Theory of cylindrical rotor machine

       Let us consider the phasor diagram for alternator as shown in the Fig. 1.
Fig. 1

       Let          E = E.M.F. induced in each phase
                      V = Terminal voltage
                      Φ = Phase angle between voltage and current 
                      δ = Power angle 
                      R= Resistance of armature 
                      X= Synchronous reatance of alternator.
...                   tanθ = Xs/R
...                   θ = tan-1 (Xs/Ra)
                     α = Φ + δ
       Power output per phase = V . I cos (V ^ I)
                                            = VI cos
       Power input,   Pi = EI cos (E ^ I)
                                 = E I cos (Φ + δ) = E I cosα = I (E cos α)
                                 = I (V cos Φ + I Ra)
                                 = VI cosΦ + I2 R
       The voltage equation of alternator is given by,

        Pis the power converted internally into electrical power from mechanical power which is given by,
        P= Eo . I

Note : With increase in δ power increases and with decrease in δ power decreases. Power in case of synchronous machines depends on the angle δ. This angle δ is called power angle.
In case of large synchronous machines,  Xs >>> R
...                θ = tan-1(Xs/R)= 90o (if resistance is neglected)
                   θ = 90o
       Substituting this value in above expression for power

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