Simulink models of faulty induction machines for drives applications

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1 Cacow Univeity of Technology Depatment of lectical and Compute ngineeing ntitute of lectomechanical negy Conveion - Simulink model of faulty induction machine fo dive application SUAY OF DOCTOA DSSTATON BY Aleando Fenández Gómez.Sc. Supevio: D. Hab. Konad Weineb Kaków 5

2 PhD Thei Bief Obective The aim of the eeach i to develop mathematical model of quiel cage induction moto and to ceate dynamic model in atlab/simulink eady to be implemented in dive application. Following the claical model of faulty model can alo be educed to a ytem of fou electical equation two equation eithe fo tato and oto cuent and two mechanical equation. The ue of model with a educe numbe of equation will educe the imulation time (Depite of the fact that technology i impoving incedible fat the time equie to un a imulation i till an impotant contain to be taken into conideation). athematical model of quiel cage induction moto have been implified conideing tee phae oto winding a the configuation of a lip-ing induction moto. The oto ba cuent ae not acceible the noi of the fault i mainly conducted by tudying the tato phae cuent in diffeent efeence fame applying oto Cuent Signatue Analyi technique. Theefoe the oto cuent ae not being ubect to any analyi. Theoetically the effect of the oto quantitie and the phyical phenomena inide the oto caue the ame effect ove the tato phae cuent in both configuation of the induction moto. The implification i a follow: in cae of conideing the quiel cage oto the numbe of oto cuent to be defined i equal to the numbe of ba plu one exta cuent which epeent the cuent flowing though one of the ing. The magneto-motive foce (F) in each of the meh i alo appoximated by a inuoidal function with mall amplitude due to the fact that it depend on the angle between ba γ = pi/n. ntead to conideing each independent meh cuent the ba have been gouped in thee et and only one meh cuent ha been conideed. The um of all F along the oto ba in both cae will be equivalent leading to the ame effect ove the tato phae cuent. The obective ae lited below: - Develop a atlab/simulink ibay of faulty dynamic induction moto model fo noi pupoe - Deign a tet-bench and a data acquiition ytem - Validation of imulation eult with expeimental data - Apply advance ignal poceing technique to the data toed - xploe the uitability of thee model fo noi of fault n the maket thee ae many oftwae tool which offe fiendly ue inteface and tool fo modelling electical ytem. Howeve atlab/simulink ha been choen due to the fact that offe the poibility of C and Hadwae Deciption anguage (HD) code geneation and the compatibility it ha with many indutial olution. The mot impotant outcome of the eeach i to have a libay of exchangeable model to invetigate new contol law that impove the ability of dive to contol the induction moto. n the coue of the thei it will be poved that depite the aumption made the model ae uitable fo tudying the behavio of a fault by mean of CSA technique widely ued by the cientific community uppoted by expeimental eult. Page

3 Cele Celem badań et opacowanie modeli matematycznych ilników indukcynych klatkowych i twozenie modeli dynamicznych z użyciem opogamowania atlab/simulink gotowych do toowania w aplikacach napędowych. Zgodnie z klaycznym modelem ilnika indukcynego modele ilnika z wadą ównież mogą być powadzone do układu czteech ównań: dwóch ównań napięć toana lub winika oaz dwóch ównań mechanicznych. Zatoowanie modeli ze zmniezoną liczbą ównań zmnieza ównież cza potzebny na ymulace (pomimo badzo zybkiego ozwou i ciągłego ulepzania technologii cza wymagany do pzepowadzenia ymulaci wciąż tanowi ważne oganiczenie któe mui zotać wzięte pod uwagę). odele matematyczne klatkowego ilnika indukcynego zotały upozczone pzez pzyęcie tófazowego uzwoenia winika ak w ilniku pieścieniowym. Pądy w pętach winika nie ą dotępne a noza uzkodzenia et pzepowadzana głównie popzez badanie pądów fazowych toana w óżnych układach odnieienia z zatoowaniem techniki CSA. Dlatego też pądy winika nie ą poddane żadne analizie. Teoetycznie wpływ właściwości winika oaz zawik fizycznych zachodzących w ego wnętzu na fazowe pądy toana et taki am w obydwu konfiguacach ilnika indukcynego. Upozczenie powadzi do natępuącego potzeżenia: w pzypadku ilnika klatkowego liczba zdefiniowanych pądów winika et ówna liczbie pętów plu dodatkowo pąd któy epezentue pąd pzepływaący pzez eden z pieścieni zwieaących. Siła magnetomotoyczna (F) w każdym z oczek klatki et ównież apokymowana funkcą inuoidalną o małe amplitudzie ze względu na fakt iż zależy ona od kąta nachylenia pomiędzy pętami γ = π/n. Zamiat ozważać pąd poedynczego oczka pęty zotały zebane w tzy gupy epezentowane pzez tylko eden pąd oczkowy w gupie. Suma wzytkich ił magnetomotoycznych wzdłuż pętów winika w obu pzypadkach będzie ówna co ma taki am wpływ na fazowe pądy toana. Poniże wymienione ą cele badawcze: - twozenie biblioteki modeli dynamicznych uzkodzonych ilników indukcynych za pomocą opogamowania atlab/simulink dla celów notycznych - zapoektowanie tanowika pomiaowego i ytemu zbieania danych - walidaca wyników ymulaci z użyciem danych doświadczalnych - zatoowanie zaawanowanych technik pzetwazania ygnałów na pzechowywanych danych - zbadanie adekwatności opacowanych modeli do celów notycznych Na ynku znadue ię wiele nazędzi opogamowania któe ofeuą pzyazne użytkownikowi intefey i nazędzia modelowania ytemów elektycznych. Niemnie ednak dla celów te pacy badawcze wybano nazędzie atlab/simulink ako że ofeue możliwość geneaci kodu C i HD (Hadwae Deciption anguage) oaz ze względu ego kompatybilność z wieloma ozwiązaniami toowanymi w pzemyśle (w ozdziale dugim pzedtawione zotaną zalety wybou pogamu atlab/simulink). Naważniezym wynikiem pacy badawcze et twozenie biblioteki wymiennych modeli w celu zbadania nowych pzepiów kontolnych któe popawiaą zdolność napędów do kontoli ilników indukcynych. W amach poniżze pacy zotanie udowodnione że pomimo poczynionych założeń modele te nadaą ię do Page

4 wpieanego pzez wyniki doświadczalne badania pecyfiki danego uzkodzenia za pomocą technik CSA powzechnie toowanych pzez śodowika naukowe. Chapte Summay The thei ha been tuctued a follow: - Chapte State of At: the common fault in will be decibed a well a the main ignal poceing technique. A eview of the main contibution in the field of induction moto fault noi and the uitability of atlab fo modelling electomechanical ytem ae alo dicued. - Chapte odelling electical machine unde fault condition: dynamic faulty machine model have been developed following the winding function appoach. The chapte will guide the lecto though the mathematical pocedue. An explanation of the phyical phenomena occuing inide the machine fo each fault will be decibed fom the point of view of mathematic. - Chapte Hamonic Balance ethod: it i a method of teady-tate analyi fo electical machine equation with peiodic coefficient which conit of a linea ytem of algebaic equation. The method take into conideation the phyical phenomena inide the machine when it i affected by a fault and thei effect on the hamonic content of the tato cuent. t i equivalent to the ymbolic calculu fo electic cicuit. - Chapte 5 Tet Bench Set-up: it include a deciption of the lab equipment ued and the etimation of the paamete. - Chapte 6 atlab-simulink mplementation of Dynamic odel: the Simulink model pefomance i analyzed uppoted by imulation eult. - Chapte 7 atlab mplementation of Steady State odel: the atlab model pefomance i analyzed uppoted by imulation eult. - Chapte 8 xpeimental eult - Validation of Simulation eult: dicuion about the imulation eult fo diffeent opeation point of the induction moto validated by expeimental data of dynamic and teady tate model. - Chapte 9 Dive Application with Faulty nduction oto model: mplementation into a Zynq all pogammable Sytem on a Chip (SoC) (A+FPGA): pactical cae of model implementation. t how the eult of the wok caied out at ABB Copoate eeach Cente Poland a pat of the tak planned within the negy Smatop poect. - Chapte Analyi and Diagnoi of lectical and echanical Fault in nduction oto: it contain a ummay of the eeach wok publihed by the autho of the thei in the field of fault noi of induction moto. - Chapte Concluion State of At The main technique ued to noe fault on electical machine ha been dicued. Some of them ae mentioned below: Page

5 . Stato Fault: the common technique ued to noe fault in tato ae []: a. agnetic Flux: a meaue of the axial flux can eveal ditotion of the ai-gap flux o compaing the voltage aco diffeent tato coil. b. oto peed: tudying the magnitude vaiation of the Hz fequency component. c. Tempeatue: degadation of the inulation mateial caue inceaed in loe. A detection of hot pot in the tato coe i ued to detect uch poblem [5]. d. Stato cuent: a it ha been hown in table the tato defect add fequency component to the tato cuent [9].. oto Fault Boken ba detection: Detection of BB typically pefomed tudying the low-fequency ideband aound the main component i. e. the elation of the ideband magnitude a fault indicato i not alway effective [9]. High fequency component aound the th th 5th 7th and PSH hamonic can be ueful [] [5] [] [6]. The FFT i the baic analyi but it ha ome diadvantage uch a the need of knowing the moto peed the confuion with mechanical fault o pecta leakage. n uch ituation WT o HT ae a good olution to ovecome thoe diadvantage [8]. n the following ection ome of the eeach wok done in thi aea i ummaized.. oto Fault ccenticity detection: The difficulty in detecting type of eccenticitie tem fom the fact that S and D uually appea imultaneouly. Both type of eccenticitie add imila additional fequencie making it difficult to tell the diffeence between them. oeove not all fequency component will appea in each moto (they depend on the numbe of oto ba). Anothe difficulty i that thoe fequencie can appea due to othe fault type. Seveal model have been popoed in liteatue [] [] [] [6] [8] [] [7] including all o main hamonic. Fo intance each autho had a paticula way of calculating the geometical length of the ai-gap in ode to appoximate the value of the pemenace function to the eal one accounting fo tato/oto lot atuation o imply the Cate coefficient. any of the analyi conducted in thi field ae baed in the compaion of the low/high fequency magnitude well known in liteatue etablihing diffeent indexe with the aim of eithe ditinguih fault o detecting the eveity level. Finally the uitability of ATAB/SUNK a imulation oftwae i alo dicued: Nowaday ATAB/SUNK offe an integated envionment to imulate the tanient and teady tate of electical machine with time-vaying vaiable unde diffeent condition which allow the imulation of a lage numbe of opeation mode. An impotant advantage of that package i the wavefom epeentation of electical ignal. The imple fact of knowing the equation i not enough to obtain eult uccefully. Thi oftwae equie a had effot in undetanding the pocedue of eolution of diffeential equation. n thi Thei ATAB/SUNK ha been ued to ceate a toolbox of Faulty nduction oto model fo analyi and fault noi pupoe due to the fact that it i a oftwae with extenive ue in the teaching and engineeing field. t povide many toolboxe elated to ignal poceing technique Digital Signal Poceo (DSP) pogamming and it offe compatibility with DAQ device fom many manufactue. oeove it allow ceating and cutomizing ue inteface fo eay viualization of model eult and/o oganization of imulation Page 5

6 option fo non-expet pogamme ue. any publication have hown Simulink model fo implementation of [7] [] [] [7]; nevethele only the healthy machine ha been tudied. odelling lectical achine unde Fault Condition Thi chapte explain the methodology followed to develop dynamic induction moto model unde fault condition: agange function and Winding Function Appoach (WFA). The diffeent phyical phenomena that occu inide the machine when it i affected by fault ae analyzed by mathematical equation leading to model with diffeent level of complexity. Thee model can be educed to two et of electical and mechanical equation following the claical model of by applying pecific tanfomation matice widely known by the cientific community with the exception of the ixed ccenticity () model. agange quation and Winding Function Appoach The inteaction of the tato and oto magnetic field i the fundamental mechanim by which the electical enegy i conveted into mechanical enegy and vice vea in. Since failue poduce a ditotion of the magnetic field it may eem logic to develop algoithm which decibe the ditibution of the magnetic field in the machine an ue oftwae baed on F to detect fault in. Nevethele thi type of analyi equie olving aplace and Poion equation which i a time conuming poce. A fault noi of i mainly baed on the tudy of the hamonic content of cuent fluxe toque and/o peed the development of model baed on goup of magnetic cicuit couple each othe povide a bette altenative to undetand the phyical phenomena aociated with failue and the fault conequence in the vaiable. Thoe electomagnetic cicuit ae compoed by a et of eitance and inductance matice. lectomechanical convete uch a induction moto can be mathematically decibed by Hamilton and agange function but in pactice only agange equation i ued a Hamilton development i much moe complicated. Auming the lineaity of the magnetic cicuit the convete equation following the agange function ae a follow: d dt ((φ) i) + i = u (. ) J d φ dφ + D dt dt = it (φ) φ i + T m (. ) Winding Function Appoach (WFA) i a method fo etimation of the machine inductance and fo the geomety definition of the ai-gap. The inductance value ae calculated a function of the linked flux along the ai-gap of the machine which i defined by o-called pemeance function. Thi method ha ome limitation due to the fact that following aumption have to be taken: - inea magnetic field - The magnetic mateial ha infinite pemeance - Fluxe coed the ai-gap adially - ddy and Hyteei cuent ae neglected Page 6

7 n addition it ha been aumed that atuation and lotting effect ae alo neglected. n ode to obtain the magnetic field ditibution i needed to define the F function of all winding. The F i quai peiodic hence it can be epeented by Fouie eie. Fo ditibuted coil in tato the geneal fom ued fo the F function i: θ(x t) = i(t) π w k ρ co ρ(x α) (.) ρ ρ= whee i(t) i the cuent flowing though the coil k ρ i the winding facto w i numbe of winding tun ρ the ode of the hamonic and α i the angle between coil. The pemeance function depend on the magnetic cicuit type and define the geomety of the ai-gap along the cicumfeence. One impotant popety of the pemeance function i that i a peiodic function. λ(x φ) i the invee of the ai-gap length: λ(x φ) = δ(x φ) A new function i intoduced: The Ampee-tun function w(x t) baed on F function. w(x t) = dθ(x t) i(t) dx = ( π ) wk ρ in ρ(x α ρ ) ρ= The final expeion fo linked flux of the winding n due to magnetic field foced by the winding k fo ρ hamonic i a follow: (. ) (. 5) ρ α nρ Ψ nk = l ( ( ( α km π ) w nk nρ in ρ(x α ρ )) B k (ς φ t)d ς) dx ρ= α nρ π ρ m= α ρm (. 6) nductance value ae obtained a nk = Ψ nk /i n (. 7) n addition thee i anothe type of inductance left: the eakage inductance. n a eal machine pat of the linked flux do not co the ai-gap fo intance thoe line that encicle only the tato and oto coil (ba). The linked fluxe can be claified in: - Stato and oto lot leakage inductance - Zig-zag leakage inductance - Diffeential leakage inductance - nd connection leakage inductance - Skewing leakage inductance Geneally total leakage inductance i accounted a the % of the elf-inductance. t may happen that the machine inductance depend on the otation angle φ. With the aim of implified the calculation following tanfomation matice ae ued to eliminate uch dependence. A a eult the convete equation can be educed to a ytem of diffeential equation with contant coefficient matice. When applying thee tanfomation matice the zeo equence of the ymmetical component can be neglected. f the teady tate of the machine i conideed fo a given peed the convete equation ae even educed to a et of imply lineal equation by mean of the Hamonic Balance ethod (HB) explained in next chapte. quation. and. can be expeed in matix fom: Page 7

8 [ U ] = [ ] [ ] + d σ U dt [ (φ) + (φ) J d φ dφ + D dt dt = T elec + T m = [( ) T (φ) ( ) T φ ] (φ) [ φ (φ) (φ) + σ] [ ] (. 8) (φ) φ (φ) [ ] + T m (. 9) φ ] Fo all the dynamic model develop on the thei the inductance and eitance ae changed accoding the fault. Fo intance when it come to model boken ba i ubtitute fo and equivalent matix eq that contain the aymmety and ymmety coefficient k a & k well known among the eeach community. The following model with fault ha been ceated: / Cage Aymmety; / Static ccenticity; / Dynamic ccenticity; / Simulation of echanical fault. oeove the electomagnetic toque T elec will depend on the tanfomation matice applied a well. xample of Final nduction moto odel Following the WFA.. odelling nduction moto echanical Fault: ccenticitie The ccenticity i inheited to the electical machine. t occu when the ai-gap i not contant which mean the ditance between the inne-cicumfeence of the tato and the oute cicumfeence of the oto i not contant. n fact that happen ince the tato and oto ae built with lot to allocate the winding. The pemeance function λ i ued to etimate the length of the ai-gap linked fluxe along the cicumfeence which coed adially the tato and oto. A imply appoach baed on how the ai-gap i defined fo othe moto topologie can be ued fo modelling eccenticitie. Fig.. how thoe topologie (All epeent machine with alient pole on tato oto o both). The poition and length of the ai-gap fo S i fixed in time and pace which coepond to type B. Conequently the pemeance function will depend on an abitay angle x epect to the tato efeence axi. n cae of D the length keep contant but the poition otate coeponding to type A. Hence the pemeance function will depend on the otational angle φ. Finally fo both poition and length change the pemeance function depend in both angle x & φ. oeove a it i a peiodic function it can be defined by Fouie eie. Page 8

9 Table Pemeance function type Type A B C Pemenace Function (xponential eie) Pemenace Function (Co. eie) λ(y) = Λ e (y) = λ(y) = Λ + Λ co (y) Λ ae the Fouie coefficient and y = x φ. = λ(x) = Λ e x = λ(x) = Λ + Λ co (x) = λ(x φ) = = = Λ e x e φ λ(x φ) = Λ + Λ co (x) co (φ) = = Change of the ai-gap egading eccenticitie can be appoximated by geometical elationhip between the machine ymmety axial axi O and the path decibed by the oto cente O.... ixed ccenticity Following the WFA applying the above pemeance function and conideing only the effect of the main F that contain p-hamonic (equation.) the inductance matice of an induction moto (equation.6) with in ymmetical component ae: - Self-nductance Stato: = ( Λ m co(mφ ) [ Λ pm co(mφ ) + ( Λ pm co(mφ ) [ Λ pm co(mφ ) - Self-nductance oto: Λ pm co(mφ ) Λ m co(mφ ) Λ pm co(mφ ) Λ m co(mφ ) σ + [ σ ] ; whee = l µ π (w k p σ (. 8) = ( Λ m co(mφ ) [ Λ pm co(mφ ) + ( Λ pm co(mφ ) [ Λ pm co(mφ ) - utual nductance ) Λ pm co(mφ ) Λ m co(mφ ) Λ pm co(mφ ) Λ m co(mφ ) σ + [ σ ] ; whee = l µ π (w k p σ (. 9) = ( ) ( Λ m co(mφ ) [ Λ pm co(mφ ) ]) [ ] + ]) [ e pγ ] + e pγ ]) [ ] ]) [ e pγ e pφ ] + e pγ e pφ ) Λ pm co(mφ ) Λ m co(mφ ) + ]) [ e pφ ] + e pφ Page 9

10 + ( Λ pm co(mφ ) [ Λ pm co(mφ ) Λ pm co(mφ ) Λ m co(mφ ) whee = l µ π (w k p ) (w k p ) (. ) Hamonic Balance ethod ]) [( e pφ+pγ ) ] + e pφ pγ n the peviou chapte it ha been hown that the convete equation can be educed to two et of fou electical and two mechanical linea diffeential equation with contant coefficient peiodic matice. Claical method baed on cicuit theoy can eaily olve the ytem in analytical fom. Futhemoe if the teady tate of the machine i conideed which mean that the olution of the mechanical equation i known the ytem can be educed to linea equation. A method fo teady tate analyi of electical machine with non-linea diffeential equation with peiodic coefficient i peented fo thoe cae in which the tanfomation matix doe not obtain matice with contant coefficient: Hamonic Balance ethod (HB). Thi methodology ha been applied to detemine the teady tate of an induction moto affected by. Additionally model fo S and D ha alo been ceated to compae with dynamic model obtained fom WFA. They have accounted the main F and the peence of ai-gap aymmety which caue the appeaance of additional hamonic of magnetic pemeance auming linea magnetic cicuit thee ymmetical tato and oto winding p pai of pole and thee phae oto meh cuent. oeove the ame aumption made in ode to obtain a dynamic model of ae alo aumed. odel of all the eccentitie ae lited below whee: - Ω o and Ω ae the angula velocity of the net and oto - i the identity matix - U and U ae matice with the elf and mutual inductance tato and oto cuent and voltage value aociated to inductance cuent and voltage hamonic - and the tato and oto eitance n the bellow equation indexe of facto (inductance and cuent) ae tictly defined and coepond to the algebaic multiple of the angula velocity. Page

11 Page HB: Static ccenticity odel (achine with p=) * U (. ) The model can be educed a only a few element ae coupled by the voltage hamonic U. The inductance and cuent vecto ae elated to pecific omega pulation which vaie accoding to the fault (Fo intance in equation. thee ae diffeent pulation). The eultant model coepond to the electical equation of the dynamic S model peented in chapte. and ae the pecific inductance and cuent value couple by the voltage hamonic. U pω Ω pω Ω Ω Ω (. )

12 Page HB: Dynamic ccenticity odel (achine with p=) A it happen with the S model D can alo be educed a only a few element ae coupled by the voltage hamonic U. Howeve the hamonic of the tato and oto cuent ae diffeent (linked to diffeent omega pulation). The eultant model coepond to the electical equation of the D model peented in chapte. and ae the pecific inductance and cuent value couple by the voltage hamonic. U Ω Ω Ω Ω pω Ω Ω (. ) * U (. )

13 Page HB: ixed ccenticity odel * U (. 5) Nevethele fom the model in natual component of it i eay to obtain the S and D model undetanding the phyical phenomena. Fo S the poition of the minimal ai-gap doe not depend on φ but only on x. By only conideing the main Fouie coefficient Λ Λ p and Λ p and the hamonic in equation.. and. the model of S can be found. Fo D apat fom the conideation taken fo the S model the angle γ ha to be ubtituted fo δ+φ whee δ i the initial poition of the minimal ai-gap. Fo D the poition of the minimal ai-gap depend on the otational angle φ.

14 atlab/simulink mplementation of Dynamic nduction oto odel The aim of the thei i developing dynamic model of fo dive application which account the effect of main F. They will be ued to tudy the inteaction of dive politie unning fault machine in ode to develop new contol law. n thi chapte dynamic model of induction moto fo dive application ae peented including ome of the model eult. Dive application ae uually employed fo ignal poceing of meauement o contol application. The implementation of the algoithm and dynamic ytem involved ae natually dicete-time a the compute execute and collect data in dicete point of the time fo intance obeve tate etimato a KF o filte. Due to the fact that model develop in the thei ae non-linea (the tate pace vaiable depend on the peed oto o tato peed) the ule fowad method ha been elected. Additionally thi method allow to find an explicit fomula of output (e.g. tato and oto cuent o fluxe). Some of the Simulink model ae dicued below: Healthy nduction oto odel The healthy induction moto model ha been ued a a efeence to analyze the diffeence between the electical machine ignatue fom each model. Fault model have been developed baed on the claical mathematical model of which mean they ae contituted by fou electical equation and two mechanical equation (with the exception of the teady tate model of ). Fig. 5. how the Simulink model of healthy. The Stuctue of the model i a follow: - Stato Voltage Supply Sytem Block: definition of the upply voltage - Tanfomation atix Block: the tanfomation matice ued to implify the electical equation (and the invee matix). - odel Block: definition of the electical moto equation baed on model fom Chapte. - lectomechanical Toque Block: calculation of the electomechanical toque - echanical Speed Block: olving the mechanical equation. Page

15 - Selecto efeence Fame Switch: tationay o otating efeence fame electo. The healthy model ha been teted fo the moto T-DF- with ampling time T = e 5 % of the load toque (. Nm). The eult ae hown below: The above eult agee with the eal value of the moto. Dynamic ccenticity nduction oto odel Fig. 5.6 how the model of Dynamic ccenticity (D) nduction oto. t contain the ame block and the Page 5

16 eult hown below have been teted in the ame condition a the Healthy achine howeve thi model doe not have the poibility of changing the efeence fame becaue the tanfomation applied to implify the model equie a pecific angle and the odel block contain the equation fo D. oeove the poitive and negative equence of the cuent and voltage can be obtained fom the model. A % of D ha been teted: n Fig. 5.7 it can be ditinguihed the chaacteitic ipple aociated to the fault. D poduce imila effect a BB fault. Sideband ( )f alo aie in the fequency pecta becaue the model include the mechanical equation. n cae of D accoding the pefomance of the moto the amplitude of the ideband vaie. Chapte 7 compae the dynamic model and the tatic model eult with the meauement and analye the behavio of the ideband. atlab mplementation of Steady State nduction oto odel The implification of the mathematical equation cannot be alway accomplihed due to the natue of the fault. Thi i the cae of which elf-inductance and mutual inductance matice depend on the angula poition of the oto. A thoe inductance ae not contant matice the model of fo cannot be found a it happen fo S D o BB fault (Dicued on the Chapte of the thei). Howeve the pecta of the tato phae cuent can be obtained fo the teady tate opeation point applying the HB (Chapte ). n the peent chapte the tato cuent pecta fo S D and model in fequency domain will be dicued by mean of the FFT. Additionally it will be explained how the tato cuent in time domain ae calculated fo each eccenticity fault a a function of the cuent and peed hamonic. The quiel cage moto ha been Page 6

17 model a a oto winding induction moto applying the aumption of tato and oto winding ae equal. Fo intance the tato cuent in time domain of the D model ae calculated a follow: The HB i olved conideing only the voltage hamonic with pulation Ω Only two cuent hamonic ae diffeent than zeo: D c (t) [ D c (t)] = [ D ] e (Ω) t + [ D (t) c U η = U n e (Ω ) t + U n e ( Ω ) t (6.) D ] e (Ω pω m ) t ; (fo U n e (Ω ) t ) ; (6. ) Applying the pinciple of upepoition the cuent hamonic fo the voltage hamonic with pulation Ω ae D c (t) [ D c (t)] = [ D D (t) ] e ( Ω) t + [( D ) ] e (Ω pω m ) t ; (fo U n e ( Ω) t ) ; (6. ) c The backwad and fowad ymmetical component can be found a: D c (t) [ D c (t)] = [ D e (Ω ) t ] + [ D e (Ω pω m ) t ] ; fo (U η η = ±); (6. ) D D (t) e ( Ω ) t D e (Ω pω m ) t c Fom equation 6. it can be poved that backwad ymmetical component i equal to the conugate fowad ymmetical component: D = D c (6.5) c Finally the time domain tato cuent ae obtained applying the invee SC tanfomation matix: D a (t) [ D b (t)] = D c (t) D [ a a ] [ D c (t)] (6. 6) c (t) a a D (t) Thi chapte include imulation of the moto model T-DF- with diffeent level of eccenticity fo all eccenticity type. n ode to peent the content thi ummay how only one of the model dicued:. D tatic model teted with % of eccenticity Simulation of % D tatic model c The above figue how the fequency pecta and the wavefom of the tato phae cuent obtained fom the model. The cuent fequency pecta how the chaacteitic left ideband aociated to the electical equation of the convete. n chapte 5 it can appeciated how the ight band appea due to olving the Page 7

18 mechanical equation. Futhemoe it can alo be een the ipple on the tato phae cuent chaacteitic of thi type of fault. A it wa mentioned the imulation eult ae dicued baed on the meauement eult on chapte 7. Validation of odel eult by xpeimental Tet n the peviou chapte the dynamic and tatic model fo D wee peented and the imulation eult wee howed. The imulation eult agee with the expected value of the eal machine when it i affected by thoe fault fo intance the additional fequencie on the tato phae cuent. Howeve the final validation i done by tudying the evolution of the ideband when the moto i woking unde diffeent condition. Dynamic ccenticity (D): eauement eult Accoding to the expeimental data the amplitude of both ideband fo each level of load doe not depend on the level of eccenticity howeve it can be obeved how the left ideband amplitude inceae and the ight ideband amplitude deceae with the load. Thoe value agee with the expected evolution of D. Dynamic ccenticity (D) Dynamic odel: Simulation eult The imulation eult how the evolution of the ideband amplitude fo diffeent level of eccenticity: Page 8

19 The imulation eult how a imila evolution of the ideband amplitude howeve the diffeence in magnitude ae highe becaue the etimation of the machine inductance i not accuate enough. Dynamic ccenticity (D) Static odel: Simulation eult Compaing the imulation eult of D between dynamic model and teady tate model light vaiation of the hamonic a well a in the tend can be obeved. The olution of the mechanical and electical equation implie that the left ideband inceae with the load but magnitude emain lowe than teady tate eult. egadle of thoe diffeence both model fulfil all the equiement accoding to the aumption taken and agee with the meauement eult. Concluion on the odel Pefomance t i woth to mention the concluion eached by the analyi done in the thei egading the pefomance of all model (dynamic and tatic). The eult have hown a coect pefomance of the model. The fequency analyi of the tato phae cuent in all model peent the chaacteitic additional fequencie. Fo teady tate imulation the fequencie aociated with the mechanical ide of the ytem do not appea. The evolution of the ideband aound the main hamonic (5 Hz) agee with expeimental data fo diffeent load condition and fault eveitie. On the othe hand if the ue eek a quantitative analyi of fault ome of the following action may be conideed in ode to obtain a bette etimation of the machine paamete fo each opeation point: - Satuation coefficient calculated by F model fo each level of load - Deign of KF which etimate the healthy machine paamete fo diffeent load condition - Conide atuation and lot effect in the calculation of the pemeance function - timation of atuation coefficient a function of the main inductance calculated by fomula and the etimated by expeiment fo each level of load - timation of oto cage eitance vaiation due to eddy cuent Page 9

20 n concluion the dynamic and teady model peented in the thei demontate that a qualitative analyi of fault can be caied out by only conideing F effect fulfilling all equiement needed fo dive application a the tendencie hown in imulation match the expeimental data. Dive Application with Faulty nduction oto model: Hadwae in the oop Simulation H n the pat the contuction of pototype wa a common pactice duing the tet phae of new idea/concept and poduct. Thi teting tage equied long peiod of time and the invetment of many eouce. Anothe impotant facto wa the afety duing the tet a the opeato could uffe accident. n the pat few decade the evolution of the compute and the development of new platfom fo modelling implementation have helped to educe the time inveted to tanfom an idea into a poduct the total cot of the whole poce and have impoved the wok condition deceaing the ik of popective accident. Hadwae in the loop imulation (H) technique have been developed to peed up the tet and development poce of embedded ytem. Thoe technique povide a platfom to tudy the inteaction between eal-time embedded ytem uch a powe electonic contol ytem with a plant (electical moto) epeented by complex mathematical model. Powe electonic contol imulation equie high-peed digital poceo which epoduce the fat dynamic epone due to the high fequency witching action of the powe electonic witche. eal-time imulation can be atified thank to the FPGA/CPU platfom ued fo H. odel develop in the thei wee implement in eal dive application at ABB eeach Coopoate Cente Poland within the negy Smatop activitie pogam with poitive eult. Page

21 mplementation of Healthy nduction oto model into Zynq-7 All Pogammable SoC - Dicuion of eult Following figue how upply voltage electomagnetic toque and oto peed ignal calculated by ZYNQ duing the execution of the Healthy machine model (Fig. 8. / Fig. 8.5) and BB model (Fig. 8.6 / Fig. 8.7) unning at the ame opeation point uing the tationay efeence fame and expeed in d-q component. The magnitude and behaviou of the machine ignatue wee equal to the imulation eult obtained in Simulink afte applying the pope cale facto. Analyi and Diagnoi of lectical and echanical Fault in nduction oto The content of thi chapte ummaize ome of the wok caied out in the field of fault noi of though imulation and expeimental data. 9. valuation of the Aymmety Facto fo BB Simulation Change of imulation: ymmety and aymmety coefficient ae ued to model BB fault. Some of the aumption taken in modelling ae eview a well a the evolution of thei value fo diffeent fault. Page

22 9.5 nteaction 9. Diagnoi of Static ccenticity v Unbalance Supply Voltage: difficultie in noi of both fault ae pointed out. Futhemoe a method to find diffeence i uggeted. 9. odelling D and Cage aymmety: the poibilitie offe by combining BB and D model fo fault noi pupoe ae invetigated uppoted by expeimental data. 9. Compaion of echanical and Boken Ba Fault by mean of Poitive and Negative Fequency Spectum Fo example: of the Stato Phae Cuent in : an altenative algoithm of Fouie tanfom ha been applied in ode to find diffeence between fault in the fequency pecta of the tato cuent. between lectical and mechanical fault by mean of CSA: tudy baed on the evolution of the ( )f ideband when an induction moto with BB i alo affected by a mechanical fault with imila fequency ange. 9. odelling D and Cage aymmety D and BB fault ae difficult to ditinguih due to the fact that ame ideband aound the main hamonic appea. n both cae the evolution of the ideband magnitude i imila fo intance egading change in the load. With the aim to binging light to thi challenge mathematical model baed on main F may be ued to tudy new algoithm of fault noi. Thee model have been teted: odel of BB model of D and a thid one that combine the fault. The eult obtained fom all model in compaion with the expeimental data eveal imila tend poving the uitability of the model fo noi pupoe. - xpeimental eult Once again tet pefomed in moto model T-DF- have hown diffeence in magnitude of the ideband. ecalling chapte 8 the left ideband magnitude inceae and the ideband magnitude deceae with the load fo one BB and D. agnitude of ideband fo BB wee highe than D. xpeimental eult when both fault occu imultaneouly hown the ame tend with highe magnitude than epaated fault: Table Sideband magnitude fo D + one BB / xpeimental eult Dyn. cc. + one B.B. (-)f % oad 6% oad 9% oad % oad Dyn. cc. + one B.B.(+)f % oad 6% oad 9% oad % oad Page

23 egading imulation eult it can be poven the ame tend in the ideband a well a the magnitude value. Soting fom highet to lowet: D + one BB / one BB / D. Table Sideband magnitude fo D + one BB / Simulation eult Dyn. cc. + one B.B. - (-)f % oad 6% oad 9% oad % oad % oad Dyn. cc. + one B.B. - (+)f % oad 6% oad 9% oad % oad % oad t i tue that diffeence between D + one BB and BB fault ae not big enough a it wa hown in expeimental eult but it i alo tue that paamete fo etimation of BB may be not fully coect. n the light of eult peented it can be concluded that mono hamonic model accounting imultaneouly BB and D fault may be ue fo noi pupoe. Concluion The main contibution of the thei ha been the development of a libay in Simulink of dynamic induction moto model unde electical and mechanical fault fo dive application. Thee model have been baed on the Page

24 winding function appoach fo mathematical modelling of accounting only effect of the main F. Futhemoe teady tate model accounting eccenticitie fault have been ceated in atlab following the HB. The main advantage of the methodology peented i that it allow developing model of diffeent type of electical machine o conideing effect of multi-hamonic. n addition effect of atuation o lotting can be taken into account by adding additional tem to the pemeance function. The eeach eek a qualitative analyi of the electical and mechanical fault by mean of CSA applied to the tato phae cuent. Simulation eult hown in the thei have mainly been focued in the analyi of the fequency pecta of the tato phae cuent with the obective of tudying the evolution of the chaacteitic fequencie fo each type of fault. Pefomance of the model ha been uppoted by expeimental data. t ha been neceay to deign a DAQ ytem fo data collecting and the etimation of the machine paamete. A imple ue gaphic inteface fo etimation of machine paamete ha alo been deigned. xpeimental eult have validated the tend hown in Simulation eult egading evolution of the fequencie aociated to fault and magnitude of machine ignatue uch a amplitude of cuent toque and peed fo diffeent opeation point of the moto. Howeve it ha been obeved a tong dependence between the magnitude of thee fequencie and the machine ignatue with the paamete. Fault noi of induction moto ha been anothe of the obective. The wok caied out in thi field ha been publihed in intenational confeence and ounal. Depite the fact that model only account main F eult poved the uitability of them fo thi pupoe. Summaizing model peented allow the ue to cay out a qualitative analyi of electical and mechanical fault on baed on main F offeing an accuate epeentation of the main fault effect ove the cuent uitable fo dive application. e f e e n c e - e l e c t e d p o i t i o n []. G.B. Kliman J. Stein.D. ndicott.a. Koegl Noninvaive Detection of Boken oto Ba in Opeating nduction oto negy Conveion Tanaction on vol. no pp []. T. J. Sobczyk P. Dozdowki nductance of electical machine winding with a non-unifom ai-gap Achiv fu lektotechnik vol. 76 pp []. T. J. Sobczyk P. Va C. Taoni odel fo nduction moto with ai-gap aymmety fo noi pupoe C Poceeding ntenational Confeence on lectical achine vol. pp []. T. J. Sobczyk K. Weineb T. Wegiel. Sulowicz Theoetical tudy of effect due to oto eccenticitie in induction moto" n ntenational Sympoium on Diagnotic fo lectical achine Powe lectonic and Dive (SDPD 99) pp [5]. T.J. Sobczyk W. aciołek ffect due to highe pace hamonic in induction moto with faulty cage Achive of lectical ngineeing PWN Waaw vol. 5 pp. -5. [6]. S. Nandi.. Bhaadwa H.A. Toliyat ixed eccenticity in thee phae induction machine: analyi imulation and expeiment nduty Application Confeence. 7th AS Annual eeting. Confeence ecod of the vol. pp [7]. B. Ozpineci.. Tolbet Simulink implementation of induction machine model - a modula appoach DC n lectic achine and Dive Confeence vol. pp Page

25 [8]. J. Faiz. T. Adekanei H. A. Toliyat An evaluation of inductance of a quiel-cage induction moto unde mixed eccentic condition negy Conveion Tanaction on vol. 8 no. pp [9]. T.J. Sobczyk W. aciołek Doe the component (-)fo in tato cuent i ufficient fo detection of oto cage fault? Poc. 5th Symp. on Diagnotic of lectic achine Powe lectonic and Dive (SDPD 5) pp []. A. Siddique G.S. Yadava B. Singh A eview of tato fault monitoing technique of induction moto negy conveion tanaction on vol. no. pp []. G.. Jokimović Dynamic imulation of cage induction machine with ai gap eccenticity Poceeding-lectic Powe Application vol. 5 no. pp []. A. Bellini C. Concai G. Fancechini. oenzani C. Taoni A. Tocani Thoough undetanding and expeimental validation of cuent ideband component in induction machine oto monitoing ndutial lectonic CON 6 - nd Annual Confeence on pp []. A. A. Anai D.. Dehpande athematical odel of Aynchonou achine in ATAB Simulink ntenational Jounal of ngineeing Science and Technology vol. no. 5 pp []. A. Aktaibi D. Ghanim Dynamic imulation of a thee phae induction moto uing atlab Simulink. [5]. C. Keiche. Golebiowki Compaion of diffeent method to detemine defect in the tato coe lectical achine (C) XXth ntenational Confeence on pp [6]. J. atinez A Belahcen A. Akkio Boken ba indicato fo cage induction moto and thei elationhip with the numbe of conecutive boken ba T lectic Powe Application vol. 7 no. 8 pp [7]. W.. eedy Simulink/ATAB Dynamic nduction oto odel fo Ue a A Teaching and eeach Tool ntenational Jounal of Soft Computing and ngineeing (JSC) vol. no. pp. -7. [8]. K. Weineb Diagnotic of an induction-moto oto by the pectal analyi of tato cuent Themal ngineeing vol. 6 no. pp. 6-. [9]. J. Anu V. Joe D. Sebatian Stato fault detection in induction moto unde unbalanced upply voltage meging eeach Aea: agnetic achine and Dive (ACA/iCD) Annual ntenational Confeence on pp. -6. B o o k []. G.. Fitchtenholz Diffeential and integal calculu tom. Waaw: PWN (in Polih) 98. []. P. Va Senole Vecto and Diect Toque Contol Oxfod: Oxfod Science Publication 998. []. J. Faile oa lectical achine edn.v. adid: cgaw-hill. []. T.J. Sobczyk ethodological apect of mathematical modelling of induction machine (in Polih) WNT Waaw. [5].. Boldea The induction machine deign handbook CC pe 9. [6]. A. D. Poulaika Handbook of fomula and table fo ignal poceing CC Pe. Page 5

26 [7]. P. Waide C. U. Bunne negy-fficiency Policy Oppotunitie fo lectic oto-diven Sytem A - ntenational negy Agency negy fficiency Seie. [8]. Kaue Paul C Waynczuk O. Sudhoff S. D Pekaek S. Analyi of electic machiney and dive ytem John Wiley & Son. P u b l i c a t i o n i u e d b y t h e a u t h o i n c o n f e e n c e []. A.J. Fenandez Gomez T.J. Sobczyk Compaion of Fouie pecta of induction machine fo cage aymmety and fault in mechanical pat of a dive C and FPT. []. A. J. Fenandez Gomez T. J. Sobczyk oto cuent ignatue analyi apply fo extenal mechanical fault and cage aymmety in induction moto Diagnotic fo lectic achine Powe lectonic and Dive (SDPD) 9th ntenational Sympoium on pp. 6- ( Xploe Digital ibay). []. A. J. Fenandez Gomez A. Dziechciaz T.J. Sobczyk athematical modeling of eccenticitie in induction machine by the mono-hamonic model Diagnotic fo lectic achine Powe lectonic and Dive (SDPD) 9th ntenational Sympoium on pp. 7- ( Xploe Digital ibay). []. A. J. Fenandez Gomez Simulink model of faulty induction machine fo dive application ntenational PhD Wokhop OWD confeence achive PTTiS vol. pp. -9. [5]. A. J. Fenandez Gomez Victo H. Jaamillo Jame. Ottewill Fault detection in electic moto by mean of the extended Kalman Filte a ditubance etimato Contol (CONTO) UKACC ntenational Confeence on pp. - 7 ( Xploe Digital ibay). [6]. A. J. Fenandez Gomez T.J. Sobczyk K. Weineb nfluence on oto Boken Ba Fault Diagnoi of echanical Toque Pulation by ean of FFT Diagnotic fo lectic achine Powe lectonic and Dive (SDPD) 5 th ntenational Sympoium on (Submitted) 5. P u b l i c a t i o n i u e d b y t h e a u t h o i n J o u n a l []. A.J. Fenandez Gomez T.J. Sobczyk nfluence of deign data of induction moto on effect of cage aymmety Pace Naukowe ntytutu azyn Napedów Pomiaów lektycznych Politechniki Woclawkie Vol. pp []. A. J. Fenandez Gomez T.J. Sobczyk nfluence of nduction oto Deign Data on ffect of Cage Aymmety Jounal of negy and Powe ngineeing vol. 7 no. 8 pp []. A. J. Fenandez Gomez. Sułowicz T.J. Sobczyk nduction moto ignatue analyi unde influence of mechanical and electical fault ntytut Napedów azyn lektycznuch KO vol. pp 9-. []. A. J. Fenandez Gomez. Sułowicz T.J. Sobczyk nfluence of mechanical fault on induction machine with electical fault Czaopimo Techniczne lektotechnika 5. Page 6