Alternative Expression for Power Developed by a Synchronous Motor

       Consider the phasor diagram of a synchronous motor running on leading power factor cosΦ as shown in the Fig. 1.
Fig. 1
       The line CD is drawn at an angle θ to AB.
       The lines AC and DE are perpendicular to CD and AE.
       and angle between AB = Ebph and Iaph is also ψ.
       The mechanical per phase power developed is given by,
       In triangle OBD,
                  BD = OB cosψ = IZs cosψ
                  OD = OB sin ψ = Ia  Zs sin
       Now    BD = CD - BC = AE - BC
      Substituting in (2),
                   IZs cosψ = Vph  cos (θ-δ) - E cosθ
       All values are per phase values
       Substituting (3) in (1),
       This is the expression for the mechanical power developed interms of the load angle δ and the internal machine angle θ, for constant voltage Vph  and constant Eph  i.e. excitation.
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