Analysis of First-Layer Failure and Weak Points in Transformer Windings Considering Cumulative Effects of Curved Copper Mechanical Properties

Ping Wang ^1*, Zihe Jiang ¹, Zidi Pan ¹, Jianghai Geng ¹, Shuguo Gao ², Zikang Zhang ¹

¹ Hebei Provincial Key Laboratory of Power Transmission Equipment Security Defense, North China Electric Power University – Baoding Campus, Baoding, China

² Power Science Research Institute of State Grid Hebei Electric Power Co., Shijiazhuang, China

Corresponding: ^*hdqdlalala@163.com

Abstract: The cumulative deformation behavior and sudden mechanical damage of transformer windings under multiple short-circuit impacts are critical issues affecting equipment safety. To address this, this paper proposes a transformer model incorporating the mechanical properties of spacers and curved copper in a split-disk winding structure, systematically investigating the deformation evolution under short-circuit impacts. First, stress-strain curves of curved copper material under different loading modes were obtained through radial bending tests. Subsequently, combining three-dimensional finite element simulation of layered disk windings, the cumulative deformation patterns of windings under multiple short-circuit impacts were analyzed, identifying the primary failure risk zone (the first-layer failure location) and pinpointing failure weak points. Finally, a concurrent failure mechanism between winding and spacer deformations was revealed by comparing the cumulative deformation development between windings and spacers. Results indicate that significant plastic deformation initially occurs in the middle layer of the medium-voltage winding, constituting the first-layer failure zone, with the edge region of the winding-spacer contact surface confirmed as the failure weak point. The established model can accurately predict winding deformation progression, providing theoretical support for anti-short-circuit design and structural optimization of transformers.

KEYWORDS: transformer, short-circuit impacts, curved copper, cumulative effect, first-layer failure, failure weak points.

1. INTRODUCTION

Modern power systems are undergoing profound transformations characterized by voltage level escalation, capacity expansion, and integration of smart technologies. As the core energy transmission apparatus, the power transformer critically determines grid reliability and economic efficiency ^[1-3]. Industry statistics reveal that short-circuit faults account for 43.7% of mechanical damage incidents in transformers, with 65% of structural instability issues directly linked to the cumulative deformation effect. This progressive failure mechanism originates from the continuous accumulation of plastic deformation in windings under electromagnetic forces, while being exacerbated by support stiffness degradation caused by viscoelastic relaxation of the insulating spacer. Notably, the increasing penetration of renewable energy integration introduces stochastic impacts and intensified peak-valley load fluctuations, leading to heightened complexity in amplitude-frequency characteristics of short-circuit currents ^[4-5]. These developments impose more stringent requirements on stability prediction for transformer windings subjected to multiple short-circuit events.

In material mechanical characterization, although existing studies have obtained fundamental mechanical parameters of copper conductors, such as elastic modulus and yield strength, through tensile tests and bending tests ^[6-9], two critical limitations remain unresolved. First, uniaxial tensile tests on conventional straight copper specimens cannot accurately reflect operating conditions. Studies [10-12] indicate that medium-voltage windings primarily endure inward compressive radial stress, while high-voltage windings exhibit outward expansive radial stress. These distinct stress paths lead to significantly different material responses, yet traditional uniaxial tensile testing methods fail to distinguish mechanical property variations caused by differing loading modes effectively. Second, specimen preparation processes may introduce material performance deviations. For example, straightening processes can cause the yield strength of copper to deviate from its actual value by approximately 8% to 15%. These methodological limitations severely restrict precise modeling of the plastic deformation process in windings under multiple electrodynamic impacts.

In-depth analysis reveals that the cumulative deformation of windings fundamentally is a superposition process of residual strain after each short-circuit impact ^[13]. When short-circuit electromagnetic forces exceed the material’s yield limit, irreversible deformation generated per impact accumulates continuously through plastic flow mechanisms, ultimately leading to irreversible alterations in structural geometry or even failure. Furthermore, as nonlinear supporting elements, insulating spacers exhibit significantly reduced energy dissipation capacity due to microcrack propagation and interfacial friction effects ^[14-15]. This synergistic interaction between plastic deformation of metallic materials and performance degradation of insulating supports induces dynamic redistribution of stress fields within windings, establishing a progressive instability development pathway.

Scholars worldwide have made progress in the study of winding cumulative effects in recent years. Studies [16-18] analyzed the deformation accumulation characteristics of transformer windings under multiple short-circuit impacts through magneto-structural coupling models, finding that winding deformation alters magnetic flux distribution, amplifying electromagnetic forces. Research [19-20] investigated the relationship between winding deformation accumulation and the number of short-circuit current impacts using finite element analysis software. Study [21] proposed a comprehensive evaluation methodology for short-circuit mechanical damage in transformer windings, revealing that multiple short-circuit impacts significantly weaken axial and radial stability, while emphasizing the critical influence of initial mechanical properties and support structure aging on cumulative effects. Although these studies have deepened the understanding of cumulative effects, their reliance on traditional cylindrical winding models has constrained the identification of primary failure risk zones and the triggering mechanisms of interlayer spacers in split-disk structures on first-layer failure.

To address the challenges mentioned above, this paper proposes a transformer model with split-disk windings that incorporates the mechanical behavior characteristics of spacer materials. The model fully accounts for the coupling interactions between windings and spacers. To further enhance the model’s reliability, significant differences in radial force patterns between high-voltage and medium-voltage windings are analyzed in depth, focusing on their effects on the mechanical characteristics of windings. Radial bending tests were designed and conducted using curved copper conductors from actual windings as specimens, from which stress-strain curves under different radial loading modes were extracted. Based on these findings, the study reveals the development patterns of stress, deformation, and first-layer failure in windings under multiple short-circuit impacts, providing critical references for enhancing short-circuit resistance and structural optimization of power transformers.

2. 3D Finite Element Simulation of Transformer

• Construction of 3D Transformer Models

This study selected a three-phase power transformer (Model SFSZ7-31500/110) as the research object, with its key parameters listed in Table 1.

Table 1 Key Parameters of the Transformer

The split-disk winding structure effectively characterizes the structural properties of transformer windings. It precisely simulates the failure behavior of windings and spacers under cumulative deformation, establishing a foundation for subsequent studies on electromagnetic distribution and cumulative deformation. Therefore, a layered disk modeling approach is adopted to reconstruct the transformer’s cylindrical high-, medium-, and low-voltage windings, with 16 spacers placed between adjacent disks. Each disk is discretized into three mesh layers along the axial direction to ensure computational reliability. The corresponding 3D geometric model is illustrated in Figure 1.

Fig.1 Transformer 3D geometric modeling

• Distribution and Analysis of Leakage Magnetic Field and Electromagnetic Forces Under Short-Circuit Condition

This study employs the finite element method to investigate the transient electromagnetic characteristics of a split-disk winding transformer under high-to-medium voltage short-circuit (H-M) conditions. To reveal the development patterns of cumulative deformation effects, a stepwise increasing current excitation mode was adopted in the simulation, where the short-circuit current was incrementally raised from 60% to 105% of the rated value ^[22], with the rated short-circuit current being 1560 A. Based on a transient magnetic-circuit coupling simulation model, the initial simulation was conducted under 60% rated short-circuit current conditions. The time-domain variation of maximum magnetic flux density within 0.00–0.25 s after short-circuit initiation was obtained. The simulation results (Figure 2) indicate that the peak magnetic flux density reached 1.68 T at 0.01 s following the short-circuit event.

Fig.2 Time-domain Variation of Maximum Magnetic Flux

Given that the leakage magnetic field intensity and winding electromagnetic forces reach their peak values at 0.01 s after short-circuit initiation, this transient characteristic point was selected as the temporal reference for analysis. The magnetic flux density distribution at 0.01 s is analyzed as shown in Figure 3. It can be observed that the leakage flux exhibits significant spatial non-uniformity, being predominantly concentrated in the air duct region between the high-voltage (HV) and medium-voltage (MV) windings.

Fig.3 Leakage Flux Distribution on the xz-Plane at 0.01 s After Short-Circuit

To intuitively analyze the leakage magnetic field distribution characteristics of windings under short-circuit conditions, the average magnetic flux density data of disks inside and outside the iron core window in high- and medium-voltage windings at 0.01 s after short-circuit were extracted, as shown in Figure 4. The results demonstrate that the medium-voltage winding exhibits higher magnetic flux density than the high-voltage winding. The axial magnetic flux density distribution follows a “high-center, low-ends” pattern, with its peak located in the central region of the winding. In contrast, the radial magnetic flux density distribution displays distinct characteristics: near-zero values at the central area and larger magnitudes with opposite directions at both ends. Notably, the leakage flux density inside the iron core window is significantly higher than in external regions. This phenomenon primarily arises from the reluctance difference in leakage flux paths. The magnetic permeability of yokes is substantially higher than that of transformer oil and winding materials, enabling leakage flux paths closed via the upper and lower yokes to exhibit lower reluctance. Consequently, stronger leakage fields are generated under the same magnetomotive force.

(a) Axial Magnetic Flux Density Distribution

(b) Radial Magnetic Flux Density Distribution

Fig.4 Magnitude Distribution of Magnetic Flux Density at 0.01 s After Short-Circuit

The average electromagnetic forces of each disk in high-voltage (HV) and medium-voltage (MV) windings were extracted to investigate the magnitude and distribution of axial and radial electromagnetic forces at 0.01 s after short-circuit. The radial and axial short-circuit electromagnetic force distributions of HV and MV windings are shown in Figure 5. Comparative analysis of magnetic flux density distribution (Figure 4) and electromagnetic force distribution (Figure 5) reveals that axial electromagnetic forces exhibit spatial patterns similar to radial magnetic flux distributions. In contrast, radial electromagnetic forces align with axial magnetic flux distributions. The axial electromagnetic forces of HV and MV windings share the same direction, whereas their radial electromagnetic forces act in opposite directions. Specifically, the radial electromagnetic force on the HV winding is directed outward along the radius, subjecting it to expansive stress, while the radial electromagnetic force on the MV winding points toward the center, inducing compressive stress. Quantitative analysis indicates that the electromagnetic forces in the MV winding are generally larger than those in the HV winding. The maximum radial electromagnetic force in the MV winding reaches 10.456×10⁶ N/m³, whereas the HV winding’s maximum radial electromagnetic force is only 7.18×10⁶N/m³. Additionally, the radial components of electromagnetic forces in high- and medium-voltage windings are significantly higher than the axial components, with the maximum radial component exceeding the axial component by approximately one order of magnitude.

(a) Axial Electromagnetic Force Distribution

(b) Radial Electromagnetic Force Distribution

Fig.5 Lorentz Force Distribution at 0.01 s After Short-Circuit

3. Analysis of Mechanical Properties of Curved Copper and Spacer Materials

Based on short-circuit electromagnetic model calculations revealing that radial electromagnetic forces dominate winding deformation, this section further investigates the mechanical characteristics of high- and medium-voltage windings under inward compressive and outward expansive radial forces. Bidirectional bending tests were conducted to obtain stress-strain curves for both radial force modes, providing essential support for subsequent simulation studies on deformation behavior under short-circuit impacts.

• Stress-Strain Curve of Curved Copper

Transformer windings are constructed using curved copper conductors, whose geometric and mechanical properties play a critical role in the overall structural stability of the windings. In traditional studies, stress-strain curves of windings are typically obtained through tensile tests on straight copper conductors. However, this method can only characterize mechanical responses under uniaxial loading and fails to reflect the complex deformation mechanisms of actual transformer windings under different radial force modes. Specifically, medium-voltage windings are subjected to inward compressive stresses, making them prone to buckling instability, while high-voltage windings experience outward expansive stresses, exhibiting higher structural stability ^[23]. Direct application of tensile test data would lead to deviations between theoretical predictions and actual operating conditions.

This study conducted bending tests on curved copper conductors based on tensile tests to address this. The testing platform is shown in Figures 6(a) and (b). Using actual parallel-wound curved copper conductors from windings as test specimens, the radial force modes of high-voltage (outward expansive) and medium-voltage (inward compressive) windings were simulated. The stress-strain curves of copper material obtained from the bending tests are shown in Figure 7.

Fig. 6 Tensile and Radial Bending Test Platform

Fig.7 Stress-strain curves of copper conductors under different tests

Experimental results demonstrate that the stress-strain curves obtained from medium-voltage windings under inward compression differ significantly from those of high-voltage windings under outward expansion. The curved shape of high-voltage windings resembles that of uniaxial tensile tests, whereas the stress-strain curve of medium-voltage windings exhibits two critical points. The first critical point occurs at a strain of 0.0361 and a stress of 83 MPa, marking the onset of buckling instability, after which the load decreases with increasing deformation. The second critical point appears at a strain of 0.056 with stress dropping to 51 MPa, indicating the material entering a secondary stabilization phase where higher loads are required to drive further deformation. A comparison of the two curves reveals that curved copper under inward compression is more prone to structural instability, while outward expansion enhances its structural stability.

• Stress-Strain Curve of Spacer

The stress-strain curve of the spacer was obtained through compression tests, as shown in Figure 8. Unlike metallic materials, the spacer exhibits significant deformability during the initial loading stage. However, its deformation rate gradually decreases with increasing strain, eventually entering a stabilization phase characterized by nonlinear stiffness enhancement. This deformation behavior originates from the closure of internal microvoids and the densification and reorganization of fibrous structures within the spacer material during compression, leading to a transition in energy dissipation mechanisms from elasticity-dominated behavior to a synergistic interaction of interfacial friction and microcrack propagation.

Fig.8 Acquisition of Spacer Stress-Strain Curve

4. Analysis of Cumulative Deformation and First-Layer Failure Locations in Windings Under Short-Circuit Conditions
   • Theoretical Analysis of Coupled Magnetic and Structural Fields in Transformer

Under short-circuit or overload conditions, transformer windings are subjected to high short-circuit currents, generating substantial electromagnetic forces. According to the Lorentz force law, the interaction between short-circuit currents and the magnetic field within the windings produces significant mechanical forces. These forces act on the winding structure, potentially causing displacement, deformation, or damage. Traditional structural analysis considers only mechanical stress while neglecting the influence of electromagnetic fields. In contrast, the coupled magnetic and structural field theory integrates both aspects, comprehensively representing the winding’s stress and deformation states.

The magnetic field in transformers can be described by Maxwell’s equations, typically categorized as low-frequency electromagnetic fields. To simplify calculations, the magnetic vector potential A is employed to represent the magnetic field. The governing equation for the magnetic field is:

Where μ is the magnetic permeability of the material in H/m, and J represents the current density in A/m². This equation can be used to calculate the leakage magnetic field distribution within the windings.

In the structural field, electromagnetic forces act as an external force on the winding structure, resulting in its deformation. The structural field satisfies the equilibrium equation:

Where σ is the stress tensor in Pa, F represents the force density generated by the electromagnetic field in N/m³. Through the stress-strain relationship, the deformation and displacement of the windings can be determined.

The magnetic and structural fields are coupled through the Lorentz force, which is expressed as:

Where B is the magnetic flux density in T, and J represents the current density in A/m². The distribution of current within the windings and the forces generated by the magnetic field directly influence the mechanical deformation of the windings.

The relationship between strain and stress can be described by the constitutive relation of linear elastic materials:

Where ϵ_ij is the strain tensor; ν denotes Poisson’s ratio; E is Young’s modulus in Pa; σ_ij represents the components of the stress tensor in Pa; and σ_kk is the volumetric stress in Pa.

When a material enters the yield stage, it transitions from elastic to plastic deformation. The Von Mises yield criterion, also known as the energy yield criterion, posits that material yielding occurs when the equivalent stress (referred to as von Mises stress) reaches the yield stress. The Von Mises yield criterion is used to determine whether a material yields under multiaxial stress states:

Where σ₁, σ₂, and σ₃ are the principal stresses in Pa; σ_e is the equivalent stress in Pa.

Under the Von Mises yield criterion, the expression for the equivalent plastic strain is defined as follows:

Where ε₁, ε₂, and ε₃ are the principal strains; ε_e is the equivalent strain.

• Deformation Analysis of Windings Under Single Short-Circuit Impact

Based on the stress-strain curves of curved copper obtained from bending tests, this study established a magnetic-solid mechanics coupling model under H-M three-phase short-circuit conditions with 60% rated short-circuit current. The overall deformation distribution of high- and medium-voltage windings at 0.01 s after the short-circuit event is shown in Figure 9. The results indicate that the deformation primarily concentrates in the middle region of the windings, exhibiting significant radial characteristics: the high-voltage winding demonstrates an outward expansion trend, while the medium-voltage winding shows an inward compression tendency. Due to the influence of yokes, the deformation magnitude of the winding portions inside the iron core window exceeds that of the sections outside the iron core window.

(a) High-Voltage Winding    (b) Medium-Voltage Winding

Fig.9 Winding Deformation Distribution at 0.01 s

To further investigate weak points in each disk layer, circumferential strain analysis was performed on the middle-layer disk and its upper spacer, as shown in Figure 10. The results reveal that the maximum principal strain in the winding concentrates at both ends of the contact area between the winding and spacer, while the spacer strain focuses on the contact edges. These high-strain regions are identified as potential weak points for circumferential structural instability and plastic damage, necessitating targeted reinforcement through material strengthening or geometric improvements in optimized designs.

(a) Disk                       (b) Upper Spacer

Fig.10 Principal Strain Distribution of Middle-Layer Disk and Its Upper Spacer

• Cumulative Deformation Results and Analysis of Windings and Spacers Under Multiple Short-Circuit Impacts

Under multiple short-circuit impacts, the cumulative deformation laws and first-layer failure locations of windings and spacers hold significant research importance. This section investigates the deformation distributions and mechanical responses of windings and spacers under different short-circuit current percentages (60%, 70%, 80%, 90%, 100%, and 110%) through simulation and analysis, revealing their mechanical behavior and structural characteristics.

4.3.1 Deformation Results and Analysis of Windings After Multiple Short-Circuit

Figure 11 demonstrates the contribution magnitude of maximum Lorentz forces in high-voltage and medium-voltage windings under different short-circuit current percentages (60%, 70%, 80%, 90%, 100%, and 110%). From the figure, it can be observed that the contribution of Lorentz forces shows an approximately proportional increase with rising short-circuit current.

Fig.11 Maximum Lorentz Force-Short Circuit Current Percentage

Figure 12 illustrates the variation of the maximum cumulative deformation values in each winding layer after each short-circuit impact as a function of short-circuit current. Despite the nearly proportional growth in Lorentz force contributions, the deformation magnitude of the windings does not exhibit entirely linear variation. This nonlinear behavior is primarily determined by the complex mechanical responses of windings under short-circuit impacts, including nonlinear deformation, stress stiffening effects, and material properties.

The results demonstrate that even under the highest 110% short-circuit current, the deformation of the high-voltage winding remains minimal, with a maximum deformation of only 1.69 mm, indicating its superior structural stability. In contrast, the medium-voltage winding exhibits significantly more severe deformation with a maximum value of 8.46 mm, necessitating further analysis of its internal mechanical behavior and deformation mechanisms. Specifically, under the 90% short-circuit current condition, abrupt deformations occur in all disk layers of the medium-voltage winding except the 1st and 9th layers, with the most drastic deformation observed in the middle of the layer disks.

(a) Deformation-Short Circuit Current for Each Layer of High-Voltage Winding

(b) Deformation-Short Circuit Current for Each Layer of Medium-Voltage Winding

Fig.12 Variation of Each Winding Layer with Short Circuit Current

Based on the analysis above, it can be inferred that the high-risk locations for first-layer failure are primarily concentrated in the middle-layer positions (Layers 4, 5, and 6) of the medium-voltage winding. Combined with the circumferential strain distribution analysis in Figure 12(a), the edge of the contact interface between this region and the spacers initiates material damage due to circumferential strain concentration, confirming this area as the failure weak point that requires prioritized attention in structural design and optimization.

4.3.2 Cumulative Deformation Process of Spacers and Prediction of First-Layer Failure Locations

Spacers exhibit concurrent failure characteristics with windings in cumulative deformation under short-circuit impacts. Figure 13 shows the variation of maximum deformation of high- and medium-voltage spacers with short-circuit current. The results reveal that the cumulative deformation amplitude of high-voltage spacers is significantly smaller than that of medium-voltage spacers. The deformation amplitude of medium-voltage spacers increases markedly with rising short-circuit current, particularly in regions where winding deformation is pronounced (middle layers), where spacer deformation becomes equally severe. This further verifies the significant concurrent failure behavior between windings and spacers. Such concurrent failure mechanisms reflect the complex mechanical interactions and stress transfer patterns between windings and spacers, providing theoretical support for further analysis of localized dynamic deformation characteristics and offering critical guidance for optimizing the design of transformer support structures.

(a) Spacer Displacement-Short Circuit Current for Each Layer of High-Voltage Winding

(b) Spacer Deformation-Short Circuit Current for Each Layer of Medium-Voltage Winding

Fig.13 Spacer Displacement Variation with Short Circuit Current

5. Multiple Short-Circuit Impact Testing and Model Validation of Transformers
   • Leakage Flux Measurement Test

This study conducted short-circuit impact testing on a decommissioned transformer (Model SFSZ7-31500/110) to validate the reliability of simulation results. The experiment strictly complied with the National Standard GB/T 1094.5-2008, focusing on monitoring changes in the internal leakage magnetic field distribution of windings during short-circuit events.

Leakage flux sensors were installed at six critical positions, including the Phase B yokes and core columns of the transformer. The electromagnetic induction method was employed to acquire magnetic flux density in real time during short-circuit events through inverse integration of induced electromotive force. The sensors were multi-turn air-core coils with dimensions of 10×50 mm, securely fixed inside the transformer using encapsulation adhesive to ensure stability during testing. These measurement points were strategically selected to capture windings’ most significant leakage flux variations, particularly peak magnetic fields during short-circuit impacts.

Fig.14 Leakage Flux Sensor Installation Locations

In the experiment, the transformer was connected to a single-phase equivalent short-circuit test circuit. The high-voltage and medium-voltage windings of Phase B were short-circuited, while the low-voltage winding was kept open-circuited, consistent with the simulation conditions. The short-circuit duration was set to 250 ms to simulate actual fault conditions. A high-frequency data acquisition system recorded the leakage magnetic field outputs from the sensors and the short-circuit current waveforms in the windings in real-time at a sampling rate of 10 kHz.

Fig.15 Leakage Flux Measurement Waveforms of Short-Circuit Test

The simulation incorporated point probes into the model in coordinate form based on the installation positions of leakage flux sensors in the experimental setup, calculating the leakage magnetic flux density at corresponding test measurement points. The variation of internal spatial leakage magnetic fields during a sudden three-phase short-circuit in the transformer was computed. The model was validated by comparing the measured and calculated leakage flux peak values under short-circuit conditions. The results are shown in Table 2.

Table 2 Summary of Leakage Flux Measurement Results

As shown in Table 2, by comparing the calculated leakage flux density from the simulation with the measured values in the experiment, the simulation results at all selected leakage flux measurement points exhibit good agreement with the experimental data. The maximum error occurs at measurement point 3, reaching 6.5%, while all errors in leakage flux density across the groups remain within 10%, meeting engineering requirements. The experimental results validate the effectiveness of the electromagnetic analysis in the established model and the accuracy of the computational results, thereby laying a foundation for studying the deformation characteristics of transformer windings.

• Cumulative Deformation Analysis Based on Multiple Short-Circuit Impact Tests

Following the short-circuit impact tests described in 5.1, the reactance variation rate of windings was measured. Multiple short-circuit impact tests were conducted by sequentially increasing the Phase B high-voltage side current from 60% to 105% of the short-circuit current. Each short-circuit impact lasted 250 ± 25 ms, with a 20-minute interval between consecutive tests. After each test, the reactance variation rate of windings was measured to assess damage severity. A reactance variation rate exceeding 2% was considered indicative of winding damage.

Table 3 presents the test currents and reactance variation rates of high- and medium-voltage windings. Line charts were plotted to visually observe trends in reactance variation rate with the number of short-circuit events (Figure 16). Experimental results show that when subjected to 90% short-circuit current, the reactance variation rate of the medium-voltage winding abruptly increased from 0.18% to 0.65%, suggesting significant mechanical deformation or local instability. At 100% short-circuit current, the reactance variation rate of the medium-voltage winding further surged to 1.58%. As the current reached 105%, the growth rate of reactance variation gradually slowed, indicating that the winding entered a hardening phase with markedly enhanced deformation resistance.

Post-test inspections revealed severe compression damage at both ends of the medium-voltage winding, with critical failure observed in its middle-layer region, as illustrated in Figure 16. In contrast, the high-voltage winding showed no significant damage under all tested conditions. These results align closely with simulation predictions, confirming the reliability of the proposed model in predicting winding damage and mechanical states.

Table 3 Short-Circuit Impact Test Data

Fig.16 Impedance Variation Rate-Number of Short Circuit Events

6. Conclusions

This study proposes a split-disk winding model incorporating spacer material properties and accounting for stress-dependent variations in copper mechanical behavior, systematically investigating cumulative deformation patterns and first-layer failure locations in transformer windings under multiple short-circuit impacts through finite element simulations and experimental validation. Key findings are summarized as follows:

1）Considering the differences in radial force modes between high- and medium-voltage windings, stress-strain curves derived from bending tests exhibit significant distinctions. The high-voltage winding, subjected to radial expansive stress, demonstrates a yield strength of 210 MPa and superior structural stability. In contrast, the medium-voltage winding under radial compressive stress shows weaker deformation resistance, with more pronounced cumulative deformation.

2）Simulation results indicate that the cumulative deformation of the medium-voltage winding begins to increase significantly at 90% short-circuit current. When the current reaches 110%, the maximum cumulative deformation reaches 8.46 mm, with the growth rate gradually decreasing as the winding enters a hardening phase and its deformation resistance strengthens. Comparatively, the high-voltage winding maintains minimal deformation due to its robust structural stability. Validation through short-circuit impulse tests confirms high consistency between simulation results and experimental data, further verifying the model’s accuracy and reliability.

3）The split-disk winding model effectively characterizes concurrent failure behavior between windings and spacers and accurately captures deformation under complex loading conditions. It particularly excels in predicting first-layer failure locations. Simulations reveal that first-layer failure zones concentrate in the middle layers of windings, with strain primarily localized at winding-spacer contact regions. High-strain areas at the edge of the contact interface between the winding and the spacers are identified as potential instability and weak points for deformation.

In summary, the proposed split-disk model combined with bending test methodologies provides a robust framework for analyzing cumulative deformation mechanisms and first-layer failure locations in transformer windings under multiple short-circuit impacts. This research offers critical theoretical foundations and engineering guidelines for optimizing short-circuit resistance and transformers’ structural design, significantly enhancing power equipment’s operational safety.

AUTHOR CONTRIBUTIONS

Ping Wang: Conceptualization; methodology; validation; writing – original draft preparation; writing – review and editing. Zidi Pan: Validation; writing – original draft; writing – review and editing. Zihe Jiang: Methodology; validation; writing – review and editing. Jianghai Geng: Conceptualization; validation; writing – review and editing. Shuguo Gao: writing – review and editing. Zikang Zhang: writing – review and editing.

ACKNOWLEDGMENTS

None

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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