Direct control methods for matrix converter and induction motor

Direct Control Methods for Matrix Converter and
Induction Machine
J. Boll, F.W. Fuchs
Institute for Power Electronics and Electrical Drives
Christian-Albrechts-University of Kiel, Germany
,
Abstract—Several methods for direct control of matrix
converter and induction machine have been developed in
recent years. To give an overview and comparison some of
them are selected and presented in this paper. Included are
the basics of Direct Torque Control, Direct Current Control
and Sliding Mode Control of matrix converters.
I. INTRODUCTION
In recent years many research results on control
methods for matrix converters have been published. In the
field of matrix converter control research work has been
done since many years [1]. Commutation and protection
issues have been investigated to a high status [2-4]. Early
papers concentrated on converter open loop control [1],
[5]. Another topic of great interest is the closed loop
control of a drive system consisting of matrix converter
and induction machine. Slip control and field oriented
control are the basic methods applied for closed loop
control [4]. Another quite new interesting topic is the
application of modern direct control methods to the
system with matrix converter and induction machine.
In this paper, the most important direct control methods
for matrix converter and induction machine are presented
to give an overview and comparison. These methods are
Direct Torque Control (DTC), Direct Current Control
(DCC) and sliding mode control.

After a short introduction to matrix converter principles
and switching constraints in section II an overview of
possible switch configurations and their resulting space
vectors will be given. In section III the basic ideas of the
three control methods mentioned above will be outlined,
starting with Direct Torque Control and Sliding Mode
Control, as these methods use the same switch
configurations of the matrix converter, and ending with
Direct Current Control. In section IV similarities and
differences of the control methods are mentioned and in
section V follows a conclusion.
II. M
ATRIX CONVERTER PRINCIPLES
The nine bidirectional switches of a matrix converter
allow any connection between the three input and output
phases as shown in Fig. 1. Some of these connections or
switch configurations are forbidden as the voltage sources
on the input side must not be short circuited and the
inductive load at the output side must not be left open.
These constraints lead to 27 allowed switch configurations
for the matrix converter which are shown in Table 1 [6].
There and in the following the input phases will be
denoted with lowercase indexes a,b,c and output phases
with uppercase indexes A,B,C. Table 1 also lists the space
vectors of output voltage v
o
(
)
CBA
o

vavavv ⋅+⋅+=
2
3
2
,
)3/2( π
=
j
ea
(1)
and input current i
i
. These can be assigned to four groups:
Group 1: In this group the output voltage vectors have
the same magnitude as the input voltage v
i
, rotate in the
same direction and have a displacement angle of 0°, 120°
and 240°.
Group 2: In this group the output voltage v
o
has the
same magnitude as v
i
, but rotates in the opposite direction
with a displacement angle of 0°, -120° and –240°
respectively.
Group 3: In this group the output vectors have a fixed
position, but a magnitude varying with a line-to-line input
voltage.

Group 4: In this group a zero vector is generated, input
and output side of the matrix converter are decoupled.
Depending on the modulation and control method all
four groups or only a selection of them are used.
III. D
IRECT CONTROL METHODS
A. Direct Torque Control (DTC)
DTC for matrix converters has been designed, analysed
and implemented as published in [7], [8] and [9]. This
control method uses only the switching combinations from
groups 3 and 4 of Table 1. As shown in Fig. 2 a) the
output voltage vectors from group 3 form a hexagon with
six vectors arranged on one axis of the hexagon. The
hexagon is divided into sectors with the output voltage
I.M.
v
a
v
b
v
c
i
A
i
a
i
c
i
b
i

B
i
C
Figure 1: Ideal matrix converter with induction machine
TABLE IOUTPUT VOLTAGE AND INPUT CURRENT AS FUNCTION OF SWITCH CONFIGURATION, INPUT VOLTAGE AND OUTPUT CURRENT [6]
Output Voltage Input Current
Switch
Configuration
A B C
v
A
v
B
v
C
v
o
|v
o
|
Α v
o
i
a
i
b
i
c
i
i

|i
i
|
Α i
i
Group Mode
abcv
a
v
b
v
c
v
i
|v
i
|
Α v
i
i
A
i
B
i
C
i
o
|i
o
|

Α i
o
1
cabv
c
v
a
v
b
a v
i
|v
i
|
Α v
i
3
2 π
+
i
B
i
C
i
A
a² i
o
|i
o
|

Α i
o

3
4 π
+
2
bcav
b
v
c
v
a
a² v
i
|v
i
|
Α v
i
3
4 π
+
i
C
i
A
i
B
a i

o
|i
o
|
Α i
o

3
2 π
+
1
3
acbv
a
v
c
v
b
v
i
*
|v
i
|
-Α v
i
i
A
i
C

i
B
i
o
*
|i
o
|
-Α i
o
4
bacv
b
v
a
v
c
a v
i
*
|v
i
|
-Α v
i
3
2 π
+
i
B

i
A
i
C
a i
o
*
|i
o
|
-Α i
o

3
2 π
+
5
cbav
c
v
b
v
a
a² v
i
*
|v
i
|
-Α v

i
3
4 π
+
i
C
i
B
i
A
a² i
o
*
|i
o
|
-Α i
o

3
4 π
+
2
6
abbv
a
v
b
v
b

2/3 v
ab
2/3 v
ab
0i
A
- i
A
0 (1-a) 2/3 i
A
3
2
i
A
11
6
π
7
bccv
b
v
c
v
c
2/3 v
bc
2/3 v
b
c
00i

A
- i
A
(a-a²) 2/3 i
A
3
2
i
A
3
6
π
8
caav
c
v
a
v
a
2/3 v
ca
2/3 v
ca
0- i
A
0i
A
(a²-1) 2/3 i
A
3

2
i
A
7
6
π
9
aabv
a
v
a
v
b
-a² 2/3 v
ab
2/3 v
ab
3
π
- i
C
i
C
0 (a-1) 2/3 i
C
3
2
i
C
5

6
π
10
bbcv
b
v
b
v
c
-a² 2/3 v
bc
2/3 v
b
c
3
π
0- i
C
i
C
(a²-a) 2/3 i
C
3
2
i
C
9
6
π
11

ccav
c
v
c
v
a
-a² 2/3 v
ca
2/3 v
ca
3
π
i
C
0- i
C
(1-a²) 2/3 i
C
3
2
i
C
6
π
12
babv
b
v
a
v

b
a 2/3 v
ab
2/3 v
ab
3
2
π
i
B
- i
B
0 (1-a) 2/3 i
B
3
2
i
B
11
6
π
13
cbcv
c
v
b
v
c
a 2/3 v
bc

2/3 v
b
c
3
2
π
0i
B
- i
B
(a-a²) 2/3 i
B
3
2
i
B
3
6
π
14
acav
a
v
c
v
a
a 2/3 v
ca
2/3 v
ca

3
2
π
- i
B
0i
B
(a²-1) 2/3 i
B
3
2
i
B
7
6
π
15
baav
b
v
a
v
a
-2/3 v
ab
2/3 v
ab
π - i
A
i

A
0 (a-1) 2/3 i
A
3
2
i
A
5
6
π
16
cbbv
c
v
b
v
b
-2/3 v
bc
2/3 v
b
c
π 0- i
A
i
A
(a²-a) 2/3 i
A
3
2

i
A
9
6
π
17
accv
a
v
c
v
c
-2/3 v
ca
2/3 v
ca
π i
A
0- i
A
(1-a²) 2/3 i
A
3
2
i
A
6
π
18
bbav

b
v
b
v
a
a² 2/3 v
ab
2/3 v
ab
3
4
π
i
C
- i
C
0 (1-a) 2/3 i
C
3
2
i
C
11
6
π
19
ccbv
c
v
c

v
b
a² 2/3 v
bc
2/3 v
b
c
3
4
π
0i
C
- i
C
(a-a²) 2/3 i
C
3
2
i
C
3
6
π
20
aacv
a
v
a
v
c

a² 2/3 v
ca
2/3 v
ca
3
4
π
- i
C
0i
C
(a²-1) 2/3 i
C
3
2
i
C
7
6
π
21
abav
a
v
b
v
a
-a 2/3 v
ab
2/3 v

ab
3
5
π
- i
B
i
B
0 (a-1) 2/3 i
B
3
2
i
B
5
6
π
22
bcbv
b
v
c
v
b
-a 2/3 v
bc
2/3 v
b
c
3

5
π
0- i
B
i
B
(a²-a) 2/3 i
B
3
2
i
B
9
6
π
23
cacv
c
v
a
v
c
-a 2/3 v
ca
2/3 v
ca
3
5
π
i

B
0-i
B
(1-a²) 2/3 i
B
3
2
i
B
6
π
3
24
aaav
a
v
a
v
a
0 0 000 0 0 25
bbbv
b
v
b
v
b
0 0 000 0 0
26
cccv
c

v
c
v
c
0 0 000 0 0
4
27
Sector d
c
e
h
g
f
d
Sector c
e
h
g
f
7,8,9,
16,17,18
10,11,12,
19,20,21
13,14,15,
22,23,24
v
o
o
Sector n
p

s
r
q
i
i
7,10,13,
16,19,22
9,12,15,
18,21,24
8,11,14,17,20,23
Ψ
S
∆Ψ
S
a) b) c)
Figure 2 Hexagonal arrangements of space vectors. a) Output voltage vectors and sectors; b) input current vectors and sectors; c) output voltage
vector direction, stator flux
S
Ψ and changing of stator flux
S
Ψ∆
within one switching period T [8]
vectors situated in the middle of each sector. A similar
configuration exists for the input current vectors
(Fig. 2b)), here the current vectors are forming the sector
boundaries.
The principle of DTC is to keep stator flux and torque
within certain limits by compairing their actual values
with the reference values via two hysteresis controllers
[10]. Fig. 2c) shows a stator flux vector

S
Ψ within the
output voltage hexagon. The small hexagon at the tip of
this vector indicates the directions
S
Ψ∆ , in which the
stator flux vector may be changed within one switching
period T by application of one of the voltage vectors
which have different directions.
Analog to basic DTC for voltage source converters a
direction of output voltage is chosen according to the
output voltage sector and the output of the hysteresis
comparators for torque and flux C
T
and C
Ψ
, respectively.
These directions are given in Table 2, designated with V
0
to V
7
. If the output of the torque hysteresis controller is
zero, a zero switch configuration from group 4 is chosen.
In all other cases a basic voltage vector direction (V
1
V
6
)
is selected.
As there are always two voltage vectors which may be

chosen for one given combination of C
T
and C
Ψ
this gives
the possibility to control another quantity. Here the input
phase angle is chosen as the two possible voltage vectors
are always arranged on the sector boundaries of the
corresponding input current sector. The sine of the
estimated input phase angle is fed to a third hysteresis
comparator. With its output C
ϕ
and the voltage vector
direction from Table 2 the switch configuration which has
to be applied to the matrix converter can be taken from
Table 3. The numbers in this table denote mode according
to Table 1.
A block diagram of the complete system is given in
Fig. 3. The reference values for torque and flux are
compared with the estimated values. The output
coefficients of the hysteresis comparators are used
together with the sector numbers of stator flux and input
voltage vectors to determine the switch configuration
according to Tables 2 and 3. The lower part shows the
estimators for torque, flux and input phase angle. These
require the knowledge of both input and output current
and voltage. However, only input voltage and output
current are measured, so the remaining values are
calculated on the basis of measured values and switch
configuration of the matrix converter.

B. Sliding Mode Control
In [11] and [12] the design of a sliding mode controller
for a matrix converter is presented. This controller is able
to operate with leading or lagging input power factor and
shows a good robustness.
Sliding mode controllers have special interest in
systems with variable structure, such as power converters
[13, 14]. Their aim is to let the system slide along a
predefined sliding surface by changing the system
structure.
For designing the sliding mode controller, the source is
assumed to be a balanced sinusoidal three phase voltage
source with frequency ω
ι
. The output voltages are
assumed to be a similar balanced system with frequency
ω
o
. The reference values for sliding mode controller
design are the output voltages and input currents. For an
easier controller design the output voltages are
transformed into ‘αβ’ coordinates by applying the
Concordia transformation. The amplitude of the input
current references is calculated from the output currents
while the input phase angle is chosen in order to get the
desired power factor. The matrix converter real input
voltages and reference currents are then transformed into a
1
5
4

3
6
2
1
5
4
3
6
2
+
+
Switch
Configuration
Calculation
Matrix
Converter
Induction
Machine
{
{
Ψ
^
S
^
T
T
*
Ψ
S
∗

C
T
C
ϕ
C
Ψ
sin(
ϕ
i
)
v
i
v
i
i
o
Switch
Configuration
o
i
o
i
Torque
& Flux
Estimator
sin(ϕ
i
)
Estimator
sin(ϕ

i
)
^
T
i
o
i
i
v
i
v
o
Switch
Configuration
Ψ
^
S
Ψ
^
S
Figure 3: Block diagram of DTC with matrix converter and
induction machine [8]
TABLE II BASIC SWITCHING TABLE FOR DTC [8, 9]
C
ψ
=-1 C
ψ
=1
Sector
C

T
=-1 C
T
=0 C
T
=1 C
T
=-1 C
T
=0 C
T
=1
c
V
2
V
7
V
6
V
3
V
0
V
5
d
V
3
V
0

V
1
V
4
V
7
V
6
e
V
4
V
7
V
2
V
5
V
0
V
1
f
V
5
V
0
V
3
V
6

V
7
V
2
g
V
6
V
7
V
4
V
1
V
0
V
3
h
V
1
V
0
V
5
V
2
V
7
V
4

TABLE III FINAL SWITCHING TABLE FOR DTC [8, 9]
Sector
C
ϕ
V
1
V
2
V
3
V
4
V
5
V
6
+1 18 21 24 9 12 15
n
-17 1013161922
+18 1114172023
o
-1 18 21 24 9 12 15
+1 16 19 22 7 10 13
p
-18 1114172023
+19 1215182124
q
-1 16 19 22 7 10 13
+1 17 20 23 8 11 14
r

-19 1215182124
+17 1013161922
s
-1 17 20 23 8 11 14
reference frame synchronized with the voltage v
a
by
application of the Park transformation, so the input
currents in ‘dq’ coordinates are received.
To design the sliding mode controller according to
[11-14] first the system state space model has to be
obtained in phase canonical form. In this form the state
variable x
n
is represented by a linear combination of all
other state variables x
i
, i∈{1, ,n-1}. The system is then
constrained to have a dynamic
n
x
&
equal to the linear
combination of all
i
x
&
. This results in a sliding surface
S(x,t), see (2), which is defined as a linear combination of
all n state variables.

∑
=
==
n
i
ii
xktxS
1
0),( k
i
>0, i∈{1, ,n} (2)
In the special case of the matrix converter the output
voltages are directly dependent on the control inputs via
the switch combination, so they do not have associated
dynamic delays. The sliding surfaces should therefore be
dependent on the average values of the ‘ab’ components
of the reference voltages. In this case the controller
frequency has to be much higher than the desired output
and input frequency in order to guarantee that the average
output voltages are equal to their reference values. This
results in two sliding surfaces for output voltage control:
.0 and 0
0)(),(
0)(),(
0
*
0
*
>>
=−=

=−=
βα
β
α
ββ
β
αα
α
∫
∫
kk
dtvv
T
k
teS
dtvv
T
k
teS
o
T
ov
o
T
ov
o
o
(3)
The input currents are like the output voltages
discontinuous variables without associated dynamic

delays. From this the control laws are similar to those of
the output voltages and the sliding surfaces can be
obtained similarly. They are expressed as functions of the
input currents and their reference values.
0 and 0
0)(),(
0)(),(
0
*
0
*
>>
=−=
=−=
∫
∫
qd
i
T
q
i
i
T
i
d
i
kk
dtii
T
k

teS
dtii
T
k
teS
q
q
i
q
i
dd
d
i
(4)
In case the system slides along the defined surfaces it is
necessary to guarantee the stability condition
0 ),( ),( <txStxS
&
.(5)
For the designed sliding mode controllers (3, 4),
condition (5) can be written as:
0)()(
*
0
*
<−⋅−
∫
xxdtxx
T
k

T
.(6)
This condition is applied to all four sliding mode
controllers. It will be verified by following conditions:
a) If S(e
x
, t)<0 then S
&
(e
x
, t)>0. This leads to (6): if
0)(
0
*
<−
∫
T
dtxx
T
k
then (x
*
-x)>0, which implies x<x
*
.
b) If S(e
x
, t)>0 then S
&
(e

x
, t)<0. This leads to (6): if
0)(
0
*
>−
∫
T
dtxx
T
k
then (x
*
-x)<0, which implies x>x
*
.
To guarantee that the system is in sliding mode at each
moment a switch configuration has to be chosen, which
results in an output voltage vector verifying all four
stability constraints. The four sliding surfaces are
compared to zero by three level comparators. This results
in nine possible error combinations each for output
voltages and input currents.
()
()
()






>
<<
−<
=
ε
εε
ε
βα
teS
teS
teS
ee
x
x
x
iv
qdo
, 1
,- 0
, 1-
,
,,
(7)
From these combinations the control vector is selected,
which defines the switch configuration to be applied to the
matrix converter. The switch configurations used in this
control method are those with fixed angular position and
the zero configurations (groups 3 and 4). For practical
realisation the comparators are adopted with a hysteresis ε

instead of zero in order to reach a bounded switching
frequency instead of infinite switching frequency for ideal
controller operation.
According to the switching constraints presented in
section II it is easy to see: if only output voltage or input
current had to be controlled separately there would always
be at least one switch configuration which fulfills all error
combinations for all reference values. However when both
input current and output voltage are considered together
sometimes no possible switch configuration is present,
especially in case of desired leading or lagging power
factors. Another problem arises from the fact that the
matrix converter has no intermediate DC link so a chosen
switch configuration influences both input current and
output voltage. Hence a choice of the switch configuration
has to be employed which satisfies both demands to the
highest possible degree. This choice has to follow criteria
which guarantee controllability of the converter with
maximum output voltage and input power factor during
minimum output voltage and input current errors.
The choice of the demanded switch configuration starts
with output voltage control. From the comparator outputs
according to (7) at first a desired sector of output voltage
is chosen. In a second decision table the proper switch
configuration for this sector is chosen according to the
present location of the input voltage vector. For this
decision the 18 switch configurations of group 3 with
fixed angular position are used. A zero configuration is
chosen when all error outputs are zero, the rotating vectors
are not considered.

There exists always more than one possible switch
configuration for output voltage control, but this is not
enough for controlling both components of the input
current. However there is chance of choosing a switch
configuratio which will satisfy either the i
d
or i
q
current
error. In case that both voltage errors e
voα
and e
voβ
are
equal to zero, full input current control is possible.
For input current control the chosen switch
configurations must cause minimum output voltage error
in order to minimise output voltage ripple. The basic idea
is to maximize the time of e
voα
and e
voβ
equal to zero
because this maximizes the input current control range.
This leads to large decision tables depending on the four
error variables and the sections of input voltage and output
current. These tables are omitted here and can be found in
[11].
C. Direct Current Control (DCC)
In [15] and [6] a DCC method for matrix converters is

presented. It is based on the analysis of the matrix
converter’s transfer characteristics. By applying a
switching state to the matrix converter a certain voltage
space vector v
o
is generated at the output terminals and
vice versa an input current i
i
. In a first step the control of
the output current i
o
is examined.
In order to minimise the current control error
orefoo
iii −=∆
,
, the output voltage vector v
o
has to be in
the same direction as
o
i∆ because of the inductive
character of the load. In order to achieve this aim the
output voltage v
o
is discretised into six sectors of 60° and
the input voltage v
i
into 12 sections of 30° respectively.
For every section the output voltage v

o
is computed for
each switch configuration from Table I and the sector
number is put into a first decision table, see Fig. 4. From
this table the preferred switching state can be chosen. For
example the desired output voltage vector is located in
sector 6 because of an output current error in the same
sector. If the input voltage vector v
i
is located in the
section between 180° and 210° the switch configurations
2, 5, 13, 14 and 24 produce the desired output voltage.
There are always at least three switching states which
produce an output voltage vector with the desired
direction, so the output current could be easily controlled.
However the input current has to be controlled
simultaneously.
In order to control the input current a PD-controller is
used to determine the sector of the desired input current i
i
.
This controller is also necessary for active damping of
oscillations of the input current which arise from the low
cutoff frequency of the input filter and the relatively low
switching frequency of the converter. To complete the
input current control it has to be taken into account that
the output currents of the matrix converter are impressed
by the inductive load. The input currents are generated
from the output currents via the present switch
configuration of the converter.

The input current vector thus can be easily computed
from the present output current vector and the switch
configuration of the matrix converter. By applying a
discretisation as above this results in a second decision
table for the input current as a function of switch
configuration and output current, which is given in Fig. 5.
From this table the desired switch configuration for input
current control can be obtained. For example if the desired
input current is located in sector 2 and the output current
1122334455661
2344556611223
3566112233445
4166554433221
5322116655443
6544332211665
7114444441111
8111111444444
9444411111144
10225555552222
11222222555555
12555522222255
13336666663333
14333333666666
15666633333366
16441111114444
17444444111111
18111144444411
19552222225555
20555555222222
21222255555522

22663333336666
23666666333333
24333366666633
25000000000000
26000000000000
27000000000000
1
23
4
56
60°
Mode
v
a
120°
180°
240°
300°
360°
v
b
v
c
v
ac
v
ca
v
ab
v

ba
v
bc
v
cb
v
o
Figure 4 Sector of output voltage as function of mode and section
of input voltage [6]
1112233445566
2556611223344
3334455661122
4665544332211
5221166554433
6443322116655
7666333333666
8222555555222
9444111111444
10666663333336
11222225555552
12444441111114
13366666633333
14522222255555
15144444411111
16333666666333
17555222222555
18111444444111
19333336666663
20555552222225
21111114444441

22633333366666
23255555522222
24411111144444
25000000000000
26000000000000
27000000000000
60°
120°
180° 300°
240°
360°
i
A
i
B
i
C
Mode
1
2
3
4
5
6
i
i
Figure 5 Sector of input current as function of mode and section o
f
output current [6]
vector is in the section between 120° and 150°, switch

configurations 6, 11, 14 and 17 are suitable. If at the same
time the situation for the output current controller is as in
the example above, only mode 14 satisfies both controllers
simultaneously.
This results in two direct controllers for both output
current i
o
and input current i
i
. As there is not always a
switch configuration which satisfies both controller’s
demands, a third decision mechanism is applied. The flow
diagram of this mechanism is shown in Fig. 6: If both
control errors are small, a zero vector (group 4) is
selected. If a switch configuration exists which satisfies
both controllers simultaneously, this configuration is
chosen. In all other cases the weighted errors are
compared to each other and the decision table for the
controller with the larger error is taken into account.
Dependent on the magnitude of the error the switch
configuration producing the lowest, medium or largest
current amplitude is chosen.
In Fig. 7 a block diagram of the control is given. It
shows the PD-controller at the mains side, which
determines the desired input current sector and amplitude.
The sector of the input voltage vector is determined by a
PLL. The output currents are measured and their space
vector is determined. From the tables in Fig. 4 and 5 the
desired switch configurations are obtained. From these the
final switch configuration is determined by Fig. 6, which

is then applied to the converter. A more detailed
description of the whole control scheme is given in [15].
IV. C
OMPARISON
The three direct control methods presented in this paper
show various differences as well as similiarities. So both
DTC and sliding mode control use the same switch
configurations of groups 3 and 4 (vectors with fixed
angular position and zero vectors) while DCC uses the
rotating vectors of groups 1 and 2 additionally.
Implementations of all three controller types show good
steady state an dynamic behaviour. The common main
problem is the time consuming process of calculation and
decision of the demanded switch configuration. This leads
to a high demand for cpu power or restricts
implementations to a rather low switching frequency.
The higher number of usable voltage vectors with DTC
for matrix converters in comparison to voltage source
converters allows to control a third value next to torque
and flux. In this case the additional control of the input
power factor has been chosen. In addition as presented in
[8] the input current quality may be improved by using
both possible switch configurations for input power factor
control during one sample period, thus including a kind of
PWM in DTC.
The presented sliding mode controllers for matrix
converters have been tested in their realisation with
operation under a wide range of input phase angles. At a
step command in input phase angle from –70 to 70
degrees they show a good steady state and dynamic

behaviour. The step response shows a fast reaction to the
new demands without remarkable overcurrents or voltage
distortions.
V. C
ONCLUSION
Modern direct control methods for matrix converters
are presented. The basic ideas of DTC, sliding mode
control and DCC for matrix converter and induction
machine are outlined as they can be found in literature. All
of these methods have been both simulated and realised in
lab prototypes by the various authors. Differences and
similarities of the selected direct control methods are
pointed out.
R
EFERENCES
[1] A. Alesina, M.G.B. Venturini, “Analysis and Design of Optimum-
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Mains
Filter
Converter
x
low pass
filter
P
K
x
PLL
P-D-
controller
Mode
selection
I
i
*
I
i
*
I
i
*
I
i
V
i
I.M.

x
I
o
*
I
o
V
i
Figure 7 Block diagram of DCC system (according to [6])
Start controller
End of controller
medium
error
medium
error
low
error
low
error
take a
zero vector
use this mode
Is the line-side or the load-side control
error out of a tolerable margin?
Is there a mode which satisfies both
controllers simultaneously (Fig. 4&5)?
Is the weighted line-side control error
larger than the load-side error?
use group-3-mode
producing

load side amplitude
largest medium lowest
use group-3-mode producing
load side amplitude
largest medium lowest
line-side preferred
load-side preferred
y
y
y
y
y
y
y
n
n
nn
n
n
n
Figure 6 Flow diagram of DCC mode selection [6]
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