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The operating environment of transformers is getting more complex with the emergence of new energy sources and power electronic devices. This complexity can cause minor internal faults in transformer windings. Under the cumulative effect, minor faults gradually develop into serious faults, resulting in transformer damage. Conventional differential protection systems may have difficulty detecting these glitches and require avoiding the problem of protection false activation caused by inrush currents. This paper proposes a new online monitoring method for transformer windings based on longitudinal branch‐circuit conductance to address this issue. First, a unified transformer equivalent circuit is proposed to represent transformers under normal conditions, inrush currents, and internal faults. Then, an online transformer monitoring method based on branch conductance is proposed, which is immune to inrush currents. This method aims to prevent delayed detection of faults during inrush currents, improving sensitivity and response speed, especially for minor turn‐to‐turn faults hidden in inrush currents. The proposed method also provides higher sensitivity to minor turn‐to‐turn faults and larger protection margins. Simulation and experimental results validate the effectiveness of this method. [ABSTRACT FROM AUTHOR]

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Copyright of Przegląd Elektrotechniczny is the property of Przeglad Elektrotechniczny and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract Due to the strong coupling effect between the internal magnetic field and the structural field of the transformer, the magnetic‐structural coupling should be considered in axial vibration process of the winding short‐circuit impact. A 110 kV transformer is taken as the research object. Firstly, the vibration modal characteristics of the transformer are calculated using the classical axial vibration model, and the spatial distribution of the leakage magnetic flux density of the iron core window is obtained based on the image method, which is used as the basis for calculating the excitation electromagnetic force. With the consideration of the non‐linear mechanical characteristic of the pad, the dynamic stiffness equation is analysed and established and the magnetic‐structural coupling correction model is constructed. Finally, the winding vibration amplitudes obtained respectively by the classical model, the magnetic‐structural coupling model, and the magnetic‐structural coupling correction model considering the dynamic stiffness are compared. The results show that, compared with the classical model, the vibration amplitude increment with the magnetic‐structural coupling correction model is less. The dynamic stiffness will hinder the vibration intensification. The magnetic‐structural coupling correction model can provide a more accurate calculation scheme for the winding vibration characteristic analysis.

Abstract Mechanical stability is one of the core capabilities of power transformers. External short‐circuit accidents are the main cause of winding instability. International Electrotechnical Commission 60076‐5 standard recommends a method to calculate the short‐circuit strength of power transformer windings by comparing the stress within windings under the effect of the maximum electromagnetic force with the critical stress of the winding. This method assumes that the maximum deformation will be produced by the maximum electromagnetic force, which corresponds to the first peak of the waveform. However, owing to the interactions between disks during the vibration process, the maximum deformation may occur after the occurrence of the maximum electromagnetic force. The hysteresis phenomenon between disk deformation and electromagnetic force is studied. The definition of the hysteresis phenomenon during the vibration process is first demonstrated, and the mechanism of the hysteresis phenomenon is investigated. The vibration model is established. By decoupling analysis, the conditions for the formation of hysteresis are proposed, and the mechanism of the hysteresis phenomenon is validated by the experiment, which is conducted on a winding sample. In the deformation formula, the term that determines the time‐varying characteristic is found. The waveform‐determining term is the difference between the two cosine components, whose frequencies are the natural vibration frequency and the electromagnetic force frequency. When the two frequencies are close, the maximum deformation lags behind the maximum force, and the hysteresis phenomenon occurs.

Abstract A slight turn‐to‐turn short‐circuit fault in the incipient stage does not trigger fuse protection, and the regular transmission and transformation functions of the transformer within the power grid are not affected very much by the incipient turn‐to‐turn short‐circuit fault. Therefore, the incipient turn‐to‐turn short‐circuit faults are often undetected, resulting in massive accidents. Incipient turn‐to‐turn short‐circuit faults lead to localized overheating in the transformer, which changes the transformer's oil‐tank surface temperature (OTST). A thermal simulation model (TSM) is presented. Based on the TSM, OTST data with different load rates and fault parameters are collected. The steady‐state and transient characteristics of OTST are analysed by extracting the OTST feature vector and the temperature difference of specific regions. The results show that the growth of the heat production value of faulty coils causes a rise in the OTST; higher faulty coils' locations lead to wider OTST differences; the temperature difference's area S can follow the incipient short‐circuit fault in the first 20 min after it occurs, which is faster than the top oil temperature. This study gives insight into the thermal behaviour of OTST, assisting in fault detection and location at the incipient fault stage.

Due to the strong coupling effect between the internal magnetic field and the structural field of the transformer, the magnetic‐structural coupling should be considered in axial vibration process of the winding short‐circuit impact. A 110 kV transformer is taken as the research object. Firstly, the vibration modal characteristics of the transformer are calculated using the classical axial vibration model, and the spatial distribution of the leakage magnetic flux density of the iron core window is obtained based on the image method, which is used as the basis for calculating the excitation electromagnetic force. With the consideration of the non‐linear mechanical characteristic of the pad, the dynamic stiffness equation is analysed and established and the magnetic‐structural coupling correction model is constructed. Finally, the winding vibration amplitudes obtained respectively by the classical model, the magnetic‐structural coupling model, and the magnetic‐structural coupling correction model considering the dynamic stiffness are compared. The results show that, compared with the classical model, the vibration amplitude increment with the magnetic‐structural coupling correction model is less. The dynamic stiffness will hinder the vibration intensification. The magnetic‐structural coupling correction model can provide a more accurate calculation scheme for the winding vibration characteristic analysis. [ABSTRACT FROM AUTHOR]

Mechanical stability is one of the core capabilities of power transformers. External short‐circuit accidents are the main cause of winding instability. International Electrotechnical Commission 60076‐5 standard recommends a method to calculate the short‐circuit strength of power transformer windings by comparing the stress within windings under the effect of the maximum electromagnetic force with the critical stress of the winding. This method assumes that the maximum deformation will be produced by the maximum electromagnetic force, which corresponds to the first peak of the waveform. However, owing to the interactions between disks during the vibration process, the maximum deformation may occur after the occurrence of the maximum electromagnetic force. The hysteresis phenomenon between disk deformation and electromagnetic force is studied. The definition of the hysteresis phenomenon during the vibration process is first demonstrated, and the mechanism of the hysteresis phenomenon is investigated. The vibration model is established. By decoupling analysis, the conditions for the formation of hysteresis are proposed, and the mechanism of the hysteresis phenomenon is validated by the experiment, which is conducted on a winding sample. In the deformation formula, the term that determines the time‐varying characteristic is found. The waveform‐determining term is the difference between the two cosine components, whose frequencies are the natural vibration frequency and the electromagnetic force frequency. When the two frequencies are close, the maximum deformation lags behind the maximum force, and the hysteresis phenomenon occurs. [ABSTRACT FROM AUTHOR]

A slight turn‐to‐turn short‐circuit fault in the incipient stage does not trigger fuse protection, and the regular transmission and transformation functions of the transformer within the power grid are not affected very much by the incipient turn‐to‐turn short‐circuit fault. Therefore, the incipient turn‐to‐turn short‐circuit faults are often undetected, resulting in massive accidents. Incipient turn‐to‐turn short‐circuit faults lead to localized overheating in the transformer, which changes the transformer's oil‐tank surface temperature (OTST). A thermal simulation model (TSM) is presented. Based on the TSM, OTST data with different load rates and fault parameters are collected. The steady‐state and transient characteristics of OTST are analysed by extracting the OTST feature vector and the temperature difference of specific regions. The results show that the growth of the heat production value of faulty coils causes a rise in the OTST; higher faulty coils' locations lead to wider OTST differences; the temperature difference's area S can follow the incipient short‐circuit fault in the first 20 min after it occurs, which is faster than the top oil temperature. This study gives insight into the thermal behaviour of OTST, assisting in fault detection and location at the incipient fault stage. [ABSTRACT FROM AUTHOR]

Abstract Precisely interpreting frequency response analysis (FRA) curves is crucial when investigating mechanical malfunctions in power transformer windings (TWs). However, many conventional explanations of FRA features cannot be validated by an equivalent circuit (EC) that represents winding structures using resistance, inductance, and capacitance components in a ladder network. Incorrect interpretation can lead to misdiagnosis and confusion in asset management. Previous ECs are often proposed by analysing winding structures without rigorous verification compared to the corresponding FRA data. The specific EC is acquired using the transfer function (TF) derived from the measured FRA data. This allows for the establishment of the relationship between TW FRA curves, TF equations, and EC topologies. The precise interpretation of FRA curves can be achieved by closely observing the FRA curves created from TFs and ECs. The remarkable similarity between the measured and modelled FRA curves verifies the authenticity of the derived ECs. This significant achievement clarifies many misunderstandings regarding FRA and represents a substantial advancement in FRA technology.

The aim of the article is to present the method of modeling the frequency response of the transformer windings with axial displacements. Frequency response analysis (often referred to as FRA or SFRA) is a powerful and sensitive method for testing the mechanical integrity of transformer cores, windings, and press frames in power transformers. The proper interpretation of FRA results is crucial in assessing winding faults. Computer modeling of transformer active part deformations is one way to expand knowledge about the impact of mechanical faults on the shape of the frequency response (FR) curve. The data collected from these models can be used as training data sets for artificial intelligence tools. An automatic tool developed from this approach would significantly improve the accuracy of the FRA method and simplify the interpretation and evaluation of results. The described study utilizes new types of lumped parameter models with input data obtained from the FEM analysis. The research conducted shows the influence of the winding axial deformation on the frequency response curve and provides information on the sensitivity of the FR curve's shape to this type of deformation. A series of tests, which involved measuring and simulating typical axial damages, were conducted to evaluate the effectiveness of the presented algorithms. [ABSTRACT FROM AUTHOR]

Precisely interpreting frequency response analysis (FRA) curves is crucial when investigating mechanical malfunctions in power transformer windings (TWs). However, many conventional explanations of FRA features cannot be validated by an equivalent circuit (EC) that represents winding structures using resistance, inductance, and capacitance components in a ladder network. Incorrect interpretation can lead to misdiagnosis and confusion in asset management. Previous ECs are often proposed by analysing winding structures without rigorous verification compared to the corresponding FRA data. The specific EC is acquired using the transfer function (TF) derived from the measured FRA data. This allows for the establishment of the relationship between TW FRA curves, TF equations, and EC topologies. The precise interpretation of FRA curves can be achieved by closely observing the FRA curves created from TFs and ECs. The remarkable similarity between the measured and modelled FRA curves verifies the authenticity of the derived ECs. This significant achievement clarifies many misunderstandings regarding FRA and represents a substantial advancement in FRA technology. [ABSTRACT FROM AUTHOR]

Abstract The lumped element network model has been proven to be an efficient tool for the interpretation of transformer Frequency Response Analysis. However, it is challenging to obtain parameters of the model if transformer design information is unavailable. In such a case, optimisation algorithms can be used for gray‐box model parameter estimation. A methodology is developed by the authors to establish a transformer network model without winding design data, and instead, end‐to‐end open circuit Frequency Response and other terminal test results are utilised; and Genetic Algorithm is applied to approximate the unknown parameters of the model. The modelling approach developed is independent of the unit number of the network model and therefore guarantees the accuracy of optimisation. Furthermore, it can deal with transformers with a complicated winding structure such as interleaved disc type winding. Two single windings, helical and interleaved disc type, and a single‐phase 144/13 kV 60 MVA transformer are used to demonstrate the method. FRA spectra produced by the best estimated gray‐box model and the corresponding white‐box model are compared. The main features in amplitude and phase spectra are well matched, with low values of Relative Standard Deviation, for both single windings and transformer. Estimated electrical parameters show a high consistency with reference values, which are calculated based on winding design data. This validates the methodology and gives confidence to apply grey‐box modelling for FRA interpretation.

The lumped element network model has been proven to be an efficient tool for the interpretation of transformer Frequency Response Analysis. However, it is challenging to obtain parameters of the model if transformer design information is unavailable. In such a case, optimisation algorithms can be used for gray‐box model parameter estimation. A methodology is developed by the authors to establish a transformer network model without winding design data, and instead, end‐to‐end open circuit Frequency Response and other terminal test results are utilised; and Genetic Algorithm is applied to approximate the unknown parameters of the model. The modelling approach developed is independent of the unit number of the network model and therefore guarantees the accuracy of optimisation. Furthermore, it can deal with transformers with a complicated winding structure such as interleaved disc type winding. Two single windings, helical and interleaved disc type, and a single‐phase 144/13 kV 60 MVA transformer are used to demonstrate the method. FRA spectra produced by the best estimated gray‐box model and the corresponding white‐box model are compared. The main features in amplitude and phase spectra are well matched, with low values of Relative Standard Deviation, for both single windings and transformer. Estimated electrical parameters show a high consistency with reference values, which are calculated based on winding design data. This validates the methodology and gives confidence to apply grey‐box modelling for FRA interpretation. [ABSTRACT FROM AUTHOR]

Abstract Temperature distribution in transformer windings is a crucial factor that influences the safe operation, and lifespan of an insulating system in an oil‐immersed power transformer. Thermal hydraulic network modelling (THNM) has been the subject of numerous studies because of its lower computation cost as compared to a computational fluid dynamics (CFD) simulation. This study proposes improvements to THNM, with primary focus on non‐uniformity of temperatures in the entry and exit vertical oil ducts, and the feasibility of using a piecewise fitting formula for Nusselt number (Nu) of convection heat transfer coefficient in transformer windings. The deviation of hot spot temperature was 0.3°C, and the location of hot spot for CFD and THNM was 34th disc and 35th disc, respectively. The calculation time of CFD and THNM was about 34 h and 35 s under the same computer hardware situations. This provides an acceptable THNM method for the rapid prediction of transformer hot spot temperature and location at low costs for digital twin.

This paper introduces an innovative methodology for precisely estimating winding capacitances ( $C_{s}$ and $C_{g}$ ) and the voltage distribution factor ( $\alpha $ ) in transformers using measured Driving Point Impedance (DPI) data. These parameters are critical for designing robust insulation systems and ensuring reliability during transient events. Unlike traditional approaches that rely on complex analytical models, impulse tests, or Finite Element Method (FEM) simulations, this method streamlines the estimation process by directly utilizing DPI measurements. Experimental validations across various winding configurations, including continuous and interleaved disc winding transformers, confirm the accuracy and versatility of this approach. The methodology presented offers substantial practical benefits for transformer condition monitoring. It facilitates efficient diagnostics of transformer deformations and impulse voltage distribution by estimating critical parameters from terminal measurements. The effect of noise on DPI data and the effectiveness of filtering techniques in enhancing parameter estimation accuracy have been rigorously analysed, demonstrating the method’s reliability. This approach is especially useful for newly constructed transformers that need design validation or for older transformers with incomplete design records. It provides a practical, efficient, and straightforward diagnostic solution, proving valuable for both researchers and engineers.

Abstract Accurately calculating axial electromagnetic force is essential to analyse transformer winding axial stability. Prior research has mainly focused on the effect of winding structure on static axial electromagnetic force and studying vibration by substituting the static force in a time‐varying function. However, the coupling effect between axial electromagnetic force and winding vibration has not been addressed, and no calculation method for the axial electromagnetic force that considers both winding meso‐structures and vibration coupling effects has been proposed. Previously the authors presented an electromagnetic force calculation model that considers winding structure characteristics, and an iterative algorithm for magnetic‐structure coupling calculation. Currently, the winding vibration model was first proposed and the dynamic calculation method was formulated. By applying the method to a typical 110kV transformer, the spatial‐temporal distribution of winding axial short‐circuit electromagnetic force was obtained. It was found that the peak value of the axial short‐circuit electromagnetic force of some windings appears at the second or third peak moment of the short‐circuit current, which is called as peak time shift phenomenon. Further stress analysis indicates that existing evaluation methods may overestimate the short‐circuit resistance of windings by only considering short‐circuit electromagnetic force under maximum peak of short‐circuit current.

Computer simulations are currently one of the most used methods on transformer’s short circuit analysis. For them to be effective, an accurate characterization of the transformer core and geometric representation of windings is essential. Hence, this work investigated the influence of core characterization and different geometric representations on magnetic flux density (MFD) and electromagnetic forces (EF) calculated during short circuits. A comparative study using simulations based on the finite-element method (FEM) were carried out for a 180 MVA transformer model. First, the influence of the nonlinear characteristic of the core B-H curve on EF was analyzed. Then, three two-dimensional (2D) axisymmetric and one three-dimensional (3D) representations were compared. Results indicate there is no significant difference in EF with a core represented by a constant value of permeability. Also, 2D-axisymmetric geometric representations underestimate radial forces and diverge significantly on axial forces in comparison with the 3D representation. Differences up to 99% between the calculated total axial forces were obtained for the analyzed cases. In addition, representations with greater level of detail result in magnetic force density up to 5.5 times greater than that obtained with the simplified representation.

Temperature distribution in transformer windings is a crucial factor that influences the safe operation, and lifespan of an insulating system in an oil‐immersed power transformer. Thermal hydraulic network modelling (THNM) has been the subject of numerous studies because of its lower computation cost as compared to a computational fluid dynamics (CFD) simulation. This study proposes improvements to THNM, with primary focus on non‐uniformity of temperatures in the entry and exit vertical oil ducts, and the feasibility of using a piecewise fitting formula for Nusselt number (Nu) of convection heat transfer coefficient in transformer windings. The deviation of hot spot temperature was 0.3°C, and the location of hot spot for CFD and THNM was 34th disc and 35th disc, respectively. The calculation time of CFD and THNM was about 34 h and 35 s under the same computer hardware situations. This provides an acceptable THNM method for the rapid prediction of transformer hot spot temperature and location at low costs for digital twin. [ABSTRACT FROM AUTHOR]

Accurately calculating axial electromagnetic force is essential to analyse transformer winding axial stability. Prior research has mainly focused on the effect of winding structure on static axial electromagnetic force and studying vibration by substituting the static force in a time‐varying function. However, the coupling effect between axial electromagnetic force and winding vibration has not been addressed, and no calculation method for the axial electromagnetic force that considers both winding meso‐structures and vibration coupling effects has been proposed. Previously the authors presented an electromagnetic force calculation model that considers winding structure characteristics, and an iterative algorithm for magnetic‐structure coupling calculation. Currently, the winding vibration model was first proposed and the dynamic calculation method was formulated. By applying the method to a typical 110kV transformer, the spatial‐temporal distribution of winding axial short‐circuit electromagnetic force was obtained. It was found that the peak value of the axial short‐circuit electromagnetic force of some windings appears at the second or third peak moment of the short‐circuit current, which is called as peak time shift phenomenon. Further stress analysis indicates that existing evaluation methods may overestimate the short‐circuit resistance of windings by only considering short‐circuit electromagnetic force under maximum peak of short‐circuit current. [ABSTRACT FROM AUTHOR]

Abstract This study presents a design study and modelling of three‐to‐five phase transformer with three‐limb magnetic core. The basics of phase transformation windings are discussed. The purpose of such winding is to produce at the secondary a balanced multiphase voltage system, from multiphase primary of different number of phases, without unbalance in the primary and secondary under load conditions. In order to overcome the imbalance due to the dispositions of the winding coils on the magnetic core, simulations using aided computer design are performed. Furthermore, this study presents a model of a three‐to‐five phase three‐limbed transformer, which is suitable for modelling the behaviour of this transformer at no‐load, under load, and under unbalance load conditions. This study is conducted by simulation and experimental tests.

Abstract The extra‐high voltage (EHV) transformer winding disks are subjected to dynamic electromagnetic forces caused by short‐circuit currents. These periodically decaying impact forces may endanger the safety of the transformer. The winding constraint conditions around the circumference are different due to the influence of axial pressure structures and magnetic boundaries. Moreover, this difference becomes more evident as the voltage and capacity increase. To investigate the spatial differences and time effects of EHV transformer short‐circuit faults, this paper proposes a reliability evaluation method based on dynamic relative displacement (DRDEM) for the first time. Firstly, the suitable and efficient analysis method is summarized by comparing the deviation among different calculated impedances and the measured value. Then, the space‐time effect of windings is obtained by the static magnetic field and dynamic structural field based on equivalent compression supports. Furthermore, a 50 MVA/110 kV transformer is designed for the destructive short‐circuit test to simulate the short‐circuit ability feature of the EHV transformer. The disassembly phenomena after all the tests indicate that the DRDEM is more adaptable in characterizing the winding ability to withstand short circuit when investigating the spatial differences and time effects.

This study presents a design study and modelling of three‐to‐five phase transformer with three‐limb magnetic core. The basics of phase transformation windings are discussed. The purpose of such winding is to produce at the secondary a balanced multiphase voltage system, from multiphase primary of different number of phases, without unbalance in the primary and secondary under load conditions. In order to overcome the imbalance due to the dispositions of the winding coils on the magnetic core, simulations using aided computer design are performed. Furthermore, this study presents a model of a three‐to‐five phase three‐limbed transformer, which is suitable for modelling the behaviour of this transformer at no‐load, under load, and under unbalance load conditions. This study is conducted by simulation and experimental tests. [ABSTRACT FROM AUTHOR]

In this paper, a modification of a conventional forward converter and a new mixed-stranded transformer winding technique are proposed for the development of a simple and high efficiency isolated dc-dc boost converter for solar photovoltaic applications. The conventional single switch forward converter topology is modified for simplification and elimination of losses due to the output filter components. A new mixed-stranded transformer winding technique is proposed to minimize the leakage inductance between the primary and tertiary windings for reducing losses. A pulse frequency modulation technique (PFM) is employed for reducing switching losses at low power operation. An experimental prototype of 300 W with a voltage step-up ratio of 1:12 has been built to obtain dc output voltage between 360-480 V for the dc input voltage of 30-40 V. Through the experimental results, it is shown that the converter can boost the input voltage according to the step-up ratio and exhibits a remarkably high dc-dc power conversion efficiency with a flat response curve. The average efficiency of around 95.5 % and peak efficiency of 97.6% are obtained. [ABSTRACT FROM AUTHOR]

The extra‐high voltage (EHV) transformer winding disks are subjected to dynamic electromagnetic forces caused by short‐circuit currents. These periodically decaying impact forces may endanger the safety of the transformer. The winding constraint conditions around the circumference are different due to the influence of axial pressure structures and magnetic boundaries. Moreover, this difference becomes more evident as the voltage and capacity increase. To investigate the spatial differences and time effects of EHV transformer short‐circuit faults, this paper proposes a reliability evaluation method based on dynamic relative displacement (DRDEM) for the first time. Firstly, the suitable and efficient analysis method is summarized by comparing the deviation among different calculated impedances and the measured value. Then, the space‐time effect of windings is obtained by the static magnetic field and dynamic structural field based on equivalent compression supports. Furthermore, a 50 MVA/110 kV transformer is designed for the destructive short‐circuit test to simulate the short‐circuit ability feature of the EHV transformer. The disassembly phenomena after all the tests indicate that the DRDEM is more adaptable in characterizing the winding ability to withstand short circuit when investigating the spatial differences and time effects. [ABSTRACT FROM AUTHOR]

Regarding the ever-increasing switching frequency of power converters, there is a lack of tools to perform a quick and effective optimization of the high-frequency transformers embedded in isolated power converters. Indeed, at high operating frequency, the geometry of the core and windings deeply impacts the overall transformer performance. Specifically, assessing accurately the current distribution in parallel-connected windings is a challenging and key issue. Winding parallelization, frequently implemented in low-voltage and high-current applications so as to decrease Joule losses, may be an ineffective solution because of skin and proximity effects. They create an unbalanced current distribution in the parallel-connected windings, which greatly impacts the ac resistance and leakage inductance of the transformer. This article proposes an innovative frequency analytical model permitting to simply and accurately compute the current distribution in the transformer windings, the ac resistance, and the leakage inductance. The proposed approach is comprehensively presented, validated using both measurements and two-dimensional finite element analysis and analyzed giving guidelines to engineers designing high-frequency transformers. [ABSTRACT FROM AUTHOR]

The number of auxiliary electric drives can exceed 100 for luxury cars. Due to their ever‐increasing prevalence, the electromagnetic emissions (EME) of these drives are becoming increasingly important. This work explores the influence of four different stator winding topologies on the electromagnetic emissions and the efficiency performance of fractional horsepower (FHP) brushless direct current (BLDC) drives. Two monofilar windings with a wire diameter of 0.15 and 0.27 mm, an untwisted bifilar winding, and a twisted bifilar winding are inspected. The parasitic stator to winding coupling capacitance is the motor's main source for common mode currents and thus, for radiated emissions. A three‐media capacitance model is introduced to allow estimating this coupling path in the design phase of the motor. Twisting the phases of a bifilar winding reduces the excitation of this path. Therefore, the radiated emissions are reduced by 5 dBμV/m ${\mathrm{B}}_{\mu \text{V/m}}$. The stator winding topology also affects the winding resistance and thus the efficiency. The monofilar winding with a wire diameter of 0.27 mm shows the lowest level of consumed power, followed by the monofilar winding with a wire diameter of 0.15 mm, the untwisted bifilar winding and the twisted bifilar winding. [ABSTRACT FROM AUTHOR]

We present new correlations for the pressure loss coefficients in two-dimensional Tee joints and 90 ∘ sharp elbows as a function of the geometric and hydrodynamic governing parameters. These are the Reynolds number of the flow (defined in the straight duct with common flow for the Tee joints), the width ratio of the perpendicular ducts and, only for the Tee joints, the mass split ratio. The analysis assumes low-to-moderate values of the Reynolds number, for which the flow remains laminar and steady. This regime is of relevance for the cooling oil flow in oil-immersed power transformer windings operated in the natural cooling mode. The new correlations have been obtained by performing a multiple regression analysis on the numerical results for combining and dividing Tee joints presented in a companion paper, and on new simulations of the flow in 90 ∘ sharp elbows following the same methodology used for the joints. As main new feature, the correlations for the pressure drop in the elements considered include an explicit dependence on the width ratio between the straight duct and the lateral branch, which is found to have a great influence on the static pressure losses and is not explicitly available from previous studies. When used for the thermal-hydraulic modeling of oil-immersed power transformer windings, the new correlations are expected to give better estimates than those currently available in the literature. • New correlations for the static pressure loss coefficients in planar T-joints and 90°elbows are obtained. • Combining and dividing flows in planar Tee joints are considered. • Correlations are obtained for moderate to low Reynolds numbers. • Explicit dependence on the width ratio is included unlike in previous studies. • Satisfactory application to thermal-hydraulic models of oil-immersed power transformer windings. [ABSTRACT FROM AUTHOR]

Frequency response analysis (FRA) suffers from the interpretation of results despite its potential ability to detect faults related to the power transformer windings. This article presents a technique for interpreting frequency responses, which is based on image processing and a deep learning method called graph convolutional neural network (CNN). The proposed procedure transfers frequency responses into 2-D images through a visualization technique. The resulting images are aggregated into a dataset to be used as the CNN input. The proposed technique is applied on frequency responses of two different winding models with short circuit (SC) faults. The SC faults with different intensities are applied on different sections of a simulated ladder model winding and a 20 kV winding of a 1.6 MVA distribution transformer. After determining the frequency response for each faulty case and applying the visualization technique, the precise locating of the SC faults is performed by the CNN. Then, the results are analyzed by performance evaluation metrics. At this stage, the high performance of the CNN in the use of 2-D images instead of the conventional method is observed. Finally, by testing the high impedance SC faults in different sections of the simulated winding model and applying the suggested method step by step, early detection of the SC fault is also performed in this article. It should be noted that the suggested technique, in addition to its accuracy and high detection speed, can be considered as an important step in automatic interpretation of frequency responses for online monitoring of transformers. [ABSTRACT FROM AUTHOR]

The design of the medium-frequency transformer (MFT) attracts increasing academic attention in recent years, in which the accuracy of the calculation method serves as the pivotal foundation. The existing 1-D based theoretical method generally fails to precisely estimate the foil winding losses under a significant 2-D edge effect. The 2-D semi-empirical methods are merely suitable for limited parameters and structures, and the pre-processing is cumbersome. The finite-element method (FEM) is accurate, yet its high computational cost makes it hard to apply in the MFT designing process. Regarding these issues, a novel 2-D semi-analytical method is proposed in this article with strict theoretical basis and sufficient generality. The foil region is divided into several rectangular elements with uniformly or linearly distributed current density, and one layer of images is placed around the magnetic core window. By deriving the basic electromagnetic relations between those rectangular elements, algebraic equations are formed with current density of the elements being the unknowns. Through the method, the whole problem turns into the process of solving algebraic equations, where all of the coefficients are obtained analytically. The new approach can achieve significantly high accuracy with acceptable computation cost, and it could suitably fit into the MFT designing process. [ABSTRACT FROM AUTHOR]

This paper presents a numerical investigation of the laminar flow and pressure drop characteristics of planar Tee joints, a canonical flow of interest for the thermal-hydraulic design of oil-immersed power transformer windings. After formulating the problem in nondimensional form, the steady, constant property flow in planar 90 ∘ Tee joints is computed numerically by integrating the Navier–Stokes equations with fully developed upstream and downstream boundary conditions. The analysis assumes a straight-through configuration in which the straight duct holds flow in the same direction before and after the junction, whereas the flow in the side branch can either divide from the incoming flow or combine with it. The analysis starts with the description of the flow patterns that emerge in the dividing and combining flow cases for all mass split ratios, 0 ≤ m ̇ 1 ≤ 1 , and a wide range of straight duct to side branch width ratios, 1 ≤ α ≤ 3 , and Reynolds numbers of the common branch, 0 ¡ Re 3 ≤ 200, representative of the cooling oil flow in oil-immersed transformer winding. Flow maps for planar Tee joints are then presented, showing the existence of different regions in the (Re 3 , m ̇ 1)-plane that exhibit different number and location of recirculation zones. Pressure distributions and secondary loss coefficients are then computed and analyzed, providing a numerical database that is used to develop new local pressure loss correlations for planar Tee joints in an accompanying paper. • A numerical study of laminar flow and pressure drop in planar Tee joints is presented. • First description including both dividing and combining flows. • Flow maps showing different recirculation zones are obtained. • A numerical database useful for the development of pressure loss correlations is generated. • Application to the thermal-hydraulic design of oil-immersed power transformer windings. [ABSTRACT FROM AUTHOR]

Monitoring of winding faults is of great significance for the assessment of the transformer maintenance status. In this study, the time series analysis is combined with frequency response analysis (FRA) for better interpretation and analysis of FRA results. Here, healthy baseline residual data are modeled using the time series analysis for faults detection of the transformer winding. Different statistical software, such as R 4.0.2 and ITSM2000, are used to analyze measured data. To detect the transformer’s winding faults, various analyses, such as the autocorrelation and partial autocorrelation functions plot, the Box–Pierce test, the Ljung–Box test, the McLeod–Li test, the turning points test, the Wallis and Moore phase–frequency test, and the Jarque–Bera test, and the order of minimum corrected Akaike’s information criteria are used. The simulation results show that the suggested method is able to classify and discriminate mechanical and electrical faults of the transformer’s winding with good accuracy. [ABSTRACT FROM AUTHOR]

This article proposes an isolated LLC resonant converter with MHz-level switching frequency that can achieve zero-voltage switching in the full-load range. In the proposed converter, conventional silicon devices are replaced with wide band-gap gallium nitride devices to reduce switching losses in the power device. A planar transformer structure with reduced winding length on the secondary side is proposed, which utilizes flux cancellation and reduces core loss while maintaining a low core volume. The path of the secondary winding is a fraction of a full turn, which reduces secondary-side losses while maintaining a turns ratio of 16:1. This planar transformer achieves the goals of decreasing core loss and volume while increasing power density. Within a limited circuit layout area, optimal points for the efficiency of core loss and copper loss were calculated. The magnetic simulation software ANSYS Maxwell was employed to verify whether the actual circuit behavior of this planar transformer conformed to the design theory. Finally, a resonant converter was achieved with a switching frequency operating at 1 MHz, input voltage of 380 V, output voltage of 12 V, output power of 800 W, power density of 55 W/cm3, and maximum efficiency of 96.5%. [ABSTRACT FROM AUTHOR]

Frequency response analysis (FRA) is regarded as the most effective technique to detect mechanical faults of transformers. Over the years, FRA measurement data have been collected by utilities into transformer asset databases. The characteristic of FRA data is fundamentally determined by the transformer's equivalent electrical circuit, which consists of inductance and capacitance parameters that are windings' design and structure dependent. Different winding types tend to have different FRA characteristics, and a transformer's design information such as winding type, dimension etc. is often not known to the utility but critically important for asset management. This study reviews the state-of-the-art transformer FRA databases and application of machine learning techniques in this field, and proposes to apply a support vector machine (SVM) model onto the FRA data to identify the winding type. The SVM model is first trained by FRA traces of transformers with known winding types, and after testing, the SVM model is then applied to FRA traces with unknown winding information. A set of data from the UK's National Grid FRA database, was used to demonstrate and verify the SVM model. All transformers used in this study are 400/275/13 kV transmission transformers, which were designed using four different winding types, namely multiple layer, plain disc, interleaved disc and single helical windings. The proposed method can successfully identify the correct winding type.

The transformer is one of the main components in the power network and transformer windings are one of the most expensive elements in the power transformer. Optimisation of winding distances is one of the most important parameters during the manufacturing of transformer. The distance between the windings in the two winding transformers is well known to transformer designers and manufacturers. However, insulation of the high voltage transformer with additional winding and tap winding is still a major problem for transformer designers. In this study, the additional winding to tap winding distance optimisation is made for a high voltage power transformer. Optimisation of the transformer's windings just not minimises the cost of the transformer but also increases the lifetime of the transformer. With additional winding and tap winding in high-voltage transformers, insulation distance is a major concern for minimising the cost and size of the high voltage transformer. In this study, an approach is made to balance the cost, size, and safety of high voltage transformers. The optimised distance and position between tap winding and additional winding are determined by using the finite element analysis. The finite element method results were also verified by making a prototype transformer.

A simple procedure to estimate series capacitance of a uniform transformer winding from its measured frequency response analysis (FRA) and shunt capacitance is presented. Unlike previously published approaches, this method does not involve any cumbersome and time-consuming curve-fitting nor running optimisation/search algorithms, and neither does it require data of winding geometry. The procedure relies on a property that is observable in the impedance function of a lossless winding, viz., the ratio of the product of squares of open circuit natural frequencies to the product of squares of short circuit natural frequencies bears a special relation to impedance function coefficients. Its feasibility was initially verified by simulation, and then by experiments on small-sized continuous-disk and interleaved-disc windings, followed by a large-sized 33 kV, 3.5 MVA continuous-disc winding, and finally on a 315 kVA 11/13.8 kV transformer. After measuring FRA, the process involves just finding roots of a polynomial, from which the initial impulse voltage distribution constant and series capacitance can directly be determined. Given these attractive features, authors believe that this method is implementable on existing FRA instruments, so that, along with routinely measured FRA, these two important constants of a winding can be displayed.

This study proposes a hybrid voltage harmonic injection circuit at the DC link of the traditional series‐connected 12‐pulse rectifier to improve the harmonic suppression performance of the rectifier, which contains an injection transformer and the auxiliary circuit. The optimum turn ratio of the injection transformer and the optimal conduction angle of the switch are designed from the viewpoint of minimising the total harmonic distortion (THD) of the input voltage in the isolated transformer. Under the optimal design, the proposed series‐connected rectifier operates as a 36‐pulse rectifier. Experimental results indicate that the THD of input voltage reduces to ∼3.19% and that of the input current is only ∼2%. [ABSTRACT FROM AUTHOR]

This study proposes a model for multi‐phase, multi‐winding, lossy transformers. A methodology is developed to decompose such transformers into a sub‐network of multi‐conductor Π‐sections, shunts and idealised (lossless) two‐winding transformers. The approach, therefore, can be used to include three‐phase transformer models in any unbalanced power flow or optimal power flow tool that is able to represent these three basic components. The study derives the mathematical formulation and an implementation is provided in Julia/JuMP/PowerModelsDistribution.jl. The obtained voltage profile for several distribution test cases deviates from OpenDSS by at most 4×10−7. A case study applies this model to optimise the tap settings in the context of conservative voltage reduction. This illustrates that the optimised tap settings can vary by as much as 30% depending on the vector group of the transformer. [ABSTRACT FROM AUTHOR]

In the energy distribution networks, the most important and valuable equipment is oil‐immersed distribution transformers. Besides, due to the key role of these transformers and their multiplicity, their lifetime monitoring is inevitable. The life of a transformer depends on the weakest solid insulation material (i.e. paper insulation). On the other hand, monitoring the transformer insulation status requires accurate information to be available about the oil temperature at every moment. Therefore, it is important to control and predict the oil temperature rise in the transformer. In this study, a new model based on fundamental heat transfer theory is proposed for thermal behaviour prediction of top oil of indoor distribution transformers using the concept of thermal resistance, namely electro‐thermal resistance model (E‐TRM). In E‐TRM, the thermal resistance network is formed by following three‐dimensional heat transfer path and assigning thermal resistance to each path. To evaluate the proposed E‐TRM, the results of this model are verified with experimental results. Moreover, the E‐TRM is used to predict the thermal behaviour of the indoor transformer in the overloading condition. At the end, the transformer loss of life is estimated based on the oil temperature and a normal cyclic overloading strategy is presented for overloading management. [ABSTRACT FROM AUTHOR]

Geomagnetically induced currents (GICs) in long high‐voltage transmission lines cause half‐cycle saturation of transformers, malfunction of protective relays, reactive power loss, and voltage instability. This study describes the design for a GIC effects mitigation device (GEMD) that can be installed at a power system autotransformer common node connection to block the flow of GIC DC flux at the cores of the autotransformers. The devices consist of variable resistors, which are controlled by a wide‐area method based on particle swarm optimisation algorithm. The effectiveness of the proposed protective electrical devices is investigated and validated through simulation studies under many operational cases. The test results obtained from 648 cases verify the high performance of GEMD. The proposed method can mitigate the reactive power loss due to GIC in the power system with average improvements by 7.9 and 7.09% over resistive and capacitive blocking devices, respectively. [ABSTRACT FROM AUTHOR]

Partial discharge (PD) investigations can identify and localise incipient failures in power transformers early, thus avoiding considerable financial losses. The feature extraction of PD signals is a fundamental step for the development of such location techniques since it directly influences the performance of a location method. This study presents a detailed comparative analysis of four traditional approaches for the obtaining of attributes towards a better set of signal features for the location of PDs. The approaches were critically compared regarding their ability to locate experimentally generated discharges between adjacent layers of a prototype winding. In order to perform such analysis, a localisation structure based on logistic regression models was elaborated, capable of determining both layers and sections of the winding affected by PDs and easily applicable in practice. The results show energy features of wavelet coefficients, obtained through the decomposition of high‐frequency current signals acquired at the winding endings, achieve better performance in the PD localisation, accurately indicating discharge occurrence points among layers and sections of the winding. [ABSTRACT FROM AUTHOR]

The sweep frequency response analysis (SFRA) technique is based on measuring the power transformer electrical transfer functions over a wide frequency range to identify the abnormal areas prior to serious failure. This study presents the proposed diagnostic adjusted R‐square technique to identify the transformer faults using the SFRA technique. The SFRA measurements are ranged up to and beyond 1 MHz. The proposed technique is used to calculate the relative factor for adjusted R‐square coefficient between the actual data and new measurement data sets. The results of the proposed method are evaluated and compared with existing Chinese Standard factor DL/T 911‐2016 and CCF factor of IEEE Std. C57.149™ Standard indicates that the suggested methodology is more reliable to identify and analyse the internal faults of the transformers. This technique is considered to be effective indicator to predict the internal physical condition inside the transformer, which moves the field forward. [ABSTRACT FROM AUTHOR]