The current-carrying capacity of tubular busbars depends on material, cross-sectional area, and cooling conditions, while capacitance is influenced by geometry and spacing relative to surrounding conductors.

Current-Carrying Capacity (Ampacity)

The current capacity of a tubular busbar is primarily determined by its cross-sectional area, material resistivity, and allowable temperature rise. For copper and aluminum busbars, the approximate formulas are:

• Copper: $I=1.2\times \text{width (mm)}\times \text{thickness (mm)}$ Amps
• Aluminum: $I=0.8\times \text{width (mm)}\times \text{thickness (mm)}$ Amps These formulas provide a quick estimate for rectangular or tubular busbars, but for hollow tubular sections, the effective cross-sectional area is reduced by the inner diameter, so the current density $J$ is calculated as:

where $A_{\text{cross-section}}=\pi (r_{\text{outer}}^2-r_{\text{inner}}^2)$ for a circular tube ( ). Design considerations include:

• Temperature rise: Must not exceed IEC 61439-1 limits (typically 70K above ambient for bare copper) ( ).
• Short-circuit withstand: Verify using the adiabatic equation to ensure the busbar can survive fault currents without exceeding material limits ( ).
• AC effects: Skin and proximity effects reduce effective cross-section at high frequencies, especially in hollow conductors ( ).
• Support spacing and mechanical strength: Tubular busbars must withstand electromagnetic forces during faults ( ).

Capacitance of Tubular Busbars

The capacitance of a tubular busbar depends on its geometry and the surrounding environment. For a single isolated tubular conductor above a ground plane, the capacitance per unit length can be approximated as:

where:

• ${\epsilon }_0$ = permittivity of free space
• ${\epsilon }_r$ = relative permittivity of surrounding medium (air ≈ 1)
• $h$ = distance to reference conductor or ground
• $r_{\text{outer}}$ = outer radius of the tubular busbar For parallel tubular busbars, mutual capacitance between conductors must be considered, which affects AC voltage distribution and transient behavior.

Practical Calculation Steps

1. Determine material and dimensions: Outer and inner diameters for tubular busbars.
2. Calculate cross-sectional area: $A=\pi (r_{\text{outer}}^2-r_{\text{inner}}^2)$.
3. Select allowable current density: Based on cooling conditions and IEC 61439-1 standards ( ).
4. Compute ampacity: $I=J\times A$.
5. Check voltage drop: $V_{\text{drop}}=I\times R$, where $R=\rho \frac{L}{A}$.
6. Evaluate capacitance: Use geometry-based formulas for isolated or parallel tubular conductors.
7. Consider AC effects: Apply skin and proximity effect derating for high-frequency operation ( ).
8. Verify mechanical and thermal limits: Ensure busbar can withstand short-circuit forces and temperature rise ( ).

Tools and References

Several online calculators can assist with these calculations, including:

• Simulations4All Busbar Sizing Calculator ( )
• CalculatorFinder Bus Bar Calculator ( )
• ECalPro Busbar Calculator ( ) These tools allow engineers to input tubular dimensions, material, and operating conditions to obtain ampacity, temperature rise, short-circuit withstand, and voltage drop. By combining these methods, engineers can accurately determine both the current-carrying capacity and capacitance of tubular busbars for safe and efficient electrical distribution.