A New Family of Matrix Converters

8/22/2019 A New Family of Matrix Converters

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IECONOl: The 27th Annual Conference of the IEEE Industrial Electronics Society

A New Family of Matrix ConvertersRobert W. Erickson

Colorado Power Electronics CenterUniversity of Colorado

Boulder, CO 80309-0425, [email protected]

Abstraci-A new fam ily of matrix co nverters is introduced, thatemploys relatively simple voltage-clamped buses and can gener-ate multilevel voltage waveforms of arbitrary magnitude andfrequency. The basic configuration includes a n ine-switch matrixthat uses four-quadrant switch cells. Each four-quadrant switchcell resembles a full-bridge inverter and can assume three volt-age levels during condu ction. Semicondu ctor devices in a switchcell are clamped to a know n constant dc voltage of a capacitor.Control of the inpu t and ou tput voltage waveforms of the pro-posed converter can be achieved through space vector modula-tion. Simulation results show how the converter can operate withany input and output voltages, currents, frequencies, and powerfactors while maintaining con stant dc voltages across all switchcell capacitors.

I. MTRODUCTIONMultilevel conversion has attracted significant attention, as away to construct a relatively high-power converter usingmany relatively-small power-semiconductor devices [1,2].This approach has the advantages of reduced switching lossand reduced harmonic content of output ac waveforms. Thepeak voltages applied to the semiconductor devices areclamped to capacitors whose dc voltages can be controlledvia feedback. When the input and output voltage magnitudesdiffer significantly, it is also possible to reduce the conductionlosses using multilevel techniques; this property can improvethe energy capture of variable-speed wind power systems.Although multilevel conversion requires a larger packagingand parts count, the total silicon area can in principle bereduced because of the reduced device voltage ratings. Thus,higher performance is attained at the expense of increasedcontrol and complexity.As the number of levels is increased, the bus bar structuresof multilevel dc-link converter systems can become quitecomplex and difficult to fabricate. A solution to this problemis the use of the simple voltage-clamped switch cell illus-trated in Fig. 2 [3]. This circuit locally clamps the voltagesapplied to the semiconductor devices to the value K Thisswitch cell is capable of producing the instantaneous voltages+


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IECONO1: 'The 27th Annua l Conference of the IEEE Industrial Electronics Society

(a)

(b)Three-phaseacsys te in 1

Three-phaseac system 2a

Fig. 3 Proposed new matrix converter, basic conf iguration.forms at both the input and output ports of the converter.

Section I11 describes control of a basic version of the pro-posed family of matrix converters. It is shown that space vec-tor control techniques can be adapted, for simultaneouscontrol of the input and output waveforms of the converter. Itis also shown that the capacitor voltages of the switch cellscan be stabilized by use of appropriate control. Simulationsconfirm the operation of the basic form of the new matrixconverters.

The proposed converters may find use in variable-speed acdrives, variable-speed wind power generation, and otherpolyphase ac-to-ac applications. They can take advantage ofthe substantial and ongoing advances in packaging and micro-controller technology, to improve the performances of ac-acpower converters.

11. CONVERTER DERIVATION AND OPERATIONA basic configuration of the proposed new multilevel matrixconverter is shown in Fig. 3. Superficially, the converterresembles a conventional matrix converter through its use of amatrix of nine four-quadrant switch cells. However, theswitch cells are realized as illustrated in Fig. 4. Each cellresembles the cells of Fig. 2, except that the cells do notrequire sources of dc power, and hence the dc voltage sourcesmay be replaced by capacitors. The transistors and diodeswithin each cell are clamped to the dc capacitor voltage,which can be regulated to a known dc value. As with theswitch cell of Fig. 2, this switch cell is capable of producingthe instantaneous voltages -+K 0, and -< when the devicesconduct, and is capable of blocking voltages of magnitudeless than V when all of the devices are off.

The use of four transistors in the switch cell of Fig. 4allows the average current to be doubled, relative to a conven-tional matrix converter whose four-quadrant switches arerealized using two transistors and two diodes. This is truebecause the currents conducted by the IGBTs are thermallylimited, and by proper control the current stresses can be

Fig. 4(a) switch c ell sym bol, (b) schematic diagram.spread over all four devices in Fig. 4.

The basic circuit of Fig. 3 is capable of limited multileveloperation. The semiconductor devices must be rated at leastas large as the peak applied line-to-line voltage. The converteris capable of both increase and decrease of the ac voltagemagnitude.

The number of voltage levels can be increased. Figure 5illustrates one approach to increasing the terminal voltage, inwhich switch cells are connected in series in each branch ofthe switch matrix. This allows increase of the terminal volt-ages without changing the voltage ratings of the semiconduc-tor devices.

The proposed multilevel matrix converter synthesizes theinput and output voltage waveforms by switching the knowndc capacitor voltages of the switch cells. This operation dif-fers from that of the conventional matrix converter in whichvoltage waveforms are synthesized on one side, and currentwaveforms on the other. Because of the symmetry of the con-verter, both step-up and step-down of the voltages are possi-ble.

Because of the inductors at both sides of the converter,cur-rent must flow continuously through the input and outputphases. Hence, operation of the switch cells must never leadto the open-circuiting of an input or output phase. Further,conduction of the switch cells must not form a closed loopwithin the branches of the switch matrix, since this couldshort-circuit the capacitors of the switch cells. Third, the volt-age applied to an open switch cell must not exceed the magni-tude of its capacitor voltage. These constraints limit thepossible connections within the switch matrix. They implythat, at any given instant, exactly five of the nine branches ofthe switch matrix must conduct. Further, the following rulesapply to the connections that are possible at a given instant:

There is exactly one connection path between any two phases.If any phase on one side (i.e., the input or output side) is con-nected directly to two conducting branches, then there must be

exactly one other phase from the same side also connecteddirectly to two conducting branches. The third phase must beconnected directly to one conducting branch.If any phase on one side (i.e., th e input or output side) is con-nected directly to three conducting branches, then the other

two phases from the same side must be each connecteddirectly to exactly on e conducting branch.

Realization of the switch cells of the proposed matrix converter:

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IECONO 1 The 27th Annual Conference of the IE EE Industrial Electronics Society

TABLE IPOSSIBLE BRANCH CONNECTION CONFIGURATIONS~ ~ ~

Phase A orU Phase B o r b Phase Cor c1branch 1branch 3 branches1 branch 2 branches 2 branches1branch 3 branches 1branch

2 branches 1branch 2 branches2 branches 2 branches 1branch3 branches 1branch 1 branch

Table I summarizes the possible configurations. There are atotal of 8 1 valid choices of branch connections.

The proposed converter can interface two asynchronousthree-phase ac systems. Both interfaces are inductive innature, wither intrinsically or through addition of seriesinductors. In the basic configuration of Fig. 3, the converterconsists of nine branches that each consist of a switch cell asin Fig. 4. To avoid interrupting the six inductor currents,exactly five branches must conduct current at any instant intime. It is important to avoid the cross-conduction and shoot-through currents that can occur when the transistors of six ormore branches conduct. However, turning off the transistorsof five or more branches does not cause a calamity, becausethe antiparallel diodes can conduct current and provide a pathfor the inductor currents to flow. Energy stored in the induc-tors is then transferred to the capacitors of the switch cells.One simple method for controlling the switching transitions isto first turn off all transistors that are to be switched off, andthen after a short delay, turn on the transistors that are to beswitched on. Other soft-switching schemes are also possible

Each switch cell of the multilevel matrix converter hasthree switch states corresponding to voltages of +Vcap, 0,- Vcap.his means that there are three switch states that aswitch cell may assume when it is used in a conductingbranch. Since there are five branches that may be turned on atany particular instant and three switch states per conductingswitch cell, the number of possible device switching combi-nations for each case of branch connection is 3,or 243, possi-ble device switching combinations. With 81 cases of branchconnections, the total number of device switching combina-tion becomes 243-81 = 19683 possible device switchingcombinations.

Figure 5 shows an example of three different deviceswitching combinations for one case of a branch connectionwith branches conducting between phases A-a, B-a, C-a,C-b, and C-c. This figure shows that it is possible to obtainfive different output voltage levels from the multilevel matrixconverter by switching only the devices of one switch cell (inbranch C-c). For this example, it is assumed that the midpointcapacitor voltage VCq is set to +240 V. Figure 5(a) produces 0volts for all line-to-line voltages on both sides of the con-verter. This is done by operating all switch cells of the con-

r71.

UTILITY SIDE MACHINE SIDEBranch Aa -240V

1Phase c=ov

=-240V

-48OV

Fig. 5connections. Five levels of output line-to-line voltages are obtained.ducting branches to produce voltages of+240 V. By changingthe switch cell connecting branches C-c to produce a voltageof zero, the converter can produce line-to-line output voltagesof - 240 V, 0 V, and +240 V, as shown in Fig. 5(b). In Fig.5(c) output line-to-line voltages of- 80 V, 0 V, and +480 Vare obtained. By alternating between the three device switch-ing combinations of Fig. 5, the basic multilevel matrix con-verter can produce five-level voltage waveforms with voltagelevels at - 480 V, - 240 V, 0,240 V, and 480 V at one side ofthe matrix converter. In each case, the nonconducting switchcells block voltages of magnitude 240 V.

The basic version of the converter, having one switch cellper branch of the switch matrix, is capable of multilevel oper-ation as illustrated in Fig. 5.However, the combinations hav-ing line-line voltages that are twice the capacitor voltages[e.g., the machine-side 480 V combination of Fig. 5(c)]require that zero voltage be applied to the opposite side [e.g.,the utility side in Fig. 5(c)]. This effectively limits the multi-level operation of the basic version of the converter to operat-ing points in which one side operates with low voltage.Nonetheless, such operation may find use in wind power andsimilar applications, where it is desirable to employ multi-level conversion to improve the converter efficiency at lowspeeds.

Figure 6 illustrates a multilevel version of the proposedmatrix converter family, in which each branch of the switchmatrix contains two series-connected switch cells. Eachswitch cell is again realized using the voltage-clamped bridgecircuit of Fig. 4.This converter is capable of producing five-level line-line voltages at the full rated operating point, withsharing of voltage stresses among the switch cells.

Three possible switching combinations, for one choice of branch

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IECON'OI :The 27th Annual Conference of the IEEE Industrial Electronics Society

Three-phaseacsysteni 1J J J

F F F Three-phasea

Fig. 6of Fig. 4in each branch of the switch matrix.A

new multilevel matrix converter containing two of the switch cells

111. CONTROLThe controller of the proposed multilevel matrix convertermust perform the following major tasks.

1 . Maintain fixed voltage (charge regulation) across all midpoint2. Synthesize input and output voltage waveforms.

capacitors.

Control that simultaneously accomplishes the above two tasksis demonstrated here. The space vector modulation techniqueis extended to the case of controlling the input and outputvoltage waveforms of the proposed converter; at the sametime, the controller regulates the capacitor voltages.

Upon analysis of all possible switching combinations, it isfound that the nineteen space vectors illustrated in Fig. 7are

Fig. 7the first quadrant are labeled; the remaining quadrants are symmetrical.Space vectors attainable b y the basic converterof Fig. 3. Values for

+paxis

Fig. 8 Reduced space vector diagram, control example.attainable at each side of the converter. Control of the input-side voltage is achieved by modulating between space vectorsadjacent to the desired reference vector [6]. Simultaneously,similar control is applied to control the output-side voltage.Even when both the input and output-side voltages are con-trolled, there exist additional degrees of freedom that can beused to control the dc capacitor voltages.

For example, consider the space vector modulation illus-trated in Fig. 8 . At a given point in time, it is desired to pro-duce the reference space vector VaF. This is accomplishedby modulating between three adjacent space vectors V, VI,and V,. The reference space vector k is expressed as a lin-ear combination of the space vectors Vo,k',, and k'*:

VREF d ,v,+d2V2+doVo (1)The duty cycles d , , d,, and do represent the durations fordevice switching combinations producing the space vectorsV,, V,, and V,, relative to the space vector modulation period.Since only three space vectors are used in this example, thethree duty cycles must add to unity. The duty cycles are foundby solution of the geometry of Fig. 8:

The term A4 in (2) is the modulation index, and its value can-not exceed unity in the above modulation scheme. Thus, thereference space vector V is synthesized by modulatingthrough switch configurations producing the space vectors Vo,V,, nd k', during a given SV M period.

With the above approach, the proposed multilevel matrixconverter is capable of operating with universal input and out-put voltage, frequency, and power factor.

To illustrate operation of the proposed new matrix con-

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IECONOl :The 27th Annual Conference of the IEEE Industrial Electronics Society

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Fig. 9 Simulated utility-side SVM ine-line voltages and inductor cur-rents, operating point l .

~ - - -- .I&..a '"-.--

_- . -_ . . . . .l:-.--#:mxTY:4 - ' ~ ~v -._ . L L L 1 - .UL.._

0 1 2 3 I 5 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 ~ 1 9 2 0 7 i Z 2 Z 3 2 4 2 5 2 6H r m r r O r d a"71

Fig. 10 Harmonic spectrum of the utility-side voltage of Fig. 9.verter, simulations of operation at two different operatingpoints are given in Figs. 9 to 13 . In these examples, the newmatrix converter interfaces a variable-speed wind generator toa 60 Hz utility. The basic (three-level line-line) operation ofthe new matrix converter is shown. Figure 8 shows simulatedvoltage and current waveforms for the three-phase ac utilityside, at operating point 1. The utility side is at 240 V, 1 1 A,60 Hz, and unity power factor. For this operating point, thegenerator side is at 240V, 25 Hz, and unity power factor. Theconverter switching frequency is set to 1 kHz. The simulatorimplements the space vector modulation described above tocontrol the new matrix converter, and hence synthesizes thedesired PW M input and output voltage waveforms. Thepulse-width modulated waveforms in Fig. 9 are line-to-linevoltages and the sinusoids are phase currents. Since this is apositive phase sequence, the set of phase currents lags the setof line-to-line voltages.

Figure 10 shows the harmonic spectrum of utility side line-to-line voltage V' .Notice the high magnitude harmonics inthe vicinity of the 18'hharmonic. These are due to the switch-ing frequency of 1kHz.

Figure 1 1 shows the generator-side voltage and currentwaveforms for the same operating point. The simulator is pro-grammed to select appropriate device switching combinationsto maintain constant dc voltages across all switch cell capaci-tors in addition to synthesizing the desired input and outputwaveforms. Figure 12 shows the regulated capacitor voltagesacross all nine switch cells. Using nine switch cells consti-

-- _I_____..__-_-___

.... .-. __ _

Fig. 1 1 Simulated generator-side SVM line-line voltages and inductorcurrents, operating point 1.

Fig. 12 Regulation of capacitor voltages, operating point I .tutes the most basic converter configuration with one switchcell per branch. All capacitor voltages are maintained within+- 12% of their nominal values.

Figure 13 illustrates the effect on the spectrum of increas-ing the switching frequency to 20 IrHz.The harmonic spec-trum of the utility side line-to-line voltage V,, is plotted.Notice that all of the high magnitude harmonics of Fig. 10 aremoved to higher harmonic numbers, corresponding to the20 kHz switching frequency.

Operation at nonunity power factor is illustrated by operat-ing point 2. At this point, the utility-side voltage and currentare 240 V, 11 A, 60 Hz, 0.5 power factor, with 1 kHz switch-ing frequency. The generator side operates at 60 V, 6.25 Hz,and unity power factor. The utility-side waveforms are illus-trated in Fig. 14. Figure 15 shows regulation of the capacitor

0 1 2 1 5 6 1 B 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 ~ Z 2 ~ 2 4 2 5 2 6n o*Fig. 13spectrum of the utility-side ine-line voltage V,,, operating point 1 .Effect of increasing the switching frequency to 20 kHz, on the

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IECONO1: The 27th Annual Conference of the IEEE Industrial Electronics Society

T I REFERENCES0 1332 iap4 4Q 6332 6564 81 9312I i l l I I I I l l 1 I I

[l] A. NABAE, . TAKAHASHI,nd H. AKAGI,A New Neutral-Point Clamped PWM Inverter, IEEE Trans. Industry Applica-tions, vol. IA-17, No . 5, Sept./Oct. 1981, pp. 518-523.[2] P. BHACWATnd V. STEFANOVIC,Generalized Structure of aMultilevel PWM Inverter, IEEE Transactions on IndustryApplications, vol. IA-19,no. 6, Nov./Dec. 1983, pp. 1057-1069.[3] F. Z . PENCnd J. S. LAI, A Multilevel Voltage-Source Inverterwith Separate DC Sources,Proceed ings IEEE Industry Appli-cations Society Annual Meeting, 1995, pp. 2541-2548.Fig. 14 Utility-side voltages, operatilngpoint 2.[4] 0. A. AL-NASEEM,Modeling an d Space Vector Control of aNovel Multilevel Matrix Converter for Variable-Speed Wind

Power Generators, Ph.D. thesis, University of Colorado, April2001.[5] A. ALESINA nd M. VENTURINI, Analysis and Design of Opti-mum Amplitude Nine-Switch Direct AC-AC Converters,IEEE

Transactions on Pow er Electronics, vol. 4 , no. 1, January 1989.[6] L. HUBERnd D. BOROJEVIC,Space Vector Modulated Three-Phase to Three-phase Matrix Converter with Input Power Fac-

tor Correction, IEEE Transactions on Industry Applications,vol. 31, no. 6, Nov./Dec. 1995.Fig. 15 R egulation of the capacitor voltages under nonunity power factor [71 s.BERNETnd R, EICHMA,

A New Family of Matrix Converters

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