energies

Review

An Overview of Applications of the Modular
Multilevel Matrix Converter

Matias Diaz 1,* , Roberto Cárdenas Dobson 2, Efrain Ibaceta 1, Andrés Mora 3, Matias Urrutia 2,
Mauricio Espinoza 4, Felix Rojas 1 and Patrick Wheeler 5

1 Electrical Engineering Department, University of Santiago of Chile, Avenida Ecuador 3519,
Santiago 9170124, Chile; efrain.ibaceta@usach.cl (E.I.); felix.rojas@usach.cl (F.R.)

2 Electrical Engineering Department, University of Chile, Avenida Tupper 2007, Santiago 8370451, Chile;
rcd@ieee.org (R.C.D.); maturrutia@ug.uchile.cl (M.U.)

3 Electrical Engineering Department, Universidad Técnica Federico Santa María, Valparaíso 1680, Chile;
andres.mora@usm.cl

4 School of Electrical Engineering, University of Costa Rica, San José 11501-2060, Costa Rica; maeb@ieee.org
5 PEMC Group, Faculty of Engineering, University of Nottingham, Nottingham NG7 2RD, UK;

pat.wheeler@nottingham.ac.uk
* Correspondence: matias.diazd@usach.cl; Tel.: +5-62-2718-3344

Received: 10 July 2020; Accepted: 6 October 2020; Published: 22 October 2020
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Abstract: The modular multilevel matrix converter is a relatively new power converter topology
suitable for high-power alternating current (AC)-to-AC applications. Several publications in the
literature have highlighted the converter capabilities, such as full modularity, fault-redundancy,
control flexibility and input/output power quality. However, the topology and control of this
converter are relatively complex to realise, considering that the converter has a large number of
power-cells and floating capacitors. To the best of the authors’ knowledge, there are no review papers
where the applications of the modular multilevel matrix converter are discussed. Hence, this paper
aims to provide a comprehensive review of the state-of-the-art of the modular multilevel matrix
converter, focusing on implementation issues and applications. Guidelines to dimensioning
the key components of this converter are described and compared to other modular multilevel
topologies, highlighting the versatility and controllability of the converter in high-power applications.
Additionally, the most popular applications for the modular multilevel matrix converter, such as
wind turbines, grid connection and motor drives, are discussed based on analyses of simulation
and experimental results. Finally, future trends and new opportunities for the use of the modular
multilevel matrix converter in high-power AC-to-AC applications are identified.

Keywords: modular multilevel matrix converters; AC-to-AC conversion; modular multilevel converters

1. Introduction

Modular multilevel cascaded converters (MMCCs) have attracted considerable attention from the
power electronic and drive research community since its introduction at the beginning of the 2000s [1].
Originally, MMCCs were proposed for high voltage direct current (HVDC) transmission systems,
but recently, they have been introduced into other fields, e.g., static compensators (STATCOMs) [2–4],
wind energy conversion systems (WECSs) [5,6], drives [7,8], etc.

Some of the well-known advantages of MMCCs are related to their modular topology,
which allows a relatively simple expansion to higher voltages and powers; redundancy; high efficiency;
robustness; and high power quality [9]. For instance, if a larger nominal voltage is required,
more power-cells can be cascaded into each cluster; if a larger nominal current is required,
then power-cells can be paralleled. Moreover, redundancy is simple to provide by including a number

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Energies 2020, 13, 5546 2 of 37

of additional power-cells in each cluster, which can be activated to replace those damaged or in a
faulty condition.

Among MMCCs, the modular multilevel converter (M2C) is a well-established topology used
extensively for HVDC transmission [2,10,11], and more recently in motor-drive applications [12–15]
with some solutions being commercially provided to the market [12,13].

However, as it has been reported in several publications, the M2C has some difficulties in
achieving good performances in applications where the electrical machine is operating at very
low-speed (low stator frequency) and at high-torque. Moreover, the M2C is not an AC-to-AC topology,
and a back-to-back connection is required if AC-to-AC conversion is necessary, and this increases the
numbers of semiconductor switches, capacitors and inductors. Therefore, other MMCC topologies,
such as the Hexverter and the modular multilevel matrix converter (M3C), have been studied in the
last few years [16,17] for high-power AC-to-AC drive applications. In particular, the M3C has shown
some advantages when the control of electrical machines operating at low-speed and high-torque is
required. Moreover, as reported in several publications [18–20], for this operating range, the M3C has
advantages when compared to other MMCC topologies. Currently, several works have highlighted
the M3C as a suitable AC-to-AC topology for high-power motor-drive applications [8,18,21].

A matrix converter topology with a resemblance to the modern M3C was first proposed by a
research group from the National Renewable Energy Laboratory for high-power WECSs [22–24]. In this
topology, filter inductances were not included in each cluster, and this produces several drawbacks.
For instance, as reported in [23], only five clusters were permitted to be switched on (simultaneously) to
avoid the problems of producing a short circuit by parallel connection of voltage sources. This problem
was solved in [25] by introducing cluster inductors (see Figure 1) allowing a continuous and regulated
cluster currents flow; i.e., with the addition of the inductances each cluster could be represented as a
controllable current source.

The topology of the M3C currently being used is shown in Figure 1. The converter is composed of
nine clusters comprising a stack of series-connected full-bridge power-cells and one inductance.
Each power-cell is composed of a full-bridge connected to a floating capacitor on the DC-side.
The voltage in this capacitor has to be well regulated in order to achieve proper and stable operation of
the converter in the whole operating range [18]. The capacitor voltage regulation is usually performed
using four linearly independent circulating currents [26,27]. In this work, the term circulating current
is utilised to refer to the internal currents of the converter which are neither present at the input a-b-c
nor present at the output r-s-t terminals.

Figure 1. M3C topology. From [28].



Energies 2020, 13, 5546 3 of 37

In the M3C, the AC-to-AC power conversion is performed without using a DC-link,
which eliminates the capacitor voltage fluctuations when the converter operates with a low-frequency
on the output-side [29,30]. Consequently, in this operating point, lower circulating currents and
common-mode voltage are required to mitigate the capacitor’s voltage oscillations compared
with those typically required in the M2C [8,21]. This advantage makes the M3C a promising
topology for high-power variable-speed drive applications, such as medium-voltage motor
drives [8,21,31], gearless Semi-Autogenous Grinding (SAG) mills [32], offshore wind-power
generators [27] and full-electric marine propulsion systems [33], where the M3C can substitute the
line-commutated converters to reduce current harmonics, to improve the power factor and to increase
the efficiency and flexibility. Additionally, in contrast to the back-to-back M2C topology, the M3C can
still be operated after a failure in a power-cell or a whole cluster, regardless of the cluster in which the
failure occurred [34].

Unlike the M2C, at the present time, there are no commercial solutions available for the M3C.
That is probably because the M3C is more complex to control, has a high component count and is
more costly to build. However, it is forecasted that shortly the M3C will replace the conventional
thyristor-based cycloconverters utilised for the control of high-power machines, e.g., the SAG mills,
as reported in [26]. Complex implementation and control have also hindered the number of works
where experimental results of this topology are reported. This is further discussed in the next sections.

This work aims to provide an extensive and thorough review of the state-of-the-art of the M3C.
This review paper is focused on describing practical implementations and applications, such as the
utilisation of the M3C in wind turbines and motor-drive systems. The contributions of this paper can
be summarised as follows.

• To the best of the authors’ knowledge, this is the first review paper discussing and comparing
experimental implementations and applications of the M3C. In the field of MMCCs, there are
other review papers available for the M2C [2,9,35–37] and Hexverter [16]; comparisons between
the M2C and M3C for motor-drive applications [8,21]; and modelling and control approaches for
the M3C (a recent review) [28]. However, those papers neither describe practical issues related to
the implementation of the M3C nor describe applications of the M3C.

• Some of the most well-known implementations of the M3C reported in the literature are listed
and classified.

• In this paper, guidelines to designing and dimensioning the most important electrical parameters
of the M3C are described.

• The M3C is compared to other MMCCs, such as the Hexverter and the M2C, in terms of component
counts and effectiveness. Results were obtained for a 10 MW case of study.

• Furthermore, a review of promissory applications for the M3C, such as wind energy, motor drives
and flexible AC transmission systems (FACTSs), is presented. Simulations and experimental
results are given to support the effectiveness of the topology in these applications.

The rest of this paper is organised as follows. Design guidelines and the details of the currently
implemented M3C prototypes are presented in Section 2. Then, the M3C, Hexverter and M3C are
compared in terms of flexibility, component counts and other technical parameters in Section 3.
Section 4 presents a summary of M3C applications such as wind turbines, motor drives and FACTSs.
After that, future research opportunities and trends and identified in Section 5. Finally, an appraisal of
the applications discussed in this paper is presented in the conclusions.

2. M3C Control and Hardware Challenges

The M3C is composed of nine cluster, as illustrated in Figure 1. Normally, each cluster of the
M3C can be represented as a controllable voltage source to simplify the analysis of the converter,
as presented in Figure 2b [27]. The connection of three clusters linking the three phases of the input
system (e.g., phases a, b, c) to one phase of the output system (e.g., phase r) has been referred to as a



Energies 2020, 13, 5546 4 of 37

sub-converter or single-phase M3C [32]. The composition of a sub-converter is presented in Figure 2c.
Additionally, the composition of each cluster comprises the connection of n power-cells connected in
cascade with one inductor Lc, as depicted in Figure 2d. Finally, the power-cell comprises a full-bridge
connected to a DC capacitor, as presented in Figure 2d.

Figure 2. M3C topology. (a) Simplified circuit of the M3C. (b) Simplified circuit of a sub-converter.
(c) Cluster. (d) Power-cell. Adapted from [28].

In this converter, the number of power-cells can be increased to reach higher power and voltage
ratios. Therefore, the control and hardware of the converter must be designed to handle the possible
addition of more power-cells. Additionally, as the voltages in the capacitors of each power-cell are
floating, the regulation of the M3C must ensure a good regulation of these floating capacitor voltages
over all the operational range. These two facts can be complicated to accomplish, as indicated in some
publications [17,28,32]. Consequently, in the following subsections, the main highlights regarding the
modelling, control and nature of the voltage oscillations are briefly revised. More details regarding
these topics can found in [28].

2.1. Control Issues and Floating Capacitor Voltage Oscillations

Analysing the circuit diagram depicted in Figure 1a, the nine cluster voltage equations of the
M3C can be expressed as follows:

Vmx︷ ︸︸ ︷ vma vmb vmc

vma vmb vmc

vma vmb vmc

 = Lc
d
dt

Ixy︷ ︸︸ ︷ iar ibr icr

ias ibs ics

iat ibt ict

+

Vxy︷ ︸︸ ︷ var vbr vcr

vas vbs vcs

vat vbt vct

+

Vgy︷ ︸︸ ︷ vgr vgr vgr

vgs vgs vgs

vgt vgt vgt

+vn

 1 1 1
1 1 1
1 1 1

 (1)

In Equation (1), the subscript m is used to represent the input-side voltages and currents;
meanwhile, the subscript g is used to represent the output-side variables. The voltage between
external neutral points is denoted by vn.



Energies 2020, 13, 5546 5 of 37

If the voltage drops in the cluster inductors are neglected, and neither common-mode voltage nor
circulating currents are utilised, the cluster voltages and the cluster currents can be expressed in terms
of the input and output matrices as follows:

Vxy = Vmx − Vgy (2)

Ixy =
1
3
(Imx + Igy) (3)

where Imx and Igy are input and output current matrices; Vmx and Vgy are input and output voltage
matrices. Note that x ∈ {a, b, c} and y ∈ {r, s, t}. Considering that each cluster is composed of n
full-bridge power-cells, every component of the Vxy matrix can be expressed as follows:

vxy =
n

∑
i=1

vxy,i =
n

∑
i=1

Sxy,i vCxy,i (4)

In Equation (4), vxy,i stands for the voltage synthesised at the output of each power-cell,
the switching state of each power-cell is represented by Sxy,i ∈ {−1, 0, 1} and vCxy,i is the floating
capacitor voltage of the ith power-cell within the cluster xy.

Additionally, the sum of all the voltages within a cluster is referred to as the cluster capacitor
voltage (CCV) as follows:

vCxy =
n

∑
i=1

vCxy,i (5)

Using the CCV definition, is possible to define the CCVs matrix:

VCxy =

 vCar vCbr vCcr
vCas vCbs vCcs
vCat vCbt vCct

 (6)

The CCVs represent the total capacitor voltages available in clusters, and they are dependent on
the instantaneous active power of their clusters. This instantaneous active power can be expressed as a
function of the cluster currents and voltages. Thus, the cluster power matrix is determined as:

Pxy = (Vmx − Vgy) ◦
1
3
(Imx + Igy) (7)

The symbol “◦” represents the Hadamard product (element by element product). Then, the CCVs
can be related to the cluster power components as follows:

d
dt

VCxy ≈
Pxy

Cv∗C
(8)

Note that in Equation (8), the power losses and the voltage drops in the inductances are neglected
(see [38]). It is also assumed that neither common-mode voltage nor circulating currents are utilised.
In addition, v∗C is defined as the desired average capacitor voltage in each power-cell and C is the
capacitance of each power-cell capacitor.

By substituting Equation (7) into Equation (8) and after some manipulations it could be shown
that low-frequency instantaneous capacitor voltage oscillation of large magnitudes could be obtained
in some operating points [32]. To illustrate this fact, the nine CCVs of an M3C are plotted as a function
of the output port frequency, representing the typical operation obtained when a electrical machine
with an almost linear back electromotive force versus rotational speed characteristic is fed by the
M3C (see Figure 3). Notice that the CCVs are normalised by nv∗C to obtain a per-unit representation.
The input-port frequency ( fm) is varied from −60 Hz to 60 Hz, whereas the output-port frequency ( fg)



Energies 2020, 13, 5546 6 of 37

is set at a fixed value of 50 Hz. Notice that considerable voltage oscillations are produced when fm is
very close or equal to ± fg. In other cases, i.e., when the frequency difference between the input and
output voltage ports is relatively large, the CCV oscillations are not considerably high.

The operation of the M3C is usually divided into the different frequency mode (DFM)
and the equal frequency mode (EFM), as depicted in Figure 3. Both modes can be defined as indicated
in [39,40]:

• The DFM is defined as the zone where the input-port frequency is lower or higher (by a given
threshold) than the output-port frequency. In this mode, the floating capacitor voltage oscillations
are not high (see Figure 3). Then, the control of the M3C needs to regulate just the mean values of
the floating capacitor voltages using mostly circulating currents.

• The EFM is defined as the zone where the absolute value of the input-port frequency is pretty
close or equal to the output-port frequency, i.e., fm ≈ ± fg. In EFM, high oscillations appear in the
floating capacitor voltages, and then mitigation signals (circulating currents and common-mode
voltage) or operation point constraints must be employed to reduce them.

Figure 3. Normalised cluster capacitor voltage (CCV) oscillations.

Control Issues

The control of the floating capacitor voltages is fundamental to provide stability and safety,
especially in the critical operating points depicted in Figure 3 . For the case fm = 0, the CCV
oscillations are somehow reduced when compared to those produced at the other critical operating
frequencies. This feature is because, in a typical drive application, the back-emf of the electrical
machine is low at low rotational speed, reducing, therefore, the power and voltage oscillations
calculated using Equations (7) and (8) (see [39,41]). Nonetheless, due to the integrating effect of the
capacitors, CCV regulation is required over the full frequencies range because even small power
variations can produce significant voltage imbalances [27]. In the cases when fm ≈ ± fg, the CCVs
can be unstable and the use of mitigation control systems is required. As indicated in [42], additional
circulating currents for mitigation purposes and the injection of common-mode voltage are required to
prevent unstable voltages in the M3C, ensuring stable operation of the converter.

Typically, the control of the M3C is performed using nested-control structures to achieve, at least,
the following control targets [8,38,39]:

• The control of the input and output currents.
• The control of the floating capacitor voltages.
• The minimisation of circulating currents and common-mode voltage (CMV).

Nested control systems based on decoupled modelling of the M3C have been proposed in the
literature [26,27,38,39,43,44]. These methodologies enable a decoupled control on input currents Imx,
output currents Igy and circulating currents Iz of the M3C. As each control system is decoupled, it is



Energies 2020, 13, 5546 7 of 37

possible to regulate the floating capacitor voltages without affecting the input and output port systems.
Linear transformations are used to enable the use of the common-mode voltage vn and the circulating
currents Iz to regulate the CCVs. Up to date, the most effective approaches seem to be those based
on a double Clarke transformation, referred to as a double−αβγ transformation [38,44], and a Σ∆
transformation referred to as diagonal [41] or Σ∆ double–αβγ transformation [39].

Most of the control systems reported in the literature (e.g., [26,27,38,39,43,44]) are based on the
three-stage nested control structure shown in Figure 4. The outer control stage regulates the CCVs
and the control of the input and output port variables. Typically, the outputs of the outer control
stage are the references required for the currents located in the inner control loops (e.g., the circulating
currents I∗z ). The second control stage regulates the currents in a decoupled manner. The control
systems depicted in Figure 4 are typically based on standard and well-known vector control methods
(e.g., field- and voltage-oriented control techniques [45–47]), with the circulating currents being
regulated using proportional controllers [38,48]). Finally, the third control stage is used to locally
balance the floating capacitor voltages in the power-cells within the same cluster. In this case, most of
the control strategies discussed in the literature (e.g., [30,49,50]) to perform this task are based on using
additional compensating signals for each cell or sorting algorithms.

Three-Stage 
Control System

Modulation
 

LCB
Control
& PWM

In
ve

rs
e 

T
ra

n
sf

or
m

Current
Control Loop

Input CCS

Circulating
CCS

Output-CCOutput CCS

2

4

2

2

2

4

9

9

Input
Controller

Average
Controller

Output
Controller

CCV
Controller

O
u
te

r 
C
on

tr
ol

 L
oo

p

Decoupling Transform
9

8

Figure 4. Three-stage control system of the M3C.

The main research challenges related to the M3C control are summarised below. Additional details
regarding this topic are addressed in [28].

• One of the most critical control tasks is to maintain the floating capacitor voltages fluctuating
within an acceptable range. The oscillations in the floating capacitor voltages are inversely
proportional to the difference between the input and output port frequencies (i.e., | fm − fg|).
Then, the operation of the M3C for similar or equal input/output port frequencies is challenging to
achieve because the large oscillations produced in the CCVs (see Equation (8)) must be mitigated
using compensation currents and common-mode voltage [39,51].

• The regulation of the internal currents of the M3C, referred to as circulating currents [18], plays a
vital role in achieving effective floating capacitor voltage regulation. Then, the measurement and
estimation of these currents must be performed while dealing with currents with several frequency
components that must be regulated without affecting the input and output port variables [43].

• In high-power applications, a high number of power-cells can be required, and then a very
high number of possible voltage vectors can be obtained (39n where n indicates the number of
power-cells [27]). Therefore, some methodologies which are based on voltage states, for example,
the space vector modulation techniques and/or finite set model predictive control, are very
difficult to implement. Therefore, other modulation techniques and methods to achieve voltage



Energies 2020, 13, 5546 8 of 37

regulation of the power-cell must be considered without increasing the complexity of the overall
control system, ensuring proper voltage balancing and ensuring low power losses [52].

2.2. Hardware Implementations of M3C

As aforementioned, the M3C is considered a suitable power converter topology for high-power,
variable-speed motor drives (including wind energy generators). Furthermore, the M3C has
been suggested as an alternative to the traditional line-commutated cycloconverters and it is
forecasted that in the future this thyristor based topology could be replaced by the M3C [26].
Nevertheless (as discussed above), until now there are no commercial solutions based on the M3C
available on the market. Some of the reasons are the high component count, cost and control complexity
required in this power converter. Therefore, more research is required in order to eliminate some of
these drawbacks [26].

The control complexity and the high component count have also hindered the implementation of
fully operational M3C prototypes. Consequently, few research groups have reported experimental
verification of M3C applications. According to [8], until 2016, just four research groups had managed
to build operational M3C prototypes. From that date until now, the research related to the M3C
has been very active. A high number of new research proposals, validated through simulations
and experimental work, focusing on the M3C, allows one to foresee an expansion of the current
knowledge about this topology [43,53–56]. Further experimental work has also been produced
in the last few years. Currently, approximately 18 journal papers reported experimental work,
as listed in Table 1. These papers have been published by research groups from the University of
Tokio [8,38,42,57,58], Tsinghua University [29,33,48] and the University of Santiago of Chile−University
of Chile [27,39,40,59]. Furthermore, research groups from the Karlsruhe Institute of
Technology [41,51,60] and the Leibniz Universitat Hannover [61] have published conference papers
discussing decoupled control strategies for the M3C. These strategies have been validated through
simulations and at least partially by experimental results.

Typically the experimental prototypes of M3C utilised in the publications presented in Table 1,
are each composed of a control platform and a power stage. As a representative example, the circuit
diagram of the experimental system employed in [27] is presented in Figure 5. In this case, a 27
power-cell prototype was utilised to perform research in the control system required for high-power
wind turbine applications. The M3C was composed of nine clusters considering three full-bridge
power-cells. The system was controlled using a digital signal processor (DSP) from Texas Instruments
(Texas, USA), and three Actel ProAsic3 field programmable gate array (FPGA) (Aliso Viejo, USA)
boards which were used for the Pulse Width Modulation (PWM), analogue-digital conversion
and overcurrent-overvoltage protection tasks. The control platform was equipped with 50 14-bit
analogue-digital channels and 54 optical fibre-based PWM channels. Additionally, two programmable
Ametek (Berwyn, USA) AC power sources were utilised to emulate the electrical grid and the
wind turbine.



Energies 2020, 13, 5546 9 of 37

Table 1. Papers where experimental results are reported and discussed. Adapted from [28].

Ref. Paper Title Year Experimental
Validation Ref. Paper Title Year Experimental

Validation

[62]
Control of a Modular
Multilevel Matrix Converter for
High Power Applications

2012
1 cell
per cluster
Subconverter

[57]

AC-Inductors Design
for a Modular Multilevel
TSBC Converter and
Performance of a Low-Speed
High-Torque Motor Drive
Using the Converter

2017
4 cells
per cluster
15 kVA

[38]

Control and Experiment of a
Modular Multilevel Cascade
Converter Based on Triple-Star
Bridge Cells

2014
4 cells
per cluster
15 kVA

[29]

A Branch Current Reallocation
Based Energy Balancing
Strategy for the Modular
Multilevel Matrix Converter
Operating Around Equal
Frequency

2018
1 cell
per cluster
low power

[63]

Independent Control of
Input Current, Output Voltage,
and Capacitor Voltage Balancing
for a Modular Matrix Converter

2015
3 cells
per cluster
3 kVA

[33]

An Optimal Full Frequency
Control Strategy for the
Modular Multilevel Matrix
Converter
Based on Predictive Control

2018
3 cells
per cluster
2.2 kVA

[30]

A Low-Speed, High-Torque
Motor Drive Using a Modular
Multilevel Cascade Converter
Based on Triple-Star Bridge
Cells (MMCC-TSBC)

2015
4 cells
per cluster
15 kVA

[48]

Optimized Branch Current
Control of Modular
Multilevel Matrix
Converters under
Branch Fault Conditions

2018
3 cells
per cluster
≈ 8 kVA

[64]

Analysis and Control of
M3C-Based UPQC for Power
Quality Improvement in
Medium/High-Voltage
Power Grid

2016
3 cells
per cluster
8 kVA

[65]
Modulation Strategy
of a 3 × 5 Modular
Multilevel Matrix Converter

2018
3 cells
per cluster

[42]

A Broad Range of Speed
Control of a Permanent
Magnet Synchronous Motor
Driven by a Modular
Multilevel TSBC Converter

2017
4 cells
per cluster
15 kVA

[39]

Vector Control of a Modular
Multilevel Matrix Converter
Operating Over the Full
Output-Frequency Range

2019
3 cells
per cluster
5 kVA

[58]

Experimental Verification
of an Electrical Drive Fed
by a Modular Multilevel
TSBC Converter When the
Motor Frequency Gets
Closer or Equal to the
Supply Frequency

2017
4 cells
per cluster
15 kVA

[53]
Distributed Control
for the Modular
Multilevel Matrix Converter

2019
3 cells
per cluster
3.6 kVA

[27]

Control of Wind Energy
Conversion Systems Based
on the Modular Multilevel
Matrix Converter

2017
3 cells
per cluster
4 kVA

[40]

Vector control strategies
to enable equal frequency
operation of the modular
multilevel matrix converter

2019
3 cells
per cluster
≈ 5 kVA

[8]

Experimental Comparisons
Between Modular
Multilevel DSCC Inverters
and TSBC Converters for
Medium-Voltage Motor
Drives

2017
4 cells
per cluster
15 kVA

[59]

Control of a Modular
Multilevel Matrix Converter
for Unified Power
Flow Controller Applications

2020
3 cells
per cluster
5 kVA

Usually the M3C implementations reported in the literature are similar to the system shown in
Figure 5. The control platforms consider the use of DSP and FPGA boards for control processing,
computer communications, analogue–digital conversion and hardware protections. The power stage
comprises the connections of full-bridge power-cells, cluster inductors and the input and output port
related hardware. Currently, the research group from the University of Tokyo has developed the most
complex M3C experimental prototype [38] reported in the literature. In this case, the prototype has
36 power-cells (four power-cells per cluster), and the control platform handles around 50 analogue
measurements and 144 gate signals.



Energies 2020, 13, 5546 10 of 37

Figure 5. Diagram of an M3C experimental prototype. Adapted from [27].

2.3. M3C Design and Dimensioning

Guidelines for the design of MMCCs have been investigated for the M2C, focusing on HVDC
and motor-drive applications [9,66–68]. Nevertheless, the dimensioning of the M3C has only been
discussed in a few papers [57,69]. Therefore, some guidelines regarding the voltage rating, number
of power-cells, cluster inductor selection and the required size of the capacitors in the power-cells
are discussed in this section. To this end, steady-state operating conditions are assumed, and thus,
the following expressions are used to define each input (subscript m) and output port’s (subscript g)
current and voltage:

vmx = Vm cos(ωmt + θx) (9)

imx = Im cos(ωmt + θx + φm) (10)

vgy = Vg cos(ωgt + δ + θy) (11)

igy = Ig cos(ωgt + δ + θy + φg) (12)

where Vm and Vg are the phase-to-neutral voltage amplitudes, and Im and Ig are the current magnitudes.
The angular frequencies are assumed as ωm = 2π fm and ωg = 2π fg. The angles φm and φg are

the phase angles, which in turn are related to the reactive power injected/consumed at the output
ports. The angle δ is the initial phase of the input port with respect to the output port at t = 0.
Besides, the angle θx, with x ∈ {a, b, c}, stands for the phase angle related to the three-phase input
systems, i.e., θa = 0, θb = −2π/3 and θc = 2π/3. The phase angles θy with y ∈ {r, s, t} can be
defined accordingly.



Energies 2020, 13, 5546 11 of 37

2.3.1. Voltage and Current Rating

As the M3C performs direct connection of two AC ports, each cluster must be able to block,
at least, the sum of the peak input and output voltages. Therefore, the CCV of a generic xy cluster
must satisfy the following restriction:

vCxy ≥ Vm + Vg + Vn = VC,min (13)

where VC,min is the minimum voltage required in the CCVs and Vn is the amplitude of the CMV.
On the other hand, the cluster current of a generic cluster xy, namely, ixy, is defined as follows:

ixy =
1
3
(imx + imy) + iz,xy (14)

The circulating current component iz,xy in the cluster current depends on the operating point of
the M3C, the control strategy used to regulate the CCVs and the maximum allowed floating capacitor
voltage oscillations, among other variables. The amplitude of the circulating current is designed as a
fraction of the cluster current without injecting circulating currents, leading to:

Iz,max = η
1
3
(Im + Ig) (15)

where η is a factor usually between 0 and 1. Therefore, the maximum cluster current must be designed
to accommodate the input and output current components plus the circulating current as follows [58]:

Ixy,max =
1
3
(Im + Ig)(1 + η) (16)

2.3.2. Number of Power-Cells

In the M3C, each cluster must be able to synthesise the same voltage; i.e., a generic cluster xy
must have a voltage level of at least VC,min, as shown in Equation (13) [7]. The number of power-cells
can be calculated based on the the blocking voltage of the semiconductors Vigbt utilised in the M3C.
Thus, the number of power-cells is determined as follows:

n =
VC,min

Vigbt
(17)

Then, the floating capacitor voltage of each power-cell can be established as:

v∗C =
VC,min

n
(18)

Additionally, some publications suggest to provide some level of redundancy in the
converter [70]. One alternative is to design the power-cell to withstand a voltage higher than the
nominal value. This methodology design allows getting a voltage margin which could be used in the
event of a fault. For instance, for a redundancy of one, i.e., to enable a cluster to operate normally in
the event of a faulty power-cell, the required nominal voltage in the capacitor voltage is:

v∗C =
VC,min

n− 1
(19)

2.3.3. Power-Cell Capacitor

The correct design of the power-cell capacitor is essential for a good performance of an M3C [20,69].
The capacitance has to be designed to buffer the peak energy variations, keeping the voltage oscillations



Energies 2020, 13, 5546 12 of 37

bounded inside a suitable range. The energy stored in every cluster of the M3C is determined
as follows:

wxy =
1
2

C
n

∑
i=1

v2
Cxy,i (20)

Then, by assuming that all the capacitor voltages have the same average voltage v∗C, the energy
variations of every cluster can be rewritten in terms of the voltage deviations of the CCVs ∆vCxy as:

∆wxy =
n

∑
i=1

∂wxy

∂vCxy,i
∆vCxy,i = Cv∗C

n

∑
i=1

∆vCxy,i = Cv∗C∆vCxy (21)

Moreover, by taking into account Equation (8), the dynamic model for the energy variations in
terms of the AC components of the instantaneous cluster power ∆Pxy can be established as:

d
dt

∆wxy = ∆Pxy, (22)

It is worth mentioning that, in the absence of CMV and circulating currents, the energy variations
in Equation (22) depend on the operating conditions of the external systems which define the AC
components of the cluster power ∆Pxy. From Equation (7), it is shown that these oscillating power
components are given at the frequencies 2ωm, 2ωg and ωm ± ωg. Consequently, for the design, the total
energy variation should be calculated considering the worst-case scenario. From this perspective,
and following the methodology presented in [69], the maximum energy variation in a single cluster
can be determined as:

∆Wxy,max =
Pg

9ωm

 1
cos φm

+ 1∣∣∣∣ ωg
ωm

cos φg

∣∣∣∣ +
( Vm

Vg|cos φg| +
Vg

Vm |cos φm |

) 2∣∣∣∣1− ωg
ωm

∣∣∣∣ +
2∣∣∣∣1+ ωg
ωm

∣∣∣∣
 (23)

where Pg = 3
2 Vg Ig cos φg is the M3C output power. .

At this stage, the capacitance of the power-cells can be easily calculated using Equations (21) and
(23) when a maximum admissible voltage ripple ∆VC,max is defined for the floating capacitor voltages.
Therefore, the minimum power-cell capacitance is given by:

Cmin =
1

nv∗C

∆Wxy,max

∆VC,max
(24)

2.3.4. Cluster Inductor

The design of cluster inductors is done by imposing a maximum value for the ripple of the
cluster current [7]. This limit ∆Ixy,max is usually set to a 10–15% of the nominal cluster current [57].
Then, the cluster inductor can be calculated as indicated in [7]:

Lc =
v∗C + 0.5 ∆VC,max

fsw ∆Ixy,max
(25)

where fsw is the output switching frequency. Note that fsw is related to the modulation method utilised
to generate the pulse signals in the M3C. For instance, if the Phase Shifted PWM (PS-PWM) method is
employed, the output switching frequency is given by fsw = 2n fc, where fc is the frequency of the
carrier signals.

It is worth mentioning that Equation (25) can be used to select the value Lc of the cluster inductor
when single-phase inductors are used. Nevertheless, cluster inductors can have different configurations.
The most straightforward approach is to implement nine single-phase, independent inductors. The use
of three-phase, three-core coupled inductors or three-phase, single-core coupled inductors has been



Energies 2020, 13, 5546 13 of 37

proposed to reduce the size and weight [7,17]. The designs and implementations of these configurations
for the cluster inductors are discussed in [57].

3. Comparison to Others MMCCs

The M3C had been compared to other MMCC topologies, such as the modular multilevel
converter (M2C) in back-to-back configuration, and the Hexverter—the most developed alternatives
for AC-to-AC applications [19–21].

The M2C topology is presented in Figure 6a. This converter is composed of six clusters
performing AC-to-DC conversion. Each cluster is built considering the cascaded connection of n
half-bridge power-cells and an inductor. If AC-to-AC conversion is required, a back-to-back topology
with two M2Cs can be used [71]. The M2C is already a well established methodology for HVDC
applications [36] and other applications, such as STATCOMs [4], WECSs [5,6], motor drives [14,15,72]
and electric vehicles in the automotive industry [73,74] have been proposed in the literature.

(1)

(2)

(1)

(+)

(-)

r
s
t

r s

t

a
b

c

DC 

Port

AC 

Port

AC Output 

Port

AC Input 

Port

(2)

(a) (b)

Figure 6. MMCC topologies. (a) M2C. (b) Hexverter.

The Hexverter topology is shown in Figure 6b. This converter is composed of six clusters,
connected in a hexagonal ring to interconnect two AC ports. Each cluster is composed of a stack of
full-bridge power-cells connected in cascade with an inductor.

From the analysis and discussion presented in [19–21], a comparison among the M2C,
Hexverter and M3C is summarised in Table 2. It is important to mention that a M2C in back-to-back
configuration is considered, which means that in fact there are two M2Cs interconnected by
their DC-ports.

To support this comparison, the following parameters are considered for the three converters:

• Nominal power: 10 MVA.
• Input-port voltage: 6 kV and 20 Hz.
• Ouput-port voltage: 6.6 kV and 50 Hz.
• The power-cells operates at 1.7 kV with a 7 mF capacitance.

The performance indicators are the number of power-cells, the normalised power rating of the
semiconductors, the unit capacitance constant (UCC), the operation in DFM (which is defined as
operation when the output port of the MMCC is connected to different frequencies AC systems,
for instance, during the starting-up of an electrical motor), the operation in EFM (i.e., when the output
port of the MMCC is connected to an AC system operating with a similar frequency to that of the input
port) and the number of circulating currents that can be used to regulate each converter. Notice that



Energies 2020, 13, 5546 14 of 37

the goodness factor utilised to measure the suitability of each topology in DFM/EFM operation is
shown as the labels ranging from - as not advisable up to +++ as very appropriate.

Table 2. Preliminary comparison of AC-to-AC MMCs. Source [19,20].

Converter Number of Power-Cells Ssw UCC DFM EFM Circulating Currents

Hexverter 42 FB 37 43.2 ms ++ - 1
Back-to-Back M2C 84 HB 24 86.5 ms + +++ 4

M3C 63 FB 32 64.8 ms +++ ++ 4

The normalised power rating of the semiconductors is defined in Equation (26) [20]. This index is
used to compare semiconductor requirements in different topologies.

Ssw=
Ssm

Sconv
=

nxy · nsm · V̂xy · Îxy

Sconv
(26)

where the number of clusters is denoted by nxy; the number of semiconductors per power-cell is nsm;
V̂xy and Îxy are the peak values of the cluster voltage and cluster current, respectively; and Sconv is the
nominal power of the converter.

The definition of the UCC index is presented in Equation (27). The UCC is a simile of the inertia
J used in electrical machines, and it is defined for MMCCs as the total energy stored in the floating
capacitors divided by the power rating [75]. The UCC is regularly used as a dimensioning parameter
to compare MMCCs [18,76].

Assuming that all the power-cells have the same capacitance C, and all floating capacitors are
charged at the same voltage level, vC, the UCC can be calculated as follows:

UCC=
1
2

C
nxy · n · v2

C
Sconv

(27)

where the number of cells is denoted by n.
As shown in Table 2, the back-to-back M2C has the lowest semiconductor current rating among the

topologies compared in this work, but the highest number of power-cells and UCC index. In general,
the back-to-back M2C is considered the most suitable solution for EFM operation because in this
operational state no mitigation signals are required to control the voltages in the floating capacitors.
Consequently, the back-to-back M2C has been extensively used in HVDC transmission systems,
where is somehow an established technology [9,35–37]. On the other hand, the operation of the M2C
in DFM involves the injection of mitigation signals to keep the regulation in the floating capacitor
voltages, resulting in decreased efficiency and an increase of the control complexity for this operating
range [14,15,77].

In DFM operation, the Hexverter and the M3C are better suited than the M2C [8,16]
because smaller voltage oscillations are produced at this operating point when the converter
(i.e., M3C or Hexverter) is feeding an electrical machine with a low back-emf during low-frequency
operation. As shown in Table 2, the Hexverter has the highest semiconductor current rating
because a compensation power (referred to as adjacent power) is required in this converter [16].
Then, higher circulating currents are needed to mitigate the capacitor voltage oscillations compared
to those required in the M3C. Additionally, there are some operational points where the injection of
common-mode voltage is required to perform balancing control. Nonetheless, the Hexverter presents
the lowest number of power-cell requirement because it is composed of just six clusters.

For the EFM operating point, it is worth mentioning that the operation in EFM is challenging
for the Hexverter and the M3C. Both converters require the injection of mitigating signals to ensure
appropriate control of the floating capacitors in EFM [39]. However, the M3C is more suitable than the
Hexverter in terms of semiconductor ratings and control flexibility for DFM and EFM operation. During



Energies 2020, 13, 5546 15 of 37

DFM, the M3C does not require the injection of mitigation signals. On the other hand, the Hexverter
requires the injection of a compensation power for balancing and mitigation purposes. Therefore,
continuous injection of common-mode voltage and circulating currents are utilised, reducing the
efficiency and increasing the built-in ratio. The M3C favourably compares to the Hexverter for EFM
operation because it has more degrees of freedom and this provides more control flexibility. As shown
in Table 2, the M3C has four circulating currents which can be manipulated to allow proper EFM
operation [39,78]. If the common-mode voltage is considered the M3C has a total of up to five degrees
of freedom for control purposes which can be used in different operating points.

It is relevant to mention that the comparison presented above strongly depends on the applications
being studied, efficiency required, total harmonic distortion allowed in the input/output voltage and
current, etc. Different scenarios can lead to different results in the comparison.

M3C, M2C and Hexverter Advantages and Disadvantages

In this section, some additional comparisons are realised and summarised for the three converters
discussed in the previous section. As shown in Table 2, the Hexverter is a suitable converter for
applications where the power to volume density is critical, mainly because it operates with fewer
power-cells in comparison with the M3C and the M2C. Nonetheless, as aforementioned, the reduced
number of cells decreases the available degrees of freedom in the converter, reducing the control
flexibility of the topology [16,20]. Regarding applications, this converter has been proposed for WECSs
and low-frequency AC transmission. However, the Hexverter is not recommended for off-shore
WECSs or any critical application due to its limited fault-tolerance.

Nowadays, the most established MMCC topology is the M2C, also referred to as the Marquardt
converter [2]. This converter is considered a well-established technology with commercial solutions
in the market for HVDC transmission and motor-drive applications. The power-cells in the M2C
are usually half-bridges. Then a reduced number of semiconductors is required in comparison with
full-bridge power-cell-based topologies such as the Hexverter and M3C. Nevertheless, the application
of the M3C in motor drives is challenging since high voltage fluctuations appear in the floating
capacitor voltages [14,15] during DFM operation.

Finally, Table 3 summarises the main characteristics of the M3C. This converter has the advantages
of high controllability with several degrees of freedom and fault-tolerance when compared with the
M3C and Hexverter [27]. For instance, it has been demonstrated that when a cluster of the M3C faults,
the converter can still operate as a Hexverter, reducing its power conversion ratio [29]. In this manner,
the M3C is a suitable topology for off-shore WECSs, where the maintenance and fault tolerance play
important roles. The application of the M3C for drive applications and low-frequency AC (LFAC)
transmission systems has also been validated [8,79]. However, the drawbacks of this topology are
its high component count, and the difficulties in EFM operation due to the high capacitor voltage
fluctuations produced at this operating point.



Energies 2020, 13, 5546 16 of 37

Table 3. Advantages and disadvantages of the MMCC topologies compared in this work.

Converter Advantages Disadvantages Proposed Applications

Hexverter – Low component count – Low control flexibility – WECSs
– High oscillations in EFM – LFAC transmission

M2C
– Excellent behaviour in EFM – High CCV oscillations in

low-frequency applications – Widely used in HVDC

– Well established technology – High component count in
back-to-back configuration

– Motor drives with low
starting torque

– Low semiconductor count

M3C
– High control flexibility – High component count – WECSs

– Fault-tolerance – High oscillations EFM – Motor drives with high
starting torque

– Excellent behaviour in DFM – LFAC transmission

4. Applications

The M3C have been indicated as an appropriate alternative for high-power AC-to-AC applications
such as wind energy conversion systems, variable-speed drives, FACTS applications and low-frequency
AC transmission. The M3C is a good alternative for WECSs and drive applications, because of its
appropriate performance in low-frequency operation. Moreover the M3C has all the advantages of
modular multilever converters, including modularity, scability, fault redundancy, etc. In consequence,
there are many areas such as FACTs and LFAC transmission where the M3C is considered a suitable
candidate. This is discussed in the next subsections where simulations and experimental results are
provided to validate the applications.

4.1. Wind Energy Conversion Systems

Wind energy has grown at a faster rate than all the other renewable energy sources in recent times.
The wind power production capacity for the whole world increased from 17.4 GW in 2000 to about
600 GW at the end of 2018. In 2018 though, 50.1 GW of wind power capacity was installed in the world
(60 GW in 2017) [80].

A significant part of the wind power capacity is installed offshore, due to the presence of
higher wind energy, the lower environmental impact, the lack of suitable onshore sites available,
etc. For offshore applications, high-power wind turbines can reduce the cost structure of offshore
WECSs [81]. Accordingly, the power rate and rotor diameters of a single WECS have increased to
12 MW and 220 m in 2020. For instance, the Haliade-X, a 12 MW WECS produced by GE (Boston, MA,
USA), has a rotor diameter of 220 m [82].

Most of the existent wind turbines are composed of low-voltage power converters,
usually implemented using back-to-back voltage source inverters based on 1700 V insulated gate
bipolar transistors (IGBTs), which are connected to 690 V low-voltage bars. Therefore, for multi-MW
wind turbines, high currents are produced at the WECSs’ outputs. To overcome this problem,
medium-voltage converters have been proposed for this task [19,22,23,27,83–85].

The M3C has also been proposed for wind energy applications since the early work of Erickson
(see [22,23]) but also in more recent papers [19,54,86–92]. In these works, the M3C is proposed for
the interconnection of the electrical generator, of a large-power WECS, to the grid. This is shown in
Figure 7.

The M3C is considered a good alternative with which to control high-power, variable-speed
generators and motors. As aforementioned, some of the main advantages are simple scalability
in the voltage range; good fault-ride-through performance [27,88]; simplicity to provide converter
fault-redundancy; and good performance when the machine is operating at nominal torque and low
rotational speed [8,21]. As discussed before, in the latter case, the frequency applied to the stator of the
electrical machine is relatively low, but also the machine back-emf is usually small. Hence, (unlike the



Energies 2020, 13, 5546 17 of 37

M2C) the voltage fluctuations in the capacitors, at this operating point, are relatively simple to control,
even without the utilisation of mitigation currents [27].

Figure 7. Implementation of a wind energy conversion system based on a Permanent Magnet
Synchronous Generator (PMSG) and an M3C. Adapted from [27,39].

The operation at high-power with similar or equal frequencies at the input and output ports of
the M3C is challenging. Some overrating of the converter (to accommodate for the required circulating
currents and common-mode voltages) could be necessary to achieve good stable performance (see [39]).
Otherwise, a M3C-based WECS would likely have to be designed to achieve nominal power output
when the machine operating frequency is ≈10% below the grid-frequency. However, as discussed
in [93], for high-power, direct-drive Permanent Magnet Synchronous Generator (PMSG) based WECS,
nominal output frequencies of around 15 Hz could be obtained in the machine side of the topology
depicted in Figure 7. Therefore, in this case the frequencies | fm ± fg| (with fg as the grid frequency
and fm as the machine frequency) have relatively large values for the whole operating range, and the
voltage oscillations produced are relatively simple to control if appropriate voltage and current
capability margins are available at the M3C.

The application of an MMCC, similar to the M3C, has also been reported for the control of
multi-channel generators in [90] (see Figure 8). Multi-channels generators have been proposed in [94]
to improve fault redundancy. Therefore, if a fault is produced in one of the phases, e.g., because of a
short circuit in the winding or a single power converter failure, then the healthy phases can be used to
supply power to the grid. In this case, the generator is derated by a factor of (n− 1)/n, where n is
the number of windings. Alternatively, the generator could be designed to maintain nominal power
operation even in the event of one phase failure.



Energies 2020, 13, 5546 18 of 37

Figure 8. MMCC topology proposed in [90] for grid-integration of multi-channel generators. (a) WECS
application. (b) Topology details.

The topology depicted in Figure 8b has also been proposed to interlink two single-phase AC
systems directly. In [95], the single-phase M3C illustrated in Figure 8b was utilised as a power
conditioner which is particularly appropriate for Scott traction systems. Besides, as shown in
Figure 8a, three identical single-phase M3Cs were proposed in [90] to interconnect a three-phase
open-winding PMSG with six lead terminals to a step-up line-frequency transformer for grid
connection. The terminals of the resulting MMCC topology are connected in a star connection, as shown
in Figure 8a, producing the primary winding voltages required to feed the power transformer.

The M3C could also be used for DFIG-based WECs. This is shown in Figure 9 and further discussed
in [86,91]. It is claimed that the M3C improves the low voltage ride-through (LVRT) performance
owing to the capability of the M3C to impose a larger voltage in the DFIG rotor, maintaining current
control and avoiding the utilisation of crowbars to demagnetise the machine. In the case crowbars are
still required, it is claimed in [91] that a smaller reduced-power device would be necessary.

Only simulation results for a three-phase symmetric fault are presented in [91]. The performance
of the proposed topology for asymmetric faults has neither been discussed nor analysed.

Figure 9. Topology based on an M3C to improve the performance of doubly-fed induction generators
during low-voltage ride-through conditions (see [86,91]).



Energies 2020, 13, 5546 19 of 37

4.2. Low-Voltage Ride-Through Control Considering Permanent Magnet Machines

To avoid stability issues in power systems with extensive penetration of wind energy systems,
the transmission system operators are enforcing stringent grid-codes to prevent the disconnection of
large WECSs during low-voltage faults in the grid. A summary of grid-codes for several countries
is reported in [96,97], and some grid-code requirements are illustrated in Figure 10. Notice that the
allowed depth and duration of the voltage fault, before disconnection of the WECS, might vary from
country to country. As stated in [96], the time-length where WECSs have to remain connected in
case of a fault might last from milliseconds up to minutes. When the voltage at the point of common
connection is operating above the line of the respective country’s grid-code, the WECS must maintain
connected. Otherwise, it can be disconnected.

Figure 10. Grid-codes utilised by several countries. If the system is operating above the respective
grid-code line, the M3C-based WECS must remain connected. Adapted from [96].

The control systems required for grid-code compliance of a M3C-based WECS utilising
a PMSG have been partially investigated in [27,87–89,98]. Experimental results for LVRT
performance are presented in [27]. In this work an experimental system composed of 27
full-bridge power-cells is used to validate the proposed LVRT algorithm which is designed
to avoid second order (100 Hz) power oscillations in the floating capacitors of the converters.
The performance of the proposed LVRT algorithm was tested for several conditions, including zero
voltage ride-through (ZVRT) (see [96] and Figure 10). Some of the experimental results obtained
in [27] are briefly discussed below.

The experimental system used in [27] is shown in Figure 11 and it considers a 27 power-cell M3C
prototype. Note that the diagram of this setup is presented in Figure 5. The grid and the machine
were emulated using programmable power supplies, which were used to analyse the performance of
the M3C for LVRT control. Using the grid-side programmable power supply, a symmetrical dip type
A fault (a three-phase short circuit) was emulated. The experimental results are shown in Figure 12.
For this test, the three grid voltages were reduced to 30% of their voltage magnitudes at t ≈ 0.2 s.
Notice that Figure 12a,b utilises a different time scale when compared to Figure 12c–e. Immediately
after the fault was applied, the active power current (grid-side of the M3C) was regulated at 0 A,
and the reactive power current was regulated to 50% of the nominal current to provide support for the
grid-voltage recovery (see Figure 12e). Notice that during the fault, the capacitor voltages are well
regulated in the prototype with a ripple component below 5% of the reference value.



Energies 2020, 13, 5546 20 of 37

Figure 11. Experimental system utilised to test the performance of a WEC-based prototype for LVRT
control. Adapted from [27,87,88].

The performance of the proposed LVRT control has also been experimentally tested considering
a dip type C fault (a short circuit between two phases), and the experimental results are shown in
Figure 13. In this case, the voltage magnitudes in phases b and c decreased to 50% of their nominal
values (see Figure 13a). For this test, the current control system regulated the grid current supplied by
the M3C to produce an active power without double frequency oscillations (see [99,100]), as depicted
in Figure 13d. However, double frequency oscillation could not be eliminated from the reactive power,
as shown in Figure 13d. Finally, the instantaneous active power oscillation in the M3C can have double
frequency oscillations, and this can produce more oscillations in the 27 floating capacitor voltages,
as shown in Figure 13c.

Figure 12. Experimental results obtained for a balanced grid fault. (a) Output port currents. (b) Input
port currents. (c) Voltages in the 27 capacitors. (d) Grid voltages. (e) Active and reactive powers.
Adapted from [27].



Energies 2020, 13, 5546 21 of 37

Figure 13. Experimental results obtained for a unbalanced grid fault. (a) Output port voltages.
(b) Output port currents. (c) Voltages in the 27 power-cell capacitors. (d) Active and reactive powers
supplied to the grid. (e) Oscillation at the M3C terminals. Adapted from [27].

4.3. Variable-Speed Drives

The market for medium-voltage motor drives has been expanding rapidly with new improved
solutions being provided to the market [101]. A good discussion of the power converters typically
used in this voltage range is provided in [26,102].

Nowadays, the three-level neutral point clamped (NPC) converter is the multilevel topology
most employed for medium-voltage applications [103]. The NPC converter was introduced in
1979 [26]), and it has been used in several applications, including the Japanese high-speed train
“Shinkasen”. Another topology with commercial applications is the multilevel converter based on
flying capacitors [104]. Alstom Power and Grid offer this converter as a 4-level flying capacitor inverter
for medium voltage drive solutions. A significant advance in the development of modular multilevel
converters for medium voltage drives was the development of the cascaded H-bridge (CHB) drive
produced by Robicon Corporation, now part of Siemens (Munich, Germany). This converter is based
on the cascade connection of full-bridges (see [105]), each of which are controlled using PWM. The main
disadvantage of the Robicon converter is that a bulky multi winding transformer is required. However,
this converter has modularity; i.e., “H” bridges can be added to the topology to increase the output
voltage level and power, and can be efficiently designed to provide fault redundancy. This converter is
considered a precursor of the modern modular multilevel topologies utilised in medium voltage drives.

In 2003, Marquardt introduced a new converter topology named the modular multilevel
converter [1,2] or the Marquartd converter. Even though the main applications of this topology
are related to HVDC transmission [26], since 2016 the M2C topology has been offered by Benshaw [12]
and Siemens [13] as a commercial solution for medium-voltage drives. Other modular multilevel
topologies proposed for medium voltage drives are the M3C and the Hexverter.

The comparison between the Hexverter, the back-to-back M2C and the M3C previously presented
in Table 1 is further expanded in this section to include more aspects related to the control of electrical
drives. Other topologies, as the series-parallel MMCC, also referred to as π-MMC, (see [106]) have



Energies 2020, 13, 5546 22 of 37

not been included in this comparison because they have not been investigated for drive applications.
Therefore, in Table 4, some topologies are compared in terms of control flexibility and degrees of
freedom available for control purposes. Additionally, the topologies of the power-cells are considered
to distinguish two types of M2C. In motor-drive applications, the M2C can be implemented using
half-bridge cells, or it can be composed of a mixture of half-bridge and full-bridge power-cells, the latter
topology being referred as a hybrid M2C [107,108].

Table 4. Modular multilevel topologies for drive applications. N.A = not applicable.

Attribute M3C M2C Hexverter BTB M2C Hybrid M2C

Circulating Currents 4 2 1 4 (2 each side) 4 (2 each side)
Common Mode Voltage Yes Yes Yes Yes Yes

DC-link Voltage Variation N.A. Usually No N.A. No Yes
Degrees of Freedom 5 3 2 6 (3 each side) 7

Reported Applications Drives, WECSs Drives, HVDC Steel mills [26] HVDC, Drives HVDC, Drives

As discussed previously in this work, the M3C is more suitable for low-frequency, high-torque
operation of drives when compared to the M2C. As discussed in [14,15], during DFM operation, high
voltages oscillations are produced in the M2C which are proportional to the magnitude of the machine
stator currents. Therefore, the M2C converter is considered more suitable for rotational loads where
the required electrical torque is quadratic with respect to the rotational speed [8,21,26]. For control
purposes, the M3C has five variables which can be utilised as degrees of freedom to balance the energy
in the converter and mitigate large voltage oscillations in the capacitors. These are four circulating
currents and the common-mode voltage, and depending on the drive design and/or operating point
of the drive, the common-mode voltage may be not required to operate the converter.

As the M3C is an AC-to-AC topology, a fairer comparison is realised when this power
converter is compared to the back-to-to back M2C and the hybrid back-to-back M2C. As mentioned,
the back-to-to back M2C has been extensively studied. On the other hand, the later topology has been
recently reported and discussed in [107,108]. One of the main benefits of the back-to-back hybrid
M2C is the capacity to reduce the DC-link voltage, which has some advantages for the low-speed
operation of variable-speed drives (see [108]). The hybrid back-to-back M2C has more degrees of
freedom in total (four circulating currents, common-mode voltage(s) and variable DC-link voltage).
Nevertheless, the circulating currents are controlled separately in the M2C; i.e., two circulating
currents are utilised on the machine-side and two circulating currents for the grid-side converter.
Moreover, one of the well-known problems of the hybrid M2C is the large circulating current required
in the grid-side M2C when the DC-link voltage is very low (see [107–109]). The comparison between
the regular back-to-back M2C and the M3C for variable-speed drives has been realised in various
publications (see [19,20]. However, it is important to mention that the performance of the hybrid
back-to-back M2C has not been thoroughly studied yet, and it is difficult to adequately compare
the performance of an M3C to the hybrid back-to-back M2C in terms of the attributes depicted in
Tables 2 and 4.

Analysing Table 2, it is confirmed that the M3C has an excellent performance when operating
a drive at low rotational speed—better than those obtained using the back to back M2C and the
Hexverter [16,20,48]. The main problem of the M3C to control motors and generators is during
operation with equal (or very similar) frequency in the input and output ports. Solutions have been
reported in [39,58,60,77,78]. The most common approach is to operate with a complementary power
factor at the input and output ports (i.e., Qg = −Qm) and synthesise a voltage of the same magnitude at
the input and machine sides (i.e., Vg = Vm) (see [39,78]). Using these conditions, the floating capacitor
oscillations are reduced. However, when this strategy is implemented using an open-loop scheme,
any deviation from the conditions Qg = −Qm and Vg = Vm may produce large capacitor voltage
oscillations and instability. Alternatively, EFM operation can be achieved by using common-mode
voltage and circulating currents. The advantage is that this approach relies on a closed-loop control



Energies 2020, 13, 5546 23 of 37

system to regulate the voltage oscillations in the capacitors. The disadvantages are that it is necessary
to increase the rating of the M3C because of the additional capacitor voltage and cluster currents
required for the common-mode voltage and circulating currents.

Simulation and experimental results for an M3C-based drive are discussed in this section.
The simulation results of a 10 MW M3C based drive have been obtained using PLECS software
(Plexim, Zurich, Switzerland). The main parameters of the M3C and induction machine (IM) are
provided in Table 5. More details are in [31,110].

Table 5. Simulation parameters of the M3C and induction machine. Based on [31].

M3C Parameters IM Parameters

Nominal Power 1 MVA Output power 1250 HP
Cells per branch 7 Line-to-line voltage 4160 V

Input Voltage/Freq. 3.00 kV/50 Hz Stator current 150 A
Cluster Inductor Lc 1.3 mH Rated speed 1189 rpm

Single cell C 4 mF Rated torque 7490 Nm
Capacitor Voltage 0.8 kV

inertia index H 80.64 ms

The speed profile used in these tests is shown in Figure 14a, and it was regulated to start at 0 Hz
and reach 30 Hz. Regardless of the machine frequency, proper balancing of the floating capacitor
voltages was achieved, as shown in Figure 14b. In this case, as presented in Figure 14c, a lineal
torque-speed load was considered. Finally, Figure 14d,e confirms that the total voltages available in
each cluster, referred to as CCVs, are properly regulated.

5.0

5.6

6.2

Time (s)

16.7

16.8

16.9

  
  
  
G

ri
d
 

P
o
w

er
 (

M
W

)

T
o
rq

u
e

(k
N

m
)

 R
o
ta

ti
o
n
al

 

S
p
ee

d
  
(H

z)

(a)

C
C

V
s

(K
V

)

  A
v
er

ag
e 

C
C

V
 (

K
V

)

(b)

(c)

(d)

(e)

1.5 2 2.5 3 3.5 4 4.5 5 5.5

0

20

40

0

2

4

0.8

0.4

0

Figure 14. Results for variable-speed operation at lineal load. (a) Rotational speed ωr. (b) Input port
power Pin. (c) Mechanical torque τm. (d) CCVs. (e) Average CCV. Adapted from [31].



Energies 2020, 13, 5546 24 of 37

The experimental results have been obtained considering the experimental setup depicted in
Figure 11a. Results for open-loop control are shown in Figure 15 using the modelling and control
strategies discussed in [39]. In this approach, the CCVs are transformed to the Σ∆ double–αβγ frame
representing unbalanced voltages. As indicated in [92], the CCVs have to be regulated at 0 V in Σ∆
double–αβγ frame to ensure equal voltage distribution in all the clusters of the M3C. In the first test,
the performance of the control system was tested considering a small frequency difference between the
input and output ports (at the beginning of the test) up to equal frequency operation. First, the input
port frequency was fm= 48 Hz and the output port frequency was set to fg = 50 Hz. Consequently,
voltage fluctuations of 2 Hz appeared in some of the CCVs, as shown in Figure 15b. The remaining
CCVs were well regulated, as shown in Figure 15b,c. In this approach, the power oscillations
are not directly controlled using closed-loop control. Therefore, the system can hardly respond to
changes in the operating points, incorrect estimations of the reactive powers, etc. Consequently, in an
experimental implementation, it is difficult to operate at equal frequencies (open-loop control) even
when it is theoretically possible. This is further demonstrated by the experimental results shown in
Figure 15d, where the performance for a step-change from 48 Hz to 50 Hz is depicted. In this case,
the control system is not able to regulate the capacitor voltage oscillations, and some of the floating
capacitors drift away from the reference value.

140

150

160

C
ap

ac
it

o
r

V
o
lt

ag
es

 (
V

)

(a)

-20

-10

0

10

20

C
C

V

V
ec

to
rs

 (
V

)

(b)

-20

-10

0

10

20

C
C

V

V
ec

to
rs

 (
V

)

(c)

0 0.2 0.4 0.6 0.8 1

Time (s)

120

140

160

180

C
ap

ac
it

o
r

V
o
lt

ag
es

 (
V

)

(d)

Figure 15. Experimental results considering open loop operation. (a) Twenty-seven floating capacitor
voltages. (b) Four CCV components. (c) Four CCV components. (d) Twenty-seven Floating Capacitor
Voltages. Adapted from [39].

In Figure 16, the closed-loop CCV control system proposed in [39] is utilised to regulate the
capacitor voltage oscillations during EFM. For this test the input/output port grid frequencies were set
to 50 Hz with different power factor demands: The output port grid operated with −3.3 kW/0 kVAr,
and the input side with 3.3 kW/2.1 kVar; the reactive power magnitude in the input side was
regulated to achieve nominal current amplitude in the input side. The regulation of the CCVs was
performed by using a combination of circulating currents and common-mode voltage.As illustrated
in Figure 16a, the M3C capacitor voltages are well regulated at v∗c = 150 V even when the input and
output frequencies are equal. Moreover, the CCV imbalances are adequately regulated, as shown



Energies 2020, 13, 5546 25 of 37

in Figure 16b,c. Experimental results from oscilloscope captures are presented in Figure 16d,e.
The floating capacitor voltage of a single power-cell, a generic cluster voltage vxy and phase-to-phase
voltages of the input and output port are displayed in Figure 16e. Finally, the three-phase input
currents are presented in Figure 16f.

(e)

(d)

200ms

20ms

150V

450V

692V

14A

Figure 16. Experimental results considering closed-loop CCV regulation in EFM. (a) Twenty-seven
floating capacitor voltages. (b) Four CCVs in Σ∆ double–αβγ. (c) Remaining CCVs in Σ∆ double–αβγ.
(d) Oscilloscope voltage waveforms. (e) Oscilloscope current waveforms. Adapted from [39].

4.4. FACTS

In the last rew decades and considering the widespread use of electronic non-linear load and
power converters, several power quality problems, such as voltage swells and sags and harmonic
distortion, have expanded in power grids. These problems have enforced the use and evolution
of FACTS devices. The integration of FACT devices is being used to improve power grid dynamic
and static behaviours, providing higher operating flexibility and better use of the power system
infrastructure [111].

Considering their connection to the power system, FACTSs can be classified as shunts,
series and combined devices [112]. Shunt FACTS, such as the STATCOM and the Static Var
Compensator (SVC), are generally used to provide voltage and power factor compensation [113].
Series FACTS, such as the series static synchronous compensator (SSSC), are used to provide impedance
line control and transmission line relief [114]. Finally, combined FACTS such as the Unified Power
Flow Controller (UPFC) are hybrid or combined control FACTS with the capability of bidirectional
power flow control; voltage and reactive power control; and the capability to increase the steady and
dynamic stability of power grids [113,114].

For high-power applications, thyristor-based FACTS are the preferred technology due to their
reliability and the higher capability of the semiconductors. However, even when thyristor-based
FACTS are reliable, they have significant disadvantages, such as low power factor, limited regulation
capability, limited redundancy, high harmonic distortion, restricted operation in cases of faults and
high output ripple. Due to these disadvantages, the development of FACT devices based on MMCCs
has gained attention as a proper and feasible alternative in the industrial market [115–117].

Examples of the use of MMCCs in FACTS applications are reported in [59,64,118]. For instance,
the connection of the M3C to provide UPFC capabilities is illustrated in Figure 17a [59,64,118]. In this
case the M3C is connected to operate as a shunt FACTS at the input-port, and as a series FACTS at the
output port. As both ports have the same frequency, the M3C must be controlled to provide precise
EFM operation.

In [118], a direct power control of an M3C for FACTS applications is proposed. This paper
studies a control system implemented in the Σ∆ double–αβγ coordinates to regulate the floating



Energies 2020, 13, 5546 26 of 37

capacitor voltages, whereas the converter provides functions of a series connected FACTS. Recently,
a control strategy implemented on the Σ∆ double–αβγframe was proposed for a M3C-based UPFC,
considering shunt and series FACTS behaviour, as discussed in [59]. The control of the input port
of the M3C regulates the average voltage, whereas the output port control is focused on power flow
compensation. The proposed vector control scheme was successfully validated through simulation
and experimental results with a 5kVA M3C prototype composed of 27 power-cells. Some of the
experimental results provided in [59] are summarised in Figure 17b,c. The active and reactive powers
of the input and output ports are separately regulated. To corroborate the response of the overall
system, step changes in the active/reactive power components are used. As shown in Figure 17c,
the capacitor voltages remain regulated at 150 V during the step variation in the power demand.
The active/reactive power injection/demand of the input/output port are depicted in Figure 17b.

Due to the control flexibility of the M3C, an extension to the control capabilities of a traditional
UPFC can be obtained. In [64], the M3C is proposed as a unified power quality conditioner (UPQC).
The UPQC has the same functionalities of a UPFC, i.e., shunt and series FACTS compensation,
plus active filter capabilities for harmonic mitigation.

(a) (b)

(c)

Time (s)

  
C

ap
ac

it
o

r 

V
o

lt
ag

es
 (

V
)

  A
ct

iv
e 

- 
R

ea
ct

iv
e 

P
o

w
er

 (
k

W
/K

v
ar

)

4

2

-4

-2

0

160

155

150

145

140

Figure 17. M3C-based UPFC. (a) Topology. (b) Floating capacitor voltage results. (c) Active and
reactive power. Based on [59].

4.5. Low-Frequency AC Transmission Systems

LFAC transmission systems, also referred to as fractional frequency transmission systems,
have been proposed as an alternative to conventional AC and DC transmission systems.
Typically, LFAC transmission is performed using a 1–20 Hz frequency range [119]. LFAC systems
have some advantages compared to 50/60 Hz and HVDC transmission systems. Firstly, because of a
reduced capacitive current component, LFAC systems have an increased use of the power capability
of the transmission cables, in comparison to standard 50 Hz or 60 Hz AC transmission systems,
thereby achieving a longer length of the AC transmission lines [120]. Secondly, the investment cost
of an LFAC transmission system is reduced in comparison to that required for HVDC transmission.
Moreover, the fault protection requirements in LFAC are much more straightforward to implement
than those required in HVDC, due to the zero-crossing nature of the AC current [121].

As for the advantages of MMCC topologies, for the HVDC connection of wind parks, the M2C is
considered the state-of-the-art technology in Europe [121]. Consequently, AC-to-AC MMCCs can be
appropriate solutions for LFAC transmission systems [122]. Several research proposals have discussed
the control of the M3C in this application [79,123–127]. The application of the M3C in the power
system shown in Figure 18 is presented in [79], where an Space Vector Modulation (SVM) control
approach is proposed. As discussed in [27], SVM control is only feasible when a small number of



Energies 2020, 13, 5546 27 of 37

power-cells is considered. Therefore, the results in [79], which are obtained with a 1-power-cell per
cluster M3C, are not an adequate reference for a real case application (with more than two cells per
cluster). A similar approach is presented in [124].

Figure 18. LFAC transmission system for offshore wind farms. Based on [79].

An M3C-based multiterminal LFAC system has been proposed in [127]. The electrical system
diagram is shown in Figure 19, considering the use of three M3Cs to perform 10–60 Hz conversion.
In [127], a novel control scheme based on a virtual synchronous generator (VSG) scheme for the
M3C-based LFAC is proposed. In [123–127], the focus is the control of the M3C from a power system
point of view. Therefore, the converter modelling and control is simplified and just M3C-output power
at input/output ports is contemplated. In those proposals, the M3C regulation considers just the
regulation of the sum of all the floating capacitor voltages. The management of the voltage imbalance in
the floating capacitors is not considered. As simulation results are presented, there are not imbalances
to control and the operation of the M3C for the LFAC systems seems to be appropriate.

Figure 19. Multi-terminal LFAC system. Based on [127].

5. Trends and Future Research for the M3C

During the last few years, more research efforts related to the M3C have produced significant
advances in areas such as modelling, control, modulation schemes, new applications, dimensioning and
other features. Nevertheless, no companies are commercialising medium- or high-voltage converters
based on the M3C, mainly due to the high cost, high number of components, control complexity and
hardware limitations. Numerous aspects should still be addressed to overcome the main disadvantages
of the M3C and to extend its utilisation into commercial applications, for instance, those described in
Section 4.

The technological improvements of semiconductor devices might contribute to upgrading
the cost-effectiveness of the topology, enhancing characteristics such as cost reduction,
efficiency, power density, specific power density and operating voltage-power limits.
Therefore, further research on dimensioning and fabrication of M3C based on high-efficiency,
fast semiconductors is required.

The extensive use of measurements and communication channels required to control an M3C is
still a practical restriction when the number of power-cells is large. When a centralised control platform
is used, just one main controller needs to handle a high amount of input-output, to compute the whole
control algorithm in one short period and to provide the switching signals to all the devices located
in the power-cells. Therefore, an interesting research area is to study the application of distributed



Energies 2020, 13, 5546 28 of 37

control algorithms to divide the computational burden and the required peripherals. Compared to
the centralised control, distributed control algorithms can offer advantages in MMCC applications,
due to the reduced number of peripherals and lesser computational burden assigned to each controller.
This research field is relatively new for MMCCs, and its benefits include the easy scalability when more
cells are integrated and the enhancement reliability of the converter. The three-stage control structure
presented in Figure 4 can be implemented in a multi-DSP-based digital control system architecture,
as proposed in [53]. The proposals for the M2C [128], can be expanded and adapted to the M3C case.

Another interesting topic for future research would be to introduce fault tolerance capability
in the M3C. At the moment, just a few works have studied the continuous operation during this
contingency [34,48]. The impact of the loss of power-cells or even a complete cluster must be analysed
and considered to design the control of the floating capacitor voltages, circulating currents and
modulation schemes. The fault capability includes two main goals: the fault identification and online
reconfiguration of the control references for the specific modified structure. For power-cell faults, the
n− 1 design criteria shown in Equation (19) can be incorporated to provide voltage margin under
power-cell faults. For cluster faults, there are some research works presenting the operation of the
M3C when a full cluster is disconnected. In [34], the failed cluster is bypassed along to other two
clusters, and the M3C is reconfigured as a Hexverter. The output power of the M3C is reduced to
approximately 70% of its nominal rate.

The ride-through capability of the M3C could be further analysed under grid-voltage
perturbations. As indicated in Equation (13), the M3C has an inherent voltage margin as the minimum
CCV is composed by the sum of the input and output voltages (see Equation (13)). When a grid-voltage
dip is produced, the available voltage in the CCVs can be used to enhance the fault-ride-through
performance of the M3C. The LVRT behaviour of the M3C has been highlighted [98]. Still, there are
other grid-voltage perturbations such as symmetrical and unsymmetrical grid-voltage dips,
harmonic contamination and flicker that could be matters for new investigations. The compensation
of harmonic distortion, or more generally, the use of the M3C for improvement of the quality of the
overall power system has not been well investigated.

Regarding applications, more research in the following fields could be required:

• Ongoing work on motor-drive applications
The use of the M3C in medium-voltage and high-voltage motor-drive applications is foreseen
to be expanded. The voltage extensibility of the M3C can be advantageously used to connect
electrical machines directly to medium-voltage grids, and then, bulky step-up transformers can
be avoided.
However, a critical drawback of the M3C in drive applications is to achieve EFM operation
without requiring a large over-rating of the converter to provide circulating currents or to
accommodate relatively large common-mode voltages. Thus, the development of enhanced
mitigation techniques for the regulation of the oscillations in EFM is required. High-performance
control strategies, with high bandwidth, reduced circulating current and reduced common-mode
voltage references must be further developed [28,58].

• Ongoing work on WECS applications
There are still research challenges related to reducing both the volume and weight of the
passive components of high-power WECSs, including transformers, inductors and power-cell
capacitors typically located in the nacelle. Then, the optimisation of the passive components of
the M3C, as preliminarily proposed in [7,17,20,69], could be focused in this aim. For this task,
other parameters have to be considered, such as size, weight and volume restrictions of the M3C.
The possible transformerless operation of the M3C in large wind turbines could be also exploited.
Currently, most of the research proposals are based on type IV PMSG-based WECS. However,
different generator-M3C configurations should be analysed. The benefits of the M3C for type
III WECSs have been studied but not experimentally verified yet. Moreover, other generators,
such as the superconducting synchronous generator, can be interfaced to the grid using the M3C,



Energies 2020, 13, 5546 29 of 37

reaching power ratios of up to 20 MW [81]. As discussed in this paper, applications of the single
phase matrix converter for multi-winding generators are also feasible and can be further studied.
As the participation of wind energy in power systems increases, it is very likely that more stringent
grid-code requirements for WECSs will be used in the coming years. Therefore, M3C based
WECSs should be able to provide new grid-supporting functionalities, and issues such as fault
ride-through requirements would have significant impacts on the design and operation of modern
WECSs. Fault-ride-through strategies such as that presented in [27] must be expanded to provide
zero-voltage and over-voltage ride-through, alongside new functionalities to provide ancillary
services, such as frequency support, short-circuit power level, voltage variations, flicker and
harmonic mitigation.

• LFAC Transmission
The research revised in this paper shows that promissory applications of the M3C in LFAC
transmission systems are possible. However, there is still work to be realised on dimensioning
and control of M3C based LFAC systems. On the one hand, the M3C can be used to connect
an LFAC system to a 50/60 Hz grid. In this case, the difference among the input and output
port frequencies is relatively high, and the capacitor of the power-cells can be designed using
a small capacitance value (see Equation (24)). Moreover, the regulation of the voltages in the
floating capacitors can be performed using circulating currents of reduced magnitudes, without
the requirement of injecting common-mode voltages. Therefore, the cost-effectiveness of the
topology is increased by a compact design of the passive components of the M3C. Nevertheless,
in this case, hundreds of kilovolts must be handle by the converter, and then efficient power-cell
voltage balancing algorithms must be developed. The current methods are not feasible or do
not consider the balancing of the voltages within a cluster when the number of power-cells is
large [125–127].

• Other applications
Regarding new applications, the M3C could be successfully applied to several industrial processes
requiring high-power AC-to-AC conversion. The first possible future application of the M3C is
related to new high-power motor-drive applications requiring high torque at zero or low-speed
operation. Some of these applications are related to conveyors, kilns, mills and extruders.
Other applications of the M3C are related to solid-state transformers. In this case,
it would be possible to connect a low-frequency AC port to a medium-frequency AC port.
Additionally, as proposed in [56], a single M3C-subconverter can be used with the same purpose
of connecting a three-phase, low-frequency and medium-voltage AC port to a single-phase,
medium-frequency and low-voltage port. One of the major advantages of using the M3C
in such applications is that the M3C can be designed to step-up or step-down the voltage.
Additionally, low-capacitance power-cell capacitors are required due to the medium frequency of
one of the port. This implies that the difference between the input and the output port frequencies
is high, and then small voltage oscillations are generated. Consequently, low circulating currents
are required for the regulation of the floating capacitor voltages. Nonetheless, the solid-state
transformer operation of the M3C has a significant challenge related to the modulation
techniques—synthesising the medium frequency voltage at the output.

The benefits of the M3C can be applied in FACTS, as presented in Section 4.4. Besides FACTS
and UPFC applications, the M3C could be used as a unified power quality conditioner. In this case,
the M3C can provide UPFC series and shunt compensation at the same time as active filtering of
harmonic contamination is performed [118]. Finally, low-voltage AC-to-AC applications can also
obtain benefits from the M3C, mainly when power quality and power density benefits outweigh cost
restrictions.

As discussed in this section, several applications can be fitted to expand the use of the M3C.
Consequently, further research will play a major role in making the M3C an industrial power converter.



Energies 2020, 13, 5546 30 of 37

It is expected that the information provided in this paper will encourage power electronics engineers
and scientists to carry out further research on the M3C.

6. Conclusions

In this paper, a detailed review of the state-of-the-art of the M3C applications has been presented.
A topology description, comparisons with other MMCC topologies and revision of the proposed
applications are presented.

The M3C is a relatively new power converter topology proposed as a future technological solution
for high-power AC-to-AC applications. However, its inherent control and hardware complexity,
plus the newness of the topology, are the main reasons why there are just about six research groups
(see Table 1) which have succeeded in realising experimental validation of control strategies related to
the M3C. Nonetheless, lots of new research proposals, validated using simulation work, are discussed.

To compare the M3C with other topologies, the M2C, the back to back M2C, the hybrid M2C and
the Hexverter have been briefly discussed in this work. A comparison between these topologies and
the M3C indicates that the former is the best suited alternative for low-speed, low-frequency operation
of drives because much-reduced mitigation currents and common-mode voltages are required for
regulating the voltage oscillations in the floating capacitors. In DFM, the M3C has some advantages
over both the M2C and Hexverter because common-mode voltage is not required and the magnitudes
of the necessary circulating currents are smaller.

Due to the aforementioned advantages, the M3C has been widely studied for high-power
applications such as WECSs and motor drives. To support the pertinence of the M3C in these
applications, simulation and experimental results have been analysed in this paper. In WECS, the main
advantages of the M3C are related to a better power density of the topology, leading to weight and
size reductions. Moreover, the high control flexibility of the converter allows some simplicity to fulfil
grid-code requirements such as LVRT.

For motor-drive systems, the M3C has been highlighted as an appropriate solution for low-speed
and high-torque applications such as conveyors and extruders. One exciting opportunity is the use of
the M3C as a replacement of line-commutated cycloconverters, which has been highly recommended
by several publications.

Additionally, the application of the M3C in LFAC transmission systems is promissory. In this case,
DFM operation is involved due to the fractional frequency of the LFAC grid. Then, small capacitor
voltage oscillations are produced, yielding simplified control requirements and compact dimensions
of the converter.

As highlighted in this article, the technological development of the M3C is still in an early
stage, with experimental assessments being performed in downscaled laboratory environments.
Therefore, it is still necessary to demonstrate and validate the effectiveness of this technology under
full-power and operational-environment applications. In this regard, further research is still needed to
achieve a higher maturity level of the M3C and reduce the gap between the current academic work
and the requirements of industrial applications.

Author Contributions: M.D. and R.C.D. worked on the conceptualisation and methodology. A.M., E.I. and M.U.
supported the state-of-the-art revision and helped to edit the paper. A.M and M.E. helped to compare control
strategies. R.C., F.R. and P.W. provided supervision on all the stages of this research work. All authors have read
and agreed to the published version of the manuscript.

Funding: This work was funded by the Agencia Nacional de Investigación y Desarrollo (ANID) of Chile,
under projects Fondecyt 11191163, Fondecyt 1180879, Fondecyt 11190852 ANID Basal FB0008 and Fondef
ID19I10370. Additionally, the support provided by the University of Santiago through project Dicyt 091813DD
is recognised.

Conflicts of Interest: The authors declare no conflict of interest.



Energies 2020, 13, 5546 31 of 37

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