Enno Lange

Extension of a d-q model of a permanent magnet excited synchronous machine by including saturation, cross-coupling and slotting effects

For the description of a permanent magnet excited synchronous machine the idealized equations of common synchronous machines can be used omitting the damping windings and replacing the current excitation by a permanent flux. For a more accurate modeling, nonideal behavior like saturation, cross-coupling magnetization and slotting effects can be included. This is done by extending the common d-q equations by additional elements. This also includes the time dependent variations of the parameters causing additional induced voltages especially at high currents and speed. The elements of the extended equations are extracted from a finite element analysis of the device under test. The derivation of the equations and a simulation of a permanent magnet excited synchronous machine with the applied theory are presented.

Acoustic Simulation of a Special Switched Reluctance Drive by Means of Field–Circuit Coupling and Multiphysics Simulation

The approach presented in this paper consists of an energy-based field-circuit coupling in combination with multiphysics simulation of the acoustic radiation of electrical machines. The proposed method is applied to a special switched reluctance motor with asymmetric pole geometry to improve the start-up torque. The pole shape has been optimized, subject to low torque ripple, in a previous study. The proposed approach here is used to analyze the impact of the optimization on the overall acoustic behavior. The field-circuit coupling is based on a temporary lumped-parameter model of the magnetic part incorporated into a circuit simulation based on the modified nodal analysis. The harmonic force excitation is calculated by means of stress tensor computation, and it is transformed to a mechanical mesh by mapping techniques. The structural dynamic problem is solved in the frequency domain using a finite-element modal analysis and superposition. The radiation characteristic is obtained from boundary element acoustic simulation. Simulation results of both rotor types are compared, and measurements of the drive are presented.

An Efficient Field-Circuit Coupling Based on a Temporary Linearization of FE Electrical Machine Models

A field-circuit coupling method is presented, whose basic idea is to extract from the finite-element (FE) model a linearized lumped parameter representation of the electrical machines, to be used in the circuit simulator model of the power electronic supply. The dynamic coupled model of the complete drive obtained this way can be iterated over a limited period of time, with a time step adapted to the high frequency of electronic commutations. When the temporary representation of the machine has come, or is expected to have come under a given accuracy threshold, a new FE simulation is performed, a new set of lumped is generated and the process is repeated. This method allows decoupling the time constants of the field problem from that of the circuit problem, which is typically one or two orders of magnitude smaller. This yields a considerable saving of computation time with a controllable, at least a posteriori, loss of accuracy.

A Circuit Coupling Method Based on a Temporary Linearization of the Energy Balance of the Finite Element Model

In this paper, a versatile method for modeling coupled magnetic field and circuit problems is presented. The field problem is solved by applying the finite element (FE) method. The nonlinear circuit equations are solved by applying the Newton-Raphson method. The finite element model and the circuit are solved separately, which in turn gives the possibility of considering different time constants for each domain. The idea is to extract values of the slowly varying lumped parameters describing the finite element model in the circuit equations at a rate related with the time constant of the finite element system, and to use them to iterate the circuit equations between two updates with a time step adapted to the significantly smaller time constant of the electric system. Contrary to the widely used numerically strong coupled methods, this paper introduces a different approach by applying an energy-based parameter identification.

A Variational Formulation for Nonconforming Sliding Interfaces in Finite Element Analysis of Electric Machines

This paper proposes the application of the Lagrange multiplier method to implement the relative motion of stator and rotor in the finite element (FE) simulations of electric machines. The nonconformity at the interface between stator and rotor regions imposes no restriction on time or space discretization. This freedom is highly valuable for domain decomposition. Through the choice of particular dual shape functions for the Lagrange multiplier, the symmetry, sparsity and positive definiteness of the linear system can be preserved. The method is applied to the 2-D simulation of a permanent magnet excited synchronous machine, and the results are compared with a conforming moving band approach with re-meshing of the air gap.

System simulation of a PMSM servo drive using the field-circuit coupling

In the development process of electrical drive trains, consisting of the motor, the power electronics and the control scheme, it is difficult to predict the exact machine and control behavior in combination with the converter. Therefore, system simulations with analytical machine models embedded in a circuit simulation environment are performed. To increase accuracy by paying attention to alternating machine parameters, such as saturation, a finite element model can be used instead of the analytical machine model. In this paper such a field-circuit coupling is applied to the simulation of a PMSM servo drive and the results are shown and discussed.

Development and validation of a fast thermal finite element solver

Nowadays, the knowledge of temperatures inside electrical machines is an important criteria, especially if further power density enhancements or frame size reductions are aimed at. Furthermore, temperature estimation in permanent magnets is an essential part of the design process for electrical machine due to their affect on the electromagnetic behaviour. In this paper a particularly fast thermal finite element solver is introduced. By use of boundary conditions for thin layer geometries and the air gap, the number of elements can be reduced significantly.

Circuit coupled simulation of a claw-pole alternator by a temporary linearization of the 3D-FE model

During the final stage in the design of electrical machines adequate models are required to predict the behavior at given points of operation. Due to its irreducible 3D flux path structure and the connected bridge rectifier, the claw pole generator is a challenging field-circuit coupled system. It can be solved either by permeance models, state space models or numerically strong coupled formulations within a Finite Element Analysis (FEA). Alternatively, a numerically weakly coupled method is presented in this paper. A temporary lumped parameter representation of the alternator seen from stator terminals is extracted from the Jacobian matrix of the linearized FE model. This lumped parameter representation of the machine is then incorporated into a circuit simulator based on the modified nodal analysis (MNA).

Biorthogonal Shape Functions for Nonconforming Sliding Interfaces in 3-D Electrical Machine FE Models With Motion

This paper discusses the application of Lagrange multipliers to restore field continuity across nonconforming surfaces in 3-D problems. The method makes it in particular possible to implement the relative motion of stator and rotor without remeshing in the 3-D Finite Element (FE) modeling of electrical machines. The choice of a special set of biorthogonal shape functions for the Lagrange multiplier makes it possible to preserve the positive definiteness of the FE system. It is shown that such a biorthogonal basis cannot be constructed canonically for a 3-D magnetic vector potential formulation. For a 3-D magnetic scalar potential formulation, however, the situation is different and a biorthogonal basis can be found.

Upwind 3-D Vector Potential Formulation for Electromagnetic Braking Simulations

The calculation of motion-induced eddy currents in massive conductors yields a 3-D convection-diffusion problem. Up-winding and SUPG formulations are well established methods to obtain stable discretizations of the scalar convection-diffusion equations in the case of singular perturbation, but there is very little reported experience with the stability of convection in the vector case, i.e., electromagnetism. Numerical experiments with the up-winding method proposed by Xu (Trans. on Mag., 2006; 42:667-670, 2006) has proven it to be insufficient. Building on the work of Heumann (Research report 2008-30, Seminar für Angewandte Mathematik, Eidgenssische Technische Hochschule, Oct. 2008), an alternative approach based on a finite-element discretization of the Lie derivative implied by the convection phenomenon is proposed.