JESTPE-2017-10-0713.R2
1
Abstract— This paper proposes a generalised commutation
strategy suitable for matrix-based isolated AC/AC conversion
stages in Solid State Transformers for use whenever there is non-
negligible leakage inductance in the isolation transformer. The
standard 4-step commutation used in matrix converters can no
longer be applied when transformer leakage inductance is present,
as overrated switching devices or dissipative snubbers would be
necessary, reducing the attractiveness of the topologies that
include matrix-based isolated AC/AC stages. A case study of a
single-phase AC/AC converter has been investigated in detail to
demonstrate the application of the proposed commutation method
to a topology that has recently been identified as the potential
building block for future multi-modular AC/AC converters for
grid applications. The proposed leakage-inductance-tolerant
commutation strategy is based on the definition of a current
decoupling phase in the commutation sequence and only needs
suitable timing of the commutation steps, without high bandwidth
voltage or current measurements. Matching simulations and
experimental results from a 3kW laboratory scale prototype are
presented to support the effectiveness of the proposed strategy.
Index Terms—4-Step Commutation, Grid interconnection,
Isolated Single-Phase AC-AC converters, Leakage-inductance,
Matrix converters, Multi-Modular converters, Solid-State
Transformers
I. INTRODUCTION
N recent years, considerable research efforts have been
directed toward power-electronic based solutions to replace
low-frequency transformers in LV and MV distribution grids as
well as in traction systems, both for AC/AC and AC/DC
conversion [1, 2]. Transformer volume and weight are critical
when space is restricted or expensive, e.g. in city centers [3] or
in locomotives [4]. In these cases, power density can be
increased using converters with medium-frequency isolation
stages [3-5]. Despite a large diversity of ratings, applications
and topologies, these solutions are referred to generically as
Solid State Transformers (SSTs). SSTs are still a developing
technology and no broad consensus has been reached yet on
their functional requirements. A first observation is that mass
and volume reduction offered by SSTs tend to be
counterbalanced by their higher cost and complexity, lower
efficiency and reliability and by their lower overload capability
Manuscript received October 30, 2017; revised May 18, 2018. This work is
supported by the Newton Picarte and Fondecyt Project Grant 1160690.
U. Nasir, A. Costabeber, P. Wheeler and J. Clare are associated with Power
Electronics & Machine Control (PEMC) research group at The University of
Nottingham, Nottingham NG7 2RD, U.K. (e-mail:
[3]. Therefore, replacing low-frequency transformers with
SSTs in existing applications would not necessarily lead to a
technical and financial success. On the contrary, SSTs can be
better deployed in dedicated scenarios where advantages can be
exploited, and limitations can be mitigated, based on system
level design considerations. The opportunity to shape these
scenarios for SSTs comes, for example, from future distribution
systems [6] and new traction systems [5, 7].
Ideally, SSTs should provide isolation enhanced by the
controllability of power converters. The SST should decouple
the load from power system perturbations, e.g. provide high
quality load voltage waveforms in presence of grid voltage
harmonics, sags, imbalances and faults [2], as well as decouple
the power system from the load behaviour, e.g. draw from the
grid sinusoidal and balanced currents with unity or controllable
power factor [3] in presence of load imbalance and/or non-
linearity and regardless the load power factor. Several
topologies [1] have been proposed for SSTs, with different
capabilities. A simplistic distinction can be made between the
fully matrix-based SSTs in Fig. 1(a), without energy storage
and hence with potentially smaller footprint, the voltage-source
ones (e.g. DAB based) with energy storage and the hybrid
solutions shown in Fig. 1(b) with a combination of voltage-
source and matrix-based stages. If energy storage is available,
the grid-load decoupling functionalities discussed above can be
inherently achieved. Instead, in a direct converter the need for
usman.nasir@nottingham.ac.uk; alessandro.costabeber@nottingham.ac.uk;
pat.wheeler@nottingham.ac.uk; jon.clare@nottingham.ac.uk).
M. Rivera is with the Department of Electrical Engineering, Universidad
de Talca, Curico, PB, 3341717 chile (e-mail: marcoriv@utalca.cl).
A Leakage-Inductance-Tolerant Commutation
Strategy for Isolated AC/AC Converters
Usman Nasir, Student Member, IEEE, Alessandro Costabeber, Member, IEEE, Marco Rivera,
Member, IEEE, Pat Wheeler, Senior Member, IEEE, and Jon Clare, Senior Member, IEEE
I
(a)
(b)
Fig. 1 Solid State Transformer (SST) architectures with matrix-based
isolation stages: (a) direct and (b) with energy storage
Converter 2Converter 1
MF/HF
AC Link
AC
Grid
2
AC
Grid
1
DC Link
MF/HF
AC Link
AC
Grid
1
AC
Grid
2
Converter 1
Converter 2
JESTPE-2017-10-0713.R2
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matching input and output instantaneous powers can lead to a
drastic reduction of the control capabilities, especially under
unbalanced operation and faults on the grid or load side.
However, in specific non-critical applications the higher power
density can be prioritized, sacrificing functionality. A recent
example that could benefit from a direct converter is the mid-
feeder compensator for LV distribution grids discussed in [8].
Whenever the SST presents a matrix-based stage coupled to
a MF transformer, such as in [8-10], the commutation process
becomes challenging in presence of non-negligible transformer
leakage inductance since no free-wheeling path is available.
The aim of this paper is not to focus on a specific SST topology
but rather to provide a methodology to enhance the
commutation process of a family of matrix-based or hybrid
converters shown in Fig. 1. The fundamental assumption
behind the commutation process in matrix topologies is that one
side of the converter can be considered a voltage source and the
other a current source during commutation. Adding a leakage
inductance in the AC link causes potential current mismatches
during commutation that must be adequately managed to
minimise the impact on the converter operation and design.
Although interleaved windings can be used to reduce the
leakage inductance, in practical applications it is not always
possible to have adequate control over the leakage, due to cost
or other system design constraints.
A current based 4-step commutation sequence for the SST in
Fig. 1(b) was proposed in [9] but the drawback of the proposed
solution is that the impact of transformer leakage inductance on
the commutation process was neglected, thus it relies on
negligible transformer leakage to successfully complete
commutation. To date, various methods have been reported in
the literature to deal with the leakage energy. For instance,
employing snubber circuits can help to mitigate the issue [11]
but at the cost of increased power losses and reduced power
density. The snubber capacitors can also cause turn-on loss in
the switches, as the energy of the capacitor is dissipated in the
switching device and an auxiliary biasing circuit would be
required to mitigate the issue [12]. A second approach can be
the introduction of a capacitor at the primary side of the
transformer, forming a parallel-resonant tank with the
magnetisation inductance [13]. This approach achieves soft-
switching but the leakage energy is dissipated in the transformer
winding resistance and tuning of the resonant tank can be
challenging. Reference [14] utilises a capacitor in series with
the leakage inductance which forms a series-resonant tank. A
common drawback of all the discussed methods is that they
require additional energy storage components to target the
commutation issue. An alternative method to deal with
commutation in the presence of leakage inductance could be to
drive the commutation by using a controllable voltage source.
This method does not need additional energy storage
components and can also avoid resonance related problems.
The source-based commutation of a single-phase DC/AC
converter presented in [15] achieves complete soft-switching of
the cyclo-converter but it does not take into account the effect
of the leakage inductance.
Other existing research into matrix-based SST topologies
pay limited attention to the impact of the leakage inductance on
the commutation process. Recently, the importance of
accounting for the leakage effect has been highlighted for a
MF/HF isolated three phase to three phase direct converter [16],
showing how the conventional 4-step commutation strategy
must be substantially reviewed to avoid over voltage across the
semiconductor devices. However, a generalised concept to deal
with the leakage energy, suitable for all SSTs with matrix-based
stages, has not been clearly addressed in the literature.
This paper proposes a new generalised commutation concept,
which provides safe commutation by naturally recirculating the
energy stored in the leakage inductance. As a case study, the
proposed concept is applied in detail to a single-phase isolated
AC/AC converter and experimentally validated on a 3kW rig.
The only requirement of the strategy is suitable timing of the
commutation steps, like the 4-step commutation used in Matrix
Converters. No fast or time-critical voltage or current
measurements are required to implement the proposed
commutation. The specific case study has been chosen
considering the potential use of the matrix-based single-phase
SST topology as the fundamental building block for a new
breed of multi-modular power converter architectures for grid
connected applications [17]. These new concepts will combine
the advantages of an SST with those of a modular, flexible and
scalable structure which can be adapted to different voltage
levels and frequencies.
The proposed commutation concept is based on the
introduction of an intermediate state, named the current
decoupling phase, during which the leakage inductance current
is modified, driven by the input voltage or by a modulated
version of it, to bring its sign and magnitude to the new value
required after commutation without requiring snubbers or
clamps. The application of the proposed concept to a minimal
circuit is briefly discussed in section II, to highlight the
simplicity and generality of the method. The specific case study
of a single-phase isolated AC-AC converter is discussed in
detail and experimentally validated in the remaining sections.
II. B
ASIC PRINCIPLE OF THE LEAKAGE-INDUCTANCE-
T
OLERANT COMMUTATION STRATEGY
As mentioned in the previous section, the basic concept of
the proposed leakage-inductance-tolerant commutation strategy
relies on the introduction of a current decoupling phase that
enables manipulation of the leakage inductance current in order
to match the sign and magnitude imposed by the output current
after commutation. To illustrate the basic idea, consider the
minimal circuit shown in Fig. 2. It is assumed that the converter
has a voltage source at the input and a current source at the
output, represented by the filter inductor L
o
. The filter inductor
is much larger than the leakage inductance, i.e. L
o
>>L
leak
, so
that during commutation the leakage inductance current can be
modified while the output current remains nearly constant. In
this simple and general example, the input voltage comes from
a previous stage of the converter, from an independent voltage
source or from a controllable voltage source.
Consider now the case where the circuit has to commutate
from State 1 in Fig. 2(a) with S
1
=ON, S
2
=OFF to State 2 in Fig.
JESTPE-2017-10-0713.R2
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2(c) with S
1
=OFF, S
2
=ON. Also, assume that I
out
>0, I
L
>0 and
V
in
<0 at the instant of commutation and that the IGBTs and
diodes in S
1
and S
2
are ideal, with zero commutation time. The
latter assumption has been made only to simplify the
commutation steps and focus on the current decoupling phase.
Under these assumptions, the first commutation step is to
open the IGBT that is not carrying current in S
1
(i.e. S
1n
) and
close the one that can carry I
out
in S
2
(i.e. S
2n
). This initiates the
current decoupling phase as shown in Fig. 2(b). With zero
input voltage V
in
, I
out
would keep flowing in the leakage
inductance and in S
1
and the circuit would not be able to safely
move to State 2 without discharging the leakage energy in S
1
or
in a clamp circuit. Instead, if a value of V
in
<0 can be applied,
V
in
will appear across the leakage inductance and will drive the
current I
L
to zero. Once the current I
L
is zero, S
1
can be
completely opened and S
2
closed, completing the decoupling
phase and reaching State 2. Note that this can be simply
achieved by an appropriate timing, and no zero-crossing
detection of the current is required. In fact, since I
L
is conducted
by the diode in S
1n
during the current decoupling phase, the
diode will naturally turn off once the current reaches zero.
The generalised concept explained above can be applied to
SST topologies suffering from the effect of non-negligible
transformer leakage inductance to achieve a safe-commutation
without using dissipative clamps or snubbers. In the coming
sections, the proposed concept has been elaborated and
validated for a specific SST topology, a single-phase isolated
AC/AC converter, as only a few contributions on modulation of
single phase isolated AC/AC converters have been reported in
the literature [9, 18-22]. Starting from the explanation of the
commutation problem in the topology under study in Section
III, the subsequent sections present a detailed analysis,
simulation and experimental validation of the proposed
commutation concept.
III. T
HE COMMUTATION PROBLEM IN A SINGLE-PHASE
ISOLATED AC/AC CONVERTER
This section introduces the idealised operation of the single-
phase isolated AC/AC converter of Fig. 3, considering an ideal
transformer and a standard 4-step commutation. The effect of
the transformer leakage inductance is then discussed, justifying
the need for a different current commutation approach. The
operating principle of the topology in Fig. 3 is similar to that of
a standard Matrix converter. The input is considered as a
voltage source while the output is assumed to be a current
source/sink. Any commutation process has to guarantee a path
for the output current and has to avoid short-circuiting the input
voltage.
In this converter, the AC input voltage is modulated using the
bidirectional input bridge and the resulting switched waveform
is applied to the transformer. This voltage is then modulated by
the output bridge to create an output current waveform with the
desired frequency.
Several modulation strategies can be used for this converter,
but their analysis is out of the scope of this paper. Similar to
Matrix Converters, the commutation can be implemented based
on input voltage magnitude or output current direction [23]. For
brevity, only the output current direction based technique is
considered here. For the ideal converter, when I
out
>0 and
commutation takes place in the output bridge only, the sequence
is shown in Fig. 4 and can be summarised as follows:
State 1: The output bridge of the converter is in steady state
with s0, s1, s2, s3 turned on. Fig. 4(a).
State 2: Non-conducting switches s1, s3 can be turned off,
with zero current (ZCS), as I
out
has a path through the
antiparallel diodes. Fig. 4(b).
State 3: The switches s5, s7 can conduct the current in the
direction of I
out
and can be turned on safely with ZCS. Fig. 4(c).
State 4: Since s5, s7 are already on, they can provide a path
for I
out
and the switches s0, s2 can be turned off with non-zero
current i.e. hard switching. Fig. 4(d).
State 5: For the bridge to reach the new steady state, the
switches s4, s6 are finally turned on with zero voltage (ZVS).
This standard 4-step commutation can be used for both the
input and output bridges. The current commutation of the two
bridges can be considered independent if the leakage
inductance of the transformer is neglected. The only
requirement is to avoid overlap between the input and output
(a) State 1 with S
1
=ON, S
2
=OFF (b) Current decoupling State (c) State 2 with S
1
=OFF, S
2
=ON
Fig. 2. Illustration of the basic concept of the proposed commutation strategy
Current Source
Voltage Source
L
leak
L
o
S
1
I
L
s
1n
s
2p
s
2n
S
2
s
1p
I
out
V
in
+
-
Current Source
Voltage Source
L
leak
L
o
S
1
I
L
s
1n
s
2p
s
2n
S
2
s
1p
I
out
V
in
+
-
Current Source
Voltage Source
L
leak
L
o
S
1
I
L
s
1n
s
2p
s
2n
S
2
s
1p
I
out
V
in
+
-
Fig. 3 Single phase MF/HF isolated AC/AC converter
JESTPE-2017-10-0713.R2
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bridge commutation sequence.
The ideal effect of a non-negligible leakage inductance can
be analysed by considering, for example, states 3 and 4. In state
3, I
L
=I
in
=I
out
but in state 4, when s0, s2 are turned off, the
current is expected to change path to s5 and s7, thus reversing
the direction of the leakage inductance current from I
in
=I
out
to
I
in
=-I
out
. The change of current direction will be opposed by the
inductance, causing an overvoltage across the output bridge. If
L
leak
is the transformer primary leakage inductance and t
OFF
is
the turn-off time of s0 and s2, then the peak of the voltage spike
V
PK
can be approximated by (1), assuming a linear current
variation during turn-off of the switches, negligible Collector-
Emitter capacitance and no clamps:
OFF
outleak
PK
t
IL
V
2
=
(1)
In practical applications, the bridges will be equipped with
dissipative clamps to protect the converter from commutation
failures. As a result, the voltage in (1) is clamped to the clamp
voltage. The drawback is that the clamp will be triggered every
time the modulation requires transitions that reverse the leakage
inductance current, thus leading to additional loss.
Minimisation of the leakage inductance as proposed in [9] will
attenuate but will not eliminate the problem. Also, minimising
the leakage inductance to acceptable levels is not always
achievable in practice. Hence, a different commutation
approach is needed to remove the undesired over-voltages and
clamp loss during current commutation.
IV. P
ROPOSED LEAKAGE-INDUCTANCE-TOLERANT
COMMUTATION STRATEGY
The assumption made in the proposed current commutation
procedure is that the output current is an equivalent current
source during commutation, but the leakage inductance current
can be modified to guarantee safe commutation. The leakage
inductance current must be reversed before the output bridge is
commutated to match the magnitude of the output current.
Therefore, a current decoupling phase can be introduced into
the commutation sequence where the output current is re-
circulated through the output bridge and the change of leakage
inductance current direction is driven by the input voltage
source [16, 24] which is applied across the leakage inductance
by the input bridge. To apply the correct voltage polarity across
the leakage inductance, the input voltage sign is detected, and
the input bridge is driven accordingly.
An example of the proposed commutation strategy is
described below for the case where the output current and input
voltage are both positive and both the input and output bridges
are commutated, as shown in Fig. 5. The generalisation to all
the possible commutation states can be obtained by rearranging
the order of the different commutation steps, as discussed in
Section V. The analysis assumes that the input voltage and
output current remain effectively constant during the
commutation interval, given that the commutation time is a
negligible fraction of the input and output fundamental periods.
A. Commutation Strategy for Vin>0, Iout>0: from s0i…s3i,
s0o…s3o ON to s4i…s7i, s4o…s7o ON
State 1 – Initial state: The converter is in steady state with a
total of 8 switches i.e. 4 switches of input bridge s0i, s1i, s2i,
s3i and 4 switches of output bridge s0o, s1o, s2o, s3o in the on
state. In this initial state:
oTin
VVV ==
(2)
Lout
IIiiii =====
6521
(3)
0
8743
==== iiii
(4)
State 2: With V
in
>0 and I
out
>0, the non-conducting switches
of both bridges i.e. s1i, s3i and s1o, s3o can be turned off with
ZCS, equations (2)-(4) remain true.
State3: The switches s5i, s7i and s5o, s7o can conduct the
current in the direction of I
out
and therefore can be turned on
safely (i.e. without short circuiting V
in
) with ZCS and equations
(2)-(4) still hold true. The current through s5i, s7i and s5o, s7o
remains zero because the antiparallel diodes of s4i, s6i and s4o,
s6o are all reverse biased.
State 4 – First “Current decoupling” state: Since the
switches s5i, s7i and s5o, s7o are now in the on state, they can
provide a path for I
out
and the switches s0i, s1i in the input
bridge can be turned off safely. Note that the switches s0i, s1i
will have hard turn off. When the input side switches are turned
off, the leakage inductance current forces the antiparallel diodes
of s4i, s6i and s4o, s6o into conduction. As a result, the output
current now circulates in s0o, s5o, s2o, s7o and in the
antiparallel diodes of the output bridge switches (which are in
the off state). This action effectively shorts the secondary of the
transformer, decoupling the input bridge from the output
bridge, and in turn decoupling I
out
from the leakage inductance
current I
L
. At the input side, the reversed input voltage appears
across the leakage inductance, driving the current toward zero.
During this state:
0=
o
V
(5)
inT
VV −=
(6)
(a) state 1 (b) state 2 (c) state 3 (d) state 4 (e) state 5
Fig. 4 Standard 4-step Current Based Commutation for the ideal converter when I
out
>0 and Commutation from s0…s3 ON to s4…s7 ON
s7
I
out
s0
I
L
s1
s6
s2
s3
s5
s4
I
in
I
out
I
in
I
L
s7
s0
s1
s6 s2
s3
s5
s4
I
out
I
in
I
L
s7
s0
s1
s6
s2
s3
s5
s4
I
out
I
in
I
L
s7
s0
s1
s6
s2
s3
s5
s4
I
out
I
in
I
L
s7
s0
s1
s6 s2
s3
s5
s4
JESTPE-2017-10-0713.R2
5
0
21
== ii
(7)
out
Iii 5.0
75
=−=
(8)
out
Iii 5.0
86
=−=
(9)
()
leakinoutL
LtVIiiI /
43
−=−=−=
(10)
State 5 – Second “Current decoupling” state: This state
begins when the leakage inductance current that started to
decrease in State 4, reaches zero. Note that, regarding the
ON/OFF state of the switches, this state is the same as the
previous state and no change has been applied. This state could
be neglected, but from the perspective of a practical
implementation where the commutation sequence will be timed
based on switching times and the worst-case leakage discharge
time, the state will be present and has been included here for
completeness. Note that this method does not require the
detection of I
L
=0 thus avoiding the need for high-bandwidth
sensors.
0
4321
=−=−=== iiiiI
L
(11)
State 6 – Third “Current decoupling” state: As the
leakage inductance was fully discharged in State 5, the switches
s4i, s6i in the input bridge can now be turned on and a negative
current through the leakage inductance will start to develop.
The output current is still circulating but the leg currents i
5
, i
6
naturally start to decrease while the currents i
7
, i
8
start to grow,
shifting the current from i
5
, i
6
to i
7
, i
8
. In this state, equations
(5)-(7) and (12)-(14) are true. Note that the switches s4i, s6i are
turned on with ZCS because the rate of change of current i
3
and
i
4
is slowed down by L
leak
. See equation (14).
()
leakinout
LtVIii /5.0
65
−==
(12)
()
leakinout
LtVIii /5.0
87
−−==
(13)
leakinL
LtViiI /
43
−=−=−=
(14)
State 7: In this state the negative leakage current which
started to develop in state 6 reaches the magnitude of I
out
which
in turn naturally commutates the output bridge. The currents i
5
,
i
6
reach zero whereas the currents i
7
, i
8
reach -I
out
:
oTin
VVV =−=
(15)
0
65
== ii
(16)
outL
IiiiiI =−=−===−
8743
(17)
State 8: The current naturally commutates from s0o, s2o to
s5o, s7o and therefore s0o, s2o can be turned off in ZCS in this
state. The current and voltage equations from the previous state
still hold true.
State 9: To complete the commutation the switches s4o, s6o
are turned on under zero voltage (ZVS) and the converter
reaches the new steady state. Note that if the turn-on and turn-
off times are assumed ideal, the commutation time corresponds
to the time required by the leakage to discharge and then
recharge, as given by equation (18). The commutation time is a
function of the AC input voltage magnitude that is driving the
(a) State1 (b) State 2 (c) State3
(d) State 4 (e) State5 (f) State 6
(g) State 7 (h) State 8 (i) State 9
Fig. 5 Steps of the proposed commutation strategy for the case V
in
>0, I
out
>0 and commutation from s0i…s3i, s0o…s3o ON to s4i…s7i, s4o…s7o ON
