Finite Element Analysis of Electrical Machines

In Finite Element Analysis of Electrical Machines the author covers two-dimensional analysis, emphasizing the use of finite elements to perform the most common calculations required of machine designers and analysts. The book explains what is inside a finite element program, and how the finite element method can be used to determine the behavior of electrical machines. The material is tutorial and includes several completely worked out examples. The main illustrative examples are synchronous and induction machines. The methods described have been used successfully in the design and analysis of most types of rotating and linear machines.
Audience: A valuable reference source for academic researchers, practitioners and designers of electrical machinery.

1 Introduction to Finite Elements.- 1.1 Introduction.- 1.2 The Galerkin Finite Element Method.- 1.3 Boundary Conditions.- 1.4 Magnetostatic Example.- 2 Nonlinear Problems.- 2.1 Introduction.- 2.2 Representation of the B-H Curve.- 2.3 The Basic Newton-Raphson Method for a Single Equation.- 2.4 Application of the Newton-Raphson Method to a First Order Element.- 2.5 Cubic Splines.- 3 Permanent Magnets.- 3.1 Introduction.- 3.2 Magnetization Models of Permanent Magnets.- 3.3 Current Sheet Equivalents.- 3.4 Example With Permanent Magnet.- 3.5 Intrinsic and Normal Hysteresis Characteristics.- 4 Eddy Current Analysis.- 4.1 Introduction.- 4.2 Eddy Currents and Skin Effect.- 4.3 Finite Element Example.- 4.4 Elliptical Description of Flux Density.- 4.5 Eddy Currents In Nonlinear Materials.- 4.6 Nonlinear Permeability Models.- 4.7 Coupling Finite Elements To External Circuits.- 4.8 Numerical Example.- 4.9 Modeling Considerations.- 5 Computation of Losses, Resistance and Inductance.- 5.1 Introduction.- 5.2 Computation of Eddy Current Loss.- 5.3 Losses In A Series Winding.- 5.4 Inductance and Reactance.- 5.5 Poynting Vector.- 5.6 Nonlinear Problems.- 6 Calculation Of Force And Torque.- 6.1 Introduction.- 6.2 Ampere’s Force Law.- 6.3 The Maxwell Stress Method.- 6.4 The Virtual Work Method.- 6.5 Using Machine Models to find Torque.- 6.6 Errors in Force Computation.- 6.7 Convergence of Force.- 7 Synchronous Machines in the Steady State.- 7.1 Introduction.- 7.2 The Basic Configuration of a Synchronous Machine.- 7.3 Steady State Operation — Excitation Calculation.- 7.4 Modeling Considerations.- 7.5 Excitation Calculation.- 7.6 Computation of Steady State Reactances.- 7.7 Direct Axis Transient Reactance, X?d.- 7.8 Direct Axis Subtransient Reactance, X?d.- 7.9 Frequency Response Curves.- 7.10 Time Constants.- 7.11 Poynting Vector Method.- 8 The Induction Motor in Steady State.- 8.1 Introduction.- 8.2 Obtaining Steady State Parameters.- 8.3 Obtaining Reactances From The Frequency Response.- 8.4 Results.- 8.5 Using Frequency Domain Data With Time Domain Solutions.- 9 Time Domain Modeling of Induction Machines.- 9.1 Introduction.- 9.2 Electromagnetic and Mechanical Theory.- 9.3 Galerkin Formulation.- 9.4 Time Discretization.- 9.5 Linearization.- 9.6 Global System of Equations.- 9.7 Examples.- 10 Air-Gap Elements for Electrical Machines.- 10.1 Introduction.- 10.2 Description of the Method.- 10.3 Application.- 11 Axiperiodic Solutions.- 11.1 Introduction.- 11.2 Finite Element Formulation for Scalar Fields.- 11.3 Calculation of Steady State Forces.- 11.4 Calculation of Transient Forces.