Iron Core Inductor Research Articles

Determining Magnetically Nonlinear Characteristics of Transformers and Iron Core Inductors by Differential Evolution

This paper deals with the differential evolution (DE)-based method for determining the magnetically nonlinear iron core characteristics of transformers and iron core inductors. The unknown iron core characteristic, approximated by the sum of exponential functions, is included in a dynamic model of the tested device. The approximation function parameters are determined by DE. The optimization objective is the best possible agreement between the measured and the dynamic model calculated currents in the time and frequency domains. Using the measured inrush currents and corresponding voltages, the magnetically nonlinear characteristic can be determined over a broad operational range. The inclusion of iron core characteristic, as determined by the proposed method, in the transformer dynamic model gives very good agreement between the measured and calculated currents in both transient and steady states.

The comparison of warm-core and cold-core designs of iron-cored HTS inductors for electric power applications

An iron-cored high-temperature superconductor (HTS) inductor has to be cooled for superconducting operation. By design, it can be either warm-cored or cold-cored. A warm cored HTS inductor has only the winding cooled in the cryostat, while a cold-cored one has both the winding and the iron-core cooled in the cryostat. Each design has its own advantages and disadvantages. By analysing the advantages and disadvantages, this paper provides some guidelines for those who are designing a practical HTS inductor for electric power applications.

Implementation of Knowledge-Based System for Iron Core Inductor Design

We describe the implementation of a knowledge-based system for designing iron core inductors. We identify the underlying issues related to the implementation of such a system. We employ a recursive design methodology based on imitating an expert human designer that is suitable for embedding in the knowledge-based system. A hybrid knowledge base, using both frame-based and rule-based paradigms, together with assertions and procedural attachment, captures inductor-oriented design expertise. The paper establishes a general framework whereby dedicated knowledge-based systems for electromagnetic design can be built. It presents results that illustrate the performance of the developed system, particularly in comparison to the standard design procedure found in the literature.

Model of Laminated Iron-Core Inductors for High Frequencies

We propose a model with frequency-dependent lumped parameters to represent the behavior of laminated iron-core inductors that are used in switching converters, i.e., for excitation frequencies above several kilohertz. The model applies to laminated iron cores with air gaps. We show that the core parameters can be calculated by using the same analytical expressions as those valid for gapless cores if a properly defined equivalent magnetic permeability is introduced instead of the iron sheet permeability. We compare the inductor model parameters calculated as functions of frequency with those obtained by measurements for two test inductors. The behavior of the inductors showed that the effects due to the eddy currents in the laminated iron core and the turn-to-turn and turn-to-core stray capacitances become significant in different frequency ranges.

Controlling linearity and permeability of iron core inductors using field orientation techniques

The availability of high quality variable inductors has always been essential to devices used in different power engineering instrumentation. Different attempts have been made to improve the characteristics of iron core inductors. This paper presents an approach through which an iron core inductor linearity and permeability ranges may be controlled. The approach is based on experimentally observed vectorial magnetization response of magnetic materials to orthogonal field components. By the aid of 2-D vector Preisach model simulations were carried out to investigate performance of a laminated steel core inductor designed according to the proposed approach. Experimental measurements for the inductance variation of a particular core were acquired and found in agreement with corresponding simulations.

Numerical errors in the scalar potential formulations used in low-frequency field problems

This paper examines the sources of numerical errors in the reduced scalar potential solution of electromagnetic field problems. A number of ways by which some of these errors may be eliminated are put forward and numerical results for the 3D geometry of an iron core inductor are compared and explanations have been attempted.

Analysis of a hysteretic circuit containing an iron-cored inductor and a semiconductor switch

The analysis is described of a power electronic circuit that contains two different types of nonlinear element: an iron-cored inductor and a semiconductor switch. The classical Preisach model is used to simulate the hysteretic characteristic of the iron-cored inductor. The voltage–current relation of the semiconductor switch, which also has a hysteretic characteristic, is represented by the piecewise-linear approximation. The steady-state analysis of hysteretic circuit is performed by the shooting method with Newton iteration. The analysis treats the hysteretic element as a transducer that depends on the discretised history of its input. The analysis reveals effects of the hysteresis on the performance of an oscillatory circuit. Residual magnetism and demagnetisation help the main capacitor to be charged and discharged by the switching action of the semiconductor switch.

Modified scalar potential solution for three-dimensional magnetostatic problems

A novel three-dimensional magnetostatic solution based on a modified scalar potential method has been developed. This method has significant advantages over the traditional total scalar, reduced scalar, or vector potential methods. The new method was successfully applied to a three-dimensional geometry of an iron core inductor and a permanent magnet motor. The results obtained are in close agreement with those obtained from traditional methods.

Applications of a new model of scalar hysteresis to a series ferroresonant circuit

In this paper the hysteretic behaviour of an iron core inductor is described by means of a new model based on a sequential algorithm. This model has been applied to study a series ferroresonant circuit. The simulations obtained using the proposed model are in good agreement with experimental results, as well as with the predictions of the classical Preisach model; nevertheless the latter may be computationally more cumbersome.

Coupling of a nonlinear diffusive electromagnetic system to a linear electric circuit

A composite electromagnetic system that includes a nonhysteretic ferromagnetic conducting body and a linear resonant circuit fed by a sinusoidal voltage source is studied. The diffusion of the magnetic field in the iron core inductor is described by means of a finite-dimensional nonlinear dynamic system obtained by applying the Galerkin method. These equations are coupled with the circuit ones. This physical system might exhibit different nonlinear phenomena: multiple periodic oscillations and even apparently completely disordered aperiodic chaotic motions. Multiple harmonic and subharmonic oscillations are investigated by computer-aided analysis using a static method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Parametrically driven variable-reluctance generator

In the parametrically driven variable-reluctance generator, the inductance of an iron-core inductor is varied at an acoustic frequency by an external force. Nonlinear effects thereby absorb mechanical power from the external force and deliver electrical power to a load connected to the inductor, with the electrical phenomena occurring at half the frequency of the mechanical phenomena. Both a theoretical description of this device and measurements in agreement with the theory are presented. Several interesting nonlinear dynamical phenomena can be observed with this simple system; it is also capable of highly efficient power transduction.

Nonlinear circuits with hysteresis

The complete solution of the dynamical equations is obtained for lumped electrical circuits containing iron-cored inductors subject to magnetic hysteresis, as described by Preisach. The states of the system are shown to be continuous piecewise smooth functions of time if the applied voltages and currents are likewise smooth, whatever the initial magnetic histories of the inductors may have been. Sufficient conditions are derived for the existence of periodic, particularly subharmonic, forced solutions for the states of the circuits, not only for the Preisach model but also for a wide class of other models of hysteresis.

Molded hearing aid and battery charger

A molded hearing aid of the self-containing type having a rechargeable battery disposed therein, in the form of a molded plug which will fit in the ear of the user. A light emitting diode is disposed through the external surface of the plug and is internally connected in series with an iron core inductor with the series combination in parallel with the internal chargeable battery. A battery charger is provided having a cup for receiving the molded plug and having a multiturn coil wound around the periphery of the cup. The coil is connected into an oscillator circuit and tuned to cause the circuit to oscillate at about 30 kHz. The oscillator coil couples to the iron core inductor in the plastic plug thereby inducing a 30 kHz ac voltage across the coil. The light emitting diode rectifies the alternating current and is connected in a polarity so as to charge the internal battery of the hearing aid. As the charging current flows through the light emitting diode, the diode is illuminated indicating to the user that charging is taking place and indicating by its brillance when the hearing aid is located in its optimum position.

A Method for the Calculation of an Apparent Time Invarying Inductance for an Iron Core Inductor

A method for measurement of the instantaneous inductance L(t) of an iron core inductor is presented as a function of the inductor current i, the rate of change di/dt of this current, and the past history of the iron core at that moment. The inductance of a filter inductor is shown as a function of unidirectional continuous and discontinous currents. The concept of an equivalent time invarying inductance L eq is formulated for the purpose of piecewise linear time-domain analysis of switching networks, and a method for its calculation is indicated. The usefulness of this new tool of analysis is confirmed by agreement of calculated and experimentally obtained data.

Mathematical model for dynamic hysteresis loops

A new mathematical model is used to represent systems characterized by dynamic hysteresis loops. The model is completely specified by three nonlinear functions: a restoring function f , a dissipation function g, and a weighting function h. Simple procedures are given for constructing these functions so the resulting model will simulate a given loop exactly. The model is shown to exhibit many important hysteretic properties, such as the presence of minor loops and an increase in area of the loops with increasing frequency. Both are observed in practice. Two examples are given to illustrate the utility and flexibility of the model. The first is from the field of biophysics and the second is a nonlinear iron-core inductor.

Lumped-circuit models for nonlinear inductors exhibiting hysteresis loops

A new mathematical model of dynamic hysteresis loops is presented. The model is completely specified by two strictly monotonically increasing functions: a restoring function f(.) and a dissipation function g(.). Simple procedures are given for constructing these two functions so that the resulting model will simulate a given hysteresis loop exactly. The model is shown to exhibit many important hysteretic properties commonly observed in practice such as the presence of minor loops and an increase in area of the loop with frequency. In the case of an iron-core inductor, the mathematical model is shown to be equivalent to a lumped-circuit model, consisting of a nonlinear inductor in parallel with a nonlinear resistor. Extensive experimental investigations using different types of cores show remarkable agreement between results predicted by the model with those actually measured. The most serious limitation of this dynamic model is its inability to predict dc behaviors. For the class of switching circuits where dc solutions are important, a special dc lumped-circuit model is also presented.

The phenomenon of ferroresonance

The presence of an iron-cored inductor in an a.c. circuit can in certain circumstances result in phenomena known as ‘ferroresonance’, and these phenomena have been the subject of much study. Over the years, ferroresonant circuits have been used in power-system applications such as airport lighting and servomotors, and in the early 1950s were considered as a serious rival to thermionic valves for use as switching devices in early computers.

The relationship of the measured A-C permeability at low inductions to the dynamic hysteresis loop geometry

Expressions relating a-c permeability and core loss to the dynamic hysteresis loop geometry are derived. It is shown that for inductions of 5 kilogauss or less, the a-c permeability associated with an iron-core inductor represented by a resistance in parallel with an inductance is equal to the slope of the major axis of the dynamic hysteresis loop. If the iron-core inductor is represented by a resistor in series with an inductor, the a-c permeability is not easily interpreted. To calculate the permeabilities and the core loss, it is necessary to measure the peak magnetic induction, the peak magnetic field, and the phase angle between them. This was done for several different materials at frequencies of 60 and 400 cps (cycles per second) and the results are compared to modified Hay bridge measurements. The two methods in most cases agree to within about 5%.

Transformers, Inductors and Filters

Transformers, inductors and filters have continually played important roles throughout the field of electronics. Relatively crude electromagnetic devices were employed in early telephone and radio communication systems and today their vastly improved descendants are still found in most electronic systems. The sizes of electronic power transformers have been reduced through the development of new core materials and suitable hightemperature insulating materials. Design methods for audio and video transformers have been evolved which, in combination with improved core materials, made it possible to provide broad-band transformers having low distortion effects. Pulse transformers were developed for radar systems and made practical the hydrogen thyratron type pulse modulator. The performance characteristics of intermediate-frequency and radio-frequency transformers have been improved and their sizes reduced through the development of pressed-powdered iron and ferrite core materials. The linearity and stability of iron-cored inductors for filters have been improved through core materials development. Nonlinear inductors were made more nonlinear through the development of rectangular hysteresis loop magnetic alloys and ferrites, providing many new types of electromagnetic devices for electronic circuitry. Advances in electronics have made obsolete some applications of transformers and inductors but also have opened up other opportunities for inductive devices of novel or new characteristics.

Extension of the dual-input describing-function technique to systems containing reactive non-linearity

Kochenburger&apos;s describing function and also the dual-input describing function due to West, Douce and Livesley are well known. These techniques enable the graphical solution of nonlinear differential equations in which the non-linear coefficient is associated with the first-order differential term to be obtained. The paper describes an extension of these methods, allowing the non-linear coefficient to be associated with any term in the differential equation.It is shown that the typical non-linearity presented by an iron-cored inductor or by a ferro-electric capacitor may be resolved into a simple feedback system containing a single non-linear element which is independent of frequency, together with elements possessing linear transfer functions. The resulting equivalent block diagram is suitable for analysis by either of the describing-function techniques. As an example, the dual-input technique is used to predict accurately jump phenomena in an iron-cored ferroresonant circuit, and the validity of the equivalent block diagram suggested is also checked by simulation on an analogue computer.