Control of three phase matrix frequency converters on base of first harmonics method in space with two time variables
A procedure for the synthesis of control signals for three phase matrix frequency converters is presented. The procedure is based on extension of the space of one time variable to the space with two time variables. An expansion of control signals in Fourier series is use.
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Інститут електродинаміки НАН України
2012
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| Zitieren: | Control of three phase matrix frequency converters on base of first harmonics method in space with two time variables / I.Ye. Korotyeyev, M. Klytta // Технічна електродинаміка. — 2012. — № 2. — С. 55-56. — Бібліогр.: 2 назв. — англ |
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Korotyeyev, I.Ye. Klytta, M. 2014-05-16T16:44:17Z 2014-05-16T16:44:17Z 2012 Control of three phase matrix frequency converters on base of first harmonics method in space with two time variables / I.Ye. Korotyeyev, M. Klytta // Технічна електродинаміка. — 2012. — № 2. — С. 55-56. — Бібліогр.: 2 назв. — англ 1607-7970 https://nasplib.isofts.kiev.ua/handle/123456789/62103 621.314 A procedure for the synthesis of control signals for three phase matrix frequency converters is presented. The procedure is based on extension of the space of one time variable to the space with two time variables. An expansion of control signals in Fourier series is use. en Інститут електродинаміки НАН України Технічна електродинаміка Перетворення параметрів електричної енергії Control of three phase matrix frequency converters on base of first harmonics method in space with two time variables Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Control of three phase matrix frequency converters on base of first harmonics method in space with two time variables |
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Control of three phase matrix frequency converters on base of first harmonics method in space with two time variables Korotyeyev, I.Ye. Klytta, M. Перетворення параметрів електричної енергії |
| title_short |
Control of three phase matrix frequency converters on base of first harmonics method in space with two time variables |
| title_full |
Control of three phase matrix frequency converters on base of first harmonics method in space with two time variables |
| title_fullStr |
Control of three phase matrix frequency converters on base of first harmonics method in space with two time variables |
| title_full_unstemmed |
Control of three phase matrix frequency converters on base of first harmonics method in space with two time variables |
| title_sort |
control of three phase matrix frequency converters on base of first harmonics method in space with two time variables |
| author |
Korotyeyev, I.Ye. Klytta, M. |
| author_facet |
Korotyeyev, I.Ye. Klytta, M. |
| topic |
Перетворення параметрів електричної енергії |
| topic_facet |
Перетворення параметрів електричної енергії |
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2012 |
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English |
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Технічна електродинаміка |
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Інститут електродинаміки НАН України |
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Article |
| description |
A procedure for the synthesis of control signals for three phase matrix frequency converters is presented. The procedure is based on extension of the space of one time variable to the space with two time variables. An expansion of control signals in Fourier series is use.
|
| issn |
1607-7970 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/62103 |
| citation_txt |
Control of three phase matrix frequency converters on base of first harmonics method in space with two time variables / I.Ye. Korotyeyev, M. Klytta // Технічна електродинаміка. — 2012. — № 2. — С. 55-56. — Бібліогр.: 2 назв. — англ |
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AT korotyeyeviye controlofthreephasematrixfrequencyconvertersonbaseoffirstharmonicsmethodinspacewithtwotimevariables AT klyttam controlofthreephasematrixfrequencyconvertersonbaseoffirstharmonicsmethodinspacewithtwotimevariables |
| first_indexed |
2025-11-27T02:52:36Z |
| last_indexed |
2025-11-27T02:52:36Z |
| _version_ |
1850795506669715456 |
| fulltext |
ISSN 1607-7970. . 2012. 2 55
621.314
CONTROL OF THREE PHASE MATRIX FREQUENCY CONVERTERS
ON BASE OF FIRST HARMONICS METHOD IN SPACE WITH TWO TIME VARIABLES
I. Ye. Korotyeyev (*), M. Klytta (**),
(*) University of Zielona Góra, Institute of Electrical Engineering,
Podgórna50, 65-246 Zielona Góra, Poland,
Tel. (+48 68) 3282 626, Fax (+48 68) 3254 615, E-mail: I.Korotyeyev@iee.uz.zgora.pl.
(**) University of Applied Sciences Mittelhessen, Department of Electrotechnics and Information Technology,
Wiesenstrasse 14, 35-390 Giessen, Germany,
Tel. (+49 641) 309 1930, Fax. - 309 2941, E-mail: Marius.Klytta@ei.thm.de.
A procedure for the synthesis of control signals for three phase matrix frequency converters is presented. The
procedure is based on extension of the space of one time variable to the space with two time variables. An expansion of
control signals in Fourier series is use. References 2, figure 1.
Key words: control synthesis, matrix frequency converter, first harmonic method, two time variables.
Let us consider a three phase matrix frequency converter (MFC) presented in Figure.
The switches aAS … cCS shown in Figure are ideal. They are turned
on and off periodically with durations defined by a matrix
( )
aA aB aC
bA bB bC
cA cB cC
d d d
t d d d
d d d
M .
The best known strategies used for control of such MFC are developed [1].
It has been shown [2] that the above mentioned control strategy is not
single-valued. In this article we consider method based on extension of the
space of one time variable to the space with two time variables and control
signals expansion in Fourier series. A synthesis of control signals is realized
using their presentation as sum of steady components and first harmonics.
Coupling between input and output voltages describes the equation
( )tV M E (1)
and between output and input currents the relation
( )T otI M I , (2)
where
cos
cos( 2 / 3)
cos( 4 / 3)
i
i
i
E t
E t
E t
E ,
cos( )
cos( 2 / 3 )
cos( 4 / 3 )
o L
o L
o L
V t
V t
V t
V ,
cos( )
cos( 2 / 3 )
cos( 4 / 3 )
i
i
i
I t
I t
I t
I ,
cos( )
cos( 2 / 3 )
cos( 4 / 3 )
o L
o
o L
o L
I t
I t
I t
I
are vectors of input and output voltages and currents with and L as frequencies of input and output signals.
Since the above cosines functions depend on three variables , L and t identically, we could replace them in the
following way
t , t , L . (3)
Let us assume that coefficients of the matrix ( )tM are periodical and are described by steady components and first
harmonics 0
1 1 1 1sin( ) cos( )k k k km m m t m t , where coefficients 0
1km , 1
s
km , 1
c
km might depend on time , 1,2,3k .
In order to find these coefficients let us multiply first row of matrix ( )tM by the vector E and expand the result in
Fourier series. We obtain in this way four equations. Two further equations result using conditions that input circuits
should not be shorted and output circuits cannot be opened, i.e. ( )t1 M 1 (where 1 is the unit vector). After solving of
these equations we get
0
11
1
3
m ; 13 1
11
6 ( 3 ) 2 (3 3) sec
( 3 3 )(3 3)
s
s m tg cs
m
tg
; 1 13
11
2( 3 cos sin )( 3 )
3 3 cos 2 3sin 2
s
c cs m seq
m .
The variables 1cs , 2cs and 3cs in above coefficients are elements of the vector V and depend on time . We
can determine all other coefficients nkm in the same way. These coefficients depend on 23
sm , 2cs and 33
sm , 3cs .
In order to find the coefficients 13
sm , 23
sm and 33
sm one uses (2) and after additional analyses they could be
chosen as follows 3 / 3s
n nm cs . After substitution one obtain the following expressions
A
B
C
a b c
aAS bAS cAS
aBS bBS cBS
aCS bCS cCS
1e
2v
2e
3e
1v 3v
oi
3
1i
2i
3i
oi1
oi2
mailto:I.Korotyeyev:@iee.uz.zgora.pl
mailto:Marius.Klytta:@ei.thm.de
56 ISSN 1607-7970. . 2012. 2
11 1 2 cos( ) cos( ) 3( 1) sin( ) / 3m q t t ;
12 1 cos( ) (3 2) cos( ) 3( 2) sin( ) / 3m q t t ;
13 1 cos( ) (3 4)cos( ) 3 sin( ) / 3m q t t .
Other coefficients can be written by shifting the argument of cosines in the following way 2 / 3 , 4 / 3 .
Then first elements of the vectors of the output voltage V calculated by (1) have the form
cos 3( 1)sin cos( )q , and the input current I calculated by (2) is as follows cos( )q
cos( ) 3( 1)sin( )t t . Other elements of the vectors V and I are obtained by similar shifting of arguments
2 / 3 , 4 / 3 and 2 / 3 , 4 / 3 . We can transform parts of these expressions in the
following way 2cos 3( 1)sin 1 3 1 cos( ) , cos( ) 3( 1)sin( )t t
21 3 1 cos( )t , where 3( 1)arctg .
Multiplying input and output vectors of current and voltage one finds input and output power of MFC
23 1 3 1 cos( ) cos( ) / 2q .
In order to obtain signals in the space of one time variable we use the substitution opposite to (3).
The synthesized control could change both the amplitude of output voltages and the amplitude and phase shift of
input currents. The power factor equal 1.0 could be obtained.
It should be noted that obtained expressions could be also transformed in expressions given in [1].
1. Alesina A., Venturini M. Solid State Power Conversion: A Fourier Analysis Approach to Generalized Transformer
Synthesis // IEEE Transactions on Circuits and Systems. 1981. Vol. 28. No. 4. Pp. 319–330.
2. Korotyeyev I.Ye., Klytta M. Solution of equations defining transformation rules of three phase matrix frequency
converters // Tekhnichna Elektrodynamika. Tematychnyi vypusk " Sylova elektronika ta energoefektyvnist". 2011. Vol. 1. Pp.
154–156.
. (*), . (**)
(*) , ,
. , 50, 65-246, . , .
. (+48 68) 3282 626, Fax (+48 68) 3254 615, E-mail: I.Korotyeyev@iee.uz.zgora.pl
(**)University of Applied Sciences Mittelhessen,
14, 35-390, . ,
Te . (+49 641) 309 1930, . - 309 2941, E-mail: Marius.Klytta@ei.thm.de.
c 3- .
.
. . 2, . 1.
: , , , .
3-
. , .
, ,
. , 50, 65-246, . ,
. (+48 68) 3282 626, Fax (+48 68) 3254 615, E-mail: I.Korotyeyev@iee.uz.zgora.pl
(**)University of Applied Sciences Mittelhessen,
14, 35-390, . ,
Te . (+49 641) 309 1930, . - 309 2941, E-mail: Marius.Klytta@ei.thm.de.
3- .
. -
. . 2, c. 1.
: , , , .
20.12.2011
Received 20.12.2011
mailto:I.Korotyeyev:@iee.uz.zgora.pl
mailto:Marius.Klytta:@ei.thm.de
mailto:I.Korotyeyev:@iee.uz.zgora.pl
mailto:Marius.Klytta:@ei.thm.de
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