## 21/11/2020

### Advantages of High Transmission Line Voltage

Advantages of high voltage transmission line

( a ) Volume of Conductor Material

Let us consider that the electrical power transmitted through transmission line is

P = 3 VLIL Cos Φ

IL  = P / 3 VL Cos Φ…. ( 1 )

Where

VL = Line voltage

IL = Line current

P = Power transmitted

Cos Φ = Power factor of the load

Resistance per conductor R = ρL / a……… ( 2 )

Total power loss W = 3I2R

= 3 ( P / 3 VL Cos Φ )2 ( ρL / a )

= 3 ( P2 /  3 VL2 Cos 2Φ ) ( ρL / a )

W = ( P2 ρL /  a VL2 Cos 2Φ ) …….. ( 3 )

Cross section area a =  ( P2 ρL /  W VL2 Cos 2Φ )

Volume of conductor = Area of conductor × Length of conductor

= aL

= ( P2 ρL2 /  W VL2 Cos 2Φ )……..( 4 )

Volume of conductor α ( 1 / VL2 Cos 2Φ )

• The volume of conductor is inversely square of supply voltage and inversely proportional to square of power factor if power transmitted, length of conductor, transmission line losses and resistivity of material is remains constant.

( b ) Decrease in voltage drop

Voltage drop = IR

= I ( ρL / a )

= I ( ρLJ / I )    ( Current density J = I / a )

=  ρLJ

% Voltage drop = [ ρLJ / V ] × 100%

• We can say that If the voltage increases, percentage voltage drop decreases.

( c ) Transmission line efficiency

Input power = Pi

Output power = P

Input power = Output Power + Losses

= P + ( P2 ρL /  a VL2 Cos 2Φ )

= P + ( P2 ρLJ /  I VL2 Cos 2Φ )     ( current density J = I / a )

As P = √ 3 VL IL Cos Φ

= P + { P2 ρLJ ( √ 3 VL Cos Φ )  /  P VL2 Cos 2Φ }

= P + { P ρLJ ( √ 3  )  /  VL Cos Φ }

= P + { ( √ 3  )  P ρLJ /  VL Cos Φ }

= P { 1 + [ √ 3 ρLJ /  VL Cos Φ ] }

Transmission line efficiency = [ Output power / Input power ] × 100%

= P / P { 1 + [ √ 3 ρLJ /  VL Cos Φ ] }× 100%

= { 1 – [ √ 3 ρLJ /  VL Cos Φ ] }× 100%

• If current density, resistivity and length of line is constant the efficiency of the transmission line is inversely proportional to line voltage and power factor of the load.

Conclusion

If the transmission line voltage increases,

• Transmission line efficiency increases
• Percentage voltage drop decreases
• Volume of conductor material decreases

Disadvantages of high voltage transmission line

• High cost of insulator of conductors
• High cost of transformer, switchgear and other protective equipments

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