New Appoach fo Optimizing Contol of Switched Reluctance Geneato R. Rebbah, A. Bentounsi and H. Benalla Abstact This pape pesents a new switching appoach that detemines the optimal contol of the Switched Reluctance Geneato (SRG) fo accomplishing maximum enegy convesions. The poposed method is based on the novel concept of ideal base speed flux/cuent cuve that optimizes the conduction angles in the mode of single-pulse and Chopping Cuent Contol (CCC) opeations. To validate the poposed contol technique, simulation esults ae povided. The pacticality of the contolle is illustated by a vaiable speed wind application of a 6/4 SRG. Index Tems Optimal contol, conduction angles, Switched Reluctance Geneato, optimization, vaiable speed, wind powe. Fo this study, we used a thee-phase 6/4 SRG epesented in Fig.1. Thee ae no windings and no magnets in the oto; thee is only a concentic coil in each stato pole. The paametes of the studied geneato ae given in Table I. Fo detemining the electomagnetic chaacteistics of the machine connected to the convete, we solve the Poisson s equation govening the poblem by the finite elements method (FEM). The implementation was caied out unde the softwae package Flux2D [4], a use-fiendly softwae which allowed us to daw the equal flux lines fom which we plotted the magnetic flux vs. phase cuents (Fig. 2). I. INTRODUCTION In the context of sustained development, electic powe geneation using non-conventional souces is eceiving an inceasing attention. Among the altenative esouces to fossils, wind enegy occupies today a place of choice. Vaiable speed powe geneation fo a wind tubine is attactive, because maximum efficiency can be achieved at all wind velocities. In this field, the switched eluctance machines compete with the classical ones due to thei multiple advantages: simplicity and obustness of the stuctues, high pefomances and educed cost, which allows them to have vaious applications ove a lage speed ange, fo motoing and geneating modes. Howeve, the dawbacks of these machines ae in paticula voltage, cuent and toque ipples, but also the powe electonics equiements [1-2]. In ode to optimize the powe convesion, a geate attention was focused to the Switched Reluctance Geneato (SRG) contol; the tun-on and the conduction angles togethe ae the key element fo optimal excitation. The conventional contol method that advances the tun-on angle as the speed incease is not sufficient to poduce optimum pefomance [3]. This pape investigates the poblem of pefomance optimization of the SRG at vaiable speed. The poposed method is based on the optimization of conduction angle to appoach the ideal base speed flux/cuent cuve that maximizes enegy convesion in both cases of single-pulse and Chopping Cuent Contol (CCC). Manuscipt eceived Septembe 29, 2009. This wok was suppoted by the Electical Engineeing laboatoy of mentoui univesity (LEC), Constantine, Algeia. R. Rebbah is with the dept. of Electical Engineeing, LEC, Constantine, Alegia. (E-mail: edjem_ebbah@yahoo.f). Fig.1. Diagam of the studied thee phase 6/4 SRG TABLE I PARAMETERS OF THE STUDIED 6/4 SRG Quantity Stack length Oute diamete Roto diamete Shaft diamete Ai-gap length Height of stato teeth Height of oto teeth Stato yoke thickness Aligned inductance Unaligned inductance Value 150 mm 250 mm 150 mm 42 mm 0.8 mm 25.6 mm 28 mm 23.6 mm 2.2 mh 0.2 mh 365
(a) (b) Fig. 2. Magnetization cuves. II. ENERGY CONVERSION SYSTEM The electo-mechanic convesion system of enegy is constituted by SRG, powe convete, contolle, position senso and so on. The topology of its powe invete is a thee-phase asymmetic half bidge whee one phase is epesented in Fig. 3. The oto of SRG is diven by a pime move. The contolle can ceate cetain contol signals accoding to the position infomation of the oto. The contol signals can dive the switches in powe invete to implement excitation and electic powe geneation. Thee ae two contollable switches (Tl, T2) and two diodes (Dl, D2) in each phase. When both Tl and T2 ae tuned on, the winding is excited; the system absobs enegy fom the pime moto and the exciting souce. When both Tl and T2 ae tuned off, the winding eleases enegy though Dl and D2, the system povides electic enegy to the load. Fom the pevious magnetic chaacteistics (Fig. 2) plotted unde Flux2D softwae, we can deduce the inductance cuves vs. oto position at diffeent excitations. Fig. 4 shows the elationship between the idealized inductance pofile and phase cuents fo geneating at single voltage pulse and PWM voltage, above base speed at which the phase cuents ae nominally constant without need fo egulation. It also epesents the speed whee the back-emf E balances the souce voltage V and esistive dop RI [5]. D2 D1 Fig. 4. Wavefoms of (a) high-speed single voltage pulse and (b) low-speed cuent chopping contol (CCC) opeations. Duing geneation, the SRG poduces negative toque that tends to oppose otation, theeby extacting enegy fom the pime move. If the phase is excited as the oto poles move though the aligned position, the oto expeiences toque opposing otation consistent with geneato opeation. The stoed magnetic enegy ( W e ) o co-enegy ( W c ) vaies with oto position to poduce the electomagnetic toque: We ( i, ) W c( ψ, ) Te = = (1) i= const ψ = const which is poduced though magnetic anisotopy. In linea mode, the magnetic flux is: ψ = L( )i (2) Thus, 1 2 We = Wc = L( ) i (3) 2 If, moeove, we suppose that the phase inductance vaies linealy with oto position, fom its maximum (aligned position) to its minimum (unaligned position) value, fo constant cuent pulse, the toque is constant ove the active oto position ange, accoding to the following expession: 1 dl Te = i 2 ( ) = const (4) 2 d Fo moto opeation: dl( ) > 0 (4a) d Fo geneato dl( ) opeation: < 0 (4b) d It is clea that the polaity of the cuent does not influence the sign of the toque. The expession of the aveage toque pe phase is: Fig. 3. One phase of the powe convete. 366
mnwmec T av = (5) 2π The enegy pe cycle is deduced fom the aea between the aligned and unaligned flux vs. cuent cuves epesented (Fig. 5). Fig. 5. Aligned and unaligned cuves at (a) CCC and (b) single pulse mode. Fig. 6. Contolles fo egulating SRG speed. whee V is the applied voltage, I is the cuent, R is the esistance pe phase, L is the inductance pe phase, d ω = is the angula speed of the oto and E ωk dt the back EMF with the coefficient: K = i = is dl d < 0 (6) Fo simplicity, we neglect the stato esistance (R=0). The value of the voltage is: V = + Vdc duing excitation phase by T 1,2 switches V= - Vdc duing geneating phase by D 1,2 fee-wheeling diodes whee Vdc is the voltage of the DC bus. The coesponding cuent wavefoms ae idealized (Fig. 7). Fig. 8 shows the simulated chaacteistics of flux, cuent, toque and speed by using MATLAB softwae; the model selected is the 6/4 SRM block poposed by T.J.E. Mille [9]. Fig. 9, 10 and 11 show the cuent cuves coesponding espectively to thee cases of the speed n compaed to the base speed nb. - In case 1 (n > nb): afte T1 and T2 ae tuned off (when excitation phase is finished) the cuent still inceases. As V< 0 and E < 0, the cuent incease is due to the fact that is the EMF is geate than the supply voltage (magnetization). This case is typical fo high speeds, when the toque is smalle (Fig. 9). III. SPEED CONTROL OF SRG SYSTEM Fo the stategy called toque demand ecognized as having a weak dynamic esponse fo vaiable winds, thee ae seveal publications [6-16]. As an altenative to the toque contol stategy, a speed contol stategy epesented in Fig. 6 has been epoted in [6]. This stategy has moe vaiation in the output powe and also the fast vaiation of the electical toque can poduce fo example moe fatigue in the gea box and dive tain of the wind tubine. This poblem can be educed with a good design of the contolle [17]. Inductance Cuent (A) Fig. 7. Wavefoms of inductance and phase cuent. The oute loop is usually concened with egulating the speed of the SRG. An application such as wind enegy would focus on egulating the speed of the SRG elative to that of the wind steam in ode to foce peak aeodynamic efficiency [5]. IV. SIMULATION RESULTS A. Cuent wavefoms The voltage equation pe phase of the SRG is given by: di V = RI + L + K ω (5) dt Fig. 8. Simulations of flux, cuent, toque and speed. 367
Cuent (A) Phase Cuent Flux (Wb) Cuent (A) Fig. 12. Flux vs. cuent and Cuent vs. time at low-speed fo CCC mode Fig. 9. Cuent at n>nb (case 1) - Fo case 2 (n= nb): it happens at tun-off angle off di whee E = Vdc and thus, fom Equation (5), = 0. dt Consequently, the cuent emains constant (Fig. 10) until the inductance eaches its minimum at enegy cycle (2). As shown in Fig. 13.a, case (2) poduces the lagest toque enegy cycle and, thus, seems moe effective in enegy convesion. - In case 3 (n < nb): in (Fig. 11), the maximum cuent is eached at off and afte that, the cuent deceases steadily, because E < Vdc, which coesponds to low speeds. A smalle toque aea is typical fo case (3). B. Enegy convesion cycles The aea enclosed by each loop epesents the enegy conveted fom mechanical to electical fom pe electical phase cycle of each phase. This loop is obtained fo each phase cycle (stoke) by dawing the gaph of the linkage flux vesus phase cuent (Fig. 12). Six loops of enegy convesion fo the studied 6/4 SRG at six diffeent speeds ae shown in (Fig. 13a) fo single-pulse mode and (Fig. 13b) fo CCC mode. At low speed we always have contol though actively chopping the cuent, the windings cuent is limited by chopping contol duing inceasing inductance (Fig. 4). Above base speed the machine stats opeating in singlepulse mode and in geneato mode the phase cuent can continue to incease even afte the excitation tuned off [3]. Flux (Wb) speed Fig. 13.b Simulation of cuent at low-speed (CCC) V. OPTIMIZATION The optimization pocedue achieved unde MATLAB softwae is applied to the contol of the SRG with the following paametes constaints (Table II). Lowe and highe limits of each vaiable define the seach egion of the pevious loop (fig.13). Afte specifying limits, the vaiable x of the objective function (7) epesents a vecto of angle values,. Then, the algoithm epesented in Fig. 14 on off is used to minimize the distance between the computed and efeence (flux/cuent) cuve in case (2) of base speed (n=nb) by changing and finding the optimal vecto x of conduction angle (Fig. 15). TABLE II PARAMETERS CONSTRAINTS Cuent (A) Cuent (A) Cuent (A) -5 < on < 10 (Degees) 35 < off < 50 (Degees) on + off <50 (Degees) 0 =(15, 50) (Degees) Fig. 10. Cuent at n=nb (Case 2) Fig. 11. Cuent at n<nb (Case 3) 368
Flux (web) on, off f ( x) = nom[( Flux( Cuent)) ( Flux( Cuent)) ef )] Computed on, 0 off0 min on, off max Cuent Fig. 17. Oigin and optimized flux/cuent cuves at n=500 pm Fig. 14. Flowchat fo the optimization method Teta Off (Deg) Flux (Wb) Fig. 18. Optimal conduction angle vesus speed Speed (pm) Fig. 15. Illustation of optimizing flux/cuent cuves Diect seach is a method fo solving optimization poblems that does not equie any infomation about the gadient of the objective function. Unlike moe taditional optimization methods that use infomation about the gadient o highe deivatives to seach fo an optimal point, a diect seach algoithm seaches a set of points aound the cuent point, looking fo one whee the value of the objective function (7) is lowe than the value at the cuent point [18]. The stuctue of objective function is: f x) = nom( Flux Flux ) + nom( Cuent Cuent ) (7) ( computed ef computed ef Fig. 16 shows the objective function value of the best point at each iteation. Fig. 17 shows optimized cuves simulation fo n=500 pm. The Objective function values impove apidly at the ealy iteations and then level off as they appoach the optimal angle conduction value (Fig. 18). Function value Best point Cuent (A) Fig. 16. Objective function values and the best point at each iteation The SRG tansfes powe in pulse, suggesting the need of an end capacito to contol the load voltage. The time vaiation of the capacito used to continuously supply the load is epesented in Fig. 19. It can be noticed that the enegy stoed in the magnetic field of excited phase flows to the end capacito and to the load when the coespondent diode is conducting [1][19]. The efficiency is calculated by the following equation: Po η = 100 [%] (8) Pe + Pm Whee Pm, P e and P o ae the mechanical input powe, the electic excitation powe and the output powe, espectively. Fig. 20 shows the vaiations of the efficiency with the otational speed fo optimized and efeence conduction angles. The dashed cuve shows the efeence efficiency and the solid cuve the optimized efficiency. This figue eveals that the efficiency of the 6/4 SRG is about 80 % in the wide egion of the otational speed. VI. CONCLUSIONS This pape has examined the poblem of choosing the conduction angles fo accomplishing optimal contol of SRG. The optimal angles ae specified by a simple method based on the optimization of conduction angle to appoach the ideal (flux/cuent) base speed cuve, and maximize enegy convesion. The diect elationship between the losses and ms phase cuent in the SRG detemine the maximum efficiency. Simulation esults ae pesented. 369
Capacito voltage Efficiency T e, T av Fig. 19. Capacito voltage Fig. 20. Efficiency with optimized conduction angles APPENDIX Electomagnetic and aveage toque espectively W c, W e, W mec Co-enegy, Magnetic enegy and Mechanical enegy espectively on, off, Tun-on, tun-off and oto angle espectively R, L Phase esistance and phase inductance espectively Flux and phase ψ, i Speed (pm) cuent espectively m Numbe of phases N Numbe of oto poles V dc, E DC-link voltage and back EMF espectively ω Angula speed REFERENCES [1] A. Fleuy, A Switched Reluctance Geneato Behavio unde Diffeent Conditions, Industial Electonics, ISIE 2007. IEEE Intenational Symposium, 4-7 June 2007, pp. 1282 1287. [2] L. Chuang, Investigation and Pactice fo Basic Theoy of Switched Reluctance Geneatos, Electical Machines and Systems, ICEMS 2005, Poceedings of the Eighth Intenational Confeence vol.1, 27-29 Sept. 2005, pp. 575 579. [3] E. Mese, Y. Soze, J.M. Kokenak, D.A.Toey, Optimal excitation of a high speed switched eluctance geneato, APEC 2000. Fifteenth Annual IEEE, vol.1, pp. 362 368, 6-10 Feb. 2000. [4] Flux-2D, softwae package fo esolution by FEM, Cedat Zist, 38 240 Meylan, Fance. [5] D. A. Toey, Switched Reluctance Geneatos and Thei Contol, IEEE Tans. Ind. Electon., vol. 49, No 1, pp. 3 14. Feb. 2002. [6] K. Buehing, L.L. Feis, Contol policies fo wind-enegy convesion systems, IEE Poc.C, Sept 1981,vol. 128, No. 5, pp. 153-261. [7] E. A. Bossanyi, Options fo vaiable speed opeation of hoizontal axis wind tubine geneatos, Repot pepaed fo Dept of Enegy by Wind Enegy Goup Alpha House, Westmount Cente. [8] P. I. Lawenson, Vaiable speed switched eluctance motos, IEE Poc. B, July 1980, vol. 127, No 4, pp 253.265. [9] T. J. Mille, Convete Volt ampee Requiement of the Switched Reluctance Moto Dive, IEEE Tans. Ind. Applic., vol. IA-21, No. 5, pp 1136-1 144, Sept/Oct 1985. [10] W F. Ray, R. M. Davis, Invete dive fo doubly salient eluctance moto: its fundamental behaviou linea analysis and implications, Electical powe applications, Decembe 1979, vol. 2, No. 6, pp 185-193. [11] R. M Davis, W. F. Ray et al. "Invete dive fo switched eluctance moto: cicuit and components atings", IEE Poc B, Mach 1981, vol. 128, No. 2, pp 126-136. [12] M. Ilk-Spong et al,, Feedback Lineaising Contol of Switched Reluctance Moto, IEEE Tans. Aut., May 1987, vol. AC-32, No. 5 pp. 371-379. [13] C. Johnson, R. Smith, Dynamics of wind geneatos on electic utility netwok, July 1976, IEEE Tans. Ind. Applic., vol. AES- I2, No 4, pp 483-493. [14] S. Vukosavic, V. Stefanovic, SRM invete topologies a compaative evaluation, IEEE Tans. Ind. Applic., vol. IA-27, No 6, Novenbe-Decembe, pp 1034-1 047. [15] B. Bose, T.J.E. Mille, Micocompute contol of switched eluctance moto, IEEE tans. Ind. Applic., vol. IA-22,No 4, pp 708-715, July / August 1986. [16] Leithead W, Wind tubine contol system modelling and design, epot pepaed fo Dpt. of enegy by lndustial Contol Unit, Univesity of Stathclyde, Glasgow. IJK. 1988. [17] R.Cadenas, Switched Reluctance Geneatos fo wind enegy application, Powe Electonics Specialists Confeence, 1995. PESC '95 Recod. 26th Annual IEEE, vol. 1, 18-22 June 1995, pp. 559 564. [18] MATLAB, language of technical computing, R2008b, 1994-2009, The MathWoks, Inc. [19] J. Faiz and R. Fazai, Modeling of losses in switched eluctance Geneatos, 2nd Intenational Confeence on Technical and Physical Poblems in Powe Engineeing (TPE-2004), Septembe 2004, Tabiz, Ian. R. Rebbah: (1979) eceived the M.S. degees fom Mentoui Univesity of Constantine. He is cuently Assistant eseache in the Depatment of Electical Engineeing at the Univesity of Constantine, Algeia, engaged in eseach. His inteests ae in the aeas of simulation and moto optimization, enegy convesion analysis, and modeling of powe convetes. He has woked towad the development of the switched eluctance geneato contols and geometies. A. Bentounsi : (1953) Afte eceiving its ''doctoateenginee'' in Pais 6, Fance, in 1980, he joined the Univesity of Constantine, Algeia, in 1984, as an Associate Pofesso. Since 1995, he is woking on his Ph.D. dissetation in collaboation with the Cegely Lab. of Ecole Centale Lyon, Fance. He was the cofounde of the Laboatoie d Electotechnique de Constantine (LEC), Algeia, in 1999. His cuent eseach inteests ae CAD & failue analysis of the electical machines and enewable enegy convesion. H. Benalla: (1957) He eceived the B.S., M.S., and Doctoate Enginee degees in powe electonics, fom the National Polytechnic Institute of Toulouse, Fance, espectively in 1981, 1984. In 1995, he eceived the Ph.D. degee in Electical Engineeing fom Univesity of Jussieu-Pais VI, Fance. Since 1996, he is with the depatment of Electotechnics, at Constantine Univesity Algeia, as a Pofesso. His cuent eseach field includes Active Powe Filtes, PWM Invetes, Electic Machines, and AC Dives 370