Modeling, Analysis and Control of Hexagram Inverter for Three- Phase Induction Motor Drive

Transcription

1 Control Theory and Informatcs ISSN (prnt) ISSN (onlne) Modelng, Analyss and Control of Hexagram Inerter for Three- Phase Inducton Motor Dre K.Rajambal Department of Electrcal and Electroncs Engneerng Pondcherry Engneerng College, Pondcherry, Inda E-mal: G.Renukade Department of Electrcal and Electroncs Engneerng Pondcherry Engneerng College, Pondcherry, Inda E-mal: Abstract Ths paper presents the modelng, analyss and control of Hexagram nerter for three phase nducton motor dre confguraton. The Hexagram nerter can be used for both three phase and sx phase applcatons. It has many adantages ncludng reduced number of swtches, modular structure leadng to easy constructon and mantenance, solated dc buses. Besdes, t has bult-n fault redundancy due to the module nterconnecton. It has lowered dc energy storage requrement compared to that of cascaded H-brdge nerter. Ths emnent feature makes the system n hgh power applcatons. A smulaton model of the Hexagram nerter fed three phase nducton motor dre s deeloped n Matlab/Smulnk enronment. Smulaton s carred out to study the dre performance at dfferent operatng condtons and the results are presented. Keywords: closed loop control, fault tolerant feature, hexagram nerter, three phase nducton motor dre 1. Introducton The medum-oltage (MV) conerters hae become a new breed n hgh-power applcatons. Numerous MV topologes hae been proposed and nestgated snce the md 1980s (Jose Rodrguez Krug 2004). The deelopment and applcaton of MV arable speed dres (VSDs) hae brought sgnfcant adantages n mproed process control, hgher effcency, and energy sangs to the ndustry (Cheng 2006). From the surey artcles (Carrasco Km 2004) t becomes clear that three topologes are faored by MV dre manufacturers: Neutral-pont-clamped (NPC) nerter (Bendre 2006-Vargas 2007); Flyng capactor (FC) nerter (Km 2004); and cascaded H-brdge (CHB) nerter (Du Rech 2007). A hgh-oltage fast recoery dode s used to clamp the oltage n NPC confguraton. The confguraton suffers from oltage unbalancng, neutral pont stablzaton at heay or dynamc loadng, hgher THD and the requrement of LC flter to reduce the braton and nose of the machne. The FC confguraton s used to clamp the oltage and oercome some of the drawbacks of NPC confguraton. Howeer the number of capactors requred ncreases, when the number of leels s hgh and complex precharge crcuts are needed (Km 2004). At present, the cascaded H-brdge nerter s the best-sellng product n the MV ASD market worldwde (Robcon). Wth the modular structure, the cascaded H-brdge nerter s easy to constructon and mantenance. And wth the separate dc buses, there s no oltage unbalancng problem. Howeer, despte ts many adantages, the cascaded H-brdge nerter stll suffers from followng drawbacks (Cengelc 1999). It employs a large number of snglephase nerter modules, solated secondary wndngs n the nput transformer, and three-phase dode rectfers, resultng n hgh manufacturng cost. The dc-bus capacte energy storage requrement s hgh due to the snglephase structure. It does not hae bult-n fault tolerant feature so that addtonal nerter modules are necessary to prode redundancy. The problems can be oercome by a new multleel nerter Hexagram nerter (Wen &.Smedley). The structure of the Hexagram nerter s shown n Fgure 1 (a). The new topology s composed of sx nterconnected VSIs n the form of sx swtch module as shown n the crcle n Fgure 1 (b). The connecton between the modules s depcted wth a connecton dagram. There are sx nner nductors connectng any of the two modules n order to lmt the crculatng current. Wth synchronzed control sgnals, small alue nductors wll be suffcent to lmt the crculatng current to a low 14 P a g e

2 Control Theory and Informatcs ISSN (prnt) ISSN (onlne) alue. Fgure 1(c) shows the connecton dagram, n whch each trangle specfes the each nerter brdge and the nner legs any two of the VSI modules nterconnected to the nductors, and the outer legs are connected wth motor termnals. Dfferng to the three-phase VSI, the Hexagram nerter has sx output termnals, whch prodes two optons to ether dre a three-phase motor (neutral not connected) or dre a sx-phase motor. Ths paper wll focus on the Hexagram nerter appled for a three-phase motor dre (Wen & Smedley 2008) and the star connected sx phase dre (Wen & Smedley 2007). The new Hexagram nerter has a modular structure and no oltage balancng concern as the cascaded H-brdge nerter; n addton, t has followng superor characterstcs: Fewer dode brdge rectfers, nerter modules, and nput transformer secondary wndngs are requred to achee the power leel. Lower dc-lnk capacte energy storage requrement due to the three-phase structure. In balanced systems, the nstantaneous power of each sx-swtch module s constant so that the capactors are not subject to low-frequency power rpples. Due to the nterconnected structure, Hexagram nerter has bult-n redundancy for fault tolerance. The nner legs of the Hexagram nerter whch are not drectly connected to the load are connected n a closed-loop. Therefore, f some swtch of the nner leg fals (open), the oerall nerter s capable of operatng at a reduced power leel. The oltage stress of ths nerter s reduced three tmes compared to a two-leel nerter wth the same output oltage. In addton, well deeloped Indrect feld orented control schemes and well deeloped SPWM technques for VSI can be drectly appled, and the sx modules nsde Hexagram nerter equally share the output power so that the components of the nerter no need to be oer desgned. Wth the symmetrcal and naturally balanced structure, the proposed Hexagram nerter has many nherent adantages. Detaled analyss of the nerter wll be conducted n secton 2 to secton 6, after that smulaton and experment results wll be gen to erfy the analyss n secton 7 and 8, then a bref concluson wll be proded n secton Hexagram Inerter for a Three Phase Inducton Motor Dre Fgure 2 shows a complete MV ASD system, composed of a transformer wth sx secondary wndngs, sx dode rectfers, sx dc capactors and a Hexagram nerter (Wen & Smedley 2008). The transformer shown s an 18- pulse transformer, wth sx Secondary wndngs arranged n 0, ±20 phase shft (two are dentcal), to achee harmonc current cancellaton n the utlty lne currents, leadng to clean nput power. The nput current total harmonc dstorton (THD) for 18-pulse rectfer s about 5-6%. The sx secondary wndngs can also be arranged n ±5, ±15, ±25 phase shft to form a 36-pulse rectfer to further reduce the nput current harmoncs, f necessary. Dode rectfers and dc capactors are used to conert the three-phase ac to dc to prode the solated dc buses for the Hexagram nerter. Replacng the dode rectfers wth the pulse wdth modulaton (PWM) oltage source conerters wll enable the VSD system wth the capablty of regenerate brakng (Wen &.Smedley 2008). 3. Analyss of Hexagram Inerter 3.1 Voltage Relatonshp The phasor dagram of the VSI module of Hexagram nerter s shown n Fgure 3. Phase Voltages of VSI modules are shown n Fgure 3 (a). It s seen that the phase of the VSI module s V olts whereas the output oltage s 3V for Hexagram nerter as shown n Fgure 3 (b).the rms phase oltages of the VSI modules are gen n equaton(1). 15 P a g e a1 o1 a3o 3 a5o 5 a2o 2 a4o4 a6o 6 b1 o1 b3o 3 b5o 5 b2o 2 b4o 4 b6o 6 c1o 1 c3o 3 c5o 5 c2o 2 c4o 4 c6o 6 Where ω s the frequency of the oltage n radus. (It should be noted that (1) s true wth restrctons on the modulaton strategy. For example, for snusodal pulse wdth modulaton (SPWM), the swtchng frequency should be an nteger multple of sx tmes the fundamental frequency). Then, the fundamental output oltages of (1)

3 Control Theory and Informatcs ISSN (prnt) ISSN (onlne) the Hexagram nerter are determned and gen n the equaton (2). 3 sn( ) AO A ' O 2V ωt BO B ' O 3 2V sn( ωt 120 ) (2) CO C ' O 3 2V sn( ω t ) From the equaton (2) the output oltage of Hexagram nerter are three tmes of the VSI modules. 3.2 Current Relatonshp Assume that the Hexagram nerter s connected to a symmetrcal three-phase load. Accordng to (2), the three-phase output currents can be expressed as sn( ) A a1 A' a 4 2I ωt B b3 B' b6 2I sn( ωt 120 ) C c5 C ' c2 2I sn( ω t ) The phase currents of the sx VSI modules satsfy the followng equaton: a 1 b 1 c 1 a 2 b 2 c 2 a 3 b 3 c 3 a 4 b 4 c 4 a 5 b 5 c 5 a 6 b 6 c 6 0 (4) Any two of the sx modules are nterconnected so that the currents nsde the nerter hae the followng relatonshp: (3) b1 b 2 a 2 a3 c3 c 4 b 4 b 5 a5 a 6 c 6 c1 Wth the nductors, the crculatng current n the loop formed by the connecton of the sx modules s lmted to a low alue and can be neglected as (6) b 1 a 2 c 3 b 4 a 5 c 6 0 Combnng (3) (6), ges the result that module 1, 3, 5 hae the same phase currents as A, B, C, and module 2, 4, 6 hae the same phase currents as A, - B, - C. The result s expressed n equaton (7) and (8). s n ( ) a 1 a 3 a 5 2 I ω t 2 I s n ( ω t ) 2 s n ( ω ) s n ( ) a 2 a 4 a 6 2 I ω t b 2 b 4 b 6 2 I s n ( ω t ) c 2 c 4 c 6 2 I s n ( ω t 6 0 ) b 1 b 3 b 5 c1 c 3 c 5 I t (7) (8) (5) 16 P a g e

4 Control Theory and Informatcs ISSN (prnt) ISSN (onlne) Ths result ndcates that when the Hexagram nerter s connected to a symmetrcal load, the phase currents of all sx modules are dentcal. The current phasor dagram s depcted n Fgure 4. Where the currents laggng the correspondng oltages by θ degree. The phase angle θ s dependent on the load characterstcs.the nstantaneous power of the sx modules s dered from (2) and (8) as p ( t ) p ( t ) p ( t ) p ( t ) p ( t ) p ( t ) 3V I co s θ (9) I II III IV V V I Ths result ndcates that the sx modules hae equal output power, and the nstantaneous power through each module s constant, so that the dc energy storage requrement s low and the dc capactor can be szed small. 4. Equalent Crcut of the Hexagram Inerter The equalent crcut of the crculatng current loop s depcted n Fgure 5.where L 12, L 23, L 34, L 45, L 56 and L 61 are the nductances of the nductors between any two of the sx modules; V b1c1, V a2b2, V c3a3, V b4c4, V a5b5 and V c6a6 are the nstantaneous oltages dependng upon the swtchng of the nerter, and L12, L23, L34, L45, L56 and L61 are the nductor currents dered under the zero crculatng current condton and satsfy the followng equaton: L12 b1 b3 L23 a2 a4 L34 c3 c5 L45 b 4 b 6 L56 a5 a1 L61 c6 c2 The loop oltage defned as the summaton of the equalent oltage sources n the crculatng current loop s calculated as gen n equaton (11) dl 12 dl 23 dl 34 dl 45 dl 56 dl 61 loop b 1c2 + a2 b2 + c 3a3 + b 4c4 + a5 b5 + c 6a6 + L12 + L23 + L34 + L45 + L56 + L (11) 61 dt dt dt dt dt dt The crculatng current wll occur when the loop oltage s not zero. Moreoer, the nductor currents can be ewed as the summaton of the currents dered at the zero crculatng current condton as gen n equaton (10) and the crculatng current s ' L 1 2 L 1 2 ' L 2 3 L 2 3 ' L 3 4 L ' L 4 5 L 4 5 ' L 5 6 L 5 6 ' L 6 1 L 6 1 lo o p In equaton (11), (V b1c1 +V a2b2 +V c3a3 +V b4c4 +V a5b5 +V c6a6 ) s the major part, snce the rest of the part equals 0 at the equal nductance condton accordng to (9) and (11); een f not, t s small due to the small nductances. In the deal stuatons (V b1c1 +V a2b2 +V c3a3 +V b4c4 +V a5b5 +V c6a6 ) equals 0 as well. Howeer, both unmatched swtchng and unequal dc buses wll cause t to be nonzero and result n the occurrence of the crculatng current. The unmatched swtchng has ery short tme duraton; small nductances such as seeral mcro henrys are suffcent to lmt the crculatng current. Consequently, the unequal dc bus s the major cause of the crculatng current. By hang the frst and fourth secondary wndngs of the transformer of the same phase angle, so are the thrd and sxth, and ffth and second; the unequal dc bus condton caused by the rpple oltages of the rectfcaton wll be entrely elmnated. (10) (12) 5. Closed Loop Control of Hexagram Inerter The ector control of ac dres has been wdely used n hgh performance control system. Indrect feld orented control (IFOC) s one of the most effecte ector control of nducton motor due to the smplcty of desgnng and constructon. In order to obtan the hgh performance of torque and speed of an IM dre, the rotor flux and 17 P a g e

5 Control Theory and Informatcs ISSN (prnt) ISSN (onlne) torque generatng current components of stator current must be decoupled sutably respecte to the rotor flux ector lke separately excted dc motor. Fgure 6 shows the complete schematc of ndrect feld orented control for nducton motor dre. The torque command s generated as a functon of the speed error sgnal, generally processed through a PI controller. The torque and flux command are processed n the calculaton block. The three phase reference current generated from the functonal block s compared wth the actual current n the hysteress band current controller and the controller takes the necessary acton to produce PWM pulses. The PWM pulses are used to trgger the oltage source nerter to dre the Inducton motor. The Performance of the ndrect ector controlled dre has been analyzed for aryng speed and torque. A PI controller s desgned to adjust the modulaton ndex of the Hexagram nerter. From the smulaton results t s found that the controller tracks the reference speed s better at hgh speed range. In the low speed range the speed error ncreases consderably and the PI controller needs further tunng to achee better performance. Ths can be done usng Artfcal ntellgence technques. 6. Comparson of Hexagram Inerter wth CHB Inerter A comparson of the Hexagram nerter and the CHB nerter s gen n Table 1 due to ther smlarty n modular structure and solated dc buses. From Table 1, followng conclusons are obtaned: Cascaded H-brdge nerter requres more components than Hexagram nerter: sx more transformer secondary solated wndngs; sx more dode rectfers, twele more semconductor swtches, sx more capactors. Although Hexagram nerter needs sx nner nductors to block the crculatng current, the nductors are ery small wth all modules synchronze controlled. The capacte energy storage requrement s low n the Hexagram nerter, snce the nstantaneous power through each power module s constant, whle the cascaded H-brdge nerter has low-frequency pulsatng power caused by the sngle-phase nature. Wth fewer components and lower component requrement, Hexagram nerter has less manufacturng cost and hgher relablty, whch makes t a compette topology for medum oltage arable speed dre applcatons. 7. Smulaton Results The three phase nducton motor dre wth Hexagram nerter s smulated n Matlab/Smulnk enronment wth the parameters gen n Appendx. The swtchng frequency for SPWM pulses s 1KHz, and the nner nductors are 50µH each. Fgure 7 shows smulaton results at rated condton for a modulaton ndex of 0.8. Fgure 7 (a) shows the 18 pulse transformer output wth a phase shft of 0º, ± 20º at the three secondares. The other three secondares wll hae the same phase shfts to achee harmonc current cancellaton n the utlty lne currents, leadng to clean nput power. Fgure 7 (b) shows the rectfer output and the oltage and current of Hexagram nerter respectely. The steady state results showng the output oltage of the nerter and speed of the nducton motor for dfferent modulaton ndces s shown n Table 2. A closed loop response of Hexagram nerter wth ndrect feld orented control s analyzed for dfferent operatng condtons and the results are presented n Fgure 8. The speed reference s set at dfferent alues and the actual speed, torque, oltage and stator current are obsered and presented n Fgure 8. The load torque s set at dfferent alues and the speed, torque, oltage and stator current aratons are shown n Fgure 9. It s seen that the ndrect feld orented controller tracks the reference speed s less than 1 sec wthout exceedng the desgn lmts. The performance of the dre under low speed/less load operatng condtons are studed through smulaton and presented n Fgure 10. The closed loop control of Hexagram dre has better performance n the low range of speed and torque condtons. 8. Fault tolerant feature of the Hexagram nerter The a 2 to a 3 leg of the nerter s opened and the output oltages and the current waeforms of the Hexagram nerter are obsered. It s seen from Fgure (11) that the nerter output s reduced to V and amps respectely at rated condton when the nner leg a 2 to a 3 opened. Therefore, the oerall nerter s capable of operatng at a reduced power leel. 9. Concluson 18 P a g e

6 Control Theory and Informatcs ISSN (prnt) ISSN (onlne) The performance nestgaton of Hexagram nerter for a three phase nducton motor dre s carred out for medum oltage hgh power applcatons. The smulaton model of the Hexagram nerter s deeloped n Matlab/Smulnk enronment. The performance of the Hexagram nerter s analyzed nto SPWM technque. The Hexagram nerter has reduced component count and requrement, bult-n fault tolerance, and full utlzaton of the three-phase structure, whch makes t a superor topology for hgh power applcatons. A closed loop ndrect feld orented controller s desgned and ts performance s studed for dfferent speed and torque condtons. It s seen that the controller tracks the reference speed s better at hgh speed range. In the low speed range the speed error ncreases consderably and the PI controller needs further tunng to achee better performance. Ths can be done usng artfcal ntellgence technques. PARAMETERS APPENDIX Parameters of the three phase nducton motor VALUES Power 7.5KW(10hp) Voltage 400V Frequency 50 Hz No. of poles 4 Stator resstance (Rs) ohm Rotor resstance (Rr) ohm Stator nductance (Ls) H Rotor nductance (Lr) H Mutual nductance H (Lm) Inerta (J) kg.m^2 Frcton (F) N.m.s References Jose Rodrguez, Jh-Sheng La & Fangzheng Peng (2002), "Multleel nerters: a surey of topologes, controls, and applcatons," IEEE Transactons on Industral Electroncs, ol. 49, No. 4. Chong. K.H. J & Klug R. D. (2004), Hgh power medum oltage dres, n Proc. Power Con, Sngapore, No , pp Bernet.S. (2000), Recent deelopments of hgh power conerters for ndustry and tracton applcatons, IEEE Trans. Power Electron., ol. 15, no. 6, pp Krug.D, Malnowsk.M & Bernet.S. (2004), Desgn and comparson of medum oltage mult-leel conerters for ndustry applcatons, n Conf. Rec. IEEE IAS Annu. Meetng, ol. 2, pp Cheng.Y, Qan.C, Crow M. L, Pekarek.S & Atctty.S. (2006), A comparson of dode- clamped and cascaded multleel conerters for a STATCOM wth energy storage, IEEE Trans. Ind. Electron., ol. 53, no. 5, pp Carrasco. J. M, Franquelo. L. G, Balasewcz.J.T, Galan.E, PortlloGusado. R. C, Prats., M. A. M, Leon. J. I & Moreno-Alfonso.N. (2006), Power-electronc systems for the grd ntegraton of renewable energy sources: A surey, IEEE Trans. Ind. Electron., ol. 53, no. 4, pp Suh, Snha.G, Manjrekar.M.D & Lpo.T.A. (1998), Multleel power conerson An oerew of topologes and modulaton strateges, n Proc. OPTIM, May 14 15, ol. 2, pp. AD-11 AD-24. Wu. B. (2005) Hgh-power conerters and AC dres, n Proc. IEEE PESC, Recfe, Brazl, Jun Bendre, G. Venkataramanan, Rosene.D & Srnasan.V. (2006), Modelng and desgn of a neutral-pont oltage regulator for a three-leel dode clamped nerter usng multple-carrer modulaton, IEEE Trans. Ind. Electron., ol. 53, no. 3, pp Yacoub.L, Haddad.K, Dessant. L. A & Fnaech.F. (2006), Lnear and nonlnear control technques for a threephase three-leel NPC boost rectfer, IEEE Trans. Ind. Electron., ol. 53, no. 6, pp Vargas.R, Cortes.P, Ammann.U, Rodrguez.J & Pontt J. (2007), Predcte control of a three-phase neutralpont-clamped nerter, IEEE Trans. Ind. Electron., ol. 47, no. 2, pp P a g e

7 Control Theory and Informatcs ISSN (prnt) ISSN (onlne) Km.I. D, Nho.E.C, Km.H. G & Ko.J.S. (2004), A generalzed undeland snubber for flyng capactor multleel nerter and conerter, IEEE Trans. Ind. Electron., ol. 51, no. 6, pp Du.Z,Tolbert.L.M,Chasson.J.N, Ozpnec.B, Hu.L & Huang.A.Q.(2006), Hybrd cascaded H-brdges multleel motor dre control for electrc ehcles, n Proc. IEEE Power Electron. Hanna.R.A & Prabhu.S.(1997), Medum-oltage adjustable-speed dres users and manufacturers experences, IEEE Trans. Ind. Appl., ol. 33, no. 6, pp Rech.C&Pnhero.J.R.(2007), Hybrd multleel conerters: Unfed analyss and desgn consderatons, IEEE Trans. Ind. Electron., ol.54, no. 2, pp Robcon Perfect Harmony Medum Voltage AC Dres. [Onlne]. Aalable: Cengelc.E, Sulstjo.S.U, Woo.B.O, Enjet.P, Teoderescu.R, & Blaabjerg.F(1999), A new medum-oltage PWM nerter topology for adjustable-speed dres, IEEE Trans. Ind. Appl., ol. 35, no. 3, pp Wen.J & Smedley.K, New conerters for hgh power applcatons. U.S and Internatonal patents pendng. Wen.J & Smedley.K(2008), A new multleel nerter Hexagram nerter for medum- oltage adjustable speed dre systems. Part II. Three-phase motor dre, Proc. IEEE PESC, Orlando, FL, Jun , pp Wen.J & Smedley.K (2007), A new multleel nerter Hexagram nerter for medum - oltage adjustable speed dres systems. Part I. Sx-phase motor dre, n Proc. POWERENG, Setubal, Portugal. Wen.J & Smedley.K(2008), Hexagram Inerter for Medum-Voltage Sx-Phase Varable dres IEEE Trans. Ind. Electron., ol. 55, no. 6, pp Wen.J & Smedley.K(2008), Hexagram rectfer-acte front end for medum oltage adjustable speed dre systems, n Proc. IEEE Transmss.Dstrb. Conf. Expo., Chcago, IL. Fgure 1. Hexagram nerter. 20 P a g e

8 Control Theory and Informatcs ISSN (prnt) ISSN (onlne) Fgure 2. Hexagram nerter for a three phase nducton motor dre. Fgure 3. Voltage phasor dagram of the Hexagram nerter. (a) Phase Voltages of VSI modules. (b) Output Voltages of the Hexagram nerter. Fgure 4. Current phasor dagram. Fgure 5. Equalent crcut of the crculatng current. Fgure 6. Closed loop control of hexagram nerter dre. 21 P a g e

9 Control Theory and Informatcs ISSN (prnt) ISSN (onlne) Fgure 7. Smulaton results of Hexagram nerter. Fgure 8. Dynamc response of Hexagram nerter dre for aryng speed. Fgure 9. Dynamc response of Hexagram nerter dre for aryng torque. 22 P a g e

10 Control Theory and Informatcs ISSN (prnt) ISSN (onlne) Fgure 10. Dynamc response of Hexagram nerter dre for low speed /less torque. Fgure 11. Fault tolerant feature of the Hexagram Inerter. 23 P a g e

11 Control Theory and Informatcs ISSN (prnt) ISSN (onlne) Table 1. Comparson of Hexagram nerter wth cascaded H-brdge nerter. Comparson condton Multleel Inerter Hexagram Inerter No. of secondary wndngs 12 6 No. of Dode brdge rectfers 12 6 No. of Power swtches No. of Inductors 0 6 No. of capactors 12 6 araton of the Hexagram nerter for dfferent Modulaton ndces. Dfferent load condtons MI-0.6 MI-0.8 MI-1 Tabl e 2. Volt age V L N r V L N r V L N r No load % load % load % load % load P a g e

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