IEEE Electrification Magazine - September 2014 - 7

years, although it requires bulky capacitors on the dc bus, the
VSI approach has been widely used for avoiding system
unbalance. However, in high-power applications, the semiconductor losses bring forth significant costs both in terms
of active energy and cooling system maintenance, which
must be taken into consideration by the railway operator.
The concept of the chopper-controlled impedance (CCI),
presented in this article, is based on series or parallel associations of ac choppers using high-frequency pulsewidth modulation (PWM) to vary reactances at the network frequency.
This approach is a low-power-loss solution and requires a
low volume of reactive elements, a fact that makes this solution very attractive in high-power, single-phase systems
such as railway networks.

Chopper-Controlled Impedance
Various converter topologies can be applied to provide ac/ac
conversion. Direct converters provide a link between the

source and the load without additional storage elements, but
the input and output frequencies are closely related. Nevertheless, passive filters are always required to filter out the
high-frequency harmonics introduced at the input and output sides by the converter switching operation.
Among the ac/ac direct converters, cycloconverters
and matrix converters are distinguished by their ability to
adjust the output frequency and voltage of a specific ac
input voltage source. They also provide bidirectional power-transfer capabilities, allowing the use of active loads
(e.g., motors in regenerative mode). On the other hand,
the ac chopper topology, which is similar to the wellknown dc chopper, provides direct ac/ac conversion
between two ac sources at the same fundamental frequency (Figure 1). The ac chopper may be considered as
an autotransformer whose turns-ratio can be electronically controlled. Nevertheless, although it can provide
instantaneous bidirectional power transfer, it allows
power flow in one direction only, according to the type of
load. AC choppers are normally designed to transfer
power between a fixed ac voltage source (e.g., the utility
grid) and a passive ac load. The load voltage [i.e., its rootmean-square (RMS) value] can be adjusted via the duty
cycle a to control the power flow, but the power exchange
(either active or reactive) is determined purely by the load
type (resistive, capacitive, or inductive).
The ideal waveforms are illustrated in Figure 2 (sinusoidal input voltage and sinusoidal output current). In this
example, the waveforms are given for the case of a 90°
leading current.
It can be easily demonstrated that the RMS value of
the output voltage fundamental V2 depends on the input
voltage RMS value V1 and can be adjusted with the duty
cycle a:
V 2 = aV 1 .

(1)

Likewise, the relationship between current RMS values
is given by
I 1 = aI 2 .

(2)

By considering the ideal waveforms, it is clear that the
ac chopper topology requires input and output filtering
elements. In any case, capacitor C F and inductor L F will be
designed to filter out the switching frequency from i 1 and
v 2 . Thus, as shown in Figure 3, the ac chopper can be used
as a step-down or a step-up converter, depending on the
connection of the network and the load. Assuming a sufficiently high switching frequency fsw, the filtering
elements L F and C F can be chosen to have a negligible
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Table of Contents for the Digital Edition of IEEE Electrification Magazine - September 2014