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The purpose of this paper is to review the mutual coupling of electromagnetic fields in the magnetic vector potential formulation with electric circuits in terms of (modified) nodal and loop analyses. It aims for an unified and generic notation.

The coupled formulation is derived rigorously using the concept of winding functions. Strong and weak coupling approaches are proposed and examples are given. Discretization methods of the partial differential equations and in particular the winding functions are discussed. Reasons for instabilities in the numerical time domain simulation of the coupled formulation are presented using results from differential-algebraic-index analysis.

This paper establishes a unified notation for different conductor models, e.g. solid, stranded and foil conductors and shows their structural equivalence. The structural information explains numerical instabilities in the case of current excitation.

The presentation of winding functions allows to generically describe the coupling, embed the circuit equations into the de Rham complex and visualize them by Tonti diagrams. This is of value for scientists interested in differential geometry and engineers that work in the field of numerical simulation of field-circuit coupled problems.

This paper aims to give a perspective about the variety of techniques which are available and are being further developed in the area of coupled field formulations, with selective bibliography and practical examples, to help postgraduate students, researchers and designers working in design or analysis of electrical machinery.

This paper reviews the recent trends in coupled field formulations. The use of these formulations for designing and non‐destructive testing of electrical machinery is described, followed by their classifications, solutions and applications. Their advantages and shortcomings are discussed.

The paper gives an overview of research, development and applications of coupled field formulations for electrical machinery based on more than 160 references. All landmark papers are classified. Practical engineering case studies are given which illustrate wide applicability of coupled field formulations.

Problems which continue to pose challenges to researchers are enumerated and the advantages of using the coupled‐field formulation are pointed out.

This paper gives a detailed description of the application of the coupled field formulation method to the analysis of problems that are present in different electrical machines. Examples of analysis of generators and transformers with this formulation are presented. The application examples give guidelines for its use in other analyses.

The coupled‐field formulation is used in the analysis of rotational machines and transformers where reference data are available and comparisons with other methods are performed and the advantages are justified. This paper serves as a guide for the ongoing research on coupled problems in electrical machinery.

The purpose of this paper is to present an algorithm of the optimization of the dynamic parameters of an electromagnetic linear actuator operating in error‐actuated control system.

The elaborated “unaided” software consists of two main parts: optimization solver and numerical model of the actuator. Genetic algorithm has been used for optimization. The coupled field‐circuit‐mechanical model for the simulation of the system dynamics has been applied. Different optimization problems have been considered. The shape of the steady‐state force‐displacement actuator characteristic has been imposed and its deviation has been minimised. Next, the total operation time of the actuator without feedback, and the setup time of the actuator with feedback are minimised. Finally, required trajectory of movement has been imposed and trajectory error is minimised.

The elaborated algorithm and the computer code can be an effective tool for field‐circuit simulation of the dynamics of an electromagnetic linear actuator that operates in an automatic control system. It enables optimal design of the electromechanical system in respect to its dynamic properties.

The elaborated algorithm and the computer code presented in this paper can be an effective tool for the field‐circuit simulation of the dynamics of an electromagnetic linear actuator that operates in an automation control system.

The purpose of this paper is to present an experimental setup for the verification of coupled electromagnetic field‐circuit simulation, called TESTCASE. By means of simple and well‐defined geometries, the comparison of different coupling approaches among each other and with measurements should be possible.

The physical setup consists of a C‐core in conjunction with a reluctance rotor. The TESTCASE is designed to work in static operation and with motion induced voltage.

Simulation results using different approaches as well as measurement results are presented. Practical issues in measurement and simulation are discussed. It was found that particular care has to be taken concerning the modeling of the air around the TESTCASE structure.

With the proposed approach, it is possible to evaluate the coupled field circuit problem on a defined and well‐known geometry. Simulation results can be compared to measurements.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

To provide a general method for coupled simulation of electrical machines and circuits, using finite element analysis and a circuit/system simulator.

The electrical machine is modelled by dynamic inductance and electromotive force (EMF), which are determined by finite element analysis and updated in time‐stepping procedure. Calculation of these parameters is based on current perturbations that are applied on linearized field equations after determining the operating point by nonlinear analysis.

Based on the case studies, the presented method can be utilized in coupled field‐circuit simulation and the results correlate with those obtained by other known methods. The results were also validated according to experimental data.

Calculation of the EMF and the presented implementation for SIMULINK have some limitations regarding the accuracy and stability of the numerical integration. In the future, the numerical methods could be still improved and the implementations could be extended to other simulators.

Since the presented methodology is of a general type, the research provides means to include field‐circuit coupling into a variety of different simulation software.

Definitions of the circuit parameters differ from the conventional ones, as a result of which the parameter extraction can be performed in computation‐effective way. The benefits of the research are met widely, since the general‐purpose methodology is not limited to any single software.

In this paper, we present a method to take into account the feedback control in software developed from coupled field circuit models. The implementation of control loops is done in a software which is able to simulate electromagnetic devices associated with power electronic circuits having a time dependent topology. The control strategy is implemented in a discrete‐time version and can manage all controllable electronic switches by means of different electric or magnetic quantities calculated during the simulation (flux, currents, voltages, …). Electrical systems involving magnetic devices, power electronic converters and their control devices can be simulated in presence of phenomena such as eddy currents or saturation of the magnetic materials.

The purpose of this paper is to develop and systemize the 3D finite element (FE) description of electromagnetic field in electrical machines.

3D FE models of electrical machines are considered. The model consists of FE equations for the magnetic field, equations describing eddy currents and equations, which describe the currents in the machine windings. The FE equations are further coupled by the electromagnetic torque to the differential equation of motion. In the presented field‐circuit model, the flux linkages with the windings are expressed by two components. Attention is paid to the description of machine winding. Both scalar and vector potential formulations are analysed. The FE equations are derived by using the notation of circuit theory. The methods of movement simulation and torque calculation in FE models are discussed.

Proposed circuit description of electromagnetic field in electrical machines conforms to the applied method of electric and magnetic circuit analysis. The advantage of the presented description is that the equations of field model can be easy associated with the other equations of the electric drive system.

The applied analogies between the FE formulation and the equivalent magnetic and electric network models help formulate efficient field models of electrical machines. The developed models after coupling to the models of supply and control system can be successfully used in the analysis and design electric drives.

The coupling between a 3D modified magnetic vector potential formulation discretized by the finite integration technique and an electrical circuit that includes solid and stranded conductors is presented. This paper describes classical time integration methods and the implicit Runge‐Kutta methods, the latter being an appropriate alternative to the first ones to solve effectively index 1 differential‐algebraic equations arising from combined simulation of electromagnetic fields and electrical circuits.

The paper seeks to present an algorithm for a dynamical field‐circuit coupled simulation of an electromagnetic linear actuator operating in automated control systems.

The mathematical model includes: a transient electromagnetic field formulation for a non‐linear conducting and moving medium, equations which describe the electric circuits of the converter and the supply system, the equation of mechanical motion, the equation describing closed‐loop control and models for the sensor and the PID controller. The numerical implementation is based on the finite element method and the step‐by‐step algorithm for time discretization. In order to account for the nonlinearity of the ferromagnetic core the Newton‐Raphson procedure has been applied. The influence of the PID controller settings on the operation of the controlled actuator is shown. Dynamic disturbances, e.g. step change of the set value of mover position or change of loading force, have been analyzed.

The elaborated algorithm and the computer code can be an effective tool for field‐circuit simulation of the dynamics of an electromagnetic linear actuator operating in an automatic control system. Only tapered plunger should be used as multi‐stable actuators.

The study provides information of value in electromagnetic research.