A Comparative Study of Control Strategies for Performance ...

Milutin G. JovanovićUniversity of Northumbria atNewcastle. School of Computing,Engineering and InformationSciences. Newcastle upon TyneNE1 8ST, UKFax: +44-191-2273598;milutin.jovanovic@unn.ac.ukJ. Electrical Systems 2-4 (2006): 208-225Regular paperA Comparative Study of ControlStrategies for PerformanceOptimisation of Brushless Doubly-Fed Reluctance MachinesJESJournal ofElectricalSystemsThe brushless doubly-fed machine (BDFM) allows the use of a partially rated inverter andrepresents an attractive cost-effective candidate for variable speed applications with limitedspeed ranges. In its induction machine form (BDFIM), the BDFM has significant rotor lossesand poor efficiency due to the cage rotor design which makes the machine dynamic modelsheavily parameter dependent and the resulting controller configuration complicated and difficultto implement. A reluctance version of the BDFM, the brushless doubly-fed reluctance machine(BDFRM), ideally has no rotor losses, and therefore offers the prospect for higher efficiencyand simpler control compared to the BDFIM. A detailed study of this interesting and emergingmachine is very important to gain a thorough understanding of its unusual operation, controlaspects and compromises between optimal performance and the size of the inverter and themachine. This paper will attempt to address these issues specifically concentrating ondeveloping conditions for various control properties of the machine such as maximum powerfactor, maximum torque per inverter ampere and minimum copper losses, as well as analysingthe associated trade-offs.Keywords: Double Fed Induction Generator, Variable Speed, Isolated Site Voltage Supplying, StatorVoltage Constant Key-Parameters, Scalar Control, Modeling.1. INTRODUCTIONWith the advent of power electronics and microprocessor technology, it has becomepossible to better control and utilise Brushless Doubly-Fed Machines (BDFMs) to the pointwhere they have started to be considered as a potential alternative to the existing drivesolutions in a variety of low to medium performance industrial applications. The two mainreasons have largely contributed to this growing interest in the machines: (1) their slippower recovery operating nature allowing the deployment of a partially-rated converter,and (2) the absence of brush gear and consequent reliable, virtually maintenance-freeoperation.The fact that the feeding converter only has to handle the slip power implies significantcost savings (up to 30%) compared to systems with fully rated inverters [1]. This isparticularly true in larger drives with limited variable speed capability (e.g. pumps [2, 3],wind turbines [3-5], heating, ventilation and air-conditioning etc.) where, despite the fallingmarket prices, the power electronic hardware still represents a major portion of the totalcost. A cost penalty would incurred for the machine but this would be more than offset bythe reduction in the converter cost (for a typical speed range of 2:1, its real power rating canbe limited to about 25% of the machine's [3, 6, 7]). Other benefits of using the smallerinverter include the improved supply quality and the lower filtering requirements, as lessharmonics are injected into the grid.The reliability of brushless design and low maintenance make the BDFMs preferable toa conventional Doubly Excited Wound Rotor Induction Machine (DEWRIM), for example,in off-shore wind power applications where these two features become crucially importantdue to the cost implications [8].Copyright © JES 2006 on-line : journal.esrgroups.org/jes

S. Drid et al: Doubly Fed Induction Generator Modeling and Scalar Controlled for Supplying...The above equations can be significantly simplified (especially the primary ones) bychoosing the generic reference frame dpq pto be aligned with the primary flux vector ( lp).This is a natural choice as the grid-connected (primary) winding is of fixed line frequencyand approximately constant flux magnitude (as Rpip

J. Electrical Systems 2-4 (2006): 208-225where z = Lp/ Lps(see Appendix inductances). Therefore, in order to minimise isdandhence maximise torque per inverter ampere under MCL conditions one needs to increaseRs/ Rpratio which, given (20) of Appendix 3 resistances, translates to: ns ³ np, As £ Apand p < q . It should be noted that the observation about the windings turns per polerelationship for improved torque per ampere performance ( n / n ³ 1) is consistent withthat made earlier.- Another important comment about the MCL control strategy is that, unlike all the othersconsidered previously, it is the only one affected by the windings pole-numbers. Thisdependence is introduced via the stator resistances (see (12) and (15)) and it means that itdoes matter which winding is a power winding and which one has a control function. Issuesrelated to this are the subject of the subsequent sections.sp3. CONTROL PROPERTIES AND TRADE-OFFSThe following analysis shall assume that the BDFRM windings have the same number ofeffective turns per pole ( ns= np) i.e. Lp = Lsand the same gauge copper wire i.e. thesame cross section ( A = A ). It will be based on the machine's normalised expressions inspTable 1 of Appendix 2 normalisations. A 6/2-pole machine with a 4-pole rotor shall beconsidered assuming k = 1/ z = 7 / 9 (equivalent to a typical Syncrel rotor saliency ratioof 8 [6]).3.1 Constant torque operationpsFig. 3 demonstrates the machine's ability to control primary (and secondary) power factorfrom leading to lagging via the secondary current angle. Notice that for a < a ( » 26ounder the conditions assumed) both power factors decrease towards zero as the primarywinding is generating large amounts of reactive power into the grid, this being taken by thesecondary winding from the inverter. It can be seen in Fig. 4 that in order to maintain theconstant flux operation of the machine in this region the a angle increases to counteractthe flux increasing effect of decreasingasangles. Ifaps s uppfssuppf> a , then the primary powerfactor again deteriorates but with the primary now absorbing reactive power from the mainssupply to flux the machine. The secondary power factor consequently improves reaching itsmaximum at a » 110o when the primary winding becomes fully responsible for the fluxs uspfproduction and theapvalues are small as shown in Fig. 4.The impact of secondary current angle variations and winding pole-numbers on themachine's copper losses can be understood from Fig. 5. It can be seen that for the p > qpole-pair combination (dashed curve) the MCL current angle is smaller than in p < q case(solid line) indicating a higher d -axis secondary current ( isdn) and inverter currentloading in the first case. This means that the torque per ampere is better under p < qcondition which conforms with the remark made earlier. At lower asangles both curvesshow a sharp increase of losses due to dominant secondary currents. The losses, asexpected, are higher when p < q since Rs > Rpand ip

S. Drid et al: Doubly Fed Induction Generator Modeling and Scalar Controlled for Supplying...10.8capacitive= 0 Q pinductiveinductive= 0 Q scapacitivePower Factor0.60.40.2SecondaryPrimary00 20 40 60 80 100 120 140Secondary current angle[degs]Fig. 3. Winding power factors for T n = 1 .180160Primary current angle [degs]1401201008060402000 20 40 60 80 100 120 140Secondary current angle [degs]Fig. 4. Current angle relationship at T n = 12.62.42.2P cu/ P cu-min: p=1,q=3P cu/ P cu-min: p=3,q=1P cu(p=1,q=3) / P cu(p=3,q=1)Copper loss ratio21.81.61.41.210.820 30 40 50 60 70 80 90Secondary current angle [degs]Fig. 5. Effects of winding pole-number combinations on copper losses at 1-pu torque3.2 Optimal control aspects at various torque levelsThe plots of (13), (14) and (15), for maximum power factor and minimum copper lossstrategies implemented in a torque controller, are presented in Fig. 6. The fact that theUSPF secondary current has a demagnetising effect (as a > p /2 i.e. i < 0 ) meansthat a significant extra d -axis current is needed in the primary to preserve constant flux inthe machine. As a result, the USPF pni is about 2.5 its UPPF value (Fig. 7) at 1-pu torque,the ratio being even higher at lower torques when most of the USPF current is fluxs uspfsd uspf216

J. Electrical Systems 2-4 (2006): 208-225producing (note the virtually flat curve in this torque range) and the UPPF current (acoupled isqnas a = p /2 and ipdn= 0 ) is small. Note from Fig. 6 that the UPPFp uppfangles are the smallest of all as the secondary current is then entirely responsible for themachine magnetization and its d -axis component is at its largest.140120Secondary current angle [degs]100806040UPPFUSPFMCL (p=1,q=3)MCL (p=3,q=1)2000 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6Torque [PU]Fig. 6. Optimal control angles at various torque levels1.8Primary Current [PU]1.61.41.210.80.6UPPFUSPFMTPIAMCL (p=1,q=3)MCL (p=3,q=1)0.40.200 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6Torque [PU]Fig. 7. Primary winding currents under optimal conditions1.81.61.4Secondary Current [PU]1.210.80.60.40.2UPPFUSPFMTPIAMCL (p=1,q=3)MCL (p=3,q=1)00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6Torque [PU]Fig. 8. Secondary winding currents for considered control methodologiesFrom Fig. 6 one can also notice the higher values for the minimum copper loss (MCL)angles at any torque when p < q . This indicates the lower secondary current magnitudes(at least 20%) compared to the p > q case as shown in Fig. 8. Therefore, as far as the217

S. Drid et al: Doubly Fed Induction Generator Modeling and Scalar Controlled for Supplying...torque per inverter ampere strategy is concerned, the use of a high pole winding for controlpurposes is a preferable option as a smaller inverter is then needed.10.9Power Factor0.80.70.60.50.4cosφ at cosφ =1p scosφ at cosφ =1s pcosφ at MTPIAscosφ pat MTPIA0.30.20.100 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6Torque [PU]Fig. 9. Power factors for different control strategiesAlong the line of the previous discussion, it would be interesting to see what influencepower factor control has on the inverter size required for a BDFRM drive system. If theUPPF is desired, then the values of asare low and the secondary power factor is poor(Figs. 3 and 9) indicating an inefficient use of the inverter, the current rating of whichwould have to be higher for a given torque as illustrated by the top characteristic in Fig. 8.The situation is diametrically opposite under the USPF conditions when the asangles areabove p /2 and the secondary carries less reactive current. One can see in Fig. 8 thati » 0.5iat T = 1 (and less at lower torque values) meaning that at least a halfsnuspfsnuppfnrated inverter can be used in this case. However, the primary power factor is then acompromise and its maximum value is 0.4 approximately (Fig. 9).For the reasons indicated above, similarly to the DEWRIM [19], a line-side bridge(PWM rectifier) of the bi-directional supply converter can be used for the primary reactivepower (and DC link voltage) regulation, and the machine-side bridge for control of torqueand secondary reactive power. In either case, one needs to trade off the size (rating) of onebridge with the other. It has been shown, however, that optimally designed radiallylaminatedreluctance rotors, as opposed to the axially-laminated counterparts, can offer asignificant overall performance improvement to the BDFRM (including the power factorincrease) to the extend that it can compete favorably with the DEWRIM of similar framesize [13]. Note that the performance enhancement considered in [13] has been achievedwith machine design parameters and under conditions (which are impossible to representanalytically) different to those assumed in this paper.If the machine is operated at the maximum torque per secondary ampere (MTPSA), theprimary power factor can be slightly improved (Fig. 9) relative to the USPF value and theinverter current rating further reduced (Fig. 8) but at the cost of moving away from theoptimum inverter VA i.e. USPF point (Fig. 9).The inverter current loading under MCL conditions for p < q is quite close to anoptimum, but only around unity or higher pu torques (Fig. 8). The corresponding primarypower factor is better than the MTPSA value but is still very low (less than 0.6 at 1-putorque) as illustrated in Fig. 10. As expected, the secondary power factor is compromisedrelative to the MTPSA strategy (especially at lower torques) its value being 0.7 at unitytorque as compared to approximately 0.95 under MTPSA conditions.218

J. Electrical Systems 2-4 (2006): 208-225Another important aspect of this analysis is to examine the impact of the two pole-numbercombinations of the windings on the power factor performance of the machine withminimum copper losses. From Fig. 10 it is evident that the secondary power factorincreases with torque for p < q (dashed curve), as opposed to p > q (dashed-dotted line).This results from the greater asangles and lower magnetising currents of the secondarywinding in the first case (Fig. 6). The situation is opposite for primary power factor, due tothe counteracting effect of the primary current angles required to maintain constant fluxoperation of the machine. This means that a decreases as a angles increase as shown inpFig. 4. As a consequence, for a primary power factor control strategy a multi-pole powerwinding and a 2-pole control winding is a better solution.From a viewpoint of minimum copper losses in the machine, the p < q case appears toallow lower losses in the torque range up to about 0.95-pu according to Fig. 11. At highertorque values, p > q seems to be more efficient. The differences in losses are morepronounced at very low torques (less than 10%), and hence the overall efficiency may beaffected more significantly, as it has a tendency to decrease at small output powers. At midrange and higher torques, however, these variations are minor (only a few percent), andtheir impact on the machine efficiency is virtually negligible. Therefore, with respect toefficiency, unless the machine is to be used at low powers relative to its rating, it isirrelevant which winding is grid connected and which is inverter fed.s0.90.8Power Factor at minimum copper losses0.70.60.50.40.30.20.1primary (p=1,q=3)secondary (p=1,q=3)secondary (p=3,q=1)primary (p=3,q=1)00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6Torque [PU]Fig. 10. Power factor performance with minimum copper losses1.061.04Pcu min(p=1,q=3) / Pcu min(p=3,q=1)1.0210.980.960.940.920.90 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6Torque [PU]Fig. 11. Influence of winding pole-numbers on minimum copper losses219

S. Drid et al: Doubly Fed Induction Generator Modeling and Scalar Controlled for Supplying...10.90.80.7TPSA / MTPSA0.60.50.40.30.20.1UPPFUSPFMCL (p=1,q=3)MCL (p=3,q=1)00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6Torque [PU]Fig. 12. Torque per secondary ampere at optimum power factors and minimum copper lossesThe final part of this paper is a comparative study of the control strategies in terms oftorque per secondary ampere (TPSA) performance. The plots in Fig. 12 represent the TPSAnormalised to the optimum MTPSA value (corresponding to as= p /2) . The results inthis figure fully match those in Fig. 8. After MTPSA strategy, the TPSA is the highestunder USPF conditions, and it is the lowest at UPPF, when the inverter current loading is amaximum (as follows from Fig. 8). Fig. 12 yet again confirms the previously madeconjecture of TPSA values being higher in the case of a machine with 2-pole primary and6-pole secondary windings and minimum copper losses.4. CONCLUSIONThis paper has performed a comprehensive comparative analysis of the BDFRM's controlproperties and has developed a set of useful expressions suitable for implementation ofvarious optimal control strategies for the machine. Aspects of power factor regulation andeffects of winding pole-numbers on the machine performance have been particularlyemphasised. The main conclusions/observations that can be made from the presentedresults are:• The inverter current rating would have to be increased approximately twice for unityprimary power factor (UPPF) control at the same torque output, as compared to theother strategies considered.• Under the UPPF conditions the secondary power factor is less than 0.3, indicating atleast three times greater inverter kVA requirement for a given power output of alossless machine. At the unity secondary power factor (USPF) and the minimuminverter kVA, the primary power factor is barely 0.4 .• The maximum torque per secondary ampere and the USPF operating characteristics arequite close, especially at lower torques where they virtually coincide.• All the performance parameters (except for the primary power factor), under minimumcopper losses conditions, generally improve with a two-pole power winding (gridconnected primary) and a multi-pole control winding (inverter-fed secondary). Theprimary power factor is better for the opposite situation (i.e. p > q).• The above optimum pole-pair relationship ( p < q)allows lower copper losses andhigher efficiency in the normal torque range, and particularly at smaller torque values.220

J. Electrical Systems 2-4 (2006): 208-225The paper has provided a valuable insight into the operation and optimal control of theBDFRM and can serve as a good reference for the interested readers wishing to initiateresearch in this direction. The consideration of the machine performance/inverter ratingtrade-offs is important as in the long run the success or failure of this interesting andunusual machine will be likely decided by whether the compromise between a largermachine for a given output torque, and a smaller size of the inverter, lead to a lower systemcost in the target applications.APPENDIX 1Inductance DefinitionsThe BDFRM's inductance 5 relationships listed below have been developed using themethod of winding functions [20] with the air-gap parameters as in Fig. 13. Theexpressions derived are, however, more general than those in [20] as they assume thenonzero permeance i.e. finite air-gap width along the rotor q -axis.3 2Primary: Lp =2m0nm pprl + L ülïp ïïïïSecondary: L = m nmprl + L ïïïï3 2s 2 0 s ls3Mutual: Lps =4m0nnn p sprlï ïýïLpnp2mz =L» nps s n ï ïïïm = yL d+ (1 -y)Lqï ïïïïnpwhere:lp,s=2p ( Ld -Lq)sinyïþnp, s@effective turns/pole/phase of the windingsL@ leakage inductances of the windingsr, l @ machine mean radius and axial length1/ L @ minimum air-gap widthd1/ L @ maximum air-gap widthqy @ pole-arc/pole-pitch ratio of the rotor (Fig. 13)Fig. 13. Inverse air-gap function for a 4-pole reluctance rotor used for inductance determination (θ ,some mechanical angle around the stator circumference; θrm , the mechanical angle of the rotor highpermeance axis)5 In practice, the actual inductance values can be identified from measurements by applying the off-line testingmethods presented in [14].221

S. Drid et al: Doubly Fed Induction Generator Modeling and Scalar Controlled for Supplying...Table 1 :Normalized control from expressions and base quantitiesi pnlsin assin( ap+ as)= =Primary quantities( 2tan a ) 2 s - Tn + Tn 2 tan2 as2tan a= i + i = 1üï ýÛ tan =i i 0 ï1pn pdn z sdnTntan asa1p 2tan as-Tnpqn-z sqn=ïþ1isdnTnpn=2 n;pn= 1- z= 1-2tan sP T Qacos fi snpPpn Tn tan as= =( )Ppn 2 + Qpn 2 Tn 2 + 4 tan 2 as - 4Tn tan as + Tn2z sin ap zTn 1+tan 2 assin( ap+ as) 2tan as= =sSecondary quantitiessnsn= w2 n= wsn pn= -pnP T P sPQf=éT ( - 1)(tan a + 1) + 2tan aùëûúwsnTn12sn 2 24tan a ê n s ss kpss2 2-1 Q1 (1/ 1)(tan 1) 2tansn- Tn kps - as + + asPtan2sn2tan as= tan =Torque, power output and copper losses2 2T = i = i sinn z sqn z snasP = P + P = T = w T1+wsnn pn sn 2 n rn nP cunP=2 2 2( - ) + ( + )( + )4rp tan as tan as Tn Tn rp rs z tan as124tan as2( + z ) + 4= P ( a ) =mcl24( p + sz)2 2 2rp rs Tn rr p szcunmincun s r rTorque & power :Base values23 lp 2wpTBB= 4 r Lpp B=rT p PCurrent & flux : i = l / L l = v / wB B p B B pAPPENDIX 2NormalisationsIn order to make machine performance expressions independent of its parameters a set ofnormalisations corresponding to the arbitrary chosen a = a = p / 4 condition has beendeveloped taking the grid voltage and frequency as bases (see Table 1).psAPPENDIX 3Stator resistance expressionConsider a single full-pitch turn of a generic P -pole sinusoidally distributed winding. Thetotal length and resistance of the turn are:-222

J. Electrical Systems 2-4 (2006): 208-225lRtt2pd= length in slots + end turn length = 2l+Prcult 2rcu pd2rcudp= = ( l + ) = ( b + )A A P A Pwhere:rd @ diameter from the centre of the stator slotscul @ length of the machine stack@ resistivity of conductive material (copper)A @ cross-sectional area of the wire usedb = l/ d @ machine's aspect ratioIf the winding has n effective turns per pole and phase then its total phase resistance is:-2rcudR = P× nRt= nP ( b + p)AApplying this to the BDFRM windings and assuming b » 0.5 for convenience (aNEMA180 frame), then the resistances of the 2q -pole secondary and 2p -pole primarywinding can be related as follows:-Rsn As p q + p= × ×R n A p + pp p sREFERENCES[1] Y. Liao, Design of a brushless doubly-fed induction motor for adjustable speed driveapplications, Proceedings of the IAS Annual Meeting, pp. 850–855, San Diego, California,October 1996.[2] B. Gorti, D. Zhou, R. Spée, G. Alexander, and A. Wallace, Development of a brushless doublyfedmachine for a limited speed pump drive in a waste water treatment plant, Proc. of the IEEE-IAS Annual Meeting, pp. 523–529, Denver, Colorado, October 1994.[3] M. G. Jovanovic, R. E. Betz, and J. Yu, The use of doubly fed reluctance machines for largepumps and wind turbines, IEEE Transactions on Industry Applications, vol. 38, pp. 1508–1516,Nov/Dec 2002.[4] L. Xu and Y. Tang, A novel wind-power generating system using field orientation controlleddoubly-excited brushless reluctance machine, Proc. of the IEEE IAS Annual Meeting, Houston,Texas, October 1992.[5] O. Ojo and Z. Wu, Synchronous operation of a dual-winding reluctance generator, IEEETransactions on Energy Conversion, vol. 12, pp. 357–362, December 1997.[6] R. E. Betz and M. G. Jovanovic, The brushless doubly fed reluctance machine and thesynchronous reluctance machine - a comparison, IEEE Transactions on Industry Applications,vol. 36, pp. 1103–1110, July/August 2000.[7] R. E. Betz and M. G. Jovanovic, Introduction to the space vector modelling of the brushlessdoubly-fed reluctance machine, Electric Power Components and Systems, vol. 31, pp. 729–755,August 2003.223

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