An Industrial Plant Consisting Primarily of Induction Motor Loads Absorbs$1000 \mathrm{~kW}$

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The Answer is (a) $(a) \begin{aligned} \phi_{L} & =\cos ^{-1} 0.7=45.57^{\circ} \ Q_{L} & =P an \phi_{L}=1000 an \left(43.57^{\circ} ight) \ & =1020.2 \mathrm{kVAR} \ \phi_{S} & =\cos ^{-1} 0.9=25.84^{\circ} \ Q_{S} & =P an \phi_{S}=1000 an \left(25.84^{\circ} ight)=484.3 \mathrm{kVAR} \ Q_{C} & =Q_{L}-Q_{S}=1020.2-484.3=535.9 \mathrm{kVAR} \ S_{C} & =Q_{C}=535.9 \mathrm{kVA} \end{aligned} (b) Synchronous motor absorbs P_{m}=\frac{1000 imes 0.746}{0.9}=828.9 \mathrm{~kW} and Q_{m}=0 \mathrm{kVAR} \begin{aligned} ext { Source } p f & =\cos \left[ an ^{-1} \frac{1020.2}{1828.9} ight] \ & =0.873 ext { Lagging } \end{aligned}$

\begin{aligned}\phi_{L} & =\cos ^{-1} 0.7=45.57^{\circ} \Q_{L} & =P an \phi_{L}=1000 an \left(43.57^{\circ} ight) \& =1020.2 \mathrm{kVAR} \\phi_{S} & =\cos ^{-1} 0.9=25.84^{\circ} \Q_{S} & =P an \phi_{S}=1000 an \left(25.84^{\circ} ight)=484.3 \mathrm{kVAR} \Q_{C} & =Q_{L}-Q_{S}=1020.2-484.3=535.9 \mathrm{kVAR} \S_{C} & =Q_{C}=535.9 \mathrm{kVA}\end{aligned}

(b) Synchronous motor absorbs

P_{m}=\frac{1000 imes 0.746}{0.9}=828.9 \mathrm{~kW}

and

Q_{m}=0 \mathrm{kVAR}

\begin{aligned} ext { Source } p f & =\cos \left[ an ^{-1} \frac{1020.2}{1828.9} ight] \& =0.873 ext { Lagging }\end{aligned}

$(a) \begin{aligned} \phi_{L} & =\cos ^{-1} 0.7=45.57^{\circ} \ Q_{L} & =P an \phi_{L}=1000 an \left(43.57^{\circ} ight) \ & =1020.2 \mathrm{kVAR} \ \phi_{S} & =\cos ^{-1} 0.9=25.84^{\circ} \ Q_{S} & =P an \phi_{S}=1000 an \left(25.84^{\circ} ight)=484.3 \mathrm{kVAR} \ Q_{C} & =Q_{L}-Q_{S}=1020.2-484.3=535.9 \mathrm{kVAR} \ S_{C} & =Q_{C}=535.9 \mathrm{kVA} \end{aligned} (b) Synchronous motor absorbs P_{m}=\frac{1000 imes 0.746}{0.9}=828.9 \mathrm{~kW} and Q_{m}=0 \mathrm{kVAR} \begin{aligned} ext { Source } p f & =\cos \left[ an ^{-1} \frac{1020.2}{1828.9} ight] \ & =0.873 ext { Lagging } \end{aligned}$

An Industrial Plant Consisting Primarily of Induction Motor Loads Absorbs $1000 \mathrm{~kW}$

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An Industrial Plant Consisting Primarily of Induction Motor Loads Absorbs 1000 kW1000 \mathrm{~kW}1000 kW

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An Industrial Plant Consisting Primarily of Induction Motor Loads Absorbs $1000 \mathrm{~kW}$

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