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A self-calibrating current transformer with nominal ratio 10 A to 100 mA, intended for low frequencies applications, was developed. It has 100 independent primary windings to be connected in series or parallel, so that it can be configured as 100:1 or 1:1 transformer (all windings in series). This last ratio permits autocalibration. Error sources are analyzed, and it is shown that differences between parallel and series configurations have uncertainties lower than 1 part in 106.

The soft-switching solid-state transformer (S4T) employs only 12 main active devices and an auxiliary resonant circuit to implement a bidirectional solid-state transformer, with an attractive feature of achieving a full range of zero-voltage-switching conditions for all the main devices. This paper covers detailed design of the power stage, auxiliary resonant circuit, and control of the S4T. The high-frequency transformer is an essential element for the S4T, and it has a unique feature of dc-biased flux. Design of such a high-frequency transformer is also discussed in detail in this paper. Soft startup, shutdown, and fast dynamic response under load transients are also attractive behaviors because of the low inertia of the S4T. Experimental results from a 208-V/10-kV·A S4T unit are presented.

An incipient short-circuit fault does not cause a severe condition in the steady-state operation of transformers, but in transient conditions - the lightning or switching - it can result in an extended turn-to-turn short-circuit fault (TSCF) and eventually in transformer outage. This study aims to determine and localise small TSCFs using the frequency response analysis. For this purpose, an appropriate mathematical model is developed, which can accurately simulate the winding transient behaviour. Using this model, turn-to-turn short-circuit patterns are extracted for different turn-to-turn faults in the winding; then, the fault location is determined by comparing the measured faulty signal with mathematical short-circuit patterns. In this study, a heuristic index is proposed to identify small TSCF locations. The presented solutions are implemented on a real winding with a nominal rating of 1600 kVA and a nominal voltage of 20/0.4 kV.

Current transformer (CT) saturation can cause the maloperation of transformer differential protection under external faults. To avoid this problem, a method based on the histogram of the normalized rotated current (NRC) is proposed. NRC is obtained by a symmetric waveform transformation of a part differential current. An index based on the histogram is defined to evaluate the NRC frequency distribution. The external faults with different degrees of CT saturation, internal faults, and transferring faults can be clearly distinguished by the proposed method. Moreover, the detection time is invariably less than a half cycle after the obvious increase of the differential current. Simulation results validated the proposed method.

This paper presents a new topology for a fully bidirectional soft-switching solid-state transformer (S4T). The minimal topology, featuring 12 main devices and a high-frequency transformer, does not use an intermediate dc voltage link, and provides sinusoidal input and output voltages. The S4T can be configured to interface with two- or multiterminal dc, single- or multiphase ac systems. An auxiliary resonant circuit creates zero-voltage-switching conditions for main devices from no-load to full-load, and helps manage interactions with circuit parasitic elements. The modularized structure allows series and/or parallel stacking of converter cells for high-voltage and high-power applications.

This paper proposes a three-phase lines to single-phase coil planar contactless power transformer. The transformer has the primary consisting of three-phase line cables arrayed in parallel on a plane and the secondary of single-phase coil. The proposed transformer is studied for application to automatic guided vehicles (AGVs). Uniform power transfer that is independent of the position of the AGVs is an important issue for this transformer, because of the sparse arrangement of the primary lines. To ensure that the transformer achieves uniform power transfer, the structure and dimensions of the primary are studied using numerical analysis. Additionally, an equivalent model of the proposed transformer, which is applicable to the imbalanced conditions, is presented. The equivalent model proves analytically that balanced three-phase voltage and balanced three-phase current conditions, which can be created using appropriate circuit configurations, enable uniform power transfer. The results of experiments in which the prototype of the transformer is applied to the target AGV confirm that under balanced-current conditions, which can be generated using a three-phase LCL circuit, the proposed transformer can transfer sufficient uniform power to drive the AGV.

The aim of this work was to work out the mechanical stresses within transformer resulting from the extreme short-circuit currents. The forces and stresses set up in transformer windings as the result of exterior or interior short-circuits or of switching operations, are measured in detail. A variety of arrangements of windings in large power transformers are described. Points at which mostly high mechanical stresses take place in concentric windings are discussed in detail. Analytical and FEM calculations for individual short circuit forces, axial and radial have been discussed. The result was then compared with actual measurements on a prototype 20 MVA 132/11.5 kV power transformer [15]. Various failure mechanisms due to these forces have been discussed. Design parameters are also discussed, whose values determine the maximum stresses which may occur in any part of the transformer. Effects of irregularity in various parts and various properties of materials have been studied and the usage of appropriate material for withstanding the dynamic effects of SC is discussed. Effect of workmanship errors on short circuit withstand capability has also elucidated. Finally, a complete model is developed. Keywords: Finite element method, Power transformer, Short circuit stress, Mechanical stresses, Axial and radial stresses, High voltage winding

In this paper, the mechanical faults of transformers including the winding radial deformation and axial displacement on 1.6 MVA transformer winding are investigated. Then, by estimating the parameters of the detailed model of this transformer winding in MATLAB software and changing these parameters in a manner that is proportional to the mechanical defects in electro-magnetic transients program software, the sampled differential current of the transformer is extracted for each disturbance. Next, the internal and external electrical faults and inrush current of the transformer are simulated. Afterwards, these signals are analyzed using maximal overlap discrete wavelet transform with Daubechies4 wavelet function, and their features are extracted. These extracted features are considered for training the classifiers of Decision Tree and artificial neural network. According to the simulation results, the proposed procedure is capable of classifying and discriminating among winding mechanical defects, internal and external electrical faults, and inrush current with a good accuracy that is the main novelty of this paper in comparison to other published works, which are limited to classifying only some of the mentioned faults.

In rotary ultrasonic machining (RUM), the rotary transformer can replace the well-established slip ring technology to supply contactless power for the revolving transducer. Such contactless energy transfer (CET) is safe and high rotation speed of the spindle is permissible. However, the transfer efficiency and output power are usually a pair of contradictions. In this paper, the self-compensation method is adopted on secondary side in order to improve the dynamic balance of the revolving part. Considering the distinct capacitive behavior of the transducer, two primary compensation topologies are given. The mathematical models are presented to identify the power transfer efficiency, transfer capability and load impedance of rotary transformer used in RUM. The effects of coil turns on transfer efficiency and load resistance are researched. An optimization method of rotary transformer used in RUM is put forward. A contactless power supply RUM system that can produce high speed, high efficiency and high output power is therefore possible.

To represent transformer behaviour during a transient state which includes high frequencies, it is necessary to consider the resonances which occur inside the transformer. One strategy is to deduce the transformer model from the measurements of the transformer’s frequency response, another one is to construct the model based on a careful representation of the inside of the apparatus. In the paper a model is presented which is compatible with EMTP-type software programs based on a finite element method (FEM) calculations and the complex permeability approximation. The model can be classified as a Grey Box transformer model, according to the terminology of the CIGRE. The model’s frequency dependent parameters are derived from limited information about the transformer geometry. State space equations are used to input the model into an electromagnetic transient calculation software program. This approach requires specific mathematical treatments to avoid stability issues during simulations. The model is validated for lightning impulse studies using the field test measurements of over-voltages that had occurred at the external transformer’s terminals.

Based on the principle of the fiber Bragg grating, a new type of fiber-optic pressure sensor for axial force measurement of transformer winding is designed, which is designed with the structure of bending plate beam, the optimization of the packaging process, and material of the sensor. Through the calibration experiment to calibrate the sensor, the field test results of the Taikai transformer factory show that the sensitivity of the sensor is 0.133 pm/kPa and the repeatability error is 2.7% FS. The data of the fiber-optic pressure sensor in different positions maintain consistent and repeatable, which can meet the requirement of the real-time monitoring of the axial force of transformer winding.

The behavior of a null-string current transformer as an inertial element was analyzed, and the transfer function was derived in accordance with the equivalent circuit of current transformer. The oscillograms of real null-string currents and their mathematical description in the time and frequency domains were presented. The spectral characteristics of mathematical models of signals depending on the form and duration of the signal observation were shown. The signal passage through the measurement transformer in the transient mode was investigated. Mathematical expressions in the time and frequency domains that describe the output signals and errors of transform of the null-string current transformer for various input actions were obtained. The experimental results are presented, in particular, the oscillograms of real transient processes for various transformers, which confirm the reliability of the used mathematical models. The relations of the parameters influencing the transform error during the transformer operation in the dynamic mode were found. A suitability of the existing null-string current transformers for power protection purposes was estimated. Requirements for new null-string current transformers taking into account the features of modern digital power-system-protection devices were formulated.

This paper describes the design, fabrication, and analysis of an ultra-thin and highly flexible current sensing transformer. The transformer windings are printed on flexible polyimide substrate layers with a magnetic foil sandwiched in between. The fabricated transformer can wrap around any electrical cable for current sensing purpose. The design of the transformer adopts a circuit model that includes the nonlinearity of the magnetic core based on the Jiles–Atherton hysteresis model, which is validated experimentally.

This paper aimed to compare obtained results and collected theory for 100 Hz frequency vibration of hydropower generator stator core and transformer core. Electromagnetic vibration with 100 Hz frequency occurred both at slow-speed salient poles synchronous generator stator core and oil-filled power transformers tank, but the nature of hydropower and transformer 100 Hz vibration was different. The vibration analysis procedure and acceptable limits for hydropower generator stator core were already covered in the standards, while the health grade system for vibration measurements of power transformer has not beet yet developed. This study discussed the experimental results aiming to extend the knowledge about reasoning for non-existing statistical health grade system, based on power transformers vibrations, measured on tank. The experimental results of hydropower generator stator and power transformer spectrum were reported. Two salient pole hydropower generator stators and four transformers with different construction (including shell-type) and different cooling system (including air forced cooling system) were chosen to present vibration spectrum results. It was demonstrated that increasing clamping pressure of the core does not always reduce 100 Hz harmonic component neither for hydrogenerator stator, nor for transformer. Bad clamping pressure and defects in core, in contrary, will not result into increase of 100 Hz component for some units. Results showed that air forced cooling equipment (fans) would not add higher harmonics to vibration spectrum of the power transformer tank. It was shown that the shell-type construction of transformer core would not necessarily result in high vibration values on tank.

The output voltage of capacitor voltage transformer (CVT) is highly influential during initiation of contingencies due to its transient behaviour. This study proposes a novel method for fundamental component phasor estimation which reduces the transient impact of CVT. The proposed method (PM) first, based on hybrid full-cycle averaging window and also least squares (LS) technique, calculates the transient components of the CVT. In the next stage, by subtracting estimated transient behaviour from fault voltage signal, the fundamental phasor component of the obtained signal can be estimated utilising discrete Fourier transformer (DFT). Also, in order to prevent instability due to off-nominal frequency sampling rate, DFT formulation is improved. Several case studies have been carried out in order to show the robustness of the PM in the realistic simulation scenarios. Results show that the PM given in this study is able to estimate fundamental phasor voltage fault signal quickly and precisely with ignorable effect from transient impacts of CVT in almost always one cycle after fault occurrence.

A 1.5 kV, 35 kW, 1 kHz silicon steel core medium-frequency transformer is designed and prototyped for a 10 kV, 0.5 MW electronic power transformer. This transformer uses 0.18 mm silicon steel as core material due to the advantages of easy processing, high saturation flux density, low noise, and low cost. The detailed design considerations and an optimal design method are presented in this paper. Different from the previous work on medium-frequency transformer design, the proposed approach takes ripples into account. Core loss model under square wave excitation with ripple and winding loss model considering sideband harmonics are established. Besides, two-dimensional finite-element simulations are adopted to obtain ac/dc resistance factors. Finally, the proposed approach is verified by experiments on prototype. The test results show performance better than expected, with desirable no-load loss and power density of 2.9623 × 106 W/m3.

A clear understanding of the vibration characteristics of power transformers is necessary to detect electrical and mechanical faults in a transformer using vibration-based monitoring strategies. This paper focuses on the measurement and analysis of the vibration frequency-response functions (FRF) of a 10-kVA distribution transformer due to mechanical and electrical excitations. The modal characteristics of the transformer are extracted from the FRFs, and can be used for reference models for future transformer fault detection. The effect of the magnetizing hysteresis in the transformer core on the measured FRF is also examined.

Transformer inrush currents during energization result in mal operation of transformer differential protection, due to the flow of magnetizing current only on the primary / source side of the transformer. A straightforward approach in recognition of inrush currents is proposed here by checking the core cause of this inrush phenomenon i.e. the magnetic saturation of the transformer core. In this method, the pseudocharacteristics were approximated in terms of orthogonal polynomials, and is used to distinguish between inrush currents and fault currents. In this method, the magnetic saturation characteristics of the transformer is modeled by defining pseudocharacteristics, and is obtained over a half cycle data window of the differential current. This data is assessed using certain criteria to detect inrush and fault currents. This method is not reliant on the transformer models and is precise in its output. The propositioned method was tested using delta-wye transformers under both fault and inrush scenarios.

As an extensive network of resistances, capacitances, and inductances, a transformer has inherent characteristic parameters that are functions of frequency. The form of these functions is predicated on the geometric design of the transformer and materials that comprise it. Any change in the structure of a transformer will be reflected in its frequency response characteristics. Of the possible changes that can take place in a transformer structure, an internal short circuit is one of the far-reaching incidents that has been recently reported for many wind-farm transformers. Detecting the location of an internal short circuit that has occurred in a transformer winding is therefore beneficial in the repair process and also in improving future designs. In an effort to identify trends with inter-turn fault locations and frequency responses, this research investigates the effect of the location of deliberately initiated internal faults on parameters such as transfer voltages and input impedances by means of sweep frequency response analysis (SFRA). The analysis of three different model transformers with different core and winding designs shows several trends in frequency response patterns, depending on the location of the internal short circuits. The paper discusses such trends as a potential use of SFRA in locating inter-turn winding failures that may result in noticeable short circuits.

In this study, the challenging problem of computing the frequency-dependent lumped parameter ladder network model for transformer winding based on impedance frequency response is investigated. It is shown that the existing conventional model is not capable of simulating the non-dominant resonances; rather, this phenomenon can be adequately modelled using extra intersection capacitors. As usual, this large-scale non-linear optimisation problem is addressed using properly lined-up genetic algorithm. To accelerate the success of the estimation, the dimension of the problem and the search space is reduced by using logical and real constraints and equations derived from the transformer geometry and its electromagnetic specifications; if this is not done, the optimisation fails. The test results on a 20/0.4 kV, 1600 kVA transformer indicates that the computed model, which is improved and detailed, is superior to the conventional one in terms of simulating the non-dominant resonances of the transformer winding. Therefore, it is more reliable for the transformer transient behaviour analysis.

Within a solid-state transformer, the isolated dc-dc converter and in particular its medium-frequency transformer are one of the critical components, as it provides the required isolation between primary and secondary sides and the voltage conversion typically necessary for the operation of the system. A comprehensive optimization procedure is required to find a transformer design that maximizes power density and efficiency within the available degrees of freedom while complying with material limits, such as temperature, flux density, and dielectric strength as well as outer dimension limits. This paper presents an optimization routine and its underlying loss and thermal models, which are used to design a 166 kW/20 kHz transformer prototype achieving 99.4% efficiency at a power density of 44 kW/dm 3 . Extensive measurements are performed on the constructed prototype in order to measure core and winding losses and to investigate the current distribution within the litz wire and the flux sharing between the cores.

This paper presents a method for calculating the internal voltage transients useful for power transformer winding modelling. The method is based on lumped parameter model of a transformer winding and the transient response is obtained using time-domain analysis. Lumped circuit parameters are calculated using self-developed solvers which are benchmarked using professional finite element method (FEM) software. The results show that the presented approach gives satisfactory results and is computationally very fast.

The vibration of a transformer tank is related to the transformer’s noise radiation and health condition. Therefore, it is important to understand the transmission of vibration from internal vibration sources in the windings and core to the transformer tank. The characteristics of this transmission are determined by direct mechanical coupling between the internal structures and the tank, and by indirect coupling through fluid–structure interaction induced by the transformer’s cooling oil. In this paper, the transmission of vibration is examined experimentally in a 110-kV power transformer with and without cooling oil. Under respective mechanical and electrical excitations, vibrations of the internal structures and transformer tank are measured simultaneously. The results allow an evaluation of the transmission efficiency of vibration from the internal structures to the tank, and the effects of fluid–structure coupling on the transmission. This experimental work improves understanding of vibration transmission in oil-filled power transformers, and explains the characteristics of a transformer’s on-line vibration.

In this paper, a novel analytical method is developed to locate and assess the severity of a true radial displacement (confined to 1 or 2 disk pairs) in an actual continuous-disk transformer winding. An analytical solution becomes possible mainly due to a simple manipulation of the system matrix, that is, to consider sum of the inverse squares of natural frequencies, instead of just the natural frequencies. This leads to an elegant expression that connects displacement location and its severity to changes in natural frequencies. For its implementation, short-circuit natural frequencies and variation of inductance as a function of winding length are the required inputs. Details of the derivation and experimental results are reported. In summary, it emerges that incipient and true radial displacements in an actual continuous-disk transformer winding can be localized with reasonable accuracy and a qualitative assessment of its severity is also possible.

In this paper, the vibration of power transformer windings is studied with the aim of identifying the winding structural condition. A winding vibration model coupled with electromagnetic force analysis is proposed to obtain the steady-state vibration distribution along the axial direction. During the experiment, the model was validated on a full size, 50 MVA, three phase power transformer. Good agreement was found between the measured vibrations and the vibrations that were calculated from the model developed in this study for a healthy winding. The effect of the winding clamping force on vibration is studied to assess the winding clamping state, and different types of winding deformations were simulated to extract diagnostic information. The preliminary study shows that it is feasible to predict the mechanical faults of transformer windings with the vibration method.

New low cost and accurate estimation method of transformer stray capacitances for wide band DC–DC converter modelling and design is proposed. The Wiener filter (WF) method is applied to estimate the transformer impedance – referred to the selected transformer winding configurations. Laboratory tests are used to adapt the filter, that is to find optimal impedance which minimises mean square error between measured, noise perturbed current and reconstructed current. Transformer transfer function peaks indicate internal LC resonances. Stray capacitances are extracted based on resonant frequencies determination. The method validation is carried out by simulation and experimental analysis, where estimated stray capacitances by WF are compared with measurements of an impedance analyser.

Regarding the importance of short circuit and inrush current simulations in the split-winding transformer, a novel nonlinear equivalent circuit is introduced in this paper for nonlinear simulation of this transformer. The equivalent circuit is extended using the nonlinear inductances. Employing a numerical method, leakage and magnetizing inductances in the split-winding transformer are extracted and the nonlinear model inductances are estimated using these inductances. The introduced model is validated and using this nonlinear model, inrush and short-circuit currents are calculated. It has been seen that the introduced model is valid and suitable for simulations of the split-winding transformer due to various loading conditions. Finally, the effects of nonlinearity of the model inductances are discussed in the following.

Experimental investigation of transient characteristics is an important way to design transformer winding insulation structures. Of the previous measuring methods, there has been the problem of direct electrical connection with the winding, which may influence the transient characteristics. This paper presents a new non-invasive method for measuring the transient voltage distribution in transformer windings based on our previous study. The measuring method is based on the capacitive sensor with the stray capacitance between sensing electrode and transformer discs as the high-voltage arm and the film capacitance as low-voltage arm. An RC integrator and impedance adapter have been designed into the measurement circuit to enhance the sensor worked in the integrating mode and broaden its bandwidth respectively. The final measurement circuit can satisfy the need for measuring various kinds of waveforms, with 0.64 Hz lower cut-off frequency and 76 MHz higher cut-off frequency, respectively. The sensor array has been set up to measure the transient voltage distribution in a transformer winding. In this case, a mathematical conversion is put forward to decouple the influence of the adjacent discs on the corresponding disc to get the voltage distribution of different discs of the transformer winding.

The transformer used in an inverter type arc welding machine is designed to use high frequency in order to reduce its size and cost. Also, selecting core materials that fit frequency is important because core loss increases in a high frequency band. An inrush current can occur in the primary coil of transformer during arc welding and this inrush current can cause IGBT, the switching element, to burn out. The transformer design was carried out in A P method and amorphous core was used to reduce the size of transformer. In addition, sheet coil was used for primary winding and secondary winding coil considering the skin effect. This paper designed the transformer core with an air gap to prevent IGBT burnout due to the inrush current during welding and proposed the optimum air gap length.

This paper presents the implementation of a thermal camera for the quantitative estimation of power losses in a high frequency planar transformer (100 kHz/ 5600 VA). The methodology is based on the observation of the transient temperature rise and determination of the power losses by means of curves representing the derivative of temperature as a function of power losses dissipated in the transformer. First, the thermal calibration characteristics had to be obtained from a simple experiment, where power losses are generated by DC current in the ferrite core and windings. Next, experimental investigations focused on the determination of the transformer power losses for a short circuit and no load, with a resistive load and with the rectifier as a load were carried out. Finally, to verify the obtained results, analytical calculations based on Dowell’s and modified Steinmetz’s equations were additionally made, which showed a good convergence. The proposed method is easy to implement and can be used as an alternative to the calorimetric method which is time-consuming and requires a complicated measurement setup.

This paper presents a study of a bendable transformer for wearable electronics. Printed on a thin and bendable film, this transformer is bendable to wrap around body limbs such as the forearm. A model using a partial equivalent circuit theory has been developed to analyze the characteristic of an inductor and a bendable transformer. The mutual inductance and self-inductance for the bendable transformer over a range of bent curvatures have been calculated based on the model and compared favorably with measurements. Simulation and experimental results of applying the bendable inductor and transformer in dc–dc converters as a 5-V 500-mA power supply are included to confirm the usefulness of the transformer and the validity of the model.

—Transformer parasitics such as leakage inductance and self-capacitance are rarely calculated in advance during the design phase, because of the complexity and huge analytical error margins caused by practical winding implementation issues. Thus, choosing one transformer architecture over another for a given design is usually based on experience, or a trial and error approach. This paper presents analytical expressions for calculating leakage inductance, self-capacitance and ac resistance in transformer winding architectures (TWAs), ranging from the common non-interleaved primary/secondary winding architecture, to an interleaved, sectionalized, and bank winded architecture. The calculated results are evaluated experimentally, and through finite element (FEM) simulations, for a RM8 transformer with a turns ratio of 10. The four TWAs such as, noninterleaved and non-sectioned, non-interleaved and sectioned, interleaved and non-sectioned, and interleaved and sectioned, for an EF25 transformer with a turns ratio of 20, are investigated and practically implemented. The best TWA for a RM8 transformer in a high-voltage (HV) bidirectional flyback converter, used to drive an electro active polymer based incremental actuator, is identified based on the losses caused by the transformer parasitics. For an EF25 transformer, the best TWA is chosen according to whether electromagnetic interference (EMI) due to the transformer interwinding capacitance, is a major problem or not.

In this paper, a complex vector model is provided for an integrated three-phase shell-type rotating transformer. The equivalent magnetic circuit is used to obtain the transformer parameters. Furthermore, using vector representation of the dq transformation, the voltage equations of the rotating transformer in double-reference synchronous frame are obtained. Thanks to the developed model, the transformer design parameters are selected such that the voltage equations in double-reference frames are decoupled. For the first time, the machine complex vector representation is exploited to design a symmetrical rotating three-phase transformer. For this purpose, two separated equivalent circuits in double-reference frames or two decoupled sequences networks are developed. The decoupled circuits simplify the analysis of the rotating transformer in the unbalanced conditions as well as balanced circuits. Being symmetrical is an important issue for the rotating transformer connected to the rotor winding of a doubly-fed induction generator. Moreover, the steady-state performance and sequence analysis of the rotating transformer are discussed. Finally, the validity of the obtained model and accuracy of the presented analysis are verified by finite element analysis and experimental tests.

Certain level of mechanical deformations in winding does not hamper the normal performance of power transformer. However, such incipient deformations if unattended could result in permanent failure of transformer. To this end, an approach is proposed to assess the severity of mechanical deformations in transformer winding. These deformations get reflected as changes in its high frequency behaviour. Hence, characterising the high frequency behaviour is essential. This requires building physically realisable ladder circuit corresponding to each winding. Thus, n-winding transformer is represented by n electrically and magnetically coupled ladder networks. In such scenario, the objective of fault diagnostics becomes very challenging. In this effort, realising the multi-winding unit by reduced-order ladder circuit model is explored. This approach essentially involves energising one winding at a time. Then, reduced-order ladder circuit of considered unit is synthesised from its measured driving-point impedance data. It is shown how these circuit models could be used for identifying mechanical deformations. To demonstrate capability of the method, two-winding model transformer is considered and deformations are introduced in its outer winding. Then, reduced-order circuit models are synthesised corresponding to healthy and faulty state of model transformer. The location of fault is identified by the changed parameter in the circuit. Further, the amount of change reveals the severity of introduced deformation. In all the cases, synthesised reduced-order circuit model agrees with that of model transformer with regard to driving-point impedance plot and results are found satisfactory., by Krupa Rajendra Shah and K Ragavan

The low- and mid-frequency model of the transformer with resistive load is analysed for different values of coupling coefficients. The model comprising of coupling-dependent inductances is used to derive the following characteristics: voltage gain, current gain, bandwidth, input impedance, and transformer efficiency. It is shown that in the low- and mid-frequency range, the turns ratio between the windings is a strong function of the coupling coefficient, i.e., if the coupling coefficient decreases, then the effective turns ratio reduces. A practical transformer was designed, simulated, and tested. It was observed that the magnitudes of the voltage transfer function and current transfer function exhibit a maximum value each at a different value of coupling coefficient. In addition, as the coupling coefficient decreases, the transformer bandwidth also decreases. Furthermore, analytical expressions for the transformer efficiency for resistive loads are derived and its variation with respect to frequency at different coupling coefficients is investigated. It is shown that the transformer efficiency is maximum at any coupling coefficient if the input resistance is equal to the load resistance. Experimental validation of the theoretical results was performed using a practical transformer set-up. The theoretical predictions were found to be in good agreement with the experimental results.

An equivalent circuit model for planar printed circuit board (PCB) transformers is presented. The model utilizes the 1-D analysis of Maxwell’s equations to develop a frequency-dependent representation of a multilayer, planar PCB transformer that can be implemented in the circuit simulation software. In this transformer model, each conductor layer is implemented as a complex impedance network, while each insulator layer is implemented as an air-cored inductor. Each magnetic core layer is modeled as a non-linear inductance whose magnetic characteristic is based on a temperature-dependent Jiles–Atherton hysteresis model. These impedances and inductances are then arranged side by side as they are arranged in the layer stack of the actual planar PCB transformer. Through this model, the skin and proximity effect in the conductors and current distribution across windings can be simulated. The developed model also enables the modeling of temperature-dependent hysteresis and saturation effects in the magnetic material. The model provides a simpler method to derive the core and winding loss of the transformer than using a finite-element analysis software. It also enables direct integration to circuit simulation tools. A prototype planar PCB transformer was used to obtain experimental data for model validation. Comparisons made show good agreement between the performance of the model and experimental results.

When the high voltage direct current (HVDC) system operates in monopole ground-return mode, DC current flows through the neutral of AC power transformer with the neutral grounded which exacerbates the vibration of the transformer. During the field test of Yibin-Jinhua HVDC system in China, the vibration detection system is deployed to detect the vibration signal of the 500 kV transformer in Luzhou substation, which is close to the grounding substation. The spectrum of the transformer vibration signal is analyzed by means of the wavelet transform, through which the vibration acoustic fingerprint and three typical characteristic parameters, i.e., the distribution percentage of spectral energy, the energy ratio of odd and even harmonics, and the waveform distortion ratio, are extracted respectively. When the HVDC system current increases from 0 A to 5 kA, the impact of DC bias on the operation condition of the 500 kV transformer is investigated through the analysis of the variation of vibration acoustic fingerprint and three characteristic parameters. It is indicated that the energy radio of odd and even harmonics of the 500 kV transformer vibration signal decreases significantly with the increase of the current. In addition, the distribution percentage of spectral energy and the vibration acoustic fingerprint change significantly. This paper demonstrates that the effect of DC bias on the operating condition of the transformer can be accurately assessed by the proposed indices.

A novel variable reactor based on transformer is proposed in the paper. In the variable reactor, a transformer with air gap is chosen, and the primary voltage is detected and used as the reference signal. A voltage-sourced inverter is applied to track the reference signal in order to yield a controllable voltage, which is applied across the secondary winding of the transformer. When the secondary-controlled voltage and the primary voltage satisfy a proportional condition, the equivalent impedance of primary winding of the transformer will vary continuously. According to the novel variable reactor, a novel shunt power quality controller is proposed and its principle is analyzed in detail. The shunt power quality controller is characterized by parallel topology and single frequency control. The approaches of decreasing the transformer leakage inductance are addressed. The experimental results verify the validity of the shunt power quality controller.

This paper deals with the problem of accounting for changes in the magnetic flux leakage of traction transformer windings under discrete cyclic load switching of traction winding sections during the simulation of continuous processes. It is proposed to take into account this change by introducing a fictitious mutual inductance and active components of the mutual impedance between the windings, which can be determined using the theory of a multiwinding transformer. A method for mathematical representation and computer simulation of the traction transformer with tapped secondary windings is considered based on the notation of the system of differential equations in the state space. Expressions for the calculation of the leakage inductance of the transformer windings and mutual inductances that take into account the change in the magnetic field of the winding leakage in the case of the discrete cyclic load switching of the tapped secondary windings. An algorithm for calculation of matrix elements of the equation of state is constructed. A simulation mathematical model of the traction transformer is developed in the Matlab/Simulink environment that takes into account the winding leakage field variation under discrete cyclic switching of the load of sections of traction windings. The adequacy of the proposed simulation mathematical model is proven by comparison of short-circuit currents obtained as a result of the simulation with currents of traction transformer short-circuit field tests.

Thanks to the awareness of safety, dry-type transformer has experienced a significant demand, lately. However, a limiting condition for an even more significant increase in its demand is that its maximum rated voltage is about 36 kV, in most of countries. Beyond this limit, dry-type transformer becomes definitely uneconomical in comparison to oil-filled transformer because of the expressive increase in dielectric clearance distances and consequent drawbacks. Thus, the aim of this work is to propose a way for overcoming this limit, based on shielding the electric field of the high-voltage windings of the dry transformer with a grounded metallic mesh. The effectiveness of the proposition is shown whereas most of the undesirable of its consequences are also evaluated. Namely, losses and temperature rise concerns as well as items of standard dielectric tests, which are analysed through computer modelling and simulation. Due to its outstanding importance, analysis of distribution of lightning impulse voltage along the high-voltage winding is also experimentally performed. The result is a set of key hints given by the authors and to be observed by transformer designers for making real the production of dry-type transformer with a rated voltage higher than 36 kV.

This paper presents an approach based on the use of transformer no-load and light load current harmonic analysis to detect the presence of an interturn fault at the incipient stage. The presence of fault is detected by performing a trend analysis of specific harmonic components and primary current magnitude. Transformer testing methods suffer from a common drawback of offline nature and require an expert opinion for accurate condition assessment. This paper presents a method that transforms no-load current harmonic analysis, which is a special test for transformer testing, into an online method at light load conditions. Thus, the necessity of complete shutdown and dependency on expert opinion is eliminated since it only requires one reference signature per phase. The proposed approach is verified for different vector groups of the three-phase core-type transformer and three independent units connected in star-star and for a fault on the low-voltage or high-voltage winding of the transformer. The presented experimentation shows that the proposed approach can detect the presence of a fault at an incipient stage involving less than 2% of turns and fault current up to 1 p.u. A case study is presented that validates the method for the transformer of a higher power rating.

Partial discharge (PD) condition monitoring inside a HV transformer generally and particularly along a transformer winding has become an important research area with the ultimate aim of providing asset health information that enables maintenance and replacement processes to be carried out effectively. As far as PD activity inside transformer windings is concerned, an electrical detection method has been developed based on the use of radio frequency current transducers and subsequent digital signal processing of captured measurement data. A localization approach based on the measurement of currents at the bushing tap point and neutral to earth connection has been developed, with the assumption that different PD source locations will generate unique signal profiles in terms of the distribution of measured current energies with respect to both frequency and time. Therefore the technique presented is based on analysis of measured current energies associated with different frequencies. Principal Component Analysis (PCA) is then applied to reduce the dimensionality of the data, whilst minimizing lost information in the original dataset. This non-linear analysis of captured current data is not practicable for the field but the process can be represented through the use of three finite impulse response filters that have the ability to perform PD source localization automatically and are straightforward to implement in monitoring hardware.