## Bundled Conductors used in Transmission Lines

• The voltage between 300 to 765 kV is known as extra-high voltage.
• An increase in transmission voltage causes a reduction in electrical loss, an increase in transmission efficiency, improvement of voltage regulation, and a reduction in conductor material.
• At EHV, if a round conductor per phase is used, then corona causes significant power loss and interference with communication circuits (crosstalk).
• Consequently, to reduce corona loss and interference with communication lines, we use a bundled conductors.
• Bundled conductors are made up of two or more conductors per phase known as sub conductor.
• The difference between a normal composite conductor and a bundled conductor is that the sub-conductor in the composite conductor touches each other and in the bundled conductors sub-conductors are separated from each other by a fixed distance of 0.2 to 0.6 meter depending on operating voltage and atmospheric condition.
• The bundled conductors have filter material and airspace inside so that the overall diameter is increased.
• Type of arrangements of Bundled Conductor-

Two conductors per phase are used.

Three conductors per phase are used.

Four conductors per phase are used.

• Reduction in corona loss and interference with communication lines.
• Bundled conductors have higher capacitance to neutral in comparison with single conductor lines therefore they have higher charging current which helps in improving the power factor.
$C_n = \dfrac{0.02412}{\log(\frac{D}{r})}$
• Recall $L \alpha \frac{1}{GMR}$GMR is the distance between conductors of the same group. In case of the bundled conductor, we have the sub conductors i.e. we have increased distance between the conductor of same phase (GMR). Therefore as GMR increases the inductance of the transmission line decreases and we know that inductance of transmission line limits power transfer capability therefore by reducing the inductance of transmission line power transfer capability of a transmission line is increased thereby improving the transmission efficiency.
${ L }=2\times { 10 }^{ -7 }\ln { \frac { GMD }{ GMR } }$
• Bundled conductors have higher capacitance and lower inductance therefore surge impedance $Z_0 = \sqrt{\frac{L}{C}}$ is lower for bundled conductor thereby increasing the power transfer of transmission line.
•  Voltage regulation of transmission line is improved
• In bundled conductors, the inductive reactance is reduced therefore voltage regulation of the transmission line is also improved.
• Reduction in skin effect.
• The bundled conductors have more surface area exposed to air therefore it has efficient cooling and hence better performance.

## Inductance of Bundled Conductors

For Duplex arrangement-

$GMR = \sqrt[4]{(r’d)^2}$
$GMR = \sqrt{r’d}$

For Triplex arrangement-

$GMR = \sqrt[9]{(r’d^2)^3}$
$GMR = \sqrt[3]{r’d^2}$

$GMR = \sqrt[16]{(r’dd(\sqrt{2}d))^4}$
$GMR = 1.09 \times \sqrt[4]{r’d^3}$

Note: From above equations of GMR, it is clear that as we go on increasing the number of sub-conductors per phase the inductance of transmission line decreases.

We can take distance from center of one bundled conductor to center of other bundled conductor to calculate GMD.

## How inductance of transmission line limits the power transfer capability of the transmission line?

Power transfer through transmission line is mainly dependent on inductance. Formula for power transfer capability is-

$P = \left(\dfrac{V_sV_r}{X_l}\right) \sin \delta$

Where, $X_l$ = inductive reactance.

By reducing the inductive reactance of transmission line we can enhance the power flow through the transmission line.

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