OPTIMAL CONTROL FOR THREE-PHASE POWER CONVERTERS SVPWM BASED ON LINEAR QUADRATIC REGULATOR

Transcription

1 INERNAIONA JOURNA o ACADEMIC RESEARCH Vol. 4. No. 3. May, 0 OPIMA CONRO FOR HREE-PHASE POWER CONVERERS SVPWM BASED ON INEAR QUADRAIC REGUAOR Har Sutkno, e Jaa, Mochamad Ahar 3, Maurdh Hery Purnomo 3 Sekolah ngg eknk Surabaya (SS Surabaya, Udayana Unerty Bal, 3 Inttut eknolog Sepuluh Nopember (IS (INDONESIA E-mal: har@tt.edu, lejaa@unud.ac.d, ahar@ee.t.ac.d, hery@ee.t.ac.d ABSRAC A three-phae power conerter pace ector PWM wth current regulaton ung PI controller typcally produce low harmonc dtorton and unty power actor wth the load change. Nonethele, t tme repone o the output oltage not optmal. h paper propoe an mproement to the conentonal three-phae power conerter pace ector PWM ung an optmal control baed on the lnear quadratc regulator and ntegral acton to mproe the output oltage repone. In th paper, the power conerter determned ung a lnearzed tatepace model and the parameter o plant model can be ound onlne ung the recure leat quare algorthm. he eedback and eed orward gan can be obtaned baed on the lnear quadratc regulator to mnmze the perormance ndex. In th ettng, an ntegral acton requred to elmnate the teady-tate error. Ung a nuodal nput, the mulaton reult demontrate that, at teady tate, the propoed method reult n the oerhoot o tme repone o the output oltage o.67% wth the ettlng tme o 0.05 ec or load change rom ull load to hal load. Key word: optmal control, power conerter, pule wh modulaton, lnear quadratc. INRODUCION Space ector PWM technque ha been ued extenely n three phae power conerter due to the low harmonc dtorton, hgh ecency and bdrectonal power low [-8]. In order or the lne current and oltage to be n-phae wth certan ampltude, the current regulator mut be requred. Although the PI controller ha typcally been ued n three-phae power conerter, obtanng the optmal tme repone o the oltage output wth repect to the load-change reman challengng due to the act that the load wll lkely change the parameter o the plant model. An optmzaton method ha been propoed ung the output regulaton ubpace and Pule Wh Modulaton (PWM technque takng the adantage o the drect power control trategy [9]. he outcome how that the oerhoot o the dynamc about 3% and the ettlng tme about 0. ec. he QR wth ntegral acton ha alo been appled n the degn o three-phae three-wre hunt acte power lter, gng the oerhoot o the output oltage on dynamc load o around 5% wth a hal cycle ettlng tme [0]. Reearch dealng wth contraned optmal control o three-phae Voltage Source Conerter (VSC baed on a mathematcal model n the ynchronou erence rame ha alo been deeloped recently []. In th ntance, the optmal control degn to mproe the tme repone o dc oltage on load change baed on lnear quadratc regulator wth ntegral acton propoed whereby the model o the three phae power conerter wth current regulator mut be lnearzed. A the parameter o the model ary a the load change, thee parameter mut be calculated onlne by ung the recure leat quare algorthm. hee parameter are ued to calculate the perormance ndex. he optmal tme repone wll then be obtaned when the perormance ndex reache the mnmum alue. Baed on the lnear quadratc regulator algorthm, both the eedback and eed orward gan can be obtaned. he ntegral acton can be added to elmnate the error output oltage. he perormance ndex ued n th paper ental the output oltage and nput control o the lne current.. HREE-PHASE POWER CONVERER SVPWM WIH CURREN REGUAOR A. hree-phae Power Conerter Fg how the man crcut dagram o the three-phae power conerter. he relatonhp between the current and the oltage o the ac de can be expreed ung the ollowng equaton: d ' ( a b c ' ' ' ' a b c (3 a b c ( (4 Baku, Azerbajan 77

2 INERNAIONA JOURNA o ACADEMIC RESEARCH Vol. 4. No. 3. May, 0 he current o the dc de can be expreed a rect d C (5 Meanwhle, the relatonhp between the oltage and current o both the dc and ac de can be obtaned repectely ung the ollowng equaton: M 3 a MS ' (6 rect S (7 b c S S S S (9 In equaton (9, S ndcate the wtch poton beng mean ON and 0 mean OFF. he pace ector PWM technque can then be appled to generate the three phae oltage o the ac de. (8 I rect I V a a S a Sb S c C N V b V c b c C + _ R V S' a S' b S' c Fg.. Crcut Dagram B. Current Regulator In th cae, the current regulator n Fg. ue an algorthm to produce the erence pace ector oltage uch that the aerage lne current oer the perod or next one perod are n phae wth the phae oltage o the power ource, wth: ( t u ( t (0 where u the nput gnal. h nput alue the rato o the lne current to the phae oltage o the power ource. he oltage erence wll be generated a ' ( t n ' u ( ( t n u I( t n I( t ( V I u CURREN REGUAOR V HREE-PHASE POWER CONVERER SVPWM V I Fg.. he Plant Dagram 78 PAR A. NAURA AND APPIED SCIENCES

3 INERNAIONA JOURNA o ACADEMIC RESEARCH Vol. 4. No. 3. May, 0 3. OPIMA CONRO BASED ON INEAR QUADRAIC WIH INEGRA ACION here are a number o tep requred n the degn o the optmal control o three phae power conerter SVPWM baed on lnear quadratc regulator wth ntegral acton. he rt tep to ormulate the lnearzed tate pace model o the plant whereby the parameter o the plant wll be obtaned by mean o the recure leat quare (RS algorthm. he econd tep to obtan the eedback and eed orward gan ung Rccat equaton n order to mnmze the perormance ndex. he nal tep to generate a control gnal. Fg.3 how the block dagram o the propoed ytem. V abc I u u K K u r K e u HREE-PHASE POWER CONVERER WIH CURREN REGUAION K K r ESIMAOR INEAR QUADRAURE AGORIHM A,B Fg. 3. Block Dagram o the propoed ytem C. nearzed State Space Model he mathematcal model o three-phae power conerter SVPWM wth current regulaton can be dered a ollow. he rected current can be calculated a rec 3mm 3m ( u( t m 3m u( t ( (3 R t rec( u( t G (4 3 m G (5 where the peak phae oltage m and peak lne current m are condered contant along the nteral. he capactor current can now be dered rom the oltage a d C C (6 (7 From equaton ( to (7, the tate equaton o the plant can be expreed a rec d C G u( t ( t F( u, (8 C C R Fg.4 how the non-lnear model o the three-phae power conerter wth current regulaton. Fg. 4. Non-lnear Model o the hree-phae Power Conerter SVPWM wth Current Regulator Baku, Azerbajan 79

4 INERNAIONA JOURNA o ACADEMIC RESEARCH Vol. 4. No. 3. May, 0 he lnearzed model o the tate equaton (8 can be theore be ormulated a ollow where d F ( u, F( u, F( uc, V u, V ( u( t uc ( u, V ( c c u F V ( ( u, G ( uc, V u C V (9 (0 F( u, G u C V c ( uc, V At teady tate, the dc output oltage wll moe toward a contant alue, o the uncton F u c, V mut be equal to zero. From equaton (9 to ( R C ( ( where d A Bu( t ( A G u C V (3 c R C B G C (4 V Fnally, t can be een rom equaton ( and (3, the parameter o power conerter model are nluenced by the load retance. he lnearzed model o the power conerter (Fg.5 demontrate that the parameter o the three-phae power conerter model ary wth the load change. Fg. 5. nearzed Model o the hree-phae Power Conerter SVPWM Recure eat Square Algorthm For the mplcty reaon, the three-phae power conerter SVPWM wth current regulator model may be expreed a a lnear model. A tate pace realzaton o the ARX model gen n dcrete equalent by: ( k A ( k Bu( k (5 he parameter o the plant (A and B can be etmated by mean o the Recure eat Square (RS algorthm, where (k and u (k are the regreor. [A B] (6 ( k [ y( k u( k ] (7 he load change wll aect the output oltage. Both control gnal u and dc oltage y are ued to etmate the parameter o the three-phae power conerter wth current regulator. Fg.6 how the block dagram o the RS etmator to obtan A and B. 80 PAR A. NAURA AND APPIED SCIENCES

5 INERNAIONA JOURNA o ACADEMIC RESEARCH Vol. 4. No. 3. May, 0 Fg. 6. RS Etmator he ollowng equaton are ued wthn the RS algorthm. K( k P( k ( k[ I ( k P( k ( k] (8 ( k ( k ( k ( k (9 ( k ( k K( k ( k (30 P( k [ I K( k ( k ] P( k (3 he ntal alue o the parameter ( (3 Fg. 7 how the RS algorthm to etmate the power conerter model. Fg. 7. Dagram o Recure eat Square Method near Quadratc Regulator wth ntegral acton For the ytem model ( k A ( k Bu( k, where nput gnal (control, and the calar perormance ndex dened below the output dc oltage and u the J k 0 (( ( k u Q ( y( k u u( k Ru( k (33 where J a calar perormance ndex Q a pote em-dente matrx R a dente matrx u the command gnal (aumed to be contant the output gnal he optmal control equence that mnmze J u( k K ( k K u (34 he eedback gan K n equaton (34 gen by K ( B SB R B SA (35 r Baku, Azerbajan 8

6 INERNAIONA JOURNA o ACADEMIC RESEARCH Vol. 4. No. 3. May, 0 where S the oluton o the algebrac Rccat equaton and the eed-orward gan S A [ S SB( B SB R K r gen by B S] A Q (36 K r ( B SB R B [ I ( A BK ] C Q (37 he problem that equaton (34 cannot elmnate the teady tate error. A mple way to oercome th by addng a term proportonal to the accumulated error to the controller output. It can be expreed a where u( k K ( k K u K z( k (38 r K a contant choen by the degner and gnal z(k gen by the ollowng recure ormula z( k z( k ( u ( k (39 Fg.8 how the optmal algorthm to calculate the eedback and eed-orward gan. In a conentonal PI controller, the proportonal gan and ntegral gan wll reman contant on the load change and theore acheng the optmal tme repone ung conentonal PI controller uneable. 4. RESUS AND DISCUSSION Fg. 8. near Quadrature Algorthm and Control In th mulaton experment, the perormance o the optmal control baed on lnear quadrature wth ntegral acton wll be compared to that o the PI controller or three-phae power conerter SVPWM wth current regulaton. he parameter o the three-phae power conerter SVPWM wth current regulaton are hown n able. he dynamc perormance meaure nclude the tme repone o the dc oltage generated on load change and the phae derence between the nput lne current and the phae oltage or both controller. he load retance wll be ared rom the ntal load R =60 Ω to 0 Ω at tme 0.5 ec. able. Parameter o three-phae power conerter Parameter Phae oltage Frequency bu oltage Inductance o Reactor Internal Retance o Reactor bu capactance oad retance on ull load Samplng Frequency Value 00 V peak 50 Hz 300V 300mH 0. ohm 000uF 60 ohm 0kHz 8 PAR A. NAURA AND APPIED SCIENCES

7 INERNAIONA JOURNA o ACADEMIC RESEARCH Vol. 4. No. 3. May, 0 Fg. 9 how the Matlab Smulnk block dagram o the power conerter ung the PI controller. he proportonal and the ntegral gan ettng are and 0. repectely. hee gan hae been choen n order to obtan the bet tme repone o the output oltage. Fg.0 how the mulaton reult o the tme repone o the dc oltage on load change ung the PI controller, howng the oerhoot o approxmately 7.5 olt (.5% at t=0.5 ec and the ettlng tme o 0.3 ec. In Fg., the lne current (phae A hown between 0.46 ec and 0.56 ec. he peak current change rom 0A to 5A. he wae orm o the lne current nuodal wth 3% total harmonc dtorton (HD and unty power actor. Fg. 9. Matlab Smulnk Dagram o Power Conerter wth PI Controller Fg. 0. me repone o output oltage ung PI Controller Fg.. he nput lne current ung PI Controller Baku, Azerbajan 83

8 INERNAIONA JOURNA o ACADEMIC RESEARCH Vol. 4. No. 3. May, 0 Fg. how the Smulnk block dagram o the power conerter wth optmal control ung Q regulator and ntegral acton. From Fg.3 and Fg.4, t can be een that the parameter o the power conerter model (A and B and gan (eedback gan K and eed orward gan K r moe toward contant alue at le than 0.05 ec at the ntal conon and on load change. h mean the tme requred by the algorthm to etmate the parameter and to obtan the gan hort. Fg.. Matlab Smulnk o the Power Conerter wth Optmal Control ung Q regulator and Integral Acton Fg. 3. he coecent A and B o conerter model Fg. 4. he eedback and eed-orward gan 84 PAR A. NAURA AND APPIED SCIENCES

9 INERNAIONA JOURNA o ACADEMIC RESEARCH Vol. 4. No. 3. May, 0 Fg.5 how the mulaton reult o the tme repone o dc oltage on load change ung QR optmal control (Q= and R=0.. he tme repone o the output oltage ocllate (underdamped wth oerhoot o approxmately 4 olt (.33% and ettlng tme o 0.05 ec. Fg.6 how the nput lne current (phae A change rom 0A peak alue to 5A wth a nuodal waeorm wth mall dtorton on teady tate. Durng the tranton, howeer, the waeorm o lne current not nuodal whch occur n hal a cycle. Fg. 5. me repone o the output oltage on load change wth QR optmal control 5. CONCUSION Fg. 6. he nput lne current (phae A on load change wth QR Optmal Control he oerhoot o the optmal control o the three-phae power conerter SVPWM wth current regulaton baed on lnear quadratc wth ntegral acton on load change rom ull load to hal load about.33% whch lower than that o the PI controller (.5%. he ettlng tme o the optmal control alo lower (about 0.05 ec compared to 0.3 ec. Both the nput lne current are n phae to the phae oltage (unty power actor wth a relately low HD o le than 5%. Ung the optmal control method, the parameter o the plant model can be obtaned onlne and th allow the controller to be ued or arou plant. Ocllaton occur at the tartng tme and eery load change o the optmal control method; howeer, the nteral o the ocllaton le than hal a cycle. REFERENCES. Rathnakumar D., akhmana Perumal J., Srnaan., A New Sotware Implementaton o Space Vector PWM", SoutheatCon, 005, Proceedng IEEE, pp.3-36, September 00.. Kocalm A., Sunter S., Smulaton o a Space Vector PWM Controller For a hree-eel Voltage- Fed Inerter Motor Dre, IECON 006-3nd Annual Conerence on IEEE Indutral Electronc. pp , 6-0 No Baku, Azerbajan 85

10 INERNAIONA JOURNA o ACADEMIC RESEARCH Vol. 4. No. 3. May, 0 3. Iqbal A., amne A., Ahra I., Mohbullah, Matlab/Smulnk Model o Space Vector PWM or hree- Phae Voltage Source Inerter ", Unerte Power Engneerng Conerence, 006. UPEC '06. Proceedng o the 4t Internatonal, ol. 3 pp , 6-8 Sept Zheng Zheng; Cong Wang; Hajun ao, Reearch on three-phae PWM recter baed on predcte control ", ICI 008. IEEE Internatonal Conerence on Indutral echnology pp.-3, -4 Aprl Saeteo S.; orrey D.A, Fuzzy logc control o a pace-ector PWM current regulator or three-phae power conerter", IEEE ranacton on Power Electronc, ol.3, Iue 3 pp.5-33, May Mn B.-D., Youm J.-H., Kwon B.-H, SVM-baed hytere current controller or three-phae PWM recter, Electrc Power Applcaton, IEE Proceedng, ol 46, Iue, pp. 5 30,, March Sutkno H; Ahar M.; Maurdh H.p.; Neural Predcte Control For A hree-phae Power Conerter SVPWM Wth Current Regulator, Proceedng o the Fourth IASED Internatonal Conerence Power and Energy Sytem Aprl -4, Sutkno H; Fadel M; Haroen Y; Ahar M; Maurdh H.,P; oad Current Control or hree-phae Power Conerter SVPWM wth Current-Regulaton, 4th Internatonal Power Electronc and Moton Control Conerence, EPE-PEMC Vazquez S.; eon J.I.; Sanchez J.A.; Galan E.; Carraco J.M.; Franquelo.G.; Domnguez E.; Ecobar G. Optmzed Drect Power Control Strategy ung Output Regulaton Subpace and Pule WhModulaton, IECON nd Annual Conerence on IEEE Indutral Electronc, pp , Bachr Kedjar, Kamal Al-Haddad, DSP-Baed Implementaton o an QR Wth Integral Acton or a hree-phae hree-wre Shunt Acte Power Flter, IEEE ranacton On Indutral Electronc, Vol. 56, No. 8,, pp.8-88 Augut Kuta, N.; Kelemen, A.; Imec, M. Contraned optmal control o three-phae AC-Dcboot conerter, IEEE Internatonal Conerence on Automaton Qualty and etng Robotc (AQR, 00 Vol. pp. 6, PAR A. NAURA AND APPIED SCIENCES