1. CHAPTER 9 Electrical Design of Overhead Lines
Principles of Power System
V K Mehta

2. Introduction
An a.c. transmission line has resistance, inductance and capacitance uniformly distributed along its length.
These are known as constants or parameters of the line.
The performance of a transmission line depends to a considerable extent upon these constants.
These constants determine whether the efficiency and voltage regulation of the line will be good or poor.

3. 9.1 Constants of a Transmission Line

4. 9.2 Resistance of a Transmission Line
i. 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.

5. 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.

6. 9.5 Inductance of a Single Phase Two-wire Line
Inductance of a Conductor

7. 9.6 Inductance of a 3-Phase Overhead Line
Inductance of a Conductor (Asymmetric)

8. 9.6 Inductance of a 3-Phase Overhead Line
Inductance of a Conductor (Symmetric d1=d2=d3)

9. Example 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

10. 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.

11. 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.

12. 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

13. 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

14. 9.10 Capacitance of a Single Phase Two-wire Line

15. 9.11Capacitance of a 3-Phase Overhead Line

16. 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.

17. 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.

18. Example 9.13: A 3-phase, 50 Hz, 66 kV overhead line conductors are placed in a horizontal plane as shown in Fig 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.

19. 11.1 Underground Cables
An underground cable essentially consists of one or more conductors covered with suitable insulation and surrounded by a protecting cover. Requirement: (i) The conductor used in cables should be tinned stranded copper or aluminium of high conductivity. Stranding is done so that conductor may become flexible and carry more current. (ii) The conductor size should be such that the cable carries the desired load current without overheating and causes voltage drop within permissible limits. (iii) The cable must have proper thickness of insulation in order to give high degree of safety and reliability at the voltage for which it is designed. (iv) The cable must be provided with suitable mechanical protection so that it may withstand the rough use in laying it. (v) The materials used in the manufacture of cables should be such that there is complete chemical and physical stability throughout.

20. 11.2 Construction of Cables
General construction of a 3-conductor cable

21. 11.2 Construction of Cables
General construction of a 3-conductor cable (i) Cores or Conductors. A cable may have one or more than one core (conductor) depending upon the type of service for which it is intended. For instance, the 3-conductor cable shown in Fig is used for 3-phase service. The conductors are made of tinned copper or aluminum and are usually stranded in order to provide flexibility to the cable. (ii) Insulation. Each core or conductor is provided with a suitable thickness of insulation, the thickness of layer depending upon the voltage to be withstood by the cable. The commonly used materials for insulation are impregnated paper, varnished cambric or rubber mineral compound. (iii) Metallic sheath. In order to protect the cable from moisture, gases or other damaging liquids (acids or alkalies) in the soil and atmosphere, a metallic sheath of lead or aluminium is provided over the insulation as shown in Fig. 11.1

22. 11.2 Construction of Cables
(iv) Bedding. Over the metallic sheath is applied a layer of bedding which consists of a fibrous material like jute or hessian tape. The purpose of bedding is to protect the metallic sheath against corrosion and from mechanical injury due to armouring. (v) Armouring. Over the bedding, armouring is provided which consists of one or two layers of galvanised steel wire or steel tape. Its purpose is to protect the cable from mechanical injury while laying it and during the course of handling. Armouring may not be done in the case of some cables. (vi) Serving. In order to protect armouring from atmospheric conditions, a layer of fibrous material (like jute) similar to bedding is provided over the armouring. This is known as serving.

23. 11.3 Insulating Materials for Cables
Properties Insulating Materials (i) High insulation resistance to avoid leakage current. (ii) High dielectric strength to avoid electrical breakdown of the cable. (iii) High mechanical strength to withstand the mechanical handling of cables. (iv) Non-hygroscopic i.e., it should not absorb moisture from air or soil. The moisture tends to decrease the insulation resistance and hastens the breakdown of the cable. In case the insulating material is hygroscopic, it must be enclosed in a waterproof covering like lead sheath. (v) Non-inflammable. (vi) Low cost so as to make the underground system a viable proposition. (vii) Unaffected by acids and alkalies to avoid any chemical action.

24. 11.20 Types of Cable Faults
Open-circuit fault.When there is a break in the conductor of a cable, it is called opencircuit fault. The open-circuit fault can be checked by a megger.
Short-circuit fault.When two conductors of a multi-core cable come in electrical contact with each other due to insulation failure, it is called a short-circuit fault.
Earth fault. When the conductor of a cable comes in contact with earth, it is called earth fault or ground fault.