---
title: "No zero sequence in line-to-line fault"
subject: "Power System Analysis II"
chapter: 5
key: "semester_5/power_system_analysis_ii:ll-fault-zero-sequence-absent"
source: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/ll-fault-zero-sequence-absent
site: BCT Engineering
---

# No zero sequence in line-to-line fault

Power System Analysis II · Chapter 5: Unsymmetrical Faults on Power Systems

- Asked in: 2082 Baishakh, 8 marks; 2076 Asoj, 8 marks (asked 2 times)
- Video: [Line to Line Fault on an Unloaded Generator/LL Fault](https://www.youtube.com/watch?v=9IhgIfJRCkM) — Dr.Nagaraja Kumari
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/ll-fault-zero-sequence-absent
- Whole chapter: https://www.bctengineer.com/md/semester_5/power_system_analysis_ii/chapter-5

## Question

From suitable diagram and mathematics show that during a line to line (double line) fault in a transmission line, zero sequence component is absent in the expression of fault current.

## Short answer

In a line-to-line fault, I_b = –I_c and I_a=0, so I_a0 = (I_a+I_b+I_c)/3 = 0. The zero sequence current is absent, and fault current I_f = –j√3 V_f/(Z_1+Z_2+Z_f) depends only on positive and negative sequence impedances.

## Answer

In a line-to-line fault there is no path to ground and the two fault currents are equal and opposite, so $I_a + I_b + I_c = 0$ and the zero sequence current $I_{a0} = 0$; the fault current depends only on $Z_1$ and $Z_2$.

**Model:** at the fault point on the line, the system is replaced by its Thevenin sequence networks: prefault voltage $V_f$ and impedances $Z_1$, $Z_2$, $Z_0$ seen from the fault point.

#### Boundary conditions (fault between phases b and c through $Z_f$)
```text
  a o-----------  Ia = 0
  b o-----+        Ib = If -->
          Zf
  c o-----+        Ic = -Ib
```
$$
I_a = 0, \qquad I_b + I_c = 0, \qquad V_b - V_c = Z_fI_b
$$

#### Sequence currents
$$
\begin{aligned}
I_{a0} &= \tfrac13(I_a + I_b + I_c) = \tfrac13(0 + I_b - I_b) = 0 \\
I_{a1} &= \tfrac13(I_a + aI_b + a^2I_c) = \tfrac13(a - a^2)I_b \\
I_{a2} &= \tfrac13(I_a + a^2I_b + aI_c) = \tfrac13(a^2 - a)I_b
\end{aligned}
$$
Hence
$$
I_{a0} = 0, \qquad I_{a2} = -I_{a1}
$$

So the zero sequence current is **absent**: with no connection to ground, current that leaves through phase b returns through phase c, and the three line currents sum to zero.

#### Voltage condition
$$
\begin{aligned}
V_b - V_c &= (a^2 - a)V_{a1} + (a - a^2)V_{a2} = (a^2 - a)(V_{a1} - V_{a2}) \\
Z_fI_b &= Z_f\,(a^2I_{a1} + aI_{a2}) = Z_f(a^2 - a)I_{a1}
\end{aligned}
$$
so
$$
V_{a1} - V_{a2} = Z_fI_{a1}
$$
With $V_{a1} = V_f - Z_1I_{a1}$ and $V_{a2} = -Z_2I_{a2} = Z_2I_{a1}$:
$$
I_{a1} = -I_{a2} = \frac{V_f}{Z_1 + Z_2 + Z_f}
$$

#### Fault current
$$
\begin{aligned}
I_f = I_b &= I_{a0} + a^2I_{a1} + aI_{a2} = (a^2 - a)I_{a1} \\
&= -j\sqrt3\,I_{a1} = \frac{-j\sqrt3\,V_f}{Z_1 + Z_2 + Z_f}
\end{aligned}
$$
$Z_0$ does not appear in the expression, confirming that the zero sequence network plays no part.

#### Interconnection of sequence networks
```text
        Ia1 -->           <-- Ia2
  +--(Ea)--Z1---o F1--Zf--o F2---Z2--+
  |                                  |
  N1 ------------------------------- N2

  Zero sequence network: not connected (Ia0 = 0)
```
The positive and negative sequence networks are connected **in parallel (in opposition)** through $Z_f$; the zero sequence network is left open.

#### Consequences
- The L-L fault current does not depend on the grounding of the neutral or on line zero sequence impedance.
- With $Z_1 = Z_2$ and $Z_f = 0$: $I_f = \frac{\sqrt3}{2}\cdot\frac{V_f}{Z_1} = 0.866 \times I_{3\phi}$, i.e. smaller than the three-phase fault current.
- Also $V_{a0} = 0$ at the fault, since the zero sequence network carries no current.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why is the zero sequence current absent in an L-L fault?
   A. Because Z0 is infinite in all systems
   B. Because the generator neutral is grounded
   C. Because the fault impedance blocks it
   D. No ground path exists; Ib = -Ic and Ia = 0, so Ia + Ib + Ic = 0
   Answer: D. Ia0 = (Ia + Ib + Ic)/3 = 0 since the fault current goes out one phase and returns in the other. (Key point: Why Ia0 = 0)

2. Which expression shows Z0 is absent from the fault current?
   A. If = -j sqrt(3) Vf/(Z1 + Z2 + Zf)
   B. If = 3Vf/(Z1 + Z2 + Z0)
   C. If = Vf/(Z1 + Z0)
   D. If = Vf/Z0
   Answer: A. Only Z1, Z2 and Zf appear because the zero sequence network is left open. (Key point: Fault current independent of Z0)

3. In an L-L fault the negative sequence current equals:
   A. Ia1
   B. -Ia1
   C. Ia0
   D. 3Ia1
   Answer: B. Ia2 = (a^2 - a)Ib/3 = -Ia1. (Key point: Relation Ia2)

4. With Z1 = Z2 and Zf = 0, how does the L-L fault current compare with the three-phase fault current?
   A. Equal
   B. Twice as large
   C. 0.866 times, i.e. smaller
   D. Three times as large
   Answer: C. If = sqrt(3)Vf/(2Z1) = (sqrt(3)/2)(Vf/Z1) = 0.866 I3phase. (Key point: L-L vs 3-phase)

## Related in Power System Analysis II

- [No zero sequence current in delta lines](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Adelta-zero-sequence-absent) — Power System Analysis II, chapter 4, asked 2×
- [L-L fault: I0 absent and I1 = −I2](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3All-fault-generator-i1-equals-i2) — Power System Analysis II, chapter 5
- [Line-to-line fault current calculation](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Aline-to-line-fault-calculation) — Power System Analysis II, chapter 5, asked 4×
- [SLG fault: sequence networks in series](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Aslg-sequence-networks-series) — Power System Analysis II, chapter 5, asked 5×
- [DLG fault sequence network connection](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Adlg-sequence-network-connection) — Power System Analysis II, chapter 5, asked 3×
- [Fault at both ends of a 50 Ω line](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Afault-points-p-q-line) — Power System Analysis II, chapter 3

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