A phase-sequence indicator is an instrument such as shown in Fig. 24.37(a) that can display the phase sequence of a polyphase circuit. A network that performs this function appears in Fig. 24.37(b). The applied phase sequence is ABC. The bulb corresponding to this phase sequence burns more brightly

Question

A phase-sequence indicator is an instrument such as shown in Fig. 24.37(a) that can display the phase sequence of a polyphase circuit. A network that performs this function appears in Fig. 24.37(b). The applied phase sequence is ABC. The bulb corresponding to this phase sequence burns more brightly than the bulb indicating the ACB sequence because a greater current is passing through the ABC bulb. Calculating the phase currents demonstrates that this situation does in fact exist:

Accepted Answer

Calculating the phase currents demonstrates that this situation does in fact exist:

[latex]Z_1=X_C=\frac{1}{\omega C}=\frac{1}{(377 rad/s)(16 \times 10^{-6}F)}=166 Ω [/latex]

By Eq. (24.39),

[latex]I_{cn}=\frac{E_{CA}Z_2-E_{BC}Z_1}{Z_1Z_2+Z_1Z_3+Z_2Z_3}\[0.5cm] =\frac{(200 V ∠120°)(200 Ω ∠0°) - (200 V ∠-120°)(166 Ω ∠-90°)}{(166 Ω ∠-90°)(200 Ω ∠0°) + (166 Ω ∠-90°)(200 Ω ∠0°) + (200 Ω ∠0°)(200 Ω ∠0°)} \[0.5cm] I_{cn}=\frac{40,000 V ∠120° + 33,200 V ∠-30°}{33,200 Ω ∠-90° + 33,200 Ω ∠-90° + 40,000 Ω ∠0°} [/latex]

Dividing the numerator and denominator by 1000 and converting both to the rectangular domain yields

[latex]I_{cn}=\frac{(-20 + j 34.64) + (28.75 - j 16.60)}{40 - j 66.4}\[0.5cm] =\frac{8.75 + j 18.04}{77.52 ∠-58.93°}=\frac{20.05 ∠64.13°}{77.52 ∠-58.93°}\[0.5cm] I_{cn}=0.259 A ∠123.06° [/latex]

By Eq. (24.40),

[latex]I_{bn}=\frac{E_{BC}Z_1-E_{AB}Z_3}{Z_1Z_2+Z_1Z_3+Z_2Z_3}\[0.5cm] =\frac{(200 V ∠-120°)(166 ∠-90°) - (200 V ∠0°)(200 ∠0°)}{77.52\times10^3 Ω ∠-58.93°}\[0.5cm] I_{bn}=\frac{33,200 V ∠-210° - 40,000 V ∠0°}{77.52\times10^3Ω ∠-58.93°} [/latex]

Dividing by 1000 and converting to the rectangular domain yields

[latex]I_{bn}=\frac{-28.75 + j 16.60 - 40.0}{77.52 ∠-58.93°}=\frac{-68.75 + j 16.60}{77.52 ∠-58.93°}\[0.5cm] =\frac{70.73 ∠166.43°}{77.52 ∠-58.93° }=0.91 A ∠225.36° [/latex]

and [latex]I_{bn} > I_{cn}[/latex] by a factor of more than 3 :1. Therefore, the bulb indicating an ABC sequence will burn more brightly due to the greater current. If the phase sequence were ACB, the reverse would be true.

Question 24.9: A phase-sequence indicator is an instrument such as shown in...

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