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Pharos University EE-272

Pharos University EE-272. Electrical Power Engineering 1 “Electrical Engineering Dep ” Prepared By: Dr. Sahar Abd El Moneim Moussa. OverHead Transmission Line Capacitance parameter. 3 - Line Capacitance The capacitance of transmission lines can be found as follows:

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Pharos University EE-272

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  1. Pharos UniversityEE-272 Electrical Power Engineering 1 “Electrical Engineering Dep” Prepared By: Dr. SaharAbd El MoneimMoussa Dr. SaharAbd El MoneimMoussa

  2. OverHead Transmission LineCapacitance parameter Dr. Sahar Abd El Moneim Moussa

  3. 3- Line Capacitance • The capacitance of transmission lines can be found as follows: a- Apply the field theory to get the electric field: Field Theory: the electric field at a point due to a linear charge distribution of charge Q C/m is always radial and of magnitude Where: Ɛo: is the permittivity of air = 8.85 x 10-12 F/m r: is the radial distance between the charge and the point Dr. Sahar Abd El Moneim Moussa

  4. b- The potential difference between any two points “a” and “b” in an electric field: Therefore: • The potential difference between point P and the point of zero potential “O” Due to charge Q is: Q c/m -Q c/m r1 r2 P Dr. Sahar Abd El Moneim Moussa

  5. The potential difference between point P and the point of zero potential “O” due to charge -Q is: • The total potential difference between point P and the point of zero potential “O” due to the two charges Q and –Q: Dr. Sahar Abd El Moneim Moussa

  6. Therefore: Dr. Sahar Abd El Moneim Moussa

  7. 3- Line Capacitance 3.1 Capacitance of single phase Two Wire line • The potential at conductor “a” will be • Similarly, the potential at conductor “b” will be ra r Q c/m -Q c/m rb D Dr. Sahar Abd El Moneim Moussa

  8. Therefore: Van=Vab/2=V Where: ra=rb=r And: Vb=-Va=V Dr. Sahar Abd El Moneim Moussa

  9. Finally: The line-to-neutral capacitance: Where, Ɛo: is the permittivity of air = 8.85 x 10-12 F/m Dr. Sahar Abd El Moneim Moussa

  10. C 3.3 Capacitanceof 3-Phase 3-WireLine with Equal Spacing • Knowing that Qa+Qb+Qc=0  DD D D b a D Dr. Sahar Abd El Moneim Moussa

  11. Finally: The line-to-neutral capacitance: Where, Ɛo: is the permittivity of air = 8.85 x 10-12 F/m Dr. Sahar Abd El Moneim Moussa

  12. C 3.4Capacitance of 3-Phase 3-WireLine with Unequal Spacing transposed line Dac DD Dbc a Dab b Dr. Sahar Abd El Moneim Moussa

  13. Dr. Sahar Abd El Moneim Moussa

  14. Where: Deq=GMD=Geometric mean distance= Finally: F/m Dr. Sahar Abd El Moneim Moussa

  15. V- Bundled Conductors The line-to-neutral caacitance: Cn =2 ᴨ Ɛo / ln [Deq /Dsc] F/m Deq = Dsc = for a two- conductor bundle Dsc = for a three- conductor bundle Dsc = 1.091 for a four-conductor bundle Dr. Sahar Abd El Moneim Moussa

  16. Example 5: A 200 km, 3-phase transmission line has its conductors placed at the corners of an equilateral triangle of 2.5 m side. The radius of each conductor is 1 cm. calculate the line to neutral capacitance of the line. Solution: (Equal Spacing) D= 2.5 m ,L=200 km ,r= 1 cm=10-2 m Cn =2 ᴨ Ɛo / ln [D /r] F/m Cn =2 ᴨ Ɛo / ln [D /r]= = 1.007 x 10-11 F/m  C = 1.007 x 10-12 x 200 x 1000 = 2 x 10 -6 F C DD D D b a D Dr. Sahar Abd El Moneim Moussa

  17. Example 6: The three conductors of a 3 phase transmission line are arranged in a horizontal plane and are 4 m apart. The diameter of each conductor is 2 cm. calculate the line to neutral capacitance per m of the line ( This example will be solved in the lecture) Dr. Sahar Abd El Moneim Moussa

  18. Example 7: The 3 phases of a TL are placed at the corners of an equilateral triangle of side 12.5 m. Each phase consists of 2 bundled conductors, the conductor diameter is 4.6 cm and the bundle spacing is 45 cm. Find C of the TL. Solution: Dab = 12.5 m D bc = 12.5 m D ca = 12.5 m D conductor=4.6 cm d= 45 cm C d a b D Dr. Sahar Abd El Moneim Moussa

  19. Deq = = 12.5 m Dsc= √rd=10.7 cm Cn =2 ᴨ Ɛo / ln [Deq /Dsc] F/m = = 7.807 x 10 -12 F/m Dr. Sahar Abd El Moneim Moussa

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