Besides, the star configuration has 4 wires: 3 phase wires and 1 neutral wire starting from the star point. The delta configuration on the other hand, has no neutral wire.
Star:
VLine = √3*VPhase
ILine = IPhase


VL1 = VF1 - VF2
VL2 = VF2 - VF3
VL3 = VF3 - VF1
VL1 + VL2 + VL3 = 0
VL1 = 2*VF1*cos 30° = 2*VF1*√3/2 = √3*VF1
The line voltage leads the phase voltage by 30°.
The line currents equal the phase currents with symmetrical charges.
The active power when connected in Y: P = 3*(VL/√3)*IL*cos φ = √3*VL*IL*cos φ
Delta:
VLine = VPhase
ILine = √3*IPhase


ĪL1 = ĪP1 - ĪP1
ĪL2 = ĪP2 - ĪP3
ĪL3 = ĪP3 - ĪP1
ĪL1 + ĪL2 + ĪL3 = 0
IL1 = 2*IP1*cos 30° = 2*IP1*3/2 = √3*IP1
The line current leads the phase current by 30°.
The line voltages equal the phase voltages with symmetrical charges.
The active power when connected in Δ: P = 3*VL*(IL/√3)*cos φ = √3*VL*IL*cos φ