An industrial load has the equivalent loading effect of Fig. 20.31. a. Develop the equivalent load diagram and sketch the power triangle. Make note of the current drawn from the 208 V three-phase supply. b. Redraw the network with an additional capacitive load that will create a unity power factor

Question

An industrial load has the equivalent loading effect of Fig. 20.31.
a. Develop the equivalent load diagram and sketch the power triangle. Make note of the current drawn from the 208 V three-phase supply.
b. Redraw the network with an additional capacitive load that will create a unity power factor load for the network.
c. For an applied frequency of 60 Hz, find the value of the required capacitor and the closest standard value.
d. Calculate the new line current with the power-factor corrective capacitor in place. How do they compare?
e. Sketch the network with the capacitor in place and find the total impedance of the network. Then calculate the line current and compare to the results of part (e).

Accepted Answer

a. [latex]Z_T=8 Ω + j 10 Ω = 12.81 Ω ∠51.34°\[0.5cm] I_L=\frac{E}{Z_T}=\frac{208 V ∠0°}{12.81 Ω ∠51.34°}=16.24 A ∠-51.34°\[0.5cm] P=I^{2}_{L}R=(16.24A)^28 Ω = 2109.9 W\[0.5cm] Q_L=I^{2}_{L}X_L=(16.24A)^210 Ω = 2637.38 VAR (L)\[0.5cm] S = VI = EI_L = (208 V)(16.24 A) = 3377.92 VA [/latex]

The load diagram and power triangle appear in Fig. 20.32.

The load draws 16.24 A from the supply.

b. The network is redrawn in Fig. 20.33 with the power-factor capacitor in place.

c. [latex]X_C=\frac{1}{2\pi fC}\Rightarrow C= \frac{1}{2\pi fX_C}=\frac{1}{2\pi(60 Hz)(2637.38 VAR)} =1.006 \mu F\[0.5cm]\hspace{30 pt} Use\quad C = 1 \mu F[/latex]

d. [latex]S = P = VI = EI = (208 V)(I_L) = 2109.9 W\[0.5cm] \hspace{30 pt} and\quad I_L=\frac{2109.9 W}{208V}=10.14 A [/latex]

Compared to 16.24 A above—a drop of 37%.

e. The network appears in Fig. 20.34.

[latex]Z_T=\frac{(8 Ω + j 10 Ω)(16.4 Ω ∠-90°)}{8 Ω + j 10 Ω - j 16.4 Ω }=20.52 Ω ∠44.17°\[0.5cm] I_L=\frac{E}{Z_T}=\frac{208 V ∠0°}{20.52 Ω ∠44.17°}=10.14 A ∠-44.17° [/latex]

as obtained above.

The value of the inserted capacitor to establish a unity power factor was therefore correctly determined through the use of the power equations.

Question 20.7: An industrial load has the equivalent loading effect of Fig....

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