Andrzej Demenko

Movement simulation in finite element analysis of electric machine dynamics

Methods of movement simulation in the coupled field-circuit analysis of rotating electric machines are considered. Special attention is paid to the application of moving band techniques in the finite element analysis of electromechanical transients. A new approach to the formulation of a band matrix as a function of rotor position is proposed. The matrix of the moving band is expressed by a trigonometric interpolating polynomial which is based on the matrices for discrete rotor positions. The method is verified by comparison of the analytical and numerical results of torque calculation and is applied in the analysis of permanent magnet motor dynamics.

Network equivalents of nodal and edge elements in electromagnetics

The paper analyzes the analogies between nodal/edge formulations of finite elements and nodal/loop (mesh) descriptions of network models of electromagnetic fields containing eddy and displacement currents. Both scalar and vector potentials are used. Two types of graphs are introduced: 1) for nodal elements; and 2) for edge elements. It is noted that edge values of potentials A and T are represented by loop quantities in graphs 2). Branch parameters such as reluctances, branch impedances and sources are described. Finally, coupled networks are discussed mixing A-V, /spl Omega/-T, and A-T models.

3D edge element analysis of permanent magnet motor dynamics

A time-stepping edge element method for the analysis of electric machine transients is presented. A system composed of a permanent magnet motor, voltage inverter and control equipment is considered. The motor windings are represented by filamentary conductors. The mathematical model includes: edge element equations using magnetic vector potential; equations that define the connections of winding and inverter elements; motion equations; and relations that describe the control system. The approach is based on the simultaneous solution of these equations and ungauged edge formulation for the magnetic field. Special attention is paid to the calculation of electromagnetic torque.

Network Representation of Conducting Regions in 3-D Finite-Element Description of Electrical Machines

The paper introduces a network description of conducting regions in electrical machines. Resistance models are considered, where loop equations are equivalent to an edge element formulation using the electric vector potential T, as well as conductance models, for which the nodal equations refer to a nodal element description by means of the scalar potential V. Network models for multiply connected regions are derived for both Omega-T-T0 and A-T-T0 formulations. A network representation of the edge value of potential T0 is suggested. Convergence of the iterations of the T-T0 method may be accelerated by supplementing equations for the edge values of T0.

Electromagnetic torque calculation using magnetic network methods

Purpose – The aim of the paper is to find the effective algorithms of electromagnetic torque calculation.Design/methodology/approach – The proposed algorithms are related to the analysis of electrical machines using the methods of equivalent magnetic networks. The presented permeance and reluctance networks are formulated using FE methods. Attention is paid to the algorithms of electromagnetic torque calculation for 3D models. The virtual work principle is applied. The principle is adapted to the discrete network models. The network representations of Maxwells stress formula are given.Findings – The proposed method of electromagnetic torque calculation can be successfully applied in the 3D calculations of rotating electrical machines. It can be used for scalar and vector potential formulations. The obtained results and their comparison with the measurements show that the method is sufficiently accurate.Originality/value – The presented formulas of electromagnetic torque calculation are universal and can ...

On the Equivalence of Finite Element and Finite Integration Formulations

The paper offers a comparative study of numerical methods of analysis of electromagnetic fields. The focus is on the finite element method (FEM) and finite integration technique (FIT), but with the cell and equivalent network approaches also considered. It is shown how the approximate integrals describing coefficients of the FEM need to be derived for a mesh with parallelepiped elements to achieve consistency with FIT equations. The equivalence of FEM and FIT formulations for a triangular mesh in 2D is highlighted. The TEAM Workshops Problem No. 7 is used as an example for numerical comparisons. Two formulations have been considered: 1) using the edge values of the magnetic vector potential A and the nodal values of the electric scalar potential V; and 2) expressed in terms of the edge values of both magnetic A and electric T-T0 vector potentials.

Three dimensional eddy current calculation using reluctance-conductance network formed by means of FE method

Reluctance-conductance network (RCN) for 3D eddy current calculation is presented. The proposed RCN has been formed by means of the FE method using the A-V formulation. The finite element is assumed to be an edge element in relation to magnetic potential A and a nodal element in relation to electric potential V. The edge values of A represent the loop fluxes in the reluctance network. The time derivatives of loop fluxes create electromotive forces in the branches of the conductance network. The RCN formed by the BE method has mutual reluctances and mutual conductances. To calculate the integrals that describe the conductances an approximate formula is proposed. This formula gives the model of rectangular prism without mutual conductances. An example of the application of the RCN method is presented. The results for the RCN with mutual conductances and the RCN without these conductances are compared.

Equivalent Formulas for Global Magnetic Force Calculation From Finite Element Solution

The paper presents the Lorentz force and Maxwell stress formulas that give the same result of global force calculation for FE method. Edge element method (EEM) using vector potential A and nodal element method (NEM) using scalar potential Ω are considered. The formulas have been obtained from virtual work principle that has been adapted to the FE model. The FE network must be regular of homogenous element to obtain the equivalent formulas for EEM and equivalent formulas for NEM. The results of force calculation using the proposed methods have been compared with the analytical results. The systems with three cuboidal magnets and an induction motor with solid rotor described in TEAM Workshops Problem No. 30 were analyzed. Moreover, repulsive forces in the systems presented by TEAM Workshops Problem No. 7 and in the system with two ring-shaped magnets have been investigated.

Finite element analysis of transient electromagnetic‐thermal phenomena in a squirrel cage motor

Purpose – The purpose of this paper is to elaborate the method and algorithm for the analysis of electromagnetic and thermal transients in a squirrel cage induction motor.Design/methodology/approach – The paper presents the special software for transient finite element (FE) analysis of coupled electromagnetic‐thermal problems in a squirrel cage induction motor. The software has been prepared and is successfully applied in the design of special squirrel cage motors, e.g. the motors working in cryogenic conditions. A time‐stepping FE method and transients analysis of an induction motor has been applied. The nonlinearity of the magnetic circuit, the movement of the rotor and the skewed slots have been taken into account. The results of computations have been compared with measurements.Findings – The method presented and the elaborated specialised software for FE analysis of electromagnetic and thermal transients are used to determine the dynamic performance of the squirrel‐cage induction motor. The results o...

Finite element analysis of saturation effects in a squirrel cage electrical machine

Presents a method for the finite element (FE) analysis of saturation effects in a squirrel‐ cage electrical machine. The proposed mathematical model includes the FE equations of the electromagnetic field, the equations which define the connection of windings, and the mechanical equation. Applies an approach based on a simultaneous solution of these equations, paying special attention to the movement simulation. Applies the time‐stepping method with a fixed grid, independent of the rotar position. In the method the motional effects are simulated by trigonometric interpolation of the results for the previous time step.