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The purpose of this paper is to develop the method of taking the eddy current losses in the laminated magnetic circuits into account during implicit transient calculations. The nonlinear magnetization characteristic of iron and the hysteresis losses can also be considered in the simulations done with the developed method.

The paper presents complex equivalent magnetic permeability derived from the presumed angular frequency in a laminated magnetic circuit. On this basis, the synthesis of a magnetic permeability as a function of the Laplace variable “s” is presented. After transformation of the variable “s” to a variable “z” of the Z transformation, it is possible to conduct discrete time calculation of transient states of magnetic circuits including the eddy current losses. An iterative process is developed to take the saturation of the magnetic circuit in these calculations into account. As regards hysteresis losses, the scalar model of magnetic hysteresis by Juhani Tellinen was implemented. The new method is validated by calculations of a two-coil transformer.

It is important to take into account the losses in sheet metal directly in the implicit transient calculations. This possibility is provided by the presented method based on the synthesis of the equivalent magnetic permeability μ^(s). The presented method was proved to be correct and efficient. The calculated sheet metal losses were compared with the results presented in literature. Good conformance of results was attained.

The method enables calculation of eddy current and hysteresis losses in laminated magnetic circuits during calculations of transient states. It does not need, unlike the previous methods, previously provided information (“a priori”) about the content of higher harmonics in waveforms. The method takes into account mutual dependence of transient waveforms of currents in the analysed system and losses of laminated magnetic circuit, expressed by eddy currents and hysteresis losses. Its implementation comes down to using in calculations a filter of the IIR type and corresponds to its calculation complexity. The author plans to use the presented method in the finite elements method transient calculations.

A new approach is a synthesis of the equivalent magnetic permeability in Laplace domain, which creates an equivalent RC circuit for permeability. Analytic equations for parameters of this equivalent circuit are original. A method for considering nonlinear magnetization characteristic and hysteresis losses was presented. In calculations of transient states of systems with magnetic circuits, one can use the developed equivalent circuit of magnetic permeability in a form of the IIR filter. Operator magnetic permeability includes fractional derivative of Laplace’s variable “vs”. Therefore, the equivalent IIR filter includes “history” of the processes that take place in the laminated magnetic circuit to the current, calculated time moment. This “history” in terms of its content is limited only by the degree of the applied IIR filter. It enables to calculate “step by step”, without previous (“a priori”) knowledge about harmonic components of the whole waveforms. It was necessary in the previously used methods, when determining parameters of magnetic permeability. The method proposed in the paper allows for calculations with taking into account direct dependence of an electric part of the system on its magnetic part.

The purpose of this study is to create an extended equivalent circuit model for a compound DC motor, consisting completely of electrical parameters and quantities.

The dynamic model of the compound DC motor is obtained by establishing the voltage equations for the armature and excitation circuit and the mechanical equation for the mechanical part. The mechanical parameters in the dynamic model are converted into electrical parameters with an electrical circuit proposed for the mechanical part. By combining the armature and excitation circuits with the electrical circuit created for the mechanical part, the extended equivalent circuit model of the compound DC motor is obtained. Because the proposed extended equivalent model is completely an electrical circuit, simulations can be made in the circuit simulation programme. Simulations of the proposed compound DC motor circuit were carried out, and the accuracy of the proposed circuit was verified by performing experimental studies with an existing compound motor.

When comparing speed and current profiles in experiments and simulations, it is seen that compound DC motor can be modelled with the proposed equivalent circuit including completely electrical elements in a simulation programme for the circuits. The results show that the proposed equivalent circuit satisfies the dynamic model of the compound motor.

In DC machine models, armature and excitation circuits are given as an electrical circuit, and mechanical part of the machine is modelled by only mechanical equations. The originality of this study is converting the dynamic model of an electrical machine consisting of electrical and mechanical equations into a completely electrical circuit. With the proposed method, the dynamic model of many motors can be converted into a completely electrical circuit. In this way, motors can be simulated as an electrical circuit in simulation programmes for the circuits, and the dynamic behaviour of motors can be obtained.

The purpose of this paper is to develop a linearized equivalent electrical circuit of a photovoltaic generator. This circuit is appropriate to confront problems such as numerical instability, increased computational time and nonlinear/non‐canonical form of system equations that arise when a photovoltaic system is modelled, either with differential equations or with equivalent resistive circuits that are generated by electromagnetic transient software packages for power systems studies.

The proposed technique is based on nonlinear and well‐tested i_pv−v_pv equations which are however used in an alternative mathematical manner. The application of the Newton‐Raphson algorithm on the i_pv−v_pv equations leads to uncoupling of the i_pv and v_pv quantities in each time step of a digital simulation. This uncoupling is represented by a linearized equivalent electrical circuit.

The application of nodal analysis equivalent resistive circuits using the proposed equivalent photovoltaic generator circuit leads to a system model based on linear algebraic equations. This is in opposition to the nonlinear models that normally result when a nonlinear i_pv−v_pv equation is used. In addition, using the proposed scheme, the regular systematic methods of circuit analysis are fully capable of deriving the differential equations of a photovoltaic system in standard form, thus avoiding the time‐consuming solution process of nonlinear models.

In this paper, a new method of using the i_pv−v_pv characteristic equations is proposed which remarkably simplifies photovoltaic systems modeling. Moreover, a very important practical application is that by using this methodology one can develop a photovoltaic generator element in electromagnetic transient programs for power systems analysis, of great value to power engineers who are involved in photovoltaic systems modeling.

dc electrified traction systems are a potential source of stray currents. The purpose of this paper is to evaluate the harmful effects (electrolytic corrosion) that an electrified railway has on nearby earth return circuits (e.g. pipelines).

The electric circuit approach, based on the earth return circuit theory, to model stray currents interference on extended structures is presented. An exact method of calculation is applicable to any dc railway system in which tracks can be represented by a single earth-return circuit (equivalent rail) with current energization. In the approximate method, the equivalent rail with current energization is modeled as a large multinode electrical equivalent circuit with lumped parameters. The circuit is a chain of basic circuits, which are equivalents of homogenous sections of the rail. The electrode kinetics (polarization phenomenon) is taken into account in the model developed.

Formulas in partially closed forms are derived applicable to the analysis of currents and potentials along a pipeline laid in the proximity with railway tracks. The attempt is undertaken, to incorporate the electrode kinetics into the simulation model in which the polarization phenomenon (Tafel equation) is modeled by a non-linear voltage source with source voltage being iteratively calculated. The polarization potential along the affected pipeline can be determined.

The pipeline electrochemical response (polarization behavior – non-linear phenomenon on the interface metal-soil electrolyte) to the dc stray currents interference is innovative incorporated into the simulation model with lumped parameters using the iterative process.

The theoretical method of converting the magnetic circuit into an electric circuit is mature, but the way to determine the inductances in the electric circuit is not reliable, especially for the core working in saturation status, and it is impossible to determine the inductances by the transformer terminal measurements, as the measurement information is not enough to determine a number of inductances. This paper aims to propose an approach of calculating the reluctances.

In this paper, an approach of calculating the reluctances is proposed based on the numerical simulation of magnetic field in transformer with different values of current excitation. The reluctance of a core segment or air region as a branch of magnetic circuit is obtained by the magnetic energy and magnetic flux. By this way, all the reluctances as function of flux can be determined, and then the inductances can be determined. The reluctances and equivalent electric circuit of three-phase integrative transformer is determined, and its validation is proved in the paper.

The single phase example shows that the proposed method has a good performances on analysis of the inrush current in deep saturation. The peak value of the inrush current derived from the proposed approach matches well with the results obtained by coupled circuit-FEM analysis, and the difference is about 4.8 per cent. For studies on dual models of single phase transformers, the leakage inductances have important effects on the peak value of the inrush current. The reluctances of three-phase transformer are calculated, and the equivalent circuit simulation results are slightly smaller than the coupled circuit-FEM simulation results.

Approach of calculating the reluctances based on the numerical simulation of magnetic field in transformer is proposed. The magnetic core and air space are divided into several segments, and the reluctance for each segment is calculated based on the energy in the region and the flux of the cross-sectional area. By applying various excitation currents, all the reluctances as function of flux can be determined, and then all the non-linear inductances including the non-linear leakage inductances are obtained. The proposed approach is reliable to determine a number of inductances in the dual electric circuit, especially for deep saturation status.

This paper aims to present a SPICE model to represent antennas in receiving mode. The model can be used to evaluate the performance of the antenna when it is coupled to several different nonlinear electric circuits. The proposed methodology is particularly suitable for rectenna applications, as it allows the analysis of different configurations for a rectenna more efficiently than using full-wave analysis simulators coupled directly to each rectifier circuit.

The model presented uses reciprocity theory to calculate the ideal voltage source of the Thevenin-equivalent circuit for an antenna. Vector fitting is then used to approximate the model to rational functions that can be converted to Resistor, Inductor and Capacitor circuits. Additional components are added to the circuit to prevent numerical instability.

Two rectennas are used to illustrate the performance of the proposed model, one based on a 2.45-GHz rectangular patch antenna and another based on a planar spiral antenna. The second antenna has impedance with positive and negative real parts along the frequency range, which could lead to numerical instabilities. The proposed method is shown to be stable while working with these negative resistance values, which may appear during circuit parameterization.

The equivalent SPICE circuit model for the antenna makes it easy to simulate nonlinear circuits connected to the antenna and perform transient analyses. The computational cost of antenna analysis is reduced, being more computationally efficient than methods that involve full-wave simulation. This characteristic makes it an interesting approach for working with rectennas, or any application where the time constant of the circuit is much longer than the period of the incident wave.

For most antenna applications, the numerical stability of the circuit can be achieved using passive enforcement. However, depending on the phase response of the antenna, the impedance that represents its far-field characteristic may present a negative real part, in which case, passive enforcement will fail. In this paper, the problem of numerical instability is solved by introducing an offset resistance and a current-controlled voltage source to the model.

The purpose of this paper is to implement the macro-modeling and passivity enforcement for the equivalent high frequency circuit model of a single-phase winding for an alternating current (AC) three-phase motor. It provides a stable and strictly passive Foster-type circuit macro-model for the winding. Consequently, a stable circuit network is guaranteed when it is connected with an external passive circuit. The equivalent circuit is validated on a three-phase permanent magnet synchronous motor. Furthermore, the corresponding three-phase windings macro-model could be obtained accordingly.

The following techniques are used: the least square method, vector fitting method, the fast residue perturbation method, circuit synthesis, sequence quadratic programming method and simulated annealing method.

This work presents an effective approach to model an equivalent high frequency circuit macro-model for a single-phase winding. Simultaneously, both the characteristics of port passivity and component passivity are guaranteed.

This paper carries out both the port passivity and the component passivity enforcement for a single-phase winding of a motor during the macro-modeling procedure. This equivalent motor winding model can be applied to obtain the conducted electromagnetic interference and the overvoltage performance analysis for an adjustable speed motor drive system.

The paper presents a method of creating electrical equivalent diagrams of magnetic circuits. The method is based on bond‐graph techniques, using flux derivative as flow variable. Couplings between magnetic and electric part of the system are represented by gyrators. Simple models of magnetic branches, including non‐linear effects due to saturation, hysteresis and eddy currents, are presented. These models can be easily combined into magnetic circuit models, which can be transformed into dual electric equivalent circuit. Various equivalent circuits of transformers are discussed. The proposed models are simple and particularly useful for system‐level simulation of power electronic and motion control systems with magnetic elements. These models can be easily developed if needed. Theoretical considerations are illustrated by examples of digital simulation and experimental results.

To synthesize equivalent circuit obtained from reduced order model of large scale inductive PEEC circuits.

This paper describes an original approach for reducing and synthesizing large parasitic RLM electrical circuits coming from inductive Partial Element Equivalent Circuit (PEEC) models. The proposed technique enables the re-use of the reduced order model in the time domain circuit simulation context.

The paper shows how to use a synthesis method to realize an equivalent circuit issued from compressed PEEC circuits.

The coupling between methods PEEC and a compressed method as Fast Multipole Method (FMM) in order to reduce time and space consuming are well-known. The innovation here is to realise a smaller circuit equivalent with the original large scale PEEC circuits to use in temporal simulation tools. Moreover, this synthesis method reduces time and memories for modelling industrial application while maintaining high accuracy.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.