Indirect space vector control of matrix converter

Indirect space vector control of matrix converter

Indirect Space Vector Control of Matrix Converter Michal Kabasta, VSB – Technical University Ostrava Abstract In this paper is presents a control strategy for three-phase matrix converter, which is based on the Space Vector Modulation technique (SVM). SVM technique is utilized to calculate the duty cycles of the active voltage vectors that must be applied in each switching cycle period, in order to satisfy the input and output requirements. SVM technique use simpler algorithm if is compare with first modulation technique proposed by Venturini. The SVM technique allows us a direct understanding of switching patterns and their characteristics from the viewpoint of analysis and control. The validity of the proposed method is proven from simulation and the output voltage and the input current generated by the model of converter are shown here. 1. Introduction Many of industrial application require AC/AC energy conversion and AC/AC converters. AC/AC converters take electrical energy and changed it to different ac system – waveforms with different amplitude, different frequency and phase. We can classify two main class of ac converters, first ist indirect ac converters and second is direct energy converters. In indirect energy converters are usually two energy stage – rectifier, which convert input ac energy to dc energy and then is here inverter for changing dc energy back to ac energy with different variables on output, if is compare with input ac energy. These two stages of energy conversion Fig. 1. are decoupled and controlled independently and average energy flow is equal. The difference between the instantaneous input and output power must be absorbed or delivered by an energy storage element within converter. This energy storage element is a capacitor or an inductor. AC DC DC AC DC LINK (a) AC AC (b) Fig. 1. (a ) indirect AC/AC (b) di rect AC /A C conv erter But if is use direct energy converter, then the energy storage element is not needed Fig. 1. (b). In direct energy converter are two main areas. First is cycloconverter and the main function is change the output frequency lower then input frequency. In this topology is impossible to get higher output frequency then frequency on input side. The desired output waveforms are making by synthesizing it from pieces of the input waveform. Second stream is matrix converter (MC) and this is better then cycloconverter for adjustable drive, because here is not any limit on the output frequency, limitation is only on output amplitude, which is smaller then input amplitude Fig. 2. This limitation can be solving using overmodulation technique. 0 0 0,4 -0,4 0,8 -0,8 1,2 -1,2 90 180 270 360 Input Voltage Output Voltage Fig. 2. I nput and outp ut wav eforms Matrix converter replace two energy conversion to only one energy conversion, because within converter is not any energy storage element. MC need special semiconductor switches. The matrix converter requires a bidirectional switch, capable of blocking voltage and conducting current in both directions – the energy flow can get from source to load and back. These bidirectional switches, consisting of a pair of devices with turn-off capability, are usually insulated gate bipolar transistors (IGBTs), in either a common collector or a common emitter back-to-back arrangement. Usually, each IGBT has an anti-parallel diode Fig. 3. Matrix converters contain an array Fig. 3. of bi- directional semiconductor switches and this array allows connection of all input lines to all output lines. 441 X International PhD Workshop OWD’2008, 18–21 October 2008 Fig. 3. Dir ec t ma trix conv erter and bidi rectional switches If the switches are arrangement as is shown on Fig. 3. then the power flow in converter is able be reverse. Thanks to absence of any energy storage element, the instantaneous power on input must be the same as the power on output side. Unfortunately reactive power input does not have to equal the reactive power output. In MC it is possible to the control of phase angle between the voltages and current at the input – the output phase angle can be different from input phase. Another good think is that the forms of waveforms at the two sides are independent. So the input can be three-phase ac and output dc, or both can be dc, or both can be ac. From this case, the MC topology is good for universal power conversion such as: AC/DC, DC/AC, DC/DC, AC/AC without any change of topology [5], [7]. 2. Control of Matrix Converter For many AC drive applications is good to use a compact voltage source converter to provide sinusoidal output voltages with varying amplitude and frequency. But if is use indirect power converter, then inside is usually large capacitor or inductor and this is not good for size of converter. In MC is not any DC-link so the MC can be smaller then common indirect converter. Of course, that MC need good control strategy, because in MC is not any natural path for commutation. The control of MC is divide to the two section. First section is direct control of matrix converter, second is indirect control of matrix converter. 2.1 Limitation of Control for MC For explanation of limitation of control is use Fig. 4. where is simplified 3ph 3ph. matrix convertor topology. Matrix converter consists nine bidirectional switches and each output phase is done from set of three switch which are connected to three input phases. Fig. 4. Simpli fi ed topo logy of 3ph. -3ph. matrix converter In this combination is possible to connect any of input phase a ,b ,c to any output phase A, B, C at any instant. If MC is supplied as the voltage sources, the input phase must not be shorted at any time and if inductive load is on output side, then the output phases can not be open. This condition is shown in Fig.5. for set of switch on output phase A. (a) (b) Fig. 5. Swit ching restricti on (a) sho rt circui t on input phases (b) op en circui t on output p hases Mathematically the conditions are below [1], [2]: If the switch function of a switch S ij in Fig. 4. is defined as 1)( = tS ij ,S ij closed { } cbai ,, ∈ , { } CBAj ,, ∈ 0, S ij open The constraints can be expressed as: 1 =++ cjbjaj SSS { } CBAj ,, ∈ (1) The control strategy based on this two basic rules, the number of legal switch states is 27. Each switch state can be described by three letter code. The code describe which output phase is connected to which input side. For example, the state of switch with name aba show, that output phase A is connected to input phase a, output phase B is connected to input phase b and output phase C is connected to input phase a. 3 Direct Control of Matrix Converter In this case, the output waveforms are made from small pieces from input waveforms. This is done selecting catch of the input phases in sequence for defined period of time. The sequence for each 442 phases is the same [3]. How this waveform looks is shown in Fig. 6. The output voltages have inside some segments from three input voltages. Input current includes segments from three output currents. Fig. 6 One o utput p hase The idea of direct control of MC is based on mathematical expression (2,3), which describe the conditions between output and input side. With help of these equations is defined the duty cycle for each switch. For output voltage:                     =           )( )( )( )()()( )()()( )()()( )( )( )( tv tv tv tmtmtm tmtmtm tmtmtm tv tv tv c b a cCbCaC cBbBaB cAbAaA C B A (2)For input current:                     =           )( )( )( )()()( )()()( )()()( )( )( )( ti ti ti tmtmtm tmtmtm tmtmtm ti ti ti C B A cCcBcA bCbBbA aCaBaA c b a (3) Where seq aA aA T t tm = )( a aA t is switch connected to the input phase a and output phase A . This equation can be represented in short form too: [ ] [ ] [ ] [ ] [ ] [ ] )()()( )()()( titMti tvtMtv O T I IO = = (4) Where [ ] )( tM is modulation matrix. Simulation result for this control for matrix converter will be show below. 4. Indirect Space Vector Control of Matrix Converter A principle of this control strategy is based on virtual DC-link in matrix converter. This DC-link is not physically present, but the switches are divide to the virtual rectifier and virtual inverter Fig. 7. The indirect space vector modulation is gaining as a standard technique in the matrix converter modulation [6], [4], [8]. M a b c S 1 S 7 V DC V DC+ I DC+ V DC- I DC- S 9 S 11 S 3 S 5 S 2 S 4 S 6 S 8 S 10 S 12 A B C Virtual Rectifier Virtual Inverter Fig. 7. Virtu al DC-link Indirect space vector modulation is equivalent circuits combining current source rectifier and voltage source inverter connected by DC-link. Inverter stage has a standard 3ph voltage source topology based on six switches S7-S12 and rectifier stage based on switches S1-S6 with same topology. This two circuit has provided platform for analyze and derive several extends PWM strategies. The basic idea of the indirect modulation technique is to decouple the control of the input current and the control of the output voltage. This is done by splitting the transfer function T for the matrix converter in (5) into the product of a rectifier and an inverter transfer function. R I T ∗ =       ⋅           =           6 5 4 3 2 1 12 10 8 11 9 7 S S S S S S S S S S S S SSS SSS SSS cCbCaC cBbBaB cAbAaA (5) where the matrix I is the inverter transfer function and the matrix R is the rectifier transfer function. This way to model the matrix converter provides the basis to regard the matrix converter as a back-to-back PWM converter without any DC-link energy storage. This means the well know space vector PWM strategies for voltage source inverter (VSI) or PWM rectifier can be applied to the matrix converter.           ⋅       ⋅           =           c b a C B A V V V S S S S S S S S S S S S V V V 6 5 4 3 2 1 12 10 8 11 9 7 (6) 443 The above transfer matrix exhibits that the output phases are compounded by the product and sum of the input phases through inverter switches S7-S12 and rectifier switches S1-S6.           ⋅      ⋅+⋅ ⋅+⋅ ⋅+⋅      ⋅+⋅⋅+⋅ ⋅+⋅⋅+⋅ ⋅+⋅⋅+⋅ =           c b a C B A V V V SSSS SSSS SSSS SSSSSSSS SSSSSSSS SSSSSSSS V V V 612511 61059 6857 412311212111 4103921019 48372817 (7) The first row represents how output phase A is built from the input phase a, b and c and this mathematical expression can be interpreted again in the graphical viewpoint. If the equivalent circuit is seen from the inverter output phase A, two switches S7 and S8 of phase A half bridge is directly connected to input phases a, b and c through six rectifier switches S1-S6. Fig. 8 . . shows how the switch set of equivalent circuit can be transformed into the relevant switch set of the nine bidirectional switched matrix converter in the case of phase A and gives an basic idea that the duty cycles of the matrix converter branch can be derived by multiplying the duty cycles of the corresponding rectifier and inverter switches in the equivalent circuit [4]. (a) (b) Fig. 8. Transfor mation from equiv alent circui t to phase A in matrix c onverte r Therefore the indirect modulation technique enables well-known space vector PWM to be applied for a rectifier as well as an inverter stage. The switches of inverter can have only eight allowed combinations, because the output must not be short though three half bridge. This eight combination can be divide into six active nonzero output voltages vector V1 ~ V6 and two zero output voltages vector V0 show in Fig. 9. . The voltage space vector V1[100] indicates that output phase VA is connected to positive rail VDC+ and the other phase VB, VC are connected to negative rail VDC- and its vector magnitude is calculated from 6 3 4 3 2 3 4 3 2 1 3 2 3 1 3 1 3 2 3 2 3 2 π ππ ππ j DC j DC j DCDC j C j BA eV eVeVV eVeVVV ⋅= =         ⋅⋅−⋅⋅−⋅= =         ⋅+⋅+= (8) Fig. 9. Hexago n for inv erter voltag e For virtual rectifier is allowed nine switching combination to avoid a open circuit in rectifier. This nine combination is divided into six active nonzero input currents vectors I1 ~ I6 and three zero input currents vector I0 Fig. 10 I1 [ab] indicates that input phase a is connected to the positive rail of the virtual DC-link VDC+ and input phase b is to the negative rail VDC Its vector magnitude is calculated from 6 3 4 3 2 3 4 3 2 1 3 2 0 3 2 3 2 π ππ ππ j DC jj DCDC j c j ba eI eeII eIeIII − ⋅= =         ⋅+⋅−= =         ⋅+⋅+= (9) Fig. 10. Hexag on for r ectifier c urrent 5. Simulation Result The control of matrix converter is simulated using the Matlab-Simulink package. Equation (2,3) is used to obtain the elements of transfer matrix M(t). The most important part of the simulation on direct 444 control for MC is the generation of the switching functions of the bidirectional switches. These functions are gate drive signals of the power switches in the real converter. Simulation of indirect space vector control of MC generate gate drive signals on different way, first is checked the sector on phases and then is choose the correspond vector from table to get the right size of amplitude. Different between direct and indirect control is, that direct control is clearly mathematically based on equation and indirect control is based on predefined rules from table. Parameters of simulation: Source voltages 230V, 50Hz, load resistance R=1,1Ω, load inductance L=0,005H 5.1. Simulation Result for Direct Control of MC Fig. 11. Input Voltages Fig. 12. Input Currents Fig. 13. Output Vol ta ges Fig. 14. Output Curren ts 5.2. Simulation Result for Indirect Control of MC Fig. 15. Inpu t Voltages Fig. 16. Inpu t Currents Fig. 17. Output Voltag es 445 Fig. 18. Output Curren ts 6. Conclusion The working principle of the MC controlled with the direct transfer function approach and basic from indirect space vector control has been presented. Both control method was explained and used to get the block diagram for the simulation. The model reproduces a very good waveform on output side. In addition, it can be observed that the MC can generate output frequencies that are not restricted by the source frequency – explanation on indirect control, where is virtual DC-link, what is the case in phase controlled cycloconverters.If is use drive system with MC, then the the drive system is made for capable of operating in all four-quadrant regions. The simulation results agree with the theoretical expectations, that the direct convert are able created sinusoidal waveforms on output side, which is necessary for good working condition of drive systems. Bibliography [1] Altun H., Sunter. S.: Matrix Converter Induction Motor Drive: Modeling, Simulation And Control, Electrical Engineering 2003 [2] Rodriguez J., Silva E., Burgos R., Blaabjerk F.: Modelling, Analysis and Simulation of Matrix Converters, 2003 [3] Alesina A., Venturini M : Analysis and Design of Optimum-Amplitude Nine-Switch Direct AC-AC Converters, IEEE Transactions on Power Electronics, Vol. 4 .No.1., 1989 [4] Osmančík L., Kabašta M.: Maticové měniče, Elosys 2007, Trencin 2007 [5] Wheeler P., Rodriguez J., Clare J., Empringham L., Weinstein A : Matrix Converters: A Technology Review, IEEE Trans. Ind. Electron., vol. 49, N◦2, April 2002 [6] Wheeler P., Clare J.C., Empringham L.: A Vector Controlled MCT Matrix Converter Induction Motor Drive with Minimized Commutation Times and Enhanced Waveform Quality, IEEE Industrial Application Society Annual Meeting, Pittsburgh 2002 [7] Clare J., Wheeler P.: Introduction to Matrix Introduction to Matrix Converter Technology, IEE Seminar 2003 [8] Kabašta M.: Metody řízení maticových měničů, Elosys 2008, Trencin 2008 Authors: Ing. Michal Kabašta VŠB – Technical University of Ostrava 17. listopadu 15 708 33 Ostrava – Poruba Czech Republic email: michal.kabasta.fei@vsb.cz 446 . control of matrix converter, second is indirect control of matrix converter. 2.1 Limitation of Control for MC For explanation of limitation of control is use Fig. 4. where is simplified 3ph 3ph. matrix. [ ] )( tM is modulation matrix. Simulation result for this control for matrix converter will be show below. 4. Indirect Space Vector Control of Matrix Converter A principle of this control strategy. Indirect Space Vector Control of Matrix Converter Michal Kabasta, VSB – Technical University Ostrava Abstract In this paper is presents a control strategy for three-phase matrix converter,