Post-Fault Speed Sensor-Less Operation Based on Kalman Filter for a Six-Phase Induction Motor

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Pot-Fault Speed Seno-Le Opeation Baed on Kalman Filte fo a Six-Phae Induction Moto Ilam M. Soliman 1, Elhuien A. Mahmoud 2, Ayman S. Abdel-Khalik 3, Huein F.

1 Pot-Fault Speed Seno-Le Opeation Baed on Kalman Filte fo a Six-Phae Induction Moto Ilam M. Soliman 1, Elhuien A. Mahmoud 2, Ayman S. Abdel-Khalik 3, Huein F. Soliman 4 1 Depatment of MEA-Sytem & Infatuctue, Altom Company, 2 Depatment of Offhoe Opeation, National Dilling Company, 3 Depatment of Electical Engineeing, Alexandia Univeity, 4 Depatment of Electical Engineeing, Ain Sham Univeity, Abtact Thi tudy intoduce a pot-fault peed etimato fo aymmetical ix-phae (6-ph) induction machine (IM) unde ingle open phae condition. The popoed technique i baed on Kalman Filte (KF) etimato. The multiphae machine model cheme i aociated with popotional integal (PI) peed contol. Alo, the indiect field-oiented contol (IFOC) i intended to be ued and followed by a hyteei cuent contolle (HCC). Diffeent opeating condition have been caied out to invetigate the etimato fidelity. The imulation tudy i pefomed uing MATLAB/ SIMULINK platfom. The imulation eult how a pomiing pefomance of the popoed peed etimato. Keywod aymmetic ix phae, multiphae machine, Kalman filte, enole opeation, peed etimation I. INTRODUCTION All Electical moto ae a vital pat fo any electical ytem, epecially in the indutial application. Many development ae caied out to enhance moto opeation, contol and potection. AC induction moto i the mot common and pactical moto among the othe type of the electical moto. Alo, it can be conideed a the bet choice in tem of obutne, lowe cot, minimal maintenance and lowe weight at a elatively wide powe ange. Multiphae AC induction moto wee eleaed in the middle of 199 due to the need of exta high powe application, including ailway taction induty, wind geneation and electic hip populion, etc.,[1,2]. Multiphae winding layout can be boadly claified into ymmetical o aymmetical winding layout. The phae belt angle between two adjacent phae i known to be the main facto to identify the machine winding cheme [3, 4]. Reliability i the main concen in the mot of indutial application. Theefoe, tudying the electical dive behaviou duing a fault condition i the key to enue the ytem inceity [, 6]. So fa, vecto contol i uually the baic technique ued fo induction machine contol [7, 8]. Alo, peed eno i commonly equied fo the indiect field oiented contol (IFOC) in ode to meaue the oto poition. Moeove the flux eno ae expenive and uneliable [9].Thu, eveal method ae peented to eliminate the peed eno fo the ix-phae induction moto. The fuzzy logic contol wa hown inenitive to paamete vaiation but ha a limited adaptable ange [1-13]. Anothe method i the model efeence adaptive ytem (MRAS) which i one of the famou method ued thank to it high obutne and fat epone Nevethele, thi method uffe fom noie and ditubance affecting the ytem [14]. Alo, high contol effot and chatteing ae the main poblem fo liding mode obeve method [1]. Theefoe, thi pape popoe an analyi of a peed etimation method with Kalman filte to eplace the peed eno. Kalman filte (KF) i uitable algoithm to the cheme which ha unknown noie uch a cuent ipple by pule width modulation (PWM), noie by modelling eo and meauement DOI: /IJRTER ZZ9SP 41

2 Intenational Jounal of Recent Tend in Engineeing & Reeach (IJRTER) Volume 4, Iue 2; Febuay [ISSN: ] eo. The popoed etimato i invetigated in diffeent cenaio. Thi i caied out not only fo loading vaiation and peed tanition fom ated peed into vey low peed, but alo teted duing the pot fault opeation. II. MODELLING OF SIX-PHASE INDUCTION MOTOR An aymmetical ix-phae winding can be obtained by plitting the tato winding of a thee phae tato into two identical halve (dual thee phae goup). The dual thee phae goup denoted a A,B,C phae goup and D,E,F phae goup, have an angula diplacement of 3 electical degee. The mathematical epeentation (α-β model) of a ix-phae induction moto can be obtained uing the decoupling (Clake ) tanfomation matix, hown in equation (1) C C 1 co co4 co co8 co9 in in4 in in8 in9 1 1 co co8 co co4 co9 3 in in8 in in4 in (1), whee [16]. The Clak tanfomation convet the oiginal ix phae cuent to a new et of othogonal cuent component called equence cuent. Thee equence cuent conit of thee pai. Each pai of cuent component fom an independent ubpace, namely, the fundamental, thid and zeo equence plan. The fundamental plan component ae denoted by the uffix α and β. While, the econday plan component ae efeed by the uffix x and y. And the zeo equence plan component ae given the uffix - and +. The fundamental plan i the only enegy conveion plan in the inuoidal ditibuted multiphae machine. While, the zeo equence component - i ignoed in the iolated ta machine. The eulting model fo a inuoidal ditibuted winding ix phae machine with two iolated ta connection i given in equation (2, 3). v i R pl pm v R pl pm i x pm M R pl M i i M pm M R pl (2) vx R pl1 ix v R pl i 1 y y x R pl 1 i x R i pl1 y (3), whee R and R ae the tato and oto eitance, L and L ae the tato and oto inductance, and L m i the mutual inductance. The voltage equation (2) can be ewitten All Right Reeved 42

3 Intenational Jounal of Recent Tend in Engineeing & Reeach (IJRTER) Volume 4, Iue 2; Febuay [ISSN: ], whee λ λ d, q v d 2 M σ 1, LL, d 1 1 i d i d i q d p q v d dt ' L d 1 1 i q i q i d q p d v q dt ' L,, ae the tato voltage and cuent component v q i d i q ae the oto flux component, and M μ LL, L τ R eq, τ L R & dq i the oto angula peed. Alo, 2 M R R R eq 2 L (4) epectively and The toque equation i given by: pm T λ i λ i () m d q q L d III. PROPOSED KALMAN FILTER SPEED ESTIMATOR Kalman filte (KF) i ued fo the enole opeation of the ix phae induction moto unde tudy. KF i one of the etimation technique that ue a eie amount of meauement ove a cetain time peiod. The algoithm of the Kalman filte ha eveal advantage; thi filte i able to take into account quantitie that ae patially o completely neglected in othe technique (uch a the vaiance of the initial etimate of the tate and the vaiance of the model eo). It povide infomation about the quality of the etimation by poviding, in addition to the bet etimate, the vaiance of the etimation eo. It ecuive tuctue allow it eal-time execution without toing obevation o pat etimate. The dawback of KF method ae the high memoy and poceing peed equiement due to matice manipulation. Two paamete ae impotant in the KF appoach. The fit paamete i the ode of the KF matice, ince it detemine the ize of the memoy equied to toe the data, and the peed of updating the value of the etimated oto peed. The econd paamete i the oto peed which included in the tate vecto. If the econd paamete i not included in the tate vecto that mean it i conideed a a contant and thi lead to a poo etimation in the tanient condition. KF can be ued a an obeve in ode to etimate the oto angula peed in the eno-le opeation of ix-phae induction moto. Two ouce of noie may affect KF pefomance. The fit i the poce noie uch a themal noie, while the econd i the meauement noie [17]. The pedictive model of the KF can be fomulated a in equation (6, 7) [18, 19]. x Ax Bu w (6) k k1 k1 k1 z Hx v (7) k k k, whee x: State of the ytem, u: A known input to the ytem, z : Meaued output. k : Time index. w: Poce noie. v: Meauement noie. A, B& H : Time-vaying dynamic coefficient, input coupling, and meauement enitivity matice All Right Reeved 43

4 Intenational Jounal of Recent Tend in Engineeing & Reeach (IJRTER) Volume 4, Iue 2; Febuay [ISSN: ] The goal of the KF i to etimate the tate vecto x which cannot be diectly meaued, whee the meauement vecto z i altenatively meaued. The tate vecto i elated to the meauement vecto by the meauement equation (4), while the ytem i govened by the poce equation (3). The KF can etimate the tate vecto even if the meauement and poce ae contaminated by noie and even if the ytem model i not accuate. The mathematical fom of the Kalman filte conit of the following five equation [11, 12]: xˆ Axˆ Bu (8) k k1 k T k k1 P AP A Q (9) T 1 ˆ K P H HP H R (1) T k k k x xˆ K z Hx (11) k k k k k P I K H P (12) k k k, whee Q& R : Poce and meauement noie covaiance matice epectively, : Kalman gain, : Eo covaiance matix and : Identity matix. The : mean a pio etimation. The ^ : mean etimated value. : Matix tanpoe. K P I T IV. PROPOSED SENSORLESS CONTROLLER The popoed ytem tuctue i hown in Fig.1. The ytem unde tudy compomie a ix-phae induction moto connected to ix phae invete. A PI peed contolle i ued to detemine the command toque baed on the peed eo. Fo the ake of compaion, the peed feedback may be taken fom the actual o the etimated peed. The feedback peed i whethe the actual peed fom the peed eno o the etimated peed calculated fom Kalman Filte obeve. The command toque i utilized to geneate the equied dq cuent component baed on tandad indiect oto field oiented contol (IRFOC). The efeence cuent i * d and * i q ae tanfomed to thei tationay fame uing Pak tanfom. Clak tanfomation i then ued to obtain the coeponding efeence phae value. Hyteei cuent contolle (HCC) i then ued to contol the ix-phae invete. The paamete of the ix-phae induction machine ued in the imulation tudy ae given in Table (1). Table 1: Paamete of the ix-phae induction machine Paamete Symbol Value Unit Stato eitance R 1 Ω Roto eitance R 1.1 Ω Stato leakage inductance L mh Roto leakage inductance L 64.8 mh Mutual inductance M.6 mh Moment of inetia J.2 kg m 2 Numbe of pole pai P 3 - Rated toque T n 1 N m Rated tato flux Ψ 1 Wb m The cae tudy conide tating the machine unde nomal healthy opeation. Afte the machine eache it teady-tate peed of 1 pm, a ingle open phae fault i aumed to occu. All Right Reeved 44

5 Intenational Jounal of Recent Tend in Engineeing & Reeach (IJRTER) Volume 4, Iue 2; Febuay [ISSN: ] machine i then ubjected to peed eduction to pm. Anothe eduction to 2 pm i then applied. The lat peed eduction i afte 8 econd fom tating to each to 1 pm (1% fom the machine ated peed). Alo two cenaio of the machine loading ae taken into account to invetigate the etimato pefomance a follow: 4.1. Scenaio 1 Stating at full load (1N.m) The machine i ubjected to loading eduction to the half of the machine ated load (N.m) afte 1 econd Finally, the machine loading inceae again afte 12 econd to it ated load (1N.m) 4.2. Scenaio 2 Stat and opeate auming a paabolic toque peed load cuve. Fig 1: Block diagam of the popoed model unde tudy V. SIMULATION RESULTS The imulation eult ae peented fo the aumed cenaio. Fo each cenaio, the following plot ae hown: Speed veu time: efeence peed, actual peed and the etimated peed ae peented duing the whole time peiod with all peed eduction behaviou. Toque veu time: the toque pofile i alo hown to decibe the loading of the machine duing the imulation time. Pecentage eo between the efeence peed and the actual peed: ωef ωact % eo x1 (13) ωef The aim fo thi atio i to identify the effect of the etimato on the actual peed. The actual peed convege to the efeence peed in all tanition level. Pecentage eo between the actual peed and the etimated peed: ωact ωet % eo x1 (14) ωact Thi eo i conideed a the main indication of the peed etimato efficiency and All Right Reeved 4

6 Intenational Jounal of Recent Tend in Engineeing & Reeach (IJRTER) Volume 4, Iue 2; Febuay [ISSN: ] Fig. 2 how the eult fo cenaio (1).Thi cenaio i conideed fo dynamic loading which i the mot evee cae. Howeve, the etimato how a good epone with all tanition level. The actual peed follow the efeence peed, and the etimated peed keep a good tacking to the actual peed fo all peed tanient fom the ated peed till vey low peed value. Although the machine i ubjected to loading vaiation fom the ated value to the half of the ating and then inceaed again to it ated load, the etimato dynamic pefomance eem acceptable. The pecentage eo i below 1% duing teady tate in geneal. Thi inceae in the etimation eo i due to the loading at vey low peed and unde fault condition. Fig. 3 diplay the eult fo cenaio (2). Thi cenaio i conideed a the mot pactical one. A load with paabolic toque peed chaacteitic (centifugal pump o popelle) ha been popoed. Excellent eult have alo been obtained duing healthy and faulty time peiod. Alo the etimato peent a good behaviou not only in diffeent loading, but alo in the vey low peed opeation. The pecentage eo ae alo vey good a they ae below 2% duing teady tate. 1 8 Refeence peed Actual peed Etimated peed 2 1 Toque poduced v Time Speed (pm) 6 4 Toque (N.m) 1 2 Time (ec) Time(ec) (2.a) (2.b) 2 % eo peed detection [(ef- act)/ef] 2 1 % eo peed detection [(act - et)/act] % eo 1-1 % eo Time (ec) (2.c) -2 Time (ec) (2.d) Fig 2: Simulation eult fo cenaio (1). (a) peed, (b) toque, (c) % eo between actual and efeence peed, (d) % eo between etimated and actual All Right Reeved 46

7 Intenational Jounal of Recent Tend in Engineeing & Reeach (IJRTER) Volume 4, Iue 2; Febuay [ISSN: ] 1 8 Refeence peed Actual peed Etimated peed 2 1 Toque poduced v Time Speed (pm) Time (ec) (3.a) Toque (N.m) Time(ec) (3.b) 1 % eo peed detection [(ef- act)/ef] 1 % eo peed detection [(act - et)/act] % eo % eo Time (ec) (3.c) -1 Time (ec) (3.d) Fig 3: Simulation eult fo cenaio (2). (a) peed, (b) toque, (c) % eo between actual and efeence peed, (d) % eo between etimated and actual peed In geneal, Thee eult eflect the excellent pefomance of the popoed Kalman filte etimato integated with the ix phae induction moto in both high peed and low peed condition. The popoed peed etimato ha alo a good dynamic epone unde tep loading. VI. CONCLUSIONS Thi pape peent the peed eno le opeation of an aymmetical ix-phae induction moto unde ingle open phae fault baed on Kalman filte etimato. Standad indiect oto field oiented contol wa employed to geneate the machine efeence cuent component. The popoed ytem wa imulated uing MATLAB/Simulink. The popoed peed etimato ha hown an acceptable tacking and a good dynamic epone unde both healthy a well a faulty cae. Futue wok will conide the expeimental implementation of the popoed etimato. REFERENCES I. Bojoi, R., et al. Multiphae electical machine and dive: A viable olution fo enegy geneation and tanpotation electification. in Electical and Powe Engineeing (EPE), 216 Intenational Confeence and Expoition on IEEE. II. Baltatanu, A. and M.-L. Floea. Multiphae machine ued in electic vehicle populion. in Electonic, Compute and Atificial Intelligence (ECAI), 213 Intenational Confeence on IEEE. III. Padmanaban, Sanjeevikuma, and Michael Pecht. "An iolated/non-iolated novel multilevel invete configuation fo a dual thee phae ymmetical /aymmetical ta-winding convete." Engineeing Science and Technology, an Intenational Jounal 19.4 (216): All Right Reeved 47

8 Intenational Jounal of Recent Tend in Engineeing & Reeach (IJRTER) Volume 4, Iue 2; Febuay [ISSN: ] IV. Matya, A.R., K.A. Bio, and D. Fodoean, Multi-phae ynchonou moto olution fo teeing application. Poge In Electomagnetic Reeach, : p V. Duan, Maio J., et al. "A Simple, Fat, and Robut Open-Phae Fault Detection Technique fo Six-Phae Induction Moto Dive." IEEE Tanaction on Powe Electonic 33.1 (218): VI. Che, Hang Seng, et al. "Potfault opeation of an aymmetical ix-phae induction machine with ingle and two iolated neutal point." IEEE Tanaction on Powe Electonic 29.1 (214): VII. Liying, Q., et al. Deign and analyi of a decoupling cuent contolle fo induction machine. in Powe Electonic and Motion Contol Confeence (IPEMC), 212 7th Intenational IEEE. VIII. Abdel-Khalik, A.S., et al. Vecto contol of multiphae induction machine unde open-cicuit phae fault. in Powe Engineeing, Enegy and Electical Dive (POWERENG), 213 Fouth Intenational Confeence on IEEE. IX. Singh, G.K., K. Nam, and S. Lim, A imple indiect field-oiented contol cheme fo multiphae induction machine. IEEE Tanaction on Indutial Electonic, 2. 2(4): p X. Mohammad Razaz, Reza Kianinezhad, Ali Hajay, "Apect of peed and cuent egulation in new model applied to ix-phae induction moto", Electical Engineeing (ICEE) nd Ianian Confeence on, pp , 214. XI. Sh. Nategh, R. Kianinezhad, S. Gh. Seifoadat, A. Pihahang, A. Ajomand, "A new obut model baed enole contol fo ix phae induction machine", Indutial Electonic and Application 29. ICIEA 29. 4th IEEE Confeence on, pp , 29. XII. Kaga, A., et al. "Impovement in peed contol of a ix-phae induction moto uing fuzzy contol and genetic algoithm." Electical Machine and Powe Electonic and 211 Electomotion Joint Confeence (ACEMP), 211 Intenational Aegean Confeence on. IEEE, 211. XIII. Moghadaian, M., et al. "Intelligent enole peed contol of ix-phae induction machine." IECON th Annual Confeence on IEEE Indutial Electonic Society. IEEE, 211. XIV. Fnaiech, M. A., F. Betin, and G. A. Capolino. "MRAS applied to enole contol of a ix phae induction machine." Indutial Technology (ICIT), 21 IEEE Intenational Confeence on. IEEE, 21. XV. Jafaifa, M., R. Kianinezhad, and S. Gh Seifoadat. "Sliding mode enole contol of ymmetical ix-phae induction machine." Electical and Electonic Engineeing, 29. ELECO 29. Intenational Confeence on. IEEE, 29. XVI. Fatemi, S.M.J.R., et al., Speed enole contol of a ix-phae induction moto dive uing backtepping contol. IET Powe Electonic, (1): p XVII. Roda, Joge, et al. "Model pedictive cuent contolle uing Kalman filte fo fault-toleant five-phae wind enegy conveion ytem." Powe Electonic fo Ditibuted Geneation Sytem (PEDG), 216 IEEE 7th Intenational Sympoium on. IEEE, 216. XVIII. Michalki, T., et al. Senole contol of five phae PMSM baed on extended Kalman filte. in Indutial Electonic Society, IECON nd Annual Confeence of the IEEE IEEE. XIX. Maei, Motafa I., Ahmed A. EI-SATTAR, and Elhuein A. Mahmoud. "Reduced ode model fo peed etimation of enole induction moto dive baed on Kalman Filte and RLS Algoithm." Intenational jounal of engineeing intelligent ytem fo electical engineeing and communication 18.1 (21): All Right Reeved 48

12th WSEAS International Conference on SYSTEMS, Heraklion, Greece, July 22-24, Feedback Signals Estimation of an Induction Machine Drive

12th WSEAS International Conference on SYSTEMS, Heraklion, Greece, July 22-24, Feedback Signals Estimation of an Induction Machine Drive 2th WSEAS Intenational Confeence on SYSEMS, Healion, Geece, July 22-24, 28 Feedbac Signal Etimation of an Induction Machine Dive CONSANIN APOSOAIA, ZOAN SZEKEY, and DONAD GRAY Electical and Compute Engineeing