29-03 2026
Calculation Method of Short-Circuit Withstand Capability for High-Voltage Switchgear
Calculation Method of Short-Circuit Withstand Capability for High-Voltage Switchgear
High-voltage switchgear is the core equipment of power transmission and distribution systems, which undertakes the functions of power distribution, control, protection and isolation in high-voltage power grids. The short-circuit withstand capability is one of the most critical performance indicators of high-voltage switchgear, which directly determines the safety and stability of the entire power system when a short-circuit fault occurs. A short-circuit fault in the power grid will generate a huge short-circuit current, which will cause severe thermal and electrodynamic effects on the switchgear, leading to equipment damage, power outages, and even serious safety accidents if the switchgear cannot withstand the impact. Therefore, accurately calculating the short-circuit withstand capability of high-voltage switchgear is of great significance for equipment design, selection, operation and maintenance, and plays a key role in ensuring the safe and reliable operation of the power system.
This article focuses on the calculation method of short-circuit withstand capability for high-voltage switchgear, elaborates on the basic principles, core calculation content, specific calculation steps and verification methods, combines relevant international and domestic standards, and provides a scientific, systematic and operable calculation framework. The total word count is about 1500 words, which is suitable for engineering and technical personnel engaged in power equipment design, operation and maintenance to reference and apply.
1. Basic Principles of Short-Circuit Withstand Capability
The short-circuit withstand capability of high-voltage switchgear refers to the ability of the switchgear to withstand the thermal effect and electrodynamic effect generated by the short-circuit current within a specified time without being damaged or losing its normal operating performance. The short-circuit fault in the power grid is usually sudden and transient, and the short-circuit current is composed of two parts: the periodic component and the non-periodic component. The periodic component is a steady-state alternating current generated by the power grid, while the non-periodic component is a transient direct current generated by the energy storage of the inductive component in the power grid, which decays exponentially with time.
The damage of short-circuit current to high-voltage switchgear is mainly reflected in two aspects: thermal effect and electrodynamic effect. The thermal effect is caused by the Joule heat generated by the short-circuit current passing through the conductor, which may lead to the overheating, melting or even burning of the conductor and insulation materials. The electrodynamic effect is caused by the electromagnetic force generated between the conductors carrying the short-circuit current, which may lead to the deformation, displacement or even fracture of the conductor, busbar and other components. Therefore, the calculation of short-circuit withstand capability mainly includes the calculation of thermal withstand capability and electrodynamic withstand capability, and both need to meet the requirements of relevant standards (such as IEC 62271-200, GB 3906-2020).
2. Core Calculation Content of Short-Circuit Withstand Capability
The calculation of short-circuit withstand capability for high-voltage switchgear mainly includes three core parts: short-circuit current calculation, thermal withstand capability calculation and electrodynamic withstand capability calculation. Among them, the short-circuit current calculation is the basis, and the thermal and electrodynamic withstand capability calculations are carried out based on the calculated short-circuit current parameters.
2.1 Short-Circuit Current Calculation
The short-circuit current is the premise of calculating the short-circuit withstand capability, and its accurate calculation directly affects the reliability of the subsequent calculation results. The short-circuit current calculation mainly includes the calculation of the short-circuit current peak value, the short-circuit current effective value (rms value) and the short-circuit current duration.
First, the short-circuit current peak value ($$I_{pk}$$) is the maximum instantaneous value of the short-circuit current, which is mainly determined by the non-periodic component. The calculation formula is: $$I_{pk} = \sqrt{2}I''K$$, where $$I''$$ is the initial short-circuit current effective value (symmetrical short-circuit current at the moment of short-circuit), and $$K$$ is the peak coefficient. For AC power grids with a frequency of 50Hz, the peak coefficient $$K$$ is usually 1.8-2.5; for power grids with large inductive reactance, $$K$$ can be taken as 2.5, and for power grids with small inductive reactance, $$K$$ can be taken as 1.8.
Second, the short-circuit current effective value ($$I_{sc}$$) is the effective value of the short-circuit current within the specified duration, which is used to calculate the thermal effect. The calculation formula is: $$I_{sc} = \frac{I''}{\sqrt{1 + (2\alpha)^2}}$$, where $$\alpha$$ is the decay coefficient of the non-periodic component, which is related to the time constant of the power grid. The time constant $$\tau$$ is usually 0.05-0.2s for high-voltage power grids, and $$\alpha = e^{-t/\tau}$$, where $$t$$ is the short-circuit duration.
Third, the short-circuit duration is the time from the occurrence of the short-circuit fault to the cut-off of the short-circuit current by the protection device, which is usually determined according to the setting of the protection system. For high-voltage switchgear, the standard short-circuit duration is usually 1s, 2s or 3s, and the specific value is determined according to the grade of the switchgear and the requirements of the power system.
2.2 Thermal Withstand Capability Calculation
The thermal withstand capability of high-voltage switchgear refers to the ability of the conductor, busbar and other components to withstand the thermal effect of the short-circuit current without melting or damaging the insulation. The calculation of thermal withstand capability is based on the principle of thermal balance, that is, the heat generated by the short-circuit current is equal to the heat absorbed by the conductor (ignoring the heat dissipation during the short-circuit duration, because the short-circuit time is short and the heat dissipation is negligible).
The core calculation formula of thermal withstand capability is the thermal effect equation: $$I_{th}^2t = \int_{0}^{t}I_{sc}^2dt$$, where$$I_{th}$$ is the thermal withstand current effective value of the switchgear, $$t$$ is the short-circuit duration, and $$I_{sc}$$ is the short-circuit current effective value changing with time.
In practical engineering calculations, the short-circuit current is usually regarded as a constant effective value within the short-circuit duration, so the formula can be simplified to: $$I_{th}^2t = I_{sc}^2t$$, that is, $$I_{th} = I_{sc}$$. However, this simplification is only applicable when the short-circuit duration is short (less than 1s) and the non-periodic component decays quickly. For longer short-circuit durations, the decay of the short-circuit current needs to be considered, and the integral calculation is required.
In addition, the thermal withstand capability of the switchgear also needs to consider the maximum allowable temperature of the conductor and insulation materials. For copper conductors, the maximum allowable temperature during short-circuit is usually 250°C, and for aluminum conductors, it is 200°C. If the temperature generated by the short-circuit current exceeds the maximum allowable temperature, the conductor will melt or the insulation will be damaged, and the switchgear will lose its short-circuit withstand capability.
2.3 Electrodynamic Withstand Capability Calculation
The electrodynamic withstand capability of high-voltage switchgear refers to the ability of the conductor, busbar, support insulator and other components to withstand the electromagnetic force generated by the short-circuit current without deformation, displacement or fracture. The electromagnetic force between two parallel conductors carrying current is the main factor affecting the electrodynamic withstand capability, and its calculation is based on Ampere's law.
The electromagnetic force per unit length between two parallel conductors is calculated by the formula: $$F = 2\times10^{-7}\frac{I_1I_2}{a}$$, where $$F$$ is the electromagnetic force per unit length (N/m), $$I_1$$ and $$I_2$$ are the currents in the two conductors (A), and $$a$$ is the distance between the two conductors (m). For high-voltage switchgear, the busbar is usually composed of multiple parallel conductors, and the total electromagnetic force on the busbar is the sum of the electromagnetic forces between each pair of conductors.
The peak value of the electromagnetic force is calculated by using the peak value of the short-circuit current: $$F_{pk} = 2\times10^{-7}\frac{I_{pk1}I_{pk2}}{a}$$. Since the short-circuit current in the same phase busbar is in the same direction, the electromagnetic force between them is attractive; while the current in the adjacent phase busbar is in the opposite direction, the electromagnetic force between them is repulsive. The maximum electromagnetic force usually occurs at the moment of the short-circuit current peak value.
After calculating the electromagnetic force, it is necessary to check the mechanical strength of the busbar and support insulator. The busbar should be checked for bending strength and torsional strength, and the support insulator should be checked for compressive strength and tensile strength. If the calculated electromagnetic force is less than the allowable mechanical strength of the components, the switchgear meets the electrodynamic withstand requirement; otherwise, the structure of the busbar or support insulator needs to be optimized (such as increasing the cross-sectional area of the busbar, reducing the distance between conductors, or increasing the number of support insulators).
3. Specific Calculation Steps
The calculation of the short-circuit withstand capability for high-voltage switchgear is carried out in the following four steps, which are logical and operable, and can ensure the accuracy of the calculation results.
3.1 Determine the Calculation Parameters
First, collect the relevant parameters of the power grid and switchgear, including: the rated voltage of the power grid ($$U_n$$), the short-circuit capacity of the power grid ($$S''$$), the time constant of the power grid ($$\tau$$), the rated current of the switchgear ($$I_n$$), the cross-sectional area of the busbar ($$S$$), the material of the busbar (copper or aluminum), the distance between the busbars ($$a$$), and the short-circuit duration ($$t$$). These parameters are the basis for the subsequent calculation, and need to be accurately collected according to the actual engineering situation and relevant design documents.
3.2 Calculate the Short-Circuit Current Parameters
Based on the collected power grid parameters, calculate the initial short-circuit current effective value ($$I''$$), short-circuit current peak value ($$I_{pk}$$) and short-circuit current effective value ($$I_{sc}$$) within the specified duration. The calculation steps are as follows:
1. Calculate the initial short-circuit current effective value: $$I'' = \frac{S''}{\sqrt{3}U_n}$$, where $$S''$$ is the short-circuit capacity of the power grid, and $$U_n$$ is the rated voltage of the power grid.
2. Determine the peak coefficient ($$K$$) according to the power grid inductive reactance, and calculate the short-circuit current peak value: $$I_{pk} = \sqrt{2}I''K$$.
3. Calculate the decay coefficient of the non-periodic component ($$\alpha = e^{-t/\tau}$$), and then calculate the short-circuit current effective value within the short-circuit duration: $$I_{sc} = \frac{I''}{\sqrt{1 + (2\alpha)^2}}$$.
3.3 Calculate Thermal Withstand Capability
According to the calculated short-circuit current effective value ($$I_{sc}$$) and short-circuit duration ($$t$$), calculate the thermal effect of the short-circuit current, and check whether the switchgear meets the thermal withstand requirement. The calculation steps are as follows:
1. Calculate the thermal effect value: $$Q = I_{sc}^2t$$.
2. Check the thermal withstand current of the switchgear: the thermal withstand current effective value ($$I_{th}$$) of the switchgear should be greater than or equal to the short-circuit current effective value ($$I_{sc}$$), that is, $$I_{th} \geq I_{sc}$$.
3. Check the maximum allowable temperature: calculate the temperature rise of the conductor caused by the short-circuit current, and ensure that it does not exceed the maximum allowable temperature of the conductor and insulation materials. The temperature rise calculation formula is: $$\Delta T = \frac{I_{sc}^2t\rho}{S^2c\rho_m}$$, where $$\rho$$ is the resistivity of the conductor material, $$c$$ is the specific heat capacity of the conductor material, and $$\rho_m$$ is the density of the conductor material.
3.4 Calculate Electrodynamic Withstand Capability
According to the calculated short-circuit current peak value ($$I_{pk}$$) and the structural parameters of the switchgear, calculate the electromagnetic force on the busbar and other components, and check the mechanical strength. The calculation steps are as follows:
1. Calculate the electromagnetic force per unit length between the busbars: $$F = 2\times10^{-7}\frac{I_{pk}^2}{a}$$ (for the same phase busbar, the currents are equal, so$$I_{pk1} = I_{pk2} = I_{pk}$$).
2. Calculate the total electromagnetic force on the busbar: $$F_{total} = F \times L$$, where $$L$$ is the length of the busbar.
3. Check the mechanical strength of the busbar and support insulator: the maximum electromagnetic force should be less than the allowable mechanical strength of the components. If it does not meet the requirement, optimize the busbar structure or increase the number of support insulators.
4. Calculation Verification and Standard Compliance
After completing the calculation of the short-circuit withstand capability, it is necessary to verify the calculation results to ensure that they meet the requirements of relevant international and domestic standards. The main verification contents include:
First, the thermal withstand current and electrodynamic withstand current of the switchgear should meet the grade requirements specified in the standard. For example, according to GB 3906-2020, the thermal withstand current of 12kV high-voltage switchgear is usually 25kA/1s, 31.5kA/1s, etc., and the electrodynamic withstand current (peak value) is 63kA, 80kA, etc. The calculated results should be greater than or equal to the standard values.
Second, the calculation method and parameters should comply with the requirements of the standard. For example, the peak coefficient, time constant and other parameters should be selected according to the standard, and the calculation formula should be consistent with the standard provisions. At the same time, the material parameters (resistivity, specific heat capacity, density, etc.) of the conductor should be selected according to the actual material used.
5. Key Notes in Calculation
In the process of calculating the short-circuit withstand capability of high-voltage switchgear, the following key points should be paid attention to to avoid calculation errors and ensure the reliability of the results:
1. The selection of parameters should be accurate: the short-circuit capacity, time constant and other parameters of the power grid should be collected according to the actual power grid situation, and the structural parameters of the switchgear should be consistent with the design documents. Any parameter error will lead to large deviations in the calculation results.
2. The influence of the non-periodic component should be considered: the non-periodic component of the short-circuit current has a great influence on the peak value of the short-circuit current and the electrodynamic effect, and cannot be ignored. The peak coefficient and decay coefficient should be selected reasonably according to the power grid characteristics.
3. The mechanical strength of the components should be fully considered: when calculating the electrodynamic withstand capability, not only the electromagnetic force on the busbar should be calculated, but also the mechanical strength of the support insulator, busbar connector and other components should be checked to avoid local damage leading to the failure of the entire switchgear.
4. Comply with the latest standards: the standards for high-voltage switchgear are constantly updated and improved, and the calculation should be based on the latest international and domestic standards to ensure that the switchgear meets the current safety requirements.
6. Conclusion
The short-circuit withstand capability is a key performance indicator of high-voltage switchgear, and its accurate calculation is the basis for ensuring the safe and stable operation of the power system. This article systematically elaborates on the calculation method of short-circuit withstand capability for high-voltage switchgear, including the basic principles, core calculation content, specific calculation steps, verification methods and key notes. The calculation process takes the short-circuit current calculation as the basis, and focuses on the thermal withstand capability and electrodynamic withstand capability, which is scientific and operable.
In practical engineering applications, engineering and technical personnel should flexibly apply the calculation method according to the actual situation of the power grid and switchgear, accurately collect parameters, strictly follow the standard requirements, and ensure that the calculated results are reliable. At the same time, combined with on-site testing and verification, the short-circuit withstand capability of the switchgear is comprehensively evaluated, which provides a strong guarantee for the design, selection, operation and maintenance of high-voltage switchgear, and promotes the safe and stable development of the power system.
