Slide 1
Unfaulted unearthed network
A B C
ΣI01 = 0
ΣI01
UA
C0
R0
IcB
IcA
UB
UC
IcC
U0=0
ΣI02 = 0
ΣI02
UA
IcB
IcA
UB
UC
IcC
• Phase-to-ground voltages form a symmetrical system and their sum equal to zero at every time instance
• Capacitive charging currents (IcA, IcB, IcC) flow through the phase-to-earth capacitances and form a symmetrical
system
• I0 measurement in feeder #1 (ΣI01) measures the sum of the charging currents of that feeder, which equals to zero
• I0 measurement in feeder #2 (ΣI02) measures the sum of the charging currents of that feeder, which equals to zero
Single phase to earth fault in unearthed network
Slide 2
Single-phase to earth fault in phase C
Equivalent circuit
Positive current direction
Busbar
UA
UB
UC
+U0
IcA
~
A
IcB
~
~
B
C
Ief
C0
• In healty phases charging current flows towars the busbar
• In faulty phase the earth fault current (sum of charging currents of the healty phases) flows towards the fault location
• Positive current direction is selected to be from busbar to feeders
Single phase to earth fault in unearthed network
Slide 3
Single-phase to earth fault in phase C - What happens to voltages?
UA
UCA
UA
UAB
UA = -UCA
UAB
+U0
UC
UBC
Voltage phasors before the fault
UB
UC
UB = UBC
UB
Voltage phasors after the fault
• Faulty phase voltage UC = 0
• Healty phase voltages equal the line voltages
• Note the direction of the voltage +U0
Single phase to earth fault in unearthed network
Slide 4
Single-phase to earth fault in phase C - What happens to currents ?
IcA + IcB
UA
IcB
This phasor is measured
in healty phases
IcB
IcA
UA = -UCA
IcA
+U0
UB
UC
UB = UBC
IcC
Charge current phasors before the fault
Charge current phasors after the fault
• Charging current leads corresponding phase voltage by 90o
• The direction of the earth fault current is opposite to that of the
charging current in healty phases: Ief vs. (IcA + IcB) = 1800
(see figure in slide 2 !)
This phasor is the earth
fault current
Ief
Single phase to earth fault in unearthed network
Single-phase to earth fault in phase C - What happens to currents ?
• By turning the +U0-phasor in order to have it pointing upwards, the previous figure can be drawn as:
UA = -UCA
+U0
UB = UBC
IcB
IcA + IcB
Direction of
currents in
healty feeders
Ief
Direction of
currents in
faulty feeder
IcA
-U0
• NOTE that in REF the characteristics for directional earth fault protection are drawn using -U0
Slide 5
Single phase to earth fault in unearthed network
Single-phase to earth fault in phase C - What happens to currents ?
• By turning the phasors so that -U0-phasor is pointing upwards, the previous figure can be drawn as:
-U0
IcA
Ief
IcA + IcB
Direction of
currents in
faulty feeder
IcB
UB = UBC
+U0
UA = -UCA
• In REF the characteristics for directional earth fault protection are drawn using -U0
Direction of
currents in
healty feeders
Slide 6
Slide 7
Earth fault in unearthed network
Assumptions:
1. Equal feeder lengths
A B C
ΣI01
- U0
2. Resistive leakage R0 losses
neglected
3. Rf = 0 ohm
4. Positive current direction is
from bus to feeders
U0
C0
ΣI01
R0
ΣI02
- U0
Ief
ΣI02
• ΣI02 ≠ Ief
• I0 measurement in healty feeder (ΣI01) includes only charging currents (healty phases) of that feeder
• I0 measurement in faulty feeder (ΣI02) includes charging currents of the galvanically connected background network, but
not the charging currents of it’s own (these flow in both directions through the measurement point and cancel each other)
• Directional EF-protection is based on the angle of measured I0 versus U0 (-U0 in REF)
Earth fault in unearthed network
Equivalent circuit
Ief
Up
U0
~
Rf
3·C0
U0 =
Up
I ef
=
2
3 ⋅ ω ⋅ C0
1 + (3 ⋅ ω ⋅ C0 ⋅ R f )
• U0 is the voltage drop which is created when Ief flows through the phase-to-earth capacitances
• Rf is NOT included in these!!! See equivalent circuit!!!
Slide 8
Slide 9
Earth fault in 100% compensated network
A B C
Assumptions:
1. Equal feeder lengths
ΣI01
- U0
2. Resistive leakage R0 losses
neglected
3. Rf = 0 ohm
4. Positive current direction is
from busbar to feeders
C0
ΣI02
L
RL
ΣI01
R0
- U0
U0
ΣI02
Ief
• Earth-fault current is cancelled by feeding an equal inductive current with a compensation coil
• I0 measurement in healty feeder (ΣI01) includes only charging currents (healty phases) of that feeder
• I0 measurement in faulty feeder (ΣI02) includes now both the resistive current created by the additonal resistor and it’s
own charging currents
• Directional EF-protection is based on the angle of measured I0 versus U0 (-U0 in REF)
Earth fault in compensated network
Slide 10
Equivalent circuit
Ief
Rf
IRL
Up
~
U0
RL
IR0
R0
IL
ω⋅L
ω⋅
IC
3·ω
ω ⋅C0
U0 =
I ef
2
 1  
1 
 +  3 ⋅ ω ⋅ C 0 −


ω
⋅
L
R


 0
2
• U0 is the voltage drop which is created when Ief flows through the impedance of the parallel connection of phase-to-earth
capacitances, reactor L, additional resistor RL and leakage resistance R0 of the lines
• Rf is NOT included in these!!! See equivalent circuit!!!
Slide 11
Earth fault in 50% under-compensated network
A B C
Assumptions:
1. Equal feeder lengths
ΣI01
- U0
2. Resistive leakage R0 losses
neglected
3. Rf = 0 ohm
4. Positive current direction is
from busbar to feeders
C0
ΣI01
R0
ΣI02
L
RL
- U0
ΣI02
U0
Ief
• 50% of the earth-fault current is cancelled by feeding an inductive current with a compensation coil
• I0 measurement in healty feeder (ΣI01) includes only charging currents (healty phases) of that feeder
• I0 measurement in faulty feeder (ΣI02) includes now only the resistive current created by the additonal resistor
(background network’s and feeders charging current flow in opposite directions in the measurement point and cancel
each other)
• Directional EF-protection is based on the angle of measured I0 versus U0 (-U0 in REF)
Slide 12
Earth fault in 150% over-compensated network
A B C
Assumptions:
1. Equal feeder lengths
ΣI01
- U0
2. Resistive leakage R0 losses
neglected
3. Rf = 0 ohm
4. Positive current direction is
from busbar to feeders
C0
ΣI02
L
RL
ΣI01
R0
- U0
U0
ΣI02
Ief
• 150% of the earth-fault current is cancelled by feeding an inductive current with a compensation coil
• I0 measurement in healty feeder (ΣI01) includes only charging currents (healty phases) of that feeder
• I0 measurement in faulty feeder (ΣI02) includes now both the resistive current created by the additonal resistor, it’s own
charging currents and the overrest of the inductive current
• Directional EF-protection is based on the angle of measured I0 versus U0 (-U0 in REF)
Slide 13
Earth fault in high resistance earthed network
Assumptions:
1. Equal feeder lengths
A B C
2. Resistive leakage R0 losses
neglected
ΣI01
- U0
3. Rf = 0 ohm
4. Positive current direction is
from busbar to feeders
C0
5. IRe = Ictot
ΣI02
ΣI02
Re
ΣI01
R0
- U0
U0
Ief
• Earth-fault current includes a resistive part defined by the size of Re (≤ 1/(3 ·ω·C0tot))
• I0 measurement in healty feeder (ΣI01) includes only charging currents (healty phases) of that feeder
• I0 measurement in faulty feeder (ΣI02) includes now both the resistive current created by the earthing resistor and
capacitive charging current of the galvanically connected background network
• Directional EF-protection is based on angle of measured I0 versus U0 (-U0 in REF)
Earth fault in high resistance earthed network
Slide 14
Equivalent circuit
Rf
Ief
Up
~
IRe
U0
Re
IC
3·ω
ω ⋅C0
U0 =
I ef
2
 1 
 + (3 ⋅ ω ⋅ C 0 )2

 Re 
• U0 is the voltage drop which is created when Ief flows through the impedance of the parallel connection of phase-to-earth
capacitances and earthing resistor Re
• Rf is NOT included in these!!! See equivalent circuit!!!