Three-phase supply, star and deltaTwo 230 volt lines. Why is it 400 between them, not 460?

A generator has three sets of windings, each creating an EMF set 120° apart. So a three-phase supply is effectively three supplies all rising and falling at different times.

• The star system produces 230 V and 400 V. 230 V × √3 (1.732) ≈ 400 V.
• Single-phase houses on a street are each connected to one line plus neutral, spread across L1, L2 and L3 to keep the load balanced. Any line to neutral = 230 V.
• Three-phase commercial and industrial supplies use all three lines. Any line to line = 400 V.
• The phases are 120° apart because 360° ÷ 3 = 120°.
• Why 400 V and not 460 V (230 + 230)? Two phases never reach their peaks at the same moment. They cross before either one peaks, so the difference between them tops out at 400 V, not double. (415 V is the old figure and no longer used.)
• Delta (the primary side) has its three windings joined end to end, so there is no star point and no neutral. On a distribution transformer the delta primary is fed at 11 kV; the star secondary gives the 230/400 V supply.
• Star (the secondary side) has a neutral. Houses put different loads on each phase, so the phases become unbalanced, and the neutral carries that out-of-balance current back.
• Two-phase supplies (two lines plus neutral) exist but are rare, only for very large properties.