1

Abstract
AC choppers are a family of ac-to-ac power converters that
can be derived from the traditional dc-to-dc converters.
Research activity in this kind of converter has recently
increased in applications for power conditioningsuch as
voltage control in the distribution system and power flow
control in the transmission systemas an alternative for
the dc-link approach compensators based on voltage
source converters. The control is simpler and the power
rating of the devices is smaller for compensators with the
same power rating; the main drawback is they cannot
control the output-voltage frequency as the matrix
converter.
This paper presents a state-of-the-art review on the
development of ac-choppers. The principle of operation is
explained by using the six switches three-phase buck
converter as an example. The main applications used in
power conditioning and power flow control are
introduced along with emerging topologies.

1. Introduction

AC choppers are a family of power converters derived
from traditional dc-to-dc converter topologies such as the
buck, boost, buck-boost and so forth [1]. Their main
application is power conditioning in the distribution system
and power flow control in the ac transmission power
systems [2-20]. They differ from a matrix converter, which is
more complex in terms of control and number of devices and
is mainly used as a motor speed controller.
There are two main differences between ac choppers and
a matrix converter. One difference is that the number of
devices for a three-phase configuration is usually 18 in the
matrix converter and 6 in traditional ac choppers.








Fig. 1. Ac-choppers (a) buck, (b) boost , (c) buck-boost , (d) Ck.

A review of AC Choppers
1
Julio C. Rosas-Caro,
2
Fernando Mancilla-David,
3
Juan M. Gonzalez-Lopez,
4
Juan M. Ramirez-Arredondo,
1
Aaron Gonzalez-Rodriguez,
1
Nacu Salas-Cabrera,
1
Mario Gomez-Garcia,
1
Hermenegildo Cisneros-Villegas,
1
Madero City Technological Institute, Tamaulipas State Mxico.
2
Department of Electrical Engineering, University of Colorado-Denver, U.S.A.
3
Manzanillo Technological University, Mexico.
4
Guadalajara Campus of CINVESTAV IPN, Mexico.
E mail: rosascarojc@hotmail.com
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The other difference is that ac-choppers are not designed
to change frequency, only the amplitude of the voltage, and
the control system is based in pulse width modulation
(PWM) with a constant duty cycle (not sinusoidal) in the
same way as dc-dc converters.
Figure 1 shows buck, boost, buck-boost and Ck dc-dc
converters with their respective three-phase ac-chopper
derivation. Srinivasan and Venkataramanan state [1] that ac
choppers follow the same equations as dc-dc converters,
and the PWM also has a constant duty cycle.
The principle operation of ac choppers, also called ac-link
converters, can be explained with the circuit shown in Fig. 2,
where the dc-dc and three-phase ac-ac buck converter are
shown. The six transistors are divided in two three-phase
switches, S
1
and S
2
, and they switch complementarily as in
the dc-dc converters. The transistor and the diode switch
are complementary when they operate in continuous
conduction mode (CCM). The ac voltage is chopped and
then filtered to obtain a voltage waveform with different
amplitude but the same shape and frequency.


Fig. 2. Buck t ype AC chopper and volt age waveforms.

According to the switching state of S
1
and S
2
in the buck
type converter, see Fig. 2, two different equivalent circuits
can be obtained, and when the three-phase switch, S
1
, is
closed while S
2
is open, the converter can be modeled as an
equivalent circuit, as shown in Fig. 3(a).

Fig. 3. Equivalent circuit s of t he ac-ac buck convert er.

It is important to notice than even if the diodes in S
2
are
able to drain the current at any time, if all three transistors in
S
2
are open, there is no path for the current to flow and the
transistor will block the line-line voltage.
During this switching state, the voltage in the inductors
can be expressed as:

2 3
2 3
2 3
1 1
1 1
1 1
3
2
1
n c
n b
n a
n c
n b
n a
L
L
L
v
v
v
v
v
v
v
v
v
(1)
Both switches cannot be closed at the same time, because
a short circuit would occur. The inductors current should
not go into an open circuit, and one switch should be
closed at any time, but only one. Then the switching period
T can be divided only two times, the time t
S1
, then the switch
S
1
is closed while S
2
is open. The time t
S2
occurs when
switch S
2
is closed while S
1
is open, andto avoid a short
circuit or an open connection of inductorsthe next
equation should hold steady for all of the time.
2 1 S S
t t T + =
(2)
The duty cycle of the converter can be defined as:
T
t
d
S1
=
(3)
The complementary of the duty cycle is:
T
t
d
S 2
) 1 ( = -
(4)
During the time t
S2
the circuit will be equivalent to the
circuit shown in Fig. 3(b), with the input voltage
disconnected and switch S
2
providing a freewheeling path
for the inductors current. During this time the inductors
current can be expressed as:

- =

2 3
2 3
2 3
3
2
1
n c
n b
n a
L
L
L
v
v
v
v
v
v
(5)
Considering that the switching period is very small
compared with the ac-cycle, in steady state, the average
voltage during one switching cycle should be equal to zero
for all inductors, and this can be expressed as:
0 ) 1 (
2 3
2 3
2 3
2 3
2 3
2 3
1 1
1 1
1 1
3
2
1
=

- - +

n c
n b
n a
n c
n b
n a
n c
n b
n a
L
L
L
v
v
v
d
v
v
v
v
v
v
d
v
v
v
(6)
From (6) it is possible to obtain (7).
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0 ) 1 (
2 3
2 3
2 3
2 3
2 3
2 3
1 1
1 1
1 1
=

- -

n c
n b
n a
n c
n b
n a
n c
n b
n a
v
v
v
d
v
v
v
d
v
v
v
d
(7)
And finally, the output voltage can be expressed in terms
of the input voltage and the duty cycle of the buck
converter.

1 1
1 1
1 1
2 3
2 3
2 3
n c
n b
n a
n c
n b
n a
v
v
v
d
v
v
v
(8)
From (8), the circuit shown in Fig. 2 behaves in ac exactly
as the traditional buck converter behaves in the dc-dc
conversion and from each dc-dc converter topology; the
three-phase ac-ac converter can be derived holding the
principle of operation [1]. It is important to notice than all
topologies in Fig. 1 need snubber circuits in order to
operate, a design procedure found in Ref. [1].

2. Applications

2.1 Voltage Control

As the traditional dc-dc converters, one of the main
applications is to control three-phase voltage amplitude and
by doing so reject variations in the input voltage [2-3]. The
traditional six switches buck ac chopper (see Fig. 2) is used
[2] to avoid the flicker effect. A topology that uses four
switches is proposed in Ref. [3], see Fig. 4, to control the
voltage in a sensitive load by reducing the number of
devices and then simplifying the control circuit. In this
topology snubber circuits across switches are not
mandatory, the resistors and capacitors connected on the
input side drain the load current during the dead time, along
with the anti-parallel diodes of switches [3].

Fig. 4. Buck t ype convert er proposed in [3].

In the case of the buck converters, the output voltage
cannot be higher than the input voltage; it can only reject
step-up variations (swells). This is an important limitation
because most voltage perturbations are step-down
variations (sags).A transformer is needed to increase the
voltage and reject sags or else another topology can be
used such as the boost, buck-boost, Ck, and so on.
In the mentioned applications, when an ac chopper is
directly used to control the voltage, the converter should be
rated to the loads power; an additional way to control the
voltage with a smaller converter is combining an ac chopper
with a transformer.
The transformer can inject the voltage in series with the
load controlling the voltage with a converter with a power
rating much smaller than the loads power rating [4-8], see
Fig. 5

Fig. 5. Volt age regulat or wit h a t ransformer and ac-chopper.

The voltage regulator shown in Fig. 5 can be considered
an ac-chopperbased dynamic voltage restorer (DVR),
which is a voltage source converter (VSC) based power
conditioner designed to control the voltage in a sensitive
load.

2.2 Power flow control

Another attractive application for ac choppers is the
implementation of Flexible Alternating Current Transmission
Systems, or FACTS, in the same way as the voltage
regulator (shown in Fig. 5) does the analog behavior of the
DVR. A pure capacitive reactance can be implemented with
(i) an ac chopper, (ii) a series injection transformer and (iii)
compensating capacitors. When connected in series with a
transmission line, this kind of compensator can operate in
ways such as the static synchronous series compensator
(SSSC). Figure 6(a) shows the series compensator proposed
by Lopes and Joos [9], which is based on the buck type four
switches ac-chopper topology proposed by Vincenti, Jin,
and Ziogas [3] and also shown in Fig. 4.
Figure 6(b) shows the series compensator based in the six
switches topology also shown in Fig. 1(a) [10]. A
comparative evaluation of series compensators has shown
that the ac-chopper compensatoralso called controller
xi controllerhas advantages over the dc-link approach,
such as a smaller power rating for the power stage and less
stored energy for the same function and power rating [11]
against the SSSC. Similarly to the voltage regulator shown
in Fig. 5, a static phase shifter can be implemented with a
parallel transformer feeding an ac-chopper and injected in
series with the transmission line.
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Fig. 6. Power flow series cont roller based on an ac-chopper (a)
proposed in [9] (b) proposed in [10].

The six switches topology [see Fig. 1(a)] was used by
Johnson and Venkataramanan [12] to implement a phase
shifter in a hybrid structure where most of the power was
handled by a conventional tap changing transformer and a
small amount of power was handled by the ac-chopper,
which was used to provide a continuous range of
compensation against the steps range given by the
conventional tap changing phase shifter. Other static phase
shifters based on the six switches topology were proposed
and studied by Kaniewski and Fedyczak [13].
The four switches topology was used for implementing a
phase shifter and a multi-module topology was proposed
[14]. Other structures were studied by Kim and Kwon [15].
In this case, the phase of the injected voltage is given by
the transformer arrangement; the ac-chopper cannot change
the phase or the frequency by itself.
This kind of static phase shifter, based on the ac chopper,
can be combined with the traditional power flow controllers
making hybrid structures such as [16] and providing a
continuous range of compensation. Furthermore, other
transformer based compensators such as the family of Sen
transformers [17-18] and static phase shifters [19-20] can be
combined with ac choppers to get a fast response.
This development along with the emerging
semiconductors technology based on silicon carbide and
recently proposed topologies make ac-chopper attractive for
practical implementations.
3. Emerging Topologies

A family of two switches three-phase ac choppers was
proposed by Peng, Cheng, and Zhang [21], see Fig. 7,
analog to Fig. 1 where the six switches ac chopper family
was shown.




Fig. 7. Two swit ches ac chopper family proposed in Ref. [21].
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The main draw back of the two switches topologies family
is that some connections in the three-phase input voltage or
load need to be open, for example in the buck converter, see
Fig. 7(a) where the input voltage is located in an open
connection (neither Y not ). The same thing occurs with
the output voltage in the boost converter and the input and
output in the buck-boost converter. The Ck converter is
the only one in the family that doesnt need an open
connection, which makes the two switches three-phase Ck
converter attractive for voltage regulation in sensitive loads.
Another advantage of reducing the number of switches is
that it reduces the number of snubber circuits.
Other new converter topologies such as the Z-source
converter [22] can be also used in dc-dc conversion [23] and
adapted to become a three-phase ac-chopper [24] in the six
switches topology, see Fig. 8(a), or in the two switches
topology [24], see Fig. 8(b).


Fig. 8. Z-source ac chopper (a) six swit ches based (b) t wo swit ches
based.

The disadvantage of the open connection is not a problem
in the power flow control where compensators are coupled
to the transmission lines with transformers and the
transformers secondary connection can be open. Ac-
chopperbased flexible ac transmission systems can be
implemented in this way, as proposed by Rosas-Caro,
Ramirez, and Peng [25].
Figure 9(a) shows the two switches ac chopper based
series compensator two switches xi controller [25], which
has the same operation of Fig. 6. The main drawbacks of the
two switches topologies are (i) the conduction losses
increase because there are more devices draining the current
and (ii) the number of switching devices decreases but the
total installed power in switching semiconductors holds the
same because each device in a two switches topology drain
three times the current of each device in a six switches
topology, the switch is three times bigger.
On the other hand, as only two gate drives and two
snubber circuits are needed, the switching process becomes
a one quadrant switching.

Fig. 9. Two swit ches based xi cont roller.

4. The Vector Switching Converter

The three-phase vector switching converter (VeSC) was
proposed and deeply analyzed by Venkataramanan [26].
Figure 10 shows a two-throw single-pole three-phase VeSC,
where two three-phase voltage sources feed one three-
phase current source switching among both three-phase
voltage sources.


Fig. 10. Three-phase vect or swit ching convert er.


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If the switches are controlled by PWM in Fig. 10, it is
possible to define duty cycles for each switch if t
1closed
is the
time when S
1
is closed, and t
2closed
is the time when S
2
is
closed, then duty cycles for each switch can be defined as:
T
t
d
closed 1
1
=
;
T
t
d
closed 2
2
=
; (9)
Both switches cannot be closed at the same time because
the input voltage sources would be in short circuit, and
both switches cannot be open at the same time because the
load would get in an open connection (the load is
considered inductive and modeled as a current source
during the switching process); one of them should be
closed while the other is open and so on. That can be
expressed as:
1
2 1
2 1
= + =
+
d d
T
t t
closed closed
(10)
According to the state of the switches, the circuit can get
two equivalent circuits, see Fig. 10, one with the load
connected to v
1
and the other one with the load connected
to v
2
. The average voltage (in a switching cycle) in the load
terminals can be expressed in terms of the duty cycles for
the switches and the input voltages as:

) (
) (
) ( ) (
) ( ) (
) ( ) (
) (
) (
) (
2
1
2 1
2 1
2 1
t d
t d
t v t v
t v t v
t v t v
t v
t v
t v
c c
b b
a a
c
b
a
(11)
The average current (in a switching cycle) for each input
voltage source can be expressed in terms of duty cycles and
the load current as:

) (
) (
) (
) (
) (
) (
t i
t i
t i
d
t i
t i
t i
c
b
a
i
ic
ib
ia
; for i = 1, 2. (12)
It can be seen from (11) that the output voltage is the
sum of the products of duty cycles, and the input voltages.
If the input voltages have different phases, a phasor
analysis can be used to get the output voltage phase [26-
27].
The topology can be extended to any number of phases
and input voltage sources, and (11) and (12) can be also
extended to represent the voltage and current in complex
interconnections. Actually, the VeSC was proposed to
control the power flow in complex interconnectionsa node
can be fed by several lines through a VeSC in order to
control the power that each line provides to this node [26],
enabling a high flexibility for the control of a very complex
interconnected system, and, therefore, most of the ac-
choppers and chopper compensators can be represented as
a specific case of the VeSC approach.
The main difference between a VeSC and a classical matrix
converter is the realization of the power switching structure
that in a classical matrix converter for three-phase power
flow control requires switches with bi-directional current
control and voltage blocking capability usually implemented
with 18 transistors. On the other hand, due to the ganging
together of appropriate throws, all three phases of a pole are
switched simultaneously. As a result, due to inherent
symmetry in three-phase voltage and current waveforms,
when all the three-phase ac ports are three wire systems, the
throws may be realized using the bi-directional current
conducting, but unidirectional voltage blocking capability
as illustrated in Fig. 10. As already mentioned, when all
switches are open even if diodes can drain current at any
time transistors will block the voltage. Furthermore, as the
duty ratio arises directly from the average value of the
switching function, the modulation strategy can be
performed by comparing the duty ratio with a saw-tooth (or
triangular) high frequency carrier, as it is done with dc/dc
converters. It doesnt need to be synchronized with the
grid.
The fundamental component averaged vector (or single-
phase) equivalent circuit of the converter system may be
represented as shown in Fig. 11, representing the converter
by means of dependent sources.

Fig. 11. (a) VeSC single phase equivalent circuit (b) Throw
realizat ions and obt ainable pole volt age.

The realizable output voltage depends on the amplitude
and phase of the input voltages and duty rations. Figure
7(b-d) shows the realizable voltage values (represented by
the gray shaded region in the phasor plane) for different
cases of input voltage sources and their phases.
It may be observed that the region of the realizable pole
voltages is given by the largest polygon whose vertices are
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the locations of the corresponding throw voltages and the
phasor origin. More information of the phasor
representation can be found in Refs. [27, 31].
New FACTS devices have been recently proposed based
on the VeSC [27-28] and the inclusion of those new FACTS
controllers in the power system has been investigated [29].
Following the trend in ac chopper development, a
simplification of the VeSC was proposed by Rosas-Caro,
Ramirez, and Peng [25] by using few switches for each
FACTS device.
Future power systems will involve complex distribution
systems with advanced solid state transformers and power
compensators. Silicon carbide (SiC) devices can break the
limits of using power converters in the power system
because of the superior properties of the material [30]. The
ac choppers are a suitable technology for controlling the
voltage in the distribution system [2-8] and the power flow
control in the transmission system [9-20, 25-30].
A topological comparison between the dc-link and the ac-
link approach for power flow control and power quality
enhancement was presented in Ref. [31].
The most attractive features of the vector switching
converter approach for power conditioning and power flow
control in contrast to the dc-link approach based on the
voltage source converter are (i) the elimination of the dc-
link that is the less reliable part of the VSC and (ii) a
reduced number of active switches in relationship to the
matrix converter, as the matrix converter can be employed to
the proposed applications but 18 switches are needed for a
three-phase configuration.
Additionally, the PWM strategy in ac choppers and
vector switching converters follows the same principle as in
dc/dc converters, which is well understood and easy to
implement [31], they can work PLL-less and asynchronous
from the grid frequency as the frequency and phase of the
signals are given by the grid frequency and the transformers
arrangement, that makes the control system insensitive to
frequency and phase variations in the grid.
The detailed comparative evaluation performed for series
compensation between ac and dc link converters suggests
further evidences of the advantages of ac link converters
[11], including smaller capacitors, and a potential lower cost.
In summary, ac link VeSC-base devices present a viable
alternative to the state-of-the-art technology, namely dc link
VSI devices, and they are worth further consideration.

5. Conclusions

This paper presents a state-of-the-art discussion of ac-
choppers, the traditional six switches family was introduced,
and the principle of operation was presented with the buck
ac-chopper. The main applications in voltage control of the
distribution system and power flow control in the
transmission system were explained. Emerging topologies of
ac choppers with few switches were discussed.
The vector switching converter shows a global approach
to representing ac choppers and new FACTS controller
based in this approach have been recently proposed, With
these applications and the advent of SiC devices, the ac
chopper and VeSC promises to become a hot topic in power
electronics research, especially in power conditioning and
power flow control where VeSC promises the development
of power compensators with smaller capacitors and a
potential lower cost.

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