2019 22nd International Conference on Electrical Machines and Systems (ICEMS)
A Novel Space Vector Modulation for the 3x5
Direct Matrix Converter
Wei Cai
Navy Submarine Academy
Qingdao, China
e-mail: caiwei19830530@163.com
Zongliang Wang
Navy Submarine Academy
Qingdao, China
Abstract—The multiphase AC motor driver system with
matrix converter has many advantages, while the control is
very complex. Instead of carrier modulation, the space vector
modulation is more used for field oriented control in the motor
drive system. Traditional space vector modulation of the
matrix converter is an evolution of the two-level inverter,
whose vectors are represented by the input phase abc. In this
paper, we present a new space vector modulation strategy for
multiphase matrix converter with a 3x5 system as an example,
based on the perspective of a three-level. This method utilizes
the three-level modulation for reference from the mature
method in fictitious inverter, and applies it to the multi-phase
matrix converter system through analysis and improvement.
For the voltage level of three-level modulation is relatively
clear, the new method is prone to get an optimal result for
different goals. On the basis of theoretical analysis and
derivation, a novel sectioned modulation method is proposed in
the paper. The simulation verify the correctness of the method.
Keywords—multiphase AC motor, direct matrix converter,
space vector modulation, perspective of three-level
I.
INTRODUCTION
Multiphase AC motor has been widely concerned by the
industry in recent years, for its many advantages such as
structural redundancy, high reliability and fault tolerance [13]. Compared with the traditional three-phase AC motor, the
multiphase AC motor reduces the rotor harmonic current loss
by reducing the amplitude and frequency of the torque ripple.
In addition, if some phases (one, two or more) of a
multiphase AC motor have open circuit or other faults, the
drive system can continue to operate at a reduced power rate.
That is to say the residual phases (the minimum two
windings in a healthy state) contribute the minimum rotating
magnetic flux and the minimum reduction. The commonly
used multiphase motors includes five-phase, six-phase
(asymmetric or symmetrical) and seven-phase motors, which
are widely used in marine electric propulsion, electric
traction (including electric and hybrid electric vehicles) and
the other more electric aircraft concepts [4-7].
For the AC motor drive system, the AC-DC-AC
converter is the most commonly used topology structure
which has many advantages such as four quadrant operation,
simple configuration, low cost, high efficiency, and so on [8].
In the case of the low harmonic requirement, the multi-level
inverter or the modular multi-level converter (MMC) with
increased output level can be adopted [9]. However, no
matter which topology above is adopted, a capacitor is
needed in the intermediate DC link to reduce output ripple,
that greatly reduces the reliability and applicability of the
system especially for some high temperature environment.
Different from the traditional AC-DC-AC converter, the
This project is sponsored by National Natural Science Foundation
(51407193).
Shuo Sun
Navy Submarine Academy
Qingdao, China
direct matrix converter (DMC) is an AC-AC transformation
device without the DC link. The intermediate capacitor is no
longer needed in the DMC, so it has the better environmental
applicability and reliability [10]. In addition, the DMC has
many advantages such as adjustable power factor, fine input
and output characteristics, energy bi-directional transmission
and etc, so it has gradually attracted much attention of many
scholars in the field of electric drive [11-12].
With the DMC fed the multiphase AC motor, we can
obtain the advantages of both in this drive system, while the
control is very complex. In general, the modulation
researches of multiphase matrix converter focus on the scalar
method based on the mathematical model, because its
mathematical meaning is clear and easy to extend to the
multiphase system. But in the motor drive system, the space
vector modulation (SVM) is more used for field oriented
control, so as to provide more superior performance of motor
control performance. In this paper, we will discuss a
multiphase SVM with a 3x5 matrix converter system as an
example, with a new perspective of three-level.
THE SPACE VECTOR MODULATION OF MATRIX
CONVERTER
II.
A. The 3x5 Direct Matrix Converter
Fig.1 is the topology of a five-phase DMC. The matrix
converter contains three-phase (ua, ub, uc) input power
supply, input filter and bidirectional switching matrix
(clamping circuit and three-phase load are not drawn), in
which bidirectional switching matrix is the core. The
bidirectional switch matrix consists of 15 bidirectional
switches. Each bidirectional switch has two IGBT and two
fast recovery diodes.
SaA
SbA
ScA
O
ua
ub
uc
L1 C1
L2
L3
C2 C3
SaB
SbB
ScB
SaC
SbC
ScC
SaD
SbD
ScD
SaE
SbE
ScE
Fig.1 The 3x5 direct matrix converter
978-1-7281-3398-0/19/$31.00 ©2019 IEEE
978-1-7281-3398-0/19/$31.00
©2019
IEEE Downloaded on June 08,2020 at 21:11:14 UTC from IEEE Xplore. Restrictions apply.
Authorized licensed use limited to: University
of Exeter.
2019 22nd International Conference on Electrical Machines and Systems (ICEMS)
B. Traditional two level SVM method in 3x5 DMC
The SVM is a kind of commonly used modulation
method in MC, including the direct-SVM and indirect-SVM.
Here we take the indirect-SVM for example to carry on the
introduction [13].
Sap Sbp Scp I pn p SAp SBp SCp SDp SEp
a
b
c
San Sbn Scn
n SAn SBn SCn SDn SEn
Fig.2 The virtual equivalent AC-DC-AC structure of 3x5 DMC
The strategy of indirect vector modulation is that the
matrix converter is equivalent to a combination of virtual
rectifier and virtual inverter, and the input current and output
voltage are vector controlled respectively. The virtual
equivalent circuit includes rectifier and inverter, as shown in
Fig.2.
The input current can be divided into 6 intervals, while
the output voltage can be divided into 10 intervals which is
shown in Fig.3. The basic vectors of each interval is
determined. Then the duty ratio of effective vector and zero
vector time can be calculated according to the concept of
vector synthesis. In order to reduce the switching number
and the power loss, we also need adjust the switching
sequence [14].
Fig.4 Three-level structure of 3x5 DMC
In this figure, abc is the input phase, ABCDE is the
output phase, pon is the high and low electrical level. The
modulation matrix Mpon assigned the abc phase to the pon
level automatically according to the input voltage level. the
) represents a high-level p (marked
red dot-dashed line (
) represents a medium-level o
as up), the black solid line (
(marked as uo), the green segment dashed line
)represents a low-level n (marked as un). Zoned area by
(
60°, the input voltage can be divided into 6 intervals, in
which each electrical level is made up by three input phase.
Using this assignment, we can get the three electrical level
input with relatively stable magnitude which can be used to
analyze the vector composition, the vector effect and the
switching of inverter side. With the three-level DC link, the
follow-up circuit can be seen as a standard three-level
inverter in which M is the modulation matrix of the inverter.
So we can control the input current vector and output voltage
vector respectively [15].
III.
Fig.3 The basic vector distribution of the output voltage in the
traditional SVM
C. Perspective of three-level in 3x5 DMC
The DMC actually is a direct type AC-AC converter,
which consists of three input voltage and the output phase
can connect to any input voltage. So if we divide the three
input voltage according to the electrical level, we can get a
high level Vp, a medium level Vo and a low level Vn. Suppose
the input voltage remains the same in each switching cycle,
the DMC can be seen as a three-level inverter structure. This
is the perspective of three-level in DMC.
With the presented perspective, we can see the DMC as a
combination of virtual rectifier and virtual “three-level”
inverter, while the traditional SVM of the DMC is an
evolution of “two-level” inverter that is shown in Fig.2. The
new control structure diagram is shown in Fig.4.
THE NOVEL SVM IN 3X5 DIRECT MATRIX
CONVERTER
A. Perspective of three-level for traditional SVM method
In the SVM strategy, we can see the 3x5 DMC as a
combination of virtual rectifier and virtual inverter. In fact,
the traditional SVM is a “two-level” modulation, for it
always chooses the maximum DC voltage at the virtual
rectifier, that is the difference between the red dot-dashed
line and the green segment dashed line in the Fig.4.
According to the description of relevant paper [16], the
SVM control of the multiphase inverter has more flexibility.
For example, the near two vectors SVPWM (NTV-SVPWM)
control, the near four vectors SVPWM (NFV-SVPWM)
control and the minimum switch loss SVPWM (MSLSVPWM) control can be selected. But they all abandone the
medium-level o in the Fig.3, that is to say one degree of
freedom of modulation is lost.
B. The novel SVM in 3x5 DMC with the perspective of
three-level
Unlike the Fig.2, the inverter in Fig.4 has three input
levels. So with the perspective of three-level, the virtual
inverter is a five-phase three-level topology, and some
mature modulation algorithms can be adopted as reference.
But before implement the new method, we must figure out
what impact that an additional medium-level have on our
output.
From the five-phase three-level modulation method in
Fig.5 [17], we can see that an additional level will bring the
following two changes. One is to add a medium vector
(ppooo, oonnn, ppoop, oonno) between the large vector and
978-1-7281-3398-0/19/$31.00 ©2019 IEEE
Authorized licensed use limited to: University of Exeter. Downloaded on June 08,2020 at 21:11:14 UTC from IEEE Xplore. Restrictions apply.
2019 22nd International Conference on Electrical Machines and Systems (ICEMS)
the zero vector (similar to the NFV-SVPWM), which is
mainly used to reduce the harmonics existes in the NTVSVPWM. The other one is to add a transition vector (ppnno)
between two large vectors to divide the modulation area into
C and D according to the angle for the harmonic reduction
furture.
Fig.5 The SVM in five-phase three-level inverter
Although we consider the DMC as a three-level inverter
in the Fig.4, we must realize that they are two different
topologies and the modulation is different. The most
important difference is that the amplitude of vectors in
DMC are changing, unlike the constant ones in inverters.
Therefore the above two types of vectors are changing. The
medium vector (ppooo, oonnn, ppoop, oonno) will
reciprocating move between the large vector and the zero
vector, so we call them the variation vector p (ppooo, ppoop)
and the variation vector n (oonnn, oonno). The other
transition vector (ppnno) will reciprocating move between
two large vectors. Because the size and direction of the
basic vector have changed, we can no longer divide the
DMC into a four-triangle structure like Fig.5.
From the view of geometric synthesis, the fundamental
method to reduce harmonics in space vector synthesis is to
select the basic vector close to the target vector as far as
possible. Furthermore, in the process of vector synthesis, the
complexity of duty cycle calculation is greatly increased by
the direction change, while the size has less influence. So
we abandon the transition vector and retain the variation
vectors. And in order to divide the vector action area more
clearly, we introduce another medium vector (called
boundary vector) in the NFV-SVPWM.
Fig.6 The vector space of three-level SVM in DMC
Take the sector 1 as an example for specific analysis,
which is shown in fig.6. In this sector, the traditional
modulation strategy in inverter have 12 vectors. But their
motion track are different in DMC for the indefinite pon
level. For example, the transition vector “ppnno” is not
fixed in the middle of large vectors “ppnnn” and “ppnnp”,
because the o level uo is changing between the maximum to
minimum. The variation vectors “ppooo”, “ppoop”, “oonnn”,
“oonno” overlap in the region A and B because of the
voltage of up-uo and uo-un is alternating high and low. While
the large vectors “ppnnp”, “ppnnn” and the boundary
vectors “pppnp”, “pnnnn” are relatively fixed. They meet
the following conditions:

2

 2π  
U L = U D 1 + 2cos 


5
 5 

(1)

U = 2 U
 M 5 D
In the formula (1), UL is the length of large vector, UM is
the length of boundary vector. For these two kinds of
vectors, we have the equation UD=up-un. If we replace the
formula as the equation UD=up-uo or UD=uo-un. We can get
the scale of the variation vector p or the n.
It can be seen from the formula and the figure, the
boundary between the region A and region B is determined.
Based on the above analysis and using the idea of the NFVSVPWM, we can propose the following novel modulation
strategies.
(1) When the target vector is located in area A (low
modulation ratio region), the boundary vectors (pppnp,
pnnnn in sector 1) is selected. The other two vectors are the
greater than and closest to the target in variation vectors
(ppooo, oonnn, ppoop, oonno in sector 1).
(2) When the target vector is located in area B (high
modulation ratio region), the boundary vectors (pppnp,
pnnnn in sector 1) is selected. The other two vectors are the
greater than and closest to the target in variation vectors and
large vectors (ppooo, oonnn, ppoop, oonno, ppnnn, ppnnp in
sector 1).
Other areas can be treated similarly. Then we can get the
the basic vector distribution of the novel SVM shown in
Fig.7.
Fig.7 The basic vector distribution of the output voltage in the
proposed SVM
C. The steps for the new novel SVM
Using the above modulation strategies, we can get the
following specific steps of the new SVM method.
(1) Calculate the length of the basic vector as following
formula.

2
 2π  
U L = 1 + 2 cos 
  ⋅ ( u p − un )
5
 5 


2
U M = ⋅ ( u p − un )
5


UVp = 2 1 + 2 cos  2π   ⋅ ( u p − uo )



5 
 5 

2
 2π  

UVn = 5 1 + 2 cos  5   ⋅ ( uo − un )



978-1-7281-3398-0/19/$31.00 ©2019 IEEE
Authorized licensed use limited to: University of Exeter. Downloaded on June 08,2020 at 21:11:14 UTC from IEEE Xplore. Restrictions apply.
(2)
2019 22nd International Conference on Electrical Machines and Systems (ICEMS)
In the formula, UL is the length of large vector, UB is the
length of boundary vector, UVp is the length of variation
vector p, UVn is the length of variation vector n. The up, uo,
un are the high-level, medium-level and low-level of the
virtual rectifier output respectively
(2) Calculate the length of the target vector according to
the output voltage.
2
4
6
8

j π
j π
j π
j π 
2
U ref =  uA e j 0 + uB e 5 + uC e 5 + uD e 5 + uE e 5 
5

2 5
5

= ⋅  u phase cos (ωt ) + j u phase sin ( ωt ) 
(3)
5 2
2

= u phase cos (ωt ) + j u phase sin (ω t )
= u phase e jθ

In the formula, U ref is the target vector, uA, uB, uC, uD, uE
is the output phase voltage whose amplitude is u phase , θ is
the phase angle of target vector.
(3) Judge the sector N where the target vector located.
2 

N = mod  θ ,
π  +1
(4)
5 

(4) Judge the area where the target vector located.
A
U ref > U B

(5)
area = 
U ref < U B
B
(5) Select the basic vectors according to the area and the
target.
Regardless where the target vector is located, the basic
vectors always include the boundary vectors. The other two
are the greater than and closest to the target in variation
vectors when the target vector locate in area A, or the
greater than and closest to the target in variation vectors and
large vectors when the target vector locate in area B.
(6) Calculate the duty time of each vector.
Considering that in five-phase virtual inverters, the
synthesis of vectors should also satisfy the zero output in the
third harmonic space. So the selected basic vectors must
satisfy the volt-second principle. The space vector
composition is shown in the Fig.8, and the expression can
be seen in the formula (6).
shown in Fig.8. Vα, Vβ is the length of the corresponding
vector in fundamental space, while the Vα-3, Vβ-3 is the length
of the corresponding vector in third harmonic space. U ref
is the length of target vector, and θk is the angle of target
vector in sector.
Solve the formula (6), we can get the result in formula (7).

Vβ − 3 ⋅ U ref ⋅ sin θ k
 d1 =
π

(Vβ − 3 ⋅ Vα + Vα −3 ⋅Vβ ) ⋅ sin

5

π


Vβ − 3 ⋅ U ref ⋅  cos θ k − sin θ k ⋅ cot 

5

d2 =
(
V
⋅
V
+
V
⋅
V
)
β −3
α
α −3
β


π


Vα − 3 ⋅ U ref ⋅  cos θ k − sin θ k ⋅ cot 

5

d3 =
(
V
⋅
V
+
V
⋅
V
)

β −3
α
α −3
β

Vα − 3 ⋅ U ref ⋅ sin θ k

(7)
d4 =
π

(Vβ − 3 ⋅ Vα + Vα − 3 ⋅Vβ ) ⋅ sin
5

 d0 = 1 − d1 − d 2 − d3 − d 4
(7) Adjuste the output sequence according to the basic
vector to ensure the minimum switching loss. For example,
the vector sequence is “pppnp-ppnnp-ppnnn-pnnnn-nnnnn”
in sector 1 with large vectors, while the sequence is “pnnnnoonnn- oonno- pppnp- ppppp” with variation vectors n.
IV.
THE SIMULATION
The three-level SVM strategy proposed in this paper is
verified by the simulation. The related parameters are shown
in Tab.1. The input side is connected to the LC filter, where
the inductor and parallel resistance for the system oscillation
damping. The output side is also connected to the LC filter,
no parallel resistance.
Tab.1 Parameters of simulation and experiment
variables
input line voltage
load resistance
input filter inductor
input filter capacitor
input filter resistance
parameters
variables
parameters
380V/50Hz
5Ω
2mH
2μF
40Ω
switching frequency
output frequency
load inductance
output filter inductance
output filter capacitance
10kHz
50Hz
8mH
5mH
2μF
The traditional NFV-SVPWM with different modulation
ratio (m=0.1 and m=0.8) is verified by the simulation which
is shown in Fig.10 and Fig.12. The upper one is the output
intervallic line voltage, the below one is the output current,
the bottomis the current harmonic content.
θk
Fig.8 The space vector composition with the proposed method
π

(d 2 ⋅Vα + d 3 ⋅ Vβ ) + (d1 ⋅ Vα + d 4 ⋅ Vβ ) ⋅ cos 5 = U ref ⋅ cos θ k

(d ⋅V + d ⋅ V ) ⋅ sin π = U ⋅ sin θ
4
β
ref
k
 1 α
(6)
5

d
V
 2 = β −3
 d 3 Vα −3

V
 d1 = β −3
 d 4 Vα −3
In the formula, d1~d4 is the corresponding duty ratio
978-1-7281-3398-0/19/$31.00 ©2019 IEEE
Authorized licensed use limited to: University of Exeter. Downloaded on June 08,2020 at 21:11:14 UTC from IEEE Xplore. Restrictions apply.
2019 22nd International Conference on Electrical Machines and Systems (ICEMS)
Fig.9 The simulation waveform with traditional SVM (m=0.1)
Fig.11 The simulation waveform with traditional SVM (m=0.8)
The novel modulation strategy with different modulation
ratio (m=0.1 and m=0.8) proposed in this paper is verified
by the simulation which is shown in Fig.10 and Fig.12. The
upper one is the output intervallic line voltage, the below
one is the output current, the bottomis the current harmonic
content.
Fig.12 The simulation waveform with proposed SVM (m=0.8)
V.
Fig.10 The simulation waveform with proposed SVM (m=0.1)
From the simulation results, it can be seen that the
proposed method has the better harmonic characteristics in
low modulation ratio region than the traditional method.
While the harmonic content with the proposed method is
slightly higher in the high modulation ratio region.
THE CONCLUSION
In this paper, we combine the multiphase AC motor with
the DMC to construct the driving system. Based on the fieldoriented control, the space vector modulation of the
multiphase DMC is analyzed. By decomposing the DMC, we
introduce a perspective of three-level in the virtual rectifier.
And we find the traditional SVM is actually a “two-level”
method with the perspective of three-level.We analyze the
influence of the new level introduction on the basic vector
and select them according to the space vector synthesis and
finally determine a new three-level modulation method with
a section modulation. The new method has better harmonic
characteristics at low modulation ratio.
REFERENCES
[1]
[2]
50
[3]
0
[4]
-50
0.1
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
WB. Kong, J Huang, M Kang and etc, “Fault tolerant control of a
multiphase motor with non-sinusoidal source under open-phase
conditions,” Electric Machines and Control, vol.17, no.5, pp.9-14,
2013.
D Casadei, M Mengoni, A Tani and etc, “Torque maximization in
high-torque density multiphase drives based on induction motors,”
IEEE Energy Conversion Congress and Exposition, ECCE 2010, pp.
3896-3902, 2010.
C Sun, S Ai, LD Hu and etc, “The development of a 20MW PWM
driver for advanced fifteen-phase propulsion induction motors,”
Journal of Power Electronics, vol.15, no.1, pp.146-159, 2015.
WJ Yu, X Liu, WB Kong, “Torque density improvement for fivephase induction motor drive with harmonic current injection in
electric vehicles application,” 21st International Conference on
Electrical Machines and Systems, ICEMS 2018, pp.2525-2528, 2018.
978-1-7281-3398-0/19/$31.00 ©2019 IEEE
Authorized licensed use limited to: University of Exeter. Downloaded on June 08,2020 at 21:11:14 UTC from IEEE Xplore. Restrictions apply.
2019 22nd International Conference on Electrical Machines and Systems (ICEMS)
[5]
N Kamal, B Mohamed, M Khoudir and etc, “Performance comparison
of open-circuit fault-tolerant control strategies for multiphase
permanent magnet machines for naval applications,” Electrical
Engineering, vol.100, no.3, pp.1827-1836, 2018.
[6] N Kamal, JF Charpentier, M Khoudir and etc, “Emulation of an
electric naval propulsion system based on a multiphase machine
under healthy and faulty operating conditions,” IEEE Transactions on
Vehicular Technology, vol.67, no.8, pp.6895-6905, 2018.
[7] B Oriano, C Mario, Z Mauro and etc, “Loss analysis of an
asynchronous multiphase motor-generator for avionics applications,”
International Journal of Applied Electromagnetics and Mechanics,
vol.48, no.2-3, pp.271-276, 2015.
[8] XH Tao, L Xu, Y Song, “A transformerless cascaded AC-DC-AC
converter for multiphase propulsion drive application,” 2011
International Conference on Electrical Machines and Systems,
ICEMS 2011, 2011.
[9] YS Kumar, G Poddar, “Medium-voltage vector control induction
motor drive at zero frequency using modular multilevel converter,”
IEEE Transactions on Industrial Electronics, vol.65, no.1, pp.125-132,
2018.
[10] DL Liliana, E Lee, W Patrick and etc, “A 20 KW matrix converter
drive system for an electro-mechanical aircraft(EMA) actuator,” 2005
European Conference on Power Electronics and Applications, 2005.
[11] SL Arevalo, P Zanchetta, W Patrick and etc, “Control and
implementation of a matrix converter based AC ground power-supply
[12]
[13]
[14]
[15]
[16]
[17]
unit for aircraft servicing,” IEEE Transactions on Industrial
Electronics, vol.57, no.6, pp. 2076-2084, 2010.
M Brahim, B Lotfi, “Matrix converter prototype for motor drive,” 3rd
International Conference on Control Engineering and Information
Technology, CEIT 2015, 2015.
HW She, H Lin, B He and etc. “Implementation of voltage-based
commutation in space vector modulated matrix converter”. IEEE
Transactions on Industrial Electronics, vol.59, no.1, pp.154–166,
2012.
TD Nguyen, HH Lee. “Development of a three-to-five-phase indirect
matrix converter with carrier-based PWM based on space-vector
modulation analysis”. IEEE Transactions on Industrial Electronics,
vol.63, no.1, pp.13-24, 2016.
W Cai, B He, JZ Sun and etc. “The research of space vector
modulation in matrix converter with perspective of three-level,” 43rd
Annual Conference of the IEEE-Industrial-Electronics-Society, 2017.
F Yu, XF Zhang, HS Li and etc, “Space vector PWM control of fivephase inverter,” Proceedings of the CSEE, vol.25, no.9, pp.40-46,
2005.
QG Song, XF Zhang, F Yu and etc, “Research on space vector PWM
of five-phase three-level inverter,” Journal of Wuhan University of
Technology (Transportation Science& Engineering), vol.30, no.5,
pp.796-799, 2006.
978-1-7281-3398-0/19/$31.00 ©2019 IEEE
Authorized licensed use limited to: University of Exeter. Downloaded on June 08,2020 at 21:11:14 UTC from IEEE Xplore. Restrictions apply.