Download - MODULATION AND CONTROL TECHNIQUES OF MATRIX CONVERTER · PDF fileswitches that connects directly the three phase source to the three phase load. The matrix converter is a direct AC-AC

International Journal of Advances in Engineering & Technology, July 2012.

©IJAET ISSN: 2231-1963

244 Vol. 4, Issue 1, pp. 244-255

MODULATION AND CONTROL TECHNIQUES OF MATRIX

CONVERTER

M. Rameshkumar1, Y. Sreenivasa Rao1 and A. Jaya laxmi2

1Department of Electrical and Electronics Engineering, DVR & Dr. HS MIC College of Engineering, JNTU Kakinada, India.

2Department of Electrical and Electronics Engineering, JNTUH College of Engineering, Hyderabad, India.

ABSTRACT

The Matrix converter is a forced commutated Cyclo-converter with an array of controlled semi conductor

switches that connects directly the three phase source to the three phase load. The matrix converter is a direct

AC-AC Converter. It has no limit on output frequency due to the fact that it uses semiconductor switches with

controlled turn-off capability. The simultaneous commutation of controlled bidirectional switches limits the

practical implementation and negatively affected the interest in matrix converters. This major problem has been

solved with the development of several multi-step commutation strategies that allow safe operation of the

switches Examples of these semiconductor switches include the IGBT, MOSFET, and MCT. Some of the

modulation techniques existing are Basic, Alesina-Venturi and Space vector Modulation Techniques. Out of the

above modulation techniques Space vector Modulation Technique is most widely used. The simulation of matrix

converter modulation and control strategies of Space vector Modulation Technique is done by using MATLAB-

Simulink.

KEYWORDS: Matrix converter, Space Vector Modulation.

I. INTRODUCTION TO MATRIX CONVERTER

The matrix converter is the most general converter-type in the family of AC-AC converters. The AC-AC converter is an alternative to AC-DC-AC converter which is called as direct converter is shown in Fig. 1. The matrix converter is a single-stage converter which has an array of m×n bidirectional power switches to connect, directly, an m -phase voltage source to an n-phase load. The AC-DC-AC converter is also called as indirect converter as shown in Fig. 2. The matrix converter is a forced commutated converter which uses an array of controlled bidirectional switches as the main power element to create a variable output voltage system with unrestricted frequency. It does not have any DC-link circuit and does not need any large energy storage elements. The key element in a matrix converter is the fully controlled four-quadrant bidirectional switch, which allows high-frequency operation. The converter consists of nine bi-directional switches arranged as three sets of three so that any of the three input phases can be connected to any of the three output lines is shown in Fig. 3. [1][3]

Fig. 1 AC to AC or Direct power Conversion



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Fig. 2 AC-DC-AC or Indirect power Conversion

Fig. 3 Matrix converter Switch Arrangement

The switches are then controlled in such a way that the average output voltages are a three phase set of sinusoids of the required frequency and magnitude. The matrix converter can comply with four quadrants of motor operations, while generating no higher harmonics in the three-phase AC power supply. The circuit is inherently capable of bi-directional power flow and also offers virtually sinusoidal input current, without the harmonics usually associated with present commercial inverters. These switches provide to acquire voltages with variable amplitude and frequency at the output side by switching input voltage with various modulation techniques.[4][5] [8]. These modulation techniques are to change the voltage transfer ratio of matrix converter and out of these methods we mainly concentrate on the venturini modulation technique and the space vector maodulation method.One of the main contributions is the development of rigorous mathematical models to describe the low-frequency behavior of the converter, introducing the “low-frequency modulation matrix” concept. The use of space vectors in the analysis and control of matrix converters in which the principles of Space Vector Modulation (SVM) were applied to the matrix converter modulation problem.

Advantages of Matrix Converter:

• No DC link capacitor or inductor • Sinusoidal input and output currents • Possible power factor control • Four-quadrant operation • Compact and simple design • Regeneration capability

Disadvantages of Matrix Converter:

• Reduced maximum voltage transfer ratio • Many bi-directional switches needed • Increased complexity of control • Sensitivity to input voltage disturbances • Complex commutation method.[5]-[8].

Section 1 describes introduction to matrix converter, Section 2 describes the various Commutation techniques for matrix converter, Section 3 describes the various modulation strategies for matrix converter, Section 4 describes the simulation of Space Vector Modulated matrix converter, Section 5 describes the simulation results and Section 6 describes conclusions of the paper.



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II. COMMUTATION TECHNIQUES FOR MATRIX CONVERTER

There are three methods of implementing the Bi-directional Switch. They are Diode Bridge Bidirectional switch arrangement, Common Emitter Bidirectional Switch arrangement, and Common Collector Bidirectional Switch arrangement. This bidirectional switch consists of two diodes and two IGBTs connected in anti-parallel as shown Fig. 4.

Fig. 4 Common emitter bidirectional switch arrangement

The diodes are included to provide the reverse blocking capability. There are several advantages in using this common emitter bidirectional switch arrangement. It is possible to independently control the direction of the current. Conduction losses are also reduced since only two devices carry the current at any one time. One possible disadvantage is that each bidirectional switch cell requires an isolated power supply for the gate drives. Therefore, the common emitter configuration is generally preferred for creating the matrix converter bidirectional switch cells. In the common emitter configuration, the central connection also allows both devices to be controlled from one isolated gate drive power supply [1],[9].

2.1 Current Commutation for the Safe Operation of Bidirectional Switch

Reliable current commutation between switches in matrix converters is more difficult to achieve than in conventional VSIs since there are no natural freewheeling 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 [7][8].

2.2 Current-Direction-Based Commutation

A more reliable method of current commutation, which obeys the rules, uses a four-step commutation strategy in which the direction of current flow through the commutation cells can be controlled. To implement this strategy, the bidirectional switch cell must be designed in such a way so as to allow the direction of the current flow in each switch cell to be controlled. A diagram for two-phase to single-phase matrix converter, representing the first two switches in the converter as shown in Fig. 5 [1].

Fig. 5 Conversion of 2-ø to 1- ø with bidirectional switches

In steady state, both the devices in the active bidirectional switch cell are gated to allow both directions of current flow. The explanation assumes that the load current is in the direction shown and



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that the upper bidirectional switch ( AaS ) is closed. When a commutation to BaS is required, the current direction is used to determine which device in the active switch is not conducting. This device

is then turned off. The device that will conduct the current in the incoming switch is then gated BaS , in this example. The load current transfers to incoming device either at this point or when outgoing device ( AaS 1) is turned off. The remaining device in the incoming switch ( AaS 2) is turned on to allow current reversals. This process is shown as a timing diagram the delay between each switching event is determined by the device characteristics as shown in Fig. 6. This method allows the current to commutate from one switch cell to another without causing a line-to-line short circuit or a load open circuit. One advantage of all these techniques is that the switching losses in the silicon devices are reduced by 50% because half of the commutation process is soft switching and, hence, this method is often called “semi-soft current commutation”. One popular variation on this current commutation concept is to only gate the conducting device in the active switch cell, which creates a two-step current commutation strategy. All the current commutation techniques in this category rely on knowledge of the output line current direction [3], [10]. However, other method called “Near-Zero” commutation method will give rise to control problems at low current levels and at startup. This method allows very accurate current direction detection with no external sensors. Because of the accuracy available using this method, a two-step commutation strategy can be employed with dead times when the current changes direction, as shown in Fig. 7. This technique has been coupled with the addition of intelligence at the gate drive level to allow each gate drive to independently control the current commutation. There is another method of commutation called relative voltage magnitude commutation. The main difference between these methods and the current direction based techniques is that freewheel paths are turned on in the input voltage based methods.

Fig. 6 Timing diagram of current commutation

Fig.7 Timing diagram of two-step semi-soft current commutation with current direction -detection within the

switch cell



248 Vol. 4, Issue 1, pp. 244-255

III. MODULATION TECHNIQUES FOR MATRIX CONVERTER

The purpose of these modulation techniques is to change the voltage transfer ratio. The different types of Modulation techniques are Basic Modulation technique, Voltage ratio limitation and optimization, Alesina –Venturini modulation technique, Scalar modulation technique, Space vector modulation technique, indirect modulation technique. The main modulation techniques which have wide applications are Venturini modulation technique and the space vector modulation technique. To describe the above methods we need some fundamentals and some switching schemes which are explained below. The basic switching states are shown in Fig. 8.[1.

Fig. 8 Basic Switching Sequence

Defining the switching function of a single switch as[1], [6], [11], [12],[13]

�� = �1, �� ℎ��0, �� ℎ�� ,�,�� ,!,"� (1)

With these restrictions, the 3×3 matrix converter has 27 possible switching states. The mathematical expressions that represent the basic operation of the MC are obtained applying Kirchhoff’s voltage and current laws to the switch array.

#$ %�&$!%�&$"%�&' = #�� %�&�� %�&�� %�&��!%�&��!%�&��!%�&��"%�&��"%�&��"%�&' #$�%�&$�%�&$�%�&'

(2) $( = ) × $where T= Instantaneous transfer matrix

#+�%�&+�%�&+�%�&' = #�� %�&�� %�&�� %�&��!%�&��!%�&��!%�&��"%�&��"%�&��"%�&',#+ %�&+!%�&+"%�&' (3)

�- =),�( where TT is the transpose matrix of T

Where $ ,$!.��$" are the output phase voltages and iA, iB and iC represent the input currents to the

matrix. The output voltage is directly constructed switching between the input voltages and the input currents are obtained in the same way from the output ones. For these equations to be valid, next expression has to be taken into consideration:

��/ + ��/ + ��/ = 1, � = �., 1, � (4)

What this expression says is that, at any time, one, and only one switch must be closed in an output branch. If two switches were closed simultaneously, a short circuit would be generated between two input phases. On the other hand, if all the switches in an output branch were open, the load current would be suddenly interrupted and, due to the inductive nature of the load, an over voltage problem would be produced in the converter.



249 Vol. 4, Issue 1, pp. 244-255

By considering that the bidirectional power switches work with high switching frequency, a low-frequency output voltage of variable amplitude and frequency can be generated by modulating the duty cycle of the switches using their respective switching functions. Let 23/%�& be the duty cycle of

switch �3/%�&, defined as

23/%�& = �3//)567which can have the following values:0 < 23/%�& < 1,

9 = �:, ;, ��, � = �., 1, �. The low-frequency transfer matrix is defined by

2%�& = <2� 2� 2� 2�!2�!2�!2�"2�"2�" = (5)

The low-frequency component of the output phase voltage is given by $(%�& = 2%�&$-%�& (6) The low-frequency component of the input current is given by +-%�& = 2%�&,�(%�& (7)

3.1. Venturini Modulation Technique

The modulation problem normally considered for the matrix converter can be stated as follows. Given a set of input voltages and an assumed set of output currents [4], [6], [14]

$� =$�> # cos%B��&cos%B�� + 2 × D/3&cos%B�� + 4 × D/3&' (8)

+� = +�> # cos%B�. � + ∅�&cos%B�. � + ∅� + 2 × D/3&cos%B�. � + ∅� + 4 × D/3&' (9)

find a modulation matrix M(t) such that the constraint equation is satisfied. In the voltage gain between the output and input voltages,

$� = I. $�> # cos%B�. �&cos%B�. � + 2 × D/3&cos%B�. � + 4 × D/3&' (10)

+� = I. cos%∅�& +�> # cos%B�. � + ∅�&cos%B�. � + ∅� + 2× D/3&cos%B�. � + ∅� + 4× D/3&' (11)

The first method attributable to Venturini is defined by above method. However, calculating the switch timings directly from these equations is cumbersome for a practical implementation. They are more conveniently expressed directly in terms of the input voltages and the target output voltages (assuming unity displacement factor) in the form

2 = JK L1 + M2$3$/N/$-OP Q for 9 = �:, ;, ��, � = �., 1, � (12)

2%�& = <2� 2� 2� 2�!2�!2�!2�"2�"2�"= (13)

This method is of little practical significance because of the 50% voltage ratio limitation. Venturini’s optimum method employs the common-mode addition technique defined to achieve a maximum



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voltage ratio of 87%. The formal statement of the algorithm, including displacement factor control, in Venturini’s key paper is re-complex and appears unsuited for real time implementation. In fact, if unity input displacement factor is required and then the algorithm can be more simply stated in the form [1], [3].

2/3 = JK R1 + M2$3$/N/$-OP + S4 7K√KU sin%B-� + X3& sin%3B-�&Y (14)

For 9 = �:, ;, ��, � = �., 1, �.��X = 0, PZK , [ZK respectively.

Noting that, the target output voltages include the common-mode addition defined in equation provides a basis for real-time implementation of the optimum amplitude Venturini method which is readily handled by processors up to sequence (switching) frequencies of tens of kilohertz. Input displacement factor control can be introduced by inserting a phase shift between the measured input voltages and the voltages$�inserted in above equation. However, like all other methods, displacement factor control is at the expense of maximum voltage ratio [1],[14].

3.2 Space Vector Modulation Technique

The SVM is well known and established in conventional PWM inverters. Its application to matrix converters is conceptually the same, but is more complex. With a matrix converter, the SVM can be applied to output voltage and input current control. Here, we just consider output voltage control to establish the basic principles. The voltage space vector of the target matrix converter output voltages is defined in terms of the line-to-line voltages [8], [12], [15]

$(%�& = PK %$ ! + .$!" + .P$" & (15)

+-%�& = PK %+ + .+! + .P+"& (16)

where . = �%/PZ/K& In the complex plane $(%�& is a vector of constant length M√3I$-ON rotating at angular frequencyB(.

In the SVM, it is synthesized by time averaging from a selection of adjacent vectors in the set of converter output vectors in each sampling period. The Table1 shows the 27 switching states of the three-phase Matrix Converter (MC). Table 1 shows all different vectors for output voltages and input currents. The group-2 consists of eighteen space vectors are constant in direction but the magnitude depends on the input voltages and the output currents for the voltage and currents space vectors respectively. On the contrary, the magnitude of the six rotating vectors remains constant and corresponds to the maximum value of the input line-to-neutral voltage vector and the output line current vector, while its direction depends on the angles of the line-to-neutral input voltage vector α and the input line current vector β.

The 27 possible output vectors for a three-phase matrix converter can be classified into three groups with the following characteristics.

� Group I: Each output line is connected to a different input line. Output space vectors are constant in amplitude, rotating (in either direction) at the supply angular frequency.

� Group II: Two output lines are connected to a common input line; the remaining output line is connected to one of the other input lines. Output space vectors have varying amplitude and fixed direction occupying one of six positions regularly spaced 60 apart. The maximum

length of these vectors is P√K × $6\]where $6\]the instantaneous value of the rectified input

voltage envelope. � Group III: All output lines are connected to a common input line. Output space vectors have

zero amplitude (i.e., located at the origin)



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Table 1 3Φ-3Φ Matrix converter switching combinations

In the SVM, the Group I vectors are not used. The desired output is synthesized from the Group II active vectors and the Group III zero vectors. The hexagon of possible output vectors is shown, where the Group II vectors are further subdivided dependent on which output line-to-line voltage is zero. The Switching times for the space vectors for the sector is given below

�1 =^|$�| $��`a b)�I sin%c& (17)

�6 =^|$�| $��`a b)�I sin%60 − c& (18)

�� =)�I − %�1 + �6& (19) Where to is the time spent in the zero vector (at the origin). There is no unique way for distributing the times (t1, t6, t0) within the switching sequence. The example for switching times is shown in Fig. 9.

Fig. 9 Switching times

For good harmonic performance at the input and output ports, it is necessary to apply the SVM to input current control and output voltage control. This generally requires four active vectors in each switching sequence, but the concept is the same. Under balanced input and output conditions, the SPVM technique yields similar results to the other methods mentioned earlier. However, the increased



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flexibility in choice of switching vectors for both input current and output voltage control can yield useful advantages under unbalanced conditions.

IV. SIMULATION OF MATRIX CONVERTER WITH SVPWM MODULATION

TECHNIQUE

The simulation diagram of matrix converter with SVPWM Modulation technique is as shown in Fig. 10. The SVPWM Modulation technique is implemented based on the consideration of Voltage & Current sector location. The important blocks in SVPWM modulation technique are Matrix converter, Duty cycle block, Switching times calculation block, pulse generation block. The Duty cycles are generated based on the Voltage and Current Vector sector location. The input to duty cycle block is the sector location and the output is the duty cycles and these are used for calculating the switching times. The input to the pulse generation block is switching times and also voltage and current sector and the output of pulse generation block are pulses to the nine switches which are directly connected to the switches of matrix converter.

Fig. 10 Simulation diagram of SVM for matrix converter



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V. SIMULATION RESULTS

The voltage and current sector is shown in the Fig. 11 which is in the form of pulses. The upper waveform shows the voltage sector location and the lower waveform shows the current sector location.

Fig. 11 Firing angles and control orders

The output voltages (Ub1,Ub2, Ub3)and output currents (Ib1,Ib2,Ib3)of three phase RL branch are shown in Fig. 12. The voltage gain transfer ratio (q) is taken as 0.8.

Fig. 12 Output Voltage and Current of SVM strategy for q =0.85



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The output voltages (Ub1,Ub2, Ub3)and output currents (Ib1,Ib2,Ib3)of three phase RL branch are shown in Fig. 13. The voltage gain transfer ratio (q) is taken as 0.6.

Fig. 13 Output Voltage and Current of SVM strategy for q =0.60

VI. CONCLUSIONS

This paper reviews some well known modulation technologies like Alesina-Venturini method and space vector method. In theory, both methods are equivalent to each other. The relationship between the input/output voltage in the time domain and the input/output reference vector in the complex space is systematically analyzed. The duty-cycle of each switch in the time domain can be represented by combination of space vectors and the reverse of the transformation is also established. The most important practical implementation problem in the matrix converter circuit is the commutation problem between two controlled bidirectional switches. This has been solved with the development of highly intelligent multistep commutation strategies. The important drawback that has been present in all evaluations of matrix converters was the lack of a suitably packaged bidirectional switch and the large number of power semiconductors. This limitation has recently been overcome with the introduction of power modules which include the complete power circuit of the matrix converter.

REFERENCES

[1] Patrick W.Wheeler, Jose Rodriguez, Jon C.Clare, Lee Empringham, Alejandro Weinstein, “Matrix converters:A Technology Review,” IEEE Transactions on Industrial Electronics, Vol. 49, No. 2, April 2002 [2]Ruzlaini Ghoni, Ahmed N. Abdalla, S. P. Koh, Hassan FarhanRashag, RamdanRazali, “Issues of matrix converters: Technical review “,International Journal of the Physical Sciences Vol. 6(15), pp. 3628-3640, 4 August, 2011

[3] EbubekirErdem, Yetkin Tatar, SedatSüter, “Effects of Input Filter on Stability of MatrixConverter Using

Venturini Modulation Algorithm”, InternationalSymposium on Power Electronics,Electrical Drives, Automation

and Motion, SPEEDAM -2010. [4] G. Kastnez, J.Rodriguez, Pawan Kumar Sen, Neha Sharma, Ankit Kumar Srivastava, Dinesh Kumar,Deependra Singh, K.S. Verma,“Carrier Frequency Selection Of Three –PhaseMatrixConverter,”International Journal of Advances in Engineering & Technology,Vol.1,Issue 3,pp.41-54, July 2011.



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[5] Jang-HyounYoum, Bong-Hwan Kwon,“Switching Technique for Current-ControlledAC-to-ACConverters” IEEE Transactions on Industrial Electronics, Vol. 46, no. 2, pp. 309-318, April 1999. [6] HulusiKaraca, RamazanAkkaya, “Control of Venturini Method Based Matrix Converter in Input Voltage Variations”, Proceedings of the International Multi Conference of Engineers and Computer Scientists, vol II IMECS 2009, March 18 - 20, 2009. [7] A. Deihimi, F. Khoshnevis, “Implementation of Current CommutationStrategies of Matrix Converters in FPGA and Simulations Using Max+PlusII” International Journal of Recent Trends in Engineering, vol. 2, no. 5, pp. 91-95, November 2009. [8] Yulong Li, Nam-Sup Choi, Byung-Moon Han, Kyoung Min Kim, Buhm Lee, Jun-Hyub Park, “Direct DutyRatio Pulse Width Modulation Method for Matrix Converters”, International Journal of Control Automation, and Systems, vol. 6, no. 5, pp. 660-669, October 2008. [9] L.C. Herrero, S. de Pablo, F. Martín, J.M. Ruiz, J.M. González, Alexis B. Rey, “Comparative Analysis of the techniques of Current Commutation in Matrix Converters”, IEEE, 2007.

[10] R. Baharom, N. Hashim , M.K. Hamzah, “Implementation of Controlled Rectifier with Power Factor

Correction using Single-Phase Matrix Converter”, pp.1020- 1025, PEDS-2009. [11]S. Ganesh Kumar, S.SivaSankar, S.Krishna Kumar, G.Uma, “Implementation of Space Vector Modulated3-Ø to 3-Ø Matrix Converter Fed Induction Motor,” IEEE, 2007. [12]J. Vadillo J. M. Echeverria, A. Galarza, L. Fontan,“Modeling and Simulation of Space Vector ModulationTechniques for Matrix Converters: Analysis of different Switching Strategies,”pp. 1299-1304.

[13] TadraGrzegorz, “Implementation of Matrix Converter Control Circuit with Direct Space Vector

Modulation andFour Step Commutation Strategy”, XI International PhD WorkshopOWD 2009, pp.321-326, 17–20 October 2009. [14] Domenico Casadei, Giovanni Serra, Angelo Tani, Luca Zarri, “Matrix Converter Modulation Strategies: A NewGeneral Approach Based on Space-VectorRepresentation of the Switch State”, IEEE Transactions On Industrial Electronics, Vol. 49, No. 2, pp. 370-381, April 2002. [15] M. Apap, J.C. Clare, P.W. Wheeler, K.J. Bradley,” Analysis and Comparison of AC-AC Matrix Converter Control Strategies”, pp-1287-1292, IEEE-2003. M. Ramesh Kumar was born in West Godavari District, Andhra Pradesh, on 27-07-1987. He completed his B.Tech. (EEE) from D. M. S. S. V. H. College of Engineering, Machiliaptnam in 2008, pursing M.Tech.(Power Electronics) from D.V.R &Dr H.S MIC college of technology, Andhra Pradesh. He has 2 National papers published in various conferences held at India. Y. Sreenivasa Rao was born in Prakasam District, Andhra Pradesh, on 10-10-1977. He completed his B.Tech. (EEE) from REC SURAT, Gujarat in 2000, M.Tech.(Power Systems) from JNTU Kakinada, Andhra Pradesh in 2006 and pursing Ph.D.(Wind Energy Conversion System) from Jawaharlal Nehru Technological University College of Engineering, Hyderabad. He has 11 years of teaching experience. He has 2 International and 1 Indian Journals to his credit. He has 3 International and 3National papers published in various conferences held at India. He is presently working as Associate Professor, DVR & Dr. HS MIC College of Technology, Vijayawada. His research interests are Modeling and Control of Wind Energy Conversion Systems, Artificial Intelligence Applications to Wind Energy Conversion Systems, FACTS & Power Quality. He is a Member of Indian Society of Technical Education (M.I.S.T.E).

A. Jaya Laxmi was born in Mahaboob Nagar District, Andhra Pradesh, on 07-11-1969. She completed her B.Tech. (EEE) from osmania University College of Engineering, Hyderabad in 1991, M. Tech.(Power Systems) from REC Warangal, Andhra Pradesh in 1996 and completed Ph.D.(Power Quality) from Jawaharlal Nehru Technological University College of Engineering, Hyderabad in 2007. She has five years of Industrial experience and 12 years of teaching experience. She has worked as Visiting Faculty at Osmania University College of Engineering, Hyderabad and is presently working as Associate Professor, JNTU College of Engineering, Hyderabad. She has 6 International and 2 Indian Journals to her credit. She has 40 International and National papers published in various conferences held at India and also abroad. She is presently guiding 15 research scholars at various universities. Her research interests are Artificial Intelligence Applications to Power Systems, FACTS & Power Quality. Her paper on Power Quality was awarded “Best Technical Paper Award” for Electrical Engineering in Institution of Electrical Engineers in the year 2006. Dr. A. Jaya laxmi is a Member of IEEE, Member of Institution of Electrical Engineers Calcutta (M.I.E), Member of Indian Society of Technical Education (M.I.S.T.E) and Member of System Society of India (S.S.I)

Download - MODULATION AND CONTROL TECHNIQUES OF MATRIX CONVERTER · PDF fileswitches that connects directly the three phase source to the three phase load. The matrix converter is a direct AC-AC

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