Page 63 - Power Electronics Handbook

56 Power semiconductor devices

leakage whereas the remaining have maximum leakage current, 4. If there
are n cells in series, then equations (1.22) and (1.23) can be written down,
where Vl is the peak-rated voltage of the thyristors and V is the maximum
voltage which can be safely applied to the series string when sharing
resistor Rpk is used.

v - v, = v, (n - 1) (1.22)

(1.23)

Solving equations (1.22) and (1.23) gives equation (1.24).
(1.24)

Provided the value of the resistor does not exceed that given by equation
(1.24), the voltage will be effectively shared across the series string of
power semiconductors, in their static state. However, when the devices are
turned on or off, sharing resistors are ineffective in ensuring equal voltages
across them. For example, the thyristors which recover their blocking state
fastest, or which turn on last, will see the full voltage of a series string,
often with disastrous effects. This transient voltage distribution is in
inverse proportion to their capacitances, and inequality can be protected
against by using a capacitor across each device, as in Figure 1.33(b), of a
value greater than the device capacitance. This slows down the rate of
change of voltage across the device during turn-off and turn-on. A
low-valued resistor is also now required, in series with the capacitance, to
limit the large discharge currents of the capacitors, which would otherwise
occur when the thyristors are turned on. The value of the capacitance C
can be obtained from empirical equation (1.25), where I, is the peak
forward current through the thyristor before commutation occurs and V, is
the maximum voltage rating of the thyristors.

(1.25)

In a normal application the sharing components for static and dynamic
operation are combined, so that each power device would have across it
both the sharing components shown in Figures 1.33(a) and (b).

RPk Rpk RPk R C R C RC
(a) (b)
Flgnre 1.33 Additions for greater equality in sharing d.c. and transient voltages: (a) d.c.
voltage sharing; (b) transient voltage sharing