Page 206 - Power Electronic Control in Electrical Systems

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194 Power electronic equipment

causes these terms to decay. The next section considers the behaviour of the oscilla-
tory components under important practical conditions.
1. Necessary condition for transient-free switching. For transient-free switching, the
oscillatory components of current in equation (6.12) must be zero. This can happen
only when the following two conditions are simultaneously satisfied:
cos a ˆ 0(i:e: sin a ˆ 1) (6:16)
n 2
^
V C0 ˆ ^ v ˆ X c i AC (6:17)
2
n 1
The first of these equations means that the thyristors must be gated at a positive or
negative crest of the supply voltage sinewave. The second one means that the
2
2
capacitors must also be precharged to the voltage ^ vn /(n 1) with the same polarity.
The presence of inductance means that for transient-free switching the capacitor
2
2
must be `overcharged' beyond ^ v by the magnification factor n /(n 1). With low
values of n, this factor can be appreciable (Figure 6.18).
Of the two conditions necessary for transient-free switching, the prechar-
ging condition expressed by equation (6.17) is strictly outside the control of the
gating-control circuits because V C0 , n,and ^ v can all vary during the period of non-
conduction before the thyristors are gated. The capacitor will be slowly discharging,
reducing V C 0 ; while the supply system voltage and effective inductance may change
in an unknown way, changing n. In general, therefore, it will be impossible to guar-
antee perfect transient-free reconnection.
In practice the control strategy should cause the thyristors to be gated in such a
way as to keep the oscillatory transients within acceptable limits. Of the two condi-
tions given by equations (6.16) and (6.17), the first one can in principle always be
satisfied. The second one can be approximately satisfied under normal conditions.
For a range of system voltages near 1 p.u., equation (6.17) will be nearly satisfied if
the capacitor does not discharge (during a non-conducting period) to a very low
2
2
voltage: or if it is kept precharged or `topped up' to a voltage near ^ vn /(n 1).
2. Switching transients under non-ideal conditions. There are some circumstances in
which equations (6.16) and (6.17) are far from being satisfied. One is when the
capacitor is completely discharged, as for example when the compensator has been
switched off for a while. Then V C0 ˆ 0. There is then no point on the voltage wave
when both conditions are simultaneously satisfied.
In the most general case V C 0 can have any value, depending on the conditions under
which conduction last ceased and the time since it did so. The question then arises,
how does the amplitude of the oscillatory component depend on V C0 ? How can the
gating instants be chosen to minimize the oscillatory component? Two practical
choices of gating are: (a) at the instant when v ˆ V C0 , giving sin a ˆV C0 /^ v; and (b)
when dv/dt ˆ 0, giving cos a ˆ 0. The first of these may never occur if the capacitor
^
is overcharged beyond ^ v. The amplitude i osc of the oscillatory component of current
can be determined from equation (6.12) for the two alternative gating angles. In
^
^
Figures 6.19 and 6.20 the resulting value of i osc relative to i AC is shown as a function
of V C0 and n, for each of the two gating angles.
From these two figures it is apparent that if V C 0 is exactly equal to ^ v, the oscillatory
component of current is non-zero and has the same amplitude for both gating angles,