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Binder2 5

This document discusses selecting switching configurations for a matrix converter based on the output voltage sector and input current sector. It provides equations (14)-(17) to calculate the duty cycles of the four switching configurations based on the output voltage vector, input current vector, and their displacement angle. It notes that some duty cycles may be negative, indicating a negative switching configuration should be selected instead. It also provides an equation (18) to check the feasibility of the control strategy by ensuring the sum of absolute duty cycle values is less than 1.

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50 views1 page

Binder2 5

This document discusses selecting switching configurations for a matrix converter based on the output voltage sector and input current sector. It provides equations (14)-(17) to calculate the duty cycles of the four switching configurations based on the output voltage vector, input current vector, and their displacement angle. It notes that some duty cycles may be negative, indicating a negative switching configuration should be selected instead. It also provides an equation (18) to check the feasibility of the control strategy by ensuring the sum of absolute duty cycle values is less than 1.

Uploaded by

vainateyagoldar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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374 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 49, NO.

2, APRIL 2002

TABLE II
SELECTION OF THE SWITCHING CONFIGURATIONS FOR EACH COMBINATION OF OUTPUT VOLTAGE AND INPUT CURRENT SECTORS

the requirements of the reference output voltage vector and input


(16)
current displacement angle. With reference to the output voltage
vector, the following two equations can be written:

(17)
(9)
Equations (14)–(17) have a general validity and can be applied
to any combination of output voltage sector and input cur-
rent sector .
(10) It should be noted that, for any sector combinations, two of
the duty cycles calculated by (14)–(17) assume negative values.
With reference to the input current displacement angle, This is due to the assumption made of using only the positive
two equations are obtained by imposing on the vectors switching configurations in writing the basic equations (9)–(12).
and the direction defined A negative value of the duty cycle means that the corresponding
by . This can be achieved by imposing a null value on the negative switching configuration has to be selected instead of
two-vector component along the direction perpendicular to the positive one.
(i.e., ), leading to Furthermore, for the feasibility of the control strategy, the
sum of the absolute values of the four duty cycles must be lower
(11)
than unity as
(12)
(18)
In (9)–(12) and are the output voltage and input current
phase angle measured with respect to the bisecting line of the The zero configurations are applied to complete the cycle
corresponding sector and differ from and according to the period.
output voltage and input current sectors. In these equations, the Introducing (14)–(17) into (18), after some manipulations,
following angle limits apply: leads to the following equation:

(13)
(19)
, , and , are the duty cycles (i.e., ) of
the four switching configurations, represents Equation (19) represents, at any instant, the theoretical max-
the output voltage sector, and represents the imum voltage transfer ratio, which is dependent on the output
input current sector. are the output voltage voltage and input current phase angles and the displacement
vectors associated respectively with the switching configura- angle of the input current vector. It is useful to note that, in the
tions I, II, III, IV given in Table II. The same formalism is used particular case of balanced supply voltages and balanced output
for the input current vectors. voltages, the maximum voltage transfer ratio occurs when (19)
Solving (9)–(12) with respect to the duty cycles, after some is a minimum (i.e., when and are equal to 1),
tedious manipulations, leads to the following relationships [10]: leading to

(20)

(14) Assuming unity input power factor, (20) gives the


well-known maximum voltage transfer ratio of matrix
(15)
converters 0.866.

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