A Combination of Shunt Hybrid Power Filter and Thyristor-Controlled Reactor for Power Quality

A Combination of Shunt Hybrid Power Filterand Thyristor-Controlled Reactorfor Power QualitySalem Rahmani,Abdelhamid Hamadi,Student Member,IEEE,Kamal Al-Haddad,Fellow,IEEE,andLouis A.Dessaint,Fellow,IEEEAbstract—This paper proposes a combined system of a thyristor-controlled reactor(TCR)and a shunt hybrid power filter(SHPF)for harmonic and reactive power compensation.The SHPF is the combination of a small-rating active powerfilter (APF)and afifth-harmonic-tuned LC passivefilter.The tuned passivefilter and the TCR form a shunt passivefilter(SPF) to compensate reactive power.The small-rating APF is used to improve thefiltering characteristics of SPF and to suppress the possibility of resonance between the SPF and line inductances.A proportional–integral controller was used,and a triggering alpha was extracted using a lookup table to control the TCR.A nonlinear control of APF was developed for current tracking and voltage regulation.The latter is based on a decoupled control strategy, which considers that the controlled system may be divided into an inner fast loop and an outer slow one.Thus,an exact lin-earization control was applied to the inner loop,and a nonlinear feedback control law was used for the outer voltage loop.Integral compensators were added in both current and voltage loops in order to eliminate the steady-state errors due to system parameter uncertainty.The simulation and experimental results are found to be quite satisfactory to mitigate harmonic distortions and reactive power compensation.Index Terms—Harmonic suppression,hybrid powerfilter,mod-eling,nonlinear control,reactive power compensation,shunt hybrid powerfilter and thyristor-controlled reactor(SHPF-TCR compensator),thyristor-controlled reactor(TCR).I.I NTRODUCTIONN ONLINEAR loads cause significant harmonic currents with poor input power factor(PF),which create serious problems at the power supply system.Traditionally,passive Manuscript received May4,2012;revised September7,2012,December30, 2012,and March21,2013;accepted May11,2013.Date of publication July10, 2013;date of current version October18,2013.This work was supported in part by the Canada Research Chair in Energy Conversion and Power Electronics at theÉcole de Technologie Supérieure,by the Fonds de Recherche du Quebec-Nature et Technologie(FRQNT),and by the National Science and Engineering Research Council of Canada.A.Hamadi and K.Al-Haddad are with the Canada Research Chair in Electric Energy Conversion and Power Electronics,École de Technologie Supérieure, Montreal,QC H3C1K3,Canada(e-mail:abdelhamidhamadi@yahoo.fr;kama. al-haddadl@ele.etsmtl.ca).S.Rahmani is with the Canada Research Chair in Electric Energy Conversion and Power Electronics,École de Technologie Supérieure, Montreal,QC H3C1K3,Canada,and also with the Electrical Engineering Department,High Institute of Medical Technologies of Tunis,University of Tunis El-Manar,Tunisia(e-mail:rsalem02@yahoo.fr).L.A.Dessaint is with the Electrical Engineering Department,École de Technologie Supérieure,Montréal,QC H3C1K3,Canada(e-mail:dessaint@ ele.etsmtl.ca).Color versions of one or more of thefigures in this paper are available online at .Digital Object Identifier10.1109/TIE.2013.2272271filters have been used to eliminate current harmonics of the supply network.However,these devices suffer from resonance. Recently,thyristor-switchedfilters(TSFs),which contain sev-eral groups of passivefilters,have been used to compensate reactive power[1].The compensation amount of TSFs can be adjusted with the variation of load power[2].However,the parallel and the series resonance could occur between TSF and grid impedance.Activefilters were developed to mitigate problems of passivefilters[3]–[5].They are more effective in harmonic compensation and have good performance[6]–[8]. However,the costs of activefilters are relatively high for large-scale system and require high power converter ratings[9],[10]. Hybridfilters effectively soften the problems of the passive filter and an activefilter solution and provide cost-effective harmonic compensation,particularly for high-power nonlinear loads[11]–[14].Many control techniques such as instanta-neous reactive power theory,synchronous rotating reference frame,sliding-mode controllers,neural network techniques, nonlinear control[15],feedforward control[16],Lyapunov-function-based control[17],etc.,have been used to improve the performance of the active and hybridfilters.Severalfilter topologies for compensating harmonics and reactive power have been reported in the literature[18]–[21].In [18],a multiconverter conditioner topology formed by an active conditioner operating in parallel with a hybrid conditioner has been proposed.The hybrid conditioner consists of one or more passivefilters in series with a low-rated active powerfilter (APF).The conditioner compensates harmonic distortion,im-balance,and reactive power in three-phase four-wire systems. This topology constitutes an effective solution at high-power levels,which is cost-effective because of the kilovoltampere rating reduction of the inverters.A hybrid configuration based on the combination of a three-phase three-level neutral point clamped(NPC)inverter and a series connection of a three-level H-bridge inverter with a novel control scheme to control the floating voltage source of the H-bridge stage has been presented in[19].In this topology,the NPC inverter is used to supply the total active power while the H-bridges operate as series activefilters for the harmonic compensation of the NPC output voltage.The rating of the series activefilter is reduced because the latter provides only the reactive power for the operation of thefloating capacitor.In[20],a combination of a thyristor-controlled reactor(TCR)and a resonant impedance-type hybrid APF for harmonic cancellation,load balancing,and reactive power compensation has been proposed.The control strategy0278-0046©2013IEEEof the system is based on the voltage vector transformation for compensating the negative-sequence current caused by the unbalance load without using phase-locked loops.A predictive current controller based on the Smith predictor is proposed to compensate the generalized current delay.A combined system of a static var compensator(SVC)and a small-rated APF for harmonic suppression and reactive power compensation has been reported in[21].The SVC consists of a Y-connected passive powerfilter and a delta-connected TCR.The APF is used to eliminate harmonic currents and to avoid resonance between the passive powerfilters and the grid impedance.In this paper,a new combination of a shunt hybrid power filter(SHPF)and a TCR(SHPF-TCR compensator)is proposed to suppress current harmonics and compensate the reactive power generated from the load.The hybridfilter consists of a series connection of a small-rated activefilter and afifth-tuned LC passivefilter.In the proposed topology,the major part of the compensation is supported by the passivefilter and the TCR while the APF is meant to improve thefiltering characteristics and damps the resonance,which can occur between the passive filter,the TCR,and the source impedance.The shunt APF when used alone suffers from the high kilovoltampere rating of the inverter,which requires a lot of energy stored at high dc-link voltage.On the other hand,as published by some authors[15],the standard hybrid powerfilter is unable to compensate the reactive power because of the behavior of the passivefilter.Hence,the proposed combination of SHPF and TCR compensates for unwanted reactive power and harmonic currents.In addition,it reduces significantly the voltampere rating of the APF part.The control method of the combined compensator is presented.A control technique is proposed to improve the dynamic response and decrease the steady-state error of the TCR.It consists of a PI controller and a lookup table to extract the requiredfiring angle to compensate a reactive power consumed by the load.A nonlinear control of SHPF is developed for current tracking and voltage regulation purposes. It is based on a decoupled control strategy,which considers that the controlled system may be divided into an inner fast loop and an outer slow one.The currents injected by the SHPF are controlled in the synchronous orthogonal dq frame using a decoupled feedback linearization control method.The dc bus voltage is regulated using an output feedback linearization control.The SHPF can maintain the low level of dc bus voltage at a stable value below50V.The proposed nonlinear control scheme has been simulated and validated experimentally to compute the performance of the proposed SHPF-TCR com-pensator with harmonic and reactive power compensation and analysis through the total harmonic distortion(THD)of the source and the load current.The proposed methodology is tested for a wide range of loads as discussed further.Simulation and experimental results show that the proposed topology is suitable for harmonic suppression and reactive compensation.II.S YSTEM C ONFIGURATION OFSHPF-TCR C OMPENSATORFig.1shows the topology of the proposed combined SHPF and TCR.The SHPF consists of a small-rating APF connected in series with afifth-tuned LC passivefilter.The APF consists of a three-phase full-bridge voltage-source pusle width modu-lation(PWM)inverter with an input boost inductor(L pf,R pf) and a dc bus capacitor(C dc).The APF sustains very low fundamental voltages and currents of the power grid,and thus, its rated capacity is greatly reduced.Because of these merits, the presented combined topology is very appropriate in com-pensating reactive power and eliminating harmonic currents in power system.The tuned passivefilter in parallel with TCR forms a shunt passivefilter(SPF).This latter is mainly forfifth-harmonic compensation and PF correction.The small-rating APF is used tofilter harmonics generated by the load and the TCR by enhancing the compensation characteristics of the SPF aside from eliminating the risk of resonance between the grid and the SPF.The TCR goal is to obtain a regulation of reactive power.The set of the load is a combination of a three-phase diode rectifier and a three-phase star-connected resistive inductive linear load.III.M ODELING AND C ONTROL S TRATEGYA.Modeling of SHPFThe system equations arefirst elaborated in123reference ing Kirchhoff’s voltage law,one can writev s1=L PFdi c1dt+R PF i c1+v CPF1+v1M+v MN v s2=L PFdi c2dt+R PF i c2+v CPF2+v2M+v MN v s3=L PFdi c3dt+R PF i c3+v CPF3+v3M+v MN v CPF1=L Tdi c1dt−C PF L T d2v CPF1dt2v CPF2=L Tdi c2dt−C PF L T d2v CPF2dt2v CPF3=L Tdi c3dt−C PF L T d2v CPF3dt2dv dcdt=1C dci dc.(1)The switching function c k of the k th leg of the converter(for k=1,2,3)is defined asc k=1,if S k is On and Skis Off0,if S k is Off and Skis On.(2)A switching state function d nk is defined asd nk=c k−133m=1c mn.(3)Moreover,the absence of the zero sequence in the ac currents and voltages and in the[d nk]functions leads to the following transformed model in the three-phase coordinates[15]:L PFdi c1dt=−R PF i c1−d n1v dc−v CPF1+v s1 L PFdi c2dt=−R PF i c2−d n2v dc−v CPF2+v s2 L PFdi c3dt=−R PF i c3−d n3v dc−v CPF3+v s3C dcdv dcdt+v dcR dc=d n1i c1+d n2i c2+d n3i c3.(4)Fig.1.Basic circuit of the proposed SHPF-TCR compensator.The system of(4)is transformed into the synchronous orthogo-nal frame using the following general transformation matrix:C123 dq =23cosθcos(θ−2π/3)cos(θ−4π/3)−sinθ−sin(θ−2π/3)−sin(θ−4π/3)(5)whereθ=ωt and the following equalities hold:C dq123=(C123dq )−1=(C123dq)T.Then,by applying dq transformation,the state space model of the system in the synchronous reference frame is given in the Appendix by(26).This model is nonlinear because of the existence of multi-plication terms between the state variables{i d,i q,V dc}and the switching state function{d nd,d nq}.However,the model is time invariant during a given switching state.Furthermore,the principle of operation of the SHPF requires that the three state variables have to be controlled indepen-dently.The interaction between the inner current loop and the outer dc bus voltage loop can be avoided by adequately separating their respective dynamics.B.Harmonic Current ControlA fast inner current loop,and a slow outer dc voltage loop, is adopted.Thefirst two equations in the model can be written as shown in the Appendix by(27).Note that thefirst and theFig.2.Inner control loop of the current i d .second time derivative TCR capacitor voltages have no sig-nificant negative impact on the performance of the proposed control technique because their coefficients are too low.Conse-quently,they can practically be ignored.Define the equivalent inputs by (28)as given in the Appendix.Thus,with this transformation,the decoupled dynamics of the current tracking is obtained.The currents i d and i q can be controlled independently.Furthermore,by using propor-tional integral compensation,a fast dynamic response and zero steady-state errors can be achieved.The expressions of the tracking controllers areu d =L PF (1−C PF L T ω2)+L Tdi d dt+R PF (1−C PF L T ω2)i d=k p ˜i d +k i˜i d dtu q =L PF (1−C PF L T ω2)+L Tdi q dt+R PF (1−C PF L T ω2)i q =k p ˜i q +k i˜i q dt(6)where ˜i d =i ∗d −i d and ˜i q =i ∗q −i q are current errors and i ∗dand i ∗q denote the reference signals of i d and i q ,respectively.The transfer function of the proportional–integral controllers is given asG i 1(s )=U d (s )˜i d (s )=k p 1+k i 1s G i 2(s )=U q (s )˜i q (s )=k p 2+k i 2s.(7)The inner control loop of the current i d is shown in Fig.2.The closed-loop transfer functions of the current loops areI d (s )I ∗d (s )=k p 1A s +k i 1k p 1s 2+ B +k p 1As +k i 1I q (s )I ∗q (s )=k p 2As +k i 2kp 2s 2+ B +k p 2As +ki 2(8)where A =L PF (1−C PF L T ω2)+L T and B =R PF (1−C PF L T ω2).The closed-loop transfer functions of the current loops have the following form:I d (s )I ∗d (s )=2ζωni s +ωni2ζs +2ζωni s +ω2ni(9)where ωni is the outer loop natural angular frequency and ζisthe damping factor.For the optimal value of the dampingfactorpensated voltage regulated model.ζ=√2/2,the theoretical overshoot is 20.79%.The following design relations can be derived:k p 1=k p 2=2ζωni L PF (1−C PF L T ω2)+L T−R PF (1−C PF L T ω2)k i 1=k i 2=(L PF (1−C PF L T ω2)+L T )ω2ni .The control law is given in the Appendix by (29)and (30).Note that the inputs q nd and q nq consist of a nonlinearity cancellation part and a linear decoupling compensation part.C.DC Bus Voltage RegulationIn order to maintain the dc bus voltage level at a desired value,acting on i q can compensate the losses through the hybrid power filter components.The output of the controller is added to the q -component current reference i q as shown in Fig.4.The third equation in the model (6)is rewrittenC dcdv dc dt +v dc R dc=d nq i q .(10)The three-phase filter currents are given by⎡⎣i c 1i c 2i c 3⎤⎦= 23i q ⎡⎣−sin θ−sin θ−2π3 −sin θ−2π3 ⎤⎦.(11)The fundamental filter rms current I c isI c =i q√3.(12)The q -axis active filter voltage v Mq is expressed asv Mq =q nq v dc =−Z PF1i ∗q 1(13)where Z PF1is the impedance of the passive filter at 60Hz andi ∗q 1is a dc component.An equivalent input u dc is defined asu dc =q nq i q .(14)The control effort of the dc voltage loop is deducedi ∗q 1=v dc−Z PF1i qu dc .(15)The dc component will force the SHPF-TCR compensator togenerate or to draw a current at the fundamental frequency.To regulate the dc voltage v dc ,the error ˜v dc =v ∗dc −v dc is passed through a PI-type controller given byu dc =k 1˜v dc +k 2˜v dc dt.(16)Fig.3illustrates the outer control loop of the dc bus voltage.Fig.4.Control scheme of the proposed SHPF-TCR compensator.The response of the dc bus voltage loop is a second-order transfer function and has the following form:V dc (s )V ∗dc (s )=2ζωnv s +ωnv2ζs 2+2ζωnv s +ω2nv.(17)The closed-loop transfer function of dc bus voltage regula-tion is given as follows:V dc (s )V ∗dc(s )=√3Z PF1k p I cdc C dcs +√3Z PF1k i I c dc C dc s 2+√3Z PF1k p I cdc C dcs+√3Z PF1k i I cdc C dc (18)where V dc is the average value of the dc voltage which is equalto 50V .The proportional k 1and integral k 2gains are then ob-tained as follows:k 1=2ζωnv (V dc C dc /√3Z PF1I c ),and k 2=ω2nv (V dc C dc /√3Z PF1I c ).By designing the dc bus voltage loop much slower than the current one,there would not be any interaction between the two loops.The proposed nonlinear controller of the proposed SHPF-TCR compensator is shown in Fig.4.Fig.5.TCR equivalent circuit.IV .M ODELING OF TCRFig.5shows the TCR equivalent circuit.Using Kirchhoff’s voltage law,the following equations in 123reference frame are obtained:v s 1=L T di LT1dt +L PF di c 1dt +R PF i c 1+d n 1v dc v s 2=L Tdi LPF2dt +L PF di c 2dt +R PF i c 2+d n 2v dc v s 3=L Tdi LPF3dt +L PF di c 3dt+R PF i c 3+d n 3v dc .(19)Fig.6.Susceptance versusfiring angle.Applying Park’s transformation,one obtainsL T(α)di LTddt=L T(α)ωi LTq+L PFωi q−L PFdi ddt −R PF i d−d nd v dc+v dL T(α)di LTqdt=−L T(α)ωi LTd−L PFωi d−L PFdi qdt−R PF i q−d nq v dc+v q.(20)The reactive part is chosen to control the reactive current so that v q=0and L f(α)ωi LTd=0di LTq dt =B(α)ω−L PFωi d−L PF di qdt−R PF i q−d nq v dc(21)where B(α)=1/L F(α)ωis the susceptance. An equivalent input u qT is defined asu qT=di LTqdt.(22)According to this expression,one deducesB(α)=u qTω−L PFωi d−L PF di qdt−R PF i q−d nq v dc.(23)On the other hand,the equivalent inductance is given byL PF(α)=L PFπ2π−2α+sin(2α).(24)The susceptance is given byB(α)=B 2π−2α+sin(2α)π(25)where B=1/L PFω0.Fig.6illustrates the susceptance versusfiring angle.A PI controller is used to force the reactive current of the SHPF-TCR compensator to follow exactly the reactive current consumed by the load.V.R ATING OF APF P ARTIn this proposed topology,the major part of the compensation is supported by the passivefilter and the TCR while the APF improves thefiltering characteristics and damps the resonance,TABLE IA PPARENT P OWER R ATINGS OF APF PARTwhich can occur between the passivefilter,the TCR,and the source impedance.The objective of the APF is to generate currents that are equal but opposite to the harmonic and reactive currents,thereby achieving sinusoidal supply currents in phase with supply voltages.On the other hand,the shunt APF when used alone suffers from the high kilovoltampere rating of the inverter,which requires high dc-link voltage.Hence,the proposed combination of SHPF and TCR reduces significantly the voltampere rating of the APF part.A.Case of Harmonic-Generated LoadThefilter rms current is only2.443A for the required APF, the load rms current is8.231A,the line rms voltage across the load is120V,and the dc bus voltage V dc is selected to be50V.B.Case of Reactive Power and Harmonic Type of LoadsThefilter rms current is2.49A for the required APF,the load rms current is9.7A,the line rms voltage across the load is 120V,and the dc bus voltage V dc is50V.Table I shows the apparent power ratings of the APF part for the harmonic-generated load and reactive power and harmonic type of loads.It is shown that the rating of the APF part used in the shunt hybridfilter is reduced from26%to5%for the harmonic-generated load and from15%to4.37%for the reactive power and harmonic type of loads.Thus,the rating reduction of the APF is the main contributor to the total cost reduction of the system.VI.S IMULATION R ESULTSThe system parameters are given in Table II.Simulations were performed numerically using the“Power System Block-set”simulator operating under Matlab/Simulink environment, in order to verify the operation of the proposed SHPF-TCRTABLE IIS PECIFICATION PARAMETERSFig.7.Steady-state response of the SHPF-TCR compensator with harmonic-generated load.compensator using the nonlinear control scheme shown in Figs.1and 5.The controller’s performance has been evaluated by achiev-ing a number of tests on the proposed SHPF-TCR compensator:1)steady-state response of the SHPF-TCR compensator to load-generating harmonics;2)dynamic response of the SHPF-TCR compensator to harmonic-produced load variations;and 3)response of the SHPF-TCR compensator to the harmonic and reactive power type of load variation.A.Harmonic Compensation of SHPF-TCR Compensator Fig.7shows the steady-state waveform of the SHPF-TCR compensator for harmonic elimination with a three-phase harmonic-produced load.The supply voltage (v s 1),the supply current (i s 1),the load current (i L 1),the SHPF-TCR current (i c 1)in phase 1,and the dc bus voltage (v dc )are depicted in this figure.Fig.8(a)and (b)shows the harmonic spectrum of the supply current before and after compensation.The THD of the supply current is brought down from 26%to 1.31%.It is found that the SHPF-TCR compensator offers a very good level of performance such that the supply current is close to sinusoidal and locked in phase with the supplyvoltage.Fig.8.Harmonic spectrum of source current in phase 1.(a)Before compen-sation.(b)Aftercompensation.Fig.9.Dynamic response of SHPF-TCR compensator under varying distorted harmonic type of load conditions.B.Response of SHPF-TCR Compensator to Harmonic-Produced Load VariationFig.9shows the SHPF-TCR compensator response to harmonic-produced load perturbation for phase 1.The load currents were subjected to a 100%step increase at 0.567s and a step decrease at 0.667s by the same amount.It is found that there is a smooth changeover from one load condition to another load condition.The dc bus voltage returns to the reference voltage value.The SHPF-TCR compensator is able to reduce harmonics in the supply currents,and it improves the supply PF to unity.Fig.10.Dynamic response of SHPF-TCR compensator under the harmonic and reactive power type ofloads.Fig.11.Harmonic spectrum of source current in phase 1.(a)Before compen-sation.(b)After compensation.C.Response of SHPF-TCR Compensator to Harmonic and Reactive Power CompensationIn order to observe the SHPF-TCR compensator behavior under both harmonic and reactive power type of load variation,the load-generating reactive power current was subjected from zero to a full load step increase and the other way around.The corresponding phase-1dynamic responses of the SHPF-TCR compensator for reactive power compensation and harmonic elimination are shown in Fig.10.It is observed from Fig.11that the supply current before compensation was quite distorted and has a THD of 16%;however,its THD is reduced to 1%after compensation.The compensated source current shown in this figure suggests that the proposed SHPF-TCRcompensatorFig.12.Steady-state response of the SHPF-TCR compensator with harmonic-produced load.can effectively compensate the load-generated harmonics and reactive power exchanged by both loads.VII.E XPERIMENTAL R ESULTSThe following tests are performed on a 3.5-kV A laboratory prototype of the SHPF-TCR compensator used to compensate harmonics and reactive power of loads.The nonlinear control system was implemented on a dSPACE DS 1104controller board,supported by a Matlab/Simulink Real-Time Workshop environment.The component values given in Table I were used for both simulation and experimentation.The set of loads consists of a diode rectifier and a star-connected combination of resistive and inductive loads.The experimental setup used to test the dynamic performance of the SHPF-TCR compensator has the following combined harmonic and reactive power type of loads.1)A three-phase diode rectifier followed by inductor L L 1=10mH in series with a resistor R L 1=40Ωis used as the harmonic-produced load.2)A three-phase star-connected resistive inductive load with inductor L L 2=20mH and resistor R L 2=27Ωis used experimentally to cause current to lag voltage and to make up a mixed load together with the three-phase harmonic-generated load.To verify the proposed nonlinear control algorithm per-formance,four different operating conditions are considered:1)steady-state performance of the SHPF-TCR compensator with a harmonic-produced load;2)dynamic performance of the SHPF-TCR compensator with harmonic-generated load;3)steady-state performance of the SHPF-TCR compensator with the harmonic and reactive power type of loads;and 4)dynamic performance of the system with the harmonic and reactive power type of loads.A.Steady-State Response of System With Harmonic-Generated LoadFig.12shows the steady-state experimental results of the proposed SHPF-TCR compensator for harmonic compensationFig.13.Harmonic spectrums of the source current and voltage in phase1.(a)Source current before compensation.(b)Source current after compensation.(c)Source voltage.with a load for phase1.In thisfigure,the supply voltage (v s1),supply current(i s1),load current(i L1),and SHPF-TCR current(i c1)are depicted.It can be seen that the source current has become sinusoidal and in phase with the source voltage. The harmonic spectrum of the supply current before and af-ter compensation and the supply voltage after compensation for phase1have been given in Figs.13(a),(b),and14(c), respectively.The THD of the supply current is brought down from26%before compensation to3%after compensation.The THD of the supply voltage after compensation is2.5%.The harmonic spectrums are recorded on a FLUKE43B power quality analyzer.B.Transient Response of SHPF-TCR Compensator to Harmonic-Produced Load VariationTo test the dynamic performance of the proposed nonlinear control,a step increase of100%and a decrease of100%in the harmonic-produced load were made.Fig.14(a)and(b) shows the transient responses of the SHPF-TCR compensator adopting the nonlinear control.At the transition period,the dc bus voltage falls or rises below its steady-state value when the SHPF-TCR compensator supplies or absorbs extra active power to or from the load,respectively.The SHPF-TCR compensator maintains compensation during the transient instants.Thus,the harmonic components of the load current are fully compensated by the system so that the line current is almost a sinusoidal waveform with unityPF.Fig.14.Dynamic response of the proposed SHPF-TCR compensator under varying harmonic-produced load conditions.(a)Step increase of the load current.(b)Step decrease of the loadcurrent.Fig.15.Steady-state response of the proposed SHPF-TCR compensator with harmonic and reactive power type of loads.C.Steady-State Harmonic and Reactive Power Compensation A combination of a three-phase diode-bridge ac–dc converter with an R−L load connected at the dc side and a three-phaseFig.16.Harmonic spectrums of the source current and voltage in phase1.(a)Source current before compensation.(b)Source current after compensation.(c)Source voltage.star-connected resistive–inductive load is chosen to study the transient operation of the SHPF-TCR system for harmonic and reactive power compensation.The PF of the reactive load is0.96.Fig.15shows the steady-state performance of the proposed SHPF-TCR compensator employing the proposed nonlinear control method for the simultaneous compensation of harmonics and reactive power for phase1.The supply voltage(v s1),the supply current(i s1),the load current(i L1) and the SHPF-TCR compensator current(i c1)are shown in thisfigure.The frequency analyses of supply voltage and supply current before and after compensation are shown in Fig.16(a)–(c).The THD of the supply current is brought down from15%before compensation to2.6%after compensation. The THD of the supply voltage after compensation is2.5%. The steady-state performance of the TCR providing reactive power compensation is shown in Fig.17.The waveforms shown in thisfigure are the phase-1source current(i s1),load current (i L1),hybridfilter current(i c1),and TCR current(i Lt1).From the experimental results,one can observe that the harmonic currents and reactive power could be effectively compensated with the SHPF-TCR compensator.The source current is close to sinusoidal and kept in phase with the source voltage.Moreover, harmonics generated naturally by the TCR have two possible paths,the parallel capacitor connected with the TCR or the activefilter.Since the activefilter controller is set to compensate only load harmonics,the latter act as high impedance to TCR current harmonics,obliging these harmonics toflow throughthe Fig.17.TCR providing reactive power compensation in steady-statemode. Fig.18.Dynamic response of the proposed SHPF-TCR compensator undervarying reactive power type of load conditions.capacitor.Therefore,one cannot see these harmonicsflowing through the source or the load.D.Reactive Power and Harmonic Type of Load Perturbation Response of SHPF-TCR CompensatorFig.18shows the transient waveforms of the SHPF-TCR compensator during the sudden variation of the reactive power and harmonic type of loads.It is found that,for a change of load current,the supply current always maintains its sinusoidal shape while being in phase with the supply voltage.These results confirm the fast dynamic performance and the ability of the proposed configuration adopting the nonlinear control strategy to compensate suitably the harmonics and reactive power for a rapid change in the load current.The THDs of the load current before and after the transient occurred are26%and 15%,respectively.The PF of the reactive load is0.96.The TCR is used to realize variable inductance for compen-sating the reactive power.This latter suffers from resonance which possibly occurs between its inductance,source/load impedance,and PF correction capacitors used in industrial applications.Passivefilters suffer from resonance problems and tuning problems due to component tolerances.The problem。