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Note for Power System-2 - PS-2 By JNTU Heroes

  • Power System-2 - PS-2
  • Note
  • Jawaharlal Nehru Technological University Anantapur (JNTU) College of Engineering (CEP), Pulivendula, Pulivendula, Andhra Pradesh, India - JNTUACEP
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UNIT-I Transmission Line Parameters Page 2

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2. TRANSMISSION LINES The electric parameters of transmission lines (i.e. resistance, inductance, and capacitance) can be determined from the specifications for the conductors, and from the geometric arrangements of the conductors. 2.1 Transmission Line Resistance Resistance to d.c. current is given by  R dc A where is the resistivity at 20o C is the length of the conductor A is the cross sectional area of the conductor Because of skin effect, the d.c. resistance is different from ac resistance. The ac resistance is referred to as effective resistance, and is found from power loss in the conductor R power loss I2 The variation of resistance with temperature is linear over the normal temperature range resistance ( ) R2 R1 T T1 T2 o temperature ( C) Figure 9 Graph of Resistance vs Temperature (R1 (T1 0) T) (R 2 (T2 0) T) Page 3

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T2 T R1 T1 T R2 2.2 Transmission Line Inductive Reactance Inductance of transmission lines is calculated per phase. It consists of self inductance of the phase conductor and mutual inductance between the conductors. It is given by: L 2 10 7 ln GMD GMR [H/m] where GMR is the geometric mean radius (available from manufacturer’s tables) GMD is the geometric mean distance (must be calculated for each line configuration) Geometric Mean Radius: There are magnetic flux lines not only outside of the conductor, but also inside. GMR is a hypothetical radius that replaces the actual conductor with a hollow conductor of radius equal to GMR such that the self inductance of the inductor remains the same. If each phase consists of several conductors, the GMR is given by 1 2 3 n GMR 2 n (d11d 12d 13....d1n ).(d 21.d 22 ....d2n )......(dn1.d n2 ..... dnn ) where d11=GMR1 d22=GMR2 . . . dnn=GMRn Note: for a solid conductor, GMR = r.e-1/4 , where r is the radius of the conductor. Page 4

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Geometric Mean Distance replaces the actual arrangement of conductors by a hypothetical mean distance such that the mutual inductance of the arrangement remains the same b a’ c b’ a c’ m GMD n’ (D aa'D ab' ...D an' ).(D ba'D bb' ...D bn' ).....(D ma' D mb' ..... D mn' ) mn' where Daa’ is the distance between conductors “a” and “a’” etc. Inductance Between Two Single Phase Conductors r1 r2 D L1 2 10 7 ln D r1 ' L2 2 10 7 ln D r2 ' where r1’ is GMR of conductor 1 r2’ is GMR of conductor 2 D is the GMD between the conductors The total inductance of the line is then LT LT L1 L2 4 10 7 2 10 ln D r1 ' 7 D2 ln r1 ' r2 ' D ln r2 ' 2 10 1/2 4 10 7 ln 7 2 ln D r1 ' r2 ' 2 10 7 2 1 2 2 ln D r1 ' r2 ' D r1 ' r2 ' If r1 = r2 , then LT 4 10 7 ln D r1 ' Page 5

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