Design of Vrile Rector for Lo Blncing n Hrmonics Elimintion H Dlvn, S W Su n Q P H Fculty of Engineering, University of echnology, Syney Browy, NSW 7, Austrli Emil: {hlvn, stevensu, qungh}@engutseuu Abstrct-his pper presents the esign of vrile inuctor with rottionl mgnetic core whose position is controlle in close-loop system his mgnetic structure fcilittes the impence chnges which my be use for lo blncing, hrmonics elimintion, trnsient response improvement, n s controlle rector in sttic VAr compenstion (SVC) he esign of the inuctor n nlysis of its impence chnge cuse by positioning movle element re crrie out by using the finite element metho As result, the vrition rnge of the impence is etermine he propose vrile inuctor is compre with typicl SVC rector he results show goo performnces in sttic vr compenstion with higher reliility n no hrmonics generte For close-loop control, seconorer sliing moe controller is esigne for position control of the rotting core vi DC motor Simultion results of the propose system present highly robust n ccurte responses without control chttering in fce of nonlinerities n isturbnces I INRODUCION he inuctnce of vrile rector cn be me justle by isplcement of one of its mgnetic prts Severl moels n structures my be opte for vrying the rector inuctnce, such s horizontl n verticl reloctle elements It shoul be note tht isplcement ssocite with verticl n horizontl movements of the core couple to n ctutor tens to be more complicte n slower thn with rottionl movement In this work, rotry isplcement is suggeste for vrile rector so tht its impence chnges with the sme pce s tht of hrmonics, lo, voltge n current unblncing Fig shows the propose structure for such vrile inuctor he current enters from conuctors,, n 5 n leves respectively from conuctor, 4, n 6 [-] - - - - - - - - Fig he propose structure for vrile rector Fig he propose structure for lo blncing in elt n str Power System Pssive Filter Nonliner Lo II Fig Series pssive filter system (SFS) Power System Pssive Filters Fig 4 Prllel pssive filter system (PFS) Nonliner Lo VARIABLE INDUCOR APPLICAIONS A Blncing the hree Phse Lo he propose structure shown in Fig cn be use for lo blncing For connection the propose filter to the lo, two possible implementtions re possible, s presente in the Figures n 4, where the elt connection of the cpcitors in the pssive filter results in three times lower cpcitnces thn for the str connection, consiering the sme inuctors n tuning frequency Notly, lthough the voltge pplie is higher thn in the str connection, this cn be consiere s prtil vntge becuse the cpcitors cn hnle more 8 Austrlsin Universities Power Engineering Conference (AUPEC'8) Pper P-4 Pge
rective power for improvement of the power fctor t the funmentl frequency If the compensting system is elt-connecte, the mgnitue of susceptnce in ech leg in str connection cn be obtine by pplying the elt-str trnsform s: γ B V bc Bγ V c Bγ V ( v ( v ( v i bc ( i c b( i c( + v i c b( + v i c( + v i bc ( v i c( v i bc ( v i c b( ) ) ) With the elt-str trnsform, the propose structure is converte to the str equivlence illustrte in Fig In this system, the reltionship between the cpcitors of the two structures is given by: CbcCc + CcC + CCbc C Cbc CbcCc + CcC + CCbc Cb () Cc CbcCc + CcC + CCbc Cc C Finlly the impence of ech leg is obtine by using the clculte susceptnce of elt legs s: Bbc Z X L X C BbcBc + BcB + BBbc Bc Z b X Lb X () Cb BbcBc + BcB + BBbc B Z c X Lc X Cc B B + B B + B B bc c c bc () expensive ue to the use of high rting switches he qulity fctor n resonnce frequency of the filter re given by X L ω Q (4), fr R X π L X C whose vlues cn be chnge by justing the system inuctnce By consiering trget function, eg current totl hrmonic istortion (HD), it is possible to chnge the inuctnce so tht it opertes optimlly [5] For the propose mgnetic structure shown in Fig for thickness of cm, the potentil n electromgnetic poles in n 9 rottion respectively cn be illustrte in Fig 5 by using the finite element metho (FEM) with the Vector Fiel softwre he flux n flux ensity istributions obtine from FEM re epicte in Fig 6 By connecting 8V power supply to the inuctor, the FEM simultion is crrie out with the use of Vector Fiel From the flowing current obtine with respect to ifferent core ngles, the resistnce remins unchnge t 4 but the structure inuctnce vlues vry corresponingly n re recore in le I heore, the propose inuctor hs n inuctnce vrying between n 9 mh his inuctor cn be use in mny pplictions which will be iscusse lter So by mesuring the phse voltge n current, the mgnitues of the propose system impences nee to be juste in orer to blnce the three-phse lo n to compenste for the rective power Further etils for this re reporte in [4] B Self-uning Hrmonic Filter Becuse of the lo vritions, voltge n current hrmonics re vrile, so single tune filters cnnot eliminte the hrmonics completely, theore these filters o not lwys operte with mximum efficiency t time he resonnce frequency of single tune filters lso chnges ue to voltge vrition n geing So they loose their initil performnce in sorbing the hrmonics Inee, the generte rective power of the cpcitors n in turn their impence is reuce by geing Moreover, series inuctnce of trnsformers chnges by voltge vritions s well Due to these effects, the resonnce frequency of the filter my chnge he isvntges of pssive filters cn be overcome by utilising vrile inuctor which cn chnge the resonnce frequency to chieve the best performnce Moreover, they re perre to ctive filters becuse ctive filters cuse hrmonics resulting from switching opertions, n they re Fig 5 he generte potentil n electromgnetic poles respectively in n 9 rottion 8 Austrlsin Universities Power Engineering Conference (AUPEC'8) Pper P-4 Pge
ABLE I INDUCANCE OF PROPOSED INDUCOR VERSUS CORE ROAION Core rottion (egree) 6 9 Inuctnce (mh) 9 96 67 99 he vrile inuctnce of the structure is function of the current, i(t), n the core rotry position, (t), so the co-energy store in the structure is: W (, )( ( )) m L i θ i t (5) By ifferentiting (5), the electromgnetic torque is clculte s δwm L( i, ) m i (5b) δθ θθ - - - - - - - - - - - - - - - - (c) - - - - - - - - - - - - - - - - () III COMPARISON OF HE PROPOSED INDUCOR WIH SAIC VAR COMPENSAOR he propose system is compre with sttic vr compenstor (SVC) he SVC is simulte by PSPICE softwre in which thyristor controlle rectors (CR) re moelle by thyristor switches In orer to mintin similrity with the propose system, the inuctor cpcity use in the CR is set equl to 9 mh with the sme supply voltge of 8V he SVC is simulte for ifferent firing ngles A Hrmonics Genertion he SVC genertes hrmonics becuse of switching elements in the CR From the current hrmonics shown in Fig 7, the 5 th hrmonic component cn rech 5 percent of the current in firing ngle Severl investigtions hve been one on hrmonics reuction in SVCs For exmple, using -pulse compenstor is one of the solutions but ue to high cost, it is not prcticl Current (%) 6 5 4 - - - - - - - - - (e) - - - - - - - (f) 4 6 8 4 6 8 Angle( ) Current (%) 5 - - 5 - - - - - - - - - - - - - - (g) (h) Fig 6 he generte flux n flux ensity respectively in (-b), (c-), (e-f) 6 n (g-h) 9 rottion 5 4 6 8 4 6 Angle( ) Fig 7 he current hrmonics of the SVC t firing ngle: 5 th n 7 th 8 8 Austrlsin Universities Power Engineering Conference (AUPEC'8) Pper P-4 Pge
Current (A) 5 5 5 5 - -5 95 5 5 5 5 ime(ms) Fig8 he phse current, inuctor current n their hrmonics of simulte compenstor in firing ngles 5 to 5 Current (A) 5 - -5 6 7 8 9 4 ime(ms) Current (A) Fig 9 he trnsient conition for firing ngle trnsmitting from 5 to 45 5 - -5 6 8 4 6 ime(ms) Fig he trnsient conition for firing ngle trnsmitting from 5 to 5, n 45 he common solution is to use filters with the SVC to reuce hrmonics It shoul be note tht if the SVC oes not generte hrmonics, it is possible to sorb more hrmonics from the power system In other wors, since the current flowing through the filter reches certin vlue, by sorbing the compenstor hrmonics, some of its cpcity to sorb the power system s rective n hrmonics currents is reuce In [6], comprehensive nlysis of the compenstor hrmonics is presente Here, for more thorough interprettion, the compenstor moel hs been simulte by using the PSPICE softwre Figure 8 shows the results of simulte compenstor in firing ngles from 5 to 5 his simultion contins the phse current, inuctor current n their hrmonics It is cler tht the mount of hrmonics increses by incresing firing ngle However, there re the r hrmonic in the SVC inuctor current which oes not pper in the phse current becuse of system symmetry n its elt structure B hree Phse Lo Blncing Both the propose system n SVC cn blnce the lo while the former moel oes not prouce hrmonics s it oes not utilise ctive elements However, it shoul be note tht in ition to hrmonics iscusse before, SVC oes generte the r hrmonics s well [7, 4] C Response ime It is known tht SVC cn perform sttic VAr compenstion within hlf cycle, inepenent of the blnce n unblnce lo Accoring to the simultion results shown in Fig 9, by chnging the firing ngle from 5 to 45, the output current chnges quickly within hlf cycle In this simultion, the firing ngle is 5 uring the first 5 cycles n it is chnge to 45 in the secon 5 cycles Moreover, the output current of compenstor becomes unblnce rpily within the hlf cycle by chnging the firing ngle from 5 to 5, n 45, shown in Fig In this simultion, the firing ngle is 5 uring the first 5 cycles n it chnges to 5, n then 45 uring the secon 5 cycles It shoul be note tht becuse the SVC is usully connecte to the power system with seprte trnsformer or it is instlle in the tertiry of power trnsformer, the compenstor currents trnsmission to the trnsformer seconry sie is elye becuse of its impence [8] Usully this ely increses the compenstion time to 5 cycles Our propose system my hve higher time constnt becuse of the mechnicl time constnt But for most types of los, lo vrition time is more thn secons heore the propose system cn be useful for compenstion for sttic VAr D he Nee for Peripherl Equipment n Comptibility to Different Voltge Levels Using power thyristors with high rtings for low voltge pplictions is not economicl Due to this fct, in prctice, SVCs re utilize in voltge levels ove kv he propose compenstor, not contining thyristors, is suggeste to be use in ifferent voltge levels without ny limittion or itionl peripherl evices, provie tht some sufficient insultion is mintine [8] E Equipment Cost SVCs re costly ue to the use of high power thyristors in their structure, protection n cooling system, n firing ngle control equipment he propose compenstor, not using soli stte switches n not requiring other mintennce consiertions n equipment, shll be implemente with much less cost compre to n SVC F Energy Sving SVC increses the current losses becuse of the hrmonics generte Furthermore, the switching losses which mount to % of the totl power re lso consierle he SVC cn perform effective compenstion in high voltge levels, theore imblnce n genertion hrmonics shoul be compenste for in the high voltge sie inste of its generting source Consequently the SVC cuses power loss in low voltge sie n hence increses energy consumption 8 Austrlsin Universities Power Engineering Conference (AUPEC'8) Pper P-4 Pge 4
Also since SVC is connecte to the network vi power trnsformer, the generte hrmonics cuse increse ey current n conuctive losses he propose compenstor, while being le to sorb hrmonics, oes not generte ny hrmonics itself Sliing Moe Controller v(t) DC Motor Vrile Rector G Moulr Instlltion n Expnsion Hving moulr n expnle structure is merit of system In mny instnces, the cpcity of compenstion system or its chrcteristics shoul be increse ue to chnges tht occur in the lo An SVC oes not hve the moulr expnsion cpility since ll the ctive evices n the connecting trnsformer re esigne for the nominl vlues n prlleling two SVCs requires mny criticl consiertions which my mke it hrly prcticl for mny pplictions In contrst, the propose system cn possess moulr n expnle structure n the user cn esily pt the system by ing other moules IV SYSEM DESCRIPION AND DYNAMIC EQUAION A block igrm of the position control system for closeloop control of the movle core is shown in Fig In this figure, erence position, obtine from the require vlue for the rector inuctnce, is compre with the ctul ngle, mesure from n solute encoer he position error is the inputs to the sliing moe controller block he commn voltge signl is the output of the controller he motor cn be escribe by the following stte equtions: θ ω (6) ω K i L Bω Kθ i u( t) K Eω + Ri + L, where i is the rmture current (A), is the ngulr spee (r/s), is the ngulr position (r) n L the totl mechnicl lo torque (Nm), incluing m given in (5) he control voltge u is the rmture voltge (V) Other system prmeters re liste s R for the totl rmture resistnce ( ), L for the rmture inuctnce plus the smoothing inuctnce ( H), B for the totl mechnicl mping ( Nms), for the totl moment of inerti (8 Kgm ), K ( Nm/A), K E ( volt/r sec l ) n K ( Nm/r) for motor constnts he control system to be implemente inclues power mplifier, DC motor, tchometer s the spee sensor, potentiometer s the position sensor, n cquisition unit to isply rel-time system outputs on PC monitor Choosing the system sttes s x θ, θ x ω, x i the stte spce eqution of system cn be estlishe s: Fig : Block Digrm of the DC motor with sliing moe controller ẋ x + u( t) 4 5 b + L y [ ] x [ x x x ], x K where, b, n L B, K, (7) K E, R 4, 5 L L V SLIDING MODE CONROLLER DESIGN Here the sliing moe theory is opte to yiel robust positioning performnce [9] For this, let us efine sliing function σ e+ ξωn e+ ωne e+ λ e+ λe (8) from esire vlues of nturl frequency ω n n mping λ ω n λ, ξ rtio ξ : λ or λ ω n, λ ξω n With time erivtives e e σ e+ λ + λ (9) e x x _ x x _ e x + x + x + x L _ e x+ x+ x+ L x _ σ Ax + Bx + Cx + Du + f φ where A + λ B λ + λ + 4 + C λ + 5 + D b + + ) L + L, x_ x_ f ( λ φ λ + λ + x_ the control output u(t) cn be esigne to consist of two 8 Austrlsin Universities Power Engineering Conference (AUPEC'8) Pper P-4 Pge 5
components, nmely, u Eq n equivlent control n u Sw switching control, ie u u Eq + u Sw () he equivlent control u Eq is etermine by the esire ynmics of the system in the sliing moe n the switching control u Sw is to compenste for uncertinties n isturbnces such tht the system stte is riven towrs the sliing surfce (reching phse) o obtin the eqution for equivlent prt, the sliing vrile shoul be constnt in nominl conition which mens: σ nominl conition Ax + Bx + Cx + Du Eq φ () heore; ueq ( Ax + Bx + Cx φ ) D For the switching prt, by consiering the Lypunov function: V σ () V σ σ V σ ( Ax + Bx + Cx σ ( f + Du By ssuming f Sw ) + Du Eq + f + D( u Eq + u Sw ) φ < F t () γt < γ σ σ ε e (4) V n selecting the gin F + γ K (5) D one cn erive u Sw K σ sign(σ ) (6) he system ynmic responses for erence position trjectory signl simulte with Mtl/Simulink re shown in Fig In this simultion, pulse signl is pplie to the system in time 5 secon s isturbnce However the performnce of the controller cn be observe Moreover, ccoring to the results, the propose controller hs very smll rise time (less thn 5 secon), settling time (out 8 secon) n overshoot (out 8%) for ifferent ngles VI CONCLUSION In this pper we hve presente the esign of vrile rector whose impence chnges with the vrition of reloctle rotry element his inuctor cn be use for VAr compenstion n lo blncing In such pplictions importnt performnces by using the propose compenstor is compre with the use of SVCs A sliing moe controller is esigne for close-loop control of the movle core positioning Robustness of the control system is verifie through simultion ) ( ) 5 7 6 5 5 4 et (egree) 5 5-5 5 5 ime 5 (secon) 5 4 45 5 ime(s) Fig : Position responses of the simulte system for ngle ACKNOWLEDGMENS he first uthor grtefully cknowleges the contribution of Nhi Chlyvi his work is supporte, in prt, by US reserch grnt 6848 n the Centre of Excellence progrmme, fune by the Austrlin Reserch Council (ARC) n the New South Wles Stte Government VII REFERENCES [] H Ok, n PP Biringer, "Control chrcteristic nlysis of ferrite orthogonl core," IEEE rns Mgnetics, vol 6, pp 888-89, 99 [] H Ok, FP Dwson, Skut, n D Lvers, "Mgnetic flui bse vrile inuctors for inuctively couple plsm pplictions," IEEE rns Mgnetics, pp 475-477, 995 [] S Rhmni, K Al-H, n HY Knn, "A comprtive stuy of shunt hybri n shunt ctive power filters for singlephse pplictions: Simultion n experimentl vliion," Mths n Computer in Simultion, vol 7, pp 45-59, 6 [4] H Dlvn, M Nguyen, N M Kwok, n Q P H, "A new hybri filter for power qulity improvement in unblnce lo conitions," Proc th Int Conf on Control, Automtion, Robotics n Vision, Hnoi Vietnm, 7-Dec 8, to pper [5] S Rhmni, K Al-H, n F Fniech, "A new PWM control technique pplie to three phse shunt hybri power filter," Proc IEEE Int Conf In Electro (IECON ), Spin, vol, pp 77-7, [6] K Wilkosz, M Sobierjski, n W Kwsnicki, "he nlysis of hrmonic genertion of SVC n SACOM by EMDC/PSCAD simultions," Proc 8th Int Conf on Hrmonic n Qulity of Power ICHQP 98, Greece, vol, pp 85-858, 998 [7] S Y Lee n C Wu, "Rective power compenstion n lo blncing for unblnce three-phse four-wire system by combine system of n SVC n series ctive filter," IEE Proc-Electr Appl, vol 47, no 6, pp 56-57, [8] D Hnson, C Horwill, BD Gemmell, n DR Monkhouse, "A SACOM-Bse Reloctle SVC Project in the UK for Ntionl Gri," Proc IEEE Power Engineering Society Winter Meeting, NewYork, USA,, pp 5-57 [9] A Snovic, L Frimn, n S Spurgeon, Vrile Structure Systems: from Principles to Implementtion series 66, IEE: Lonon, UK, 4 8 Austrlsin Universities Power Engineering Conference (AUPEC'8) Pper P-4 Pge 6