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 C_c and core to sheath capacitance C_e 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 = C_c

Core to sheath capacitance = C_e

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

       C_eq = 3C_c

       Where

       C_eq = 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

       C_N = C_e + C_eq

             = C_e + 3C_c

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 C_e which are in parallel. 
• Let us consider that this capacitor is C₁ therefore

C₁ = 3C_e

C_e = C₁ / 3…….. ( 1 )

( 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 = C_c + C_c / 2 + C_s / 2

     = ( C_c + C_c / 2 ) + C_s / 2

     = ( 3C_c / 2 ) + C_s / 2

     = ½ ( 3C_c + C_s )

      = ½ C_N

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

Let us consider that this capacitor is equal to C₃.

C₃ = 2C_c + C_s

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