3 Performance estimation for a three-phase PM synchronous machine

Transcription

1 Assignent Pefoance estiation fo a thee-phase PM synchonous achine The goal of the thid assignent is to get expeience of equivalent cicuit ethod (ECM) used fo ough sizing of a sevo oto. The estiated achine pefoance fo ECM is copaed with theal and agnetic odels in finite eleent ethod (FEM). In this pefoance analysis the tepeatue ise and the electoagnetic toque poduction is calculated. The expected expeience fo this assignent is questioned below What is agnetic shea stess and how this could be used fo sizing of electical achines. How agnetic flux density and electic cuent density ae elated to the agnetic shea stess? What and how lage is sheet cuent density? How ECM is used fo efining (o optiising) the input fo FEM estiations? Advantages and disadvantages on the agnetic design foulation, design tool ipleentation in MATLA/FEMM envionent and the validity of the esults. How to intepet the esults: toque, echanical powe, heat powe, cooling and tepeatue ise: ae the esults ealistic? 3. Getting stated Quick pogessing guide Ceate poject ap, Use MATLA to execute the task, un FEMM fo MATLA, visualise (open FEMM sepaately) and study the esults. open M-scipt, find design paaetes, change the paaetes that you need and cay out the tasks in assignent. Get suppot fo the theoetical pat of the achine foulation 3. and paaeteisation 3.4. Notice that You select size of the achine and equivalent cicuit odels ae used to specify the agnetic ant theal situation fo a peanent agnet synchonous achine. This thee-phase achine has accoding to a design choice slot pe pole and phase. This esults that -pole achine has 6 slots, 4-pole slots and so on. Use only the sketch (Matlab figue ) to obseve that the geoety is fine befoe executing Fe fo Matlab Thee ae a set of design paaetes that ae used to specify the achine. These paaetes ae optiized within ECM and veified in FEM by You. Matlab is used to wite LUA scipt and execute FEMM that eads the scipt Matlab executes FEMM fo C:\Poga Files\fe4\bin\fe.exe so if thee ae anothe installation diectoy then soe coections need to be ade in the end of the -file 3. Analysis object The hoe assignent focuses to a toque capability and powe ating of an AC sevo oto. Thee diffeent oto fae sizes () ae given (in table below) whee each of the have thee diffeent stato laination stack length l that influences the oveall length (A) of the achine

2 Assignent 3-9 house, which includes sensos, contol cicuities. The active volue of the achine is deteined as /4(Do -Di ) l, which excludes the end-windings, and the coesponding cooling aea of the achine is assued to be Do l. Moto fae size Oute/inne diaete Do/Di [] Stack length l [] 90 80/ / / / / / / / /30 80 Do Hc A The pevious figue shows a fou-pole achine with suface ounted agnets in the oto and 3-phase concentated (non-ovelapped) winding in the stato. 3.3 Machine powe and toque In an electoagnetic synchonous achine, the speed of echanical otion is tied to the electic fequency, and vice vesa. The echanical aangeent of the windings and a subsequent enegizing of the coils (aatue agnet) keep the peanent agnets (field agnet) to follow the taveling agnetization wave at the sae speed. This agnetic coupling is based on the nube of agnetic pole-pais N p / pesented in the achine. As a esult, the oto of a synchonous oto otates exactly at the supply fequency o a subultiple of the supply fequency. Powe balance Ideally the input powe equals to the output powe. So in case of tansfoe the input and the output powe is both electic. In case of otating electic achine the input powe can be eithe electic o echanic depending if the achine is in otoing o geneating ode, espectively. P U I T, (3.) Without consideing any vaiation in space o tie, the agnitude of voltage U is connected to the agnitude of back electootive foce E and this in tun to the deivative of the flux linkage Ψ and physical agnetic flux Φ. The agnetic flux is descibed again by the flux density and the agnetic coss section aea A. This tie the induced voltage is not due to the altenating and agnetising piay cuent but fo the otation of the agnetised oto. U E N N A, (3.) Siilaly the peak value of the electic cuent I is diectly elated to total cuent including all the winding tuns N and this is connected to cuent density J and the winding conducto aea A e. J A I e N, (3.3) Independent of nube of winding tuns the powe becoes

3 Assignent P J A A T e (3.4) Whee toque is T J Ae A (3.5) In this case the excitation speed ω equals to the actual otation speed (-pole achine) and the lossless toque is applied o deliveed to the oto shaft. Toque poduction Accoding to the Loentz foce law thee is a echanical foce F w on any cuent-caying wie I placed in a agnetic field. The coon length of field and wie is expessed with l. F I (3.6) w l This foce is expessed as toque in espect to a efeence point that distance fo the foce point is. Tw Fw (3.7) The su of toques of N wies along a peiphey, which is defined by the adius, becoes T T d F l NI (3.8) 0 w It can be tepting to conside (tie) invaiant field and cuent but otating electical achines ae taking advantage of altenating field seen fo cuent caying coil point of view. Theefoe the peak values of the cuent I and flux density is used. Apat fo that, the cylindical aea πl =A gap is eplaced by a agnetic aea A that agnetic flux Φ pieces. The cuent caying wies NI is eplaced by the coss-section aea of the wies A e and the cuent density J applied in the wies. T l NI A Ae J (3.9) Magnetic shea stess The su of tangential foces, which is the poduced by the inteaction of flux and cuent, establishes toque between the oto and stato. The su of foces ove the oto suface that causes toque is known as agnetic shea stess shea. F F T T N shea 3 A l l V (3.0) gap As it is seen Figue 3. the agnetic shea stess becoes athe convenient paaete to define the cylindical oto volue V. When connecting the specific toque and agnetic shea stess to the agnetic flux density and electic cuent density then a new paaete sheet cuent density K [A/] is defined: T V A A J K e shea (3.) l The sheet cuent density chaacteizes the suface cuent along the gap peiphey.

4 Assignent I σ shea Figue 3. Applied foces on the oto cylinde due to cuent caying conducto placed in the agnetic field Magnetic design An aay of suface ounted peanent agnets is used to establish agnetic excitation of the achine. The ectangula shape of the gap flux density wavefo is ainly deteined by the angula width of peanent agnets. (θ) stato ge θ θ g oto 0 π π Figue 3. Roto with suface ounted agnets and flux density wavefos along ai-gap Peviously, it is shown that agnetic flux density and sheet cuent density wave agnitudes ae diectly connected to agnetic shea stess and toque capability of an electic achine. Heeby a nube of new paaetes ae defined specifying the location and chaacte of the flux density Maxiu flux density in the ai-gap g Magnitude of the fundaental coponent of flux density in the ai-gap g The fundaental and the haonic coponents fo the peak value of the gap agnetic flux density ae given by gh 4 g h,3,5, sinh k h. (3.) The agnet width coefficient k is the atio of the peanent agnet width w p to pole width o pole pitch k N P w p (3.3) The elative agnet length is chosen as a copoise between cost and achine pefoance. The axiu flux density in the ai-gap, g, is defined as a taget value, which is late

5 Assignent deteined by the actual opeation point of the agnetic coe caying the flux. The height of the peanent agnets h p is deived fo the siplified agnetic cicuit, which assues that coe is infinitely peeable and thus accoding to Apee s law the agnetic cicuit has two eleents: p 0 p h p g g k 0 C 0, (3.4) This equation consides 0% lage agnetic ai-gap than actual echanic ai-gap. The actual gap ties the Cate s coefficient k C =. is used fo PM achines and this takes into consideation agnetic flux paths and stato slots as well as the effects of actual peeability that is not infinite. Accoding to the assuption of the sae coss-section aea, the constant flux and taking into account the MMF dop in the agnetic cicuit, leads to a easonable value fo the peak gap flux density and coesponding thickness fo the peanent agnets. g (3.5) h p g p g k C. (3.6) In this agnetic design it is initially decided that The echanical ai-gap is g=0.8 wide The peanent agnet coves k =/3 of pole pitch The agnitude fo the fundaental gap flux density suppose to be g =0.9 T The stato and oto coe suppose to be able to cay the flux density without going into deep satuation whee satuation flux density is sat =.6 T This design initialization esults that with a stong ae eath (NdFe) agnet, whee =.T and μ p =.06 esults H c =-900kA/, the (inial) height of the agnet suppose to be p.06 hp g kc (3.7). g sin k sin 3 This is expectedly the sallest height fo the peanent agnets that is able to agnetise the aigap to g =0.9 T with infinitely peeable coe. As the agnetic flux fo the agnets is elated to aea Φ p = A p athe than to the height of the agnet in the agnetisation diection then the incease of the agnet thickness h p not only backs up the desied flux and flux density but also educes the isk of patial o full deagnetization of the peanent agnet. Anyway this is actually you task to analyse weathe the assuption is useful fo design. The agnetic coe in stato and oto suppose to be able to cay the sae agnetic flux that is defined by axiu flux density and peanent agnet aea. If the peanent agnet and the coe have the sae length then the thickness of the stato yoke and the oto yoke has to be:

6 Assignent h sy g hy wp (3.8) sat The inial agnetic coe width h sy and h y deceases with nube of poles since w p deceases with nube of poles. As the yoke divides the total agnetic flux pe pole into two halves ½ appeas in the pevious equation. In this assignent the stato yoke is taken equal to the stato tooth width and the definition of stato inne diaete deteines ainly the oto yoke thickness. Estiation of powe losses Once again, the powe losses ae estiated accoding to the loss oigin in diffeent pats of the device. The total heat powe is expessed as a su of losses, which ae outcoe of powe loss density and the geoety of the electic as well as the agnetic cicuit. P loss A l p A l p P P (3.9) e e e cu fe The conducto loss fo the diect cuent P cu is expessed though the powe loss density, which depends on esistivity ρ and the cuent density squae J, and the volue of the conducto V e. P JAe len cu I R J Ael e J Ve (3.0) N Ae N The eagnetization loss in the agnetic coe fo the syetic sinusoidal excitation is found fo the specific loss data k fe at cetain agnetization fequency and agnetic induction ove the coe volue V P fe k fe V p fev, (3.) Fo sinusoidally vaying agnetic flux density the feous losses in the coe pat ae the su of the hysteesis and the eddy cuent losses (Steinetz odel). Eddy cuent losses ae usually sepaated to aco o classical eddy cuent losses and ico o anoalous o excess losses. Powe losses ove a volue of coe i.e. specific coe losses can be expessed as p fe f c f / 3 n c f c. (3.) h ec a Instead of angula speed an excitation fequency is chosen. Fo the selected echanical fequency f ech =50 Hz and 3000 p, the electic fequency need to inceased when inceasing the nube of poles Np f f ech. (3.3) Theefoe it is expected that the coe losses ae inceasing due to the inceased agnetisation speed. Estiation of cuent liit The ain pupose of a theal equivalent cicuit is to evaluate the heat dissipation as a function of geoety, loss distibution and ateial popeties. The aount of allowed losses ust be in accodance with the pedefined cooling capability and the theal liit. A syetic (stato) pat of theal equivalent cicuit is shown in Figue 3.3 and the coesponding definition of nodal losses and node tepeatues in Table 3..

7 Assignent The pupose of the theal equivalent cicuit is to define the cuent liit fo the specified geoety and opeation point. The agnetic flux density is ecalculated in agnetic equivalent cicuit fo the stato yoke and tooth and the powe losses accoding to that. Powe losses in the end tuns and convection in the end tun egion is not included as these ae not consideed in and copaed with D FEM. Figue 3.3 3D theal equivalent cicuit of suface ounted PMSM that includes /Ns wide odel ove a half axial length of the achine. Table 3. Node tepeatues and the coesponding heat souces. The sybols of the heat souce as well as the location in the initial odel file ae shown. Node Tepeatue Sybol Souce Sybol Powe losses Roto coe oto Coe losses P oto 0 Peanent agnet agnet Eddy cuent loss in the agnet P agnet 0 3 Ai-gap gap Ai dynaic fiction loss / cooling P gap 0 4 Stato tooth tooth Coe losses in the stato tooth P fe.teeth >0 5 Slotted winding coil Coppe losses P cu.dc.slot >0 6 Stato yoke yoke Coe losses in the stato yoke P fe.yoke >0 7 Coolant coolant Heat dissipation P coolant 0 8 Side abience side Heat dissipation P side 0 9 End winding end Coppe losses P cu.dc.end Design tool and odel The design odel is built in Matlab file EMK_task_3.. The odel consists of a ain function [ch]=emk_task_3(), which in tun includes achine (geoety) paaeteization con, ateial paaeteization and odeling d, and two sub functions:. [geo.,ch]=emk_geo_(d,con) that is geoetic odeling, includes design equations togethe with equivalent cicuit odels and akes geoetic odeling i.e. defines egions in pola coodinate syste and adds additional (ateial) data into vaiable geo. ch includes soe collected calculation esults fo ECM. EMK_gofe_(geo,d,task) geneates lua scipt that defines FE analysis in FEMM. The selection between heat tansfe and electoagnetis is ade in con.fe. This function autoatically executes the coesponding pepocesso, solve and post pocesso which is defined in the geneated LUA scipt

8 Assignent Geoety paaeteization The ateials and the geoety of the achine ae paaeteized and defined in the assignent file EMK_task_3.. The geoetic paaetes ae. the oute adius of the stato coe o, the inne adius of oto coe i, the inne stato adius si and the length of the stato laination stack h (instead of l) ae the ain paaetes these ae the paaetes that you ae asked to change,. the adial width of the ai-gap g=0.8e-3 the thickness of the ain slot insulation ins=0.5e-3 and additional paaetes such as the thickness of the housing cylinde hhc=5e-3, the tooth tip paaetes htt=e-3, hts=3e-3, Kso=0.5 ae pedefined and do not need to be changed, 3. a constant value is given to the agnet width facto K=/3,while the slot width facto Ks is vaiable 4. The est of the geoetical paaetes ae dependent paaetes Ks defines the tooth width *wt and the sae width is used fo the stato yoke hsy=*wt wt=(si+hts)*sin(pi/ns*(-ks)) whee Ns=3*Np stands fo nube of slots and Np fo nube of poles Housing cylinde o Stato coe Phase winding ins Slot insulation is Roto coe Peanent agnets htt 0.5 ap i a0s a3s as as hy hp hts hsy g hhc Figue 3.4 A section of PMSM that descibes the achine pats and defines all necessay paaetes to descibe the geoety 3.5 Assignent and scope of the analysis The analysis object of this assignent is a sevo PMSM and analysis pocess consists of the following steps. Fist the size of the achine is selected accoding to the fist non-nubeed table in the beginning of this docuent. The size paaetes ae highlighted in the saple code:. Calculate you initial achine and ty to optiize it by inceasing the toque by changing thee diffeent paaetes and keep tepeatue below 80 degees of Celsius. Define and pesent 3 iteations whee you ty to ipove the pevious iteation of the design.

9 Assignent Expess you expectations when intoducing the changes and otivate you choices. The paaetes ae descibed below and highlighted late in the saple code: a. nube poles Np=, Np=4, Np=6, etc b. Relative width of slots Ks in the ange of c. Inne adius of stato si=o-(o-i)*( ) 3. Study the FEM on heat tansfe and copae the esults to the expectations based on theal equivalent cicuit odel 4. Study the FEM on electoagnetis and copae the esults to the expectations based on agnetic equivalent cicuit odel and toque expession 5. Challenge youself and estiate: powe, efficiency, agnetic shea stess and sheet cuent density (look at the pevious equations fo these last two paaetes). In ode to validate the calculation esults find a suitable achine design to eet the pefoance of the coecial AC sevo oto fo aong baldo.co, abb.co, eesonindustial.co, kollogen.co, etc. The scipt (as it is) has the following achine paaeteization in the beginning of the -file con.n_p = 4; % nube of poles con.k_s = 0.4; % slotting facto con.h = 00.0e-3; % axial length of achine, con.hp = 3e-3; % height of peanent agnets, con.o = 50.0e-3; % oute adius of stato coe, con.i = 5.0e-3; % inne adius of oto coe, con.si = con.o-(con.o-con.i)*0.6; % inne adius of stato coe, con.j = 4e+6; % initial cuent density con. =.6; % initial flux density con.th = 0; % coil hot-spot tepeatue con.tab = 40; % abient tepeatue con.fe = 50; % supply agnetization fequency con.conv = 0; % convection facto This scipt ceates 3 figues: And povides soe feedback fo the calculations J [A/^] - peak cuent density 50% fill coil.387e+007 [Vs/^] - peak flux density: gap sth syk yk Ploss [W] - losses: wslot wend sth syk Tep [C] - tepeatues: ot wslot syk wend T [N] - toque Include (all) figues, nubes and design/leaning outcoes into you assignent epot.