Dtrbuted Parallel Operaton of Modfed Deadbeat Controlled UPS Inverter Meng WAG, Fangheng LI, Yadong LIU, Lpe HUAG State Key Lab of Power Sytem Department of Electrcal Engneerng, nghua Unverty Bejng, 100084, Chna Abtract- A novel control cheme propoed for the parallel operaton of UPS module. In th cheme, each UPS n parallel controlled by a modfed deadbeat control method. he tradtonal deadbeat control ha a robut problem to parameter mprecon, whch retrct t applcaton. A proportonal element added n the propoed method to olve th problem. he modfed deadbeat controlled nverter ha good tatc performance and fat dynamc repone and nentve to parametrc devaton. A dtrbuted control method ued here to reale parallel operaton. All the UPS module are connected by two common lne. One provde a phae gnal to ynchrone the output voltage. he other one provde the average current gnal for the ntantaneou average current-harng control. Experment are carred out on three 1kVA on-lne UPS module. he theoretc analy and expermental reult how that the ytem act atfactorly both n teady tate and dynamc proce. he load dtrbuton among UPS module prece n dfferent load condton, and the real abundance can be acheved. I. IRODUCIO owaday, unnterrupted power upple are wdely ued to provde contnuou electrcal power to load that cannot afford unexpected power falure. Furthermore, the parallel operaton of modulared UPS unt can be a oluton to both capablty and relablty. It convenent and economc to change the power capacty by adjutng the number of UPS unt n parallel. Bede, X redundancy operaton can greatly mprove the relablty of the ytem. Recently, many cholar focu on the reearch of the parallel operaton and the dgtal control cheme of UPS nverter. o acheve the good performance of a parallel UPS ytem, there are two man requrement: (1) Hgh performance of each UPS n parallel. he dynamc repone hould be fat, and the output voltage hould have a low HD. (2) Proper current dtrbuton among nverter. For th target, the output voltage of each UPS hould have the ame ampltude, frequency, and phae. A current-harng control alo neceary to reduce the crcular current. o lmt the output voltage dtorton and mprove the performance of UPS nverter, varou dgtal control method have been propoed, uch a repettve control, deadbeat control, ldng mode control, and etc. Derved from tate equaton, deadbeat control ha fat dynamc repone and can elmnate the tate varable error n everal control perod. However, the hgh entvty to parameter mmatche, model uncertante, and noe on the ened varable of the deadbeat control tll retrct t applcaton [1,2,3]. h problem can be much more erou n the parallel operaton of everal deadbeat controlled UPS module. For a parallel ytem, each output voltage of the UPS module hould have the ame ampltude, frequency and phae; otherwe the crcular current would ncreae power lo and even make the ytem untable. Bede, a current-harng control ndpenable to enure the proper current dtrbuton among module even f there ome dfference between the output of UPS module. Among all the currentharng control cheme, the ntantaneou current-harng cheme have good performance both on current dtrbuton and voltage regulaton [4,5,6]. hey can be clafed a mater-lave current-harng cheme, average current-harng cheme, maxmum current-harng cheme, and crcular-chan current-harng cheme. her common advantage that the current regulated at every wtch perod o that the ytem ha fat dynamc repone when load change. In th paper, the dtrbuted parallel operaton of deadbeat controlled UPS nverter realed n experment baed on DSP MS320LF2407A. A modfed deadbeat control cheme propoed here. It can effectvely mprove the robutne of deadbeat control wth the expene of a lttle ncreaed tatc error and lower dynamc repone. A novel dtrbuted operaton of UPS nverter wth ntantaneou average currentharng cheme mplemented wth two common lne provdng ynchronou phae gnal and average current gnal repectvely. II. MODIFIED DEADBEA COROL A. Sytematc Analy u ac Makoto SAKAE GS Yuaa Power Electronc Ltd Oaka 5691115,Japan V 1 D 1 D 2 U d U V 3 u n D 3 d V 2 V 4 Fgure 1. Dagram of a ngle-phae UPS L D 4 L C C o u o he crcut of a ngle-phae UPS hown n Fg.1. It manly cont of the rectfer part and the nverter part. Here we manly focu on the nverter part. It uually ha the nverter brdge, the output flter and the load. o mplfy the analy, 1-4244-0655-2/07/$20.00 2007 IEEE 1727
the two capactor n the DC de are uppoed to have the ame contant voltage U d. u n the output voltage of nverter brdge, and n the two level pattern t ether U d or U d. If the output voltage u o and the nductance current L are choen a tate varable, and the load current o treated a dturbance, the ytem tate equaton x A x B u D (1) where x uo L, 0 1/ C ; 1/ L 0 D 1/ C 0, n o y C x (2) A, 0 1/ L C 1 0. he dcrete tate equaton can be expreed a where B, xk ( 1) xk ( ) Gk ( ) P( k) H (3) 11 12 e A 21 (4) 22 ( A /2) G 2U e B g g (5) d 1 2 1 A ( I e ) p1 p2 1 A d ( ) 1 2 PA D (6) HUA Ie h h (7) the control perod, k ( ) the actng tme of potve voltage U d n the kth control perod. B. radtonal Deadbeat Method he requred pule wdth k ( ) can be computed by makng u o (k1) n the frt equaton n (1) equal to the voltage reference u ref (k1). he deadbeat control law 1 11 12 p1 h1 k () uref ( k1) uo () k L() k o() k (8) g g g g g 1 1 1 1 1 Deadbeat control depend on the prece mathematcal model of the controlled object. In deal condton, the calculatng parameter ued n (8) are dentcal wth the actual parameter of the nverter. However, the prece ytemc model dffcult to obtan, and the actual parameter may change durng operaton. Here we ue ymbol wth ^ a calculatng value and ymbol wthout ^ a actual value. he actual control law of tradtonal deadbeat control can be rewrote a 1 11 12 p1 h1 k () uref ( k1) uo () k L() k o () k (9) g1 g1 g1 g1 g1 Fg.2 how the dcrete ytem block dagram of the tradtonal deadbeat control. he tranfer functon from U ref () to X() X ( ) ˆ ˆ 1 [C G( I ) G C ] G (10) Uref ( ) he tranfer functon from voltage reference to output voltage Uo( ) C X ( ) ˆ ˆ 1 G ( ) C [C G( I ) G C ] G Uref ( ) Uref ( ) 2 [ g ( g g ) ]/ q ( ) (11) where 1 2 12 1 22 o q () g [ g g g g ] g( ) U ( ) ref 2 1 1 11 2 12 122 1 11 21( g112 g112) 22( g111 g111) 2 11 12 11 12 Io( ) C Pˆ P C Gˆ X ( ) 1/(C Gˆ ) G 1/ ( ) C Hˆ ˆ H C G C ˆ Fg.2 Dcrete ytem block dagram of tradtonal deadbeat control If the calculatng value and the actual value are the ame, t tranfer functon can be mplfed a G () 1 (12) Equaton (12) mean that wth the tradtonal deadbeat control, the output voltage follow the reference n cae that there no parametrc mmatch. However, t not alway the cae n practce. A typcal UPS nverter condered to tudy the nfluence of parametrc devaton. he calculatng parameter are: U d =185 V, L =1.3 mh, C =20F. Fg.3(a) how the module track of and of the tranfer functon n tradtonal deadbeat control, when L change, and U d and C are the ame a calculatng value. One of (11) alway tay n orgn and not plotted. Smlarly, Fg.3(b) and Fg.3(c) how the module track when C and U d change repectvely. Accordng to the clacal control theory, the module of each hould be le then 1 to enure the ytem table. When actual parameter match calculatng value, the counteract the, and we get (12). However, when there parametrc mmatch, the ytem can ealy become untable. A hown n Fg.3, when the actual nductance L maller than calculatng nductance L, or the actual capactor C maller than C, or the actual DC lnk voltage U d bgger than U d, the ytem ha a outde the unt crcle n Z-plane and become untable. he poor robutne make the tradtonal deadbeat control almot mpractcable n UPS applcaton. p ole (a) when L change (b) when C change 1728
(c) when U d change Fg.3 Module of and n tradtonal deadbeat control (a) when L change C. Modfed Deadbeat Method o deal wth the robut problem wth deadbeat control and make t applcable n UPS, a modfed control method propoed here. A how n Fg.4, a proportonal element k w added to the control dagram of the new method. Comparng Fg.2 and Fg.4, we can ee that t return to the tradtonal deadbeat control when k w =1. I ( ) o U ( ) C Pˆ P ref C Gˆ X( ) 1/(C Gˆ ) k G 1/ w ( ) C Hˆ ˆ H C G C ˆ Fg.4 Dcrete ytem block dagram of modfed deadbeat control he control law of the modfed deadbeat method kw kw11 kw12 p1 h1 k () uref ( k1) uo () k L() k o () k (13) g1 g1 g1 g1 g1 where uually 0k w 1. he tranfer functon from voltage reference to output voltage n the modfed method U ˆ o( ) C X ( ) C G ˆ 1 G ( ) C [ ( I ) G C ] G Uref ( ) Uref ( ) kw 2 k [ w g1 ( g ) ]/ ( ) 212 g122 l (14) where 2 l () g 1 [ g1 11kwg2 12kw g122 g111 ] gk 2 w ( 1112 ) ( g k g ) ( g g k ) 11 12 21 1 12 w 1 12 22 1 11 1 11 w he propoed deadbeat control wth a proportonal element ha better robutne compared wth the tradtonal method. Fg.5 how the module track of and of the tranfer functon n the modfed deadbeat control (k w =0.7) when the actual nductance L, the actual capactor C, and the actual DC lnk voltage U d change repectvely. We can ee that n th cae the ytem can reman table a long a L larger than 0.913mH (70.23% L ), C larger than 9.82F (49.1% C ), and U d maller than 264.5V (146.94% U d ). Compared wth the tuaton n tradtonal deadbeat control method, t obvou that contrant n the propoed method are much le trct, and the control method ha better robutne when actual parameter devate from calculatng parameter. (b) when C change (c) when U d change Fg.5 Module of and n modfed deadbeat control he proportonal element mprove the robutne of the deadbeat control, whle t caue a lttle ncreaed tatc error. From (14) we can get the frequency repone by ubttutng wth e j j j U o(j ) kwe ( ge 1 g2 12 g1 22) G (j ) j U (15) ref (j ) l( e ) where U (j ) and U (j ) are voltage reference phaor and ref o output voltage phaor repectvely. In UPS nverter, the voltage reference u ref a ne wave wth the frequency of 50 H, and ac 314 rad/. he control frequency 20 kh n experment, and the correpondng control perod 50. Suppoe that the actual parameter match the calculatng parameter, Fg.6 how the module and phae of G (j ac) when k w change. he teady tate error between output voltage and voltage reference ncreae wth the decreae of the value of k w. When k w =0.7, the ampltude error 2%, and the phae error -0.009.he ytem tll ha good teady tate performance. 1729
Fg.6 he nfluence of k w on teady tate performance he above analy how that the modfed deadbeat method greatly mprove the robut problem whch retrct the applcaton of the tradtonal deadbeat control. h method can be appled nto parallel UPS ytem to enhance the control performance. III. PARALLEL OPERAIO Fg. 7 llutrate the tructure of a UPS parallel ytem. wo common lne provdng gnal p and oa are neceary to reale dtrbuted parallel operaton. p a quare wave provdng frequency and phae nformaton to ynchrone voltage reference of all the parallel module. oa the average oberved output current of UPS module. oa p UPS 1 UPS 2 Fg.7 he dagram of a UPS parallel ytem A. Synchronaton of Output Voltage he output voltage of each UPS module n a parallel ytem hould have the ame ampltude, frequency and phae. Snce the voltage control method of each UPS nverter can be mplfed a a proportonal element, the reference voltage of each UPS module hould be exactly the ame. he ampltude accordance convenent to reale n dgtal proceor. A the ampltude tored n the proceor a dgtal quantty, we can mply make the dgtal quantte of all the UPS n parallel ame to each other. he frequency and phae accordance realed though the common gnal p. A common lne tranmt p to the proceor of each UPS, and the proceor generate nuodal gnal accordng to the phae of p. Fgure 8 how the phae ynchronaton of the voltage reference u r and the gnal p. p A phae control unt baed on a MCU(mcro controller unt) added to each UPS n order to generate the hared gnal p. In th paper, t realed by DSP. Fg.9 llutrate the phae control unt and t connecton to the correpondng common lne. p generated from all the gnal pj by an AD operaton, p p1p2... p (16) pj a phae gnal generated by the phae control unt of the UPS j. When AC man normal (both the RMS value and the frequency are approprate), gnal pj wll trace the phae of AC man by DPLL(dgtal phae locked loop). When AC man abnormal, pj generated by the MCU wth a crytal of hgh accuracy. And the MCU adjut pj lghtly to make t trace p. UPS j u n n pj p Fg.9 he phae control unt of UPS j p B. Current Sharng Control Only the ynchronaton of output voltage cannot guarantee the proper output current dtrbuton among UPS module. A current harng control neceary to adjut the output current of each UPS nverter accordng to current reference. A common lne ued to tranmt the ntantaneou average current gnal oa a the reference. Each UPS compare oa wth t own output current oj. he voltage reference gnal u r adjuted accordng to the current error gnal ocj. he control cheme hown n Fg.10. u r _ ocj k c _ oa oj UPS nverter u rj SPWM Fg.10 he current harng control of UPS j he man crcut of the parallel ytem hown n Fg11. L lnj the nductance of the load lne of UPSj, and R lnj the retance of the load lne. u oj the output voltage of UPSj, and u the output voltage of the parallel ytem. UPS 1 UPS 2 u o1 u o2 L ln1 L ln2 R ln1 R ln2 o1 o2 u Z load u oj u r Fg. 8 he phae ynchronaton of u r and p UPS u o L ln R o ln Fg.11 he output de of the UPS parallel ytem 1730
From Fg.11, t hold Uo1() U () Uo2() U () Uo () U () U()... Lln1Rln1 Lln2Rln2 Lln Rln Zload () (17) Snce t uually hold that Lln j Rln j Z ( ) load, t can be deduced from (17) that U() [ Uo1() Uo2()... Uo ()]/ (18) Suppoe the cloe-loop tranfer functon of UPSj G j (). o avod confuon, the output voltage and output current wthout current harng control have 0 n the upper rght quarter, whle the output quantte wth current harng control do not have 0. When the current harng control not ued, 0 Uo j() Gj() Ur() (19) Combnng (18) and (19), we can get 0 0 j 1 U ( ) ( U ( )/ ) (20) Equaton (20) how that wthout current harng control, the output voltage of the parallel ytem the average of the output voltage of all the UPS nverter n parallel. When the average current harng control ued, Uref j() Ur () kc[ Ioa () Io j()] (21) and Uo j() Gj() Uref j() (22) 0 U() Gj() kc[ Ioa() Io j()] Combng (18) and (22), we get U () U ()/ j1 j1 [ U ( ) G ( ) k ( I ( ) I ( ))]/ Accordng to the control law, 0 j c oa oa (23) (24) j1 I () I ()/ he tranform functon of the ame type UPS nverter are almot the ame, namely G1() G2() G () (25) Combng (23),(24) and (25) 0 0 U() ( U ()/ ) U() (26) j1 Equaton (26) how that the current harng control ha no nfluence on the output voltage of the parallel ytem, whch tll the average output voltage of all the UPS nverter. he current harng control ndependent of the nner voltage control of the UPS nverter. Snce the current harng control ha no nfluence on t, the output voltage u can be treated a a dturbance to the current control loop. he control dagram of one nverter wth current harng control hown a Fg.12. For deadbeat control, G j () can be mplfed a a proportonal element. Accordng to the clacal control theory, the current harng control element can reman table no matter what k c. oa ocj k c u refj u r G j () u oj u 1 L R Fg.12 Control dagram of one nverter wth current harng control Accordng to Fg.11, t hold U I ( Lln j j ac Rln j) U (27) where ac 314 rad/. From (22) we can get 0 ( I oa I ) kcg U U (28) Combnng (27) and (28), we get 0 0 I ( kcg Lln j j ac Rln j) I oa kcg U U (29) Snce the nductance and the retance of the load lne uually mall, t can be Lln j j ac Rln j kcg (30) So (29) can be mplfed a 0 I oc j I oa I ( U U )/ k (31) c From (23) and (31) we get 0 1 0 I oc j [ U ( U )]/ kc (32) j 1 If U or ymbole the rated output voltage of ngle UPS nverter, and Pr ymbole the relatve accuracy of the output voltage (1%~2%), there Ioc j 2P or Uor / kc (33) It how that the maxmum crcular current only relatve to the current harng control gan k c, and ha no relaton wth the load of the parallel ytem. By changng the value of k c, we can adjut the precon of current harng control ealy. IV. EXPERIMES A three-cell prototype bult baed on DSP MS320LF2407A to verfy the control cheme we propoed here. he parameter are: Rated output voltage: 100V(rm)/50H Rated capacty: 1KVA/700W Output flter: L1.3mH, C20µF Swtchng frequency: f=20 kh Fg.13~15 how the output voltage of the ytem and the output current of each UPS n parallel n dfferent load condton. hey are retance load, rectfer load, and no load repectvely. able I record the expermental reult at heavy load, lght load, rectfer load, and no load. he reult prove that however the load change, the ytem performance atfactorly. he RMS value of output voltage n the range of 1002%, and the HD below 2%. he current dtrbuton among nverter proper under all knd of condton. ln ln oj 1731
Fg.13 hree module operatng n parallel wth retor load (u :100V/dv, o1, o2,and o3 : 5A/dv) Fg.14 hree module operatng n parallel wth rectfer load (u :100V/dv, o1, o2,and o3 : 5A/dv) Fg.15 hree module operatng n parallel wth no load (u :100V/dv, o1, o2,and o3 : 5A/dv) ABLE I EXPERIMEAL RESULS UDER DIFFERE CODIIOS U o (V) HD of u o I o1 (A) I o2 (A) I o3 (A) Heavy load 100.8 1.68% 2.50 2.66 2.60 Lght load 101.5 1.67% 1.10 1.32 1.06 Rectfer load 101.5 1.67% 1.62 1.76 1.89 o load 102.0 1.62% 0.37 0.30 0.36 Fg.16 how the dynamc proce when a econd UPS plugged nto the parallel. We can ee that the current harng ha a fat dynamc repone wth lttle dturbance to the output voltage when the load change. Fg.16 he econd UPS plugged nto ytem wth rectfer load (u :100V/dv, o1, o2 : 5A/dv) V. COCLUSIO h paper propoe a new way to mprove the parallel performance of UPS nverter. Deadbeat control appled to each UPS nverter n parallel becaue of t fat dynamc repone and good waveform qualty. A modfed deadbeat control wth a proportonal element propoed here to deal wth the man drawback of the tradtonal deadbeat method- the robut problem. A dtrbuted control method ued here to reale parallel operaton of UPS module. he ynchronaton of output voltage neceary for parallel operaton, and the average current-harng control enure the proper load dtrbuton among the module. he theoretc analy and expermental reult how that the control cheme ha everal feature: 1) he parallel ytem mple n tructure wth only two common lne connectng UPS module. 2) All UPS module are exactly the ame and real redundancy acheved. 3) he control cheme eay to reale n DSP and nentve to parametrc devaton. 4) Load harng prece n dynamc repone and teady tate. 5) Output voltage ha good qualty under varou knd of condton. REFERECES [1] Xao Sun, Ym-Shu Lee, and Dehong Xu. Modelng, Analy, and Implementaton of Parallel Mult-Inverter Sytem Wth Intantaneou Average-Current-Sharng Scheme. IEEE ran. on Power Electronc.2003, Vol,18, o.3, pp.844-856. [2] Yu-ka Chen, Yu-en Wu, a-fu Wu, Chung-Png Ku. ACSS for Paralleled Mult-Inverter Sytem wth DSP-Baed Robut Control. IEEE ran. on Aeropace and Electronc Sytem.2003, Vol.39, o.3, pp. 1002-1015 [3] YK Chen, F Wu, YE Wu, CP Ku. A current-harng control trategy for paralleled mult-nverter ytem ung mcroproceor-baed robut control. Electrcal and Electronc echnology, 2001. ECO. Vol.2, pp. 647-653. [4] Paolo Mattavell. An Improved Deadbeat Control for UPS Ung Dturbance Oberver. IEEE ran. on Indutral Electronc.2005, Vol. 52, o.1, pp. 206-212 [5] Yadong Lu, Yan Xng, Lpe Huang, and Sakane, M. Progrevely convergng deadbeat control for UPS nverter. Appled Power Electronc Conference and Expoton, 2006. Vol.2, pp. 809-813. [6] W Guo, S Duan, and Y Kang. A new dgtal multple feedback control trategy for ngle-phae voltage-ource PWM nverter. Electrcal and Electronc echnology, 2001. ECO. Vol. 2, pp. 809-813 1732