Journal of Power and Energy Engineering, 2015, 3, 136-145
Published Online April 2015 in SciRes. http://www.scirp.org/journal/jpee
http://dx.doi.org/10.4236/jpee.2015.34020
How to cite this paper: Tadra, G., Fedyczak, Z. and Szcześniak, P. (2015) Model Predictive Control Circuit of the Current
Source Matrix Converter. Journal of Power and Energy Engineering, 3, 136-145. http://dx.doi.o rg/10.4236/jpee.2015.34020
Model Predictive Control Circuit of the
Current Source Matrix Converter
Grzegorz Tadra, Zbigniew Fedyczak, Paweł Szcześniak
Power Electronics Department, Institute of Electrical Engineering, University of Zielona Gora, Zielona Góra,
Poland
Email: G.Tadra@iee.uz.zgora.pl, Z.Fedyczak@iee.uz.zgora.pl, P.Szczesniak@iee.uz.zgora.pl
Received January 2015
Abstract
In this paper, a new predictive control strategy for current source matrix converter (CSMC) is
presented. Proposed predictive control strategy allows for creating output voltages with boost
type voltage transfer ratio and desired frequency. The description of predictive control circuit of
the CSMC is presented. Furthermore the simulation test results to confirm functionality of the
proposed control strategy and converter properties under this strategy are shown.
Keywords
AC/AC Frequency Converters, Current Source Matrix Converter, Predictive Control Strategy
1. Introduction
An alternative for commonly used indirect (AC/DC/AC) frequency converters with DC storage elements is con-
stantly searched for. One of the proposed alternatives is the direct voltage source matrix converter (VSMC). The
main disadvantage of the VSMC, virtually limiting its industrial application in power networks or electric drives,
is the relationship between the input and output voltages (voltage transfer ratio). The quotient of the rms values
of these voltages (while retaining their sinusoidal shape) is lower than 1 [1]-[5]. In this respect, hybrid matrix
converters, where an additional DC/DC converter and a small capacitor for energy storage are used, have more
favorable properties due to the fact that their voltage transfer ratio can be higher than 1 [6] [7]. Such transfer ra-
tio is also characteristic for direct and indirect matrix reactance frequency converters (MRFC) [8]-[11] and di-
rect current source matrix converters (CSMC) [12]-[15]. MRFC and CSMC are converters without the DC
energy storage alike VSMC. So far, modeling, analysis and studying the properties of these converters has in-
cluded two control strategies: 1) modified classical control strategy based on low frequency transfer matrix [1]
and 2) modified space vector modulation [3]. Simplified topology of CSMC with ideal switches as well as ideal
current and voltage sources is shown in Figure 1. Results of the analyses CSMC under control strategy 1) pre-
sented in paper [12] shows that the achievement of the voltage transfer ratio higher than 1 is possible.
Furthermore, input power factor can be controlled but not irrespective of output power factor which is the
main disadvantage of this solution. Studies of CSMC under control strategy 2) presented in [13]-[15] also proves
that the voltage transfer ratio higher than 1 can be obtained, but other than in [12], the input power factor can be
G. Tadra et al.
137
Figure 1. Simplified topology of current source matrix converter.
controlled independently of the output power factor [14].
Carried out in recent years, an intensive research of the use of the predictive control strategy implemented in
power electronic converters yielded a number of very good results [16]-[19]. The use of those control strategies
in VSMC allows for the improvement of their properties especially in relation to the dynamic ones [17]-[18].
That is why predictive control strategies are also interesting for CSMC.
The aim of this article is to propose and describe the model predictive control (MPC) circuit for CSMC. The
proposed control strategy is presented in Section 2.
In Section 3 control circuit is proposed, simulation test results to confirm functionality of the proposed control
strategy and converter properties under this strategy are presented in section IV. The conclusion is drawn in the
last section
2. Control Description
Simplified functional diagram of the proposed control system for direct CSMC is shown in Figure 2. Following
parts of the control circuit can be distinguished: 1) model predictive sub-circuit, 2) optimization sub-circuit.
Generally, the predictive model sub-circuit is used for the prediction of the phase load voltages
( )
,,
abc
uuu
and
phase source currents
( )
,,
ABC
iii
for all 27 allowed switch configurations. Optimization sub-circuit generates
control signals for the CSMC switches. Those control signals are generated according to switch configuration
selected for optimal (smallest) cost function value.
Diagram describing the steps realized in every k sampling period by the proposed control system is shown in
Figure 3. The initial action is the measurement of all the instantaneous values of the source phase voltages
()
123
,,
SS S
uuu
, input currents
( )
,,
ABC
iii
and output phase voltages
( )
,,
abc
uuu
. In the next step, for each of
the allowed CSMC switch configurations (SC)
jK
S
()
1,, 27x=
collected in Table 1 [14], output currents
( )
,,
ak bk ck
iii
of the CSMC are determined with the use of Equation (1) (mathematical model describing the
CSMC current relations) [12]-[15]. For the previously calculated output currents by means of differential Equa-
tion (2) and its discrete form obtained by the forward Euler approximation-Equation (3), instantaneous output
voltages
for the next
( )
1k+
sampling period are predicted.
o
aaA aBaC AA
bbA bB bC BB
ccAcBcC CC
i sssii
i sssii
i sssii
 
 
= ==
 
 
 
iT
(1)
where: iA, iB, iCphase input currents, ia, ib, icphase output currents, Ttransfer matrix,
{ }{}
open , ,,,C
clos
1, , ,
, e0
jK
jK jK
Sj abc
S
sK AB
== =
sjKstate function of the switches
jK
S
,
oo
o
d
d
FL
CtR
= +
uu
i
(2)
()( )( )
oo o
11
DD
F LF
TT
kk k
C RC

+=+ +


ui u
(3)
G. Tadra et al.
138
Figure 2. Simplified block scheme of the current source matrix converter with model predic-
tive control circuit.
Figure 3. Steps diagram for the proposed model predictive control strategy.
G. Tadra et al.
139
Table 1. Allowed switching configurations of the CSMC with vector representarions of output currents (
L
i
oo
e
β
=
ii
) and
input voltages (
S
i
ii
e
α
=uu
).
Nr A B C uAB uBC uCA
i
u
αS ia ib ic
o
i
L
β
1 a a a 0 0 0 0 - 0 0 0 0 -
2 b b b 0 0 0 0 - 0 0 0 0 -
3 c c c 0 0 0 0 - 0 0 0 0 -
4 a c c uca 0 uca 2/3uca π iA 0 iA
2
3
a
i
π6
5 b c c ubc 0 ubc 2/3ubc 0 0 iA iA
2
3
a
i
π2
6 b a a uab 0 uab 2/3uab π iA iA 0
2
3
a
i
5π6
7 c a a uca 0 uca 2/3uca 0 iA 0 iA
2
3
a
i
5π6
8 c b b ubc 0 ubc 2/3ubc π 0 iA iA
2
3
a
i
π2
9 a b b uab 0 uab 2/3uab 0 iA iA 0
2
3
a
i
π6
10 c a c uca uca 0 2/3uca
π3
iB 0 iB
2
3
b
i
π6
11 c b c ubc ubc 0 2/3ubc
2π3
0 iB iB
2
3
b
i
π2
12 a b a uab uab 0 2/3uab
π3
iB iB 0
2
3
b
i
5π6
13 a c a uca uca 0 2/3uca
2π3
iB 0 iB
2
3
b
i
5π6
14 b c b ubc ubc 0 2/3ubc
π3
0 iB iB
2
3
b
i
π2
15 b a b uab uab 0 2/3uab
2π3
iB iB 0
2
3
b
i
π6
16 c c a 0 uca uca 2/3uca
π3
iC 0 iC
2
3
c
i
π6
17 c c b 0 ubc ubc 2/3ubc
2π3
0 iC iC
2
3
c
i
π2
18 a a b 0 uab uab 2/3uab
π3
iC iC 0
2
3
c
i
5π6
19 a a c 0 uca uca 2/3uca
2π3
iC 0 iC
2
3
c
i
5π6
20 b b c 0 ubc ubc 2/3ubc
π3
0 iC iC
2
3
c
i
π2
21 b b a 0 uab uab 2/3uab
2π3
iC iC 0
2
3
c
i
π6
22 a b c uab ubc uca - - iA iB iC - -
23 a c b ubc uca uab - - iC iA iB - -
24 b a c uca uab ubc - - iB iC iA - -
25 b c a uab uca ubc - - iB iA iC - -
26 c a b uca ubc uab - - iA iC iB - -
27 c b a ubc uab uca - - iC iB iA - -
where:
[ ]
T
oabc
iii=i
load currents vector,
[ ]
T
oabc
uuu=u
output voltages vector, TDdiscretization
time.
In the next step Equation (4) is used for cost function calculations, which is described for all allowed switch
configurations
( )
1,, 27x=
. The cost function is expressed as a sum of coordinate subtracts of the reference
and the predicted output voltages vectors. Vector coordinates are obtained by using Equations (5) and (6) [20].
( )( )
1
11
xx
xoooo
gu uku uk
αα ββ
∗∗
=−++ −+
(4)
Co
1 1212
2
30 3232
a
ob
oc
u
uu
uu
α
β
∗∗

−−
 

= =
 

 
 

Tu
(5)
G. Tadra et al.
140
( )
( )()
Co
11
1
x
ox
x
o
uk k
uk
α
β

+= +

+


Tu
(6)
where:
o
u
α
,
o
u
β
,
( )
1
x
o
uk
α
+
,
( )
1
x
o
uk
β
+
coordinates of the space vector representations of the reference
and predicted voltages,
C
T
Clarke transformation matrix for symmetrical system.
Further, taking into account E quatio ns (7) and (8), using Equation (9) values of the phase input currents are
calculated.
T
AaA bA cAaa
iBaB bBcBbb
CaC bCcCcc
u sssuu
u sssuu
u sssuu
 
 
= ==
 
 
 
uT
(7)
where: uA, uB, uCmatrix converter input phase voltages, ua, ub, ucmatrix converter output phase voltages,
T
T
transposed transfer matrix.
d
d
S
SSSS i
LR
t=+−
iiuu
(8)
()( )( )( )
( )
11
SD D
SS Si
SS
RT T
kk kk
LL

+=++ −


ii uu
(9)
where:
[ ]
T
S ABC
iii=
i
phase input currents vector;
[ ]
T
123SSS S
uuu=u
phase source voltages vector;
[ ]
T
i ABC
uuu=u
input phase voltages vector.
Next for all possible switch configurations
( )
1,, 27x=
the cost function, expressed by Equation (10) [17],
[21] is described. This cost function allows for determining the value of the factor thanks to which, the influence
of the switch configuration on the input power factor can be determined. Switch configuration for the next dis-
cretization period is selected basing on Equation (11)global cost function. Switching configuration x for which
gx has smallest value is selected. The value of the global cost function depends on individual cost functions
1x
g
,
2x
g
and weighing factors A and B values. The values of the weighing factors are preset depending on the im-
portance of the individual cost functions (Atracking reference output voltages values, Binput power factor).
()()
{
}
( )()( )()
2
Im 111111
xx
xS SxSSSS
gQkkukik ukik
βα αβ
= =+⋅+≈+⋅+−+⋅+ui
(1)
where:
S
u
—space vector representation of source voltages,
Sx
i
complex conjugate of the space vector repre-
sentation of predicted input currents for x switches configuration,
S
u
α
,
s
u
β
space vector coordinates of
S
u
,
,
xx
SS
ii
αβ
space vector coordinates of
Sx
i
.
12xxx
g AgBg=⋅ +⋅
(2)
3. Control Circuit
In Figure 4 basic functional schema of the control circuit is shown. Furthermore tasks division for hardware in
which they are implemented is shown. The control circuit consists of 1) analog/digital (A/D) converters (Analog
Devices Inc. AD7679) for currents iA, iB, iC and voltages
1S
u
,
2S
u
,
3S
u
; ua, ub, uc measurement, 2) Two Digit-
als Signal Processors (DSP) for all calculations (Analog Devices Inc. ADSP21836), 3) Field Programmable
Gate Array (FPRG) for commutation strategy (Xilnix XC3S200).
4. Test Results
Studies of the discussed model predictive control for CSMC have been carried out for the circuit parameters
collected in Table 2. The simulation test results have been obtained by means of Matlab Simulink. Simulation
setup is shown in Figure 5.
In Figure 6 example of the space vector geometrical interpretations for reference
o
u
and obtained
o
u
output
voltages of the CSMC are shown. Vector locus for reference and obtained output voltage space vector represen-
tations are shown in Fig ur e 6, its coordinates are shown in Figure 6. In selected time period (tk to
( )
1k
t
+
)
output voltage space vector tops and its coordinates predicted for all 27 switching configurations are
G. Tadra et al.
141
Figure 4. Control circuit basic schema.
Figure 5. Example of the space vector geometrical interpretation
for output reference
o
u
and obtained
o
u
voltages of the
CSMC, a) vector locus, b) α coordinates, c) β coordinates. (No. 1
to 27-x-SC number).
G. Tadra et al.
142
shown. It can be seen that predicted vector closest to the reference vector (with smallest g) is selected in time
moment
( )
1k
t
+
. In Figure 7 for transfer ratio higher than one and three different frequencies 50 Hz, 25 Hz, 75
Hz CSMC currents and voltages’ time waveforms are presented. The response of the circuit to the output refer-
ence voltage changes is shown in Figure 8. In Figure 9 the response of the circuit to the output frequency
changes is presented. As it can be seen from Figure 8 and Figure 9 output voltage of the current source matrix
converter under proposed model predictive control strategy reaches its reference with a very fast dynamics.
Figure 6 . Simulink model for simulation of model predictive control of current source matrix converter.
Figure 7. Simulation input voltages (uA, uB, uC), output voltages (ua, ub, uc) and input currents (iA, iB, iC) for reference output
voltage amplitude 260 V and frequency (a) 50 Hz, (b) 25 Hz, (c) 75 Hz.
G. Tadra et al.
143
Figure 8. Simulation time waveforms of the input (uA, uB, uC), output (ua, ub, uc) voltages and input currents (iA, iB, iC) for
variable reference output voltage amplitude |uo|.
Figure 9. Simulation time waveforms of the input (uA, uB, uC), output (ua, ub, uc) voltages and input currents (iA, iB, iC) for
variable output voltage frequency fo.
Table 2. Simulation circuit parameters.
Parameter Sym bo l Values
Phase source voltage/frequency uS/fS 230 V/50 Hz
Output voltage/frequency uO/fO Adjustment
Discretization time TD 10 µs
Resistance RS/RL 0.5 Ω/250 Ω
Inductance LS 15 mH
Capacitance CF 20 mF
G. Tadra et al.
144
5. Summary
In this paper, model predictive control and a control circuit of the current source matrix converter has been pre-
sented. Proposed control strategy allows obtaining output voltages with desired frequency and amplitude. Vol-
tage transfer ratio for CSMC under presented control strategy can be higher than 1. Reference values are reached
with fast dynamic. Furthermore, the input power factor can be controlled but it highly depends on circuit ele-
ments and set parameters. Future investigations will be focused on the improvement of the input power factor
control and experimental implementation of the proposed control strategy in current source matrix converter.
Acknowledgements
This work was supported by the European Union, Human Capital within the project "Scholarships for PhD stu-
dents studying faculties recognized as particularly important for the development of Lubuskie voivodeship",
Sub-8.2.2, Action 8.2, Priority VIII.
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