Three-Phase Power and Drives
Line Voltage, Phase Voltage and Imbalance
Understand different connection voltages and what an unbalanced neutral carries.
You are applying “Line Voltage, Phase Voltage and Imbalance” to a real system and need the concept, assumptions and verification boundary to stay clear.
Identify line-to-line, line-to-neutral and winding voltage in wye and delta connections, apply the square-root-of-three relation only under its balanced sinusoidal assumptions, and understand neutral current from load imbalance and triplen harmonics.
- Select or check first
- Name the connection before using √3. The familiar V_LL = √3 V_LN relation requires a balanced sinusoidal wye set. Delta branch voltage equals the line-to-line voltage because each branch is physically connected between two lines. These statements are not interchangeable.
- Controlling assumption
- Circuit state, waveform, source impedance, ratings, temperature and protection topology match the equipment being analysed.
- Top risk
- Three-phase measurements are hazardous and connection-specific. Do not infer voltage from wire color or nominal labels. Use qualified personnel, appropriate PPE, an instrument and probes rated for the installation category, and an approved procedure. Isolate and verify absence of voltage before changing connections.
- Proof
- Check the exact manufacturer data, units and limits, then verify the result by calculation, measurement or a controlled acceptance test.
Start with the basics Optional foundation before “Line Voltage, Phase Voltage and Imbalance”
Electrical-engineering basics
Electrical behaviour becomes easier to reason about when every voltage has a reference and every current has a complete return path.
- Voltage
- Voltage is potential difference between two points. A voltage statement is incomplete unless both points or its reference are known.
- Current
- Current is charge flow through a path. It does not disappear after a component; in a complete circuit it returns to the source.
- Resistance and impedance
- Resistance opposes steady current. Impedance extends that idea to changing signals and can depend on frequency through capacitance and inductance.
- Power and heat
- Electrical power is the rate of energy transfer. Some becomes useful output and some becomes heat that must stay within component and enclosure limits.
- Rating versus operating point
- A rating is a limit or qualified condition, not a target. The operating point must remain inside all relevant voltage, current, power, temperature and timing limits.
How to use this article: Draw the source, load, reference and return path before calculating. Treat exposed or stored electrical energy as hazardous until isolation is proved.
On this page
The word phase can refer to a source waveform, a line conductor or one physical winding, so a bare phrase such as phase voltage is ambiguous. Start by naming the two measurement points and the connection. Line-to-line voltage is measured between two line conductors. Line-to-neutral voltage is measured between one line and the source or load neutral. Winding voltage is the voltage across one branch of a wye or delta-connected load.
Wye and delta expose different voltages to a branch
Diagram description
The photographed components are illustrative winding branches. The lower note confines the square-root-of-three relation to balanced sinusoidal wye conditions.
Balanced sinusoidal wye voltage
|V_LL| = √3·|V_LN|
A line-to-line voltage is the phasor difference between two equal line-to-neutral voltages separated by 120 degrees. Vector subtraction gives √3, not ordinary scalar subtraction. The corresponding line-to-line phasor is also shifted by 30 degrees relative to the chosen line-to-neutral reference.
- V_LL
- RMS line-to-line voltage phasor or magnitude, V
- V_LN
- RMS line-to-neutral voltage phasor or magnitude, V
A balanced 400 V line-to-line wye system has about 400/√3 = 231 V line-to-neutral. The familiar 230/400 V labels are nominal system values, not a promise of an exact measured voltage.
Delta branch voltage
V_phase,Δ = V_LL
This follows from the topology: every delta branch connects directly between a pair of lines. It does not mean wye and delta windings of the same impedance draw the same line current or produce the same power.
| Connection | Branch terminals | Branch-voltage relationship |
|---|---|---|
| Four-wire wye | Line to neutral/star point | V_phase = V_LN; balanced sinusoidal |V_LL| = √3|V_LN| |
| Three-wire wye | Line to internal star point | Branch voltage depends on source and load balance; star point may shift |
| Delta | Line to line | V_phase,Δ = V_LL by connection |
The neutral carries the vector sum left by the phase currents
Diagram description
The illustration's scope is fundamental-frequency load imbalance in a four-wire wye system. It does not cover harmonic neutral current, which requires an additional check.
Neutral-current phasor sum
I_N = −(I_A + I_B + I_C)
Equal sinusoidal fundamental currents spaced 120 degrees sum to zero. If branch magnitudes or angles differ, the vector sum is not zero and the neutral carries the remainder. Arithmetic addition of RMS magnitudes gives the wrong answer for ordinary fundamental imbalance.
- I_N
- neutral-current phasor, A
- I_A, I_B, I_C
- phase-current phasors with stated directions, A
If only one line-to-neutral branch carries 10 A and the other two are open, the neutral carries 10 A in the return path—not 30 A and not zero.
| Cause | Possible observation | Consequence |
|---|---|---|
| Uneven single-phase loads | Different phase currents | Neutral current and unequal feeder drop |
| Loose or high-resistance connection | Voltage displacement and local heating | Equipment undervoltage/overvoltage or fire risk |
| Open neutral | Floating load star point | Dangerous redistribution of line-to-neutral voltages |
| Source voltage imbalance | Unequal line or phase voltage | Disproportionate motor current imbalance and heating |
| Nonlinear electronic loads | Harmonic-rich phase currents | Triplen harmonics can accumulate in neutral |
Triplen harmonics do not cancel like the fundamental
Third-harmonic current and other triplen orders—9th, 15th and so on—are zero-sequence components in a three-phase four-wire system: the corresponding components in the three phases can be in phase with one another. They therefore add in the neutral instead of canceling. A system may have equal phase RMS currents yet significant neutral current when nonlinear line-to-neutral loads are present.
| Question | Required evidence |
|---|---|
| Are phase currents balanced? | Per-phase RMS magnitude and phase relationship |
| Are loads nonlinear? | Current waveform or harmonic spectrum, especially triplen orders |
| Is the neutral continuous and correctly terminated? | De-energized inspection and approved tests |
| Can neutral current exceed a phase-current assumption? | Applicable wiring standard, load study and conductor derating |
| Are protection and switching poles appropriate? | System earthing arrangement and governing rules |
Why a lost neutral can damage line-to-neutral loads
In an unbalanced wye load with no solid neutral reference, the common load point can shift. The branch voltages then divide according to the connected impedances rather than remaining at the nominal line-to-neutral value. One load can receive undervoltage while another receives damaging overvoltage. Turning loads on or off can move the voltages again, so the fault can look intermittent.
Use Why Three-Phase Power Runs Motors Smoothly for phase spacing and sequence. The safe measurement sequence in Using a Multimeter and a Diagnostic Sequence remains essential; it does not replace three-phase training or site procedures.
One-minute questions
Questions to answer before you apply this lesson
What should I select or check first for Line Voltage, Phase Voltage and Imbalance?
Name the connection before using √3. The familiar V_LL = √3 V_LN relation requires a balanced sinusoidal wye set. Delta branch voltage equals the line-to-line voltage because each branch is physically connected between two lines. These statements are not interchangeable.
Which assumption can change the conclusion?
Circuit state, waveform, source impedance, ratings, temperature and protection topology match the equipment being analysed.
What can go wrong if I copy the example directly?
Three-phase measurements are hazardous and connection-specific. Do not infer voltage from wire color or nominal labels. Use qualified personnel, appropriate PPE, an instrument and probes rated for the installation category, and an approved procedure. Isolate and verify absence of voltage before changing connections.
How do I verify the result in the real system?
Check the exact manufacturer data, units and limits, then verify the result by calculation, measurement or a controlled acceptance test.
Sources and further reading
- Definition of Reactive Power — Electrical Installation GuideSchneider Electric · 2026-10-13Manufacturer engineering guide reviewed for three-phase use of line-to-line voltage, line current and √3 relationships under the stated conditions.
- Sizing the Neutral Conductor — Electrical Installation GuideSchneider Electric · 2026-10-13Reviewed for fundamental phase-current cancellation, triplen-harmonic accumulation in the neutral and conductor-sizing implications.
- Three-Phase Monitoring Relays — Function DescriptionABB · 2026-10-13Manufacturer documentation reviewed for phase imbalance, star-point displacement and interrupted-neutral monitoring limitations.
- Other Lamp Technologies — Constraints and RecommendationsSchneider Electric Electrical Installation Guide · 2026-10-13Reviewed for the practical example of triplen harmonic currents from nonlinear line-to-neutral loads adding in the neutral.