[IEEE IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society - Vienna,...
Transcript of [IEEE IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society - Vienna,...
Independent Control of Input Current and OutputVoltage for Modular Matrix Converter
Yuma Hayashi, Takaharu TakeshitaNagoya Institute of TechnologyGokiso, Showa, Nagoya, Japan
[email protected], [email protected]
Masakazu Muneshima, Yugo TadanoMeidensha Corporation
515, Kaminakamizo, Higashimakado, Numazu, Shizuoka, [email protected], [email protected]
AbstractβThis paper presents independent control of inputcurrent and output voltage for Modular Matrix Converter(MMxC). The MMxC is a multi-level converter without atransformer that converts from the high voltage AC to highvoltage AC with arbitrary amplitude and frequency. The controlmethod is difficult due to the simultaneous control of the inputcurrent and output voltage. The authors propose a novel controlmethod that is divided into two parts of the positive-sequencecircuit for the input current control, and the zero-sequence circuitfor the output voltage control. The effectiveness of the proposedcontrol method has been verified by simulations and experiments.
Index Termsβmodular matrix converter, converter control,current control, capacitor voltage balancing.
I. INTRODUCTION
Modular Matrix Converter (MMxC) is a multi-level con-verter without a transformer that converts from the highvoltage AC to high voltage AC with arbitrary amplitude andfrequency. The applications of an MMxC are high voltagelow frequency motor drive, high voltage wind generator anda frequency converter between 50 and 60 Hz.
Fig.1 shows the main circuit configuration of an MMxCthat consists of multiple modules constructed with H-bridgeand a dc capacitor. The circuit configuration of an MMxChas been proposed in a configuration without arm inductor πΏπ
[1]. The control method by space vectors has been proposedin papers [2], [3]. Since it is difficult to keep the continuity ofthe arm current in the arm constructed several series modules,the circuit configuration installed arm inductors πΏπ has beenproposed in the paper [4]. In the configuration with arm induc-tors, the control method has been proposed [5]-[8]. The controlmethod is complicated due to the simultaneous control bothinput current and output voltage. In the configuration using thez-winding three-phase inductors, the literatures [9],[10] haveproposed the independent control of input and output currentand indicated simulation results. However, the control methodis complicated because of fixed and rotational transformationsand Ξ£ Ξ modulation.
This paper presents a simple control method based onan independent control between the input current and theoutput voltage on the rotational frame. In the proposed controlmethod, the independent control between input current and theoutput voltage on the sub converter is realized and capacitorvoltage balancing loop is added.
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Fig. 1. Main circuit of Modular Matrix Converter
The proposed control theory on the configuration with thearm of three modules connected in series is developed. In theconfiguration of more than three series modules, the theory isdirectly applicable.
The effectiveness of the proposed control method has beenverified by simulations and experiments.
II. CIRCUIT CONFIGURATION AND ANALYTICAL MODEL
A. Circuit Configuration
Fig.1 shows the main circuit configuration of an MMxC.The MMxC consists of nine arms between the input terminalsπ , π, π and the output terminals π , π , π . Each arm isconstructed by three modules connected in series. The armreactor πΏπ for the arm current continuity is installed in eacharm in series. Each module consists of a H-bridge and a dccapacitor. The three arms connected to the output terminal π’
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is called as sub converter π . Since the module can generatethree output voltage levels of the dc capacitor voltage π£π, 0and βπ£π, the each arm can generate seven output voltage levelsbetween 3π£π and β3π£π.
B. Analytical Model
Fig.2 (a) shows the analytical model of sub converter π .The arms are expressed by the voltage sources π£βπππ’, π£βππ π’
and π£βππ‘π’. The load in phase π’ is a inductive load of π β πΏseries circuit. The input voltages ππ, ππ , ππ‘ and the outputvoltage references π£βπ’, π£
βπ£ , π£
βπ€ are given using the effective line
voltage πΈ, the phase angle π, angular frequency π of the inputvoltage, and the effective line voltage π β
πΏ , the phase angle πβπΏ,angular frequency πβ
πΏ of the output voltage reference by thefollowing equations.β‘
β£ ππππ ππ‘
β€β¦=
β2
3πΈ
β‘β£ cos πcos(π β 2π/3)cos(π + 2π/3)
β€β¦ (1)
π = ππ‘ (2)β‘β£ π£βπ’π£βπ£π£βπ€
β€β¦=
β2
3π βπΏ
β‘β£ cos πβπΏcos(πβπΏ β 2π/3)cos(πβπΏ + 2π/3)
β€β¦ (3)
πβπΏ = πβπΏπ‘ (4)
The sub converter π in Fig.2 (a) is divided into two circuitsof the positive-sequence circuit for input current control inFig.2 (b), and the zero-sequence circuit for the output voltagecontrol in Fig.2 (c). In the positive-sequence circuit in (b), theload current is zero because the load current is treated as zero-sequence current. In order to obtain the constant dc capacitorvoltage π£π, the input currents ππππ’, πππ π’, πππ‘π’ are controlledto be the unity power factor by the output voltages π£βπππ’,π£βππ π’, π£βππ‘π’. In the zero-sequence circuit in Fig.2 (c), the eacharm generates the same output voltage π£ππ’ for controlling the
output voltage π£π’. The load current ππ’ flows as zero-sequencecurrent. The arm current ππ’/3 in each arm flows.
The relations of the arm voltages and currents are obtainedas follows; β‘
β£ π£βπππ’
π£βππ π’
π£βππ‘π’
β€β¦=
β‘β£ π£βπππ’ + π£βππ’π£βππ π’ + π£βππ’π£βππ‘π’ + π£βππ’
β€β¦ (5)
β‘β£ πππ’ππ π’ππ‘π’
β€β¦ =
β‘β£ ππππ’ + ππ’/3πππ π’ + ππ’/3πππ‘π’ + ππ’/3
β€β¦ (6)
III. CONTROL METHOD
Fig.3 shows a proposed control block diagram of subconverter π .
A. Input Current Control
The transformation matrix of the synchronous rotating πβπframe with the input voltage is given by the following equa-tion.
[πΆππ] =
β2
3
[cos π cos(π β 2π/3) cos(π + 2π/3)βsin π βsin(π β 2π/3) βsin(π + 2π/3)
](7)
By using transformation matrix in (7), the input voltage ππ, ππ and ππ‘ in (1) is transformed to ππ and ππ on π β π frame asfollows; [
ππππ
]=
[πΈ0
](8)
The positive-sequence voltage equation in Fig.2 (b) is obtainedas follows; β‘
β£ ππππ ππ‘
β€β¦ =
π
ππ‘πΏπ
β‘β£ ππππ’πππ π’πππ‘π’
β€β¦ +
β‘β£ π£βπππ’π£βππ π’π£βππ‘π’
β€β¦ (9)
The voltage equation on πβ π frame is obtained from (7) and(9) as follows;[
ππππ
]=
π
ππ‘πΏπ
[ππππ’ππππ’
]+ ππΏπ
[0 β11 0
][ππππ’ππππ’
]+
[π£βπππ’π£βπππ’
](10)
where, ππππ’ and ππππ’ are active and reactive currents, respec-tively.
Substituting (8) into (10) and solving ππππ’ and ππππ’, thetransfer function from the arm voltages π£βπππ’ and π£βπππ’ to theinput currents ππππ’ and ππππ’ are obtained by (11).[
ππππ’ππππ’
]=
1
π πΏπ
{[πΈ0
]β[π£βπππ’π£βπππ’
]β ππΏπ
[0 β11 0
][ππππ’ππππ’
]}(11)
Fig.3 shows the control block diagram of sub converter π .From (11), the block diagram of positive sequence circuit inFig.3 is obtained. The control block of the positive-sequencecircuit in Fig.3 [A] Input Current Control is constructedby the current PI control, π β π decupling control and thecompensation for the source voltage. The current referencesare given by the average dc voltage control πβπ , capacitor
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[B] Average CapacitanceVoltage Control
[A] Input Current Control
[E] Output Voltage Control Output
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[F] Feed Forward Control
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voltage balance control among π , π and π phases πβπππ’πΆ , andthe feed forward control of the load power πβππ’πΉ as follows;[
πβπππ’πβπππ’
]=
[πβπ + πβππ’πΉπβπππ’πΆ
](12)
B. Average Capacitance Voltage Control
The instantaneous power ππ absorbed to the sub converterπ is obtained from (10) by the following equation.
ππ=[ ππππ’ ππππ’]
[π£βπππ’π£βπππ’
]β [ ππππ’ ππππ’]
[ππππ
]= ππππ’πΈ (13)
Fig.4 (a) and (b) shows the equivalent circuits for modulecapacitors of sub converter π and one capacitor, respectively.Since the instantaneous power ππ is supplied to the ninecapacitors provided, the instantaneous power ππ is expressedusing the average one equivalent capacitor voltage π£ππ’ and theequivalent capacitor current ππ as follows;
ππ=9π£ππ’ππ (14)
From (13) and (14), the equivalent capacitor current ππ isobtained by (15).
ππ =πΈ
9π£ππ’ππππ’ (15)
The relation between the average one capacitor voltage π£ππ’ andthe equivalent capacitor current ππ is given by the following
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(a) Module Capacitance (b) Average Module Capacitance
Fig. 4. Capacitor voltage of sub converter π
equation.
π£ππ’ =1
πΆ
β«ππππ‘ (16)
From (15) and (16), the Average Capacitor Voltage Circuitin Fig.3 is obtained. The capacitor voltage is regulated byPI controller using the error between the capacitor voltagereference π£βππ’ and the detected value π£ππ’ as shown in Fig.3[B] Average Capacitance Voltage Control.
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C. Voltage Balancing Control of Series Capacitors
The average capacitor voltage π£πππ’ connected in series atthe arm ππ’ is obtained as follows;
π£πππ’ =1
3(π£πππ’1 + π£πππ’2 + π£πππ’3) (17)
The voltage errors πππππ’1, πππππ’2 and πππππ’2 between thecapacitor voltages and the average voltage π£πππ’, and therelation among voltage errors are obtained.
β‘β£ πππππ’1
πππππ’2
πππππ’3
β€β¦ =
β‘β£ π£πππ’1 β π£πππ’π£πππ’2 β π£πππ’π£πππ’3 β π£πππ’
β€β¦ (18)
πππππ’1 + πππππ’2 + πππππ’3 = 0 (19)
For suppressing the unbalance of capacitor voltage, the ca-pacitor of higher voltage is much charged or little discharged.Function πππ’ based on the sign of the input current ππππ’ isdefined as
πππ’ =
{1 : ππππ’ β₯ 0β1 : ππππ’ < 0
(20)
The output voltage references π£βπππ’1, π£βπππ’2 and π£βπππ’3 aredetermined using the output voltage reference π£βπππ’ of armππ’ and the function πππ’ as follows;
β‘β£ π£βπππ’1
π£βπππ’2
π£βπππ’3
β€β¦ =
1
3
β‘β£ π£βπππ’
π£βπππ’
π£βπππ’
β€β¦+ πππ’
β‘β£ πππππ’1
πππππ’2
ππ£πππ’3
β€β¦ (21)
Fig.5(a) shows example of series capacitors voltage unbalanceunder π£πππ’3 > π£πππ’ > π£πππ’1 > π£πππ’2 in arm ππ’. Fig.5(b)shows the output voltage references of the modules underππππ’ β₯ 0 according to (21). Also , Fig.5(c) is in the case ofππππ’ < 0. The control block is [C] Voltage Balancing Controlof Series Capacitors in Fig.3. The series capacitor balancingcontrol does not influence to the arm output voltage becausethe amount of errors is zero in (19). The capacitor voltages inthe arms π π’ and π‘π’ can be similarly controlled.
D. Capacitor Voltage Balancing Control among Arms
The capacitor voltage errors πππππ’, ππππ π’, ππππ‘π’ from theaverage voltage π£ππ’ in sub converter π are given by thefollowing equation.
β‘β£ πππππ’
ππππ π’
ππππ‘π’
β€β¦ =
β‘β£ π£πππ’ β π£ππ’π£ππ π’ β π£ππ’π£ππ‘π’ β π£ππ’
β€β¦ (22)
The voltage error vector Λππππ’ on πβ π frame is obtained bytransforming (22) using the transformation matrix in (7) asfollows;
Λππππ’ =
[πππππ’
πππππ’
]= [πΆππ]
β‘β£ πππππ’
ππππ π’
ππππ‘π’
β€β¦ (23)
It is controlled by Fig.3 [D] Capacitor Voltage BalancingControl among Arms to zero in the Λππππ’.
E. Output Voltage Control
The output voltage is controlled by a zero-sequence circuitin Fig.2 (c). The three arms ππ’ π π’ and π‘π’ generate the samearm voltage π£βππ’ that is sum of the output voltage reference π£βπ’and the voltage drop across the input reactor πΏπ .
π£βππ’ = π£βπ’ + πΏππ
ππ‘(ππ’3) (24)
The zero-sequence circuit is independent from the positive-sequence circuit, the arm voltage references π£βππ’ can be addedto the phase voltage references calculated from the positive-sequence circuit as shown in Fig.3 [E] Output Voltage Control.
F. Feed Forward Control
For suppressing capacitor voltage fluctuations, the feedforward control of the instantaneous load power in Fig.3 [F]Feed Forward Control are derived. The instantaneous outputpower ππ’ in phase π is obtained from the output voltagereference π£βπ’ and the output current ππ’ by (25).
ππ’ = π£βπ’ππ’ (25)
In order to supply the input power equal to the load power, theinput active current reference πβππ’πΉ for feed forward in phaseπ is given by (26).
πβππ’πΉ =π£βπ’ππ’πΈ
(26)
IV. SIMULATION RESULTS
A. Simulation conditions
Fig.6 shows simulation circuit. Table I shows the simulationconditions. The source voltage is 200 V, 60 Hz for the samecondition of experiments. The Output voltage reference forapplying to 1.5 kVA inductive load is 120V, 10Hz. The averagecapacitor voltage reference π£βπ of 100 V is given.
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Fig. 6. Simulation circuit for MMxC
TABLE ISIMULATION CONDITIONS
Source voltage πΈ, π 200 V, 2πΓ60 rad/sArm reactor πΏπ 4 mHModule capacitor πΆ 1000 πFLoad π , πΏ 9.8 Ξ©, 20 mHOutput voltage reference π β
πΏ , πβπΏ 120 V, 2πΓ10 rad/s
Capacitor voltage reference π£βπ 100 VCarrier frequency ππ(= 1/2ππ ) 5 kHz
B. Simulation Waveforms
Fig.7 shows the voltage and current waveforms in simula-tion results. The colors of red, blue and green on the three-phase waveforms indicate the phases π , π and π , respectively.The sinusoidal source currents ππ of unity input power factorare obtained. The output voltage π£π’π£ is the sinusoidal wave-form with multi-level voltage. The sinusoidal output current ππ’are obtained. The input currents πππ’, ππ π’ and ππ‘π’ consist of onethird of the output current ππ’ and the sinusoidal source currentof 60 Hz. The capacitor voltages keep around 100 V withthe fluctuation voltage of 8 V. The voltages waveforms π£πππ’1,π£πππ’2 and π£πππ’3 of series capacitors are overlapped becausethe small unbalance voltages.
V. EXPERIMENTAL RESULTS
A. Experimental Conditions
Fig.8 shows the experimental circuit. Table II shows theexperimental conditions. The arm is constructed by one mod-ule.The source voltage is 200 V, 60 Hz for the same condition
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of simulations. The Output voltage reference for applying to1.5 kVA inductive load is 120V, 10Hz. The average capacitorvoltage reference π£βπ of 300 V is given.
B. Experimental waveforms
Fig.9 shows the experimental waveforms. The source cur-rents ππ of unity input power factor with distortion are ob-tained. The output voltage π£π’π£ is the sinusoidal waveformwith multi-level voltage. The sinusoidal output current ππ’ areobtained. The input currents πππ’, ππ π’ and ππ‘π’ consist of onethird of the output current ππ’ and the sinusoidal source currentof 60 Hz. The capacitor voltages keep around 300 V with thefluctuation voltage of 20 V.
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TABLE IIEXPERIMENT CONDITIONS
Source voltage πΈ, π 200 V, 2πΓ60 rad/sInput reactor πΏπ 4 mHModule capacitor πΆ 1500 πFLoad π , πΏ 9.8 Ξ©, 20 mHOutput voltage reference π β
πΏ , πβπΏ 120 V, 2πΓ10 rad/s
Capacitor voltage reference π£βπ 300 VCarrier frequency ππ(= 1/2ππ ) 5 kHz
VI. CONCLUSIONS
This paper presents a simple control method for a modularmatrix converter based on an independent control between theinput current and the output voltage on the rotational frame.In the proposed control method, the independently control ofinput current and the output voltage on the sub converter isrealized, and capacitor voltage balancing loop is added.
In the configuration with the arm of three modules con-nected in series, the stable operation waveforms have beenobtained by simulations. In the configuration with the arm ofone module, the experimental results have been obtained andbasic operations have been verified. Therefore the effectivenessof the proposed control method has been verified.
REFERENCES
[1] R. Erickson and O. Al-Naseem, βA new family of matrix converters,βin Industrial Electronics Society, 2001. IECONβ01. The 27th AnnualConference of the IEEE, vol. 2, 2001, pp. 1515 - 1520 vol.2.
[2] S. Angkititrakul and R. Erickson, βControl and implementation of a newmodular matrix converter,β in Applied Power Electronics Conference andExposition, 2004. APECβ04. Nineteenth Annual IEEE, vol. 2, 2004, pp.813 - 819 vol.2.
[3] S. Angkititrakul and R. W. Erickson, βCapacitor voltage balancing controlfor a modular matrix converter,β inConf. Rec. IEEE-APEC 2006.
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-600
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600
Fig. 9. Experiment results
[4] C. Oates, βA methodology for developing chainlink converters,β in PowerElectronics and Applications, 2009. EPEβ09. 13th European Conferenceon, sept. 2009, pp. 1 - 10.
[5] C. Oates and G. Mondal, βDc circulating current for capacitor voltagebalancing in modular multilevel matrix converter,β in EPE 2011 Birm-ingham, aug. 2011.
[6] D. C. Ludois, J. K. Reed, and G. Venkataramanan, βHierarchical controlof bridge-of-bridge multilevel power converters,β in Industrial Electron-ics, IEEE Transactions on, vol. 57, no. 8, pp. 2679 - 2690, aug. 2010.
[7] A. Korn, M. Winkelnkemper, P. Steimer, and J. Kolar, βDirect modularmulti-level converter for gearless low-speed drives,β in EPE 2011 Birm-ingham, aug. 2011.
[8] W. Kawamura and H. Akagi βControl of the modular multilevel cascadeconverter based on triple-star bridge-cells (MMCC-TSBC) for motordrives,β in ECCE 2012, sept. 2012, pp.3506 - 3513
[9] F. Kammerer, J. Kolb, and M. Braun, βA novel cascaded vector controlscheme for the modular multilevel matrix converter,β in IECON 2011Melbourne, Nov. 2011.
[10] F. Kammerer, J. Kolb, and M. Braun, βFully decoupled current controland energy balancing of the Modular Multilevel Matrix Converter,β inEPE/PEMC 2012, sept. 2012.
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