Condition for Maximum Power Developed In Synchronous Motor

The value of δ for which the mechanical power developed is maximum can be obtained as,

Note : Thus when R_a is negligible, θ = 90^o for maximum power developed. The corresponding torque is called pull out torque.

1.1 The Value of Maximum Power Developed

       The value of maximum power developed can be obtained by substituting θ =δ in the equation of P_m.

       When R_a is negligible,     θ = 90^o  and cos (θ) = 0 hence,

.^..               R_a = Z_s cosθ   and X_s = Z_s sinθ

       Substituting   cosθ = R_a/Z_s in equation (6b) we get,

        Solving the above quadratic in E_b we get,

       As E_b is completely dependent on excitation, the equation (8) gives the excitation limits for any load for a synchronous motor. If the excitation exceeds this limit, the motor falls out of step.

1.2 Condition for Excitation When Motor Develops (P_m ) R_max

       Let us find excitation condition for maximum power developed. The excitation controls E_b. Hence the condition of excitation can be obtained as,

       Assume load constant hence δ constant.

       but    θ = δ  for P_m = (P_m)_max

         Substitute            cosθ = R_a/Zs

        This is the required condition of excitation.
Note : Note that this is not maximum value of but this is the value of foe which power developed is maximum.
       The corresponding value of maximum power is,