Grid Connected Quasi-Z-Source Direct MatrixConverter

Omar Ellabban1,2, Senior Member, IEEE and Haitham Abu-Rub1, Senior Member, IEEE1Electrical and Computer Engineering Department, Texas A&M University at Qatar, Doha, Qatar

2 Electrical Machines and Power Engineering Department, Helwan University, Cairo, Egypt

Abstract— This paper proposes a new three-phase ac-ac convertertopology based on the Z-source concept and the conventional directmatrix converter (DMC), it is called quasi-Z-Source direct matrixconverter (QZSDMC). It could provide buck-boost function and makethe role of frequency changer. Compared with the traditional ac-dc-acconverter, it uses fewer devices and realizes direct ac-ac powerconversion, so as to have higher efficiency and better circuitcharacteristics. Compared with the traditional direct matrix converter,it provides wider voltage regulation range and improves input-outputvoltage transformation ratio. The proposed converter is tested as a gridconnected converter for interfacing renewable energy sources. Thecircuit topology, operating principle, control method and simulationresults are given to verify the feasibility of the proposed converter.

Keywords: Z-source converter (ZSC); Quasi-Z-source converter(QZSC); Quasi-Z-source direct matrix converter (QZSDMC).

I. INTRODUCTION

In recent years, matrix converters (MC) attractednumerous researchers because it can convert an AC powersupply voltage directly into an AC output voltage of variableamplitude and frequency without the need of an intermediatedc link, in addition, it provide a bidirectional power flow, acontrollable input power factor, and more compactdesign [1]. However, matrix converter has not becomecommercial so far due to its several unsolved problems. Themost critical problem is the reduced voltage transfer ratio,which defines as the ratio between the output voltage and theinput voltage, which is being constrained to 0.866, if inputand output waveforms should be sinusoidal. Thisdisadvantage strongly reduces the amount of possible MCapplications [2].

There are some discussions to improve the voltage transferratio for the MCs. One of the easy solutions is to connect atransformer between the power supply and the MC. However,the commercial frequency transformer applied in the powergrid frequency is bulky. On the other hand, a matrix-reactance frequency converter (MRFC), which consists of aMC and an AC chopper, have a voltage gain greater than one.The MRFCs comprise two groups: the integrated and cascadematrix-reactance frequency converters, IMRFC and CMRFCas shown in Fig. 1, respectively [3], [4], [5]. Unfortunately,the IMRFC typology has some disadvantages. First, thecontrol algorithm becomes complicated due to the requiredregular synchronizing between the MC and the chopper.Second, the voltage gain value is strongly dependents on thecircuit and the load parameters. Finally, the input powerfactor deteriorates, even for a resistive load. The CMRFCtopology has less passive components compared by theIMRFC topology; however, it has limited voltage gain,complicated damping control of the input current anddisturbed output current.

(a) IMRFC

(b) CMRFCFig. 1 Integrated and cascade matrix-reactance frequency converters

topologies [5]

The Z-source converter (ZSC) is an innovative powerelectronics converter technology presented recently. Itemploys a unique impedance network to couple the maincircuit of the converter to the power source. With propercontrol, the ZSC can buck or boost input voltage to a desiredmagnitude, which might be greater than the available dc busvoltage. The ZSC uses shoot-through (ST) state, turning ONtwo switches from the same phase leg, to boost the inputvoltage. Therefore, ST state now is one of the converter’snormal operating states and no longer a potential danger forthe circuit [6].

Therefore, by introducing the Z-source network to theconventional direct matrix converter (DMC), (Fig. 2a), whichwas recently proposed as Z-source direct matrix converter(ZSDMC), as shown in Fig. 2b, overcomes the low voltagegain of the traditional DMC; in addition, the Z-sourcenetwork allows the short circuit, which makes the ZSDMCcommutation easier [7]. The ZSDMC is derived from thetraditional DMC by only adding three inductors, capacitors,switches and diodes. However, the ZSDMC has a limitedvoltage boost ratio (voltage gain can only reach 1.15),inherited phase shift caused by the Z-source network, which

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makes the control inaccurate, and also discontinuous currentin the front of Z-source network. However, for the quasi-Z-source direct matrix converter (QZSDMC), as shown in Fig.2c, the voltage gain can go to 4-5 times or even higherdepending on the voltage rating of the switches, no phaseshift and lower switch voltage and current stress, in addition,this circuit has continuous input current [7].

The paper is organized as follows: section II presents thecircuit description; analysis and ST generation of theproposed QZSDMC; section III, describe the controlalgorithm of the grid connected QZSDMC; finally, sectionIV demonstrate the simulation results.

(a)

(b)

(c)Fig. 2 (a) Conventional Direct Matrix Converter (DMC); (b) Z-source directmatrix converter (ZSDMC) and (c) quasi-Z-source direct matrix converter

(QZSDMC)

II. QUASI-Z-SOURCE DIRECT MATRIX CONVERTER

The QZS network includes six inductors( , , , , , ), six capacitors ( , , , ,, ), and additional three bidirectional switches( , , ). One gate signal can be used to control these threeadditional switches because they have the same switchingstate. Therefore, the drive signal for , and can bedenoted as .

To study the operation principle, the QZSDMCs can besectioned into two switching states: ST and NST states. Fig. 3illustrates the equivalent circuits during these states for theQZSDMC. During the ST state in Fig. 3a, switch Sx is offand the output of QZSDMC is shorted for boost operation.While, during the NST state in Fig. 3b, switch Sx is on fornormal DMC operation. Due to the symmetry of the system,inductors of the QZS-network ( , , , , , )have the same inductance ( ), and the capacitors( , , , , , ) also have the same capacitance( ).

For one switching cycle, Ts, the time interval of the STstate is , and the time interval of the NST state is , thus,= + , and the ST duty ratio is = / . From Fig.3a, during the ST state, the following voltage equationsresulted in:= + − − (1)

where signifies the voltage, and the subscript andare the capacitors 1 and 2 of phase-x; and for theinductors 1 and 2 of phase-x; x = a, b, c. Over the NST state,its equivalent circuit is illustrated in Fig. 3b, and one can get:= + + − − (2)

The average voltage of the inductors over one switchingcycle, in steady state, should be zero, and owing to thesymmetric voltages of three-phase capacitors, one gets:= (3)

Define B as the boost factor and it is expressed as:= = (4)

where is the voltage amplitude of input voltage source andis the output voltage amplitude of the QZS-network.

(a)

(b)Fig. 3 Equivalent circuit of the QZSDMC: (a) ST state; (b) NST state

All the ST boost control methods that have been appliedfor the traditional ZSC can be applied to the QZSDMC with amodification of the carrier envelope. Fig. 4 illustrates thesimple boost PWM control strategy for the QZSDMC. Thecarrier waveform has the same envelope with the three-phasesource voltages, , and . The top envelope formed bythe maximum voltage among the three input phase voltages,and the bottom envelope formed by the minimum voltageamong them. While each switching period, the triangularcarrier is correlated with the output voltage references , ,and to produce their PWM signals ( , , ). The STreferences are used to insert the ST duty ratio in the finaloutput PWM signals. The ST pulses are generated by

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correlated the ST references with the carrier waveform, asillustrated in Fig. 5. The PWM pulse sequences , ,should be distributed to nine ac switches in order to generatethe expected PWM pulses [8].

Fig. 4 Simple boost PWM control for the QZSDMC

Fig. 5 Switching signals using simple boost method for QZSDMC

The simple boost control is achieved through two STreferences, in which both references are correlated to bothenvelopes by:

, = ( ) (5)

where will determine the ST duty ratio with a limitationthat the resultant minimum value of the top ST referenceshould be less than 0.5 p.u. and greater than . Therefore,1 ≥ ≥ (1 + 4 )/3 for the top ST reference, and itsnegative value is (− ) for the bottom ST reference. Themodulation index should be less than 0.5, given that theoutput references , , and can be with any frequency,any phase angle and with no harmonic injection. and

are the top and bottom envelopes of the source voltages,respectively. For the simple boost control, the ST intervalfrom the top reference can be determined by:= (6)

Where and are the ST duration per switching cycle andswitching time, respectively, and its ST duty ratio in halfcarrier cycle is:= (7)

Matrix converters have a nine bi-directional switches ,with turn-off capability, which allow the connection of eachone of the three output phases to any one of the three inputphases. Assuming that the matrix converter is fed by abalanced three-phase system with frequency , andconsidering that it is connected to the mains using a RLCinput filter, the input phases must never be short-circuited

and, due to the presence of an inductive load, the outputcurrents cannot be interrupted. Then, it is possible to obtain27 switching combinations. A nine-element matrix withelements representing the state of each bi-directionalswitch (if switch is off then = 0, else = 1), can beused to represent the output voltages ( , , ) as functionsof the input voltages ( , , ):= ∙ (8)

where , and are the QZS impedance networkoutputs 0[1].

III. PROPOSED GRID CONNECTED QZSDMC SYSTEM

The main goals of the grid interface control technique areto ensure the required power in a three phase grid duringbattery discharge and to provide enough charge power duringbattery charging. By regulating the capacitor voltage andhence the dc-link voltage at a certain level, the Z-sourceinverter can be conveniently regulated by a current controlmethod. Thus, an effective algorithm for the AC currentcontrol is needed. The controller for the AC side of theinverter was designed in the stationary reference frame usinga proportional plus resonance controller (PR), its transferfunction is[9]:( ) = + (9)

where , and are the proportional gain, the integralgain and the angular frequency at the fundamental frequency.The resonance controller gives an infinite gain at thefundamental frequency which results in integral action at thatparticular frequency while removing the steady state error.

Fig. 6 shows the control strategy of a grid connectedQZSDMC. Where P* is the required power injected into ordrawn from the grid. Using this power and the measured gridvoltage components in the stationary reference frame, , ,the reference currents are calculated by:∗ = ∙ ∗∗ = ∙ ∗ (10)

The phase angle θ of the grid voltage is detected by a PLLand is used in the abc-dq and dq-abc transformations. TwoPR controllers are used to control the d-q axis output currentcomponents. The output of these controllers is transformedfrom dq to abc to generate the modulation signals, as shownin Fig. 6.

IV. SIMULATION RESULTS

In order to verify the proposed grid connected QZSDMCsystem performance, simulations are carried out usingMATLAB/SIMULINK software using the parameters inTable 1. The proposed grid connected QZSDMC is tested forunity voltage gain operation, where the input RMS linevoltage is equal to the grid RMS line voltage, as shown inFig. 7 during the time interval 0-0.5 sec. in addition, the

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proposed system is tested for voltage gain greater that unity,as shown in Fig. 7 during the time interval 0.5-1 sec, asnoticeable from the figure the injected power to the grid isnot affected and the output voltage remains constant. Theproposed system is also tested under input voltage frequencychange, where the input frequency is equal to 30Hz duringthe time interval 0.3-0.4 sec, after that it is equal to 50Hzduring the time interval 0.4-0.5 sec and finally, it is 70Hz

during the time interval 0.5-0.6 sec, as shown in Fig. 8, wherethe output voltage and power remain unaffected. Finally, thesystem is subjected to output power change, where the outputpower is changed from 5 to 10 kW and the systemperformance is not affected. Therefore, the proposed systemis able to reject and disturbance in the input voltageamplitude; input voltage frequency and output power, whichverify the system stability.

Fig. 6 Proposed grid connected QZSDMC system

Fig. 7 System performance under variable input source voltage amplitude

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Fig. 8 System performance under variable input source frequency

Fig. 9 System performance under output power step

Table 1 Simulation System ParametersParameter ValueInput source parametersInput RMS LL voltage 380 VInput frequency 50 HzInput filter parametersInput filter inductance 1 mHInput filter capacitance 40 µFQZSDMC parametersQZS-network inductance, L 800 µHQZS-network capacitance, C 50 µFQZSDMC Switching frequency, Fs 10 kHzOutput filter parametersInput filter inductance 2 mHInput filter capacitance 40 µFGrid parametersGrid RMS LL voltage 380 VGrid frequency 50 z

V. CONCLUSIONThis paper proposed a new QZSDMC topology based on

the Z-source concept and conventional direct matrixconverter, its circuit structure and operating principle isintroduced, detailed control method and simulation results aregiven. Different disturbance, such as: input voltage change;input frequency change and output power change, areintroduced to verify the system robustness. The proposedconverter can be used for interfacing renewable energysources as it is a direct ac/ac converter with a voltage gaingreater than unity. The proposed converter topologycombines the advantage of both: the direct matrix converterand the Z-source concept.

The preliminary simulation results presented in this workare attractive enough to verify the proposed system and to

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justify additional research work to develop a more efficientQZSDMC grid connected system.

REFERENCES

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[3] Zbigniew Fedyczak and Pawel Szczesniak, “Matrix-reactance frequencyconverters using an low frequency transfer matrix modulationmethod”, Electric Power Systems Research, Vol. 83, no. 1, pp. 91-103,February 2012.

[4] Grzegorz TADRA, “Implementation of the Cascade Matrix ReactanceFrequency Converter using Space Vector Modulation method”, ElectricalReview, 4b/2012.

[5] Zbigniew Fedyczak, Pawel Szczesniak, Grzegorz Tadra and MariusKlytta, “A comparison of basic properties of the integrated and cascadematrix-reactance frequency converters”, 15th International PowerElectronics and Motion Control Conference (EPE/PEMC), 2012, 4-6Sept. 2012.

[6] F. Z. Peng, “Z-source inverter”, IEEE Transactions on IndustryApplications, Vol. 39, No. 2, pp. 504-510, Mar/Apr. 2003.

[7] Baoming Ge, Qin Lei, Wei Qian and F. Z. Peng, “A Family of Z-SourceMatrix Converters”, IEEE Trans. Ind. Electron, vol.59, no.1, p. 35-46,Jan. 2012.

[8] Qin Lei, Fang. Z. Peng, Baoming Ge, “Pulse-Width-Amplitude-Modulated Voltage-Fed Quasi-Z-Source Direct Matrix Converter withmaximum constant boost” the twenty-Seventh Annual IEEE AppliedPower Electronics Conference and Exposition (APEC), 5-9 Feb. 2012.

[9] Zhang S., Tseng K.J., Nguyen T.D., Wang X. and Vilathgamuwa D.M.,“Design of a robust grid interface system for PMSG-based wind turbinegenerators,” IEEE Transactions on Industrial Electronics, Vol. 58, No. 1,pp. 316- 328, Jan. 2011.

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