Finding the Performance Parameters of Switching Transients A capacitor is connected across the secondary of an input transformer, as shown in Figure 17.21a, with zero damping resistance R = 0. The secondary voltage is Vs = 120 V, 60 Hz. If the magnetizing inductance referred to the secondary is

Question

Finding the Performance Parameters of Switching Transients

A capacitor is connected across the secondary of an input transformer, as shown in Figure 17.21a, with zero damping resistance R = 0. The secondary voltage is [latex]V_s = 120 V[/latex], 60 Hz. If the magnetizing inductance referred to the secondary is [latex]L_m = 2 mH[/latex] and the input supply to the transformer primary is disconnected at an angle of [latex]θ= 180°[/latex] of the input ac voltage, determine (a) the initial capacitor value [latex]V_0[/latex], (b) the magnetizing current [latex]I_0[/latex], and (c) the capacitor value to limit the maximum transient capacitor voltage to [latex]V_p = 300 V[/latex].

Accepted Answer

[latex]V_s = 120 V, V_m = \sqrt{2} imes 120 = 169.7 V, heta = 180, f = 60 Hz, L_m = 2 mH, and \omega = 2\pi imes 60 =377 rad/s[/latex].

a. From Eq. (17.37),

[latex]V_c = V_m \sin heta[/latex] (17.37)

[latex]V_c = 169.7 \sin heta= 0[/latex].

b. From Eq. (17.38),

[latex]I_0=-\frac{V_m}{\omega L_m }\cos heta =\frac{169.7}{377 imes 0.002}=225 A [/latex]

c. [latex]V_p = 300 V[/latex]. From Eq. (17.48),

[latex]C=\frac{I_0 V_m}{V^2_p\omega }[/latex] (17.48)

the required capacitance is

[latex]C=225 imes \frac{169.7}{300^2 imes 377}=1125.3 \mu F[/latex]

Question 17.5: Finding the Performance Parameters of Switching Transients A...

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