Overview of Single Phase Matrix Converter
Application
Maxym Vorobyov
Riga Technical University (Latvia)
maksims.vorobjovs@rtu.lv
Abstract—This paper presents the SPMC topology which
have many advantages as a minimal passive device use. It is very
flexible and it can be used as a lot of converters. For example in
that work are presented classical AC-AC converter, rectifier
solution with and without power factor correction, and DC-DC
solution where SPMC is presented as for quadrant chopper.
flow directions markers (“A” – forward direction, “B”opposite direction) of each switch.
I. INTRODUCTION
A lot of theoretical studies have investigated on matrix
converter but haven’t found many practical applications in of
it. Matrix converter has been known to offer an “all silicon”
solution for AC-AC conversion, removing the need for
reactive energy storage components used in conventional
rectifier-inverter based system. Developing of matrix
converters starts with the work of Venturini and Alesina
published in 1980[1], [2]. They presented the power circuit of
the converter as a matrix of bidirectional power switches and
they introduced the name “matrix converter.” One of their
main contributions is the development of a rigorous
mathematical analysis to describe the low-frequency behavior
of the converter, introducing the “low-frequency modulation
matrix” concept. In their modulation method, also known as
the direct transfer function approach, the output voltages are
obtained by the multiplication of the modulation (also called
transfer) matrix with the input voltages[3]. Most attention
was concentrated on tree phase matrix converter topology.
Single-phase Matrix converter or SPMC was first
implemented by Zuckerbeger[4]. Now presented a lot of
possible application of it starts from conventional matrix
converter application AC-AC conventional and finished with
DC solutions.
Aim of this paper is overview solution of existing SPMC
application possibilities. Describe switching strategies of each
SPMC application solution. Compare it with conventional
solution and conclude how SPMC may be used.
II. SINGLE-PHASE MATRIX CONVERTER DESIGN
The matrix converter is a forced commutated converter
which uses an array of controlled bidirectional switches as the
main power elements to create a variable output voltage
system with unrestricted frequency. It does not have any dclink circuit and does not need any large energy storage
elements. The key element in a matrix converter is the fully
controlled four-quadrant bidirectional switch, which allows
high-frequency operation[3].
The SPMC consist of a matrix of a matrix of input and
output lines with four bidirectional switches connecting the
single phase input to the single phase output at the
intersections[4].The SPMC is presented in Fig. 1. Vin is input
and Vout output voltage. It comprises four bidirectional
switches S1-S4 “A” or “B” where “A” and “B” is current
Fig. 1. Single phase matrix converter scheme.
III. BIDIRECTIONAL SWITCH
The matrix converter requires a bidirectional switch
capable of blocking voltage and conducting current in both
directions. Unfortunately, there are no such devices currently
available, so discrete devices need to be used to construct
suitable switch cells.
The diode bridge bidirectional switch cell arrangement
consists of an insulated gate bipolar transistor (IGBT) at the
center of a single-phase diode bridge arrangement as shown
in Fig. 2. The main advantage is that both current directions
are carried by the same switching device, therefore, only one
gate driver is required per switch cell. Device losses are
relatively high since there are three devices in each
conduction path. The direction of current through the switch
cell cannot be controlled. This is a disadvantage, as many of
the advanced commutation methods described later require
this.
The common emitter bidirectional switch cell arrangement
consists of two diodes and two IGBTs connected in
antiparallel as shown in Fig. 3(a). The diodes are included to
provide the reverse blocking capability. There are several
advantages in using this arrangement when compared to the
previous example. The first is that it is possible to
independently control the direction of the current. Conduction
losses are also reduced since only two devices carry the
current at any one time. One possible disadvantage is that
each bidirectional switch cell requires an isolated power
supply for the gate drives.
The common collector bidirectional switch cell
arrangement is shown in Fig. 3(b). The conduction losses are
the same as for the common emitter configuration. An oftenquoted advantage of this method is that only six isolated
power supplies are needed to supply the gate drive signals.
201
However, in practice, other constraints such as the need to
minimize stray inductance mean that operation with only six
isolated supplies is generally not viable. Therefore, the
common emitter configuration is generally preferred for
creating the matrix converter bidirectional switch cells.
Both the common collector and common emitter
configurations can be used without the central common
connection, but this connection does provide some transient
benefits during switching. In the common emitter
configuration, the central connection also allows both devices
to be controlled from one isolated gate drive power supply[3].
V. COMMUTATION PROBLEM
The commutation problem is an important practical issue to
be considered in the employment of matrix converter. Since
there are no freewheel path, it is difficult to reliably
commutate current from one switch to another. In theory, the
switching must be instantaneous and simultaneous to prevent
a load current interruption or a short circuit. However
simultaneous commutation of switches in matrix converters is
difficult to achieve without generating overcurrent or
overvoltage spikes that can in turn destroy power
semiconductors. At any time during switch turn ‘OFF’ there
should be a path for inductive load current to flow to prevent
large overvoltage that would destroy switches; thus limiting
practical implementation of matrix converters [12].
VI. SPMC MODES
SPMC is very flexible topology with high level of
integration. That topology can be used for different modes
depended on switch commutation strategy.
In this part explained SPMC different modes like
conventional converters: chopper, buck, boost, rectifier,
rectifier with power factor correction, cycloconverter. These
converters modes may be realized without difficult additional
components like transformers or additional active
components[4], [7], [9], [11], [13–19].
Fig. 2. Diode bridge bidirectional switch.
A. SPMC as a AC-AC converter or cycloconverter
Fig. 3. Switch cell. (a) Common emitter back to back. (b) Common collector
back to back.
IV. SINUSOIDAL PULSE WIDTH MODULATION
The Sinusoidal Pulse Width Modulation (SPWM) is a wellknown wave shaping technique in power electronics as
illustrated in Fig. 4. For realization, a high frequency
triangular carrier signal, Vc, is compared with a sinusoidal
reference signal, Vr, of the desired frequency. The crossover
points are used to determine the switching instants[5–10].
Fig.4. Formation of SPWM.
The magnitude ratio of the reference signal (Vr) to that of
the triangular signal (Vc) is known as the modulation index
(mi). The magnitude of fundamental component of output
voltage is proportional to mi. The amplitude Vc of the
triangular signal is generally kept constant. By varying the
modulation index, the output voltage could be controlled[11].
First is conventional mode for matrix converters. Change
the AC voltage amplitude and frequency without DC link and
additional bulky passive components.
Control system is designed to generate the sinus pulse wide
modulation SPWM patterns that are used to control the power
switches. The switching angles, of the 4 bi-directional
switches Sij (i = 1,2,3,4 and j = a, b which are presented in
previous section). The following rules are then applied;
At any time ‘t’, only two switches Sij(i =1, 4 and j = a) will
be in ‘ON’ state and conduct the current flow during positive
cycle of input source (state 1), with S2a turn ‘ON’ for
commutation purpose.
At any time ‘t’ only two switches Sij(i = 1, 4 and j =b) will
be in ‘ON’ state and conduct the current flow during negative
cycle of input source (state 2), with S2b turn ‘ON’ for
commutation purpose.
At any time ‘t’ only two switches Sij(i = 2, 3 and j =b) will
be in ‘ON’ state and conduct the current flow during positive
cycle of input source (state 3), with S1b turn ‘ON’ for
commutation purpose.
At any time ‘t’ only two switches Sij(i = 2, 3 and j =a)
will be in ‘ON’ state and conduct the current flow during
negative cycle of input source (state 4), with S1a turn ‘ON’
for commutation purpose[17].
Results of switching strategy application are shown for two
frequencies 25Hz and 100Hz on Fig. 6, 7.
The commutation switch needs a period of overlap as
illustrated in Fig. 5 to prevent switches from overvoltage
pikes. The sufficient time delay ‘td’ between each switch
commutation was needed. Taking into account of those
factors, the final sequences of switching are as tabulated in
Table 1 (for one cycle) with a sample of the switching pattern
shown in Fig. 6 and 7.
202
This will allow for the current to decay until zero prior to
the next switching sequence. This method allows for
elimination of switching spikes during switching and
commutation processes[17].
In conventional controlled rectifier, free-wheeling diodes
are used for this purpose. In SPMC this does not exist, hence
the need to develop a switching sequence to allow energy
dissipation as illustrated in Fig. 8 and 9.
Fig. 5. Sample Timing for commutation strategies.
TABLE I
SWITCHING STRATEGY OF SPMC AS AC-AC CONVERTER
Input
freq.
Target
Output
freq.
150Hz
100Hz
50Hz
50Hz
25Hz
12,5Hz
Time
Interval
State
PWM
Switch
Commutation
Switch
1
2
3
4
5
6
1
2
3
4
1
2
1
2
3
4
1
2
3
4
5
6
7
8
1
3
1
2
4
2
1
3
4
2
1
2
1
4
3
2
1
4
1
4
3
2
3
2
S4a
S3b
S4a
S4b
S3a
S4b
S4a
S3b
S3a
S4b
S4a
S4b
S4a
S3a
S3b
S4b
S4a
S3a
S4a
S3a
S3b
S4b
S3b
S4b
S1a & S2a
S2b & S1b
S1a & S2a
S1b & S2b
S2a & S1a
S1b & S2b
S1a & S2a
S2b & S1b
S2a & S1a
S1b & S2b
S1a & S2a
S1b & S2b
S1a & S2a
S2a & S1a
S2b & S1b
S1b & S2b
S1a & S2a
S2a & S1a
S1a & S2a
S2a & S1a
S2b & S1b
S1b & S2b
S2b & S1b
S1b & S2b
Fig. 6. Switching pattern generator 100Hz.
B. SPMC as rectifier
SPMC can be used as a rectifier or a rectifier with power
factor correction[12], [20–27]. Switch commutation strategy
for simple realization is shown in Table 2. Vin is AC and
Vout is DC.
Commutation problems occur when inductive (R and L)
loads are used at turn-off, resulting in possible voltage spikes
due to rapid change in direction of current in short time
duration. A systematic switching sequence is required that
allows for the energy flowing in the IGBTs to decay.
TABLE 2
SWITCHING STRATEGY OF SPMC AS SIMPLE RECTIFIER
Switch
Pos.
cycle
Neg.
cycle
S1a
S1b
S2a
S2b
S3a
S3b
S4a
S4b
PWM
OFF
OFF
OFF
ON
OFF
ON
OFF
ON
OFF
ON
OFF
OFF
OFF
PWM
OFF
Fig. 7. Switching pattern generator 25Hz.
Fig. 8 shows the positive cycle operation with switch S1a
controlled by PWM, whilst switches S3a and S4a always
turned ‘ON’ prior to any switching functions. A similar
arrangement is developed for the negative cycle
implementation as illustrated in Fig. 9 where S3b controlled
by PWM whilst S1a and S2a always turned ‘ON’ prior to any
switching functions. The switching sequence of safecommutation is outlined in Table 2.
To ease understanding, the interval t0 to t6 of Fig. 10
describe the various steps of operation during one switching
period. The time delay ‘td’ provides dead-time between
commutating switch allowing for the current to decay until
zero prior to the next switching sequence. The solid line
(bold) in the diagram represents the safe commutation switch
203
during a particular step. One complete switching cycle is
divided to six steps and the steps are described as follows
Fig. 8. Proposed save commutation strategy positive state.
By using SPMC topology, it is possible to develop a
control rectifier incorporated with PFC for maintaining a
sinusoidal input current through proper control. The block
diagram of the PFC is as shown in Fig. 13[26]. This is
achieved through Fig. 9: Safe commutation strategy (negative
state) implementation of boost inductance in series with the
supply and suitable control the switches of SPMC. The
proposed controlled rectifier with PFC using SPMC is
tabulated in Table 3[26].
Control electronics was used to generate an active pulse
width modulation (APWM) using boost technique that is
piloted by a current control loop (CCL) where the function of
filtering unit is as shown in Fig. 14[26]. The overall switching
sequence in SPMC operation as controlled rectifier
incorporated with PFC is shown in Fig. 15[26].
Fig. 9. Proposed save commutation strategy negative state.
To ease understanding, the interval t0 to t6 of Fig. 10
describe the various steps of operation during one switching
period. The time delay ‘td’ provides dead-time between
commutating switch allowing for the current to decay until
zero prior to the next switching sequence. The solid line
(bold) in the diagram represents the safe commutation switch
during a particular step. One complete switching cycle is
divided to six steps and the steps are described as follows;
Step 1 (t0~t1): at time t0, S3a and S4a is turned ‘ON’.
Step 2 (t1~t2): at time t1, S1a is turned ‘ON’ (after delay
time) with the PWM switching pattern (providing overlap
period). During this stage, current is flowing in the inductance
(energized) through S1a and de-energized (commutation
operation) through the S3a and S4a due to S1a ‘OFF’.
Step 3 (t2~t3): at time t2, S1a is completely turned ‘OFF’
and the inductive load is de-energized due to overlap period
of S3a and S4a.
Step 4 (t3~t4): at time t3, S1a and S2a is turned ‘ON’ and
provided the overlap period before S3a is turned ‘ON’.
Step 5 (t4~t5): at time t4, S3a is turned ‘ON’ with the PWM
switching pattern (similar operation as step 2).
Step 6 (t5~t6): at time t5, S3a is completely turned ‘OFF’.A
completed period is ended[12].
Fig. 10. Switch timing of SPMC with commutation strategies.
C. SPMC as rectifier with power factor correction
The used of RC loads with rectifier function using SPMC is
shown in Fig. 11. By referring to Fig. 1, during the positive
cycle, the pair of switches S1a and S4a is turning ‘ON’,
whilst the pair of switches S2b and S3a is turning ‘ON’
during the negative cycle in the SPMC. This produces a
current wave shape that is different from the voltage as shown
in Fig. 12, non-sinusoidal but periodic in nature. The leading
power factor is expected due to the use of RC load[26].
Fig. 13. Block diagram of APF function.
204
TABLE 3
SWITCHING STATE FOR CONTROLLED RECTIFIER WITH PFC
Switch
Pos.
cycle
Neg.
cycle
S1a
S1b
S2a
S2b
S3a
S3b
S4a
S4b
ON
OFF
OFF
OFF
OFF
apwm
ON
OFF
OFF
apwm
OFF
ON
ON
OFF
OFF
OFF
Proposed DC chopper is as shown in Fig.17. It has similar
structure with those of the SPMC as shown in Fig. 1, the
difference being the input dc voltage. Practical realization of
matrix converters requires the use of four-quadrant switch
capable of bi-directional operation. In comparison with
conventional dc chopper of Fig.16 it has 4 bi-directional
switches as opposed to the use of 4 switch and 4 diodes in
conventional dc chopper. This arrangement was chosen
because it allows within each switch independent control of
the current in both direction. This back-to-back bi-directional
arrangement of the matrix converter also has lower
conduction losses than a diode bridge switch arrangement
during commutation of the load current. In this circuit
configuration, the IGBTs were used because of its high
switching frequency and high current handling capabilities.
Diodes arranged in series to provide the reverse voltage
known as a dc to dc converter. It is considered a dc equivalent
blocking capability[29].
Fig. 14. Filter Power unit Function.
Fig. 17. DC chopper using SPMC.
Fig. 15. Switching pattern before compensation.
VII.
SPMC AS DC CHOPPER
A DC Chopper converts directly from DC to DC and also
known as a dc to dc converter[28–31]. It is considered a dc
equivalent of AC transformer with a continuously variable
turn’s ratio. It can be used to step down or step up a dc
voltage source. Apart from those applications it can also be
used in regenerative braking of DC motors, DC voltage
regulators and also used in conjunction with a inductor, to
generate a dc current source, especially for current source
inverter applications[29]. A conventional DC chopper is as
illustrated in Fig. 16.
Fig.16. Conventional dc chopper.
The implementation of the SPMC as a dc chopper requires
different bi-directional switching arrangements depending on
the desired operational requirements of the four quadrants
defined. The magnitude of the output voltage of the converter
is controlled by PWM variations in duty cycle. The switching
sequences are designed to follow Table 4[29].
TABLE 4
SWITCHING PATTERN FOR FOUR-QUADRANT DC-TO-DC MATRIX
CONVERTER
Switches
First
Quadrant
Second
Quadrant
Third
Quadrant
Fourth
Quadrant
S1a
PWM
OFF
OFF
OFF
S1b
OFF
ON
OFF
OFF
S2a
OFF
OFF
PWM
OFF
S2b
OFF
OFF
OFF
ON
S3a
OFF
PWM
ON
OFF
S3b
ON
OFF
OFF
ON
S4a
ON
OFF
OFF
PWM
S4b
OFF
ON
ON
OFF
First quadrant
The load current flows from the supply to the load. To
achieve this condition, SIa and S4a are turned-on and act as a
power switch performing the required converter operation
synthesizing the output dependent on the control algorithm
being developed. During turn-off of Sla, switches S3b and
S4a are maintained as continuously ON during this cycle; S4a
205
to complete the loop for current return and acts in conjunction
with S3b to provide free-wheel operation whenever S1a is
turned off[29].
Second quadrant
The loads current flows out of the load. To achieve this
condition, Switch S3a and S4b will operate while Slb will be
continuously turned-on, the voltage E will drives current
through the load and when both switch S3a and S4b are turn
off, load dissipates energy through S lb to the supply[29].
Third quadrant
It is the reverse of first quadrant, where the load current
flows from the supply to the load through a different route.
To achieve this condition, S2a and S3a are turned-on and act
as a power switch performing the required converter
operation synthesizing the output dependent on the control
algorithm being developed. During turn-off of S2a, switches
S3a and to complete the loop for current return and acts in
conjunction with S4b to provide free-wheel operation
whenever S2a is turned OFF[29].
Fourth quadrant
The loads current flows out of the load. To achieve this
condition, Switch S3a and S4a will operate continuously
turned on, the voltage E will drives current through the load
and when both switch S3a and S4a are turn off, load
dissipates energy trough S1b to the supply[29].
VIII.
DISCUSSION
It is only part of converter topologies witch can be realized
with SPMC. It can work also ho inverter[32–34], buck, and
boost. Inverter combined with buck or boost topology with
positive or negative direction. To realize buck-boost topology
necessary use extra components like Z-branch [35–41] or
extra switches. SMPC characteristics are not so good than as
is bridge converter but it already close for it.
IX. CONCLUSIONS
Overview of single phase matrix converter is presented and
that topology is explained. A few switching strategies of
SPMC are presented. These strategies can be used for
replacement of conventional converters topologies.
SPMC can be used as universal converter if
necessary use different energy conversion with one converter.
SPMC is very flexible topology with high integration level.
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