Page 208 - Power Electronic Control in Electrical Systems

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196 Power electronic equipment

whatever the value of the natural frequency n. For any value of V c0 less than ^ v, gating
with v ˆV C0 always gives the smaller oscillatory component whatever the value of n.
The conditions for transient-free switching appear in Figure 6.20 in terms of the
precharge voltage required for two particular natural frequencies corresponding to
n ˆ 2:3 and n ˆ 3:6.

6.2.5.3 Switching a discharged capacitor
In this case V C0 ˆ 0. The two gating angles discussed were: (a) when v ˆ V C 0 ˆ 0;
and (b) when dv/dt ˆ 0 ( cos a ˆ 0). In the former case only equation (6.17) is
satisfied. From equation (6.12) it can be seen that in the second case (gating when
dv/dt ˆ 0) the oscillatory component of current is greater than in the first case
(gating when v ˆ V C0 ˆ 0). An example is shown in Figure 6.21 and Figure 6.22.

Fig. 6.21 Switching a discharge capacitor; circuit diagram.
1
1 v 0
v 0
–1
–1
2
2 1
1 v C 0
–1
v C 0
–2
–1
–2
1
0
v 1
1 –1
v 1 0
–1 4
3
2
1
i
2 0
–1
1
–2
i 0
–3
–1
–4
–2
(a) (b)
Fig. 6.22 Switching transients with discharge capacitor. (a) gating when v ˆ v C0 ˆ 0; (b) gating when dv=dt ˆ 0.