Design and Mechanical Strength Verification of Short-Circuit Withstand Capability for Power Transformers

1. Introduction
Power transformers are critical components in electrical power systems, responsible for transmitting and distributing electrical energy efficiently across different voltage levels. However, during their operational lifespan, transformers frequently encounter abnormal operating conditions, among which short-circuit faults are the most destructive. A short-circuit fault in a power system generates extremely high short-circuit currents, which induce intense electromagnetic forces (EMFs) in the transformer's windings and core. These forces can lead to severe mechanical deformation, insulation damage, or even complete failure of the transformer if its design fails to withstand such stresses.
The short-circuit withstand capability of a power transformer directly determines the reliability, safety, and service life of the entire power grid. According to statistics from the International Council on Large Electric Systems (CIGRE), approximately 30% of transformer failures worldwide are attributed to insufficient short-circuit withstand capability. In recent years, with the rapid expansion of power grids and the increasing penetration of renewable energy sources (such as wind and solar power), the complexity of system operations has escalated, making short-circuit faults more frequent and unpredictable. This has further highlighted the urgency of optimizing the design of transformers' short-circuit withstand capability and enhancing the rigor of mechanical strength verification.
This paper systematically explores the key design principles for improving the short-circuit withstand capability of power transformers, focusing on winding structure optimization, material selection, and electromagnetic force calculation. Additionally, it details the methods and standards for mechanical strength verification, including static and dynamic stress analysis, finite element simulation, and prototype testing. By integrating theoretical analysis with practical engineering cases, this study aims to provide technical guidance for transformer manufacturers and power system operators to enhance the robustness of transformers against short-circuit faults.
2. Key Design Factors for Short-Circuit Withstand Capability
The short-circuit withstand capability of a power transformer is primarily determined by its ability to resist the mechanical stresses induced by short-circuit currents. The design process must comprehensively consider the generation mechanism of electromagnetic forces, the mechanical properties of materials, and the structural stability of components. The following sections elaborate on the core design factors.
2.1 Electromagnetic Force Calculation
When a short-circuit fault occurs, the short-circuit current flowing through the transformer's primary and secondary windings generates a strong magnetic field. The interaction between the current and the magnetic field produces two types of electromagnetic forces: radial forces and axial forces.

  • Radial Forces: Radial forces act perpendicular to the axis of the windings. In a typical concentric winding structure, the magnetic field generated by the inner winding exerts an outward radial force on the inner winding, while the outer winding experiences an inward radial force. The magnitude of the radial force is proportional to the square of the short-circuit current and the number of turns in the windings. Mathematically, the radial force per unit length of the winding can be expressed as:

    Fr=2π⋅rμ0⋅Isc2⋅N

where
μ0
 is the permeability of free space (
4π×10−7H/m
),
Isc
 is the rms value of the short-circuit current,
N
 is the number of turns, and
r
 is the average radius of the winding. Radial forces tend to cause the inner winding to expand and the outer winding to contract, which may lead to winding deformation, such as bulging or collapsing.

  • Axial Forces: Axial forces act parallel to the axis of the windings and are primarily caused by the non-uniform distribution of the magnetic field along the height of the windings. In transformers with fractional turns or uneven winding arrangements, the axial magnetic flux density varies, resulting in a net axial force. The axial force can be calculated using the formula:

    Fa=21⋅μ0⋅Bax⋅Isc⋅L

where
Bax
 is the axial magnetic flux density and
L
 is the effective length of the winding. Axial forces may cause the windings to shift vertically, compress the insulation pads between winding discs, or even damage the lead connections.
Accurate calculation of these electromagnetic forces is the foundation of the design process. Modern transformer design software, such as ANSYS Maxwell and COMSOL Multiphysics, utilizes finite element analysis (FEA) to simulate the magnetic field distribution and calculate the electromagnetic forces with high precision. These tools consider factors such as core saturation, winding geometry, and current waveform, ensuring that the calculated forces reflect real-world operating conditions.
2.2 Winding Structure Design
The winding structure is a critical determinant of the transformer's ability to withstand short-circuit forces. Different winding types, such as concentric windings, layer windings, and helical windings, exhibit varying mechanical strengths and electromagnetic characteristics. The selection and optimization of the winding structure must balance electrical performance (e.g., copper loss, insulation reliability) and mechanical robustness.

  • Concentric Windings: Concentric windings are the most widely used structure in power transformers due to their simplicity and excellent electrical performance. To enhance short-circuit withstand capability, the design of concentric windings should focus on the following aspects:

  • Winding Support: The windings should be supported by rigid insulation cylinders and end rings to resist radial expansion and contraction. The insulation cylinders, typically made of pressboard or epoxy resin, must have sufficient compressive strength (usually ≥ 15 MPa) to withstand the radial forces.

  • Disc-to-Disc Insulation: In disc-type concentric windings, the insulation pads between adjacent discs play a crucial role in transmitting axial forces. The pads should be made of high-density insulation materials (e.g., TIVAR®) with low creep deformation under compression. The number and arrangement of the pads should be optimized to ensure uniform force distribution.

  • Winding Tightness: The windings must be tightly wound to minimize the gap between turns, which reduces the risk of turn-to-turn displacement under radial forces. During the manufacturing process, the windings are often pre-compressed using hydraulic presses to achieve a tight structure.

  • Helical Windings: Helical windings are commonly used in low-voltage, high-current transformers (e.g., distribution transformers) due to their low AC resistance. However, their mechanical strength against short-circuit forces is relatively low compared to concentric windings. To improve their short-circuit withstand capability, helical windings are often designed with:

  • Axial Stiffeners: Metal or insulation stiffeners are inserted between the winding layers to enhance axial rigidity and prevent layer shifting.

  • End Clamps: Rigid end clamps made of steel or aluminum alloy are used to secure the winding ends, reducing the impact of axial forces on the lead connections.

2.3 Material Selection
The selection of high-performance materials is essential for improving the mechanical strength of transformers. The key materials involved in the design include conductor materials, insulation materials, and structural materials.

  • Conductor Materials: The windings are typically made of copper or aluminum conductors. Copper conductors have higher mechanical strength (tensile strength: 200–300 MPa) and better electrical conductivity compared to aluminum conductors (tensile strength: 100–150 MPa). However, aluminum conductors are more cost-effective and lighter, making them suitable for large transformers where weight reduction is a priority. To enhance the mechanical strength of aluminum windings, alloying elements such as magnesium and silicon are often added, increasing their tensile strength to 180–250 MPa.

  • Insulation Materials: Insulation materials not only provide electrical insulation but also contribute to the mechanical stability of the windings. The main insulation materials used include:

  • Pressboard: Pressboard is a widely used insulation material for winding supports and end rings. It has high compressive strength (≥ 20 MPa) and good thermal stability (continuous operating temperature: 105°C for class A insulation).

  • Epoxy Resin: Epoxy resin-based composites, such as glass fiber-reinforced epoxy (GFRE), are used for high-voltage transformers due to their excellent mechanical strength (flexural strength: ≥ 150 MPa) and chemical resistance. GFRE insulation cylinders can withstand higher radial forces than traditional pressboard cylinders.

  • Nomex Paper: Nomex paper (aramid fiber paper) is used for turn-to-turn insulation in high-temperature transformers (class H insulation, continuous operating temperature: 180°C). It has high tensile strength (≥ 200 MPa) and good dimensional stability, reducing the risk of insulation damage under mechanical stress.

  • Structural Materials: Structural materials, such as the transformer tank, core clamps, and winding supports, must have sufficient rigidity to withstand the mechanical vibrations and forces induced by short-circuit currents. The tank is typically made of low-carbon steel (e.g., Q235) with a thickness of 6–12 mm, depending on the transformer's rating. Core clamps are made of high-strength steel (e.g., Q345) to secure the core laminations and prevent core displacement under electromagnetic forces.

3. Mechanical Strength Verification Methods
Mechanical strength verification is a critical step in ensuring that the transformer design meets the required short-circuit withstand capability. It involves both theoretical analysis and experimental testing to evaluate the structural integrity of the transformer under short-circuit conditions. The following sections introduce the main verification methods.
3.1 Static Stress Analysis
Static stress analysis focuses on evaluating the maximum stress and deformation of the transformer's components under the steady-state electromagnetic forces generated by short-circuit currents. This analysis assumes that the short-circuit current is constant (i.e., ignoring the transient effects of current decay) and uses static structural mechanics principles to calculate the stress distribution.
The process of static stress analysis typically involves the following steps:

  1. Modeling: A 3D finite element model of the transformer's windings, core, and structural components is constructed using FEA software (e.g., ANSYS Mechanical, Abaqus). The model includes detailed geometry, material properties (e.g., Young's modulus, Poisson's ratio), and boundary conditions (e.g., fixed supports at the tank base).

  1. Force Application: The electromagnetic forces calculated in Section 2.1 (radial and axial forces) are applied to the winding model as distributed loads. The forces are mapped to the finite element mesh based on the magnetic field distribution.

  1. Stress Calculation: The FEA software solves the static equilibrium equations to calculate the stress distribution (e.g., von Mises stress) and deformation of the components. The von Mises stress is used to evaluate the mechanical strength of ductile materials (such as copper and steel) since it accounts for the combined effects of tensile, compressive, and shear stresses.

  1. Strength Check: The maximum von Mises stress in each component is compared to the allowable stress of the material. The allowable stress is typically set as a fraction of the material's yield strength (e.g., 60–80% of the yield strength) to ensure a sufficient safety margin. For example, if the yield strength of copper is 150 MPa, the allowable stress may be set to 90 MPa (60% of the yield strength). If the maximum calculated stress is less than the allowable stress, the component is considered to meet the mechanical strength requirements.

Static stress analysis is widely used in the early design stage to identify potential weak points in the structure, such as areas with high stress concentration. For example, the corners of the winding end rings and the lead connection points are often areas of high stress and may require design modifications (e.g., adding fillets to reduce stress concentration).
3.2 Dynamic Stress Analysis
Unlike static stress analysis, dynamic stress analysis considers the transient nature of short-circuit currents and the dynamic response of the transformer structure. Short-circuit currents typically have a high initial peak value (up to 20–30 times the rated current) followed by a decay to a steady-state value. This transient current induces time-varying electromagnetic forces, which can cause the windings and core to vibrate dynamically. The dynamic response of the structure may lead to higher stress levels than those calculated in static analysis, especially if the natural frequency of the structure is close to the frequency of the transient forces (resonance effect).
Dynamic stress analysis involves the following key steps:

  1. Transient Electromagnetic Force Calculation: The time-varying short-circuit current waveform is obtained from power system simulations (e.g., using PSCAD/EMTDC or ETAP). The electromagnetic forces are calculated at each time step based on the current waveform and the magnetic field distribution.

  1. Modal Analysis: A modal analysis is performed to determine the natural frequencies and mode shapes of the transformer structure. The natural frequency is the frequency at which the structure vibrates freely, and the mode shape describes the pattern of vibration. For transformers, the natural frequencies of the windings typically range from 50 Hz to 500 Hz, depending on the winding size and support structure.

  1. Transient Dynamic Analysis: The transient electromagnetic forces are applied to the finite element model, and the dynamic response (displacement, velocity, acceleration, and stress) of the structure is calculated over time. The analysis considers the material damping (typically 2–5% for insulation materials) to simulate the energy dissipation during vibration.

  1. Resonance Check: The dynamic stress analysis checks for resonance by comparing the frequency of the transient forces to the natural frequencies of the structure. If the force frequency is within 10–20% of a natural frequency, resonance may occur, leading to a significant increase in stress and deformation. In such cases, the design must be modified to shift the natural frequency away from the force frequency (e.g., by increasing the stiffness of the winding supports).

Dynamic stress analysis is particularly important for large power transformers (rated power ≥ 100 MVA) since their large size and low stiffness make them more susceptible to dynamic vibrations. For example, a 500 kV transformer with a winding height of 3 meters may have a natural frequency of 100 Hz, which is close to the frequency of the transient short-circuit forces (50 Hz or 60 Hz, depending on the power system frequency). Resonance in such cases can cause the windings to vibrate violently, leading to insulation damage and winding deformation.
3.3 Prototype Testing
Prototype testing is the most direct and reliable method to verify the short-circuit withstand capability of a transformer. It involves subjecting a physical prototype to simulated short-circuit conditions and measuring the mechanical and electrical performance of the transformer before and after the test. Prototype testing is required by international standards, such as IEC 60076-5 (Power transformers – Part 5: Ability to withstand short circuit) and IEEE C57.12.90 (Standard Test Code for Liquid-Immersed Distribution, Power, and Regulating Transformers).
The main types of prototype tests for short-circuit withstand capability include:

  1. Short-Circuit Current Test: In this test, the transformer is connected to a short-circuit test system that can generate the rated short-circuit current. The test current is applied to the transformer's windings for a specified duration (typically 2–3 seconds) to simulate a short-circuit fault. During the test, the following parameters are measured:

  • Winding temperature rise (to ensure that the insulation is not damaged by excessive heat).

  • Vibration and noise levels (to evaluate the dynamic response of the structure).

  • Winding deformation (using techniques such as low-voltage impulse testing or winding resistance measurement).

  1. Impact Test: The impact test is designed to simulate the high initial peak current of a short-circuit fault. The test involves applying a high-current impulse (peak value up to 100 kA) to the windings for a short duration (typically 10–20 ms). After the test, the transformer is inspected for mechanical damage, such as winding displacement, insulation cracking, or lead breakage.

  1. Destructive Test: In some cases, destructive tests are performed to determine the ultimate short-circuit withstand capability of the transformer. The test current is gradually increased until the transformer fails (e.g., insulation breakdown or winding deformation). The results of destructive tests are used to validate the design assumptions and improve the safety margin of the transformer.

Prototype testing provides valuable data that cannot be obtained from theoretical analysis alone. For example, during a short-circuit current test, it may be discovered that the winding end rings have higher stress levels than predicted by the FEA model, indicating a need to increase the thickness of the end rings. Additionally, testing can reveal manufacturing defects (e.g., loose winding supports) that may compromise the transformer's mechanical strength.


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