Transformer Equivalent Circuit Research Articles

An Integration SPWM Strategy for High-Frequency Link Matrix Converter With Adaptive Commutation in One Step Based on De-Re-Coupling Idea

When matrix converter (MC) and high-frequency link (HFL) are combined together, they become more complex and gain a safe commutation for the use of high-frequency transformer. To realize energy conversion and transmission, and to achieve reliable and safe commutation at the same time are particularly important and desirable. HFL matrix converter (HFLMC) can be divided into two types: high-frequency link matrix inverter (HFLMI) and high-frequency link matrix rectifier (HFLMR). A three-phase output HFLMI is selected as the object of this study, and a novel integration sinusoidal pulse width modulation (SPWM) control strategy with one-step adaptive commutation based on De-Re-coupling idea is proposed for it. After expounding on the De-Re-coupling idea, a kind of HFLMC equivalent circuit model based on the high-frequency transformer equivalent circuit is built up. Then, a detailed analysis of the voltage stress on power devices of the HFLMC by using this model is performed. A safe operation evaluation criterion of HFLMC is also gained. A suggestion of how to select carrier wave for integration SPWM is ascertained through detail discussion, and two kinds of specific Re-coupling logic circuits are presented, and at last some experimental results are shown to make a certification for feasibility and effectiveness of the new proposed SPWM strategy.

압전 변압기 특성을 이용한 T5급 응용회로 동작 및 해석에 관한 연구

압전 변압기와 CCFL, 형광등의 전기적 등가회로에 의한 PSPICE 모델을 제시하였고, 차세대 35W급 초절전형 삼파장 T5 형광램프용 고효율 형광등 안정기를 개발하였다. 이 안정기는 역률개선회로와 인버터에 압전 변압기를 채용하여 T5 형광램프의 점등실험을 하였으며, 압전 변압기의 효율적인 구동과 정확한 주파수 공급을 위하여 PLL방식을 사용하였다. In This Paper, at the PSPICE model is presented by Piezoelectric Transformer and CCFL and equivalent circuit of fluorescent light. Highly effective fluorescent light release for next generation is developed for 35W supremacy model three wave length T5 fluorescent lamps. Lighting a candle experiment of T5 fluorescent lamps is carried out by employing Piezoelectric Transformer power-factor improvement circuit and inverter. PLL method is used for supplying a correct frequency of Piezoelectric Transformer operating.

Augmented Short-Circuit Test for the Measurement of Transformer Equivalent-Circuit Parameters with Large Series Branch Impedances

An augmented short-circuit test is described for the determination of equivalent-circuit parameters of single-phase transformers with large series-branch impedances. This test may be conducted at rated currents with the transformer connected to a reduced voltage supply. Thus harmonics in current and voltage waves are negligible. This test is therefore free from harmonics-associated errors. Based on test results, phasor equations are found which give formulae for the equivalent-circuit parameters with series-branch impedance split into low- and high-voltage components.

Algorithm to identify the excitation inductance of power transformer with wye-delta connection

An algorithm to identify the excitation inductances of three-phase power transformer with wye-delta connection is proposed. Existing methods of determining the excitation inductances of three-phase transformers require that all winding currents to be known, making them impractical on some wye-delta transformers where the delta winding currents are not measured. Based on the transformer equivalent circuit, the proposed algorithm eliminates the influence of the delta circulating current, allowing the excitation inductances to be calculated using the line currents of the delta connection side directly. The algorithm's accuracy has been verified by electromagnetic transients program including direct current (EMTDC) simulations, which show that the proposed algorithm is able to differentiate accurately and sensitively between transformer inrush and fault conditions. This lends itself to applications in the area of transformer protection.

Equivalent circuit for high-voltage partial-core resonant transformers

An equivalent circuit model for the partial-core resonant transformer is presented. A model which omits core losses is first introduced and is verified on a sample air-core resonant transformer. Partial-cores are then introduced into the transformer and the resonant characteristics are re-measured. The model is modified to account for the core losses and then verified against the measured data. Comparisons and transformations between the model and the Steinmetz ‘exact’ transformer equivalent circuit are given. A procedure for measuring the equivalent circuit inductances is described and then used to investigate the inductance variation with core displacement characteristics of the sample transformer in both axial-offset and centre-gap arrangements. In a capacitive load test the sample transformer was linear to a significantly higher voltage when using the centre-gap arrangement.

Transformer Equivalent Circuit from Field Measurements

In this paper, transformer equivalent circuit parameters are obtained using the Newton-Raphson method and field measurements at the two ends of the transformer. This may become necessary if a new or rewound transformer replaces an existing transformer during maintenance and the parameters of the new or rewound transformer have to be determined.

Modelling dynamic hysteresis loops and iron losses by the use of equivalent circuits

PurposeThe aim of the paper is the formulation of a simple hysteresis model entirely based on generally accepted concepts.Design/methodological/approachAccording to this, the modelling of loops has been achieved by the application of the Langevin‐Weiss law of magnetization to transformer equivalent circuits. The loops are generated by the change of the phase of current, introduced by the resistance modelling iron loss. Differential circuit equations have been solved with the help of standard Mathcad procedures.FindingsIn spite of the simplicity of such approach, the accuracy of hysteresis loops and iron loss approximations is better than in PSpice simulations and the model can be easily extended to dynamic loops.Research limitations/implicationsThe application of the model is limited to lower frequencies, where the rise of frequency leads to the widening of the loops without the radical change of their shapes.Practical implicationsPresented approach may be useful in simplified analysis of low frequency transformer circuits and in the primary explanation of hysteresis phenomena for teaching purposes.What is original/value of paperContrary to other models based on saturation curves, the dynamic hysteresis loops presented in this paper are obtained with the use of basic laws and concepts, without the introduction of any additional assumptions and the separate treatment of the lower and upper branches of the loops.

Study on the transformer equivalent circuit of eddy current nondestructive evaluation

The modeling of a practical configuration of nondestructive evaluation (NDE) by eddy currents (EC) generally requires extended analytical or numerical developments. This is a drawback to any understanding of the EC NDE principle and of its basic features. Nevertheless, it is possible to exploit a simple equivalent circuit based on an analogy with the operation of an electrical transformer. In this model the EC sensor constitutes the primary of the transformer whereas the evaluated conductive plate forms the transformer secondary and its electrical load. In this paper, thanks to the transformer analogy, the author obtains a simple analytical expression of the impedance of the EC sensor by using a distributed constant representation of the evaluated plate. This expression allows to exhibit some fundamental features of the EC NDE method.

Frequency‐range widening of three‐transformer CATV divider using a bead‐type ferrite core

AbstractThis paper describes the frequency‐range widening of a three‐transformer CATV divider consisting of one divider transformer and two matching transformers, all of which use a bead‐type ferrite core. For frequency‐range widening, the shape and material of the ferrite core, transformer windings, and transformer packaging are theoretically studied by means of a newly proposed high‐frequency transformer equivalent circuit. For the divider designed based on the theoretical study, excellent measurement results are obtained in the frequency range of 20 to 3000 MHz, including a divider loss of 3.6 to 4.6 dB and more than 20 dB of coupling loss between terminals. In the design emphasizing a flat frequency characteristic at some expense of divider loss from a low to intermediate frequency range, the flatness is found to increase to about ±0.3 dB. © 2001 Scripta Technica, Electron Comm Jpn Pt 2, 84(9): 46–55, 2001

Negative inductance and numerical instability of the Saturable Transformer Component in EMTP

Numerical instability of the EMTP built-in model, the Saturable Transformer Component for the three-winding case, has been the topic of interest of the EMTP community for the past twenty years. Through theoretical analysis and computer simulation, the source of the numerical instability of the component is identified as the use of the negative inductance in the equivalent circuit of the transformer. A simple modification of the structure of the component is suggested, and the numerical instability is eliminated. The modification is supported by theoretical analysis and verified by the benchmark test of the GPU line energization test of 1973. The stability of the three-winding transformer equivalent circuit with a negative inductance is discussed in detail. A topology-based and duality-derived single-phase three-winding transformer model is described.

Models of magnetic circuits and their equivalent electrical diagrams

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.

THE COMPARISON OF THE METHODS USED FOR ESTIMATION OF CURRENT TRANSFORMER METROLOGICAL PROPERTIES

In the paper, research results on applying field methods in the process determining the parameters of a current transformer equivalent circuit have been published. The metrological characteristics were determined by solving a non‐linear electrical circuit, that is, the equivalent circuit of a current transformer, assuming different values of the forcing current and load. The method gave satisfactory results (the curve 1 in Figure 1) but was found to be time and labour‐consuming. The determination of non‐linear characteristics of RFe and Xµ elements of the equivalent circuit of a current transformer, using field methods, required carrying out a number of calculations of field distributions at the current transformer no‐load state, with different forcing currents and allowing for the magnetization characteristic of the core as well. The total magnetic energy at no‐load state is related to the main flux which permits to determine the Xµ magnetizing reactance, for a given saturation state of the core. On the basis of the calculated distribution of the vector potential, the Bmax magnetic flux density may be calculated in each element of the core and then, the total core losses and the RFe resistance may be calculated using the p = ƒ(Bmax) characteristics of the core sheet loss. Using field methods makes it possible to determine the X2r leakage reactance of the secondary winding, on the basis of the magnetic energy related to the leakage flux of the secondary winding, independently from the shape or localization of the core and the windings as well, while using the analytic method, the formulas used are true only for cylindrical coaxial windings located on the same column of the core. These formulas have been derived with the assumption that the distribution of the flux in the gap between the windings is uniform and that the flux is divided equally between the primary and the secondary windings, which is not true actually. The obtained characteristics of the RFe and the Xµ non‐linear elements, approximated by n‐degree polynomial, and also X2r were used as the input data for solving the non‐linear circuit, in order to determine the error characteristics.

Study of internal stresses intransformer windings due to lightning transient phenomena

This paper presents a method for the numerical determination of internal stresses in transformers due to lightning, in particular a suitable model of the transformer winding, special consideration being given to distribution transformers. An appropriate methodology for the capacitance and inductance calculations is also considered. The program EUIM (equivalent uncoupled inductive model) was developed in order to obtain a transformer equivalent circuit without coupled branches. The calculated values were verified by means of measurements made on experimental prototypes.

Five-legged core transformer equivalent circuit

Five-legged core transformer equivalent circuit

Single Chip IC with Head Drivers and Pre-Amplifiers for Home VCR

The first designing has been made of a fully integrated home VCR IC including head drive amplifiers, Pre-amplifiers and Rec/PB peripheral switches. In order to obtain a good C/N ratio (Carrier to Noise ratio), pre-amp design was optimized by CAD simulation with head and rotary transformer equivalent circuits derived from S parameters measured with a network analyzer. An obtained high C/N ratio of 57.5dB at 4MHz is excellent in comparison to those of conventional discrete transistors. The head drive amplifiers were designed in consideration of reducing power consumption. Head peripheral switches are completely incorporated into one chip with drive amps and pre-amps. Thus the peripheral components number was reduced by 1/2 and the power consumption was reduced to 1/2~1/5 compared with conventional types.

Grounding of gas insulated substations

The Grounding of Gas Insulated Substations (GIS) presents several unique problems not encountered in the grounding, of conventional substations. For the purposes of this paper, Gas Insulated Substations are defined as high-voltage, compact, metal-enclosed minisubstations which are compressed gas insulated at maximum rated voltages of 72.5 kV and above. The metal enclosure is grounded and consists of the outer sheath for the substation equipment and the coaxial gas insulated bus. The maximum voltage developed on the grounded outer sheath during fault conditions is calculated using coupling techniques and a transformer equivalent circuit. By setting limits on the maximum outer sheath voltage to station ground, the maximum distance between grounding points can be determined for the safety of personnel in a Gas Insulated Substation.

Equivalent Circuits for Transformers and Induction Motors

Equivalent Circuits for Transformers and Induction Motors

Characterizing Transmission Transformers for Multiple Use

A method is developed that enables the transformer designer to graphically present the total response of any transmission transformer. The method centers about "Response Contours" which are the loci of constant response on an impedancefrequency plane. The contours enable the designer or the user to apply a transformer anywhere within its entire region of useful response. This method differs from the conventional approach where a transformer is designed and characterized for a specific application, but by nature is capable of a wide range of application. Using "Response Contours", a previously coded transformer may be used in many applications thereby avoiding needless duplications of design. The contours may be easily and directly predicted from the conventional transformer equivalent circuit elements. The theoretical contours are very accurate for units with bandwidths exceeding one decade of frequency. The method developed here is applied to the complex transfer ratio, transformer loss and phase response for both matched and mismatched terminations. However, the concepts may be easily extended to reflection coefficient in the frequency domain and pulse response in the time domain.

The circuit dynamics of plasma

Equations applicable to the behaviour of plasma in bulk are derived and discussed. Starting with the equations of plasma dynamics the total and thermal energy equations are integrated over all space. Certain bulk variables such as the geometrical dimensions of a conductor and the total charge in a circuit are then introduced. Subsequent definition of various circuit parameters and the introduction of generalized e.m.f.'s permit the integrated equations to be expressed in terms of the bulk variables. Using the fact that the total energy is constant, it is possible to obtain the equations of circuit dynamics, applicable to a plasma, in Lagrangian form. The derivation is not rigorous, relying for its validity on physical arguments and the consistency of the final equations with those of plasma dynamics. Again, the proof is confined to cases in which the nature of the functions determining the distribution of mass, current and charge density throughout the volume of a conductor are time-independent. The generalized e.m.f. concept is unfamiliar; it mainly arises from coupling between the electrical and thermal properties of a plasma. It is shown that these e.m.f.'s lead to a form of magneto-resistive coupling and, even in the absence of Hall currents, an apparent anisotropic resistivity. A general proof of the equivalent transformer circuit is given.

A method of analysis of transformer impulse voltage distribution using a digital computer

With the increasing need for economical design of transformer insulation in large present-day power transformers, it is highly desirable to be able to predict at the design stage the distribution of impulse voltages throughout the windings. The paper presents a method of impulse voltage calculation using high-speed digital computer techniques which appears sufficiently accurate and flexible to provide a basis for a routine design procedure.The derivation of the transformer equivalent circuit is discussed, together with the computer programme for the solution of the resulting differential equations. The advantages of the method are indicated, and the results are compared with other recent theoretical work and with direct tests on an experimental transformer.The relative importance of the various winding parameters in the construction of the equivalent circuit is determined experimentally. Finally, possible extensions of the method are discussed and the possibility of complete automation of the procedure is indicated.