The absence of modulator in model based predictive control technique for different converter topologies generates a variable switching frequency that produces high frequency harmonics and higher stress on the power semiconductor devices. In this paper, a novel model based predictive control strategy with a fixed switching frequency applied to a three-phase cascade H-bridge multilevel STATCOM is introduced with the aim to increase the performance of classical model predictive control. Simulation results show increased performance of the proposed control method in terms of current waveform total harmonic distortion.CONACYT – Consejo Nacional de Ciencia y TecnologíaPROCIENCI

Comparatore Franco, Leonardo David

Gregor Recalde, Raul Igmar

Pacher Vega, Julio Cesar

Renault, Alfredo

Rivera, Marco

Rodas Benítez, Jorge Esteban

English

Repositorio Institucional CONACYT

Model Based Predictive Current Control for aThree-Phase Cascade H-Bridge MultilevelSTATCOM Operating at Fixed Switching FrequencyL. Comparatore, R. Gregor, J. Rodas, J. Pacher and A. RenaultLaboratory of Power and Control SystemsUniversidad Nacional de AsunciónLuque, ParaguayM. RiveraDepartment of Electrical EngineeringUniversidad de TalcaCuricó, ChileAbstract—The absence of modulator in model based predictivecontrol technique for different converter topologies generatesa variable switching frequency that produces high frequencyharmonics and higher stress on the power semiconductor devices.In this paper, a novel model based predictive control strategy witha fixed switching frequency applied to a three-phase cascadeH-bridge multilevel STATCOM is introduced with the aim toincrease the performance of classical model predictive control.Simulation results show increased performance of the proposedcontrol method in terms of current waveform total harmonicdistortion.Index Terms—Cascade H-bridge converter, fixed switchingfrequency, model based predictive control.NOMENCLATURECHB Cascade H-bridge.MBPC Model based predictive control.MSE Mean squared error.PCC Point of common coupling.STATCOM Static synchronous compensator.THD Total harmonic distortion.I. INTRODUCTIONThe major reasons for the growing interest in the use ofMBPC technique are the evolution of data processing capa-bilities of the digital signal processors, its nonlinear operation,fast dynamic response and simplicity to represent differentcontrol objectives by a cost function. Classical MBPC methodconsists in use a precise mathematical model of the system tohave an accurate prediction of the behavior of the controlledvariables, where the prediction is carried out for each possibleswitching state, that in power converters, there are alwaysa limited number of valid switching states. Next, an opti-mization process uses this information to evaluate a definedcost function for each prediction to provide the control actionthat minimizes such cost function. Then, the control actionselected is applied in the next sampling time [1]. The classicMBPC has the particularity to provide a variable switchingfrequency, due to the absence of modulator. In terms of powerquality, not only the spread spectrum and the high frequencyharmonics are shown in the output waveforms but also thehigh stress on the power semiconductor devices. In order tosolve these issues, a novel approach for different topologiesand its applications has been presented: three-phase activerectifier [2], two-level voltage source inverters [3]-[5], directmatrix converters [6], [7], active power compensators [8],neutral pointed clamping converters [9] and 7-level CHBback-to-back converter [10]. Of all of the different topologiesand their applications, the CHB multilevel converters-based isone of the most commonly used and an attractive topologydue to their modularization, extensibility, control simplicityand high-quality output [11], [12].The purpose of this paper is to use a MBPC strategy withfixed switching frequency, in order to control a three-phaseCHB 7-level STATCOM. Noteworthy that the proposal is notinnovative, however, still now is not recorded in the literatureneither simulations results nor experimental results of thiscontrol technique applied to three-phase CHB 7-level converterfor STATCOM applications. The proposed control approachconsists in to include a modulation stage in the optimizationalgorithm of the classical MBPC, to generate the duty cyclesfor two active switching states and one null switching statewhich are applied to the CHB 7-level STATCOM using aswitching pattern procedure. An optimization process con-sidering a defined cost function allows calculating the dutycycles of each switching state.II. CHB CONVERTER-BASED STATCOM MODELFig. 1 shows the three-phase 7-level CHB converter-basedSTATCOM coupled to the power grid and the load througha shunt power filter (Lf -Rf ), connected in the PCC. TheSTATCOM is composed by three cells H-bridge per phasewith an independent DC-link for each cell. All DC-link buseshave the same voltage vdc and the same capacitance Cdcvalues. Each cell contains four switching devices which areactivated with digital signals sφij , being φ the correspondingphase (a, b or c), i the cell number (1, 2 or 3) and j theswitching device (1, 2, 3 or 4). With the purpose of avoidinga short-circuit in the DC-link, the signals sφi1 and sφi3 arecomplementary to sφi2 and sφi4 respectively. Then, to adjust978-1-5090-5339-1/17/$31.00 © 2017 IEEEFig. 1. Three-phase 7-level CHB converter-based STATCOM system connection.the output voltage vφc , only 2nc = 6 signals are needed. Eachphase have nc = 3 number of cells and ε = 22nc = 64possible switching states. Furthermore, each switching statecorresponds to a switching function Fφs =∑nci=1 Fφi , whereFφi is the switching function for the cell i, whose possiblevalues are shown in Table I.TABLE ISWITCHING FUNCTIONS FOR THE CELL “i”sφi1 sφi3 sφi2 sφi4 Fφi1 0 0 1 +11 1 0 0 00 0 1 1 00 1 1 0 −1The output voltage can be synthesized as a function of theDC-link voltage vdc and the switching function Fφs as:vφc = Fφs vdc (1)Using Kirchhoff’s circuit laws, the continuous time-domainmodel of the CHB converter-based STATCOM is:diφcdt=vφsLf− RfLfiφc −vφcLf(2)where iφc is the current injected by the CHB converter-basedSTATCOM and vφs the grid voltage.The discrete time-domain model is obtained by using theforward-Euler discretization method:iφc (k+1) =(1− RfTsLf)iφc (k)+TsLf{vφs (k)− vφc (k)}(3)being Ts the sampling time, k identifies the actualdiscrete-time sample and iφc (k + 1) are the predictions of theSTATCOM phase currents made at sample k.III. PROPOSED PREDICTIVE CONTROL WITH FIXEDSWITCHING FREQUENCYThe classical MBPC technique uses the predictive modelrepresented by (3) to predict the behavior of the future statesof all possible switching states. Then, the predicted errors forcurrent tracking are calculated as follows:eiφc (k + 1) = iφ∗c (k + 1)− iφc (k + 1) (4)where the superscript (∗) indicates a reference variable.The cost function (for each phase φ) is defined as a quadraticmeasure of the predicted error, as follows:gφ =‖ eiφc (k + 1) ‖2 (5)where ‖ . ‖ denotes the magnitude of the variable.Finally, the switching state that generates the minimumvalue of the defined cost function is selected by an opti-mization process clearly described in the Algorithm 1. Thisoptimum switching state is applied in the next sampling timeduring the whole switching period.Algorithm 1 Optimization algorithm of the classic MBPC1. Initialize gaopt :=∞, gbopt :=∞, gcopt :=∞, η := 02. Compute ia∗c (k + 1), ib∗c (k + 1) and ic∗c (k + 1)3. while η ≤ ε do4. Compute iac (k + 1), ibc(k + 1) and icc(k + 1)5. Compute eiac (k + 1), eibc(k + 1) and eicc(k + 1)6. Compute ga, gb and gc7. if ga < gaopt then8. gaopt ← ga, F as,opt ← F as,η9. end if10. if gb < gbopt then11. gbopt ← gb, F bs,opt ← F bs,η12. end if13. if gc < gcopt then14. gcopt ← gc, F cs,opt ← F cs,η15. end if16. η := η + 117. end whileA. Classical vs. proposed MBPCThe main difference between the proposed method and theclassical MBPC, is that the proposed method proceeds as(a) (b)Fig. 2. Block diagram for: (a) the classic MBPC, (b) the proposed MBPC at fixed switching frequency.space vector modulation. In space vector modulation, eachsector is defined by two adjacent vectors (and one null vector),nonetheless, in this work, the “sectors” are defined by twoconsecutive active (or no-null) states and one null state (pleaserefer to Appendix). For simplicity, always η = 1 is usedas null state (where η is the state number, defined in theAppendix). Then, the first sector is the one between switchingstate number η = 2 and switching state number η = 3,the second sector, the one between switching state numberη = 3 and switching state number η = 5, and so on. The twooptimum states are chosen by an optimization process thatevaluates the predicted errors separately for each predictionand are applied during specified times, being their duty cyclesinversely proportional to the respective cost functions.The block diagram of the classic MBPC method and theproposed method are shown in Fig. 2, where the switchingpattern block is highlight.B. Cost function optimizationThe new cost function (for each phase φ) for the proposedmethod is defined as the sum of the cost functions gφ1,2 definedby (5) whose respective weighting factors are the duty cyclesτφ1,2 for the two active states, leaving the equation as:gφ = τφ1 gφ1 + τφ2 gφ2 (6)The switching state that generates the lowest value of thecost function must be applied higher time, i.e., the dutycycle must be inversely proportional to the cost function. Theduty cycles for the two active switching states and one nullswitching state are calculated by solving:τφ0 = Kφ/gφ0τφ1 = Kφ/gφ1τφ2 = Kφ/gφ2τφ0 + τφ1 + τφ2 = 1(7)where τφ0 correspond to the duty cycle of a null state whichis evaluated only one time and Kφ is the constant of propor-tionality.The expressions of the duty cycles for each switching stateare given solving (7) for Kφ as:τφ0 = gφ1 gφ2 /(gφ0 gφ1 + gφ1 gφ2 + gφ0 gφ2)τφ1 = gφ0 gφ2 /(gφ0 gφ1 + gφ1 gφ2 + gφ0 gφ2)τφ2 = gφ0 gφ1 /(gφ0 gφ1 + gφ1 gφ2 + gφ0 gφ2) (8)Being the turn-on times (Tφ0 , Tφ1 and Tφ2 ) the products ofmultiplying the duty cycles (τφ0 , τφ1 and τφ2 ) by the samplingtime, respectively.Finally, the optimization process (for each phase φ) isillustrated in Algorithm 2.Algorithm 2 Optimization algorithm of the proposed method1. Initialize gφopt :=∞, η := 02. Compute i∗c(k + 1)3. Compute iφc 0(k + 1)4. Compute eiφc 0(k + 1)5. Compute gφ0 = gφ0 (k + 1)6. while η ≤ % do7. Compute iφc 1(k + 1) and iφc 2(k + 1)8. Compute eiφc 1(k + 1) and eiφc 2(k + 1)9. Compute gφ1 = gφ1 (k + 1) and gφ2 = gφ2 (k + 1)10. Compute τφ0 , τφ1 and τφ211. Compute gφ = τφ1 gφ1 + τφ2 gφ212. if gφ < gφopt then13. gφopt ← gφ14. Compute Tφ0 , Tφ1 and Tφ215. Fφs1,opt ← Fφs1,η, Fφs2,opt ← Fφs2,η9. end if10. η := η + 111. end whileC. Switching patternAt the end of the optimization process, the two optimumactive switching states (Fφs1,opt and Fφs2,opt) and the one nullswitching state are applied during their respective turn-ontimes using the switching pattern procedure that is shown inFig. 4, similar to [3], [4].Fig. 3. Switching pattern for the optimal switching states.D. Current reference generatorUsing the following Clarke’s transformation matrix:T =√23 1 −12 −120√32 −√321√21√21√2 (9)the instantaneous α− β current references are:[iα∗ciβ∗c]=1(vαs )2 + (vβs )2[vαs vβsvβs −vαs] [P ∗cQ∗c](10)where the instantaneous active and reactive power referencesideally are:P ∗c = 0Q∗c = −QL(11)being QL = vsαiLβ − vsβiLα the instantaneous reactive loadpower to be compensate.Finally, the STATCOM phase currents references used inthe optimization process are:[ia∗c ib∗c ic∗c ]′= T−1[iα∗c iβ∗c 0]′(12)where the superscript (′) indicates the transposed matrix.IV. SIMULATION RESULTSIn order to validate the effectiveness of the proposedmethod, simulation results in Matlab/Simulink environmentwere carried out, considering the electrical parameters shownin Table II. The performance of the proposed method arecompared with the results obtained with the classical MBPCimplementation, in both cases considering a 25 kHz of sam-pling frequency.A good current tracking is presented in Fig. 4 (upper),having a reduction in the MSE from 0.4206 A to 0.3207 A.Moreover, in Fig. 4 (bottom) it is possible to notice how theinstantaneous reactive power is compensated (Qc = −QL).The big spikes are consequence of the application of the nullvector in the switching pattern.TABLE IIPARAMETERS DESCRIPTIONElectric power gridPARAMETER SYMBOL VALUE UNITGrid frequency fe 50 HzGrid voltage vs 310.2 V7-Level CHB STATCOMFilter resistance Rf 0.09 ΩFilter inductance Lf 3 mHDC-link voltage vdc 154 VLoad parametersLoad resistance RL 23.2 ΩLoad inductance LL 55 mHPredictive control parametersSampling time Ts 40 µsSimulation step – 1 µsA comparison analysis between the proposed method andthe classical MBPC is shown in Fig. 5 considering; (upper)the switching pattern, (middle) the output voltages of theSTATCOM and (bottom) the THD of the analyzed outputvoltage. As shown in Fig. 5 (b) a more sinusoidal outputvoltage vac is obtained with respect to the output voltage than inFig. 5 (a) due to the switching pattern procedure. Furthermore,the operation at fixed switching frequency produces a moreconcentrated spectrum in exchange of a higher THD parameterof the output voltage (due to the way in which the sectors weredefined).Additionally, considering the interval 0.05 to 0.09 s, Fig. 6shows the improvement obtained in the THD performanceparameter of the grid current, that is about 65% (a drop from6.61% to 2.32%) using the proposed method.Fig. 4. CHB STATCOM response: (upper) current tracking, (bottom) reactivepower compensation.(a) Classical MBPC response (b) Proposed MBPC at fixed switching frequency responseFig. 5. Comparison performance considering: (upper) the switching pattern of the output voltage of the STATCOM obtained (middle) the output voltage ofthe STATCOM and (bottom) the THD of the output voltage.(a) Classical MBPC response (b) Proposed MBPC at fixed switching frequency responseFig. 6. Comparison performance considering: (upper) the grid current and (bottom) the THD of the grid current.V. CONCLUSIONIn this paper, a MBPC operating at fixed switching fre-quency applied to the three-phase CHB 7-level STATCOMhas been proposed. From the simulation results it is possible toconfirm a good capability of the proposed control technique tocompensate the reactive power and better performance in termsof THD and MSE, compared with the results obtained by theclassical MBPC. A comparative simulation results performedwith reference to the classical predictive control also showimprovements relative to the output voltage waveform.ACKNOWLEDGMENTThe authors would like to thank to the Paraguayan Go-vernment for the economical support they provided throughthe CONACYT Grant 14-INV-096. This work was also madepossible by the FONDECYT Regular Project No 1160690.REFERENCES[1] S. Kouro, M. A. Perez, J. Rodriguez, A. M. Llor, and H. A. Young,“Model predictive control: MPC’s role in the evolution of powerelectronics,” IEEE Ind. Electron. Mag., vol. 9, no. 4, pp. 8–21, 2015.[2] L. Tarisciotti, P. Zanchetta, A. Watson, J. C. Clare, M. Degano, andS. Bifaretti, “Modulated model predictive control for a three-phase activerectifier,” IEEE Trans. Ind. Electron., vol. 51, no. 2, pp. 1610–1620,2015.[3] M. Rivera, F. Morales, C. Baier, J. Muoz, L. Tarisciotti, P. Zanchetta, andP. Wheeler, “A modulated model predictive control scheme for a two-level voltage source inverter,” in Proc. ICIT, Seville, 2015, pp. 2224–2229.[4] M. Rivera, “A new predictive control scheme for a VSI with reducedcommon mode voltage operating at fixed switching frequency,” inPOWERENG, Riga, 2015, pp. 617–622.[5] M. Tomlinson, T. Mouton, and R. Kennel, “Finite-control-set modelpredictive control with a fixed switching frequency vs. linear control forcurrent control of a single-leg inverter,” in Proc. PRECEDE, Valparaiso,2015, pp. 109–114.[6] M. Vijayagopal, P. Zanchetta, L. Empringham, L. D. Lillo, L. Tarisciotti,and P. Wheeler, “Modulated model predictive current control for directmatrix converter with fixed switching frequency,” in Proc. EPE ECCE-Europe, Geneva, 2015, pp. 1–10.[7] M. Vijayagopal, L. Empringham, L. de Lillo, L. Tarisciotti, P. Zanchetta,and P. Wheeler, “Current control and reactive power minimization of adirect matrix converter induction motor drive with modulated modelpredictive control,” in Proc. PRECEDE, Valparaiso, 2015, pp. 103–108.[8] R. Rabbeni, L. Tarisciotti, A. Gaeta, A. Formentini, P. Zanchetta,M. Pucci, M. Degano, and M. Rivera, “Finite states modulated modelpredictive control for active power filtering systems,” in Proc. IEEEECCE, Montreal, 2015, pp. 1556–1562.[9] M. Norambuena, H. Yin, S. Dieckerhoff, and J. Rodriguez, “Improvedfinite control set model predictive control with fixed switching frequencyfor three phase NPC converter,” in Proc. PCIM Europe, Nuremberg,Germany, 2016, pp. 1–8.[10] L. Tarisciotti, P. Zanchetta, A. Watson, S. Bifaretti, and J. C.Clare, “Modulated model predictive control for a seven-level cascadedH-bridge back-to-back converter,” IEEE Trans. Ind. Electron., vol. 61,no. 10, pp. 5375–5383, 2014.[11] R. Gregor, A. Renault, L. Comparatore, J. Pacher, J. Rodas, D. Gregor,J. Muñoz, and M. 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IECON, Flo-rence, 2016, pp. 3672–3677.APPENDIXTABLE IIISWITCHING FUNCTIONS FOR A THREE-PHASE 7-LEVEL CHBCONVERTER-BASED STATCOM SYSTEMSφη η Fφs,ηsφ11 sφ13 sφ21 sφ23 sφ31 sφ330 0 0 0 0 0 1 00 0 0 0 0 1 2 -10 0 0 0 1 0 3 10 0 0 0 1 1 4 00 0 0 1 0 0 5 -10 0 0 1 0 1 6 -20 0 0 1 1 0 7 00 0 0 1 1 1 8 -10 0 1 0 0 0 9 10 0 1 0 0 1 10 00 0 1 0 1 0 11 20 0 1 0 1 1 12 10 0 1 1 0 0 13 00 0 1 1 0 1 14 -10 0 1 1 1 0 15 10 0 1 1 1 1 16 00 1 0 0 0 0 17 -10 1 0 0 0 1 18 -20 1 0 0 1 0 19 00 1 0 0 1 1 20 -10 1 0 1 0 0 21 -20 1 0 1 0 1 22 -30 1 0 1 1 0 23 -10 1 0 1 1 1 24 -20 1 1 0 0 0 25 00 1 1 0 0 1 26 -10 1 1 0 1 0 27 10 1 1 0 1 1 28 00 1 1 1 0 0 29 -10 1 1 1 0 1 30 -20 1 1 1 1 0 31 00 1 1 1 1 1 32 -11 0 0 0 0 0 33 11 0 0 0 0 1 34 01 0 0 0 1 0 35 21 0 0 0 1 1 36 11 0 0 1 0 0 37 01 0 0 1 0 1 38 -11 0 0 1 1 0 39 11 0 0 1 1 1 40 01 0 1 0 0 0 41 21 0 1 0 0 1 42 11 0 1 0 1 0 43 31 0 1 0 1 1 44 21 0 1 1 0 0 45 11 0 1 1 0 1 46 01 0 1 1 1 0 47 21 0 1 1 1 1 48 11 1 0 0 0 0 49 01 1 0 0 0 1 50 -11 1 0 0 1 0 51 11 1 0 0 1 1 52 01 1 0 1 0 0 53 -11 1 0 1 0 1 54 -21 1 0 1 1 0 55 01 1 0 1 1 1 56 -11 1 1 0 0 0 57 11 1 1 0 0 1 58 01 1 1 0 1 0 59 21 1 1 0 1 1 60 11 1 1 1 0 0 61 01 1 1 1 0 1 62 -11 1 1 1 1 0 63 11 1 1 1 1 1 64 0

Model based predictive current control for a three-phase cascade h-bridge multilevel STATCOM operating at fixed switching frequency

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Model based predictive current control for a three-phase cascade h-bridge multilevel STATCOM operating at fixed switching frequency

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