In this paper, a scheme for reactive power compen- sation and neutral current elimination based on model predictive control strategy is proposed. In this context, a H-bridge four-wire two-level active power filter is presented. The main feature of the proposed method focuses on the compensation of reactive power and neutral current elimination for unbalanced load in order to improve the power factor. This approach predicts the future behavior of the control actions considering all possible switching states. The proposed method selects the optimal switching vector by using an optimization process considering a defined cost function. The effectiveness of the proposed control approach is evaluated through simulations.CONACYT – Consejo Nacional de Ciencia y Tecnologí

Comparatore Franco, Leonardo David

Gregor Recalde, Raul Igmar

Pacher Vega, Julio Cesar

Renault, Alfredo

Rivera, Marco

Rodas Benítez, Jorge Esteban

English

Repositorio Institucional CONACYT

978-1-5090-1629-7/16/$31.00 c© 2016 IEEEModel Predictive Current Control with NeutralCurrent Elimination for H-Bridge Two-Level ActivePower FiltersA. Renault*, M. Rivera†, L. Comparatore*, J. Pacher*, J. Rodas* and R. Gregor**Laboratory of Power and Control Systems, Facultad de Ingenierı́a, Universidad Nacional de AsunciónE-mail: {arenault, lcomparatore, jpacher, jrodas, rgregor }@ing.una.py†Department of Industrial Technologies, Universidad de TalcaE-mail: marcoriv@utalca.clAbstract—In this paper, a scheme for reactive power compen-sation and neutral current elimination based on model predictivecontrol strategy is proposed. In this context, a H-bridge four-wiretwo-level active power filter is presented. The main feature of theproposed method focuses on the compensation of reactive powerand neutral current elimination for unbalanced load in orderto improve the power factor. This approach predicts the futurebehavior of the control actions considering all possible switchingstates. The proposed method selects the optimal switching vectorby using an optimization process considering a defined costfunction. The effectiveness of the proposed control approach isevaluated through simulations.Index Terms—Active power filters, H-bridge converter, predic-tive current control, neutral current elimination.I. INTRODUCTIONIn the last decades, the use of electronic-based powerloads increased greatly and consequently the contaminationof the distribution systems. In order to solve the variousproblems of power quality in distribution systems, activepower filters (APF) and multilevel static synchronous com-pensators (M-STATCOM) are considered one of the bestand the most popular solution [1]. The purpose of using afour-wire APF, is to perform the suppression of harmoniccurrent, reactive power compensation, power factor correc-tion and neutral current elimination [2], [3]. This can beachieved by the injection of currents at the point of commoncoupling (PCC) [4]. This type of APF usually requires fourH-bridge voltage source inverters (VSI) which provides neutralcurrent through the fourth H-bridge [5], or three H-bridge VSIwith star configuration and accessible neutral-wire [6].As main contribution, and complementing previous works,i.e. [7], a method for power compensation and neutralcurrent elimination applied to a three-phase four-wire H-bridgetwo-level APF is proposed by using predictive current control.Predictive model is obtained from the dynamic equations of thecompensation system. Simulation results have been analyzedin order to verify the effectiveness of the proposed method.This paper is organized as follows: Section II describesthe three-phase four-wire H-bridge APF topology. Section IIIdiscusses the proposed model-based predictive control (MPC)strategy. Section IV discusses the effectiveness of the proposedmethod considering the simulation results. Finally, concludingremarks are summarized in Section V.II. THREE-PHASE FOUR-WIRE H-BRIDGE APF TOPOLOGYFig. 1 shows the proposed three-phase four-wire two-levelH-bridge APF topology, consisting in one H-bridge cellsper phase. The different H-bridge cells have an independentDC-link (Cdc). Each cell contains four switching devices,resulting in a total of 16 power switchers. Consequently, fourswitching signals (Sfij ) are needed in order to controlledeach cell, where f represents the phase (a, b, c and n), i thecell number in the corresponding phase (1, 2, 3 or 4) and jthe switching device corresponding to the cell (1, 2, 3 or 4),respectively.Table I shows the allowed combinations of activation signalsand the respective output voltages corresponding to the Cell1of the phase “a”, where vdc is the voltage of the capacitor.Similar allowed combinations are defined for the other cells.Other possible combinations are not permitted because theycause a short circuit in the DC-link of the cell. To avoid this,only two activation signals and they complementary levels areused as shown in Fig. 1 for the particular case of Cell1.A. Two-level H-bridge APF modelThe dynamic model of the circuit configuration (Fig. 2) canbe obtained by using Kirchhoff’s circuit laws. For modelingpurposes, it is assumed that the three-phase voltage sourcesare balanced and all modules have the same capacitance andvoltage in their DC side. The two-level H-bridge APF isconnected at the PCC. Applying Kirchhoff’s voltage law forthe AC side of the APF, the following equations are obtained:diabcncdt=vabcnsLf− RfLfiabcnc −ncSfijvabcndcLf(1)dvabcndcdt=Sfij iabcncCdc− vabcndcRdcCdc(2)where nc is the number of cells, Rdc is a resistor connectedin parallel to the capacitor Cdc that concentrates the overalllosses in the DC side, Sfij is the commutation functionand the resistor Rf is the parasitic (series) resistance of theinductor Lf .Fig. 1. Three-phase four-wire two-level H-bridge APF.TABLE IALLOWED COMBINATIONS OF ACTIVATION SIGNALSSa11 Sa13 Sa12 Sa14 vac1 0 0 1 +vdc1 1 0 0 00 0 1 1 00 1 1 0 −vdcIII. PREDICTIVE CONTROL STRATEGYFor two-level H-bridge APFs, the differential equation thatmodels the AC side is [8], [9]:diabcncdt=vabcnsLf− vabcncLf− Rf iabcncLf(3)The predictive model can be obtained by using a forwardEuler discretization method from the continuous time-domainmodel represented by (3), which yields to the followingequation:iabcnc (k + 1) =(1− RfTsLf)iabcnc (k)+TsLf{vabcns (k)− vabcnc (k)} (4)where k identifies the actual discrete-time sample, Ts is thesampling time, and iabcnc (k + 1) are a prediction of the APFphase currents made at sample k.Fig. 3 shows the proposed scheme of the predictivecurrent control technique applied to the three-phase four-wiretwo-level H-bridge APF system. In the proposed control thepredicted errors are computed for each possible voltage vectoras:eiabcnc (k + 1) = iabcn∗c (k + 1)− iabcnc (k + 1) (5)being eic the APF current errors in the AC side, respectively.For each of them a cost function is evaluated. The cost functionhas been typically defined as a quadratic measure of thepredicted error, which can be defined as [7]:J(k + 1) =‖ eiabcnc (k + 1) ‖2 (6)Fig. 2. Two-level H-bridge APF connection.A. Reference generationThe instantaneous active and reactive power references areobtained from the Clarke transformation approach in α−β−0reference frame by using the following transformation matrix:T =√23 1 −12 −120√32 −√321√21√21√2 (7)Applying (7), the α−β− 0 current references in the AC sideof the APF are obtained from [10]:[i∗cαi∗cβ]=1(vsα)2 + (vsβ)2[vsα vsβvsβ −vsα] [P ∗cQ∗c](8)and i∗c0 simplified is:i∗c0 = iL0 (9)where the superscript (∗) denotes the reference variablesand P ∗c , Q∗c are the instantaneous active and reactive powerreferences and the P ∗c0 is the zero sequence instantaneouspower, respectively. In order to allow an unitary power factorat the grid side and considering which ideally the APF do notabsorb any active power, the instantaneous power referencescan be written as [11]:P ∗c = 0 (10)Q∗c = −QL = vsαiLβ − vsβiLα (11)P ∗c0 = −PL0 = −iL0vs0 (12)being QL the instantaneous reactive and PL0 is the zerosequence instantaneous power, in the load power to becompensate by the two-level H-bridge APF system. TheSTATCOM phase currents references used in the optimizationprocess are:Fig. 3. Block diagram of the proposed control scheme.iabc∗c = T−1[i∗cα i∗cβ i∗c0]′(13)where the superscript (′) indicates the transposed matrix.B. Optimization processThe optimization is performed by exhaustive search overall possible switching vectors of the control action. If n is thenumber of H-bridge cells per phase (f ), then each vector Sfijconsists in 2n choice signals, where j = 1, ..., φ; being φ thenumber of phases. Moreover, the number of possible switchingvectors per phase can be defined as ε = 22n. During theoptimization process, both, the cost function and the predictivemodel must be computed 4 times at each sampling periodto guarantee optimality, since there are 4 possible switchingvectors for the case study. These switching vectors representall possible output voltages of the STATCOM, vac , vbc , vcc andvnc , connected at the PCC point. The output voltages can berepresented by the following equation:vacvbcvccvnc =vc1vc2vc3vc4 vdc (14)where vc1, vc2, vc3 and vc4 are the optimal levels ofthe three-phase four-wire two-level H-bridge APF system(−1, 0, 1).IV. SIMULATION RESULTSThe proposed control strategy was simulated usingMATLAB/Simulink considering 40 kHz of samplingfrequency and 342 V of the DC side [12]. The electricalparameters as well as the MPC parameters are shown inTable II. Numerical integration using Runge-Kutta methodhas been applied to compute the evolution of the variablesstep by step in the time-domain.Algorithm 1 Optimization algorithm1. Initialize Jao :=∞, Jbo :=∞, Jco :=∞, Jno :=∞, η := 02. Compute the STATCOM reference currents. Eqn. (13)3. while η ≤ ε do4. Sfij ← Sηfij∀ i = 1, 2, 3, 4 & j = 1, 2, 3, 45. Compute the STATCOM prediction currents. Eqn. (4)6. Compute the errors. Eqn. (5)7. Compute the cost function. Eqn. (6)8. if Ja < Jao then9. Jao ← Ja, Sopta ← Saij10. end if11. if Jb < Jbo then12. Jbo ← Jb, Soptb ← Sbij13. end if14. if Jc < Jco then15. Jco ← Jc, Soptc ← Scij16. end if17. if Jn < Jno then18. Jno ← Jn, Soptn ← Snij19. end if20. η := η + 121. end whileFig. 4 (upper) shows the active and reactive power on the gridside. The active power remains constant load balanced, whenthe unbalance occurs to 0.04 s, oscillates due to impedancevariations and current circulating in the load. While thereactive power is maintained in the near average zero beforeand after the load unbalance. In Fig. 4 (bottom) iac , iaL andias currents are observed, respectively.On the hand Fig. 5 system behavior in balanced load isobserved during the first 0.04 s. At that moment the load ischanged in the phase “a”, which makes the load is unbalanced.The dynamics of the system tracks the reference current ia∗c ,,,,,,,Fig. 4. Two-level H-bridge APF transient response, active and reactive powercompensation.TABLE IIPARAMETERS DESCRIPTIONTwo-Level CHB STATCOMPARAMETER SYMBOL VALUE UNITElectric frequency of the grid fe 50 HzVoltage of the electric grid vs 310,2 VFilter resistance Rf 0,09 ΩFilter inductance Lf 3 mHDC-link voltage vdc 342 VLoad parametersLoad resistance RL 23,2 ΩNeutral load resistance RLn 1 ΩChange load RL 40 ΩLoad inductance LL 55 mHPredictive control parametersSampling time Ts 25 µsActive power reference P ∗c 0 WIdeal Reactive power reference Q∗c −QL VARZero sequence instantaneous power P ∗c0 −PL0 Weven if the load imbalance occurs, the system has performedwell by injecting reactive power.Then, in Fig. 6 the current in phase “a” of the APF, iac andia∗c to unbalance load occur, as current monitoring occurs.Moreover, Fig. 7 system dynamics is observed in the neu-tral charge inL, as the injected current inc and reference in∗cSTATCOM. Even at 0.04 s. the system has load balancingand load current inL is zero, the neutral current injected by theAPF. When the load unbalance occurs, the current injected bythe APF and the neutral current of the load 180 degrees so thatcompensate. It can observed that the neutral current of the inssource it is on average approximately zero, which meets theparameters of calculation and design of active filter.Fig. 5. Dynamic response evolution of vac , ias and current tracking consideringa reactive power step with a load change in the phase “a”.Fig. 6. Dynamic response evolution of iac , iac and current tracking consideringa reactive power step with a load change in the phase “a”.Fig. 7. Dynamic response evolution of inc , in∗c and inL neutral current in theload and injection current compensating filter neutral load with a load changein the phase “a”.V. CONCLUSIONIn this paper, a predictive current control technique for atwo-level H-bridge APF has been proposed and analyzed. Ithas been shown that it is possible to compensate the reactivepower and instantaneous neutral current in unbalanced loadfor improving the power factor of the mains. The simulationresults confirm the ability of the proposed technique in thefield of instantaneous reactive power compensation and neutralcurrent for unbalanced load.ACKNOWLEDGMENTThe authors would like to acknowledge the financial supportof FONDECYT Regular 1160690 project and ParaguayanGovernment support provided by means of a CONACYTproject 14-INV-096.REFERENCES[1] S. A. Kamran and J. Muñoz, “Study of a state-of-the art M-STATCOM,”in Proc. ICIT, 2015, pp. 2733–2738.[2] M. Kumar and M. Mishra, “Three-leg inverter-based distribution staticcompensator topology for compensating unbalanced and non-linearloads,” IET Power Electron., vol. 8, no. 11, pp. 2076–2084, 2015.[3] A. K. Balasubramanian and V. John, “Thermal test method for highpower three-phase grid-connected inverters,” IET Power Electron., vol. 8,no. 9, pp. 1670–1680, 2015.[4] G. Buticchi, D. Barater, C. Concari, and G. Franceschini, “Single-phaseseries active power filter with transformer-coupled matrix converter,”IET Power Electron., vol. 9, no. 6, pp. 1279–1289, 2016.[5] E. Fabricio, C. Jacobina, and V. Nobrega, “Four-wire shunt compensatorbased on H-bridge Y-connected converters,” in Proc. IECON, 2014, pp.5184–5190.[6] H. Huang, R. Xu, and H. Wang, “The study of three-phase four-wireshunt active power filter,” in Proc. MEC, 2013, pp. 3496–3499.[7] R. Gregor, L. Comparatore, A. Renault, J. Pacher, J. Rodas, S. Toledo,and M. Rivera, “A novel predictive-fixed switching frequency techniquefor a cascade H-Bridge multilevel STATCOM,” in Proc. IECON, 2016.[8] S. Mikkili and A. K. Panda, “Power quality issues and solutions–review,”Int. J. Emerg. Elec. Power Syst., vol. 16, no. 4, pp. 357–384, 2015.[9] A. Hamidi, A. Ahmadi, M. S. Feali, and S. Karimi, “Implementationof digital FCS-MP controller for a three-phase inverter,” Electr. Eng.,vol. 97, no. 1, pp. 25–34, 2015.[10] A. K. Panda and R. Patel, “Adaptive hysteresis and fuzzy logiccontrolled-based shunt active power filter resistant to shoot-throughphenomenon,” IET Power Electron., vol. 8, no. 10, pp. 1963–1977, 2015.[11] L. B. G. Campanhol, S. A. O. da Silva, and A. Goedtel, “Applicationof shunt active power filter for harmonic reduction and reactive powercompensation in three-phase four-wire systems,” IET Power Electron.,vol. 7, no. 11, pp. 2825–2836, 2014.[12] Y. Li, Z. Ye, N. He, J. Wu, C. Hu, and D. Xu, “Efficiency improvementof a SiC-MOSFET 500 kHz ZVS inverter,” in Proc. PEDG, 2016, pp.1–8.

Model predictive current control with neutral current elimination for H-bridge two-level active power filters

http://repositorio.conacyt.gov.py/bitstream/20.500.14066/3273/1/14-inv-096art9.pdf

Model predictive current control with neutral current elimination for H-bridge two-level active power filters

Abstract

Similar works

Full text

Available Versions

Repositorio Institucional CONACYT