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27/03/2021

Capacitance of Three Core Cable

 

  • Let us consider the three core belted cable. 
  • As there is potential difference exists between core to core of cable and core to sheath of cable, electrostatic field set up between them. 
  • There is core to core capacitance Cc and core to sheath capacitance Ce exists in the three core cable. 
  • The core to core capacitance is delta connected whereas core to sheath capacitance is star connected.

Core to core capacitance = Cc

Core to sheath capacitance = Ce


capacitance-of-three-core-cable.png

  • The three core to core delta connected capacitance is converted into equivalent star connection.

       Ceq = 3Cc

       Where

       Ceq = Equivalent star connection of delta connected core to core

                 Capacitance

  • There, the total capacitance is equal to parallel combination of core to sheath capacitance and equivalent star connection of core to core capacitance of cable. 
  • The capacitance between core to neutral

       CN = Ce + Ceq

             = Ce + 3Cc


core-to-neutral-capacitance-of-cable.png

Measurement of capacitance of cable

( 1 ) Three cores bunched together

  • The three cores of cable are bunched together and capacitance is measured between cores and sheath of cable. 
  • As the three cores are bunched together, there is no capacitance between cores. There exists capacitance between core and sheath Ce which are in parallel. 
  • Let us consider that this capacitor is C1 therefore

C1 = 3Ce

Ce = C1 / 3…….. ( 1 )


capacitance-of-three-cores-bunched-together.png


( 2 ) Capacitance between two cores is measured with third core connected to the sheath

  • The capacitance between two cores is measured with the third core connected to the sheath. 
  • This eliminated one core to sheath capacitance. Let us consider that this capacitance is C2.

C2 = Cc + Cc / 2 + Cs / 2

     = ( Cc + Cc / 2 ) + Cs / 2

     = ( 3Cc / 2 ) + Cs / 2

     = ½ ( 3Cc + Cs )

      = ½ CN

capacitance-between-two-cores-is-measured-with-third-core.png


( 3 ) Capacitance between two cores shorted with the sheath and third core

Let us consider that this capacitor is equal to C3.

C3 = 2Cc + Cs


capacitance-of-two-core-shorted-with-sheath.png


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