Derivation of line and phase relations in star and delta:

Star connection:

• The three phase windings have one end of each connected to a common neutral point; the other ends form the three line terminals.
• Line current = phase current: IL = Iph (the same current flows through the winding and the line).
• Line voltage: the line voltage is the phasor difference of two phase voltages, which are 120 degrees apart. By phasor addition, VL = root 3 x Vph.
• Vector diagram: three phase voltages VRN, VYN, VBN at 120 degrees; the line voltage VRY is the phasor sum of VRN and (-VYN), equal to root 3 Vph and leading the phase voltage by 30 degrees.

Delta connection:

• The three windings are connected end to end to form a closed loop, the junctions forming the three line terminals.
• Line voltage = phase voltage: VL = Vph (each winding is directly across two lines).
• Line current: the line current is the phasor difference of two phase currents, giving IL = root 3 x Iph.
• Vector diagram: three phase currents at 120 degrees; the line current is root 3 times the phase current and lags the phase current by 30 degrees.
• Power in both cases: P = root 3 x VL x IL x cos phi.