CASADEI et al.
: MATRIX CONVERTER MODULATION STRATEGIES 371
The input/output relationships of voltages and currents are
related to the states of the nine switches and can be written in
matrix form as
(1)
(2)
with
Fig. 1. Basic scheme of matrix converters.
(3)
In this paper, a new general and complete solution to the
problem of the modulation strategy of three-phase matrix con- The variables are the duty cycles of the nine switches
verters is presented. This solution has been obtained using the and can be represented by the duty-cycle matrix . In order
duty-cycle space-vector (DCSV) approach, which consists of a to prevent a short circuit on the input side and ensure uninter-
representation of the switch state by space vectors. In this way, rupted load current flow, these duty cycles must satisfy the three
the previously mentioned strategies can be considered as a par- following constraint conditions:
ticular case of the proposed one.
A review of the well-established modulation techniques is (4)
presented in the Section II of this paper. Then, in Section III, (5)
the new approach is illustrated in order to determine a general- (6)
ized modulation technique.
From this unitary point of view, some modulation techniques The determination of any modulation strategy for the matrix
are described and compared with reference to maximum voltage converter can be formulated as the problem of determining,
transfer ratio, number of commutations, and ripple of the input in each cycle period, the duty-cycle matrix that satisfies the
and output quantities. It should be noted that the analysis is con- inputoutput voltage relationships (1), the required instanta-
cerned with modulation techniques that do not utilize informa- neous input power factor, and the constraint conditions (3)(6).
tion about the output currents. The solution of this problem represents a hard task and is not
Finally, the paper emphasizes that the generalized SVM tech- unique, as documented by the different solutions proposed in
nique, obtained by using more than one zero configuration in literature.
each cycle period, represents the general solution to the problem It should be noted that in order to completely determine the
of the modulation strategy for matrix converters. modulation strategy it is necessary to define the switching pat-
tern, that is, the commutation sequence of the nine switches. The
use of different switching patterns for the same duty-cycle ma-
II. MODULATION DUTY-CYCLE MATRIX APPROACH trix leads to a different behavior in terms of the number of
switch commutations and ripple of input and output quantities.
The basic scheme of three-phase matrix converters is repre-
sented in Fig. 1. A. AlesinaVenturini 1981 (AV Method)
The switching behavior of the converter generates discon-
A first solution, obtained by using the duty-cycle matrix
tinuous output voltage waveforms. Assuming inductive loads approach, has been proposed in [1]. This strategy allows the
connected at the output side leads to continuous output cur- control of the output voltages and input power factor and can
rent waveforms. In these operating conditions, the instantaneous be summarized in the following equation, valid for unity input
power balance equation, applied at the input and output sides power factor ( ):
of an ideal converter, leads to discontinuous input currents. The
presence of capacitors at the input side is required to ensure con-
tinuous input voltage waveforms.
In order to analyze the modulation strategies, an opportune
converter model is introduced, which is valid considering ideal (7)
switches and a switching frequency much higher than input and
output frequencies. Under these assumptions, the higher fre- Assuming balanced supply voltages and balanced output con-
quency components of the variables can be neglected, and the ditions, the maximum value of the voltage transfer ratio is 0.5.
input/output quantities are represented by their average values This low value represents the major drawback of this modula-
over a cycle period . tion strategy.
