Effect of bundled conductors on L and C

A bundled conductor is a phase conductor made of two or more sub-conductors (usually 2, 3 or 4) in parallel, held a short distance apart (about 30–50 cm) by spacers. Bundling is used on EHV lines (220 kV and above).

 2-bundle     3-bundle      4-bundle
  o---o         o           o---o
   d           / \          |   |
              o---o         o---o

Self GMD of a bundle

Since $d \gg r$, the bundle's self-GMD is many times larger than the radius of a single conductor.

Effect on inductance

$$L = 2\times10^{-7}\ln\frac{D_m}{D_s}$$

A larger $D_s$ makes $\ln(D_m/D_s)$ smaller, so inductance per phase decreases (typically by 25–35% for a 2–4 bundle). Lower series reactance raises the power transfer limit ($P_{max} = V_SV_R/X$) and improves voltage regulation and stability.

Effect on capacitance

$$C = \frac{2\pi\varepsilon_0}{\ln(D_m/D_s)}$$

The same larger $D_s$ makes the denominator smaller, so capacitance per phase increases. Charging current rises, but surge impedance $Z_c = \sqrt{L/C}$ falls, so the surge impedance loading ($V^2/Z_c$) increases.

Example

For $r = 2$ cm, $D_m = 12.6$ m, a single conductor gives $L = 2\times10^{-7}\ln(12.6/0.0156) = 1.34$ mH/km; a twin bundle with $d = 40$ cm gives $D_s = \sqrt{0.0156\times0.4} = 0.079$ m and $L = 1.01$ mH/km.

Other benefits

• Lower surface voltage gradient, so less corona loss and radio interference.
• Higher current capacity per phase and lower reactance.