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International Journal of Electrical and Electronics Engineering Research (IJEEER) ISSN 2250-155X Vol. 3, Issue 3, Aug 2013, 47-58 © TJPRC Pvt. Ltd.

A 4-LEG MATRIX CONVERTER BASED DTC OF INDUCTION MOTOR N. VENKATESWARLU & K. NARASIMHA RAJU Department of Electrical and Electronics Engineering, K L University, Guntur, Andhra Pradesh, India

ABSTRACT This paper presents Space Vector Modulation strategy for a 4-leg Matrix Converter to control Induction motor. Matrix Converters (MC) are compact voltage source converters capable of providing variable voltage and variable frequency at the output. Compared with traditional topologies the MC does not require an intermediate dc link and provides sinusoidal output waveform with minimum higher order harmonics. This is used to Space Vector Modulation (SVM) algorithm for the voltage control of converter. The paper proposes a direct torque control (DTC) scheme for a matrix-converter-fed induction motor drive system. DTC is a high performance motor control scheme with fast torque and flux responses. The proposed modulation technique for control of Induction Motor. Finally, the Simulation results are carried by using MATLAB/SIMULINK Platform.

KEYWORDS: Matrix Converter, Space Vector Modulation (SVM), Direct Torque Control INTRODUCTION Matrix converter offers a number of advantages, including simple and compact power circuit, generation of load voltage with arbitrary amplitude and frequency, sinusoidal input and output currents, and operation with unity power factor for any load [1]–[3]. It has found more and more applications in motor drive, power supply, wind generation, dynamic voltage restorer, etc. Three approaches are widely used when developing modulation strategies for matrix converters. The first one is the Alesina–Venturini modulation strategy based on transfer function analysis and has been proposed in [8] and [9]. The second one is the space vector modulation (SVM) strategy, including indirect SVM and direct SVM proposed in [10] and [11], respectively. The SVM modulation strategy is often used in matrix converter for it has some advantages, such as immediate comprehension of the required commutation processes, a simplified control algorithm, and maximum voltage transfer ratio without adding third harmonic components. However, these conventional modulation strategies are derived under the assumption that the input voltages are well balanced and sinusoidal. In practice, the matrix converter may operate under abnormal input-voltage conditions, in terms of unbalance, non-sinusoid, and surge (sudden rising or sudden dropping). Due to lack of dc-link capacitors for energy storage, the matrix converter is highly sensitive to disturbances in the input voltages. For most of the modulation strategies, the unbalanced and nonsinusoidal input voltages can result in unwanted output harmonic voltages. The shorttime input-voltage surge could bring the voltage surge on the load side instantly [13], [14]. Several techniques that reduce this influence of the abnormal input voltages for these conventional modulation strategies have been reported. Since the Direct Torque Control (DTC) method has been proposed in the middle of 1980‟s, DTC method becomes one of the high performance control strategies for AC machine to provide a very fast torque and flux control [3]. There are no requirements for coordinate transformation, no requirements for PWM generation and current regulators. It is widely known to produce a quick and fast response in AC drives by selecting the proper voltage space vector according to the


N. Venkateswarlu & K. Narasimha Raju

switching status of inverter which is determined by the error signal of reference flux linkage and torque with their estimated values and the position of the estimated stator flux. For such advanced reasons, the combination of the advantages of the matrix converter with those of the direct torque control method is effectively possible according to [4]. However, this research just focuses on some simulation results and the experimental results are not given sufficiently. Moreover, the drawback which still exists in the DTC method is that the capability of input power factor control: the conventional DTC for MC can only control the input power factor at the unity power factor by a hysteresis controller. One space vector is applied to matrix converter to control both the output voltage requirement with the 6-fix fixed directions, and the controlled input current vector just roughly follows the continuous input voltage vector by the 6-fixed input current vector directions. As a result, the DTC method for MC totally depends on the input power factor hysteresis controller: estimate the correct sine value of the displacement angle between the input current and input voltage vectors based on the continuous measured voltage and the discrete calculated current. With this estimation and the hysteresis controller, the DTC for MC can cause the wrong controlled vector and also a lot of harmonic components inside the input current waveform due to using only 1 space vector for the whole sampling control period.

Figure 1: A 4-Leg Matrix Converter

Figure 1 shows a diagram of a 4-leg matrix converter attached to a generator, the idea being that the converter can be used to provide any type of power supply required from a mobile generator, whether it be a 3-phase load or 1, 2 or 3 sets of single-phase loads. The complete mobile generator system is shown in Figure 2 for providing a standalone field power supply. In this system a variable speed generator that allows operation over a wide engine RPM without compromising AC output power quality. The power converter, output waveform control and output filter have been designed to give a supply of 208VAC line-line with an output frequency range of 50 Hz to 400Hz [5].

Figure 2: Standalone Power Supply System

A 4- Leg Matrix Converter Based DTC of Induction Motor


SPACE VECTOR MODULATION All Space Vector Modulation (SVM) techniques use a set of vectors that are defined as instantaneous spacevectors of the voltage and currents at the input and output of the converter. These vectors are created by the various different switching states that the converter is capable of generating. For the standard 3x3 matrix converter there are 27 (3 3) switching states [4]. However with the extra output leg this obviously extends the total number of switching states of the converter to 81 (34), all of which are shown in Table 1. As was seen before, not all of these switching states are useful as some produce a moving, or rotating vector. A rotating vector is one that is non-stationary in the αβγ space. As these are moving vectors, they are not fixed in magnitude or direction, and we are therefore unable to easily utilize them. These are shown in Table 1, labelled as the „Rotating Vectors‟ and can be seen to be those switching states that have all 3 input phases switched to different output lines. The only useful states for most SVM techniques are those that use either a single input phase (Zero Vectors) or 2 input phases (Stationary Vectors). Looking once again at Table [1] it can be seen that, after discarding the switching states that create the rotating vectors, we are left with 45 useful states, of which 3 are zero vectors.

Figure 3: Input and Output Vector Spaces, Each Showing a Single Highlighted Sector with the Associated Switching States Where Required Now, as can be seen in Table [1], the switching states that produce stationary non-zero vectors are labelled in pairs, positive and negative. This has been because either switching state can be used to generate the required output space vector, purely depending on the sign of the input voltage. Taking +1, and -1 for example, with V positive the switching state +1 can be used, but with V negative the switching state -1 can be used to generate precisely the same output. Knowing this symmetry helps us, as it increases the possible number of switching states that can be used to generate any output voltage vector. With a matrix converter, control over the input current and output voltage space-vectors can be effectively decoupled from one another, allowing the output voltage to be generated independently from the input, and the input current phase to be controlled irrespective of the output voltage [4]. With this split between input and output, we therefore need to be able to define each vector space individually. As such, the input, having only 3-phases, is transformed into the well known hexagonal form in αβ space, with its 6 switching vectors, just as seen when utilizing the SVM technique for the 3x3 matrix converter [4], noting that the vector space for the input current is rotated p/6 about the origin when compared to the voltage vector space, as shown in Figure 3(b). While the output, having 4-phases, is transformed into a 3-dimensional (αβγ) space, with 14 switching vectors


N. Venkateswarlu & K. Narasimha Raju

describing a volume [1, 2, 3]. Figure 3 shows us all these vector spaces, and upon closer inspection it can be demonstrated that this volume in Figure 3(c) is a superset of the 2-dimensional case in Figure 3(a) when viewed along the γ-axis. The darker shaded areas in both parts (a) and (c) of Figure 3 show the smallest bounded area/volume for each case, triangle and tetrahedron, with the lighter shaded area in Figure 3(b) being that prism formed when the volume is viewed down the γ -axis, and one sector is highlighted. These prisms are made from 4 tetrahedrons, the smallest bounded volume, and each aligned on top of each other in the γ -axis dimension [1]. So, with the input space requiring 6 switching vectors, and the output requiring 14 switching vectors, and remembering the inherent symmetry of the vectors and switching states, it can be seen that for each stationary input space vector there are 7 (42/6) associated switching state pairs, giving 14 possible switching states in total. Likewise, for each stationary output space vector there is 3 (42/14) associated switching state pairs, giving a total of 6 possible switching states. For any set of input voltages, and a given set of output demand voltages, the corresponding input and output sectors can be ascertained. As we are controlling the input current for a unity power factor, the input current vector will always follow that of the input voltage vector. Knowing this, it allows the easy determination of the input current sector for any set of input voltages [4]. Then, the output voltage sector needs to be calculated, but unfortunately there is no simple mathematical formula that will solve it easily. Therefore the output demand voltage sector is determined using the following method [3]. Firstly, the output demand voltage is likewise transformed from the normal output voltage space into the 3dimensional αβγ space by using the following vector transform

This then produces a vector within the 3 dimensional spaces shown in Figure 3(c). As stated above, this 3dimensional Volume can be seen to be made up from 6 prisms, with each prism being made up of 4 tetrahedrons. With the output voltage in αβγ space, it is thus easy to calculate which of these 6 prisms the voltage vector resides in. Once this is calculated, the exact sector (tetrahedron) which the voltage vector lies within needs to be found. Fortunately, this process is easily possible by comparing the signs of the output demand voltages in „abc‟ space, with the polarities of the non-zero switching vectors of the 4 tetrahedrons (sectors) within the prism, with the correct output voltage sector being the one whose signs match [3]. Now that both the input and output sectors are known, then these can be used to define the required switching states. This is achieved by comparing the two sets of switching states, one set generated from the stationary input vectors bounding the input current sector, and a similar set for the output voltage sector. For example, looking at Figure 3, with the input current in sector 1 as highlighted in Figure 3(b), and the output voltage in highlighted sector in Figure 3(c), to generate the required space vectors the following switching states can to be used Input: ±1, ±3, ±4, ±6, ±7, ±9, ±10, ±12, ±13, ±15, ±16, ±18, ±19, ±21 Output: ±1, ±2, ±3, ±4, ±5, ±6, ±13, ±14, ±15

A 4- Leg Matrix Converter Based DTC of Induction Motor


Only those matching switching state pairs, that appear in both the input and output sets, could allow both the input and output to be controlled, leaving us with Matching switching states: ±1, ±3, ±4, ±6, ±13, ±15 Now, these are just the 12 possible switching states that could be used, with a further limitation formed by the input voltages. With this selection of switching state pairs, it can be seen from Table 1 that although all three input lines are being switched, they are being switched in a way that only uses the two line-line voltages Vab and Vca. Whilst the current is in sector 1, Vab is always positive, while Vca will always be negative. From this, and looking at table 1 once more, it is relatively straightforward to see that the switching states required generating the output voltage and controlling the input current are Switching states: +1, -3, -4, +6, +13, -15 One thing to be noted is that for the input and output sectors there are 2 fixed input space-vectors and 3 fixed output space-vectors created by using these 6 switching states, which gives 2 switching states per output space vector and 3 switching states per input space-vector. These are such that for each output vector, it‟s two Switching states correspond to each of the 2 input vectors, and As follows from that, the 3 switching states for each input vector correspond to each of the 3 output vectors. This can be seen clearly in Figure 4

Figure 4: Input and Output Voltage Modulation Techniques The next step is to calculate how much each space-vector contributes to creating the output, or controlling the input. Now, from Figure 4(b), it is relatively easy to write out a set of equations that define the demand voltage


And for the input current, looking at Figure 4(a) it is possible to write down a set of equations [4] such that the input current is in phase with the input voltage (


N. Venkateswarlu & K. Narasimha Raju

( ( and overall

where V0 are the output voltage vectors, ii the input current vectors and d the duty ratios for the 6 switching states, while βi is the input current phase angle, measured from the centre line of the sector and Ki is the input current sector. If we look at equations (6) to (8) we can see that they are made up of pairs of switching state input currents (eg i I and iII ), and that these pairs are each associated with a different output voltage vector as can be seen in equations (3) to (5). Now, for each voltage vector, the two associated switching states produce a current of the same magnitude, therefore the above equations (6) to (8) can be reduced to

Now, substituting this into equation (3) gives us

The equations for the other duty ratios can be similarly produced. The only unknowns left in these equations are the magnitudes for the 3 output voltage vectors, and shown in Figure 4 (b) and equations (3) to (5). Unfortunately, these values do not solve well algebraically, and so an alternative vector method has been used, using the formula for calculating the intersection between a line and a plane

Where P1 and P2 are known points on the line, P3 is a known point on the plane, n is the normal vector to the plane and u is variable. By taking one face of the tetrahedron in Figure 4(b) as a plane, says OV2 V3, the normal to the plane can be found by calculating the cross product of the two vectors V2 and V3 while letting P3 equal any point on the plane, O, V2 or V3 can be used. Then having P1 equal the demand voltage, and P2 – P1 equal the vector V1, it is trivial to then calculate u, the magnitude of V1 required to generate the output voltage. Once one of the magnitudes is known, it is then a simple task to either repeat this process for the remaining 2 vectors, or to fall back to more conventional techniques to calculate the required magnitudes. Now these magnitudes are known, it is possible to then go ahead and calculate the duty ratios for each of the 6 switching states.

DTC MODULATION FOR MATRIX CONVERTER The control algorithm of MC is very complex. Two kinds of control technologies which are used “independence output voltage” and “input current control algorithm” are (1) Venturini algorithm that based on transformation function; (2)

A 4- Leg Matrix Converter Based DTC of Induction Motor


space vector modulation (SVM) algorithm, in which two categories are commonly used: Direct Transfer Function (DTF); Indirect Transfer Function (ITF). The SVM is an algorithm that compounds space vector and zero vector within a control period, in which, a new vector is obtained and can be modulated continuously. The modulation strategy of MC contains vector choice and time switching computation. The vector choice is based on the input and output vector, the controlled object and the relative control theory. Figure 5 is the defined sector of output voltage and input current vector.

Figure 5: (a) The Defined Sector of Output Voltage Vector; (b) The Defined Sector of Input Current Vector


Figure 6: Simulation Circuit of SVM Matrix Converter

Figure 7: Source Current


N. Venkateswarlu & K. Narasimha Raju

Figure 8: Load Voltage

Figure 9: Spectrum Analysis of the Load Voltage

Figure 10: Spectrum Analysis of the Source Current

Figure 11: Source Voltage and Source Current Case 2

Figure 12: Simulation Circuit of DTC SVM Based Matrix Converter


A 4- Leg Matrix Converter Based DTC of Induction Motor

Figure 13: Source Current

Figure 14: Load Voltage

Figure 15: Load Current

Figure 16: Speed Curve

Figure 17: Electromagnetic Torque


N. Venkateswarlu & K. Narasimha Raju

CONCLUSIONS This paper has described a Space Vector Modulation technique for a Matrix Converter with four output legs. The better control effect is obtained by combining DTC with SVM based on flux linkage reference model. The experiment result has shown that the control system has fast response, steady dynamic performance, and lesser torque pulsation. Simulation model is developed and the simulation results are presented.


P W Wheeler, J C Clare, N Mason,” Space Vector Modulation for a 4- Leg Matrix Converter” IEEE,2005


Ryan M.J, Lorenz R.D and De Doncker R.W, “Modeling of Multileg Sine-Wave Inverters: A Geometric Approach”, IEEE Transactions on Industrial Electronics, Vol. 46, No. 6, December 1999


Ryan M.J, De Doncker R.W and Lorenz R.D, “Decoupled control of a 4-Leg Inverter via a New 4x4 Transformation Matrix”, PESC '99


Zhang R, Prasad H, Boroyevich D and Lee F.C, “Three-Dimensional Space Vector Modulation for Four-Leg Voltage Source Converters”, IEEE Transactions on Power Electronics, Vol. 17, No. 3, May 2002


Casadei D, Serra G, Tani A, and Zarri L, “Matrix Converter Modulation

Strategies: A New General

Approach Based on Space-Vector Representation of the Switch State”, IEEE Transactions on Industrial Electronics, Vol. 49, No. 2, April 2002 6.

Katsis. D, Zanchetta P., Wheeler P.W., Clare J.C., Empringham L., Bland, M, “A Three-Phase Utility Power Supply Based on the Matrix Converter”, IEEE Industrial Application Society Annual Meeting, November 2004.


R. Zhang, D. Boroyevich, V.H. Prasad, H.-C. Mao, F.C. Lee, and S. Dubovsky. A three-phase inverter with a neutral leg with space vector modulation. In Proc. IEEE APEC‟97, volume 2, pages 857–863, February 1997.


Domenico Casadei, Giovanni Serra, and Angelo Tani. Reduction of the input current harmonic content in matrix converters under input/output unbalance. IEEE Trans. Ind. Electron., 45(3):401–411, June 1998.


L. Huber and D. Borojevic. Space vector modulator for forced commutated cycloconverters. In Proc. IEEE IAS Annual Meeting ‟89, San Diego, CA, 1989.

10. L. Huber and D. Borojevic. Space vector modulation with unity input power factor for forced commutated cycloconverters. In Proc. IEEE IAS Annual Meeting ‟91, 1991. 11. L. Huber, D. Borojevic, and N. Burany. Analysis, design and implementation of the space-vector modulator for forced commutated cyclo convertors. Electric Power Applications, IEEE Proceedings B, 139(2):103–113, March 1992. 12. L. Huber and D. Borojevic. Space vector modulated three phase to three-phase matrix converter with input power factor correction. Industry Applications, IEEE Transactions on, 31(6):1234–1246, November 1995. 13. V.H. Prasad, D. Borojevic, and R. Zhang. Analysis and comparison of space vector modulation schemes for a four-leg voltage source inverter. In Applied Power Electronics Conference and Exposition, 1997. APEC ‟97 Conference Proceedings 1997. Twelfth Annual, volume 2, pages 864–871, February 1997. 14. Muhammad H. Rashid. Power Electronics Handbook: Devices, Circuits and Applications. Academic Press, 2nd edition, 2006

A 4- Leg Matrix Converter Based DTC of Induction Motor


15. P. W. Wheeler, P. Zanchetta, J. C. Clare, L. Empringham, M. Bland, and D. Katsis. A utility power supply based on a four-output leg matrix converter. IEEE Trans. Ind. Appl., 44(1):174–186, February 2008.


VENKATESWARLU.N was born in Vinukonda, Andhra Pradesh, India on August 6 th 1989. He received B.Tech degree in Electrical and Electronics Engineering from Khader Memorial College of Engineering and Technology, Devarakonda, affiliated to JNTU University Hyderabad, Andhra Pradesh, India in June 2010. He is currently Pursuing M.Tech in Power Electronics and Drives at K L University, Vaddeswaram, Guntur district, AP, India.

NARASIMHA RAJU.K was born in Kakinada, Andhra Pradesh, India on August 15 th 1980. He received B.Tech degree in Electrical and Electronics Engineering from DMSSVH College of Engineering and Technology, Machilipatnam, affiliated to JNTU University Hyderabad, Andhra Pradesh, India in June 2002 and Masters (M.Tech) in Power Electronics and Drives from JNTU College of Engineering, Hyderabad, India in May 2012. He is currently working as Assoc. Prof in K L University in Electrical and Electronics Engineering. His research interest includes Power Electronics and Drives, Power Converters

6 a 4 leg matrix full  

This paper presents Space Vector Modulation strategy for a 4-leg Matrix Converter to control Induction motor. Matrix Converters (MC) are com...

6 a 4 leg matrix full  

This paper presents Space Vector Modulation strategy for a 4-leg Matrix Converter to control Induction motor. Matrix Converters (MC) are com...