A single-phase $100-\mathrm{kVA}, 2400 / 240-\mathrm{volt}, 60-\mathrm{Hz}$ distribution transformer is used as a step-down transformer. The load, which is connected to the 240 -volt secondary winding, absorbs $80 \mathrm{kVA}$ at 0.8 power factor lagging and is at 230 volts. Assuming an ideal transformer, calculate the following: (a) primary voltage, (b) load impedance, (c) load impedance referred to the primary, and (d) the real and reactive power supplied to the primary winding.

Question

Quizplus · Accepted Answer

The Answer is $(a) E_{1}=\frac{N_{1}}{N_{2}} E_{2}=\frac{2400}{240}(230)=2300 \mathrm{~V} (b) \bar{S}_{2}=\bar{E}_{2} \bar{I}_{2}^{*} ; \bar{I}_{2}=\left(\frac{\bar{S}_{2}}{\bar{E}_{2}} ight)^{*}=\left[\frac{80 imes 10^{3} \angle \cos ^{-1} 0.8}{230 \angle 0^{\circ}} ight]^{*}=347.8 \angle-36.87^{\circ} \begin{aligned} \bar{Ƶ}_{2}=\frac{\bar{E}_{2}}{\bar{I}_{2}}=\frac{230 \angle 0^{\circ}}{347.8 \angle-36.87^{\circ}} & =0.6613 \angle 36.87^{\circ} \Omega \ & =0.529+j 0.397 \Omega \end{aligned} (c) \bar{Ƶ}_{1}^{\prime}=\left(\frac{N_{1}}{N_{2}} ight)^{2} \bar{Ƶ}_{2}=100 \bar{Ƶ}_{2}=66.13 \angle 36.87^{\circ} \Omega (d) P_{1}=P_{2}=80(0.8)=64 \mathrm{~kW} Q_{1}=Q_{2}=64 an \left(36.87^{\circ} ight)=48 \mathrm{kVAR}$
(a)

E_{1}=\frac{N_{1}}{N_{2}} E_{2}=\frac{2400}{240}(230)=2300 \mathrm{~V}

(b)

\bar{S}_{2}=\bar{E}_{2} \bar{I}_{2}^{*} ; \bar{I}_{2}=\left(\frac{\bar{S}_{2}}{\bar{E}_{2}} ight)^{*}=\left[\frac{80 imes 10^{3} \angle \cos ^{-1} 0.8}{230 \angle 0^{\circ}} ight]^{*}=347.8 \angle-36.87^{\circ}

\begin{aligned}\bar{Ƶ}_{2}=\frac{\bar{E}_{2}}{\bar{I}_{2}}=\frac{230 \angle 0^{\circ}}{347.8 \angle-36.87^{\circ}} & =0.6613 \angle 36.87^{\circ} \Omega \& =0.529+j 0.397 \Omega\end{aligned}

(c)

\bar{Ƶ}_{1}^{\prime}=\left(\frac{N_{1}}{N_{2}} ight)^{2} \bar{Ƶ}_{2}=100 \bar{Ƶ}_{2}=66.13 \angle 36.87^{\circ} \Omega

(d)

P_{1}=P_{2}=80(0.8)=64 \mathrm{~kW}

Q_{1}=Q_{2}=64 an \left(36.87^{\circ} ight)=48 \mathrm{kVAR}

A Single-Phase 100−kVA,2400/240−volt,60−Hz100-\mathrm{kVA}, 2400 / 240-\mathrm{volt}, 60-\mathrm{Hz}100−kVA,2400/240−volt,60−Hz Distribution Transformer Is Used as a Step-Down Transformer

A Single-Phase $100-\mathrm{kVA}, 2400 / 240-\mathrm{volt}, 60-\mathrm{Hz}$ Distribution Transformer Is Used as a Step-Down Transformer