This document discusses different types of unsymmetrical faults in power systems, including single line-to-ground (L-G), line-to-line (L-L), and line-to-line-to-ground (L-L-G) faults. It analyzes these faults using sequence networks to model the positive, negative, and zero sequences. For L-G faults, all three sequence currents are equal. For L-L faults, only the positive and negative sequences are present. For L-L-G faults, all three sequences are present and connected in parallel by the fault impedance.

1. Unsymmetrical Fault Analysis
Prof. V. B. Pandya

2. Introduction
• After fault occurrence system becomes
unblananced
• Types
1. Single line to ground ( an L – G fault)
2. Double line (an L – L fault)
3. Double line to ground (an L – L – G fault)
4. One conductor open fault
5. Two conductors open fault
• First three are shunt/short circuit faults
and last two are series/open circuit faults

3. Sequence networks of generator
Ic1
Ia1
Ib1
Ib2
Ia2
Ic2
Ia0
Ib0
Ic0

4. An L – G fault
• Consider an unloaded generator with neutral grounded via
Zn and an LG fault takes place on phase – a through Zf
Terminal boundary conditions:
f
1.Va Ia Z IfZ f
2. I b 0
3. I c 0
I a1 1 a a2 Ia
Ia2 1 1 a2 a Ib
3
Ia0 1 1 1 Ic
Ia
I a1 Ia2 Ia0
3

5. An L – G fault cont..
• As has been seen, all three sequence currents are equal that
shows three sequence networks viz. positive, negative and zero
seq. networks form series interconnection with each other.

6. An L – G fault cont..
• Magnitude of fault current:
Va Va1 Va 2 Va 0 IaZ f I fZ f
Va1 Ea I a1Z1 , Va 2 0 I a 2 Z 2 , Va 0 0 I a0Z0
f
( Ea I a1Z1 ) (0 I a 2 Z 2 ) (0 Ia0 Z0 ) Ia Z
Ea I a1Z1 Ia2Z2 Ia0 Z0 ( I a1 Ia2 I a 0 )Z f
Since I a1 Ia2 Ia0
Ea
I a1 f
Z1 Z2 Z0 3Z
f 3Ea Z0 Z0 g 3Z n
I
Z1 Z2 Z0 3Z f

7. An L – L fault
• Consider an unloaded generator with neutral grounded
via Zn and an L-L fault takes place between phases b & c
Terminal boundary conditions:
1. I a 0
f
2. I b Ic I
f
3.Vb Vc Ib Z IfZ f

8. An L – L fault conti…
2
I a1 1 a a Ia
Ia2 1 1 a2 a Ib
3
Ia0 1 1 1 Ic
1 2 1 2
Ia0 0, I a1 (a a ), I a 2 (a a )
3 3
I a1 Ia2

9. An L – L fault conti…
Va1 1 a a2 Va
Va 2 1 1 a2 a Vb
3
Va 0 1 1 1 Vc
1 2 1
Va1 (Va aVb a Vc ), Va 2 (Va a 2Vb aVc )
3 3
1
Va1 Va aVb a 2 (Vb I b Z f )
3
1
Va ( a a 2 )Vb a 2 I b Z f )
3
1
(Va Vb a 2 I b Z f ) 1
3
1 2 f 1
Va1 a Ib Z (Va Vb )
3 3

10. An L – L fault conti…
Similarly
1
Va 2 Va a 2Vb a (Vb I b Z f )
3
1
Va ( a a 2 )Vb aI b Z f )
3
1
(Va Vb aI b Z f ) 2
3
1 f 1
Va 2 aI b Z (Va Vb )
3 3

11. An L – L fault conti…
1 2 f 1
Va1 a Ib Z Va 2 aI b Z f (equ1 equ 2)
3 3
1 2 f 1
Va1 a ( I b1 I b 2 I b 0 ) Z Va 2 a ( I b1 I b 2 I b 0 ) Z f
3 3
1 2 2 f 1
Va1 a (a I a1 aI a 2 I a 0 ) Z Va 2 a (a 2 I a1 aI a 2 I a 0 )Z f
3 3
1 f 1
Va1 I a1 (a 1) Z Va 2 I a 2 (a 2 1) Z f
3 3
1 f 1
Va1 I a1 (a 1) Z Va 2 I a 2 (a 2 1) Z f
3 3 3
1 f 1
Put I a1 Ia2 , Va1 I a1Z Va 2 Ia2Z f
2 2
1
Va1 Va 2 ( I a1Z f I a 2 Z f ) I a1Z f Ia2Z f
2

12. An L – L fault conti…
Now Va1 Ea I a1Z1 , Va 2 0 Ia2Z2 I a1Z 2
Va1 Va 2 ( Ea I a1Z1 ) (0 I a 2 Z 2 ) I a1Z f
( Ea I a1Z1 ) ( I a1Z 2 ) I a1Z f
Ea
I a1
Z1 Z2 Zf
Now fault current
If Ib I b1 Ib 2 0
a 2 I a1 aI a 2 I a1 (a 2 a)
f (a 2 a ) Ea j 3 Ea
I
Z1 Z2 Zf Z1 Z2 Zf

13. An L – L sequence network interconnection
• Zero sequence network does not appear and positive and
negative sequence networks are connected via drop in Zf

14. An L – L – G fault
• Consider an unloaded generator with neutral grounded via Zn
and an L-L-G fault takes place between phases b, c & ground

15. An L – L – G fault conti…
Terminal boundary conditions:
1. I a 0 2. I b Ic I f
3.Vb Vc IfZ f
Va1 1 a a2 Va
Va 2 1 1 a2 a Vb , I a Ia0 I a1 Ia2
3
Va 0 1 1 1 Vc
Ia Ia0 I a1 Ia2 0 4
1 2 1
Va1 (Va aVb a Vc ) (Va Vb )
3 3 5
1 1
Va 2 (Va a 2Vb aVc ) (Va Vb )
3 3
1 1 1
Va 0 (Va Vb Vc ) (Va 2Vb ) (Va Vb ) Vb
3 3 3

16. An L – L – G fault conti…
1
Va 0 Vb (Va Vb )
3 6
f f 1
Va 0 I Z (Va Vb )
3
From equ ns 4, 5, 6
f f 1
Va1 Va 2 Va 0 I Z (Va Vb )
3
1 1
Ia0 ( I a Ib Ic ) (Ib Ic )
3 3
1 f 1 f
(0 I ) I
3 3
I f 3I a 0 7
Va1 Va 2 Va 0 IfZ f
Va 0 3I a 0 Z f

17. An L – L – G sequence network interconnection
• Positive, negative and zero sequence network including fault
impedance drop are in parallel from equation 7

18. An L – L – G fault conti…
f f f
Va1 Va 2 Va 0 I Z Va 0 3I a 0 Z
f
(i ) Ea I a1Z Va 0 3I a 0 Z
f
Ea I a1Z Ia0 Z0 3I a 0 Z 8
Ea I a1Z1
Ia0 f
Z0 3Z
(ii ) Va1 Ea I a1Z1 Va 2 0 Ia2Z2
Ea I a1Z1
Ia2
Z2
9

19. An L – L – G fault conti…
As I a I a1 Ia2 Ia0 0, put equ ns 8,9 in this one
Ea I a1Z1 Ea I a1Z1
I a1 0
Z2 Z 0 3Z f
Ea I a1Z1 Ea I a1Z1
I a1 0
Z2 Z2 Z 0 3Z f Z 0 3Z f
Z1 Z1 1 1
I a1 1 Ea
Z2 Z 0 3Z f Z2 Z 0 3Z f
1 1
Z2 Z 0 3Z f Z 0 3Z f Z2
I a1 Ea Ea
Z1 Z1 Z 0 3Z f Z 2 Z1 Z 0 3Z f Z1Z 2
1
Z2 Z 0 3Z f
Ea
I a1
Z 2 Z 0 3Z f
Z1
Z2 Z 0 3Z f

20. Thank You