Important Formula of Transmission Line Parameters

( 1 ) Resistance of the conductor           R = ρL / a          Where R = Resistance L = Length of conductor a = Area of conductor ρ = Resistivity of conductor

 

( 2 ) Inductance of conductor L = Nφ / I    = Flux Linkage / Ampere    = ψ ( Symbol Psi ) / I    ( Where ψ = Flux linkage )

 

( 3 ) Inductance of conductor due to internal flux Internal flux linkage ψint = µI / 8π weber – turns / meter         Where µ = Permeability                        = µ0 µr           µ0 = Absolute permeability = 4 π × 10 – 7           µr = Relative permeability        ψint = (4 π × 10 – 7 ) × I / 8π              = (  I / 2 ) 10 – 7   ……………. ( 1 )      Lint  = (  1 / 2 ) 10 – 7

 

( 4 ) Inductance of conductor due to external flux linkage ψout = ( 2I × 10 – 7 ) Ln {( D – r ) / r } weber – turns  / meter Where D = Diameter of conductor r = Radius of conductor Ln = Log natural I = Current If D >> r Flux linkage ψexternal = ( 2I × 10 – 7 ) Ln { D  / r } .. ( 2 ) Inductance = ( 2 × 10 – 7 ) Ln { D  / r }

 

( 5 ) Inductance of single conductor ψ = ψinternal + ψexternal     = equation ( 1 ) + equation ( 2 )    = (  I / 2 ) 10 – 7  + ( 2 × 10 – 7 ) Ln { D  / r }             = ( 2 × 10 – 7 ) × I [ Ln { D  / r’ } ]    Where r’ = re – ¼ = 0.7788r                                        = GMR of conductor         L = ( 2 × 10 – 7 ) [ Ln { D  / r’ } ] Inductance of single phase two wire circuit L = ( 4 × 10 – 7 ) Ln { D  / r’ } Inductance per conductor L = ( 2 × 10 – 7 ) Ln { D  / r’ }

 

( 6 ) Inductance single phase composite conductors         L = ( 2 × 10 – 7 ) Ln { Dm  / Ds }  H / m    = ( 2 × 10 – 7 ) Ln { GMD  / GMR }  H / m    = 0.2 Ln { GMD  / GMR }  mH / km The GMD of bundle conductor can be found by taking root of product of distances from each conductor of a bundle to every other conductor of bundle. GMR = Geometrical mean radius           = √ ( r’D )                     ( for two conductors )           = [ ( r’D2 ) ]1/3                ( for three conductors )           = 1.09 × [ ( r’D3 ) ]1/4       ( for four conductors )

 

( 7 ) Inductance of three phase unsymmetrical spacing three         conductor ( transposed ) L = ( 2 × 10 – 7 ) Ln { Deq  / Ds }  H / m Where Deq = ( D12 ×  D23 × D32 )1/3 D = Distance between conductors D12 ≠ D23 ≠ D31 Inductance of three phase symmetrical spacing three conductor Inductance of a conductor L = ( 2 × 10 – 7 ) Ln { D  / r’ }  H / m

 

( 8 ) Capacitance of conductors C = Q / V Farad / meter Where C = Capacitance in Farad Q = Charge in coulomb V = Voltage

 

( 9 ) Capacitance between two conductors a and b Cab = πε / Ln ( D / r )       = 1 / [ 36 Ln ( D / r ) ]   Micro Farad / kilo-meter

 

( 10 ) Capacitance between conductor to neutral = 2 × Capacitance between two conductors = 1 / [ 18 Ln ( D / r ) ]   Micro Farad / kilo-meter = 2πε/ Ln ( D / r )

 

( 11 ) Unsymmetrical conductor spacing in the three phase           transposed system If there are three conductors a, b, c placed unsymmetrical Capacitance of conductor = 2πε / Ln ( Deq / r ) Farad / meter  Where Deq = ( D12 ×  D23 × D32 )1/3

 

( 12 ) Symmetrical conductor spacing in the three phase transposed system Capacitance per phase = 2πε/ Ln ( D / r ) Where D12 = D23 = D31 = D

 

( 13 ) Capacitance of single conductor due to effect of earth  C = 2πε0 / Ln ( 2h / r ) Farad / meter Where h = Distance of image ground conductor and earth surface

 

( 14 ) Capacitance of single phase transmission line due to effect of earth Capacitance of conductor             = 2πε / Ln ( D / r × 2h / √ 4h2 + D2 ) Capacitance of single phase between conductors                = 1 / 36 Ln { D × 2h / r × √ ( 4h2 + D2 ) } Where h = Distance of ground image conductor and earth surface

 

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