Swarm Intelligence Based Controller for Electric Machines and Hybrid Electric Vehicles Applications

Transcription

1 Swam Intllignc Basd Contoll fo Elctic Machins and Hybid Elctic Vhicls Applications Oma Hgazy 1, Am Amin, and Joi Van Milo 1 1 Faculty of Engining Scincs Dpatmnt of ETEC- Vij Univsitit Bussl, Pow and Elctical Machins Dpatmnt, Faculty of Engining Hlwan Univsity, 1 Blgium Egypt 9 1. Intoduction Swam Intllignc in th fom of Paticl Swam Optimization (PSO) has potntial applications in lctic divs. Th xcllnt chaactistics of PSO may b succssfully usd to optimiz th pfomanc of lctic machins and lctic divs in many aspcts. It is stimatd that, lctic machins consum mo than 50% of th wold lctic ngy gnatd. Impoving fficincy in lctic divs is impotant, mainly, fo two asons: conomic saving and duction of nvionmntal pollution. Induction motos hav a high fficincy at atd spd and toqu. Howv, at light loads, th ion losss incas damatically, ducing considably th fficincy. Swam intllignc is usd to optimiz th pfomanc of th applications; ths applications a psntd as follows: Losss Minimization of two asymmtical windings induction moto Maximum fficincy and minimum opating cost of th-phas induction moto Optimal lctic div systm fo ful cll hybid lctic vhicls. In this chapt, a fild-ointd contoll that is basd on Paticl Swam Optimization is psntd. In this systm, th spd contol of two asymmtical windings induction moto is achivd whil maintaining maximum fficincy of th moto. PSO slcts th optimal oto flux lvl at ach opating point. In addition, th lctomagntic toqu is also impovd whil maintaining a fast dynamic spons. A novl appoach is usd to valuat th optimal oto flux lvl by using Paticl Swam Optimization. PSO mthod is a mmb of th wid catgoy of Swam Intllignc mthods (SI). Th swam intllignc is basd on al lif obsvations of social animals (usually inscts), it is mo flxibility and obust than any taditional optimization mthods. PSO algoithm sachs fo global optimization fo nonlina poblms with multi-objctiv. Th a two spd contol statgis xplaind in th nxt sctions. Ths a fild-ointd contoll (FOC), and FOC basd on PSO. Th statgis a implmntd mathmatically and xpimntal. Th simulation and xpimntal sults hav dmonstatd that th FOC basd on PSO mthod savs mo ngy than th convntional FOC mthod.

2 16 Elctic Machins and Divs In this chapt, anoth application of PSO fo losss and opating cost minimization contol is psntd fo th induction moto divs. Two statgis fo induction moto spd contol a poposd. Ths statgis a maximum fficincy statgy (MES), basd PSO, and minimum opating cost Statgy. Th poposd tchniqu is basd on th pincipl that th flux lvl in a machin can b adjustd to giv th minimum amount of losss and minimum opating cost fo a givn valu of spd and load toqu. In th dmonstatd systms, th powtain componnts sizing and th pow contol statgy a th only adjustabl paamts to achiv optimal pow shaing btwn soucs and optimal dsign with minimum cost, minimum ful consumption, and maximum fficincy fo Elctic Vhicls (EVs) and Hybid Elctic Vhicls (HEVs). Thi slction gatly influncs th pfomanc of th div systm in Hybid Elctic Vhicls applications. In this sction, th dsign and pow managmnt contol a invstigatd and optimizd by using Paticl Swam Optimization.. Losss minimization of two asymmtical windings induction moto In this sction, a fild ointation basd on Paticl Swam Optimization (PSO) is applid to contol th spd of two-asymmtical windings induction moto. Th maximum fficincy of th moto is obtaind by th valuation of optimal oto flux at ach opating point. In addition, th lcto-magntic toqu is also impovd whil maintaining a fast dynamic spons. In this sction, a novl appoach is usd to valuat th optimal oto flux lvl. This appoach is basd on Paticl Swam Optimization (PSO). This sction psnts two spd contol statgis. Ths a fild-ointd contoll (FOC) and FOC basd on PSO. Th statgis a implmntd mathmatically and xpimntal. Th simulation and xpimntal sults hav dmonstatd that th FOC basd on PSO mthod savs mo ngy than th convntional FOC mthod [Hgazy, 006; Amin t al., 007; Amin t al., 009]. Th two asymmtical windings induction moto is tatd as a two-phas induction moto (TPIM). It is usd in many low pow applications, wh th phas supply is not adily availabl. This typ of moto uns at an fficincy ang of 50% to 65% at atd opating conditions. Th convntional fild-ointd contoll nomally opats at atd flux at any valus with its toqu ang. Whn th load is ducd considably, th co losss bcom so high causing poo fficincy. If significant ngy savings a quid, it is ncssay to optimiz th fficincy of th moto. Th optimum fficincy is obtaind by th valuation of th optimal oto flux lvl. This flux lvl is vaid accoding to th toqu and th spd of th opating point. PSO is applid to valuat th optimal flux. It has th staightfowad goal of minimizing th total losss fo a givn load and spd. It is shown that th fficincy is asonably clos to optimal..1 Mathmatical modl of th moto Th d-q modl of an unsymmtical windings induction moto in a stationay fnc fam can b usd fo a dynamic analysis. This modl can tak in account th co losss. Th d-q modl as applid to TPIM is dscibd in [Hgazy, 006; Amin t al., 009]. Th quivalnt cicuit is shown in Fig. 1.

3 Swam Intllignc Basd Contoll fo Elctic Machins and Hybid Elctic Vhicls Applications 163 M L lm L l (1/k)ωλ d + i qs i q + - V qs R qf iqf L mq - + V ds A i ds L la L lr i d L md kωλ q R df idf R Fig. 1. Th d-q axs two-phas induction moto Equivalnt cicuit with ion losss. Th machin modl may b xpssd by th following voltag and flux quations: Voltag Equations (1): Flux Equations: vqs = m i qs + pλ qs (1) vds = a i ds + pλds () 0 = i (1/ k)* ω λ + pλ (3) q d q 0 = i + k* ω λ + pλ (4) R ds q d 0 = i R + L ( pi + pi pi ) (5) qf qf mq qs q qf 0 = i R + L ( pi + pi pi ) (6) df df md ds d df λ = L i + L ( i + i i ) (7) qs lm qs mq qs q qf λ = L i + L ( i + i i ) (8) ds la ds md ds d df

4 164 Elctic Machins and Divs λ = L i + L ( i + i i ) (9) q l q mq qs q qf λ = L i + L ( i + i i ) (10) d lr d md ds d df Elctical toqu quation is xpssd as: P 1 T = ( k Lmq id( iqs + iq iqf) L md iq( ids + id iqf ) (11) k T T = j pω + B ω (1) l m m. Fild-Ointd Contoll [FOC] Th stato windings of th moto a unbalancd. Th machin paamts diff fom th d axis to th q axis. Th wavfom of th lctomagntic toqu dmonstats th unbalanc of th systm. Th toqu in quation (11) contains an AC tm; it can b obsvd that two valus a psntd fo th fd magntizing inductanc. It is possibl to liminat th AC tm of lcto-magntic toqu by an appopiat contol of th stato cunts. Howv, ths lations a valid only in lina conditions. Futhmo, th modl is implmntd using a non-fd quivalnt cicuit, which psums som complicatd masumnt of th magntizing mutual inductanc of th stato and th oto cicuits. Th indict fild-ointd contol schm is th most popula schm fo fild-ointd contolls. It povids dcoupling btwn th toqu and th flux cunts. Th lctic toqu must b a function of th stato cunts and oto flux in synchonous fnc fam [Popscu & Navapscu, 000]. Assuming that th stato cunts can b imposd as: Wh: k= M sd / M sq s ds i s qs i s ds1 = i (13) s qs1 P T M i M i = k i (14) s s s s = sq qs λ d sd ds λ q L By substituting th vaiabls i ds, and i qs by auxiliay vaiabls i ds1, and i qs1 into (15) th toqu can b xpssd by (15) PM T = i i sd s s s s λ λ qs1 d ds1 q L In synchonous fnc fam, th lctomagntic toqu is xpssd as: PM T = i i sd λ λ qs1 d ds1 q L (16) (17) T = PM sd i λ qs1 L (18)

5 Swam Intllignc Basd Contoll fo Elctic Machins and Hybid Elctic Vhicls Applications 165 ds1 i λ = (19) M sd M = (0) ω sd ω i qs1 τ * λ.3 Synchonous fnc fam fo losss modl It is vy complx to find th losss xpssion fo th two asymmtical windings induction moto with losss modl. In this sction, a simplifid induction moto modl with ion losss will b dvlopd. Fo this pupos, it is ncssay to tansfom all machin vaiabls to th synchonous fnc fam. Th voltag quations a wittn in xpandd fom as follows [Hgazy, 006; Amin t al., 006; Amin t al., 009]: di qs diqm vqs = miqs + Llm + Lmq + ω( Llaids + Lmdidm) (1) dt dt dids didm vds = aids + Lla + Lmd ω( Llmiqs + Lmqiqm ) () dt dt diq di qm ωsl 0 = i q + Ll + Lmq + ( LlRid + Lmdidm) (3) dt dt k did didm 0 = i Rd+ LlR + Lmd k* ωsl( Li lq + Lmqqm i ) (4) dt dt qs q qf qm i + i = i + i (5) ds d df dm i + i = i + i (6) Wh: v dm ω LlLmqs = iqs (7) L qm ω mds ds v = L i (8) Th losss in th moto a mainly: a. Stato copp losss, b. Roto copp losss, c. Co losss, and v qm vdm df = ; idf = Rqf Rdf i

6 166 Elctic Machins and Divs d. Fiction losss Th total lctical losss can b xpssd as follows P losss = P cu1 + P cu +P co (9) Wh: P cu1 : Stato copp losss P cu : Roto copp losss P co : Co losss Th stato copp losss of th two asymmtical windings induction moto a causd by lctic cunts flowing though th stato windings. Th co losss of th moto a poducd fom th hystsis and ddy cunts in th stato. Th total lctical losss of moto can b wittn as: v qm vdm Plosss = miqs + aids + iq + Rid + R + qf R (30) df Th total lctical losss a obtaind as follows: P L mqs ω LlLmqs T L ωlmds λ losss = m a + L LR df R L mds qf Lmds P λ K (31) T * ωsl = (3) P * λ Wh: ω = ω + ω sl, and ω sl is th slip spd (ad/sc). Equation (31) is th lctical losss fomula, which dpnds on oto flux (λ ) accoding to opating point (spd and load toqu). Th total losss of th moto ( TP ) a givn as follows: losss TP losss = P losss + P Fic = P in - Pout (33) Wh: Efficincy ( η ) = P Fiction pow losss = F ω, and Output pow (P out ) = T L ω. out Pout + TP losss (34).4 Losss minimization contol schm Th quation (33) is th cost function, th total losss, which dpnds on oto flux (λ) accoding to th opating point. Figu psnts th distibution of losss in moto and its vaiation with th flux. As th flux ducs fom th atd valu, th co losss dcas,

7 Swam Intllignc Basd Contoll fo Elctic Machins and Hybid Elctic Vhicls Applications 167 but th moto copp losss incas. Howv, th total losss dcas to a minimum valu and thn incas again. It is dsiabl to st th oto flux at th optimal valu, so that th fficincy is optimum [Hgazy, 006; Amin t al., 006; Amin t al., 009]. Fig.. Losss vaiation of th moto with vaying flux PSO is applid to valuat th optimal flux that minimizs th moto losss. Th poblm can b fomulatd as follows: minimiz TP = Γ (,T, ) (35) losss λ L ω.4.1 Paticl Swam Optimization (PSO) Paticl swam optimization (PSO) was oiginally dsignd and intoducd by Ebhat and Knndy [Ebahat, Knndy, 1995; Ebahat, Knndy, 001]. Paticl Swam Optimization (PSO) is an volutionay computation tchniqu (a sach mthod basd on a natu systm). It can b usd to solv a wid ang of optimization poblms. Most of th poblms that can b solvd using Gntic Algoithms (GA) could b solvd by PSO. Fo xampl, nual ntwok taining and nonlina optimization poblms with continuous vaiabls can b asily achivd by PSO [Ebahat, Knndy, 001]. It can b asily xpandd to tat poblms with disct vaiabls. Th systm initially has a population of andom solutions. Each potntial solution, calld a paticl. Each paticl is givn a andom vlocity and is flown though th poblm spac. Th paticls hav mmoy and ach paticl kps tack of its pvious bst position (call th pbst) and with its cosponding fitnss. Th xit a numb of pbst fo th spctiv paticls in th swam and th paticl with gatst fitnss is calld th global bst (gbst) of th swam. PSO can b psntd by th concpt of vlocity and position. Th Vlocity of ach agnt can b modifid by th following quations: (36 & 38): k 1 v + = w v + c *( pbst s ) + c *( gbst s ) (36) k k k i 1 1 i i

8 168 Elctic Machins and Divs Stat Rad moto paamts Dtmination of th nw opation conditions (spd and toqu) Run th Simulik modl of two asymmtical windings induction moto with losss Calculation of moto cunts vaying th oto flux lvl using PSO calculation of th cost function Is th valu of th cost function is minimum? No Ys st this valu as optimum point and cod th cosponding optimum valus of th fficincy and th oto flux load No A all possibl opating conditions optimizd Ys End Fig. 3. Th flowchat of th xcution of th PSO [Hgazy, 006)

9 Swam Intllignc Basd Contoll fo Elctic Machins and Hybid Elctic Vhicls Applications 169 ωmax ωmin ω = ωmax * it (37) it Using th abov quations, a ctain vlocity can b calculatd that gadually gts clos to (pbst) and (gbst). Th cunt position (saching point in th solution spac) can b modifid by th following quation: max Wh: ν k : Cunt vlocity of agnt i at itation. ν i k+1 : Modifid vlocity of agnt i 1, : andom numb distibutd [0,1], S k i : cunt position of agnt i, ω : wight function fo vlocity of agnt i, c 1, c : positiv constants; [c1+ c< 4]. ω max : Initial wight, ω min : Final wight, it max : Maximum itation numb, it : Cunt itation numb. S k+ 1 S k v k 1 i = + i + i (38) In (35), th losss fomula is th cost function of th PSO. Th paticl swam optimization (PSO) tchniqu is usd fo minimizing this cost function. Th PSO is applid to valuat th optimal oto flux that minimizs th moto losss at any opating point. Figu 3 psnts th flowchat of th xcution of PSO, which valuats th optimal flux by using MATLAB /SIMULINK. Th optimal flux is th input of th indict oto flux ointd contoll. Th indict fildointd contoll gnats th quid two fnc cunts to div th moto cosponding to th optimal flux. Ths cunts a fd to th hystsis cunt contoll of th two-lvl invt. Th switching pattn is gnatd accoding to th diffnc btwn th fnc cunt and th load cunt though th hystsis band. Figu 4 shows a whol contol diagam of th poposd losss-minimization contol systm. V dc V dc main T * ϕ* FO i qs * =i a f. i ds * = i b f. Hystsis-band cunt contol Fou Switch Invt [FSI] Roto aux flux optimal i b actual PSO i a actual Tl N M/C Paamts Fig. 4. Th poposd losss minimization contol systm.

10 170 Elctic Machins and Divs.5 Simulation sults In this sction, th poposd application is implmntd numically using MATLAB- SIMULINK to validat th pfomanc of th poposd contol statgy. Th moto usd in this study has th following paamts, which w masud by using xpimntal tsts. Tabl 1 shows moto paamts. Th usd paamts of th PSO a shown in Tabl. Tabl 1. Moto Paamts Ratd pow V F M A X Lm X La X L 750 w 0 v 50 Hz 4.6 Ω 10.6 Ω 4.31 Ω Ω Ω 4.84 Ω X mq 89.65Ω X md Ω R qf 1050Ω R df 1450Ω J kg.m B N.m.sc/ Pol pai Th optimal oto flux povids th maximum fficincy at any opating point. Th a six-cass of th moto opation a studid by using FOC basd on PSO. PSO will valuat th optimal oto flux lvl. This flux is fd to th FOC modul. Figu 5 shows th pfomanc of th moto at cas (1) (T L =0.5 PU, N =0.5 N atd ), whn PSO is applid sidby-sid FOC as shown in Fig.4. Tabl. PSO Algoithm paamt Population siz 10 Max. it 50 c1 0.5 c 0.5 Max. wight 1.4 Min. wight [ 0,1] [ 0,1] Low Bound 0. Upp Bound

11 Swam Intllignc Basd Contoll fo Elctic Machins and Hybid Elctic Vhicls Applications 171 (a) (b) (c) (d) () (f) Fig. 5. Simulation sults of th moto at cas (1).Spd-tim cuv, (b) Toqu-tim cuv, (c) Th stato cunt in q-axis, (d) Th stato cunt in d-axis, () Total Losss against itations, (f) Efficincy against itations

12 17 Elctic Machins and Divs Figu 6 illustats th compaison btwn FOC and FOC basd PSO contol mthods at diffnt opating points. Figu 7 psnts th optimal flux, which is obtaind by applying PSO. Tabl 3 psnts th summay of th sults of FOC and FOC basd PSO mthods. Fig. 6. th compaison btwn FOC and FOC basd PSO Fig. 7. Th optimal flux at diffnt load toqu FOC FOC basd PSO Cass T L (PU) N (pm) λ (PU) η (%) λ Optimal (PU) η (%) Impovmnt (%) (1) N atd () N atd (3) N atd (4) N atd (5) N atd (6) N atd Tabl 3. Summay of th sults of th two contolls

13 Swam Intllignc Basd Contoll fo Elctic Machins and Hybid Elctic Vhicls Applications 173 In pactical systm, th flux lvl basd on PSO at diffnt opating points (toqu and spd) is calculatd and stod in a look up tabl (LUT). Th us of look up tabl will nabl th systm to wok in al tim without any dlay that might b ndd to calculat th optimal point. Th poposd contoll would civ th opating point (toqu and spd) and gt th optimum flux (λ optimal ) fom th look up tabl. It will gnat th quid fnc cunt. It is noticd that, th fficincy with th FOC basd on PSO mthod is high than th fficincy with th FOC mthod only..6 Expimntal sults To vify th validity of th poposd contol schm, a laboatoy pototyp is built and tstd [Hgazy, 006; Amin t al., 006; Amin t al., 009]. Th basic lmnts of th poposd xpimntal schm a shown in Fig. 8 and Fig. 9. Th xpimntal sults of th moto a achivd by coupling th moto to an ddy cunt dynamomt. Th xpimntal sults a achivd using two contol mthods: Fild-Ointd Contol [FOC], and Fild-Ointd Contol [FOC] basd on PSO. Th fnc and th actual moto cunts a fd to th hystsis cunt contoll. Th switching pattn of th two-lvl fou-switch invt [FSI] is gnatd accoding to th diffnc btwn th fnc cunts and th load cunts. Figu 10 shows th xpimntal sults of th moto with FOC at cas (1), wh th moto is loadd by T L = 0.5 PU. Figu 11 shows th xpimntal sult of th moto with FOC basd on PSO at cas (1). Th cass a summaizd in Tabl 4. Switching Pattn Two dc-supply ω f + - PI PSO T * φ* Indict Fild-Ointd ω actual i s qs i s ds dq-->ab tansfom I a_f I b_f INTER-FACE i a i b 4 Hystsis cunt contoll ω actual I aact I bact Invt Roto Shaft ncod T l N M/c paamats Fig. 8. Block diagam of th poposd xpimntal schm [Hgazy, 006; Amin t al., 009] Cass FOC FOC with PSO Impovmnt λ Pow η λ Pow η (%) (PU Input (W) (%) (PU Input (W) (%) (1) () Tabl 4. Th summay of th two-cass

14 174 Elctic Machins and Divs D D R S D s 1 1 S D R s E dc G 1 S C s G S C s i qs E dc D D oto main S R D s S 4 3 D 4 R s G S C s G4 S C s i ds aux Fig. 9. Th pow cicuit of Fou Switch Invt [FSI] (a) (b)

15 Swam Intllignc Basd Contoll fo Elctic Machins and Hybid Elctic Vhicls Applications 175 Fig. 10. Expimntal sults of FOC mthod; th fnc and actual spd, (b) th fnc and actual cunt in q-axis, (c) Th fnc and actual cunt in d-axis (c) (a) Fig. 11. Expimntal sults of FOC mthod basd on PSO. (a) Th fnc and actual cunt in q-axis, th fnc and actual cunt in d-axis (b)

16 176 Elctic Machins and Divs Finally, ths sults dmonstat that, th FOC basd on PSO mthod savs mo ngy than convntional FOC mthod. Thus, th fficincy with PSO is impovd than it's at FOC. 3. Maximum fficincy and minimum opating cost of induction motos This sction psnts anoth application of PSO fo losss and opating cost minimization contol in th induction moto divs. Two contol statgis fo induction moto spd contol a poposd. Thos two statgis a basd on PSO and calld Maximum Efficincy Statgy and Minimum Opating Cost Statgy [A. Hamid t al. 006]. Th poposd tchniqu is basd on th pincipl that th flux lvl in th machin can b adjustd to giv th minimum amount of losss and minimum opating cost fo a givn valu of spd and load toqu. Th main advantags of th poposd tchniqu a; its simpl stuctu. It is a staightfowad maximization of induction moto fficincy and its opating cost fo a givn load toqu. As was dmonstatd, PSO is fficint in finding th optimum opating machin's flux lvl. Th optimum flux lvl is a function of th machin opating point. Th main induction moto losss a usually split into fiv componnts: stato copp losss, oto copp losss, ion losss, mchanical losss, and stay losss [Kioskidis & Magais, 1996]. Th fficincy that dcass with incasing losss can b impovd by minimizing th losss. Copp losss duc with dcasing th stato and th oto cunts, whil th co losss ssntially incas with incasing ai-gap flux dnsity. A study of th copp and co losss componnts vals that thi tnds conflict. Whn th co losss incas, th copp losss tnds to dcas. Howv, fo a givn load toqu, th is an ai-gap flux dnsity at which th total losss is minimizd. Hnc, lctical losss minimization pocss ultimatly coms down to th slction of th appopiat ai-gap flux dnsity of opation. Sinc th ai-gap flux dnsity must b vaiabl whn th load is changing, contol schms in which th (oto, ai-gap) flux linkag is constant will yild sub-optimal fficincy opation spcially whn th load is light. Thn to impov th moto fficincy, th flux must b ducd whn it opats und light load conditions by obtaining a balanc btwn copp and ion losss. Th challng to ngins, howv, is to b abl to pdict th appopiat flux valus at any opating points ov th complt toqu and spd ang which will minimiz th machins losss, hnc maximizing th fficincy. In gnal, th a th diffnt appoachs to impov th induction moto fficincy spcially und light-load. a. Losss Modl Contoll (LMC) This contoll dpnds on a moto losss modl to comput th optimum flux analytically. Th main advantag of this appoach is its simplicity and it dos not qui xta hadwa. In addition, it povids smooth and fast adaptation of th flux, and may off optimal pfomanc duing tansint opation. Howv, th main poblm of this appoach is that it quis th xact valus of machin paamts. Ths paamts includ th co losss and th main inductanc flux satuation, which a unknown to th uss and chang considably with tmpatu, satuation, and skin ffct. In addition, ths paamts may vay du to changs in th opating conditions. Howv, with continuing impovmnt of volutionay paamt dtmination algoithms, th disadvantags of moto paamts dpndncy a slowly disappaing. b. Sach Contoll (SC) This contoll masus th input pow of th machin div gulaly at fixd tim intvals and sachs fo th flux valu, which sults in minimum pow input fo givn

17 Swam Intllignc Basd Contoll fo Elctic Machins and Hybid Elctic Vhicls Applications 177 valus of spd and load toqu. This paticula mthod dos not dmand knowldg of th machin paamts and th sach pocdu is simpl to implmnt. Howv, som disadvantags appa in pactic, such as continuous distubancs in th toqu, slow adaptation (7sc.), difficultis in tuning th algoithm fo a givn application, and th nd fo pcis load infomation. In addition, th pcision of th masumnts may b poo du to signal nois and distubancs. This in tun may caus th SC mthod to giv undsiabl contol pfomanc. Moov, nominal flux is applid in tansint stat and is tund aft th systm achs stady stat to an optimal valu by numous incmnts, thus lngthning th optimization pocss. Thfo, th SC tchniqu may b slow in obtaining th optimal point. In addition, in al systms, it may not ach a stady stat and so caus oscillations in th ai gap flux that sult in undsiabl toqu distubancs. Fo ths asons, this is not a good mthod in industial divs. c. Look Up Tabl Schm It givs th optimal flux lvl at diffnt opating points. This tabl, howv, quis costly and tim-consuming pio masumnts fo ach moto. In this sction, a nw contol statgy uss th loss modl contoll basd on PSO is poposd. This statgy is simpl in stuctu and has th staightfowad goal of maximizing th fficincy fo a givn load toqu. Th sulting induction moto fficincy is asonably clos to optimal. It is wll known that th psnc of unctaintis, th oto sistanc, fo instanc maks th sult no mo optimal. Digital comput simulation sults a obtaind to dmonstat th ffctivnss of th poposd mthod. 3.1 Dfinition of opating statgis Th following dfinitions a usful in subsqunt analyss. Rfing to th analysis of th induction moto psntd in [A. Hamid t al. 006], th p-unit fquncy is Th slip is dfind by Th oto cunt is givn by s a ω ω + ω s = = (39) ωb ωb ω ω s s = = (40) ωb ωs + ω Th lctomagntic toqu is givn by I ' = φ m ' + sa X ' l (41) ' sa T φ = ' m ' + sa X l (4)

18 178 Elctic Machins and Divs Th stato cunt is latd to th ai gap flux and th lctomagntic toqu as: Wh 3 φ 5 φ T φ I s = S1 φm + S + S + CL (43) m m m C L = 1 + Th ai gap flux is latd to th lctomagntic toqu as: ' x x l m φ = m sa ' ' + sa Th fficincy is dfind as th output pow dividd by th lctic pow supplid to th stato (invt losss a includd): ' x l in T (44) Pout Efficincy ( η ) = (45) P Maximum fficincy statgy In MES (Maximum Efficincy Statgy), th slip fquncy is adjustd so that th fficincy of th induction moto div systm is maximizd [A. Hamid t al. 006]. Th induction moto losss a th following: 1. Copp losss: ths a du to flow of th lctic cunt though th stato and oto windings and a givn by: ' ' cu s s I I P = + (46). Ion losss: ths a th losss du to ddy cunt and hystsis, givn by ( 1 ) ϕ ( 1 ) ϕ P = K + S a + K + S a (47) co m h 3. Stay losss: ths ais on th copp and ion of th moto and a givn by: m ' cu st ω P = C I (48) 4. Mchanical losss: ths a du to th fiction of th machin oto with th baings and a givn by: Pfw = Cfw + ω (49) 5. Invt losss: Th appoximat invt loss as a function of stato cunt is givn by:

19 Swam Intllignc Basd Contoll fo Elctic Machins and Hybid Elctic Vhicls Applications 179 K K Pinv 1invis invis = + (50) Wh: K 1inv, K inv a cofficints dtmind by th lctical chaactistics of a switching lmnt wh: K1inv= , Kinv= Th total pow losss a xpssd by: Th output pow is givn by: = = + + ' K( 1+ S ) a ϕ + Kh( 1+ S) a ϕ + C m m st ω I ' ' Pcu Pco P losss s Pfw Pinv s s P I I i + K + K i 1inv s inv s (51) Th input pow is givn by: P ω out = T L (5) P in ' ' Pout P = Pcu + Pco + Ps + Pfw + Pinv = losss s I + s I + ' K( 1+ S ) a ϕ + Kh( 1+ S) a ϕ + C m m st ω I = + Th fficincy is xpssd as: i K T 1inv inv s L s K i ω (53) η = s I s + ' I + K ' + K 1inv i s + T ω ( 1+ S ) a φ + Kh ( 1+ S ) aφ K inv i + TL ω s L m m + C st ωi Th fficincy maximization of th induction moto poblm can b fomulatd as follows: Maximiz ' (54) η, ω, ω ) (55) ( T L s Th maximization should obsv th fact that th amplitud of th stato cunt and flux cannot xcd thi spcifid maximum point Minimum opating cost statgy In Minimum Opating cost Statgy (MOCS), th slip fquncy is adjustd so that th opating cost of th induction moto is minimizd. Th opating cost of th induction machin should b calculatd ov th whol lif cycl of th machin. That calculation can b mad to valuat th cost of th consumd lctical ngy. Th valu of avag ngy cost considing th pow facto pnaltis can b dtmind by th following stags [A. Hamid t al. 006]: 1. If 0 PF < 0.7

20 180. If 0.7 PF 0.9, If PF 0.9, PF = PF C = C Χ Elctic Machins and Divs (56) 3. If 0.9 PF 1, If 0.95 PF 1, PF = PF 0.5 C = C 1 + (57) 0 Χ PF 0.7 C = C 1 + (58) 0 Χ If th avag ngy cost C is calculatd, it can b usd to stablish th psnt valu of losss. Th total cost of th machin is th sum of its initial cost plus th psnt woth valu of losss and maintnanc costs. 1 PW = C T N P out 1 (59) L η Wh: PW L = psnt woth valu of losss C0 = ngy cost p kwh, C = modifid ngy cost p kwh T = unning tim p ya (Hs / ya) N = valuation lif (yas) P out = th output pow (kw) η = th fficincy Th opating cost minimization of th induction moto poblm can b fomulatd as follows: Minimiz PW L ( T, ω, ω ) L s (60) 3. Simulation sults Th simulation is caid out on a th-phas, 380 V, 1-HP, 50 Hz, and 4-pol, squil cag induction moto. Th moto paamts a R s =0.0598, X ls =0.0364, X m =0.8564, X l =0.0546, R =0.0403, K =0.0380, K h =0.0380, C st =0.0150, C fw =0.0093, S 1 =1.07, S =-0.69, S 3 =0.77. Fo cost analysis, th following valus w assumd: C 0 =0.05, N=15, T=8000. Th task of PSO contoll is to find that valu of slip at which th maximum fficincy occus. At ctain load toqu and oto spd, th PSO contoll dtmins th slip fquncy ω s at which th maximum fficincy and minimum opating cost occu. Th block diagam of th optimization pocss basd on PSO is shown in Fig.1. To obsv th impovmnts in fficincy using th suggstd PSO contoll, Fig. 13 shows th fficincy of th slctd machin fo all opating conditions using convntional mthods (constant voltag to fquncy atio, fild ointd contol statgy) and using th poposd PSO contoll at diffnt oto spd lvls, W = 0. PU, and W = 1 PU spctivly [A. Hamid t al. 006]. This figu shows that a considabl ngy saving is achivd in compaison with th convntional mthod (fild ointd contol statgy and constant voltag to fquncy

21 Swam Intllignc Basd Contoll fo Elctic Machins and Hybid Elctic Vhicls Applications 181 atio) spcially at light loads and small oto spd. Figu 14 compas th fficincy of th induction moto div systm und th maximum fficincy statgy with th minimum opating cost statgy at W = 1 PU. It is obvious fom th figu that th fficincy is almost th sam fo both statgis fo all opating points. Fig. 1. Th poposd div systm basd on PSO contoll

22 18 Elctic Machins and Divs Fig. 13. Th fficincy of th induction moto using th maximum fficincy statgy compad with th fficincy using th convntional mthods at (a) W = 0. PU, (b) W = 1 PU [A. Hamid t al. 006]. Fig. 14. Th fficincy of th induction moto using th maximum fficincy statgy compad with th fficincy using minimum opating cost statgy at W= 1 PU

23 Swam Intllignc Basd Contoll fo Elctic Machins and Hybid Elctic Vhicls Applications 183 Tabl 5 shows th fficincy compaison using fw xampls of opating points. Figu 15 compas th pow facto of th induction moto div systm und th maximum fficincy statgy with th minimum opating cost statgy at W = 1 PU. Finally, th poposd PSO-contoll adaptivly adjusts th slip fquncy such that th div systm is opatd at th minimum loss and minimum opating cost. It was found that th optimal systm slip changs with vaiations in spd and load toqu. Whn compaing th poposd statgy with th convntional mthods fild ointd contol statgy and constant voltag to fquncy atio). It was found that a significant fficincy impovmnt spcially at light loads fo all spds. On th oth hand, small fficincy impovmnt is achivd at na atd loads (s Fig.13, and Fig.15). Tabl 5. Som xampls of fficincy compaison und diffnt Load toqu lvls and W = 1 PU [A. Hamid t al. 006]. Fig. 15. Th pow facto of th induction moto using th maximum fficincy statgy compad with th fficincy using minimum opating cost statgy at W= 1 PU [A. Hamid t al. 006] 4. Optimal lctic div systm fo ful cll hybid lctic vhicls Although th a vaious FC tchnologis availabl fo us in vhicula systms, th poton xchang mmban FC (PEMFC) has bn found to b a pim candidat, sinc

24 184 Elctic Machins and Divs PEMFC has high pow dnsity and low opating tmpatus whn compad to th oth typs of FC systms. A stand-alon FC systm intgatd into an automotiv powtain is not always sufficint to satisfy th load dmands of a vhicl. Although FC systms xhibit good pow capability duing stady-stat opation, th spons of ful clls duing tansint and instantanous pak pow dmands is lativly poo. Thus, th FC systm can b hybidizd with supcapacitos (SC) o battis to mt th total pow dmand of a hybid lctic vhicl (HEV) [Van Milo t. al, 006; Paladini t. al, 007]. In this sction, a nw contol statgy basd PSO algoithm is poposd fo th Ful Cll/Supcapacito hybid lctic vhicls to optimiz th lctic div systm [Hgazy & Van Milo, 010]. Many factos influnc on th pfomanc of th lctic div systm. Ths factos a mass, volum, siz, fficincy, ful consumption and contol statgy. Thfo, th PSO is poposd to minimiz th cost, th siz and th mass of th powtain soucs (Ful cll, and supcapacito) as wll as minimum ful consumption and impovs th fficincy of th systm. PSO algoithm sachs fo global optimization fo nonlina poblms with multi-objctiv. Fo a givn diving cycl, th siz and th cost of ful cll and supcapacito a minimizd by idntifying th bst numb of units of ach, spctivly. Th mthods hav bn dsignd to achiv th optimal sizing. Ths a convntional mthod, tial and o, as was mntiond in [Wu & Gao, 006], GA, and PSO. In addition, th hydogn consumption is minimizd by th valuation of th optimal pow distibution btwn ful cll (main souc) and supcapacito (auxiliay souc). Th contol statgis a implmntd to minimiz th hydogn consumption and maintain th stat of chag (SOC) of th supcapacito ( SOCinitial =SOCfinal), which a contol statgy basd on Efficincy Map (CSEM), Contol statgy basd on PSO (CSPSO), and contol statgy basd on GA (CSGA). 4.1 Systm dsciption Th pow systm configuation is illustatd in Fig.16. A hybid ful cll/supcapacito vhicl utilizs a PEM ful cll as th main pow souc and a supcapacito as th auxiliay pow souc. A multipl-input pow lctonic convt (MIPEC) is poposd to intfac th taction div quimnts. In th MIPEC, th FC is connctd to DC Bus Fig. 16. Th div systm of th Ful Cll/Supcapacito Hybid Elctic Vhicl

25 Swam Intllignc Basd Contoll fo Elctic Machins and Hybid Elctic Vhicls Applications 185 via a Boost DC/DC convt (η B = η conv ) and th supcapacito is connctd to DC Bus via a Buck/Boost convt (η B/B = η conv ). Th dsid valu of th DC-Bus voltag is chosn to b 400 V with vaiations of ± 10% a pmissibl. Th pow supplid by th powtain has to b obtaining fom th pow dmand pdictd by th dynamics of th vhicl. Th fficincy of ach componnt in th hybid powtain is takn into account. A dtaild modl of th powtain is built in MATLAB /SIMULINK Modling of th vhicl pow dmand Th load foc of th vhicl consists of gavitational foc, olling sistanc, aodynamic dag foc, and acclation foc. Hby, th load pow quid fo vhicl acclation can b wittn as [Hgazy & Van Milo, 010; Hgazy t. al 010] P load ( F + F + F + F ) * V g oll AD acc = (61) η GB F = M. g. sin( α ) g F = M. g. f.cos( α) oll F AD = 0.5 ρ. C. A. V a D F F = M. acc dv dt V = ω. w w Th total lctic pow quid fom soucs can b xpssd as: (6) (63) (64) (65) (66) P q P = load (67) η. η. η m Inv Conv Th paamts of th vhicl a givn in Tabl 6. Th analysis of FCHEV is pfomd with two standad diving cycls: 1. Th Fdal Tst Pocdu (FTP75) Uban;. Th Nw Euopan Diving Cycl (NEDC) Suppos that th fficincis of th moto (η m ), invt (η Inv ), and MIPEC (η Conv = η B = η B/B ) a 0.90, 0.94 and 0.95, spctivly. M Vhicl mass (kg) 1450 A f Font Aa (m).13 f Rolling Rsistanc Cofficint ω C D Aodynamic Dag Cofficint (CD) Tabl 6. Vhicl Paamts [Wu & Gao, 006] 0.9 ρ a Radius of th whl (m) Ai dnsity (kg/m3)

26 186 Elctic Machins and Divs 4. Optimal powtain dsign Th fist goal of optimization algoithm, PSO, is to minimiz th cost, th mass, and th volum of th ful cll (FC) and supcapacito (SC). It is assumd that, th cost, th mass and th volum of th ful cll and supcapacito a a function of th numb of th paalll units N fcp and N scp, spctivly. Th multi-objctiv cition should b agggatd in a singl objctiv function if th dsign objctiv is to mbody a uniqu solution. Th objctiv function can b fomulatd as follows: ( x ) = w cos 1 t + wmass + wvolum (68) F 3 cos t = C1. Nfcs. Nfcp + C. Nscs. Nscp (69) Th cofficints of th tms in F(x) w chosn to flct th impotanc of minimizing th cost, th mass and th volum. Suppos that w1, w, and w3 a 0.35, 0.35, and 0.3, spctivly. Figu 17 psnts th flowchat of th xcution of PSO, which valuats th optimal numb of th FC units and th supcapacito units by using MATLAB /SIMULINK. Th layout of th ful-cll stack and layout of th supcapacito systm a shown in Fig.18 (a) and (b), spctivly. Th constaints of th optimization poblms a mntiond in [Hgazy & Van Milo, 010]. Fig. 17. Th flowchat of th xcution of PSO [Hgazy t. al 010]

27 Swam Intllignc Basd Contoll fo Elctic Machins and Hybid Elctic Vhicls Applications 187 (a) (b) Fig. 18. (a) Layout of th FC; (b) Layout of th SC

28 188 Elctic Machins and Divs Basd on minimizing th objctiv function F(x) in (68), th sults of th optimal dsign and componnts sizing of th FC/SC powtain a shown in Fig.19. Th analyss and paamts of th FC and th SC a mntiond in [Hgazy & Van Milo, 010]. (a) Th optimal numbs of clls of FC and SC (b) Th cost of th FC/SC componnts

29 Swam Intllignc Basd Contoll fo Elctic Machins and Hybid Elctic Vhicls Applications 189 (c) Th mass of th FC/SC componnts (d) Th mass of th FC/SC componnts Fig. 19. Th Compaativ of th optimal dsign btwn diffnt mthods fo FC/SC HEV 4.3 Optimal Pow Contol (OPC) Th scond goal of th PSO is to minimiz th vhicl ful, hydogn, consumption whil maintaining th supcapacito stat of chag. As a hybid powtain is und considation, a pow managmnt statgy is quid to dfin what both th FC and SC pows a. Th global optimization algoithms, such as GA and dynamic pogamming (DP), achiv an optimal pow contol fo FC/SC hybid lctic vhicl, which lads to th lowst hydogn consumption and maintains th supcapacito SOC [Sinoqut t. al 009; Sundstom & Stfanopoulou 006]. In this study, th optimal pow contol can b achivd by using PSO and GA fo a givn diving cycl. Suppos that th dg of hybidization of th ful cll is K fc at tim t and K soc, Popotional contoll gain, which usd to adapt th SOC duing chaging fom th FC. A balanc quation can natually b stablishd, sinc th sum of pow fom both soucs has to b qual to th quid pow at all tims:

30 190 Elctic Machins and Divs P q ( t) = Pfc( t) + Psc( t) (70) Pfc( t) Kfc ( t) = P q ( t) Th nt ngy consumd fom th FC at tim t can b computd as follows: t Pfc( t) Efc( t) = dt η ( Pfc( t)) 0 (71) (7) Th cost function can b xpssd as follows: 1 N Pfc Opti ( k) F ( x) = ΔT Elow K = 0 η ( Pfc Opti ( k)) Th Optimal ful cll pow output, P fcopti, is calculatd basd on th SOC of th supcapacito and pow dmand, P q, as follows: (73) Pfc Opti SOC f SOC( k) ( k) = Kfc( k) P ( ) + ( ) ( ) q k Ksoc k Pfc max Pfc min ( SOC max SOC min ) / (74) Fig. 0. Th block diagam of th Optimal pow Contol Wh: N= T/ΔT is numb of sampls duing th diving cycl, and ΔT=1s is th sampling tim. Th block diagam of th optimal pow contol basd on optimization algoithm is shown in Fig.0. Basd on minimizing th objctiv function F (x) in (73), th sults of th optimal pow shaing basd PSO and th compaativ study fo th FC/SC powtain a summaizd in Fig.1 [Hgazy t. al 010].

31 Swam Intllignc Basd Contoll fo Elctic Machins and Hybid Elctic Vhicls Applications 191 (a) Th pow shaing btwn FC and SC on NEDC diving cycl (b) Th pow shaing btwn FC and SC on FTP75 diving cycl

32 19 Elctic Machins and Divs (c) Th Compaativ of th hydogn consumption btwn contol statgis (d) Th Hydogn impovmnts with spct to pu ful cll without SC Fig. 1. Th sults of th optimal pow Contol fo FC/SC

33 Swam Intllignc Basd Contoll fo Elctic Machins and Hybid Elctic Vhicls Applications Conclusion This chapt dals with th applicability of swam intllignc (SI) in th fom of paticls swam optimization (PSO) usd to achiv th bst pfomanc fo th lctic machins and lctic divs. In addition, by analyzing and compaing th sults, it is shown that contol statgy basd on PSO is mo fficint than oths contol statgis to achiv th optimal pfomanc fo ful cll/supcapacito hybid lctic vhicls (FCHEV). It is vy impotant to not that, ths applications w achivd without any additional hadwa cost, bcaus th PSO is a softwa schm. Consquntly, PSO has positiv pomiss fo a wid ang of vaiabl spd div and hybid lctic vhicls applications. 6. Indx I List of pincipal symbols ω : synchonous spd ω : oto spd p : diffntial opato m, a : main, auxiliay stato windings sistanc : oto winding sistanc R fq,d : quivalnt ion-loss sistanc(d and q axis) L lm,l la : main, auxiliay stato lakag inductanc L md,l m q : magntizing inductanc (d& q axis) L l : oto lakag inductanc K : tuns atio auxiliay/main windings T : lctomagntic toqu J : intia of moto λ ds,qs : stato flux(d and q axis) λ d,q : oto flux(d and q axis) V ds,qs : stato voltag (d and q axis) i ds,qs : stato cunt (d and q axis) M : mutual inductanc 7. Rfncs Amin. A. M. A., Kofally. M. I., Sayd. A. A. and Hgazy. O.T. M., (009), Efficincy Optimization of Two Asymmtical Windings Induction Moto Basd on Swam Intllignc, IEEE Tansactions on Engy Convsion, Vol. 4, No. 1, Mach 009 Amin. A. M. A., Kofally. M. I., Sayd. A. A. and Hgazy. O.T. M., (006), Losss Minimization of Two Asymmtical Windings Induction Moto Basd on Swam Intllignc, Pocdings of IEEE- IECON 06, pp , Pais, Fanc, Nov Amin. A. M. A., Kofally. M. I., Sayd. A. A. and Hgazy. O.T. M., (007), Swam Intllignc-Basd Contoll of Two-Asymmtical Windings Induction Moto, accptd fo IEEE. EMDC07, pp , Tuky, May 007. Ebhat. R, Knndy. J, (1995), A Nw Optimiz Using Paticls Swam Thoy, Poc.

34 194 Elctic Machins and Divs Sixth Intnational Symposium on Mico Machin and Human Scinc (Nagoya, Japan), IEEE Svic Cnt, Piscataway, NJ, pp , A. Hamid Radwan H., Amin Am. M. A., Ahmd Rfaat S., and El-Gammal Adl A. A.,(006), Nw Tchniqu Fo Maximum Efficincy And Minimum Opating Cost Of Induction Motos Basd On Paticl Swam Optimization (PSO), Pocdings of IEEE- IECON 06, pp , Pais, Fanc, Nov Hgazy Oma, (006), Losss Minimization of Two Asymmtical Windings Induction Moto Basd on Swam Intllignc, M.Sc., Hlwan Univsity, 006. Hgazy Oma, and Van Milo Joi, (010), Paticl Swam Optimization fo Optimal Powtain Componnt Sizing and Dsign of Ful cll Hybid Elctic Vhicl, 1th Intnational Confnc on Optimization of Elctical and Elctonic Equipmnt, IEEE OPTIM 010 Hgazy Oma, Van Milo Joi, Vbugg Bavo and Ellabban Oma, (010), Optimal Pow Shaing and Dsign Optimization fo Ful Cll/Batty Hybid Elctic Vhicls Basd on Swam Intllignc, Th 5th Wold Batty, Hybid and Ful Cll Elctic Vhicl Symposium & Exhibition EVS-5 Shnzhn, China, Nov. 5-9, 010. Knndy. J and Ebhat.R, (001), Swam Intllignc, Mogan Kaufmann Publishs, Inc., San Fancisco, CA Kioskidis, I; Magais, N., (1996), Losss minimization in scala-contolld induction moto divs with sach contolls" Pow Elctonics, IEEE Tansactions, Volum: 11, Issu:, Mach 1996 Pags: 13 0 Popscu. M, Navapscu. V, (000),A mthod of Ion Loss and Magntizing Flux Satuation Modling in Stationay Fam Rfnc of Singl and Two Phas Induction Machins, IEE 000, Conf. pow Elc. & Vaiabl Spd Divs, Sundstom Oll and Stfanopoulou Anna, (006), Optimal Pow Split in Ful Cll Hybid Elctic Vhicl with diffnt Batty Sizs, Div Cycls, and Objctivs, Pocdings of th 006 IEEE Intnational Confnc on Contol Applications Munich, Gmany, Octob 4-6, 006. Van Milo Joi, Chng Yonghua, Timmmans Jan-Mac and Van dn Bossch Pt, (006), Compaison of Ful Cll Hybid Populsion Topologis with Sup- Capacito, IEEE, EPE-PEMC 006, Potoož, Slovnia Wu Ying, Gao Hongwi, (006),Optimization of Ful Cll and Supcapacito fo Ful-Cll Elctic Vhicls, IEEE Tansactions On Vhicula Tchnology, Vol. 55, No. 6, Novmb 006.

35 Elctic Machins and Divs Editd by D. Mioslav Chomat ISBN Had cov, 6 pags Publish InTch Publishd onlin 8, Fbuay, 011 Publishd in pint dition Fbuay, 011 Th subjct of this book is an impotant and divs fild of lctic machins and divs. Th twlv chapts of th book wittn by nownd authos, both acadmics and pactitions, cov a lag pat of th fild of lctic machins and divs. Vaious typs of lctic machins, including th-phas and singl-phas induction machins o doubly fd machins, a addssd. Most of th chapts focus on modn contol mthods of induction-machin divs, such as vcto and dict toqu contol. Among oths, th book addsss snsolss contol tchniqus, modulation statgis, paamt idntification, atificial intllignc, opation und hash o failu conditions, and modlling of lctic o magntic quantitis in lctic machins. Sval chapts giv an insight into th poblm of minimizing losss in lctic machins and incasing th ovall ngy fficincy of lctic divs. How to fnc In od to coctly fnc this scholaly wok, fl f to copy and past th following: Oma Hgazy, Am Amin, and Joi Van Milo (011). Swam Intllignc Basd Contoll fo Elctic Machins and Hybid Elctic Vhicls Applications, Elctic Machins and Divs, D. Mioslav Chomat (Ed.), ISBN: , InTch, Availabl fom: InTch Euop Univsity Campus STP Ri Slavka Kautzka 83/A Rijka, Coatia Phon: +385 (51) Fax: +385 (51) InTch China Unit 405, Offic Block, Hotl Equatoial Shanghai No.65, Yan An Road (Wst), Shanghai, 00040, China Phon: Fax: