Star and delta connection relations

The two ways of connecting a three-phase system are star (Y) and delta (Δ).

1. Star connection

One end of each of the three phase windings is joined at a common neutral point N. The other ends are the line terminals R, Y and B.

     R ●
        \
         ● N ── (neutral, 4th wire)
        / \
     Y ●   ● B

Phasor diagram (RYB sequence, V_RN as reference):

   V_BN (+120°)                       V_RY = V_RN − V_YN
       ↖                            ↗  (leads V_RN by 30°)
          ↖                      ↗
             ↖                ↗
                ↖          ↗  30°
                   ●─────────────────► V_RN (0°)
                ↙
             ↙
   V_YN (−120°)

Relations:

• Line voltage V_L = √3 V_ph (each line voltage leads its phase voltage by 30°)
• Line current I_L = I_ph

2. Delta connection

The windings are joined end to start to form a closed loop. The lines are connected to the three junctions.

          R
         / \
        /   \
       Y─────B

Phasor diagram of currents (I_RY as reference). The line current is I_R = I_RY − I_BR:

   I_BR (+120°)
       ↖
          ↖
             ●──────────────────► I_RY (0°)
          ↙     ↘
       ↙           ↘
   I_YB (−120°)       ↘ I_R = I_RY − I_BR (lags I_RY by 30°)

For a balanced load the magnitude of I_R is √3 I_ph, and it lags the phase current I_RY by 30°.

Relations:

• Line voltage V_L = V_ph
• Line current I_L = √3 I_ph

Summary

For both, P = 3 V_ph I_ph cos φ, where φ is the angle between phase voltage and phase current.