Speed Contol of Switched Reluctance Moto Fed by PV Sytem Uing Ant Colony Optimization Algoithm A. S. Ohaba 1, E. S. Ali 2 and S. M. Abd Elazim 3 1 Reeach Intitute, Powe Electonic and Enegy Conveion, NRC Blg., El-Tahi St., Dokki, 12311-Giza, Egypt, Email: ohaba68@hotmail.com 2 Electic Powe and Machine Depatment, Faculty of Engineeing, Zagazig Univeity, Zagazig, Egypt, Email: ehabalimalialama@yahoo.com 3 Electic Powe and Machine Depatment, Faculty of Engineeing, Zagazig Univeity, Zagazig, Egypt, Email: ahaeldeep@yahoo.com Abtact- Thi pape popoe a peed contol of Switched Reluctance Moto (SRM) upplied by Photovoltaic (PV) ytem. The popoed deign of peed contolle i fomulated a an optimization poblem. Ant Colony Optimization (ACO) algoithm i employed to each fo optimal Popotional Integal (PI) paamete of peed contolle by minimizing the time domain objective function. The behaviou of the popoed ACO ha been etimated with the behaviou of Genetic Algoithm (GA) in ode to pove the upeio efficiency of the popoed ACO in tuning PI contolle ove GA. Alo, the behaviou of the popoed contolle ha been etimated with epect to the change of load toque, vaiable efeence peed, ambient tempeatue, and adiation. Simulation eult confim the bette behaviou of the optimized PI contolle baed on ACO compaed with optimized PI contolle baed on GA ove a wide ange of opeating condition. Simulation eult have hown the validity of the popoed technique in contolling the peed of SRM. Key-Wod: Ant Colony Optimization; Genetic Algoithm; High Speed SRM; Speed Contol; PI Contolle; Photovoltaic Sytem. 1. Intoduction Ove the pat decade, the witched eluctance moto (SRM) have been the focu of eveal eeache [1 2].The SRM ha a imple, ugged, and low-cot tuctue. It ha no Pemanent Magnet (PM) o winding on the oto. Thi tuctue not only educe the cot of the SRM but alo offe high peed opeation capability fo thi moto. Unlike the induction and PM machine, the SRM i capable of high peed opeation without the concen of mechanical failue that eult fom the high level centifugal foce. In addition, the invete of the SRM dive ha a eliable topology. The tato winding ae connected in eie with the uppe and lowe witche of the invete. Thi topology can pevent the hoot though fault that exit in the induction and pemanent moto dive invete. Moeove, high efficiency ove wide peed ange and contol implicity i known meit of the SRM dive [3-4]. Seveal Atificial Intelligence (AI) technique have been addeed in liteatue to olve poblem elated to the peed contol of SRM. In lat few yea, Fuzzy Logic Contol (FLC) ha eceived much attention in the contol application. In contat with the conventional technique, FLC fomulate the contol action of a plant in tem of linguitic ule dawn fom the behaviou of a human opeato athe than in tem of an algoithm yntheized fom a model of the plant [5-13]. It offe the following advantage: they do not equie an accuate model of the plant, they can be deigned on the bai of linguitic infomation obtained fom the peviou knowledge of the contol ytem and give bette pefomance eult than the conventional contolle. Howeve, a had wok i inevitable to get the effective ignal when deigning FLC. Alo, it equie moe fine tuning and imulation befoe opeational. Anothe AI appoach like Atificial Neual Netwok (ANN) fo deigning adaptive peed contol of SRM i peented in [14-15]. The ANN appoach ha it own advantage and diadvantage. The pefomance of the ytem i impoved by ANN baed contolle but, the main poblem of thi contolle i the long taining time, the electing numbe of laye and the numbe of neuon in each laye. H optimization technique have been applied to obut peed contol poblem [16-17]. Howeve, the impotance and difficultie in the election of weighting function of the H optimization poblem have been epoted. Alo, the additive and/o multiplicative uncetainty epeentation cannot teat ituation whee a nominal table ytem E-ISSN: 2224-350X 376 Volume 9, 2014
become untable afte being petubed. Moeove, the pole-zeo cancellation phenomenon aociated with thi appoach poduce cloed loop pole whoe damping i diectly dependent on the open loop ytem. On the othe hand, the ode of the H baed contolle i a high a that of the plant. Thi give ie to complex tuctue of uch contolle and educe thei applicability. Recently, global optimization technique have attacted the attention in the field of contolle paamete optimization. Genetic Algoithm (GA) i illutated in [18] fo optimal deign of peed contol of SRM. Depite thi optimization technique equie a vey long un time that may be eveal minute o even eveal hou depending on the ize of the ytem unde tudy. Swaming tategie in fih chooling and bid flocking ae ued in the Paticle Swam Optimization (PSO) and peented in [19] fo optimal deign of peed contol of diffeent moto [20-22]. Howeve, PSO uffe fom the patial optimim, which caue the le exact at the egulation of it peed and the diection. In addition, the algoithm cannot wok out the poblem of catteing and optimization [23, 24]. Alo, the algoithm pain fom low convegence in efined each tage, weak local each ability and algoithm may lead to poible entapment in local minimum olution. A elatively newe evolutionay computation algoithm, called Bacteia Foaging (BF) cheme ha been peented by [25 27] and futhe etablihed ecently by [28 34]. The BF algoithm depend on andom each diection which may lead to delay in eaching the global olution. In ode to olve the above mentioned poblem and dawback, thi pape popoe the ue of a new evolutionay algoithm known a Ant Colony Optimization (ACO) algoithm to deign a obut peed contolle fo SRM. ACO i multi-agent ytem in which the behaviou of each ingle agent, called atificial ant o ant i inpied by the behaviou of eal ant [35]. ACO ha been uccefully employed to optimization poblem in powe ytem uch a powe quality enhancement [36], optimal eactive powe dipatch [37]. The featue of technique peentation i diffeent fom othe method ince it can be implemented eaily; flexible fo many poblem fomulation and finally it capability in avoiding the occuence of local optima fo a given poblem [38]. Thi pape popoe a new optimization algoithm known a ACO fo contolling high peed SRM upplied by PV ytem. ACO i ued fo tuning the PI contolle paamete to contol the duty cycle of DC/ DC convete and theefoe peed contol of SRM. The deign poblem of the popoed contolle i fomulated a an optimization poblem and ACO i employed to each fo optimal contolle paamete. By minimizing the time domain objective function epeenting the eo between efeence peed and actual one, the ytem pefomance i impoved. Simulation eult aue the effectivene of the popoed contolle in poviding good peed tacking ytem ove a wide ange of load toque, ambient tempeatue and adiation with minimum ovehoot/undehoot and minimal ettling time. Alo, thee eult aue the upeioity of the popoed ACO method in tuning contolle compaed with GA. 2. Sytem unde Study The ytem unde tudy conit of PV ytem act a a voltage ouce fo a connected SRM. The peed contol loop i deigned uing ACO. The peed eo ignal i obtained by compaing between the efeence peed and the actual peed. The output of the ACO contolle i denoted a duty cycle. The chematic block diagam i hown in Fig. 1. Fig. 1. The oveall ytem fo SRM contol. 2.1 Contuction of SRM The contuction of a 8/6 (8 tato pole, 6 oto pole) pole SRM ha doubly alient contuction [39]. Uually, the numbe of tato and oto pole i even, and the contuction i well explained a in Fig 2. The winding of the SRM ae imple than thoe of othe type of moto, and winding exit only on tato pole, and i imply wound on it with no winding on the oto pole. The winding of oppoite pole i connected in eie o in paallel foming a numbe of phae, and exactly half the numbe of tato pole, and the excitation of a ingle phae excite two tato pole. The oto ha a imple laminated alient pole tuctue without winding. SRM have the advantage of educing coppe loe while it oto i winding. It tamping ae made pefeably of ilicon teel, epecially in highe efficiency application. Fo E-ISSN: 2224-350X 377 Volume 9, 2014
aeopace application the oto opeate at vey high peed, equiing the ue of cobalt, ion and othe vaiant. The ai gap i kept a minimum a poible (0.1 mm to 0.3 mm), and the oto and tato pole ac hould be kept the imila. It i advantageou if the oto pole ac i lage than the tato pole ac [40-41]. The contuction of an 8/6 SRM (tato and oto) i hown in Fig. 2. Fig. 2. The SRM 8/6 pole contuction. Toque i developed in SRM due to the tendency of the magnetic cicuit to adopt the configuation of minimum eluctance i.e. the oto move in line with the tato pole thu maximizing the inductance of the excited coil. The magnetic behaviou of the SRM i highly nonlinea. The tatic toque poduced by one phae at any oto poition i calculated uing the following equation [40-41]. Co enegy W (, i) di (1) Static toque T dw / d tatic (2) Fom equation (1) and (2) a imila tatic toque matix can be etimated whee cuent will give the ow index and will give the column index a in [40-41]. The value of developed toque can be calculated fom the tatic toque look up table by uing econd ode intepolation method by ued them the cuent value and. The value of actual peed can be calculated fom the following mechanical equation: d / dt ( T (, i) T mech ) / J (3) whee, the peed eo i obtained fom the diffeence between the oto peed and it efeence. The value of oto angula diplacement can be calculated fom the following equation: d / dt (4) whee δ i the angle coeponding to the diplacement of phae A in elation to anothe phae i given by: 1 1 2 ( ) (5) N N whee N and N ae the numbe of oto and tato pole epectively. Alo, the poitive peiod of phae i detemined by the following equation: 1 duty peiod 2 ( ) C qn (6) whee q i numbe of phae and C i the commutation atio. C can be calculated by the following equation. 1 1 C 2 ( ) (7) whee, ae the tato and oto pole ac epectively. Duation of negative cuent pule i depended on the toed enegy in phae winding. On unning, the algoithm i coected by PI contolle. Thi method i uitably with pecial ange fo tun on angle. The paamete of SRM ae hown in appendix. 2.2 Photovoltaic Sytem Sola cell mathematical modelling i an impotant tep in the analyi and deign of PV contol ytem. The PV mathematical model can be obtained by applying the fundamental phyical law govening the natue of the component making the ytem [42]. To ovecome the vaiation of illumination, tempeatue, and load eitance, voltage contolle i equied to tack the new modified efeence voltage wheneve load eitance, illumination and tempeatue vaiation occu. I-V chaacteitic of ola cell ae given by the following equation [43-44]: q o V I R AKT c c I I I e 1 (8) c ph o I I I AKT ph o c V ln I R (9) c q I c o o q o V n IR n AKT I I I e 1 (10) ph o E-ISSN: 2224-350X 378 Volume 9, 2014
WSEAS TRANSACTIONS on POWER SYSTEMS teted; buck convete i a tep down convete, while boot convete i a tep up convete [45-46]. In thi pape, a hybid (buck and boot) DC/DC convete i ued. The equation fo thi convete type in continuou conduction mode ae: k (15) V V B 1 k ph k 1 (16) I I ph B k whee k i the duty cycle of the Pule Width Modulation (PWM) witching ignal. V and I B B ae the output convete voltage and cuent epectively. The Matlab/Simulink of PV ytem can be imulated a hown in Fig. 3. n AKT I ph I o I (11) V ln n IR q I o o whee; G (12) I I k T T ph 1000 c i q E o 1 g 1 3 T T AK T (13) I I e o o T The module output powe can be detemined imply fom (14) P V.I whee; I and V : Module output cuent and voltage, : Cell output cuent and voltage, I and V c c : The light geneation cuent and I and ph voltage, V ph : Cell evee atuation cuent, I : The hot cicuit cuent, I c Io : The evee atuation cuent, R T K qo KT G E g A T : The module eie eitance, : Cell tempeatue, : Boltzmann' contant, : Electonic chage, Fig. 3. Matlab/Simulink fo PV ytem. : (0.0017 A/ C) hot cicuit cuent tempeatue coefficient, : Sola illumination in W/m2, : Band gap enegy fo ilicon, 3. Objective Function A pefomance index can be defined by the Integal of Time multiply Abolute Eo (ITAE). Accodingly, the objective function J i et to be: t (17) J = t e dt t 0 whee e w w efeence actual Baed on thi objective function J optimization t poblem can be tated a: Minimize J ubjected t to: (18) K min K K max, K imin K i K imax p P p Thi pape focue on optimal tuning of PI contolle fo peed tacking of SRM uing ACO algoithm. The aim of the optimization i to each fo the optimum contolle paamete etting that minimize the diffeence between efeence peed and actual one. On the othe hand, in thi pape the : Ideality facto, : Refeence tempeatue, : Cell ating atuation cuent at T, o : Seie connected ola cell, n : Cell tempeatue coefficient. k i Thu, if the module paamete uch a module eie eitance ( R ), evee atuation cuent ( I ), and ideality facto (A) ae known, the I-V o chaacteitic of the PV module can be imulated by uing equation (12 and 13). PV ytem i ued in thi pape to powe SRM. The paamete of PV ytem ae given in appendix. I 2.3 DC-DC Convete The choice DC-DC convete technology ha a ignificant impact on both efficiency and effectivene. Many convete have been ued and E-ISSN: 2224-350X 379 Volume 9, 2014
goal i peed contol of SRM and finally deigning a low ode contolle fo eay implementation. 4. Oveview of ACO and GA Optimization Technique 4.1 Ant Colony Optimization The fit ACO algoithm wa intoduced by Maco Doigo [35]. The development of thi algoithm wa inpied by the obevation of ant colonie. The behaviou that povided the inpiation fo ACO i the ant foaging behaviou, and in paticula, how ant can find hotet path between food ouce and thei net. When eaching fo food, ant initially exploe the aea uounding thei net in a andom manne. While moving, ant leave a chemical pheomone tail on the gound. The pheomone quantity depend on the length of the path and the quality of the dicoveed food ouce [47]. An ant chooe an exact path in connection with the intenity of the pheomone. The pheomone tail evapoate ove time if no moe pheomone i laid down. Othe ant ae attacted to follow the pheomone tail. Theefoe, the path will be maked again and it will attact moe ant to ue the ame path. The pheomone tail on path leading to ich food ouce cloe to the net will be moe fequented and will theefoe gow fate. In thi way, the bet olution ha moe intenive pheomone and highe pobability to be choen. The decibed behaviou of eal ant colonie can be ued to olve optimization poblem in which atificial ant each the olution pace by taniting fom node to node. The atificial ant movement uually aociated with thei peviou action that toed in the memoy with a pecific data tuctue [48]. The pheomone conitencie of all path ae updated only afte the ant finihed it tou fom the fit node to the lat node. Evey atificial ant ha a contant amount of pheomone toed in it when the ant poceed fom the fit node. The pheomone that ha been toed will be evenly ditibuted on the path afte atificial ant finihed it tou. The amount of pheomone will be high if atificial ant finihed it tou with a good path and vice vea. The pheomone of the oute pogeively deceae by evapoation in ode to avoid atificial ant tuck in local optima olution [48-49]. The ACO algoithm can be divided into the following tep: Step 1: Initialization In thi tep, the following paamete ( n, m, t, d,,,, q, max max a and ) o of ACO algoithm ae initialized. whee n : Numbe of node, m : Numbe of ant, t : Maximum iteation, max d : Maximum ditance fo each ant tou, max : Paamete detemine the elative impotance of pheomone veu ditance ( > 0), : Heuitically defined coefficient (0 < < 1), : Pheomone decay paamete (0 < < 1), q : Paamete of the algoithm (0 < q < 1), a a : Initial pheomone level, o The maximum ditance fo evey ant tou d max can be calculated uing the following equation: n 1 d max d (19) max i i 1 d i = max(u) (20) d : Ditance between two node, i u : Unviited node, : Cuent node. Step 2: Povide fit poition Geneate fit poition andomly; the fit node will be elected by geneating a andom numbe accoding to a unifom ditibution, anging fom 1 to n. Step 3: Tanition ule The pobability fo an ant k at node i to chooe next node j can be expeed a: ( t) ( t) k ij ij P ( t) ; i, j T k (21) ij ( t) k ij ij ij T whee : The pheomone tial depoited between ij ij k T node i and j by ant k, : The viibility and equal to the invee of the ditance ( 1/ d ), ij ij : The path effectuated by the ant k at a given time. Step 4: Local pheomone updating Local updating pheomone i diffeent fom ant to othe becaue each ant take a diffeent oute. The E-ISSN: 2224-350X 380 Volume 9, 2014
initial pheomone of each ant i locally updated a hown below. ( t 1) (1 ) ( t) (22) ij ij o Step 5: Fitne function Afte all ant attactive to the hotet path that having a tonget pheomone, the bet olution of the objective function i obtained. Step 6: Global pheomone updating Amount of pheomone on the bet tou become the tonget due to attactive of ant fo thi path. Moeove, the pheomone on the othe path i evapoated in time. The pheomone level i updated by applying the following equation: ( t 1) (1 ) ( t) ( t) (23) ij ij ij Step 7: Pogam temination The pogam will be teminated when the maximum iteation i eached o the bet olution i obtained without the ant tagnation. The popoed pocedue tep ae hown in Fig. 4. The paamete of ACO ae hown in appendix. Stat Initialization; Inet paamete, contol limit and initial pheomone Geneate the initial poition andomly of each ant Apply tate tanition ule Apply local pheomone updating ule Fitne function evaluation Apply global pheomone updating ule the uele ha woked pefectly fo centuie and it i a good method fo optimization. GA i uch an optimization method. It i baed on the mechanic of natual election and natual genetic. The each poce i vey imila to the natual evolution of biological ceatue in which ucceive geneation of oganim ae given bith and aied until they ae able to beed. Jut like in animal kingdom, only the fittet will uvive to poduce while the weaket will be eliminated [50]. Fou main paamete affect the pefomance of GA: population ize, numbe of geneation, coove ate, and mutation ate. Lage population ize and lage numbe of geneation inceae the likelihood of obtaining a nea-global optimum olution, but ubtantially inceae poceing time. Coove among paent chomoome (olution vecto) i a common natual poce and taditionally i given a ate that ange fom 0.6 to 1.0. In coove, the exchange of paent infomation poduce an offping. A oppoed to coove, mutation i a ae poce that eemble a udden change to an offping. Thi can be done by andomly electing one chomoome fom the population and then abitaily changing ome of it infomation. The benefit of mutation i that it andomly intoduce new genetic mateial to the evolutionay poce, pehap theeby avoiding tagnation aound local minima. A mall mutation ate le than 0.1 i uually ued [51]. A flowchat fo the GA algoithm i hown in Fig. 5. The paamete of GA ae hown in appendix. Stat Input paamete boundaie and maximum geneation numbe iteation numbe Geneate initial population Max iteation i eached Calculate the fitne of each individual of population Stop Fig. 4. Flow chat of the popoed ACO algoithm. Maximal numbe of geneation? No Ceate new Geneation Selection, Coove, and Mutation 4.2. Genetic Algoithm (GA) In the animal kingdom, animal evolve and geneate accoding to the ole of uvival of the fittet. In natue, animal fight contantly fo food, helte and mate. Thu, only the fittet will uvive and the weak will peih. Thi mechanim of weeding out Ye Output of the bet individual End Fig. 5. Flow chat of GA algoithm. E-ISSN: 2224-350X 381 Volume 9, 2014
WSEAS TRANSACTIONS on POWER SYSTEMS Moeove, the actual peed tack the efeence peed apidly. The ettling time i appoximately 0.06, and 0.064 econd fo ACO and GA epectively. Hence, the popoed ACO i capable of poviding ufficient peed tacking compaed with GA. 5. Reult and Simulation Load Toque (N.m) In thi ection, the upeioity of the popoed ACO algoithm ove GA in deigning PI contolle fo peed contol of SRM i illutated. Fig. 6. how the vaiation of objective function with two optimization technique. The objective function deceae monotonically ove geneation of ACO and GA. Moeove, ACO convege at a fate ate (35 geneation) compaed with GA (50 geneation). Moeove, computational time (CPU) of both algoithm i compaed baed on the aveage CPU time taken to convege the olution. The aveage CPU fo ACO i 32.1 while it i 43.9 fo GA. The popoed ACO methodology and GA ae pogammed in MATLAB 7.1 and un on an Intel(R) Coe(TM) I5 CPU 2.53 GHz and 4.00 GB of RAM. The mentioned CPU time i the aveage of 10 execution of the compute code. Table 1. how the paamete of PI contolle, aveage ettling time, and aveage pecentage ovehoot baed on two optimization technique. It can be een that the paamete fo ACO ae malle than GA. Hence, compaed to GA, ACO geatly enhance the time domain chaacteitic fo SRM. Objective function Speed (.p.m) Fig. 7. Step change in load Toque. Fig. 8. Change in peed due to tep load toque. Iteation Fig. 6. Change of objective function fo diffeent optimization technique. ACO GA KP Ki 0.0349 0.0126 8.0125 8.6354 Aveage ettling time (econd) 0.057 0.063 Contol ignal Table. 1. Compaion between ACO and GA. Aveage pecentage ove hoot 16.13 17.02 5.1 Repone unde tep change in load toque Fig. 7 how the tep change in load toque of SRM. The peed epone and contol ignal fo thi cae ae hown in Fig. 8-9 epectively. Thee Figue indicate the capability of the ACO in educing the ettling time and ytem ocillation ove GA. E-ISSN: 2224-350X Fig. 9. Change in contol ignal due to tep load toque. 382 Volume 9, 2014
WSEAS TRANSACTIONS on POWER SYSTEMS Contol ignal. 5.2 Repone unde vaiable peed and load toque: In thi cae, the ytem epone unde vaiation of efeence peed and load toque ae obtained. Fig. 10. how the vaiation of the load toque a an input ditubance while the paamete of PV ytem ae contant. Moeove, the ytem epone fo diffeent contolle ae hown in Fig. 11 and 12. It i clea fom thee Fig.; the popoed ACO algoithm outpefom and outlat GA in contolling the peed of SRM and educing ettling time effectively. Theefoe, compaed with GA baed contolle, ACO baed contolle geatly enhance the ytem pefomance. Fig. 12. Change in contol ignal. Load toque (N.m). 5.3 Repone unde vaiable load toque, efeence peed and PV paamete In thi cae, vaiation of load toque, efeence peed, and PV paamete ae applied. Fig. 13 how the change of load toque, adiation and tempeatue epectively. Moeove, the ytem epone fo both contolle ae hown in Fig. 14 and 15. It i clea fom thee Fig, that the popoed ACO i moe efficient in impoving peed contol of SRM compaed with GA. Alo, the popoed contolle ha a malle ettling time and ytem epone i quickly diven with the efeence peed. Thu, the potential and upeioity of the popoed ACO ove GA i demontated. Tempeatue Speed (.p.m) Radiation Load toque Fig. 10. Change in load toque. Fig. 11. Change in peed. Fig. 13. Change in load toque, adiation and tempeatue. E-ISSN: 2224-350X 383 Volume 9, 2014
WSEAS TRANSACTIONS on POWER SYSTEMS Speed (.p.m) Table. 2. Value of pefomance indice. Pefomance index IAE ISE ITSE ACO 12.0937 19.1421 72.1439 GA 13.3529 20.9312 76.3588 6. Concluion In thi pape, a new method fo peed contol of SRM (8/6 pole) i popoed via ACO. The deign poblem of the popoed contolle i fomulated a an optimization poblem and ACO i employed to each fo optimal paamete of PI contolle. By minimizing the time domain objective function, in which the diffeence between the efeence and actual peed ae involved; peed contol of SRM i impoved. Simulation eult emphai that the deigned ACO baed PI contolle i obut in it opeation and give a upeb pefomance ove GA fo the change in load toque, efeence peed, adiation, and tempeatue. Beide the imple achitectue of the popoed contolle, it ha the potentiality of implementation in eal time envionment. Contol ignal Fig. 14. Change of peed fo diffeent contolle. Appendix The optimization paamete ae a hown below: a) Genetic paamete: Max geneation=100; Population ize=50; Coove pobabilitie=0.75; Mutation pobabilitie =0.1. b) ACO paamete: n =10, m =5, t =5, d max 5.4 Robutne and pefomance indice To demontate the obutne of the popoed contolle, thee diffeent pefomance indice ae ued. Thee indice ae: The Integal Abolute value of the Eo (IAE), the Integal of the Squae value of the Eo (ISE), and the Integal of the Time multiplied Squae value of the Eo (ITSE). It i woth mentioning that the lowe the value of thee indice i, the bette the ytem epone in tem of time domain chaacteitic [52]. Numeical eult of pefomance obutne fo vaiation of load toque, efeence peed, and PV paamete ae lited in Table 2. It can be een that the value of thee indice coeponding to ACO ae malle compaed to thoe of GA. Thi demontate that the ovehoot, undehoot, and ettling time ae educed by applying the popoed ACO baed contolle. E-ISSN: 2224-350X max =49, =2, =0.6, =0.1, q =0.6, o =0.1. a c) SRM paamete: N =8, N =6, Rating peed =13700.p.m, C =0.8, q =4, Phae eitance of tato=17 ohm, Phae inductance of aligned poition=0.605 H, Phae inductance of unaligned poition=0.1555 H, Step angle=15o. d) A = 1.2153; E = 1.11; I = 2.35e-8; I =4.8; o c g T =300; K= 1.38e-23; n =36; q =1.6e-19; k o i =0.0021. Fig. 15. Change in contol ignal fo diffeent contolle. Refeence [1] T. J. E. Mille, Switched Reluctance Moto and thei Contol, Oxfod Science Publication, London, 1993. [2] A. Veltman, D. W. J. Pulle, and R. D. Doncke, Fundamental of Electical Dive, ISBN: 978-1-4020-5503-4, Spinge-Velag 2007. 384 Volume 9, 2014
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