V = Terminal phase voltage applied to the armature (V)
Ia = Armature current/phase (A)
Eb = Back EMF to the motor (V)
Ra = Armature resistance/phase (Ω)
Xs = Synchronous reactance/phase (Ω)
Zs = Impedance/phase (Ω)
ϕ = Phase angle between line current and line voltage.
α = Load angle (Load angle = Angle between Back EMF and terminal voltage)
ZS=Ra+jXs=jXS (as resistance is very small so neglected)
Ia== Power input to the motor
(P) =V×Ia×cosϕ W per phase
From the phasor
AB=Ebsinα=IaXscosϕ P=V×Ia×cosϕ=sinα Mechanical losses are neglected then Input electrical power = Mechanical power developed
∴ Per phase developed Mechanical power is P
=sinα