Electrical busbar calculations

Electrical busbar calculations involve determining the appropriate cross-sectional area (size) of the busbar to safely and efficiently carry the expected current load. The calculation formula for busbar sizing is based on the maximum allowable temperature rise, the resistivity of the busbar material, the ambient temperature, and the permissible current density. The most commonly used formula for busbar calculation is known as the "Kelvin's Law for Busbars." Here's the formula:

Kelvin's Law for Busbars:

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I = (K * ΔT * A) / L

Where:

• I is the current-carrying capacity of the busbar (in amperes, A).
• K is the factor representing the material's resistivity and temperature coefficient.
• ΔT is the maximum allowable temperature rise of the busbar above the ambient temperature (in degrees Celsius, °C).
• A is the cross-sectional area of the busbar (in square millimeters, mm²).
• L is the effective length of the busbar (in meters, m).

Calculation Steps:

1. Determine the maximum allowable temperature rise (ΔT) for the busbar based on the material's thermal characteristics and safety limits. This value typically ranges from 30°C to 50°C, depending on the application and busbar material.

2. Determine the material-specific factor (K) using the following formula:

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   K = 234.5 / (ρ * (1 + α * ΔT))
   

   Where:

   • ρ is the resistivity of the busbar material (in micro-ohm per meter, µΩ/m).
   • α is the temperature coefficient of resistivity of the material (in per degree Celsius, °C⁻¹).

3. Determine the current density (J) based on the application and safety standards. Common values for current density range from 1.5 A/mm² to 5 A/mm².

4. Calculate the required cross-sectional area (A) of the busbar using the formula:

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   A = I / (J * 10⁶)
   

   Note: The current density (J) is converted from A/mm² to A/m² by multiplying by 10⁶.

5. Once you have the required cross-sectional area (A), you can select the nearest standard busbar size available in the market or design a custom busbar with the calculated dimensions.

It's important to note that busbar calculations are complex and depend on various factors, such as the busbar arrangement (single, double, or sandwich), the number of conductors, ambient temperature, and the presence of any forced cooling systems. For critical applications or complex systems, it is advisable to consult with electrical engineering experts or use specialized software tools to perform accurate busbar calculations.