##### Tutorial: 3

- 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.

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### Advantages of Bundled Conductors

- 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})}

{ 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}

For Quadruplex arrangement-

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.

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

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

Where, X_l = inductive reactance.

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