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

When R

_{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

Solving the above quadratic in E

_{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

Assume load constant hence δ constant._{b}. Hence the condition of excitation can be obtained as,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,

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