12-09-2012, 05:30 PM
Modelling, Analysis and Simulation of Matrix Converters
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Abstract
This paper analyzes the basic working principles
of Matrix Converters ( MC ) . A simple model is proposed
to represent the power circuit, including the input
filter. The MC is controlled using the direct transfer function
approach (Venturini method ). The control signals for
the power switches are generated in a very clear form. The
converter is simulated using Matlab- Simulink to allow for
using more sophisticated control strategies. As a result, a
very simple, flexible and effective simulation tool has been
developed, allowing the students for running their own simulations
and studies with very reduced effort. Practically all
major aspects in the operation and control of the MC can
be studied with this model.
Introduction
THE Matrix Converter is an array of bidirectional
switches as the main power elements, which interconnects
directly the power supply to the load, without using
any dc-link or large energy storage elements.
The most important characteristics of matrix converters
are: 1) simple and compact power circuit; 2) generation of
load voltage with arbitrary amplitude and frequency; 3) sinusoidal
input and output currents; 4) operation with unity
power factor; 5) regeneration capability. These highly attractive
characteristics are the reason for the tremendous
interest in this topology.
The development of this converter starts with the early
works of Venturini and Alesina, published in 1980 [1], [2].
They presented the power circuit of the converter as a matrix
of bidirectional power switches and they introduced
the name ”matrix converter”. Other major contribution of
these authors is the development of a rigorous mathematical
analysis to describe the low-frequency behavior of the
converter. In their modulation method, also known as the
direct transfer function approach, the output voltages are
obtained by the multiplication of the modulation matrix
with the input voltages. A conceptually different control
technique is introduced later, using the ”fictitious dc link”
idea [3], [4].
Power Circuit and Working Principle of the
Converter.
In general, the matrix converter (MC) is a single-stage
converter with m£n bidirectional power switches, to connect
an m-phase voltage source to an n-phase load. The
MC of 3 £ 3 switches, shown in Fig. 1, is the most important,
from a practical point of view, because it connects
a three-phase source to a three-phase load, typically
a motor. In the basic topology of the MC shown in Fig.1,
vsi; i = fA;B;Cg are the source voltages, isi; i = fA;B;Cg
are the source currents, vjn; j = fa; b; cg are the load voltages,
with respect to the neutral point of the load n and
ij ; j = fa; b; cg are the load currents.
The Commutation Problem.
In order to approximate the behavior of ideal bidirectional
switches, many technical feasible solutions have been
proposed. We will concentrate us in the most popular one,
and refer the interested reader to [8], [9] and [10].
The considered solution uses the topology of Fig. 2 to
implement a bidirectional switch. In Fig. 2 TA and TB
are simply IGBT transistors and D1 and D2 are diodes.
Due to D1 and D2, if both transistors are off, there will
be no current circulation, that is, the considered topology
can block voltages of any polarity. If, for example, V1 >
V2, TA is on and TB is off, it will be current flow in the
direction indicated by Fig. 2. In the contrary case, i.e. if
V1 < V2, TB is on and TA is off, it will be current flow in
the opposite direction. The previous characteristics make
the presented topology a bidirectional switch. It is worth
noting that, although the topology of Fig. 2 is the basis of
a bidirectional switch, the time required to turn on or off
an IGBT makes the commutation a non-trivial task.
Conclusions.
The working principle of the MC controlled with the direct
transfer function approach has been presented. All
necessary equations have been clearly explained and used
to obtain the block diagram for the simulation, which can
de easily understood with the approach used in this paper.
The model reproduces in a very good form the behavior
of the converter including the effect of the input filter.
In addition, other aspects like operation under abnormal
conditions and overmodulation can be easily and directly
simulated.