Wye & delta connections
The key idea
Three impedances and three supply wires can meet in two ways. In wye, each impedance runs from one phase to a shared neutral point. In delta, each impedance runs between a pair of phases. The parts and the supply are the same in both connections. The delta connection puts √3 times the voltage across each impedance, and the load draws three times the power.
The idea
A three-phase supply gives you two voltages at once. The voltage between any phase and the neutral point is the phase voltage. On a European low-voltage system it is 230 V. The voltage between any two phases is the line voltage, which is √3 times larger. On the same system it is 400 V. The connection decides which of the two voltages your impedances sit across.
In wye (also called star), each impedance runs from one phase to a common center point. Each impedance sees the phase voltage of 230 V. The wire and the impedance are in series. The current in the supply line is therefore the same as the current in the impedance.
In delta, each impedance runs between two phases. The three impedances close into a triangle. Each impedance now sees the full 400 V line voltage. Each supply line feeds two impedances at once. The line current is therefore √3 times the current inside any one impedance.
Now combine the two effects. The √3 increase in voltage across each impedance drives a √3 increase in the current through it. The power formula multiplies the two increases. Delta therefore delivers exactly three times the power of wye from the same supply and the same three impedances.
This ratio matters in practice. A motor starts in wye at reduced power, and then it runs in delta at full power. A wrong connection destroys equipment for the same reason.
The two voltages also differ in time. The phase voltage in wye is smaller than the line voltage, and it also lags the line voltage by 30°. A transformer often has a wye side and a delta side. The 30° displacement then travels with the connection.
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. In delta, each impedance sees the full line voltage, and the load takes 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 takes √3 times its rated voltage if someone reconnects it in delta. Each element then makes nine times the design heat, because the power in a resistor rises with the voltage squared.
- Wye–delta starting uses the 3× ratio on purpose. A motor that starts in wye draws one third of its power and one third of its current. The switch to delta then gives the motor full torque after it turns.
- The 30° shift becomes transformer vector groups. A wye–delta transformer moves the phase angle by 30°. Every protection decision downstream must respect that shift, and so must every decision to parallel two transformers.
- Only wye gives you a neutral point. Wye offers a neutral point that you can earth and that carries unbalance. Delta has no neutral point. That choice drives the earthing arrangements and the 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 and by 30°:
line and phase voltage
VLL = √3 · Vph · Vph = VLL ∠−30° / √3
In wye, each impedance carries the line current directly. In delta, each line feeds two impedances, and the currents combine with the same √3 and 30° geometry:
delta line current
Iline = √3 · IZ
Total three-phase power for the same impedance Z and 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). The powers are therefore V²/Z per phase. The √3 and 3× ratios do not depend on the power factor.
See it in Phasor
In Phasor, transformer and load elements carry their connection as a property. The property is wye or delta, with or without an earthed neutral. The single-line diagram draws one wire. The connection choice still decides the phase voltages, the zero-sequence path, and the earth-fault behavior that the studies compute.