Modulation Method for Matrix Converter Alesia and Venturini Method

An intensive research interest in the field of matrix converter started with the
publishing of the paper about matrix converter by alesia and venturini in 1981.In
this paper they proposed a duty cycle approach towards the matrix converter problem.
Initially the problem of the papers it has only limited voltage transfer ratio of 0.5. The
aim when using the Alesina and Venturini modulation method is to find a modulation
matrix which satisfies the following set of equations.
v0 (t) = m(t).vi (t) (2.4)
ii (t) = m(t)T .i0 (t) (2.5)
The elements of m(t) that satisfies the above two equations are
mij (t) = 1/3 ∗ α1 {1 + q ∗ cos[(ω0 − ωi ) + 2/3 ∗ π ∗ (i − j)]}+
1/3*α2 {1 + q ∗ cos[(ω0 − ωi ) + 2/3 ∗ π ∗ (2 − i − j)]}(2.6)
where
α1 = 1/2[1 + (tan(φi )/tan(φ0 ))] (2.7)
α2 = 1 − α1 (2.8)
q = V0 /Vi (2.9)
In 1989 both the anthers proposed a new optimum AV method with improved
voltage transfer ratio of 0.866. In addition to this using this method we can improve the input power factor control.

Simplified matrix converter model

A simplified three phase matrix converter model is shown in Figure below and
consists of 9 ideal bidirectional switches which allows each of the three output lines to be connected to any of the three input lines. The three converter inputs are connected to a 3 phase system, vR , vS , vT , which represent the voltages after the input filter. The output lines are connected to a three phase current source, iA , iB and iC , which acts as the load. Input voltages and output currents are given by equations given below.

where vR , vS and vT are three-phase input sinusoidal voltages and Vin is the peak
value of the input voltages. Assuming that the output voltage waveforms are sinusoidal and assuming a linear load, the output currents iA , iB and iC are also sinusoidal. Iout is the peak value of the output currents and φo is the phase between output voltages and currents. ωi and ωo are the input and output angular frequencies respectively. The column matrices viP h and ioP h provide a compact mathematical form of expressing the input voltages and output currents, respectively.
The nature of these voltage and current sources leads to restrictions on the possible states of the matrix converter switches. Firstly, lines which are connected to a low impedance source must never be short-circuited. If these lines are short-circuited, the current rises to a value that will destroy the semiconductor switches. Also, lines connected to a high impedance source must not be left open-circuited. The converter must always provide a path for the output current. In order to fulfil these restrictions, only one of the three switches associated with each output line must be closed at any given time. Using the existence function of each switch, the constraints can be expressed as

sj1 + sj2 + sj3 = 1J ∈ 1, 2, 3

These constraints lead to only 27 possible combinations of switches or states
of a three phase matrix converter.

Basic Current Commutation in Matrix Converter

Reliable current commutation between switches in matrix converters is more
difficult to achieve than in conventional VSI's since there are no natural free wheeling paths. The commutation has to be actively controlled at all times with respect to two basic rules. These rules can be visualized by considering just two switch cells on one output phase of a matrix converter. It is important that no two bidirectional switches are switched on at any instant. This would result in line-to-line short circuits and the destruction of the converter due to over currents. Also, the bidirectional switches for each output phase should not all be turned off at any instant. This would result in the absence of a path for the inductive load current, causing large over voltages. These two considerations cause a conflict since semiconductor devices cannot be switched instantaneously due to propagation delays and finite switching times.
The two simplest forms of commutation strategy intentionally break the rules
given above and need extra circuitry to avoid destruction of the converter. In overlap current commutation, the incoming cell is fired before the outgoing cell is switched off.
This would normally cause a line-to-line short circuit but extra line inductance slows
the rise in current so that safe commutation is achieved. This is not a desirable method since the inductors used are large. The switching time for each commutation is also greatly increased which may cause control problems.
Dead-time commutation uses a period where no devices are gated, causing
a momentary open circuit of the load. Snubber's or clamping devices are then needed across the switch cells to provide a path for the load current. This method is undesirable since energy is lost during every commutation and the bidirectional nature of the switch cells further complicates the snubber design. The clamping devices and the power loss associated with them also results in increased converter volume.

Bi-directional switch realisation in matrix converters

Reliable current commutation between switches in matrix converters is more
difficult to achieve than in conventional VSIs since there are no natural free wheelin paths. The commutation has to be actively controlled at all times with respect to two
basic rules. These rules can be visualized by considering just two switch cells on one
output phase of a matrix converter. It is important that no two bidirectional switches
are switched on at any instant. This would result in line-to-line short circuits and the
destruction of the converter due to over currents. Also, the bidirectional switches for
each output phase should not all be turned off at any instant. This would result in the
absence of a path for the inductive load current, causing large over voltages. These
two considerations cause a conflict since semiconductor devices cannot be switched
instantaneously due to propagation delays and finite switching times.
The two simplest forms of commutation strategy intentionally break the rules
given above and need extra circuitry to avoid destruction of the converter. In overlap current commutation, the incoming cell is fired before the outgoing cell is switched off.
This would normally cause a line-to-line short circuit but extra line inductance slows
the rise in current so that safe commutation is achieved. This is not a desirable method since the inductors used are large. The switching time for each commutation is also greatly increased which may cause control problems.
Dead-time commutation uses a period where no devices are gated, causing
a momentary open circuit of the load. Snubber or clamping devices are then needed
across the switch cells to provide a path for the load current. This method is undesirable since energy is lost during every commutation and the bidirectional nature of the switch cells further complicates the snubber design. The clamping devices and the power loss associated with them also results in increased converter volume.

MATRIX CONVERTER upto now

The first analysis of all-silicon converter structures was carried out by L. Gyur-gyi
and B. R. Pelly in 1976[8]. The Unrestricted Frequency Changer (UFC), which was the
name that they gave to the converter. UFC was possible to cite bilateral power flow,
unlimited output frequency range, good input voltage utilisation and no input current and output voltage subharmonic components. The converter required only nine bilateral switches and had relatively low switching frequencies. The main disadvantage of the UFC structures treated in was that they generated large unwanted input current and output voltage harmonics. The order of these harmonics was generally low which made them difficult to filter out. So UFC is fail to impress as a all-siliconn converter. A major advance in the modulation theory of matrix converters was made by A. Alesina and M. Venturini in 1981[1]. The name matrix converter was given by these two. They partially solved the main disadvantage of the UFC with the introduction of PWM voltage control scheme which can eliminate athe unwanted harmonics by a greather amount. Unfortunately, the proposed scheme had a serious drawback. The maximum output to input voltage ratio that could be achieved was only 0.5. The same two authors later proposed an improved method which increased the output/input ratio to 0.866 by adding zero sequence components to the desired output voltages . Space vector modulation techniques were first employed by Huber in 1989 to control a 3 phase-3 phase matrix converter. Although it was possible to obtain the maximum output input voltage ratio using this technique, it was not possible to control input current displacement factor. After a while the same authers put forward a new paper that uses space vector PWM approach in both input as well as output. By using SVPWM in input and output we obtained a more sinusoidal input current and control of input displacement factor[6].
A drastically different waveform synthesis approach was proposed by P. Zio-
gas[9]. They split the matrix converter into a fictitious rectifier and a fictitious inverter and instead of using the matrix converter to assemble its output voltage directly from consecutive chops of the input voltage, the input voltage was first rectified to create a fictitious dc bus and then inverted at the required output frequency. This technique was referred as the indirect function approach and it allowed the use of well-known techniques for controlling the fictitious rectifier and inverter. A paper by Huber resented a modulation technique which employed space vectors in both the rectifier and inverter.
The use of space vector modulation at the input end allows sinusoidal input current
and control of the input displacement factor. After that many different approaches have been proposed in matrix converter topology includig predictive current loop techniques,fuzzy logic control, hysteresis current control,sliding control modulation etc.[5].















[1] M. Venturini and A. Alesina, “The generalized transformer: A new bidirec-
tional sinusoidal waveform frequency converter with continuously adjustable in-
put power factor,”in Proc. IEEE PESC‘80, 1980, pp. 242 to 252.
[2] Jiacheng Wang,Bin Wu,Dewei (David) Xu,and Navid R. Zargari, “Indirect Space
Vector Based Modulation Techniques for High-Power Multi-Modular Matrix Con-
verters”,.
[3] Patrick W. Wheeler,Jose Rodriguez,Jon C. Clare,Lee Empringham and Alejandro
Weinstein,Matrix Converters: A Technology Review IEEE TRANSACTIONS
ON INDUSTRIAL ELECTRONICS”, VOL. 49, NO. 2, APRIL 2002.
[4] Amit Kumar Gupta,and Ashwin M. Khambadkone,‘Space Vector PWM Scheme
for Multilevel Inverters Based on Two-Level Space Vector PWM”,IEEE TRANS-
ACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 53, NO. 5, OCTOBER
2006.
[5] Roberto A. Petrocelli,“New modulation method for matrix converters”,A thesis
submitted to the University of Manchester for the degree of Doctor of Philosophy.

MATRIX CONVERTER Introduction

Matrix converters are AC to AC power converter topology that can generate required amplitude and frequency AC sinusoidal wave form conventional AC source
based mainly on semiconductor switches with minimal requirement for passive components. It consist of nine bi-directional switches arranged in matrix manner such that any input phase can be directly connected to any output phase. In most of the cases a three input three output converter will consist of bidirectional switches arranged in 3 row and 3 column manner resembles to a matrix of nine bi-directional switches, hence the term ‘Matrix converter ’. The process of switching on and off the bidirectional switche made the variable frequency and amplitude signals at the output of the matrix converter.
The matrix converters are intensively researched area in the last decade. This
interest is reflected in the number of articles that are published in the field of matrix
converter. This interset is mainly due to the fact that a all-silicon converter that can
completely replace the conventional AC-DC-AC inverters. The matrix converter can
provide the amplitude and frequency conversion, bi-directional power flow and input displacement factor control without the presence of bulky life limitted capacitors and other passive elements.
Despite of advantage of matrix converters, they are not used commonly in most
of the industries. There are several reasons for the selection of conventional AC-DC-AC inverter over the matrix converter. Firstly, Even though the matrix converter topology was started in 1970 breaktrough in the field of the matrix converter happned in last decade.So still its considered as a new technology. Secondly, the number of the semiconductor switches in a matrix converter is greater than the number used in a DC-link converter. Therefore, the cost of implementation of a matrix converter is larger than a conventional dc-link converter of the same ratings.Finally, the amplitude of the output voltages generated by a matrix converter is limited to 0.866 of the input voltage amplitude for the most popular modulation methods. Therefore, electrical motors or any other standard device connected as load to a matrix converter do not operate at their nominal rated voltage.
Even though Matrix converter has some disadvantages its very attractive for
some application. Firstly, there are applications where energy storage elements like
capacitors and inductors are to be avoided. For example, the large electrolytic capacitors of a dc-link converter is one of the elements that decreases the reliability of the converter. Secondly, the cost of power semiconductors continues to fall and there is no evidence to suggest that this trend will change for the future. On the other hand, the real cost of energy storage elements is not falling. For this reason, matrix converters will became increasingly more cost competitive. Thirdly, a matrix converter is a very attractive solution when regeneration is required. The bidirectional power flow capability and input displacement factor control of matrix converters make them an ideal solution for same application. Finally, there are applications where the converter size, weight and performance is of major concern. The lack of bulky energy storage elements and the integration of semiconductors in power modules specifically designed for matrix converters mean that large power density factors are achievable employing matrix converters.
In this paper proposed a new multilevel modulation technique by cascading
the H-bridge inverter and rectifier. In indirect matrix converter inveter side and rectifier side are seperated and they are connected by fictious DC link. The MMMCs are similar to the cascaded H-bridge (CHB) converter in both structure and features such as modular design, good waveform quality, and allowing the use of low voltage power devices. Besides, they have inherent four quadrant operation capability and can be used iregenerative applications. Regarding modulation strategy, none of those for operating the CHB converter or the conventional MCs can be directly borrowed for the MMMCs.
This paper is dedicated to the design of indirect space vector based modulation techniques for the MMMCs.