Three-phase systems
The key idea
The grid does not send one wave. It sends three copies of the same wave, each one started a third of a cycle later. Spaced like that, the three always add up to zero — and together they deliver smooth, constant power.
The idea
A single AC wave has a problem: its power pulses. Twice every cycle, the wave passes through zero, and for that instant it delivers nothing. Motors fed this way vibrate, and every part of the system must be sized for the peaks.
Three-phase fixes this with timing. Take three identical waves — call them A, B and C — and shift each one by 120°, one third of a cycle. Now, at every instant, at least two phases are carrying. The total power delivered is perfectly constant, and a motor built for three phases turns with smooth torque.
There is a second gift. At every instant, the three waves sum to exactly zero. In a balanced system, the current that goes out on one phase comes back on the other two. No separate return conductor is needed — three wires do the work of six.
Try it
Turn on Show the sum and watch the dashed line: flat zero, always.
- Phase A
- Phase B
- Phase C
Each phase is a copy of the same wave, started a third of a cycle later. Turn on the sum: it is zero at every instant. That is why a balanced system needs no return conductor.
Why it matters
- Almost every network you will model is three-phase. Generation, transmission and distribution all run on it; single-phase circuits are the last few meters to small loads.
- "Balanced" is the standard assumption. When the three phases carry equal load, one phase tells you everything — which is why a single-line diagram can draw one line instead of three.
- Unbalance is where faults live. A fault on one phase breaks the symmetry. Analyzing that needs the method of symmetrical components — coming to this learning center with the short circuit concepts.
The math, if you want it
The three phase voltages are vA = Vm sin(ωt), vB = Vm sin(ωt − 120°), and vC = Vm sin(ωt − 240°). Their sum is zero for every t — the three unit phasors 1∠0°, 1∠−120°, 1∠−240° add to nothing. Between any two phases, the line-to-line voltage is √3 times the phase voltage, which is why 230 V phase circuits live on a 400 V system, and total three-phase power is P = √3 · VLL · I · cos φ.
See it in Phasor
Phasor models the balanced three-phase network through its single-line diagram: one drawn line stands for all three phases. The rotating field on the home page shows the three phasors and their waves — the same picture as the widget above.