An Improved Active-Front-End Rectifier Using Model Predictive Control

Transcription

1 An Improved Actve-Front-End Rectfer Ung Model Predctve Control M. Parvez* and S. Mekhlef Power Electronc and Renewable Energy Reearch Laboratory (PEARL) Dept. of Electrcal Engneerng Unverty of Malaya 5060 uala Lumpur, Malaya E-mal: Nada M. L. Tan Dept. of Electrcal Power Engneerng Unvert Tenaga Naonal ajang 4000, Malaya E-mal: Hrofum Akag Dept. of Electrcal and Electronc Engneerng Tokyo Inttute of Technology Tokyo 5-855, Japan E-mal: Abtract-Th paper nvetgate an mproved actve-front-end (AFE) rectfer ung model predctve control. The model predctve control (MPC) algorthm utlze the dcrete behavor of the power converter to determne the approprate wtchng tate by defnng a cot functon. The performance of the AFE rectfer ha been verfed wth.0 kw expermental etup whch how that the effcency of the MPC controlled AFE-rectfer 96.8% and operated wth acceptable THD (4.0%) of nput current and very low DC voltage rpple. An effcency comparon performed between the MPC and VOCbaed PWM controller of the AFE rectfer whch enure the effectvene of MPC controller. Moreover, the tablty of the MPC method ha been analyzed wth the root locu, dcrete z- doman frequency repone technque (Nyqut dagram) and non-lnear expermental ytem. The reult confrm that, the control ytem of AFE rectfer table a t operate wth nfnte gan margn and very fat dynamc repone. eyword-model predctve control (MPC); actve front end (AFE) rectfer; tablty analy; AC-DC power converon. I. INTRODUCTION The actve-front-end (AFE) rectfer ncreangly ued n varou ndutry applcaton a well a houehold applance due to t bdrectonal-power-flow and grd ynchronzaton capablte []. The control ytem of th AFE rectfer hould be hghly table and effcent for preventng hgh total harmonc dtorton (THD) n nput current, low power factor, ac voltage dtorton, rpple n DC current and DC voltage pulaton []. The clacal control of AFE rectfer generally baed on voltage-orented control (VOC) cheme, whch decompoe the actve and reactve power n tatonary α-β co-ordnate and ynchronze the power wth rotatng d-q reference frame by characterzng the current control loop ung PI controller [, 4]. Moreover, everal control method uch a vrtual-flux-orented PWM control [5], drect power control (DPC) [6, 7], drect torque control (DTC) [8, 9], fuzzy-logc control [0] and ldng mode nonlnear control [] have been alo propoed to mprove the effcency and performance of the AFE rectfer. The MPC cheme ha become an attractve mode of control technque for three-phae AFE rectfer comparng wth all the clacal oluton dcued above due to t mple and ntutve concept wth fat dynamc repone [, ]. Moreover, th MPC algorthm very eay to confgure wth Fg.. Three-phae actve front-end-rectfer topology. contrant and non-lnearty [4-7]. The fat and powerful mcroproceor are avalable today to mplement the MPC very ealy a t requre hgher number of calculaton compared wth all the clacal control [8, 9]. Depte the good performance of MPC algorthm, there reman ome lmtaton, beng one of the mot mportant ue the tablty. Recently, the tablty analy of MPC controlled power converter, whch modeled a lnear ytem ha been preented n [0]. The Lyapunov tablty nvetgaton of MPC method ha been etablhed n []. Furthermore, the Luenberger dturbance and t tablty ha been oberved n []. So far, the cloe-loop tablty whch a very mportant apect of the MPC controlled AFE rectfer ha not yet been condered. Th paper propoe a MPC algorthm that appled to mprove the performance of the AFE rectfer. The tablty crteron of th MPC algorthm ha been elaborately nvetgated wth root locu technque, dcrete z-doman frequency repone (Nyqut dagram) and non-lnear expermental ytem. The ret of the paper organzed n the followng manner. The actve-front-end (AFE) rectfer topology elaborately decrbed n ecton II. The tablty of the propoed MPC controlled AFE rectfer analyzed n ecton III. The performance of the MPC controlled AFE rectfer verfed wth a.0 kw expermental et-up and compared wth compared wth VOC-baed PWM controlled rectfer n ecton IV. Fnally the concluon are drawn n ecton V /5/$ IEEE

2 II. DESCRIPTION OF AFE RECTIFIER TOPOLOGY A. Sytem Confguraton Fg. how the three-phae actve front end (AFE) rectfer topology whch cont of x IGBT-Dode (S -S 6 ) wtche. The AFE rectfer connected wth the three-phae voltage upply (v ) ung the lne flter nductance (L ) and retance (R ). A DC capactor (C ) connected acro the retve load to reduce DC voltage rpple. In order to avod hort crcut, the two wtche n each leg of the AFE rectfer hould be operated n a complementary mode. Hence, the gatng gnal S a, S b and S c determne the wtchng tate of the three-phae AFE rectfer a follow:, S on and S off S a = () 0, S off and S on, S on and S 4 off S b = () 0, S off and S 4 on, S 5 on and S 6 off S c = () 0, S 5 off and S 6 on Therefore, the wtchng functon vector ( S ) of the AFE rectfer can be expreed a, S = ( S a + ω S S c ) b + ω (4) jπ / where, ω = e, the unty vector. The output voltage pace vector ( v rec ) of the AFE rectfer can be preented wth phae to neutral voltage (v ao, v bo and v co ) a, vrec = ( v ao + ω v vco ) bo + ω. (5) Th output voltage pace vector ( v rec ) can alo be related to the DC bu voltage (V ) and the wtchng vector ( S ) a, v = S rec V. (6) There are eght poble voltage vector that can be obtaned from the eght conequence wtchng tate of the wtchng gnal S a, S b and S c, whch are lted n Table I. The AFE rectfer connected to the three-phae AC voltage ource through the nput flter nductance L and retance R a hown n Fg.. By applyng rchhoff voltage law at the ac de of the rectfer, the relatonhp between the threephae AC voltage and rectfer nput voltage vector are, d v = L + R + vao + ωv bo + ω vco dt (7) vno + ωvno + ω vno. TABLE I. VOLTAGE SPACE VECTORS OF THE AFE RECTIFIER Swtchng State Voltage pace vector S a S b S c v conv v = v = ( / ) V j( / ) V The pace-vector model of three-phae AC voltage ( v ) and current ( ) can be derved from phae voltage and current a, v = ( va + ω v b + ω vc ) and = ( a + ω b + ω c ), (9) where v a, v b, and v c are phae voltage; a, b, and c are phae current of three-phae AC voltage ource. Threfore, the nput current dynamc of the AFE rectfer can be evaluated from (5) and (7) a, d R = + v v L rec. (0) dt L L B. MPC Formulaton MPC algorthm utlze the dcrete nature of the wtchng devce and fnte number of vald wtchng tate of the power converter. It mportant to derve a dcrete tme model for the power converter ytem becaue the predctve controller formulated n dcrete tme doman. To etmate the next amplng value of the nput current conderng current and voltage meaurement at the k th ample tme, a dcrete model of the nput de hould be employed. For kt t (k+)t, wth T beng the amplng tme, the ytem model dervatve dx/dt can be expreed from the Euler approxmaton to ncreae fat dynamc repone a, d ( k + ) ( k). () dt T Ung the above approxmaton, the dcrete tme model of predctve nput current for the next (k+) amplng ntant of the AFE rectfer can be derved a follow, R ( ) T T k + = ( k) + L L 0 0 v = ( / ) V + j( / ) V v = / V 0 4 ( ) v = / V ( ) 0 v 6 = ( / ) V j( / ) V 0 v 7 = ( / ) V + j( / ) V v 8 = 0 ( rec( [ v k) v k) ] (8) ()

3 V ref MPC + T eq v err v R + L Sa Sb Sc v V load v V V _ref p + + T nner v V C V ref ref V V Fg. : Propoed MPC control cheme for actve-front-end rectfer topology. C. Cot Functon The man objectve of MPC algorthm to mnmze the error wth fat dynamc repone between the predcted and reference value of the dcrete varable. To acheve th objectve, an approprate cot functon e defned wth a meaurement of predctve nput error. Hence, the cot functon for the actve front end rectfer can be expreed wth abolute error between the predctve and reference value of nput current a, e = ref ( k + ) p( k + ) () where, e the cot functon for the AFE rectfer. The reference and predcted nput current of the AFE rectfer are ref ( k + ) and p ( k +), repectvely. D. Control Scheme Fg. how the propoed control trategy of the MPC algorthm to operate the AFE rectfer. The three-phae nput current of the rectfer ( k) of th current ( k ) meaured and the future value + predcted by ung () for each one of eght poble wtchng vector ( S ). Th future value of three-phae nput upply current ( k +) compared wth the reference current ref ( k + ) by utlzng the cot functon (e) of (). Th reference current calculated from the three-phae nput upply voltage vector ( v ) and retve load termnal DC voltage ( V ) by ung PI controller. Fnally, the wtchng tate that mnmze the cot functon, elected for the next amplng nterval. III. TANSFER FUNCTION AND STABILITY ANALYSIS A. Tranfer Functon The tranfer functon of the MPC controlled AFE rectfer can be derved from t mplfed control cheme, whch preented n Fg.. Th control tructure contng of two cacaded control loop a nner nput current control loop and outer DC lnk voltage control loop. Fg. : Smplfed block dagram of (a) nner nput current control loop and (b) outer DC lnk voltage control loop. ) Current Control Loop: Fg. (a) how the mplfed block dagram of nner nput current control loop conderng the DC lnk voltage contant. Therefore, the varaton of upply voltage the only dturbance gnal. The error voltage (v err ) the dfference between the reference and predcted value of the rectfer voltage. There are many delay n the current control loop uch a the proceng tme of the MPC algorthm, A/D converon tme, and delay tme of the converter, whch have to be taken nto account for the control degn. Commonly, all delay are grouped together to form ngle frt-order delay element wth equvalent tme contant (T eq ). In lterature [], t ha been tated that the converter delay wth MPC algorthm.5 tme of t amplng tme at 00 µ amplng tme wth the TMS0C DSP proceor. The choce of equvalent delay (T eq ) motly depend on the amplng tme and the peed of the real tme nterfacng proceor whch are uually ynchronzed. The computaton tme of the control algorthm (T c ) mut be horter than half of the amplng tme (T ). From the control pont of vew t neceary to defne the total delay that vare n the range 0.5 T to T dependng on the actual control gnal. The tattcal executon delay of the MPC controller aumed to be 0% of the amplng tme T (n cae of powerful dspace TMS0F40 proceor) where T 50 µ. In addton, conderng the A/D converon delay 5% of amplng tme T, the equvalent tme contant T eq can be obtaned by utlzng the equaton of T eq =T - (0%+5%)T a, T eq = 0.85T. (4) The propoed MPC controlled AFE rectfer ue only RL flter to connect wth three-phae upply voltage. So the control plant become frt-order delay element wth a tranfer functon. Hence, the tranfer functon of the current control loop can be derved wth the equvalent tme contant and nput RL flter a, G () = MPC (5) TeqL + ( RTeq + L) + ( R + MPC ) 4

4 v Sa Sb Sc V Fg. 5: Schematc layout of expermental etup. TABLE II. EXPERIMENTAL PARAMETERS Parameter value and unt Varable and Parameter Value Unt Rated Power.0 kw Fg. 4: The tablty analy of current control loop wth (a) Root Locu technque and (b) Nyqut dagram. where, MPC the contant gan of the MPC, whch can be defned wth the ampltude rato of the meaured and reference current. ) DC Lnk Voltage Control Loop: The dynamc model equaton at the DC lnk voltage of the AFE rectfer, dv v C = load = dt V load. (6) The mplfed DC lnk voltage control loop preented n Fg. (b). Thu, the tranfer functon of th DC lnk voltage control loop can be obtaned from PI controller, nner current loop delay element T nner =T eq and the DC lnk voltage dynamc equaton a, (v p () ) + v G v =. (7) (V C T nner + ( V C + v p) + v B. Stablty Analy Although the model predctve control ytem compoed of nner current and outer voltage control loop, the nner nput current control loop reponble for the overall control ytem tablty [, 4, 5]. Therefore, the tablty analy of the nner current control loop carred out wth dcrete z-doman analy, whch done by aumng the ample delay wth Root-locu and Nyqut dagram. The z-doman tablty analy baed on the current cloed-loop tranfer functon, MPC ytem plant, delay element, and ron loe n the nductor. Root-locu a powerful method for tablty analy and tranent repone of the cloe-loop control ytem whch ued to oberve the Supply Voltage (v ) 0 V rm Supply Frequency (f ) 50 Hz Reference DC-lnk (V ) 90 V Input Flter Inductance (L ) 5 mh Input Flter retance (R ) 0. Ω Samplng Tme (T ) 50 µs Load retance (R Load) 00 Ω Capactor value (C) 000 µf effect of loop gan varaton. Moreover, the method can plot the root of any polynomal wth real parameter that hamper the ytem lnearty. Fg. 4(a) depct the root locu of the nner cloe loop current control tranfer functon whch preented n (5). The root locu technque confrm the tablty of the model predctve control a the locu path lyng on the left half of the S-plane. The tablty of the cloe-loop control ytem further analyzed wth dcrete z-doman frequency repone becaue of the ambgute of root locu ketch, nonlnear ytem tablty, and lead compenator for teady-tate error and tranent repone. The Nyqut crteron can determne the effect of tme delay on the relatve tablty of cloe-loop ytem. Fg. 4(b) how the Nyqut plot of the current control loop whch enure the cloe loop tablty. IV. EXPERIMENTAL RESULTS AND ANALYSIS The performance of the MPC controlled AFE rectfer nvetgated wth.0 kw expermental confguraton. The expermental verfcaton carred out by ung the rapd prototypng and real-tme nterface ytem dspace wth DS04 control card whch cont of Texa Intrument TMS0F40 ub-proceor and the Power PC 60e/50 MHz man proceor. The chematc layout and the expermental ytem of the MPC controlled AFE rectfer preented n Fg. 5. The parameter lted n Table II are employed for expermentaton. 5

5 A. Expermental Reult The voltage meaured wth dfferental probe [PINTE DP-5] and the current wth current tranducer [LEM LA 5- NP]. The current tranducer output voltage gan et at.0 V output to meaure.0 A current. Fg. 6(a) how the meaured voltage and current of phae A wth DC lnk reference voltage tep change repone, whch prove the unty power factor and the tablty of the controller. The performance of the model predctve control for AFE rectfer verfed wth the meaured three-phae nput current and the phae-to-phae voltage at the rectfer end, whch are depcted n Fg. 6(b) & 6(c), repectvely. The three-phae current accurately trackng the reference current albet a tranent tme of 0.06 ec, whch enure the accuracy and fat dynamc repone of the control algorthm. The tablty and performance of the MPC controlled AFE rectfer alo can be analyzed wth the output DC lnk voltage & current at the teady tate and tranent condton. Fg. 6(d) how that the teady tate output DC voltage and current are lnear n wde tme range wth very low voltage and current rpple, whch ndcate the good performance of the MPC algorthm. The output DC voltage & current ncreae rapdly wth the tep change n DC reference voltage, confrmng the effectvene and tablty of the MPC algorthm. Fnally, the harmonc analy of three-phae nput current of the AFE rectfer llutrated n Fg. 6(e), whch how the total harmonc dtorton (THD) 4.0%. The THD of nput current meaured wth FLUE 75 Power Logger. The accuracy of th power logger ±0.% of t full cale. B. Rectfer Effcency The effcency of MPC controlled AFE rectfer meaured wth FLUE 75 Power Logger. The effcency of the AFE rectfer meaured n MPC method agant the power tranfer range from 0.5 kw to.0 kw. In order to confrm the effectvene of MPC algorthm, the effcence of MPC controlled AFE rectfer are compared wth VOCbaed PWM controlled AFE rectfer, preented n Fg. 7. The voltage-orented control (VOC) cheme decompoe the actve and reactve power n tatonary α-β co-ordnate and ynchronze the power wth rotatng d-q reference frame by characterzng the current control loop ung two PI controller. Th VOC-baed PWM method appled n the.0 kw AFE rectfer wth employng the ame parameter and meaurement technque a n MPC algorthm. The MPC algorthm comparatvely mpler than the VOC-baed PWM technque a t ue only one PI regulator. Th MPC algorthm accurately track the reference value and generate the optmum wtchng gnal by utlzng the cot functon n every amplng ntant (T ). Th optmum wtchng gnal reduce the undered conducton loe of Fg. 6: Expermental reult: (a) Input lne voltage (V a) and current ( a) of phae A, (b) Three phae nput current, (c) Phae to phae voltage at the AFE rectfer end, (d) Output DC voltage and current at.8 kw &.98 kw power tranfer and (e) THD of nput current at.98 kw power tranfer. IGBT wtche. Moreover, the unty power factor alo mantaned wth the MPC algorthm a t accurately track the reference current and keep zero phae-hft between the nput AC voltage and current. Hence, the effcency of MPC controlled AFE rectfer ha been ncreaed wth reduced IGBT wtchng loe and mnmzed reactve power. Although, MPC algorthm ha varable wtchng frequency problem, the effcence aocated wth the MPC control are 6

6 Fg. 7: Effcency comparon between MPC & VOC-baed PWM control. tll hgher compared to the VOC-baed PWM control method. Fg. 7 confrm that the maxmum effcency ha been acheved at.0 kw power tranfer for both control method, where the converter effcency ung MPC method 96.8 %, whle the effcency 95.6% ung VOC-baed PWM control method. It can be een that the effcence of the AFE rectfer decreae wth the ncreae of the power tranfer. The flow of current ncreae wth the power tranfer whch reult the ncreae of conducton and wtchng lo. But, tll the MPC how the better effcency than the VOCbaed PWM control. V. CONCLUSION An mproved actve front-end-rectfer ung model predctve control ha been preented n th paper. The mproved performance of the propoed MPC controlled AFE rectfer ha been verfed wth a.0 kw expermental ytem. The expermental reult how that, the AFE rectfer operated wth 96.8% effcency where t nput current ha an acceptable THD (4.0%) level and the rpple n the DC voltage very low. 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