Transformer inter-turn short circuit fault location method based on multi-field coupling and frequency response method fusion

Abstract

The application discloses a transformer inter-turn short circuit fault positioning method based on fusion of multi-field coupling and frequency response method and belongs to the technical field of power transformer fault diagnosis. The method firstly constructs a three-dimensional geometric model of a transformer, is coupled with an external circuit into a field-circuit coupling model, obtains leakage magnetic flux density distribution and winding parameter mutation under inter-turn short circuit, then uses the frequency response method to obtain a frequency response curve, carries out fault qualitative detection by analyzing distortion characteristics, constructs a low-frequency inductance matrix simplified model after qualitatively confirming the fault, calculates equivalent inductance variation, precision factor and position factor, and realizes quantitative positioning of the fault axis. The application deeply fuses the electromagnetic field-circuit multi-field coupling and the frequency response method, can complete quantitative positioning only by using low-frequency band data, does not need complex signal processing or additional hardware modification, is verified by combining the response surface method, has high calculation efficiency, and provides a reliable technical means for rapid diagnosis of transformer offline faults.

Description

Technical Field

[0001] This invention relates to the field of power transformer fault diagnosis technology, and in particular to a method for locating inter-turn short-circuit faults in transformers based on the fusion of multi-field coupling and frequency response methods. Background Technology

[0002] As the core hub of power grid energy conversion, the operational reliability of power transformers directly affects the safety and stability of the power system. Most transformer failures stem from insufficient short-circuit withstand capability of the short-circuit windings or insulation damage caused by collisions or temperature rises. With the widespread development of electrification, the structure and winding method of transformer windings have become increasingly complex, leading to a corresponding increase in the probability of transformer failures. During operation, the outer insulation layer between winding turns is affected by temperature, electromagnetic forces, and mechanical wear, causing the insulation material to gradually deteriorate, resulting in exposed windings and triggering inter-turn short-circuit faults. When such faults occur, the overcurrent generated by the short-circuit ring excites a strong leakage magnetic field, which in turn generates enormous electromagnetic forces and thermal stress, forcing the windings to undergo plastic deformation or even burn out. Due to the enclosed structure of large oil-immersed transformers, the location of faults is difficult to determine directly by visual inspection. Traditional maintenance relies on hanging the transformer cover for inspection, which takes several weeks, causing serious economic losses and power outages.

[0003] Among existing fault diagnosis technologies, short-circuit impedance method and vibration method have low sensitivity to minute deformations, while frequency response method (FRA) has become the mainstream technology for deformation detection because it can reflect subtle changes in the equivalent parameters of the winding. However, current research has two major limitations: First, it often analyzes electromagnetic characteristics in isolation, neglecting the coupling effect of electromagnetic force and thermal stress, making it difficult for existing models to reflect the multi-physics interactions of actual equipment. Second, FRA positioning often relies on changes in a single parameter, making it difficult to balance accuracy and engineering practicality, and the error increases significantly under complex fault scenarios. Specifically, existing technologies include thermodynamic inverse calculation models using temperature field analysis, which use the temperature distribution data of the outer wall of the oil tank to estimate the spatial location and heat generation power of the short circuit point inside the winding; methods that rely on the induced voltage of the detection coil to estimate the voltage applied to the transformer and detect the fault phase and winding through voltage deviation; methods that use the frequency response method to identify the location of the transformer winding with inter-turn short circuit faults and use a hyperbolic model to predict the fault location; methods that identify the fault by fitting the relationship curves between the electrical characteristics such as voltage and current before and after the transformer inter-turn short circuit fault and the number of windings and the fault location; and methods that combine deep learning and neural networks to complete the intelligent fault location identification of the winding based on the characteristic laws of the frequency domain curve of the oscillation wave during the transformer inter-turn short circuit fault. However, these existing methods either rely on complex signal processing techniques, require additional hardware modifications, or require a large amount of training data, making it difficult to meet the actual needs of on-site maintenance for low cost, high accuracy, and without affecting the normal operation of transformers.

[0004] Therefore, there is an urgent need to propose an efficient location method that does not affect the normal operation of the transformer, is low-cost, highly accurate, and can identify the location of inter-turn short-circuit faults of different degrees at different locations of the winding. Summary of the Invention

[0005] The purpose of this invention is to provide a transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method, so as to solve the problems mentioned in the background art.

[0006] This invention is achieved through the following technical solution: A transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response methods includes the following steps: S1. Based on the structural parameters of the transformer under test, construct a three-dimensional geometric model of the transformer including the core, high-voltage winding, and low-voltage winding. S2. Construct an external circuit model to simulate the transient characteristics of a transformer, and couple the external circuit model with the three-dimensional geometric model to form a field-circuit coupled model; through the bidirectional data interaction of the field-circuit coupled model, obtain the spatial leakage flux density distribution caused by the surge of short-circuit loop current in the winding under the inter-turn short-circuit fault state, as well as the sudden change of the equivalent circuit parameters of the winding. S3. Based on the field-circuit coupling model, the frequency response curve of the transformer winding is obtained by using the frequency response method, and the presence of inter-turn short circuit fault is qualitatively detected by analyzing the distortion characteristics of the frequency response curve. S4. When a fault is detected in the qualitative test, a simplified model of the low-frequency inductance matrix of the transformer winding is constructed. Based on the sudden change in the equivalent circuit parameters of the winding caused by the fault, the change in equivalent inductance before and after the fault is calculated, and the accuracy factor used to characterize the parameter deviation is calculated based on the change. S5. Based on the accuracy factor, calculate the location factor used to associate the fault location with the accuracy factor; S6. The winding position corresponding to the minimum value of the position factor is determined as the fault location of the inter-turn short circuit.

[0007] Furthermore, in step S2, the external circuit model is configured according to the actual connection group of the transformer; the bidirectional data interaction refers to: importing the winding inductance parameters calculated by the three-dimensional geometric model into the external circuit model in real time, and simultaneously feeding back the current excitation calculated by the external circuit model to the three-dimensional geometric model in real time, so as to form a data iteration closed loop.

[0008] Furthermore, in step S3, the distortion characteristics of the frequency response curve are analyzed to qualitatively detect the fault, specifically including analyzing at least one of the following: frequency offset of the peak, amplitude change rate of the peak or trough, and number of newly added resonant points in the high-frequency band.

[0009] Furthermore, in step S4, a simplified low-frequency inductance matrix model of the transformer winding is constructed, specifically including: short-circuiting the winding port and ignoring the influence of capacitance in a preset low-frequency domain, and converting the winding into a stepped inductance network that retains only the inductance parameters, thereby forming the simplified low-frequency inductance matrix model.

[0010] Furthermore, in step S4, the equivalent inductance is the sum of all elements in the inductance matrix; the change in the equivalent inductance is the difference between the equivalent inductance before the fault and the equivalent inductance after the fault.

[0011] Furthermore, in step S4, the precision factor The following relationship must be satisfied: In the formula, The change in the equivalent inductance is the amount of change. For the self-inductance of the faulty winding, For equivalent mutual inductance; The precision factor is obtained by solving this relationship. The value of .

[0012] Furthermore, step S4 also includes: The entire winding is divided into N winding segments along the axial direction to construct an Nth-order inductance matrix; The difference between the equivalent inductance of the entire winding before and after the fault is taken as the change in the equivalent inductance of the entire winding. Based on this change in the equivalent inductance of the entire winding and the corresponding self-inductance and equivalent mutual inductance of the entire winding, the accuracy factor is calculated. Solve the relational expression to calculate the accuracy factor of the entire winding; Each winding segment is treated as a potential fault segment, and the segmentation accuracy factor corresponding to each winding segment is calculated.

[0013] Furthermore, in step S5, the position factor is calculated as follows: for each winding segment, the ratio of the full winding accuracy factor to the segment accuracy factor of that winding segment is calculated, and the absolute logarithm of the ratio is taken as the position factor corresponding to that winding segment; wherein, the winding segment corresponding to the minimum position factor is the axial position where the fault is located.

[0014] Furthermore, following step S6, a verification step S7 is also included: Based on the spatial leakage flux density distribution and winding current distribution obtained from the field-circuit coupling model, the radial electromagnetic force and axial electromagnetic force of each part of the winding are calculated. Using the calculated electromagnetic force data of each part as samples, a response surface model reflecting the mapping relationship between the winding electromagnetic force and the input variables is constructed by fitting the response surface method. The accuracy of the field-path coupling model and fault location results is verified by comparing the calculation results of the response surface model with the experimental measurement results or the detailed finite element calculation results.

[0015] Furthermore, constructing the response surface model specifically includes: The sample point distribution of the input variables is determined by experimental design methods, and the input variables include at least the winding current and the deformation radius of the winding; The radial and axial electromagnetic forces of the windings corresponding to each sample point are obtained using the field-circuit coupling model or experimental data. The response surface methodology is used to fit the sample data to establish an explicit mapping relationship between the winding electromagnetic forces and the input variables.

[0016] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: 1. This invention achieves bidirectional data iteration closed loop between electromagnetic field and circuit by constructing a field-circuit coupling model, accurately capturing the electromagnetic transient law of inter-turn short circuit fault, and overcoming the limitation of traditional pure circuit simulation that ignores the nonlinear change of magnetic field distribution.

[0017] 2. This invention deeply integrates the qualitative detection capability of frequency response law with the quantitative positioning algorithm of low-frequency inductor matrix. It can achieve accurate fault location using only low-frequency data without introducing complex signal processing technology, thus balancing positioning accuracy and engineering practicality.

[0018] 3. This invention proposes a two-factor positioning algorithm based on accuracy factor and position factor. The positioning process does not rely on additional hardware modifications, the method has low implementation cost, is easy to deploy on site, and has good engineering application prospects.

[0019] 4. This invention introduces a verification step based on the response surface methodology, which significantly improves computational efficiency while ensuring model accuracy, providing an efficient tool for rapid on-site diagnosis. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only preferred embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a schematic diagram of the overall process of the transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method provided by the present invention.

[0022] Figure 2The transformer model and short-circuit winding schematic diagram are provided for the transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method provided by the present invention.

[0023] Figure 3 The coupling circuit and its switching timing control circuit are provided by the present invention for a transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method.

[0024] Figure 4 The diagram shows the time-varying high-voltage side operating current and short-circuit loop current waveforms of the transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method provided by the present invention.

[0025] Figure 5 A schematic diagram of the leakage flux density distribution in the outer winding of the core for the transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method provided by the present invention.

[0026] Figure 6 This invention provides a schematic diagram of the spatial leakage magnetic flux of a transformer under different operating conditions, varying with time and location, based on the transformer inter-turn short-circuit fault location method fused with multi-field coupling and frequency response.

[0027] Figure 7 This is a schematic diagram comparing the frequency response curves after the inductance parameters are changed due to the winding deformation in the transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method provided by the present invention.

[0028] Figure 8 This is a schematic diagram comparing the frequency response curves after the longitudinal capacitance parameters of the winding deformation change in the transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method provided by the present invention.

[0029] Figure 9 This is a schematic diagram comparing the frequency response curves after the winding deformation changes and the ground capacitance parameters in the transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method provided by the present invention.

[0030] Figure 10 This is a schematic diagram comparing the frequency response curves after the winding deformation parameters change in the transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method provided by the present invention.

[0031] Figure 11 A simplified stepped equivalent model of the low-frequency domain winding for the transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method provided by the present invention is shown in the figure.

[0032] Figure 12This is a schematic diagram of the transformer inter-turn short-circuit fault location technology process provided by the present invention, which is based on the fusion of multi-field coupling and frequency response method.

[0033] Figure 13 A schematic diagram of an experiment for testing the electromagnetic force of a three-phase transformer winding, based on a transformer inter-turn short-circuit fault location method that integrates multi-field coupling and frequency response methods, provided by this invention.

[0034] Figure 14 A schematic diagram of the high-voltage winding current waveform of a three-phase transformer under rated load, based on the transformer inter-turn short-circuit fault location method provided by the present invention, which is based on the fusion of multi-field coupling and frequency response method.

[0035] Figure 15 A schematic diagram of the assumed winding deformation of a three-phase transformer for the transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method provided by the present invention.

[0036] Figure 16 This diagram illustrates the effect of radial deformation of the high-voltage winding of a three-phase transformer on electromagnetic force in a transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response methods provided by this invention.

[0037] Figure 17 This diagram illustrates the effect of radial deformation of the low-voltage winding of a three-phase transformer on electromagnetic force in a transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response methods provided by this invention. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of the present invention more apparent, exemplary embodiments according to the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are merely a part of the embodiments of the present invention, and not all of the embodiments of the present invention. It should be understood that the present invention is not limited to the exemplary embodiments described herein. Based on the embodiments of the present invention described herein, all other embodiments obtained by those skilled in the art without inventive effort should fall within the protection scope of the present invention.

[0039] In the following description, numerous specific details are set forth in order to provide a more thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention can be practiced without one or more of these details. In other instances, certain technical features well-known in the art have not been described in order to avoid obscuring the invention.

[0040] It should be understood that the invention can be embodied in various forms and should not be construed as being limited to the embodiments set forth herein. Rather, providing these embodiments will make the disclosure thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

[0041] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. When used herein, the singular forms “a,” “an,” and “the” are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the terms “comprising” and / or “including,” when used in this specification, identify the presence of the stated features, integers, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups. When used herein, the term “and / or” includes any and all combinations of the associated listed items.

[0042] To fully understand this invention, a detailed structure will be presented in the following description to illustrate the technical solution proposed by this invention. Optional embodiments of the invention are described in detail below; however, in addition to these detailed descriptions, the invention may have other embodiments.

[0043] This embodiment provides a transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response methods. A three-phase power transformer of SZ-50 MVA / 110 kV is used as the simulation research object, and an experimental platform of SS-10kVA / 380V three-phase transformer is built for experimental verification. The method specifically includes the following steps: Step S1: Construct a three-dimensional geometric model of the transformer Based on the structural parameters of the transformer under test, a three-dimensional geometric model of the transformer, including the core, high-voltage winding, and low-voltage winding, is constructed. To ensure the engineering applicability of the simulation results, a high-fidelity three-dimensional finite element simulation model needs to be established.

[0044] This embodiment uses an SZ-50 MVA / 110 kV three-phase power transformer as the simulation object. Its main technical parameters are shown in Table 1: Table 1. Specific technical parameters of the three-phase transformer.

[0045] The main geometric parameters of the transformer are shown in Table 2: Table 2 Main geometric parameters of three-phase transformers

[0046] Based on the above structural parameters, a three-dimensional geometric model of the transformer was established in the finite element simulation software. The fault turn was located on phase B of the high-voltage side. The established model and the location of the fault turn are as follows. Figure 2As shown.

[0047] Step S2: Constructing the field-circuit coupling model and analyzing electromagnetic transient characteristics To simulate the complete dynamic process of a fault from oscillation to stabilization, a three-dimensional transient field model with "field-circuit" coupling is constructed. The external circuit adopts the YNd11 connection method consistent with the actual transformer, specifically including: HW_A and HW_C are the inductances of the A-phase and C-phase high-voltage windings, respectively; HW_B is the inductance of the non-short-circuit portion of the B-phase high-voltage winding; HW_SC is the short-circuit turn inductance of the B-phase high-voltage winding; and LW_A, LW_B, and LW_C are the inductances of the three-phase low-voltage windings. The coupling circuit and its switching timing control circuit are as follows: Figure 3 As shown.

[0048] A two-way data interaction closed loop is achieved between the external circuit model and the 3D geometric model: the winding inductance parameters calculated by Maxwell finite element software are imported into the external circuit model in real time, while the current excitation calculated by the external circuit model is fed back to the electromagnetic field model in real time. This two-way coupling mechanism avoids the limitation of traditional pure circuit simulation ignoring the nonlinearity of magnetic field distribution, and can accurately reflect the dynamic nonlinear relationship between winding inductance and current when a fault occurs.

[0049] Based on the above model, a short circuit occurs on the 8th turn of the B-phase high-voltage side as an example for solution. The solution yields the transformer operating phase current varying with time and the short-circuit fault turn current on the B-phase high-voltage side varying with time, as follows: Figure 4 As shown.

[0050] from Figure 4 It can be observed that the fault only significantly affects phase B, while the peak current and phase change of phases A and C are both less than 5%. This verifies that the three-phase transformer still has good fault phase isolation characteristics under multi-phase coupling conditions. At the same time, this phase difference also provides an important phase identification basis for subsequent fault location.

[0051] from Figure 4 It can be seen that the short-circuit current of the faulted turn exhibits a typical three-stage transient characteristic of impact-oscillation-steady-state. Specific data shows that the peak short-circuit current is 43.68 kA, and the effective value is 30.88 kA. This peak value is approximately 117.7 times the rated current of the high-voltage winding (IN=262.4 A). Such a large short-circuit current will generate enormous Joule heating and electromagnetic force impact in the winding turns, which is the fundamental cause of further damage to the winding insulation and plastic deformation.

[0052] The transformer leakage magnetic field is a three-dimensional transient eddy current field containing multi-medium nonlinearity. This invention uses the A-φ-A method for solution. Based on the fundamental relationship between vector magnetic potential A and magnetic flux density B, B = ... ×A, derives the calculation expressions for leakage flux density components in each direction in a rectangular coordinate system. The A-φ-A method, by using different combinations of potential functions in the conductive and non-conductive regions respectively, can effectively handle the continuity conditions of field quantities at complex dielectric interfaces inside the transformer, ensuring the convergence and accuracy of leakage magnetic field calculations.

[0053] The spatial distribution of leakage flux density was obtained through post-processing calculations. Taking the outer winding of the B-phase core window as the research area, leakage magnetic field calculations were performed for both rated load operation and inter-turn short-circuit fault operation, resulting in the spatial leakage flux density distribution of the outer winding of the core window as follows: Figure 5 As shown, the dynamic spatial leakage flux distribution of the transformer under different operating conditions varies with time / location, as shown in the figure. Figure 6 As shown.

[0054] The comparative results show that under rated load operating conditions, the leakage flux density is spatially uniformly distributed with a low peak value. However, when an inter-turn short-circuit fault occurs, the short-circuit loop current generates a highly concentrated strong leakage magnetic field in a localized area, with the peak leakage magnetic field strength reaching 0.75T, approximately five times the peak value under rated load conditions. This severe distortion and localized concentration effect of the leakage magnetic field is the direct cause of the enormous unbalanced electromagnetic force experienced by the winding, and also the physical root cause of the winding deformation. The accurate acquisition of the above electromagnetic transient parameters provides crucial boundary conditions and physical basis for subsequent frequency response analysis and fault location.

[0055] Step S3: Qualitative Fault Detection Based on Frequency Response Method Based on the field-circuit coupling model, the frequency response curve of the transformer winding is further obtained using the frequency response method (FRA). Inter-turn short-circuit faults cause abrupt changes in the equivalent circuit parameters of the winding, specifically including a decrease in equivalent self-inductance, a change in longitudinal capacitance, and a change in capacitance to ground. These changes in equivalent parameters directly induce characteristic distortions in the frequency response curve; by systematically analyzing the distortion characteristics, the presence of a fault can be qualitatively detected.

[0056] The effects of single-parameter variation and multi-parameter synchronous variation on the frequency response curve were studied using PSPICE equivalent circuit simulation, as detailed below: (a) The influence of changes in self-inductance parameters When winding deformation causes a change in the effective length of turns, the winding self-inductance decreases accordingly. Using a 10% decrease in self-inductance as the simulation condition, the obtained frequency response curves are compared... Figure 7As shown in the figure. The results indicate that in the 10kHz–100kHz frequency band, the wave peak shifts significantly to the right, and the series resonant frequency increases; a new parallel resonant trough appears in the 100kHz–300kHz high-frequency band. The physical mechanism of these changes is that the decrease in inductance directly leads to an increase in the series resonant frequency f = 1 / (2π√(LC)), while the asymmetric change in the inductance matrix introduces new resonant modes in the high-frequency band.

[0057] (II) The Influence of Variation in Longitudinal Capacitance Parameters Longitudinal capacitance mainly exists between adjacent turns of the winding, and its magnitude depends on the inter-turn distance and the characteristics of the insulating medium. Using a 15% reduction in longitudinal capacitance as the simulation condition, frequency response curves are obtained for comparison. Figure 8 As shown in the figure. The results indicate that changes in longitudinal capacitance have little impact on the low-frequency range, but new troughs appear in the 100kHz–300kHz frequency range. This is because the longitudinal capacitance mainly participates in the formation of the high-frequency resonant circuit, and changes in its parameters alter the pole distribution in the high-frequency range.

[0058] (III) Impact of changes in ground capacitance parameters The capacitance to ground exists between the winding and the core and tank, and is a crucial parameter determining the overall impedance characteristics of the winding. Using a 20% reduction in the capacitance to ground as the simulation condition, the frequency response curves are compared. Figure 9 As shown in the figure. The results show that the first, fourth, and seventh resonant points shift significantly to the right and their amplitudes decrease significantly. Overall, the longitudinal capacitance mainly dominates the frequency response characteristics in the high-frequency band, while the capacitance to ground affects the impedance characteristics across the entire frequency band, and its changes will cause a coordinated shift of multiple resonant points.

[0059] (iv) The impact of synchronous changes in multiple parameters In actual inter-turn short-circuit faults, due to the simultaneous occurrence of insulation material failure and winding deformation, the self-inductance, longitudinal capacitance, and capacitance to ground of the winding often exhibit synchronous changes. Using the simultaneous change of these three parameters to varying degrees as a simulation condition, frequency response curves are obtained for comparison. Figure 10 As shown in the figure, the results indicate that the peak shifts by approximately 12% towards higher frequencies, the amplitude decreases by about 8 dB in some frequency bands, and two distinct parallel resonance troughs are added in the high-frequency band. Compared with changes in a single parameter, the curve differences caused by synchronous changes in multiple parameters are more significant and the characteristics are richer, providing sufficient spectral basis for reliable qualitative fault detection.

[0060] This embodiment achieves qualitative detection of inter-turn short-circuit faults by analyzing three distortion features: the frequency shift of the peak, the rate of change of the amplitude of the peak or trough, and the number of newly added resonant points in the high-frequency band. Compared with detection methods that rely on a single feature, this multi-feature fusion judgment strategy effectively improves the reliability and robustness of the detection.

[0061] Step S4: Construct a simplified model of the low-frequency inductor matrix and calculate the accuracy factor. Once step S3 qualitative detection confirms the existence of an inter-turn short circuit fault, further quantitative fault location analysis is conducted.

[0062] The transformer winding exhibits purely inductive characteristics under low-frequency excitation. Short-circuiting the winding terminals 2-0, in the low-frequency range of 20Hz to 700kHz, the winding impedance is purely inductive, and the impedance angle is a stable 90°. At this point, the secondary influence of the capacitance parameters can be ignored, and the winding can be equivalently represented as a stepped inductance network retaining only the inductance parameters. Based on this physical premise, the winding is simplified into an 8th-order inductance matrix model, as follows... Figure 11 As shown, this simplified low-frequency inductor matrix model significantly reduces model complexity and computational load while maintaining positioning accuracy, laying the foundation for engineering applications.

[0063] Equivalent Inductance The inductance is defined as the algebraic sum of all elements in the inductance matrix, and its expression is:

[0064] In the formula, The first inductor in the inductor matrix The element in row j-th column covers all self-inductance and mutual inductance components.

[0065] When an inter-turn short circuit occurs in a winding stage, the short-circuited turn forms a closed short-circuit loop with the adjacent normal turn, causing a decrease in the self-inductance of that stage of the winding. Simultaneously, the mutual inductance between that stage and other stages also decreases accordingly. Based on Kirchhoff's voltage law, a set of post-fault loop voltage equations is established. The short-circuit turns ratio is defined as the ratio of the number of short-circuited turns to the total number of turns on the primary side. The winding resistance exhibits a linear distribution with the number of turns, and the self-inductance is proportional to the square of the number of turns. Using a leakage flux correction formula, the unknown inductance and mutual inductance parameters in the equations are solved.

[0066] The verification was performed under a simulated operating condition where a short circuit occurred in the second-stage winding, and both self-inductance and mutual inductance decreased by 25% simultaneously. The calculation process and results are as follows: Before the fault, the equivalent inductance of the entire winding was obtained by summing all elements of the inductance matrix, and the calculated value was 457.32 μH. After the fault, due to the decrease in self-inductance of the second stage winding and the decrease in mutual inductance between this stage and other stages, the equivalent inductance of the entire winding decreased to 446.94 μH. The change in equivalent inductance can then be obtained. It is 10.38 μH.

[0067] The change in equivalent inductance is a composite function of the fault degree and fault location. To decouple these two influencing factors, a precision factor ε is introduced as the core indicator characterizing parameter deviation. The following relationship must be satisfied: In the formula, This is the change in equivalent inductance (obtained by measurement or calculation). The current self-inductance of the faulty winding. For equivalent mutual inductance; equivalent mutual inductance The formula for calculating it is twice the sum of all off-diagonal elements in the inductance matrix, that is:

[0068] By solving the above relationship, the precision factor is obtained. The value of . In the second-level short-circuit simulation condition of this embodiment, the calculated accuracy factor for the entire winding is 0.754, and the accuracy factor for the segmented winding is also 0.754. Accuracy factor The value range is [0,1]. The closer the value is to 1, the smaller the parameter deviation. The closer the value is to 0, the more severe the change in parameters caused by the fault.

[0069] Step S5: Multi-level expansion of the positioning algorithm and calculation of location factors To achieve accurate fault location along the winding axis, the single-fault level analysis method in step four needs to be extended to multiple segments of the entire winding.

[0070] The entire high-voltage winding is uniformly divided into N winding segments along the axial direction, constructing an Nth-order inductance matrix. The fineness of the division can be flexibly adjusted according to the actual positioning accuracy requirements; the larger N is, the higher the axial positioning resolution. For each winding segment, its corresponding inductance parameters and equivalent inductance are calculated according to the method in step four.

[0071] The difference between the equivalent inductance of the entire winding before the fault and the equivalent inductance of the entire winding after the fault is taken as the change in the equivalent inductance of the entire winding. Based on this change and the self-inductance and equivalent mutual inductance of the entire winding, the accuracy factor of the entire winding is calculated according to the same solution formula as in step four. The overall winding accuracy factor reflects the comprehensive impact of a fault on the winding as a whole.

[0072] Each winding segment is considered as a potential fault segment. Based on the changes in self-inductance and mutual inductance corresponding to the occurrence of a short circuit in that segment, the segment accuracy factor corresponding to each winding segment is calculated. The segment accuracy factor reflects the degree of matching between local parameter changes and global parameter changes when the fault is located in that segment.

[0073] A position factor is introduced as the core positioning indicator for correlating fault location with accuracy factor. The position factor is calculated as follows: for each winding segment, the overall winding accuracy factor is calculated. Piece accuracy factor of the winding segment The ratio of the two values ​​is used as the position factor corresponding to the winding segment, and the absolute value of the logarithm of the ratio is taken as the position factor. Its expression is:

[0074] The physical meaning of the position factor is: when the assumed fault location matches the actual fault location, the overall winding accuracy factor... With corresponding piecewise precision factor The ratios should be highly consistent, with the logarithm close to 1 and the value close to 0. Conversely, if the assumed fault location deviates from the actual fault location, the segmented accuracy factor will not accurately reflect the change in the overall winding accuracy factor, leading to a significant increase in the position factor. Therefore, the minimum position factor theoretically corresponds to the most probable fault location.

[0075] In this embodiment, when a short circuit occurs in the simulated second-stage winding, the position factor for the second stage is calculated to be the minimum value of 0.000 (0 after taking the logarithm), accurately corresponding to the actual fault location. To further verify the universality and robustness of the algorithm, short-circuit faults of different degrees were simulated in windings from the first to the eighth stage. Under each short-circuit condition, the minimum value of the position factor accurately pointed to the corresponding fault segment, achieving a 100% accuracy rate. This result demonstrates that the positioning algorithm based on the dual-factor (accuracy factor - position factor) has good fault level identification capability and anti-interference performance.

[0076] Figure 12 The complete process of the above-mentioned transformer inter-turn short circuit fault location technology is systematically summarized in the form of a flowchart.

[0077] The core advantages of this positioning algorithm are: it only needs to utilize equivalent inductance data in the low-frequency band (20Hz~700kHz), without requiring complex signal processing and feature extraction of the high-frequency response curve; the entire calculation process involves only basic matrix and logarithmic operations, without iterative optimization or training; and the algorithm implementation relies solely on conventional impedance measurement equipment, without requiring additional hardware modifications such as detection coils, vibration sensors, or temperature sensors. These characteristics make this method highly feasible for engineering implementation and economical.

[0078] Step S6: Determine the location of the fault Based on the position factor distribution curve calculated in step S5, the winding segment corresponding to the minimum position factor is determined as the final fault location of the inter-turn short circuit. In this embodiment, the position factor of the second-stage winding is the global minimum value of 0.000. Based on this, it is determined that the fault is located in the second-stage winding on the high-voltage side, which is completely consistent with the preset short circuit location, and the positioning accuracy reaches the single-stage winding level.

[0079] Step S7: Experimental verification and efficiency analysis based on response surface methodology To fully verify the accuracy of the field-path coupling model and the effectiveness of the fault location method, an experimental verification platform was built and systematic comparative tests were conducted.

[0080] (I) Construction of the experimental platform The experimental platform uses an SS-10kVA / 380V three-phase transformer with a rated capacity of 10kVA and a rated voltage of 380V. It is primarily used to simulate transformer fault characteristics, particularly suitable for the reproduction and analysis of inter-turn short-circuit faults. The platform includes the transformer body, a magnetic field probe, a gaussmeter, an oscilloscope, a load resistor, and a data acquisition system. The magnetic field measurement tool is a CH-3600 three-channel gaussmeter equipped with a high-precision magnetic field probe. Its range is ±300kGs (±30T), and its resolution reaches 1mGs (0.1μT). The digital end can measure magnetic fields in the 0–60kHz frequency range, meeting the measurement requirements for power frequency and low-order harmonic leakage magnetic fields. The overall layout of the experimental platform and the magnetic field probe measurement points are shown below. Figure 13 As shown.

[0081] (II) Electromagnetic force calculation and current waveform verification For the experimental calculation of the electromagnetic force of the winding, an indirect measurement method is adopted, which measures the external leakage flux density and internal current of the winding, and then calculates the corresponding electromagnetic force of the winding based on the spatial leakage flux distribution of the winding. The advantage of this method is that it does not require the installation of force sensors inside the winding, thus avoiding modifications to the transformer body structure.

[0082] Taking phase B winding as the phase with inter-turn short-circuit fault, the current waveforms obtained from experimental measurement and finite element simulation are compared as follows: Figure 14 As shown, both experimental and simulated waveforms are presented. The comparison results demonstrate that the experimental and simulated current waveforms are highly consistent in terms of amplitude, phase, and transient change trends, with a waveform correlation coefficient exceeding 0.95. This verifies the high fidelity of the established field-circuit coupling model in simulating electrical transient characteristics.

[0083] Based on the spatial leakage flux density distribution and winding current distribution calculated using the field-circuit coupling model, and combined with the Ampere force formula, the radial and axial electromagnetic forces at various parts of the winding were calculated. Comparison data of electromagnetic forces show that the relative error range between the experimental and simulated values ​​for radial force is 6.0%–9.4%, and the relative error range for axial force is 5.4%–9.2%, with an average relative error of approximately 7%. Due to the symmetrical structure of the three-phase transformer, the leakage flux distribution of each phase winding exhibits a similar pattern, resulting in high accuracy in leakage flux calculation. This error level fully meets the accuracy requirements of the GB / T 40661-2021 standard, "Frequency Response Method for Testing Winding Deformation of Power Transformers."

[0084] (III) Construction and accuracy verification of response surface model While directly using the three-dimensional finite element method for electromagnetic force calculation offers high accuracy, the computation time is excessively long (typically exceeding 450 seconds for a single operating condition), making it difficult to meet the timeliness requirements of rapid on-site diagnosis. To address this efficiency bottleneck, this invention introduces the response surface methodology to construct a surrogate model, enabling rapid estimation of electromagnetic forces.

[0085] The sample point distribution of the input variables is determined using the Design of Experiments (DOE) method. The input variables include at least the winding current amplitude and the winding deformation radius. The winding deformation radius describes the degree of radial displacement of the winding under electromagnetic force, assuming the deformation is as follows: Figure 15 As shown, the radial and axial electromagnetic forces of the winding corresponding to each sample point are obtained using a field-circuit coupling model. Then, the response surface methodology is used to fit the sample data with a polynomial formula to establish an explicit mapping relationship between the winding electromagnetic force and the input variables.

[0086] To verify the accuracy of the response surface model, 12 sets of current samples were extracted for comparative verification. The verification results are as follows: Figure 16 , Figure 17 As shown, the predicted values ​​of the response surface model and the calculated values ​​of the radial electromagnetic force of the high-voltage winding, the axial electromagnetic force of the high-voltage winding, the radial electromagnetic force of the low-voltage winding, and the axial electromagnetic force of the low-voltage winding are compared.

[0087] The results show that the maximum relative error in predicting the radial electromagnetic force of the high-voltage winding does not exceed 5%; the maximum relative error in predicting the axial electromagnetic force of the low-voltage winding does not exceed 9%; and when the winding current exceeds 400A, the prediction error of the response surface model is further reduced to below 1%. Specifically, after considering the influence of the winding deformation radius in the model input, the prediction accuracy of the axial force of the low-voltage winding is improved by 12%, the prediction accuracy of the radial force is improved by 6%, and the prediction accuracy of the axial force of the high-voltage winding is improved by 12%. This result fully demonstrates the necessity and importance of incorporating deformation parameters into the response surface model to improve prediction accuracy.

[0088] (iv) Efficiency comparison of different calculation methods To systematically evaluate the efficiency advantage of the response surface methodology in winding electromagnetic force calculation, three methods—full-order finite element method, simplified model method, and response surface methodology—were used to calculate single-phase transformer models, three-phase transformer models, and sample data under 12 different winding excitations.

[0089] Error evaluation uses the calculation result FS(i) of the full-order finite element method as the benchmark value, and adopts the mean relative error MRE as the evaluation index, which is defined as follows:

[0090] In the formula, For the sample size, To simplify the calculations using model-based or response surface methodology, These are the values ​​calculated using the finite element method.

[0091] The detailed comparison results of the three calculation methods are shown in Table 3: Table 3 Comparison of Calculation Efficiency of Winding Electromagnetic Force

[0092] It should be noted that the model building time (27932s) of the response surface methodology is mainly consumed in the finite element calculations for the initial sample points, which are completed offline in one go. Once the response surface model is established, the calculation time for each subsequent electromagnetic force prediction is only 0.5s, which is about 900 times (about two orders of magnitude) more efficient than the 450.3s calculation time of the finite element method. In terms of model accuracy, the average relative error of the response surface methodology is 1.13%, slightly better than the 1.34% of the simplified model method, and far below the 5% error threshold acceptable for engineering applications.

[0093] The high accuracy of the three-phase transformer response surface model is largely due to the inherent symmetry of the three-phase winding structure. This symmetry effectively reduces the nonlinear deviation in the response surface fitting process, enabling the polynomial model to accurately describe the physical field distribution with fewer undetermined coefficients.

[0094] Based on the above experimental verification and efficiency analysis results, it can be concluded that: (1) the established field-circuit coupling model is highly consistent with the experimental results in terms of current waveform, leakage magnetic field distribution and electromagnetic force, and the model error is within the allowable range of engineering standards; (2) the proposed two-factor fault location algorithm can accurately identify the winding segment where the fault is located; (3) the response surface model has achieved a significant improvement in computational efficiency while ensuring prediction accuracy, providing a reliable technical reference for the rapid on-site diagnosis and maintenance of offline faults of power transformers, and has important engineering application value.

[0095] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response methods, characterized in that, The method includes the following steps: S1. Based on the structural parameters of the transformer under test, construct a three-dimensional geometric model of the transformer including the core, high-voltage winding, and low-voltage winding. S2. Construct an external circuit model to simulate the transient characteristics of a transformer, and couple the external circuit model with the three-dimensional geometric model to form a field-circuit coupled model; through the bidirectional data interaction of the field-circuit coupled model, obtain the spatial leakage flux density distribution caused by the surge of short-circuit loop current in the winding under the inter-turn short-circuit fault state, as well as the sudden change of the equivalent circuit parameters of the winding. S3. Based on the field-circuit coupling model, the frequency response curve of the transformer winding is obtained by using the frequency response method, and the presence of inter-turn short circuit fault is qualitatively detected by analyzing the distortion characteristics of the frequency response curve. S4. When a fault is detected in the qualitative test, a simplified model of the low-frequency inductance matrix of the transformer winding is constructed. Based on the sudden change in the equivalent circuit parameters of the winding caused by the fault, the change in equivalent inductance before and after the fault is calculated, and the accuracy factor used to characterize the parameter deviation is calculated based on the change. S5. Based on the accuracy factor, calculate the location factor used to associate the fault location with the accuracy factor; S6. The winding position corresponding to the minimum value of the position factor is determined as the fault location of the inter-turn short circuit.

2. The transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method according to claim 1, characterized in that, In step S2, the external circuit model is configured according to the actual connection group of the transformer; the bidirectional data interaction refers to: importing the winding inductance parameters calculated by the three-dimensional geometric model into the external circuit model in real time, and simultaneously feeding back the current excitation calculated by the external circuit model to the three-dimensional geometric model in real time, so as to form a data iteration closed loop.

3. The transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method according to claim 1, characterized in that, In step S3, the distortion characteristics of the frequency response curve are analyzed to qualitatively detect the fault. Specifically, this includes analyzing at least one of the following: the frequency offset of the peak, the amplitude change rate of the peak or trough, and the number of newly added resonant points in the high-frequency band.

4. The transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method according to claim 1, characterized in that, In step S4, a simplified low-frequency inductance matrix model of the transformer winding is constructed, which specifically includes: short-circuiting the winding port and ignoring the effect of capacitance in the preset low-frequency domain, and converting the winding into a stepped inductance network that retains only the inductance parameters, thereby forming the simplified low-frequency inductance matrix model.

5. The transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method according to claim 1 or 4, characterized in that, In step S4, the equivalent inductance is the sum of all elements in the inductance matrix; the change in the equivalent inductance is the difference between the equivalent inductance before the fault and the equivalent inductance after the fault.

6. The transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method according to claim 5, characterized in that, In step S4, the precision factor The following relationship must be satisfied: In the formula, The change in the equivalent inductance is the amount of change. For the self-inductance of the faulty winding, For equivalent mutual inductance; The precision factor is obtained by solving this relationship. The value of .

7. The transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method according to claim 6, characterized in that, Step S4 also includes: The entire winding is divided into N winding segments along the axial direction to construct an Nth-order inductance matrix; The difference between the equivalent inductance of the entire winding before and after the fault is taken as the change in the equivalent inductance of the entire winding. Based on this change in the equivalent inductance of the entire winding and the corresponding self-inductance and equivalent mutual inductance of the entire winding, the accuracy factor is calculated. Solve the relational expression to calculate the accuracy factor of the entire winding; Each winding segment is treated as a potential fault segment, and the segmentation accuracy factor corresponding to each winding segment is calculated.

8. The transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method according to claim 7, characterized in that, In step S5, the position factor is calculated as follows: for each winding segment, the ratio of the full winding accuracy factor to the segment accuracy factor of the winding segment is calculated, and the absolute logarithm of the ratio is taken as the position factor corresponding to the winding segment; wherein, the winding segment corresponding to the minimum position factor is the axial position where the fault is located.

9. The transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method according to claim 1, characterized in that, Following step S6, a verification step S7 is also included: Based on the spatial leakage flux density distribution and winding current distribution obtained from the field-circuit coupling model, the radial electromagnetic force and axial electromagnetic force of each part of the winding are calculated. Using the calculated electromagnetic force data of each part as samples, a response surface model reflecting the mapping relationship between the winding electromagnetic force and the input variables is constructed by fitting the response surface method. The accuracy of the field-path coupling model and fault location results is verified by comparing the calculation results of the response surface model with the experimental measurement results or the detailed finite element calculation results.

10. The transformer inter-turn short-circuit fault location method based on the fusion of multi-field coupling and frequency response method according to claim 9, characterized in that, Constructing the response surface model specifically includes: The sample point distribution of the input variables is determined by experimental design methods, and the input variables include at least the winding current and the deformation radius of the winding; The radial and axial electromagnetic forces of the windings corresponding to each sample point are obtained using the field-circuit coupling model or experimental data. The response surface methodology is used to fit the sample data to establish an explicit mapping relationship between the winding electromagnetic forces and the input variables.

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