Neutral current in star systems
Three Phase Systems · Lesson 8 · Intermediate
Purpose
Calculate star-system neutral current as a phasor sum and recognise unbalance and triplen-harmonic effects.
Learning objectives
- Apply KCL at the star point
- Explain balanced cancellation
- Calculate a simple unbalance
- Recognise triplen addition
Neutral current is determined by the vector sum of the phase currents at the star point. Equal sinusoidal fundamental currents cancel, but unbalance and certain harmonics prevent that cancellation.
Core theory
With a consistent current direction, IN = −(IL1 + IL2 + IL3). For equal fundamental currents spaced 120 degrees, the vector sum is zero.
Unequal magnitudes or phase angles produce neutral current. Maximum neutral current does not necessarily coincide with maximum total demand, so arithmetic subtraction of current magnitudes is unreliable.
Third and other triplen harmonic currents from nonlinear single-phase loads are in phase in the neutral and add rather than cancel. Neutral sizing and cable heating therefore need a harmonic assessment.
| Term | Meaning | Symbol | Unit |
|---|---|---|---|
| Neutral current | Return current equal to the negative phasor sum of line currents | IN | A |
| Unbalance | Inequality of phase current magnitude or angle | Not applicable | Not applicable |
| Triplen harmonic | Odd multiple of the third harmonic that can add in a four-wire neutral | Not applicable | Not applicable |
IN = −(IL1 + IL2 + IL3)Apply Kirchhoff current law using complex phase currents.
A as a phasorAssumptions: Sinusoidal fundamental currents; Ideal neutral.
- Components: 10∠0° = 10 + j0 A; 10∠−120° = −5 − j8.66 A.
- Sum: Line-current sum = 5 − j8.66 A.
- Magnitude: |IN| = √(5² + 8.66²) = 10 A.
Neutral-current magnitude is 10 A.
Reasonableness check: Two equal vectors separated by 120° have a resultant equal to either vector's magnitude.
- Adding phase magnitudes directly
- Assuming balanced fundamentals prove zero harmonic neutral current
- Opening a neutral to measure its effect
Where this appears in practice
Neutral assessment is essential for offices, data centres, EV charging, LED loads, and other nonlinear single-phase load concentrations.
Knowledge check
Do equal third-harmonic currents on all three phases cancel in the neutral?
No. Triplen components are co-phasal in the neutral and add.
Answer: No. Triplen components are co-phasal in the neutral and add.
Practical exercise
Use rectangular components to calculate neutral current for three supplied unequal phase-current phasors.
Summary
- Neutral current is a vector sum
- Balanced fundamentals cancel
- Triplen harmonics can add
Sources and review
- IEC 60038: IEC standard voltages: IEC; 2009+A1:2021; International
- Broken PEN: IET Wiring Matters; Issue 84, 2021; United Kingdom
- Minimizing unnecessary live testing for initial verification: IET Wiring Matters; Issue 105, 2025; United Kingdom
Editorial review date: 2026-08-22. Professional electrical review is pending.