CHAPTER 9

Electrical Design of Overhead Lines

Principles of Power System

V K Mehta

Introduction1. An a.c. transmission line has resistance, inductance and

capacitance uniformly distributed along its length.

2. These are known as constants or parameters of the line.

3. The performance of a transmission line depends to a considerable extent upon these constants.

4. These constants determine whether the efficiency and voltage regulation of the line will be good or poor.

9.1 Constants of a Transmission Line

9.2 Resistance of a Transmission Linei. R = ρl/a

ii. In a single phase or 2-wire d.c line, the total resistance (known asloop resistance) is equal to double the resistance of either conductor.

iii. In case of a 3-phase transmission line, resistance per phase is the resistance of one conductor.

9.3 Skin Effect• The tendency of alternating current to concentrate near the surface of

a conductor is known as skin effect• the effective area of cross-section of the conductor through which

current flows is reduced.• the resistance of the conductor is slightly increased when carrying an

alternating current.

9.5 Inductance of a Single Phase Two-wire Line• Inductance of a Conductor

9.6 Inductance of a 3-Phase Overhead Line

• Inductance of a Conductor (Asymmetric)

9.6 Inductance of a 3-Phase Overhead Line

• Inductance of a Conductor (Symmetric d1=d2=d3)

Example 9.1. A single phase line has two parallel conductors 2 metres apart. The diameter of each conductor is 1·2 cm. Calculate the loop inductance per km of the line.

• Spacing of conductors, d = 2 m = 200 cm• Radius of conductor, r = 1·2/2 = 0·6 cm

• Loop inductance per meter length of the line= 10−7(1 + 4 loged/r) H

• = 10−7 (1 + 4 loge 200/0·6) H = 24·23 ×10−7 H

• Loop inductance per km of the line=24·23 ×10−7 ×1000 H• = 24·23 ×10−4 H = 2·423 mH

Example 9.3. Find the inductance per km of a 3-phase transmission line using 1·24 cm diameter conductors when these are placed at the corners of an equilateral triangle of each side 2 m.

Example 9.4. The three conductors of a 3-phase line are arranged at the corners of a triangle of sides 2 m, 2·5 m and 4·5 m. Calculate the inductance per km of the line when the conductors are regularly transposed. The diameter of each conductor is 1·24 cm.

Example 9.5. Calculate the inductance of each conductor in a 3-phase, 3-wire system when the conductors are arranged in a horizontal plane with spacing such that D31= 4 m ; D12= D23= 2m. The conductors are transposed and have a diameter of 2·5 cm

9.10 Capacitance of a Single Phase Two-wire Line

9.11Capacitance of a 3-Phase Overhead Line

Example 9.11: A single-phase transmission line has two parallel conductors 3 metres apart, radius of each conductor being 1 cm. Calculate the capacitance of the line per km. Given that ε0=8·854×10−12F/m.

Example 9.12: A 3-phase overhead transmission line has its conductors arranged at the corners of an equilateral triangle of 2 m side. Calculate the capacitance of each line conductor per km. Given that diameter of each conductor is 1·25 cm.

Example 9.12: A 3-phase, 50 Hz, 66 kV overhead line conductors are placed in a horizontal plane as shown in Fig. 9.26. The conductor diameter is 1·25 cm. If the line length is100 km, calculate (i) capacitance per phase, (ii)charging current per phase, assuming complete transposition of the line.