Intro to three-phase
What you’ll learn
- Why power is generated and distributed as three phases, 120° apart.
- Line and phase values: what each voltage and current means.
- Wye: line voltage = √3 × phase voltage. Delta: line current = √3 × phase current.
- The common systems — 120/208, 347/600 and 277/480 V — and where they come from.
- Three-phase power, P = √3 × V × I × PF, and phase rotation.
Three-phase power is three AC supplies on three conductors, each the same voltage and frequency but timed 120° apart — a third of a cycle. At any instant the three add up to zero, which is why they can share a return path or need none at all, and together they make the rotating magnetic field that turns every industrial motor. Two ideas carry you through: the difference between line and phase values, and the number √3 ≈ 1.732.
Why three phases
A generator with three sets of coils spaced 120° around the stator makes three voltages 120° apart for almost no extra effort. What you get for it: power that flows steadily instead of pulsing to zero twice a cycle, a magnetic field that rotates on its own (so a three-phase motor needs no starting capacitor), and more power moved per kilogram of copper. That is why the grid, big buildings and industry are three-phase, and a house simply takes one phase of it through a transformer.
Line values and phase values
Line values are measured on the conductors: line-to-line voltage, and the current in each line conductor. Phase values belong to each individual winding (or load element): the voltage across it and the current through it. How they relate depends on how the three windings are joined.
| Wye (star) | Delta | |
|---|---|---|
| Voltage | Vline = √3 × Vphase | Vline = Vphase |
| Current | Iline = Iphase | Iline = √3 × Iphase |
| Neutral | Yes — the centre point | No (except a centre-tapped high-leg delta) |
The systems you will meet
Wye systems are named by both voltages, phase then line: 120/208 V (apartments, commercial, both countries), 347/600 V (Canadian commercial and industrial — 347 V lighting), and 277/480 V (the US equivalent — 277 V lighting). Each pair is √3 apart.
1. Checking the pairs
- 120 × 1.732 = 207.8 → 208 V.
- 347 × 1.732 = 601.0 → 600 V (the nominal figures are rounded).
- 277 × 1.732 = 479.8 → 480 V. Going the other way: 480 ÷ 1.732 = 277.1 V.
2. A delta-connected load
- Three heater elements in delta on 240 V, each drawing 10 A.
- Each element sees the full line voltage: 240 V.
- Each line current: 1.732 × 10 = 17.3 A — not 20, and not 10.
Three-phase power
- S = √3 × VL × ILvolt-amps
- P = √3 × VL × IL × PFwatts
- IL = P ÷ (√3 × VL × PF)line amps
3. A balanced 208 V load
- 30 A per line at 208 V, resistive (PF = 1).
- P = 1.732 × 208 × 30 × 1 = 10,808 W ≈ 10.8 kW.
- Balanced wye, so the neutral carries 0 A: the three 30 A currents, 120° apart, cancel.
Phase rotation
The order the phases peak in — A, B, C or A, C, B — is the phase rotation. It decides which way a three-phase motor turns. Swap any two line leads and the rotation reverses; that is exactly what the forward/reverse starter does. A phase-rotation meter tells you the sequence before the motor is ever coupled to its load.
Try one: the high leg of a 120/240 V delta
The centre tap sits in the middle of one 240 V winding. From it to the opposite corner is 240 × √3 ÷ 2 = 240 × 0.866 ≈ 208 V — the “high leg” or “wild leg”. The other two phases are 120 V to the tap.
On the job
Tips from the job
- Know the system before you meter it: on 347/600 V, a lighting circuit is 347 V to neutral — not 120. On 277/480 V it is 277 V.
- Check rotation with a phase-rotation meter before you couple a motor to a pump or a conveyor. Bumping it to see which way it spins is not always safe.
- A heavily loaded neutral on a 120/208 V wye usually means unbalance or electronic loads. Measure it; don’t assume it is zero.
- High-leg (four-wire) delta services still exist, mostly in older US buildings. One phase is about 208 V to neutral — never feed a 120 V load from it. Marking rules are in your code book.
Common mistakes
- Using line-to-neutral voltage in P = √3 × V × I. The formula takes line-to-line voltage and line current.
- Multiplying by √3 twice — once on the voltage and again on the power.
- Assuming “600 V system” means 600 V to ground on a wye. It is 347 V to the grounded neutral.
- Swapping all three leads to reverse a motor. Only two.
Check yourself
8 questions. Tap an answer — it is marked straight away and the reason opens under it. Get 80% or better and the lesson is ticked off on the year page.
Not started yet.
-
How far apart are the three phases of a three-phase supply?
Answer and why
C. Three phases share the 360° of a cycle equally: 360 ÷ 3 = 120° between each.
-
In a wye system, the line-to-line voltage is…
Answer and why
B. Vline = √3 × Vphase. 120 × 1.732 ≈ 208; 347 × 1.732 ≈ 601; 277 × 1.732 ≈ 480.
-
A 347/600 V wye system. What is the line-to-neutral voltage?
Answer and why
B. 347 V is line-to-neutral (the phase voltage); 600 V is line-to-line. Canadian commercial lighting often runs at 347 V; the US equivalent is 277 V on a 277/480 system.
-
In a delta connection, the line current is…
Answer and why
B. Each line feeds two windings of the delta, whose currents are 120° apart, so Iline = √3 × Iphase. 10 A in each winding → 17.3 A in each line.
-
In a delta connection, the line-to-line voltage is…
Answer and why
A. Each winding is connected straight across two lines, so it sees the full line voltage.
-
Power of a balanced three-phase resistive load: 208 V, 30 A per line?
Answer and why
B. P = √3 × VL × IL × PF = 1.732 × 208 × 30 × 1 ≈ 10,808 W.
-
On a perfectly balanced wye load, the neutral current is…
Answer and why
B. Three equal currents 120° apart add to zero at every instant. Unbalance (and some harmonic currents) is what puts current on a three-phase neutral.
-
A three-phase motor runs backwards. The fix is to…
Answer and why
A. Swapping any two lines reverses the phase rotation, and the rotating field turns the other way. Swapping all three in a row keeps the same rotation.
Questions people ask
Why is three-phase used instead of single-phase?
Three phases deliver power smoothly (the total never drops to zero the way a single phase does twice a cycle), they make a rotating magnetic field so motors start and run without extra parts, and they move more power for the amount of copper. Almost all generation and industrial loads are three-phase; houses take one phase off it.
Where does √3 come from?
Two phase voltages 120° apart do not add or subtract straight. The difference between two equal vectors 120° apart works out to √3 (about 1.732) times either one — that is simple triangle geometry. So line-to-line is √3 × line-to-neutral in a wye.
What is 120/208 V?
A wye system with 120 V from each phase to neutral and 120 × √3 ≈ 208 V between phases. It is common in apartment and commercial buildings in both Canada and the US. Two phases and a neutral give 120/208 V — not 120/240 V — which is why 240 V appliances run a little weak on it.
Related
- Wye and delta (glossary) — the short version.
- Single-phase transformers — the lesson before this one.
- Magnetism and motors — what three phases do inside a motor.
- Single & three phase formulas — printable, with √3.
- Wye-delta starting — the connection used as a starter.
- All second year lessons
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