Short Notes: Underground Cables | Short Notes for Electrical Engineering - Electrical Engineering (EE) PDF Download

 Page 2


 
 
 
 
 
Power Factor Correction 
Usually, to improve the supply side power factor we connect a capacitor device like capacitor 
bank or synchronous condenser (synchronous motor under over excited condition). 
Suppose, initially a load of real power 
1
P & lagging pf 
1
cos ? is connected & we want to 
improve pf to 
2
cos ? lagging ? ?
21
? ? ? & we connect a capacitive device which consumes real 
power ? ?
C
P & thus net real power after connection. 
2 1 C
P P P ?? 
2 2 2 1 1 1
Q P tan ; Q P tan ? ? ? ? 
C 1 1 2 2
Q P tan P tan ? ? ? ? 
In case of capacitor bank, 
C
P0 ? 
12
PP ??  
If we wish to calculate capacitance per phase  
(in both voltage control & pf correction ) 
2
C ph
Q 3 CV    ? ? ?   
C
2
ph
Q
C
3V
?
?
 
 
Insulation resistance 
           
R
R ln
2 l r
?? ?
??
??
?
??
 
           L = length of cable 
           R = Outer radius (sheath radius) 
           R = conductor radius  
 
Capacitance Model 
          
C
C : Core capacitance 
          
S
C : Core to sheath capacitance 
 
 
 
 
 
Page 3


 
 
 
 
 
Power Factor Correction 
Usually, to improve the supply side power factor we connect a capacitor device like capacitor 
bank or synchronous condenser (synchronous motor under over excited condition). 
Suppose, initially a load of real power 
1
P & lagging pf 
1
cos ? is connected & we want to 
improve pf to 
2
cos ? lagging ? ?
21
? ? ? & we connect a capacitive device which consumes real 
power ? ?
C
P & thus net real power after connection. 
2 1 C
P P P ?? 
2 2 2 1 1 1
Q P tan ; Q P tan ? ? ? ? 
C 1 1 2 2
Q P tan P tan ? ? ? ? 
In case of capacitor bank, 
C
P0 ? 
12
PP ??  
If we wish to calculate capacitance per phase  
(in both voltage control & pf correction ) 
2
C ph
Q 3 CV    ? ? ?   
C
2
ph
Q
C
3V
?
?
 
 
Insulation resistance 
           
R
R ln
2 l r
?? ?
??
??
?
??
 
           L = length of cable 
           R = Outer radius (sheath radius) 
           R = conductor radius  
 
Capacitance Model 
          
C
C : Core capacitance 
          
S
C : Core to sheath capacitance 
 
 
 
 
 
 
 
 
 
 
Capacitance per phase 
ph S C
C C 3C ?? 
Calculating 
S
C & 
C
C 
1)  Any of two cores or conductors are connected to  
       sheath & capacitance is measured between remaining  
       core & sheath. 
 
 
1 S C
C C 2C ?? 
 
 
2) All three cores are connected together & capacitance is  
measured between any core & sheath. 
2S
C 3C ? 
2
S
C
C
3
? 
2
C1
C
2C C
3
?? 
12
C
CC
C
26
??
??
??
??
 
               
12
ph S C
3C C
C C 3C
26
? ? ? ? 
3) Any one of core is connected to sheath & capacitance is 
 measured between remaining 2 cores. 
               
CS
3
3C C
C
22
??
 
               
ph 3
C 2C ?
 
 
 
 
 
 
Page 4


 
 
 
 
 
Power Factor Correction 
Usually, to improve the supply side power factor we connect a capacitor device like capacitor 
bank or synchronous condenser (synchronous motor under over excited condition). 
Suppose, initially a load of real power 
1
P & lagging pf 
1
cos ? is connected & we want to 
improve pf to 
2
cos ? lagging ? ?
21
? ? ? & we connect a capacitive device which consumes real 
power ? ?
C
P & thus net real power after connection. 
2 1 C
P P P ?? 
2 2 2 1 1 1
Q P tan ; Q P tan ? ? ? ? 
C 1 1 2 2
Q P tan P tan ? ? ? ? 
In case of capacitor bank, 
C
P0 ? 
12
PP ??  
If we wish to calculate capacitance per phase  
(in both voltage control & pf correction ) 
2
C ph
Q 3 CV    ? ? ?   
C
2
ph
Q
C
3V
?
?
 
 
Insulation resistance 
           
R
R ln
2 l r
?? ?
??
??
?
??
 
           L = length of cable 
           R = Outer radius (sheath radius) 
           R = conductor radius  
 
Capacitance Model 
          
C
C : Core capacitance 
          
S
C : Core to sheath capacitance 
 
 
 
 
 
 
 
 
 
 
Capacitance per phase 
ph S C
C C 3C ?? 
Calculating 
S
C & 
C
C 
1)  Any of two cores or conductors are connected to  
       sheath & capacitance is measured between remaining  
       core & sheath. 
 
 
1 S C
C C 2C ?? 
 
 
2) All three cores are connected together & capacitance is  
measured between any core & sheath. 
2S
C 3C ? 
2
S
C
C
3
? 
2
C1
C
2C C
3
?? 
12
C
CC
C
26
??
??
??
??
 
               
12
ph S C
3C C
C C 3C
26
? ? ? ? 
3) Any one of core is connected to sheath & capacitance is 
 measured between remaining 2 cores. 
               
CS
3
3C C
C
22
??
 
               
ph 3
C 2C ?
 
 
 
 
 
 
 
 
 
 
 
Dielectric loss in a UG cable 
                
2
ph ph
P 3 C V tan ? ? ?            
   where tan loss tangent ?? 
                
ph
1
tan
cR
??
?
 
                 R = Insulation resistance