# A three-phase, $50\;Hz$ salient-pole synchronous motor has a per-phase direct-axis reactance $\left( {{X_d}} \right)$ of $0.8\;pu$ and a per-ph

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A three-phase, $50\;Hz$ salient-pole synchronous motor has a per-phase direct-axis reactance $\left( {{X_d}} \right)$ of $0.8\;pu$  and a per-phase quadrature-axis reactance $\left( {{X_q}} \right)$ of $0.6\;pu$. Resistance of the machine is negligible. It is drawing full-load current at 0.8 pf (leading). When the terminal voltage is $1\;pu$, per-phase induced voltage, in $pu$, is _________.

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$\begin{array}{l} {X_d}\; = \;0.8,\phi \; = \;36.86\\ {X_q}\; = \;0.6,{R_a}\; = \;0\\ \tan {\rm{\psi }} = \frac{{Vsin\emptyset + {I_a}.{X_q}}}{{V\;cos\emptyset }}\\ \psi = 56.30 \end{array}$

for synchronous motor at leading p.f.

$\begin{array}{l} \psi \; = \;\phi \; + \;\delta \\ \Rightarrow \delta \; = \;19.70^\circ \end{array}$

Now, $E\; = \;V\;cos\delta \; + \;{I_d}{X_d}$

$\begin{array}{l} {I_d}\; = \;{I_a}\;sin\;\; = \;0.831\\ E\; = \;\left( 1 \right)\;cos\;\left( {19.7} \right)\; + \;\left( {0.831} \right)\;\left( {0.8} \right)\; = \;1.606 \end{array}$