LCL Interface Filter Design for Shunt Active Power Filters

Transcription

1 [Downloaded from on Sunday, November 4, 00 at 8::03 (TC) by Retriction apply.] Advance in Electrical and Computer Engineering Volume 0, Number 3, 00 LCL nterface Filter Deign for Shunt Active Power Filter Alexandru BTOLEAN, Mihaela POPESC, Daniel MARN, Mircea DOBRCEAN Faculty of Electromechanical, Environmental and ndutrial nformatic Engineering niverity of Craiova Bd. Decebal nr.07, RO Craiova Abtract Thi paper i focued on finding the parameter of a econd order interface filter connected between the power ytem and the hunt active filter baed on witching frequency of the active filter. Many publication on power active filter include variou deign method for the interface inductive filter which take into account the injected current and it dynamic. Compared to thee one, the approach preented in thi paper i oriented toward the deign of the interface filter tarting from filter tranfer function by impoing the performance of the filter. order filter and a econd order filter. ndex Term Active filter, Deign methodology, Filtering, Paive filter, Sytem analyi and deign. NTRODCTON Active power filter baed on voltage ource inverter topology are widely ued to improve power quality of nonlinear load at the point of common coupling to the network. The witching device of the voltage ource converter bridge are driven with pecific control trategie to inject a three phae current into the power upply in order to compenate the load harmonic current, the reactive power and load current imbalance. A DC-bu capacitor i ued to provide back-up power (Fig. ). To accurately produce the compenating current, the control of power converter i carried out uing pule wih modulation (PWM) method of high modulation frequency. Since the PWM converter generate undeirable current harmonic around the modulation frequency and it multiple, it i neceary to adopt certain meaure to reduce the harmonic ditortion of the output current. Traditionally, a paive filter of L, LC or LCL type i ued to interface the voltage ource inverter to the power upply. ually, the interface filter i deigned to atify the following two criteria [], []: - to enure the dynamic behavior of the current, i.e. d d, () Lh c where Lh i the harmonic current of the load and c i the current injected by the active filter; - to prevent the harmonic component generated by the witching frequency from propagating into the power network. Two type of interface filter are commonly ued, a firt Digital Object dentifier 0.436/AECE AECE Fig.. Baic tructure of a three phae active power filter A. Firt order filter The firt order paive filter called injection inductor i the mot ued olution to connect the active power filter to the point of common connection. t conit of an inductor having the inductance L f and the internal reitance R f. Such a filter doe not allow atifying imultaneouly the two deign criteria. n eence, the only viable value of the inductance complie with () and lead to a good dynamic of the active filter. n the worth cae cenario, a low value of L f allow mot of witching harmonic current to flow into the power network and conequently to diturb adjacent electrical equipment. n practice, the firt order L type filter cannot uually provide ufficient attenuation for the modulation frequency current harmonic. On the contrary, a high value of the injection inductor prevent the harmonic current from propagating into the upply ytem but affect the active filter dynamic and the quality of compenation diminihe [3]. Therefore, a good deign of the firt order paive filter i a compromie between the dynamic and the effectivene of the active power filter. 55

2 [Downloaded from on Sunday, November 4, 00 at 8::03 (TC) by Retriction apply.] Advance in Electrical and Computer Engineering Volume 0, Number 3, 00 B. Second order filter Thi type of filter comprie two inductor and a capacitor connected in a T-ection a it i hown in Fig.. The popularity of the LCL filter among all output filter ued in the field of power electronic application i due of the fact that a good attenuation i achieved with a reaonable filter cot. ( ) ( ) + c ( ) ( ) ( ) c L ( ) c L, (6), (7), (8) After ome proceing tep, the expreion (6)-(8) take the following form: ( )( LC ) ( ) C ( )( L C) ( ) C + + ( ), (9) c + ( ), (0). () c C Figure 4 illutrate the block diagram aociated to the expreion (6), (7) and (8). Fig.. Equivalent chema of the LCL interface filter. TRANSFER FNCTON OF THE SECOND ORDER FLTER The equivalent configuration of the filter in Fig. 3 how that, if the upply voltage i inuoidal, the filter behave like a hort-circuit related to uperior order harmonic [4]. Fig. 4. Block diagram of the econd order interface filter Thu, applying the tranfiguration theorem give the following equivalent tranfer function [5]: C + ( + L C)( + L C) ( ) LC ( ), () Fig. 3. Equivalent configuration of the interface filter at the fundamental and harmonic frequencie According to Kirchhoff law, the following equation can be expreed: i + i i c, () di u uc L, (3) di u c u L (4) duc ic C (5) n the domain of the Laplace tranform, the above equation become: C ( ) ( + LC ) ( ) ( + L C)( + L C), (3) Suppoing that the input and output quantitie are harmonic current i and i, condition () 0 allow expreing the equivalent tranfer function: C ( + L C)( + L C) + ( + L C)( + L C) C L C Thu, it can be arranged a: ( ) L C, (4). (5) + 56

3 [Downloaded from on Sunday, November 4, 00 at 8::03 (TC) by Retriction apply.] Advance in Electrical and Computer Engineering Volume 0, Number 3, 00. FLTER PARAMETERS n order to find the frequency characteritic of the filter, the tranfer function i arranged in the tandard form of a econd order ytem which make evident the reonance natural frequency ω n and the damping ratio ξ [6], H ω. (6) T + ξt + + ξω + ω n Taking into account (5), it reult: ξt 0, (7) i.e. ξ 0, (8) T L C, (9) ω n. (0) L C The attenuation veru frequency characteritic in Fig. 5 illutrate the maximum attenuation at natural frequency and a attenuation of -40dB/decade over the cutoff frequency. ω cutoff ω n. () Fig. 5. Frequency repone of interface filter From the operation point of view, the interface filter ha to reject the witching harmonic without affecting the harmonic to be compenated. For thi reaon, the cutoff frequency mut be below the witching frequency in order to obtain a rejection current lope of -40dB/decade. Beide, the minimum frequency which determinate the filter pa band mut exceed the highet harmonic frequency to be compenated by the active power filter. Hence, taking into account condition (5) and the uperior pa band limit of f n which ha no influence on the input ignal, the following condition are expreed: f f n, () π L C n n, (3) π L C f N where f i the witching frequency and f N i the lowet frequency among the harmonic frequencie to be rejected by the interface filter. The previou expreion can be written a: LC, (4) π f LC, (5) 8π fn repectively π L C. (6) f 8π fn By impoing f 0 khz and the highet order of the harmonic to be filtered N50 (i.e. f N.5 khz), the inequalitie (6) became LC (7) A the product L C domain i large, the filter behaviour will be analyzed for different value of thi product a well a for different value of L and C. V. FLTERNG PERFORMANCES Computer imulation have been carried out in order to determine the performance of the interface filter. The nonlinear load conit of a full three-phae controlled rectifier upplying a DC motor. The tak of the hunt active power filter i to compenate both the uperior order harmonic and the reactive power. A DC-bu voltage of 600 V and a RMS harmonic current of 0 A have been taken into conideration. The filtering performance have been appreciated by comparing the current injected before and after filtering a well a by comparing the upply current with and without interface filter. Thu, the effectivene of the interface filter i illutrated in Fig. 6 which how the output current of the active filter. t ocillate around the et point at the witching frequency of the voltage inverter and the aociated error exceed 5 A (Fig. 6a). t can be een that the ocillation are much diminihed (about ±.5 A) at the output of the interface filter. Moreover, there are a lot of zone where the output current i uperpoed on it et point (Fig. 6b). The harmonic pectra in Fig. 7 before and after filtering point out even better the efficiency of the interface filter. A it can be een in Fig. 7a, the output current of the active filter before interface filter alo contain, beide the harmonic to be compenated (bellow 5t order), other uperior harmonic up to 50th order among the mot ignificant one are grouped round the 00th order which correpond to the witching frequency of 0 khz. Their weight related to the fundamental component required to compenate the reactive power get near to 0% (Fig. 7a). 57

4 [Downloaded from on Sunday, November 4, 00 at 8::03 (TC) by Retriction apply.] Advance in Electrical and Computer Engineering Volume 0, Number 3, 00 where i the fundamental component of the ueful load current after filtering. Thi weight value i of 65% before filtering and of 8% after filtering. The ame apect are pointed out by the waveform of the upply current with and without interface filter (Fig. 8 and Fig. 9). Very relevant i the value of the total harmonic ditortion factor (THD) which diminihe from 5.39% to the acceptable value of 7.86% after filtering. Fig. 6. Current provided by the active filter: a) before filtering; b) after filtering On the other hand, the harmonic up to 50th order of the current after the interface filter are left unchanged while the other harmonic are trongly attenuated (Fig. 7b). For intance, the harmonic family grouped round the witching frequency i attenuated to about 5%. Fig. 8. nfiltered power upply current waveform and it harmonic pectrum Fig. 7. Harmonic pectra of the current provided by the active power filter: a) before interface filter; b) after interface filter Very ignificant i the weight of uperior order harmonic which i defined a 300 k k 5 Pk 5: 300, (6) Fig. 9. Filtered power upply current waveform and it harmonic pectrum Moreover, to emphaize the filtering effectivene, the magnitude of the harmonic to be compenated provided by the reference current calculation block are compared with thoe of the harmonic injected into the upply network (Fig. 0). t can be noticed a little attenuation of the harmonic magnitude tarting with the 5th order, but the 58

5 [Downloaded from on Sunday, November 4, 00 at 8::03 (TC) by Retriction apply.] Advance in Electrical and Computer Engineering Volume 0, Number 3, 00 influence of thi attenuation on the current THD doe not exceed %. Beide, it can be een that the interface filter introduce undeirable harmonic into the power ytem, uch a the 6th harmonic, whoe weight i, nonethele, inignificant [6]. the power line and the line current waveform i cloe to a inuoide. Fig.. Dynamic repone of the active power filter Fig. 0. Comparion between the harmonic pectra of the reference current (current to be compenated) and the current after the interface filter V. OPTMM DESGN OF THE NTERFACE FLTER A the inequality (6) i not ufficient to determinate the interface filter parameter, the detailed analyi of the influence of the value of product L C and of the two parameter (L and C) on the total harmonic ditortion factor of the upply current allowed u to point out the following concluion:. There i an optimum value of product L C which lead to a minimum value of the current THD (Fig. ). Thi one correpond to the minimum value given by relation (6).. At the optimum value of the L C product, the upply current THD can be reduced by increaing the inductance value. 3. The increae of the inductance L over 4mH require the increae of voltage acro the compenation condener in order to enure the dynamic behaviour of the current. 4. For the analyzed ituation, the minimum value of THD correpond to L 5mH and C 0.μF. The correct deign of the interface filter parameter ha alo a poitive influence on the dynamic performance of the active power filter. A detailed analyi of the current evolution how that a Γ-filter compoed only of L and C lead to unacceptable value of current pule through active filter and both condener (compenating condener and interface filter condener) - Fig. 3 and Fig. 4. Thi occur becaue of energy flow between the two capacitor, through a very low impedance circuit which conit of on-tate reitance of the tranitor and reitance / inductance of the conductor in circuit). Thu, the current pule increae a interface Γ- filter capacitance increae. Therefore, the addition of the inductance L to the Γ- L C filter i abolutely required. Fig. 3. Filtered output active filter current by uing a Γ- interface LC filter Fig. 4. Output active filter current for a high capacitance of the Γ- interface LC filter Fig.. Total harmonic ditortion factor of the upply current veru product L C for C 0.μF Thu, a it can be een in Fig., the filtering proce tart immediately after connecting the active power filter to The reult of a great many imulation pointed out that a L value of L /0 lead to reaonable current pule of.5 N without altering filtering performance. Thu, the power upply current THD i of about 7.86 % with a LC filter (Fig. 9) and of about 7.% with a LCL filter (Fig. 5). 59

6 [Downloaded from on Sunday, November 4, 00 at 8::03 (TC) by Retriction apply.] Advance in Electrical and Computer Engineering Volume 0, Number 3, 00 t i hown that the minimum upply current THD can be obtained by chooing the minimum value of the product of inductance and capacitance according to relation (6). Moreover, the inductance value which minimize the upply current THD i about 4 mh. t i alo pointed out that an LC filter i not a viable olution for the interface filter and that the bet value of the inductance at the active power filter output i of L /0. By uing an interface filter deigned in accordance with the propoed method, the power upply current agree to the exiting tandard [7], [8]. Fig. 5. Power upply current after filtering, by uing an LCL interface filter. V. CONCLSONS Thi paper preent on a new approach of the interface filter deign by impoing it performance baed on filter tranfer function taking into account the witching frequency of the active filter. The performance refer to the ignificant attenuation of the witching harmonic without affecting the harmonic to be compenated and they are achieved by impoing the cutoff frequency and the pa band amplification. By a correct choice of the inductance value, the filter behavior i ignificantly improved and the impoed criteria for uch a filter are enured. f the witching frequency i choen to be below the cutoff frequency of the interface filter but over the frequency of the highet-order harmonic to be compenated (e.g. 5 khz for a witching frequency of 0 khz), the filter operation i much improved by the ignificant diminution of the witching harmonic of 00th and 00th order. REFERENCES [] H. Akagi, Active Harmonic Filter, Proceeding of the EEE, Vol. 93, No., Dec [] A. L. Montenegro, Advanced power electronic for wind-power generation buffering, niverity of Florida, 005. [3] B. C. Parikhith and J. Vinod, Higher Order Output Filter Deign for GridConnected Power Converter, Fifteenth National Power Sytem Conference (NPSC), T Bombay, pp , 008. [4] M. Lierre, F. Blaabjerg, and S. Hanen, Deign and control of an LCL-filter baed three-phae active rectifier, EEE Tran. nd. Appl., vol.4, no.5, pp. 8-9, 005. [5] C. Marin, D. Popecu, E. Petre, C. onete, and Dan Seliteanu,Teoria itemelor, Editura Sitech, Craiova, 005. [6] P. Peltoniemi, R. Pöllänen, M. Niemelä, and J. Pyrhönen, Comparion of the Effect of Output Filter on the Total Harmonic Ditortion of Line Current in Voltage Source Line Converter Simulation Study, nt. Conference on Renewable Energy and Power Quality, Mallorca, 006. [7] Standard Recommended Practice and Requirement for Harmonic Control in Electrical Power Sytem, 993. [8] Limit for Harmonic Current Emiion, nternational Electrotechnical Commiion Standard EC , March