Calculated impedance of 10kV busbar

The total impedance of a 10kV busbar is the combination of its resistance and reactance, calculated based on conductor material, geometry, length, and operating frequency.

Components of Busbar Impedance

1. Resistance (R): This depends on the busbar material (typically copper or aluminum), its cross-sectional area, and length. The DC resistance per meter is calculated as:

where $\rho$ is the resistivity of the material, $L$ is the busbar length, and $A$ is the cross-sectional area. Temperature corrections are applied because resistance increases with heating inside switchgear enclosures . 2. Reactance (X): Reactance arises from the busbar's inductance and is influenced by the spacing between phases and the busbar width. For a single-bar-per-phase system, the approximate reactance per meter is:

where $d$ is the center-to-center spacing between phases and $b$ is the bar width . 3. AC Effects: At 50/60 Hz, skin effect and proximity effect increase the effective resistance, especially for thick busbars (>10mm for copper). AC resistance is calculated as:

where $k_s$ is the skin effect factor .

Total Impedance Calculation

The total impedance per unit length is:

For the entire busbar, multiply by the busbar length $L$ to get the total impedance in ohms:

The magnitude of the total impedance is:

Practical Considerations

• Busbar Material: Copper has lower resistivity than aluminum, reducing R.
• Busbar Geometry: Wider and thicker bars reduce resistance but may increase skin effect.
• Phase Spacing: Larger spacing increases reactance.
• Frequency: Higher frequency increases reactance and AC resistance.
• System Voltage: For a 10kV busbar, the line-to-line voltage is used in voltage drop and short-circuit calculations .

Example

For a 10kV, 2-meter copper busbar with 1000 mm² cross-section and 0.2 m phase spacing:

• DC resistance: $R_{DC}=\rho ·L/A\approx 0.000034·2/0.001=0.068\Omega$
• Reactance: $X\approx 0.2·\ln (2·0.2/0.01)\approx 0.2·\ln (40)\approx 0.737\mu \Omega /m$
• Total impedance magnitude: $|Z|\approx \sqrt{{0.068}^2+(0.000737{)}^2}\approx 0.068\Omega$ This shows that for short busbars, resistance dominates, while reactance becomes more significant for longer busbars or higher frequencies . In summary, the total impedance of a 10kV busbar is calculated by combining the AC-corrected resistance and the inductive reactance, considering material, geometry, length, and operating frequency, and is essential for accurate short-circuit, voltage drop, and protection studies.