Wye & delta connections
The key idea
Three impedances and three supply wires can meet in two ways: each impedance from one phase to a shared neutral point (wye), or each impedance between a pair of phases (delta). Same parts, same supply — but delta puts √3 times the voltage across each impedance, and the load draws three times the power.
The idea
A three-phase supply offers two voltages at once. Between any phase and the neutral point is the phase voltage: 230 V on a European low-voltage system. Between any two phases is the line voltage, √3 times larger: 400 V on the same system. The connection decides which of the two your impedances sit across.
In wye (also called star), each impedance runs from one phase to a common center point, so it sees the 230 V phase voltage. The supply wire and the impedance are simply in series, so the current in the line is the current in the impedance.
In delta, the three impedances close into a triangle, each one strung between two phases. Each impedance now sees the full 400 V line voltage. And because every supply line feeds two impedances at once, the line current is √3 times the current inside any one impedance.
Now stack the two effects. √3 times the voltage across each impedance drives √3 times the current through it, and power multiplies the two together. Delta therefore delivers exactly three times the power of wye, from the same supply and the same three impedances.
That factor of three is put to work deliberately: a motor can start in wye at reduced power, then switch to delta to run at full power. It is also why a wrong connection destroys equipment — the same ratio, uninvited.
One more difference hides in the timing. The phase voltage is not just smaller than the line voltage — it lags it by 30°. A transformer often has a wye side and a delta side, and that 30° displacement travels with the connection. It becomes the transformer's vector group.
Try it
Flip the connection and watch the table. In wye, each impedance sees the line voltage divided by √3 and the load takes 4 kW. Switch to delta and each impedance sees the full line voltage. The same three impedances now take 12 kW.
total power: 4.0 kW
| Wye · selected | Delta | |
|---|---|---|
| Voltage across each Z | 231 V | 400 V |
| Current through each Z | 5.8 A | 10.0 A |
| Current in each line | 5.8 A | 17.3 A |
| Total power | 4.0 kW | 12.0 kW |
The supply is 400 V line-to-line, and the load is resistive. Flip the connection to delta. Each impedance then sees √3 times the voltage, so it draws √3 times the current. The supply delivers three times the power through the same three wires.
Why it matters
- Ratings depend on the connection. A heater bank rated for 230 V in wye sees √3 times its rated voltage if someone reconnects it in delta. Power in a resistor rises with the voltage squared, so each element now makes nine times its design heat.
- Wye–delta starting uses the 3× ratio on purpose. Started in wye, a motor draws one third of its current and one third of its power. The switch to delta then gives it full torque once it is turning.
- The 30° shift becomes transformer vector groups. A wye–delta transformer moves the phase angle by 30°. Every protection decision downstream, and every decision to parallel two transformers, has to respect that shift.
- Only wye gives you a neutral point. A wye point can be earthed, and it carries the unbalance current; delta has no neutral at all. That one choice drives the earthing arrangement and the network's behavior under unbalanced load.
The math, if you want itOptional — the page reads completely without it
The two voltages of a three-phase supply differ by √3 in size and 30° in time:
line and phase voltage
VLL = √3 · Vph · Vph = VLL ∠−30° / √3
In wye, each impedance simply carries the line current. In delta, each line feeds two impedances, and their currents combine with the same √3 and 30° geometry:
delta line current
Iline = √3 · IZ
Total three-phase power for the same impedance Z on the same supply:
wye vs delta power
Pwye = VLL²Z cos φ · Pdelta = 3 · VLL²Z cos φ
The widget uses a resistive load (cos φ = 1), so each phase simply dissipates V²/Z, but the √3 and 3× ratios hold at any power factor.
See it in Phasor
In Phasor, transformer and load elements carry their connection as a property: wye or delta, with or without an earthed neutral. The single-line diagram draws one wire, but the connection you chose still decides the phase voltages, the zero-sequence path, and the earth-fault behavior the studies compute.