---
title: "No zero sequence current in delta lines"
subject: "Power System Analysis II"
chapter: 4
key: "semester_5/power_system_analysis_ii:delta-zero-sequence-absent"
source: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/delta-zero-sequence-absent
site: BCT Engineering
---

# No zero sequence current in delta lines

Power System Analysis II · Chapter 4: Unbalanced System Analysis

- Asked in: 2072 Chaitra, 6 marks; 2083 Baishakh (new course), 5 marks (asked 2 times)
- Video: [Zero Sequence Current Component in Star and Delta Connection](https://www.youtube.com/watch?v=jFWQQqOddOk) — Basic Electrical
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/delta-zero-sequence-absent
- Whole chapter: https://www.bctengineer.com/md/semester_5/power_system_analysis_ii/chapter-4

## Question

With suitable mathematical aid, show (justify) that in a delta connected system, zero sequence components of current are absent in the line currents.

## Short answer

In a delta connection, the three line currents always sum to zero since there is no neutral path, so their zero-sequence component (Ia0 = (Ia+Ib+Ic)/3) is zero. Zero-sequence currents can circulate within the closed delta but never appear in the line currents.

## Answer

In a delta connected system there is no neutral or ground return path, so the three line currents always add to zero; hence their zero sequence component $I_{a0} = \frac13(I_a+I_b+I_c)$ is zero.

#### Line currents of a delta
```text
            a
           /\
   Ia -->  /  \
     Iab  /    \  Ica
         /      \
 Ib --> b--------c <-- Ic
           Ibc
```
Applying KCL at the three corners:
$$
\begin{aligned}
I_a &= I_{ab} - I_{ca} \\
I_b &= I_{bc} - I_{ab} \\
I_c &= I_{ca} - I_{bc}
\end{aligned}
$$

#### Zero sequence line current
$$
\begin{aligned}
I_{a0} &= \frac13 (I_a + I_b + I_c) \\
&= \frac13\left[(I_{ab}-I_{ca}) + (I_{bc}-I_{ab}) + (I_{ca}-I_{bc})\right] \\
&= 0
\end{aligned}
$$
This holds for any values of the delta currents, balanced or unbalanced. So **line currents into a delta never contain zero sequence components**.

#### Phase (delta) currents in sequence form
Let the delta currents have components $I_{ab0}, I_{ab1}, I_{ab2}$. Then
$$
I_a = I_{ab} - I_{ca}
$$
For the zero sequence part, $I_{ab0} = I_{bc0} = I_{ca0}$, so it cancels in every line current. For positive and negative sequence:
$$
I_{a1} = (1 - a)\,I_{ab1} = \sqrt3\,\angle -30^\circ\, I_{ab1}, \qquad
I_{a2} = (1 - a^2)\,I_{ab2} = \sqrt3\,\angle 30^\circ\, I_{ab2}
$$

#### Consequences
- A zero sequence current can **circulate inside the delta** (for example, from induced zero sequence voltages or third harmonics) but it cannot leave the delta into the lines.
- In the zero sequence network, a delta connected load or winding is **open from the line side**. For a transformer, the delta winding is shown as a short to the reference on its own side (current circulates) but open to the line.
- Similarly, the line-to-line voltages of any system have no zero sequence component because $V_{ab}+V_{bc}+V_{ca} = 0$.

## Check yourself

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

1. Zero sequence line current is absent in a delta because:
   A. Line currents always sum to zero, as there is no neutral return path
   B. Delta voltages are always balanced
   C. Delta impedances are zero
   D. Zero sequence current is blocked by the source
   Answer: A. Ia0 = (Ia+Ib+Ic)/3 and KCL gives zero sum for a delta. (Key point: Why I0 is zero)

2. Substituting Ia=Iab-Ica, Ib=Ibc-Iab, Ic=Ica-Ibc into Ia0 = (Ia+Ib+Ic)/3 gives:
   A. Iab/3
   B. 0, whatever the delta currents are
   C. 0 only if delta currents are balanced
   D. Ia1
   Answer: B. Each delta current appears once with + and once with -, so they cancel for any values. (Key point: Mathematical proof)

3. What can happen to zero sequence current in a delta winding?
   A. It flows out through the lines to ground
   B. It becomes positive sequence
   C. It can circulate inside the delta but cannot enter the lines
   D. It is doubled in the lines
   Answer: C. Phase currents may have equal zero sequence parts that circulate, cancelling in each line current. (Key point: Circulating current)

## Related in Power System Analysis II

- [No zero sequence in line-to-line fault](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3All-fault-zero-sequence-absent) — Power System Analysis II, chapter 5, 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
- [Sequence impedances and zero sequence comment](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Asequence-impedance-star-load-zero) — Power System Analysis II, chapter 4, asked 2×
- [Zero sequence Thevenin impedance at bus 2](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Azero-sequence-thevenin-bus2) — Power System Analysis II, chapter 4
- [Sequence networks of Y load, neutral current](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Astar-load-sequence-networks-neutral) — Power System Analysis II, chapter 4, asked 2×
- [Sequence voltages, currents and powers (2072)](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Asequence-voltages-currents-powers-2072) — Power System Analysis II, chapter 4

## Related in other subjects

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- [Delta connected coils line current and power](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Adelta-coils-7ohm-0-03h-400v) — Basic Electrical Engineering, chapter 8
- [Delta load phase currents, power, line currents](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Adelta-load-100v-6-8-4-3-ohm) — Basic Electrical Engineering, chapter 8
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