In this study, a positive feedback loop between gap occurrence during vibration and residual deformation of spacers is identified, based on which a transformer failure path under multiple external short-circuit impacts is demonstrated. A three-stage analysis is performed. First, two prestress application methods, namely, elastic and fixed methods, are differentiated. The nonlinear and nonstretchable characteristics of spacers are illustrated. The criterion of gap occurrence in the fixed-application method is investigated. A case study is conducted to analyze the possibility of gap occurrence. Subsequently, the effect of the gap on the vibration process is analyzed. Owing to the gap, the vibration intensity of the entire winding is amplified, and the stress on the conductors and spacers is exacerbated. The mechanism of this phenomenon is explicated. Finally, based on the experimental results in which the amplitudes of cyclic loads first increase and then decrease, the unidirectional change in the residual deformation is observed. Under cumulative impacts, the residual deformation is greater, and the gap occurs more easily, thus contributing to the winding collapse under multiple short-circuit impacts.

Short‐circuit forces, which result in violent vibration of power transformer windings, are induced by the interaction between the short‐circuit currents and the leakage magnetic induction. During vibration, the rearrangements of disks affect the magnetic flux distribution, which leads to time‐varying equivalent reactance and further changes of currents and forces. When a short‐circuit accident occurs, these processes happen simultaneously and constantly. In this article, the influence of circuit parameters on short‐circuit currents is analyzed. The strongly coupled phenomenon between equivalent circuit, magnetic field and structural field is explicated, and the method to obtain vibration process with strongly coupled phenomenon considered is proposed. Then the strongly coupled effect on vibration process is investigated. The vibration process is characterized by the time‐varying currents, electromagnetic forces and displacements. The space coefficient is defined to represent the magnetic flux distribution. The changes of maximum value and its occurrence time of the characteristic parameters are obtained. The peak values of the short‐circuit forces and displacements increase and the waveforms change, which is caused by the distortions of leakage magnetic flux and the changes of spatial ampere‐turn balance during vibration. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

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 Transformer winding turns often consist of multiple parallel strands. The spatial position variation of each strand affects the leakage inductance of each branch, resulting in an uneven distribution of short‐circuit currents within the winding turns. And this unevenness persists even when transposition structures are implemented. Traditional methods in transformer analysis frequently overlooked the distribution characteristics of short‐circuit currents when calculating electromagnetic forces. A frequency‐domain calculation method for analysing the current distribution in winding turns was proposed, with a deviation of less than 3% compared to existing analysis methods. Two typical 110 kV transformer models were utilised to investigate the influence of uneven current distribution on the spatial distribution of electromagnetic forces. The spatial distribution of short‐circuit electromagnetic forces in low‐voltage (LV) windings exhibited significant changes, with maximum change rates of 10% and 61.2% for axial and radial electromagnetic force, respectively, in a LV winding with 4 parallel strands. The research also analysed how strand radial width and axial height affect current distribution unevenness and proposed specific design principles to mitigate these disparities in winding design. The findings offer valuable insights for selecting structural parameters and assessing short‐circuit stability during transformer design.

High density pressboard made of cellulose is a crucial component of power transformers because it combines good mechanical and electrical insulation properties that are well suited to power transformer design requirements. It is critical to characterize the mechanical properties of pressboards under various operating conditions in order to ensure a properly functioning transformer. In this paper, the stress-strain curves for pressboards with different total thickness and different mechanical stress loading parameters were studied. According to the fitting curves obtained by the tests, it can be found that the value of the strain of the thinner pressboards is 0.05 larger than that of the thicker pressboards under the same stress. In addition, the different loading speeds will affect the deformation of the pressboards. The faster loading speed in the range considered in this paper, the larger strain of the pressboards is. Through analysis, the relationship between the nonlinear coefficient of the mechanical properties of the pressboards and the deformation strength of the winding is a power exponential distribution.

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.

The Faraday effect optical magnetic field sensor has broad application prospects in power systems, and the temperature stability of the sensor has always been the focus of research. Existing researches mostly focus on the influence of temperature on the Verdet constant of the magneto-optical material, but there are other temperature factors that are not taken into account, which limits the improvement of the temperature stability of the sensor. In this paper, the effect of magneto-optical crystal (TGG) temperature on the optical rotation coefficient and static operating point of the sensor’s sensing function was studied. It was found that the crystal temperature has a significant effect on the optical rotation coefficient and static operating point in the sensing function. The optical rotation coefficient and static operating point fluctuate periodically with the change of crystal temperature. Through the theoretical analysis of the influence mechanism of temperature, it was found that the interference of multiple reflected light in the magneto-optical crystal has a significant influence on the optical rotation coefficient and static operating point. The mechanism of temperature affecting the sensing function was proposed: temperature affects the phase of reflected light through thermo-optical effect and thermal expansion effect, changes the interference state of reflected light, and then affects the optical rotation coefficient and static operating point. Quantitative calculations were carried out on the influence of temperature using the theoretical model. The calculation results are in good agreement with the experimental data. This article provides a theoretical basis for the optimal design of such sensors.

The safe operation of power transformers is critical for the stability of power grid. The external short circuit is one of the major threats of the transformers. When an external short circuit occurs, the transformer windings would endure large electromagnetic force and vibrate violently. Accurate calculation of winding vibration is necessary for better designed windings with improved mechanical and insulation strength. The short-circuit electromagnetic force consists of DC component, fundamental frequency component and double frequency component. Different frequency components have different amplitudes and produce different displacement and stress distribution in the windings. In this paper, the influence of frequency components on vibration characteristics is investigated. The displacement distributions under the effect of different components are obtained. According to the results of the case study, it is worth to notice the influence of the fundamental frequency component on the short-circuit vibration process. For the spatial distribution, the amplitudes of vibration parameters are larger at certain positions, which implies that more attention should be paid to these positions in order to improve reliability of power transformers. The distribution characteristics are in accordance with the mode shape theory.

When an external short circuit occurs, the axial electromagnetic force increases dozens of times. Under the effect of the axial short-circuit electromagnetic force, the transformer windings vibrate violently. The spatial distribution of the disks is constantly changing during vibration, which can change the temporal and spatial distributions of the leakage magnetic field and the axial electromagnetic force. This process is called the strong coupling phenomenon of the structural field and the leakage magnetic field. In this article, a strong coupled magnetic-structural model is proposed by using the analysis method. The strong coupling equations, where the independent variables are the axial position of the disks, are obtained. The vibration process with strong coupling phenomenon considered can be obtained. The accuracy of the strong coupling model is verified by the iterative method. By comparing the results calculated by the strong coupling model with those calculated by the weak coupling model, the influence of the strong coupling phenomenon on the vibration process is obtained. Due to the influence of the strong coupling phenomenon, the winding vibration intensity increases and the maximum displacement of the disks can be doubled, which implied that the strong coupling phenomenon cannot be ignored when investigating the short-circuit strength of power transformers.

The buckling of transformer windings caused by radial short-circuit electromagnetic force is one of the significant causes of transformer failures, threatening the safe operation of the entire power system. Comparing the maximum stress in the windings with the critical buckling stress is an essential criterion for analyzing whether the buckling will occur. Hence, it is vitally important to obtain an accurate stress distribution in windings under radial electromagnetic force. Studies have shown that the thin paper insulation wrapped around the conductors can affect the mechanical strength of windings. Therefore, it is necessary to consider the influence of paper insulation on stress distribution in the research. In this paper, the copper-paper layered ring winding model, which can be analyzed as a 2D stress distribution problem, has been constructed. The governing equation for this model in polar coordinate has been acquired. Because of the assumed close contact, the displacement and radial stress must match at the copper-paper interface. By solving the equations, the stress distribution can be obtained. As a calculation sample, the low-voltage (LV) winding of a type of 110 kV transformer has been studied. There are two Continuously Transposed Conductors (CTCs) that wound in parallel in one disk, so the model contains two layers of copper and one layer of paper. The hoop stress distribution and the radial stress distribution have been calculated. The results show that the hoop stress varies more than 15% from the innermost radius to the outermost radius and the radial stress is small in comparison. The hoop stress in the paper layer is much smaller than that in the copper layer. The obtained results have been verified using the finite-element method.

Oil immersed inverted current transformer is vulnerable to overvoltage in the transmission line during operation. The accumulative effect of switching impulse voltage can degrade the main insulation and lead to a reduction in insulating property. Frequency domain spectroscopy (FDS) can be used to reflect the insulating property of oil-paper insulation. In order to investigate the FDS characteristics of oil-paper insulation under repeated switching impulse voltage, samples of oil-paper insulation with different thickness were made. Afterwards, the FDS of samples was tested with different number of repeated switching impulse voltage and applied voltage. The results show that more impurities occur in oilpaper insulation under repeated switching impulse voltage, which has a greater impact on the FDS results. Therefore, the FDS characteristic curves can reflect the deterioration characteristics of oil-immersed inverted current transformers under repeated switching impulse voltage. The role of impurities concentration and motion characteristics in the degradation process of oil-paper insulation was analyzed.

Oil immersed inverted current transformer is vulnerable to overvoltage in the transmission line during operation. The accumulative effect of switching impulse voltage can degrade the main insulation and lead to a reduction in insulating property. In order to investigate the deterioration characteristic of main insulation of oil immersed inverted current transformer under the accumulative effect of switching impulse voltage and indicate the insulation deterioration, we studied the E-N characteristic of oil-paper insulation with different thickness and gave corresponding semi-empirical formulation to characterize the deterioration characteristic of main insulation of oil immersed inverted current transformer. The influence of insulation thickness on insulation deterioration of oil paper was studied as well. The results show that, the oil-paper insulation has a significant accumulative effect under switching impulse voltage. The E-N characteristic of oil-paper insulation conforms to power exponential distribution. With the increase of insulation thickness, the single minimum breakdown electric field strength decreases gradually.

When an external short-circuit fault occurs, the transformer windings will be subjected to short-circuit electromagnetic force, and accidents such as winding tiltiing and buckling will occur, which seriously endangers the operating safety of the power system. At present, a winding in which multiple continuous transposed conductors (CTCs) wound in parallel is widely used in transformers. In order to suppress the circulating current, the transposition structure is generally adopted, and the structure of the winding is changed. This will affect the leakage magnetic field distribution, and then change the distribution of electromagnetic force. In this paper, a type of 110kV transformer adopting transposition structure in the low-voltage (LV) winding is studied, and a parametric modeling method is proposed to describe the transposition process of the wire. The local finite element model (FEM) including the winding transposition structure is constructed by analyzing the superposition change of the magnetic field at the transposition position. The model contains iron core, 16 low-voltage winding disks, 20 medium-voltage (MV) winding disks. The cloud diagram of the leakage magnetic field of the CTCs at the transposition area and the change of the leakage magnetic field along the circumferential were obtained. The research results show that the leakage magnetic field at the transposition changes significantly and the force of the conductor at the transposition is significantly different from that at the non-transposition area.

SF 6 /N 2 mixed gas, as a typical binary mixed gas with synergistic effect, is a simple and effective SF 6 environmental protection measure. It has been gradually applied to gas-insulated power equipment such as GIS. In order to develop a mixed-gas 126 kV GIS disconnecting switch, breaking characteristics under typical operation conditions are carried out. A circuit breaking test for bus-transfor current was established, and a bus-transfor current breaking test was carried out. It was found that under different conditions, the arc time of the mixed gas was significantly longer than that of SF 6 . Under the condition of 30V/1600A, the arc time of 28% mixed gas is increased by about 29% compared with SF 6 . The arcing time of the mixed gas with 40% mixing ratio is similar. The arcing time will increase when the gas pressure decreases. The operation speed of the disconnecting switch has a small effect on the breaking. After 100 tests, the contactor was slightly ablated after the 30V/1600A test but still passed the test. However, the contactor was severely ablated under the 100V/1600A breaking condition and failed the test. A small capacitive current breaking test circuit was set up, and a small capacitive current breaking test was carried out. It is found that the mixing ratio, gas pressure, and switching operation speed have the same effect on the arcing time as the bus-transfor current breaking test. Compared with SF 6 , the breaking performance is significantly reduced. The arcing time of 28% mixed gas in the 126kV test is increased by about 25%. No insulation discharge occurred after 50 tests, and it was judged that the test passed. In summary, the breaking performance of the mixed gas is significantly lower than SF 6 , which will make the arcing time and the contactor ablation increase, and even the breaking failure. An improved method of adding copper-tungsten arcing contactor was proposed, after which the test sample was improved, and the type test was passed.

For continuous or spiral windings which feature multiple continuously transposed conductors (CTC) wound in parallel, the transposition structure is commonly used to suppress circulation between conductors. This introduces a local asymmetry in transformer windings. Fault analyses have shown that building an asymmetric structure in transformers increases deformation risk in these windings. Researchers have yet to fully investigate this asymmetric structure. This study was conducted to observe the influence of transposition structure in a 110 kV transformer. The conductor's relative position forms three patterns during the transposition process; two parameters are established to describe the position-changing process. A finite-element method (FEM) model is built to investigate the magnetic field and electromagnetic force distributions. The results indicate that the transposition structure distorts the magnetic field distribution. The maximum distortion factor of the axial component of magnetic flux density (B-z) along the axial direction caused by the transposition structure is 14.6%. The transposition structure only changes the radial change slope of B-z. The gap caused by the transposition process aggravates imbalance in the ampere-turns distribution, increasing the amplitude of the radial component of magnetic flux density (B-r) at the middle height of the transformer low voltage (LV) winding. The maximum amplitude of B-r at the transposition structure increases by 513%. The Lorentz force over the CTCs remains constant from before to after the transposition process, though its linear density over the CTCs is unevenly distributed throughout. The axial component F-z varies from -31 to 10 kN/m, while the radial component F-r varies from -146 to -51 kN/m. The results show that the initial stage of the CTC height rising segment is a weak point and should be strengthened in the manufacturing process.

Winding transposition structures are commonly built into transformers to suppress winding circulation and minimize loss. They alter the distribution of the transverse leakage magnetic field and electromagnetic force. Researchers have not yet considered the winding transposition structures when investigating the transverse leakage magnetic field distribution. The relative position of conductors in a transposition structure is analyzed in this paper, and a scale model experiment is conducted to verify the effect of the structure. In the meantime, a finite element method model which includes the winding transposition structure of the scale models is established and verified by comparison with experimental observations. Then, the distribution of the transverse leakage magnetic field and the axial electromagnetic force of the 110 kV transformer under rated tapping are obtained. The transverse leakage magnetic field and axial electromagnetic force in the low-voltage winding are affected by the transposition structure, while the high-voltage winding is not affected. Compared with models without transposition structure, the amplitude of the axial electromagnetic force linear density of the 40th winding disk under rated tapping increases from a value close to zero to 25 N/m. The transposition structure needs to be considered when calculating the electromagnetic force and winding mechanical characteristics.