Page 261 - Rashid, Power Electronics Handbook

250 J. Espinoza

where V on is the rms ac output phase voltage, I o1 is the rms inverters in the following, although similar results are obtained
fundamental line current, and f is an arbitrary ®lter-load for single-phase VSIs.
angle. Hence, the dc link voltage expression can be further
simpli®ed to the following:
14.5.1 Feedforward Techniques in Voltage
Source Inverters
I o1 p  I o1
v ðtÞ¼ 3 V cosðfÞ¼ 3 V cosðfÞ ð14:61Þ The dc link bus voltage in VSIs is usually considered a constant
o
i
on
I I
i i
voltage source v . Unfortunately, and due to the fact that most
i
p  practical applications generate the dc bus voltage by means of
where V ¼ 3V is the rms load line voltage. The resulting
o on a diode recti®er (Fig. 14.35), the dc bus voltage contains low-
dc link voltage expression indicates that the ®rst line-current
order harmonics such as the sixth, twelfth,... (due to six-pulse
harmonic I generates a clean dc current. However, as the
o1 diode recti®ers), and the second if the ac voltage supply
load line currents contain harmonics around the normalized
features an unbalance, which is usually the case. Additionally,
sampling frequency f , the dc link current will contain if the three-phase load is unbalanced, as in UPS applications,
sn
harmonics but around f sn as shown in Fig. 14.33h. Similarly, the dc input current in the inverter i also contains the second
i
in carrier-based PWM techniques, the dc link current will
harmonic, which in turn contributes to the generation of a
contain harmonics around the carrier frequency m (Fig. second voltage harmonic in the dc bus.
f
14.25).
The basic principle of feedforward approaches is to sense
In practical implementations, a CSI requires a dc current
the perturbation and then modify the input in order to
source that should behave as a constant (as required by PWM
compensate for its effect. In this case, the dc link voltage
CSIs) or variable (as square-wave CSIs) current source. Such
should be sensed and the modulating technique should
current sources should be implemented as separate units and
accordingly be modi®ed. The fundamental ab line voltage in
they are described earlier in this book.
a VSI SPWM can be written as
p

v ðtÞ v ðtÞ 3
cb1
ca1
14.5 Closed-Loop Operation of Inverters v ab1 ðtÞ¼ ^ v D ÿ ^ v D 2 v ðtÞ; ^ v > ^ v ; ^ v cb1
D
ca1
i
ð14:62Þ
Inverters generate variable ac waveforms from a dc power
supply to feed, for instance, ASDs. As the load conditions where ^ v is the carrier signal peak, ^ v and ^ v are the
usually change, the ac waveforms should be adjusted to these D ca1 cb1
ca
cb
new conditions. Also, as the dc power supplies are not ideal modulating signal peaks, and v ðtÞ and v ðtÞ are the modu-
lating signals. If the dc bus voltage v varies around a nominal
i
and the dc quantities are not ®xed, the inverter should V value, then the fundamental line voltage varies proportion-
compensate for such variations. Such adjustments can be i
ally; however, if the carrier signal peak ^ v is rede®ned as
done automatically by means of a closed-loop approach. D
Inverters also provide an alternative to changing the load
v ðtÞ
i
operating conditions (i.e., speed in an ASD). ^ v ¼ ^ v Dm ð14:63Þ
D
There are two alternatives for closed-loop operation Ð the V i
feedback and the feedforward approaches. It is known that the
where ^ v is the carrier signal peak (Fig. 14.36), then the
feedback approach can compensate for both perturbations (dc Dm
resulting fundamental ab line voltage in a VSI SPWM is
power variations) and load variations (load torque changes).
However, the feedforward strategy is more effective in mitigat- p 
ing perturbations as it prevents its negative effects at the load v ab1 ðtÞ¼ v ðtÞ ÿ v ðtÞ 3 V i ð14:64Þ
ca1
cb1
side. These cause-effect issues are analyzed in three-phase ^ v Dm ^ v Dm 2
FIGURE 14.35 Three-phase topology with a diode-based front-end recti®er.