**High power semiconductor components are changing the scenery for reactive power control in the transmission and distribution sector. The matrix converter is one such reactive power control device which has been enabled by such components and which is finding applications in this field.**

Current and classical methods of reactive power compensation include fixed capacitor and reactor banks, static VAR compensators (SVC) and Statcom devices. Solutions, such as Statcom, DVR and SVC systems, tend to deal with one problem only, such as harmonics or reactive power. Static shunt compensators suffer from source voltage oscillations, while, static series compensators cannot operate in nonlinear load condition correctly [1]. There are two ways of influencing voltage and current of a transmission line: Series FACTS devices (series converter) or SSSC (static synchronous series compensator) are used to control the series injecting voltage and phase angle through a series transformer. Shunt FACTS device (SVC) or Statom (static synchronous compensator) are used to control the reactive power flow and current in the transmission line. By combining both shunt and series connected converter, the basic unified power flow controller (UPFC) configuration is obtained (Fig. 1).

The heart of the UPFC is the AC/AC converter, which is commonly realised by using back to back converters connected via a DC link. The design may be improved by making use of matrix converters.

*Matrix converter (MC) basics*

The MC is a direct AC to AC converter with the ability to control voltage and phase angle and is basically a power device without a DC energy storage element. The MC is exactly what the name implies, a matrix of semiconductor switches that connects the incoming conductors to the outgoing conductors. Input and output filters allow waveform shaping. Each incoming conductor is connected to each outgoing conductor. The output waveform is controlled by driving the switches between on and off state (chopping) in accordance with a switching algorithm. The basic form is shown in simple form for a three phase system in Fig. 2. The switches S represent bidirectional semiconductor devices.

The MC converter technique has been around for many years, but development has been restricted by the lack of suitable high power and high speed semiconductor device . Availability of devices such as the silicon carbide transistor have made it possible to realise the full potential of the technology.Matrix converters achieve three-phase AC/AC conversion without any intermediate energy storage element. This has the potential to increase power density (output power per converter volume) significantly. Furthermore, omitting the electrolytic capacitor in the DC link improves the system reliability. Output current is thus drawn directly from the input, and there is no intermediate stage. One of the advantages of the MC is that the energy required for applying the controls is obtained directly from the incoming line and not from a stored energy source, as would be the case with Statcom, SVC and DVR systems.

**MC operation**

The input waveform is divided into time segments, and within each segment, samples of varying width of each input phase are combined in a sequence to produce the required output waveform. The chopped input waveform segments combine in a sequential manner to form a continuous output waveform, of the required frequency and phase angle. The sampling rate has to be set much higher than both input and output frequencies, and the duration of each sample is controlled in such a way that the average value of the output waveform within each sample period tracks the desired output waveform. This is illustrated in a very simple format in Fig. 3 for the circuit shown in Fig. 1. The output waveform will depend on the switching algorithm used ,and several different waveforms can be used to achieve the same output.

**Matrix converter forms**

The MC has developed into two basic forms, the conventional matrix converter (CMC) and the indirect matrix converter (IMC). The CMC has the form shown in Fig. 2,while the IMC consists of two stages as shown in Fig 4.

The IMC consists of two stages, a rectifier feeding the DC link, and a converter. The DC link does not contain a storage element. It is possible to simulate this configuration based on the CMC configuration when analysing CMC control methods. This method is used when applying SVM techniques to CMC.**Switching control methods**

With nine bi-directional switches, the matrix converter can theoretically assume 512 (2^{9}) different combinations of switching states, but not all of them can be usefully employed. Regardless to the control method used, the choice of the matrix converter switching states combinations (matrix converter configurations) to be used must comply with two basic rules. Taking into account that the converter is supplied by a voltage source and usually feeds an inductive load, the input phases should never be short-circuited and the output currents should not be interrupted. From a practical point of view these rules imply that one and only one bi-directional switch per output phase can be switched on at any instant. By this constraint, in a three phase to three phase matrix converter the permitted switching combinations are 27 (3^{3}) [1].

A number of control and modulation methods have been developed for the MC. The first and highly relevant method is called the direct transfer function approach, also known as the Venturini method [3]. Here, the output voltage is obtained by the product of the input voltage and the transfer matrix representing the converter. A very important solution for the control of MCs comes from the use of pulse width modulation (PWM) techniques previously developed for voltage source inverters. The simplest approach is to use carrier-based PWM techniques. An alternative powerful solution currently in use is to apply space-vector modulation (SVM) in MCs.

In all methods each cycle is divided into equally sized sampling intervals. During the sampling intervals the switches connect each input line to an output in sequence. Considering one of the output phases, *V _{a}*, each input phase is connected in sequence to the output phase. For a balanced three phase system, the instantaneous sum of the three input phase voltages is always zero. If the connection times of the three phases during the sampling interval

*Venturini method*

In the converter control strategy proposed by Venturini the average output voltage in each arm of the matrix converter is obtained from samples of input voltages. In Venturini modulation, each arm of the converter is switched sequentially within a sampling period *T _{s}*. Considering only one arm of the matrix converter, in this case three-phase to one-phase, there are three switches in each interval sampling and the time intervals in each switching called

Many control strategies based on PWM methods which allow for output voltage regulation while maintaining unity power factor on the input side have been applied to different kinds of MCs, For simplicity, consider a carrier-based modulation method applied to a three-phase-to-single-phase MC, which can be easily extended to a three-phase-to-three-phase or multilevel converter. The technique is based on a sinusoidal PWM (SPWM), which is a well-known shaping technique in power electronics where a high-frequency triangular carrier signal is compared with a sinusoidal reference signal. In this method, the switching pulses are generated by using a logical table as a function of the input voltages and the desired levels on the output side. An example of the unfiltered output voltage obtained by this method is given in Fig. 7.

*Space vector modulation*

The space-vector approach is a pulse width modulation method based on the instantaneous space vector representation of input and output voltages and currents. Among the 27 possible switching configurations available in three-phase MCs, only 21 are useful in the SVM algorithm. The first 18 switching configurations determine an output voltage vector and an input current vector, having fixed directions (Fig. 8). The magnitude of these vectors depends upon the instantaneous values of the input voltages and output line currents, respectively. The last three switching configurations determine zero input current and output voltage vectors. The SVM algorithm for MCs has the inherent capability to achieve full control of both the output voltage vector and the instantaneous input current displacement angle. currents, respectively.

Fig. 9 shows the output waveform of a SVM modulated MC [4].

Barriers hindering development include, among others, a lack of semiconductor components in more complex modules than single transistors. Bi-directional switches are used in the converters. Basic configurations of such bidirectional switches made in Si technology are presented in Fig. 10. Such configurations of Insulated Gate Bipolar Transistors (IGBTs) and diodes allow conducting currents in both directions and blocking voltages for positive and negative polarity.

The bi-directional switch must be able to block direct and reverse voltage and to conduct the current in both directions, and is one of the major challenges for the power stage design of a three-phase to three-phase matrix converter, as few are available in the market.and it is cheaper to build the bi-directional power switch using discrete components.

Another problem, tightly related to the bi-directional switches implementation, which has represented a main obstacle to the industrial success of the matrix converter, is the commutation problem. The commutation issue basically rises from the absence, in the matrix converters, of static freewheeling paths. As consequence it becomes a difficult task to safely commutate the current from one bi-directional switch to another, since a particular care is required in the timing and synchronisation of the switching pulses.

*Input filter*

Although the matrix converter is sometimes presented as an all silicon solution, due to the lack of the bulky and expensive DC-link capacitors of traditional indirect frequency converter, it also requires a minimum of reactive components, represented by the input filter. The input filter acts as an interface between the matrix converter and the AC mains (Fig. 1). Its basic feature is to avoid significant changes of the input voltage of the converter during each sampling cycle, and to prevent unwanted harmonic currents from flowing into the AC mains. As matter of fact, due to the discontinuous input currents, the matrix converter behaves as a source of current harmonics, which are injected back into the AC mains. The principal method of reducing the harmonics generated by static converters is provided by input filter using reactive storage elements.

**References**

[1] A Dasgupta, et al: “Matrix converter as UPFC for transmission line compensation”, ICPE, 2007.

[2] M Kaliamoorthy: “Fundamentals of matrix converters”, Lecture notes.

[3] J Rodrigez, et al: “A review of control and modulation methods for matrix converters”, IEEE Transactions on Industrial Electronics, January 2012.

[4] J Kolar: “Review of three-phase PWM AC-AC converter topologies”, IEEE Transactions on Industrial Electronics, December 2010.

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