IEC 60949: Calculation of Thermally Permissible Short-Circuit Currents

IEC 60949 provides guidelines for calculating the thermally permissible short-circuit currents while accounting for both adiabatic and non-adiabatic heating effects. This document includes key principles, formulas, and their practical applications.

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1. Introduction

Short-circuits in electrical systems generate significant heat due to high currents. Proper calculation of the maximum short-circuit current is essential to:

• Prevent thermal damage.
• Ensure system safety and performance.
• Determine the correct sizing of conductors and protective devices.

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2. Key Equations for Short-Circuit Calculations

The thermal effects caused by short circuits can be calculated using the following equations:

Heat Generated During Short Circuit:
\[ Q = I^2 \cdot R \cdot t \]

Temperature Rise in a Conductor:
\[ \Delta T = Q / (m \cdot c) \]

Resistance as a Function of Temperature:
\[ R_T = R_0 \cdot (1 + \alpha \cdot (T - T_0)) \]

Maximum Permissible Short-Circuit Current (Adiabatic):
\[ I_{\text{max}} = \sqrt(A \cdot \rho \cdot c \cdot \Delta T / t) \]

Non-Adiabatic Correction Factor for Temperature Rise:
\[ k = \Delta T_{\text{adiabatic}} / \Delta T_{\text{non-adiabatic}} \]

Adjusted Short-Circuit Current (Non-Adiabatic):
\[ I_{\text{non-adiabatic}} = k \cdot I_{\text{adiabatic}} \]



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3. Key Parameters in Calculations

To accurately determine the thermally permissible short-circuit currents, the following material properties are considered:

• Cross-sectional area of the conductor (\(A\)).
• Resistivity of the conductor material (\(\rho\)).
• Specific heat capacity (\(c\)).
• Initial temperature (\(T_0\)) and final permissible temperature (\(T\)).
• Duration of the short circuit (\(t\)).

Thermal Properties of Common Materials:

Copper:

• Resistivity: \(1.72 \times 10^{-8}\)
• Specific Heat Capacity: \(385\)
• Melting Point: \(1083\)

Aluminum:

• Resistivity: \(2.65 \times 10^{-8}\)
• Specific Heat Capacity: \(900\)
• Melting Point: \(660\)

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4. Steps for Applying IEC 60949

Follow these steps for practical implementation:

• Determine the material, cross-sectional area, short-circuit current, and fault duration.
• Calculate the heat generated using \(Q = I^2 \cdot R \cdot t\).
• Estimate the temperature rise using \(\Delta T = Q / (m \cdot c)\).
• Adjust for non-adiabatic heating using the correction factor \(k\).
• Verify that the calculated final temperature is within the permissible range for the insulation and conductor material.

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5. Example Calculation

Given Data:

• Material: Copper
• Cross-sectional area (\(A\)): \(16 \, \text{mm}^2\)
• Short-circuit current (\(I\)): \(10,000 \, \text{A}\)
• Fault duration (\(t\)): \(0.5 \, \text{s}\)
• Initial temperature (\(T_0\)): \(20^\circ \text{C}\)
• Final permissible temperature (\(T\)): \(250^\circ \text{C}\)

1. Calculate heat generated:
  \[ Q = I^2 \cdot R \cdot t \]

2. Estimate temperature rise:
  \[ \Delta T = Q / (m \cdot c) \]

3. Apply non-adiabatic correction:
  \[ I_{\text{non-adiabatic}} = k \cdot I_{\text{adiabatic}} \]

4. Verify temperature limits:
  Ensure \(T_0 + \Delta T \leq T_{\text{final permissible}}\).

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6. Key Considerations for Safe Design

To ensure the safety and reliability of electrical systems under short-circuit conditions:

• Use protective devices (e.g., circuit breakers) to limit the fault duration.
• Select materials with suitable thermal and electrical properties.
• Account for non-adiabatic effects in prolonged fault conditions.
• Apply safety margins to account for variations in material properties.

Maximum Temperatures:

• PVC Insulation: 70–105°C
• XLPE Insulation: 90–130°C
• Bare Conductors: 250–400°C (varies by material)

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7. Conclusion

IEC 60949 provides a robust framework for calculating short-circuit currents, ensuring thermal safety for conductors and insulation. By considering non-adiabatic effects, engineers can optimize designs and prevent overheating.

Key Points:

• Use material-specific parameters for precise calculations.
• Apply non-adiabatic corrections for more accurate results.
• Verify that the calculated temperatures comply with permissible limits.

References:

• IEC 60949 Standard
• Practical Applications in Short-Circuit Management
• Thermal and Electrical Properties of Conductors

Below are the core formulas from IEC 60949: Calculation of Thermally Permissible Short-Circuit Currents, formatted simply for clarity:





These formulas cover the core thermal and electrical principles used in IEC 60949 to calculate thermally permissible short-circuit currents. Let me know if you need a practical example or further clarification!

Reference:

IEC 60949 - Calculation of thermally permissible short-circuit currents, taking into account non-adiabatic heating effects

IEC 60287 - Calculation of the current rating

IEC 61443 - Short-circuit temperature limits of electric cables with rated voltages above 30 kV (Um = 36 kV)