Understanding the Force & Energy: Synchronous Motors - Power & Torque

Demonstrative Video

Power Flow within Synchronous Motor

\[\begin{aligned} I_{a} & =\dfrac{E_{R}}{Z_{s}}=\dfrac{V-E_{b}}{Z_{s}}=\dfrac{V-E_{b}}{R_{a}+jX_{s}} \end{aligned}\]
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for one armature phase of a syn motor:

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Power developed by Synchronous Motor

Since, \(X_s >> R_a\)

\[\begin{aligned} E_{b}\sin\alpha & =I_{a}X_{s}\cos\phi\\ \Rightarrow VE_{b}\sin\alpha & =VI_{a}X_{s}\cos\phi\\ \Rightarrow VI_{a}\cos\phi & =\dfrac{E_{b}V}{X_{s}}\sin\alpha\\ P_{in} & =\dfrac{E_{b}V}{X_{s}}\sin\alpha \end{aligned}\]
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\[\begin{aligned} &\boxed{P_m = \dfrac{3E_bV}{X_s}\sin\alpha}~~~-\mbox{three phase}\\ &\boxed{T_g = 9.55P_m/N_s}~~~N_s~\mbox{in rpm}\\ & (P_m)_{max} = \dfrac{E_bV}{X_s} \end{aligned}\]

Torques of a Synchronous Motor