1. Presentation Course: Power System Presented BY: M.Hamza Usman Roll No# BSEE-01123114 Date: 10, November 2015. Section(B) To: Sir, Kashif Mehmood

2. Chapter 9: Electrical Design Of Overhead Lines

3. Introduction:  Transmission of of electric power is done by 3-phase, 3-wire overhead lines.  An a.c. transmission line has i. resistance ii. inductance iii. capacitance constants or parameters of the line. which are uniformly distributed along its length. These are known as constants or parameters of the line.

4. 9.1 Constants of a Transmission Line  These constants determine whether the efficiency and voltage regulation of the line will be good or poor.

5. (i) Resistance. It is the opposition of line conductors to current flow. ( ii ) Inductance. When an alternating current flows through a conductor, a changing flux is set up which links the conductor. Due to these flux linkages, the conductor possesses inductance.  Mathematically, inductance is defined as the flux linkages per ampere i.e Inductance, L = ψ / I (And its unit is henry) ψ = flux linkages in weber-turns I = current in amperes  ( iii ) Capacitance. Any two conductors separated by an insulating material constitute a capacitor. Capacitance exists between any two overhead line conductors. The capacitance between the conductors is the charge per unit potential difference i.e., Capacitance, C = Q / v (And its unit is farad)

6. 9.2: Resistance of a Transmission Line  The resistance of transmission line conductors is the most important cause of power loss in a transmission line. The of a line conductor having, and is Mathematically: R = ρI l a resistance R Resistivity ρ Length l area of cross section a  In case of a 3-phase transmission line, resistance per phase is the resistance of one conductor.

7. 9.3: Skin Effect  The tendency of alternating current to flow near the surface of a conductor is known as skin effect.  Note: For a direct current, inductance is zero and hence the current distributes uniformly over the entire cross section of the conductor.

8. Skin effect depends upon the factors: ( i ) Nature of material ( ii ) Shape of wire ( iii ) Diameter of wire(increases with the diameter of wire) ( iv ) Frequency (increases with the increase in frequency) skin effect is negligible when the supply frequency is low (< 50 Hz) And conductor diameter is small (< 1cm).

9. 9.4: Flux Linkages In order to find the inductance of a circuit, the determination of flux linkages is important. We shall discuss two important cases of flux linkages. 1.Flux linkages due to a single current carrying conductor. If a conductor carrying current, This current will set up magnetic field. The magnetic lines of force will exsist inside the conductor as well as outside the conductor. Types: (i)Flux linkages due to internal flux. (ii) Flux linkages due to external flux. 2. Flux linkages in parallel current carrying conductors. As In parallel circuits the current does not remain the same but also divided into each nodes therefore flux linkages also changes.

10. 9.5: Inductance of a Single Phase Two- wire Line A single phase line consists of two parallel conductors which form a rectangular loop of one turn. When an alternating current flows through such a loop, a changing magnetic flux is set up. Note: It may appear that inductance of a single phase line is negligible because it consists of a loop of one turn and the flux path is through air of high reluctance.

11. 9.7: Concept of Self-GMD and Mutual-GMD ( i ) Self-GMD (D s ) ( Geometric mean distance ) The geometric mean distance between two symmetrical angular conductors is very nearly equal to the distance between corresponding points on the two conductors.  It can be proved mathematically that for a solid round conductor of radius r, the self-GMD or GMR = 0·7788 r. Factors:  self-GMD of a conductor depends upon the size and shape of the conductor  self-GMD of a conductor is independent of the spacing between the conductors.

12. ( ii ) Mutual-GMD (Dm) ( Geometrical mean distances ) The mutual-GMD is the geometrical mean distances is from one conductor to the other conductor.  The mutual-GMD between two conductors is equal to the distance between their centres.

13. 9.9: Electric Potential The electric potential at a point due to a charge “ is the work done in bringing a unit positive charge from infinity to that point”. Electric potential due to some important conductor arrangements. (i)Potential at a charged single conductor. ( ii ) Potential at a conductor in a group of charged conductors.

14. 9.11: Capacitance of a 3-Phase Overhead Line In a 3-phase transmission line, the capacitance of each conductor is considered instead of capacitance from conductor to conductor. Two cases arises here: ( i ) Symmetrical Spacing. ( ii ) Unsymmetrical spacing

15. Important Summary: ( i ) The power loss in an overhead transmission line is mainly due to Line conductor resistance. ( ii ) If the length of a transmission line increases, its inductance is increased. ( iii ) If the length of the line is decreased, its capacitance is decreased. ( iv ) The d.c. resistance of a line conductor is less than its a.c resistance. ( v ) The skin effect is less for stranded conductor than the solid conductor. ( vi ) A neutral plane is one where electric intensity is zero. ( vii ) If the supply frequency increases, then skin effect is increased ( viii ) If the conductor diameter decreases, inductance of the line is increased

16. CHAPTER REVIEW TOPICS Q1. What do you understand by the constant of an overhead transmission line? Q2. What is skin effect ? Why is it absent in the d.c. system ? Q3. Find an expression for the flux linkages (i) due to a single current carrying conductor (ii) in parallel current carrying conductors