described. Detailed expressions of integral equations for axially symmetrical open and confined field cases derived from the basic general 3-D formula are given. Mathematical singularities encountered in the equations are analytically removed and an iterative solution procedure is adapted. Numerical results obtained for several test cases during the developmental stage of this method are presented.

S. Chow

Papers

An integral-equation/singularity-method approach for 3-D electromagnetic field determination in the end region of a turbine-generator

Electromagnetic field computations using the method of singularities

Singularity/integral equation method development for 3-D electromagnetic field calculation