Electric Power Generation, Transmission, and Distribution

voltage and with a larger ripple. The resulting DC bus voltage for a sag down to 50% is shown in
Fig. 31.11, together with the absolute value of the supply voltage. If the new steady state is below the
minimum operating voltage of the DC=DC converter, or below a certain protection setting, the
equipment will trip. During the decaying DC bus voltage, the capacitor voltageV(t) can be obtained
from the law of conservation of energy:

1

2

CV^2 ¼

1

2

CV 02 Pt (31:12)

where a constant DC bus loadPhas been assumed. From Eq. (31.12) the voltage as a function of time is
obtained:

VtðÞ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

V 02 

2 P

C

t

r

(31:13)

Combining this withEq. (31.11)gives the following expression:

VtðÞ¼V 0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1  4 e

t

T

r

(31:14)

230 V ac

non-regulated dc voltage

regulated

dc voltage

voltage

controller

FIGURE 31.10 Typical power supply to sensitive single-phase equipment.

1

0.8

0.6

0.4

0.2

0

024

Time in cycles

Voltage

6810

FIGURE 31.11 Absolute value of AC voltage (dashed) and DC bus voltage (solid line) for a sag down to 50%.