Understanding Salient Pole Alternators: Unveiling Two-Reaction Theory

Demonstrative Video


Operation of Salient-Pole Machine

  • \(\Rightarrow\) uniform air-gap \(\Rightarrow\) reactance remains the same irrespective of the spatial position of the rotor \(\Rightarrow\) possess one axis of symmetry (pole or direct axis)

  • \(\Rightarrow\) non-uniform air-gap \(\Rightarrow\) reactance varies \(\Rightarrow\) two axes

    • field pole axis (direct or d-axis)

    • axis passing through center of inter-polar space (quadrature or q-axis)

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  • d-axis \(\Rightarrow\) Both field and armature mmfs

  • q-axis \(\Rightarrow\) Only armature mmf


Two-Reaction Theory (proposed by Blondel)

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\[\begin{aligned} \mbox{internal power-factor angle,}~\Psi & =\mbox{between}~E_{0}~\mbox{and}~I_{a}\\ \mbox{power angle,}~\delta & =\mbox{between}~E_{0}~\mbox{and}~V\\ E_{0} & =V+I_{a}R_{a}+jI_{d}X_{d}+jI_{q}X_{q}\\ I_{a} & =I_{d}+I_{q} \end{aligned}\]
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\[\begin{aligned} E_{0} & =V\cos\delta+I_{q}R_{a}+I_{d}X_{d}~\mbox{generating}\\ & =V\cos\delta-I_{q}R_{a}-I_{d}X_{d}~\mbox{motoring} \end{aligned}\]
for motor for generator and If we neglect

Power Developed by Syn Generator

\[P_{d}=\dfrac{E_{0}V}{X_{d}}\sin\delta+\dfrac{V^{2}\left(X_{d}-X_{q}\right)}{2X_{d}X_{q}}\sin2\delta\]