A Scroll Compressor with a High Performance Induction Motor Drive for the Air Management of a PEMFC System for Automotive Applications

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1 A Scoll Compesso with a High Pefomance Induction Moto Dive fo the Ai Management of a PEMFC System fo Automotive Applications Benjamin Blunie Student Membe, IEEE, Macello Pucci Membe, IEEE, Giansalvo Ciincione Membe, IEEE and Abdellatif Miaoui Univesité de Technologie de BelfotMontbéliad (UTBM), Belfot CEDEX 9, Fance benjamin.blunie@utbm.f, abdellatif.miaoui@utbm.f ISSIACNR (Institute on Intelligent Systems fo the Automation), Palemo, Italy macello.pucci@ieee.og Dipatimento di Ingegneia Elettica Industiale, Politecnico di Toino, Italy g.ciincione@ieee.og Abstact This pape poposes a technological solution with a scoll compesso diven by a high pefomance induction machine dive fo the ai management of PEMFC (Poton Exchange Membane Fuel Cells) fo automotive applications. The toquespeed chaacteistics of a eal scoll compesso have been measued and then emulated by a bushless IMPM (intenal Mounted Pemanent Magnets) machine contolled in toque. This emulated scoll compesso has been diven by a field oiented contolled (FOC) induction moto dive. The whole ca model as well as the PEMFC have been implemented by softwae on the same DSP which implements the dive contol algoithm; in this way the hadwaeintheloop stuctue has been employed fo emulating the behaviou of a eal ca including the electical supply of the PEMFC. The whole system has been tested with a classic Euopean diving cycle. Two expeimental igs have been setup, one fo chaacteizing the scoll compesso and the othe fo emulating the entie vehicle. The expeimental esults have shown that the speed efeence pofile, obtained duing a uban diving cycle, is followed coectly and that the tanktowheel efficiency emains at quite high values confiming the goodness of the poposed technological solution. The hadwaeintheloop appoach of the expeimental ig allows tests to be pefomed to veify the opeation in steady and tansient states with low cost and educed employment of the Fuel Cell stack, with esulting inceased duability. Index Tems fuel cell ai management,automotive applications, highpefomance moto dives, compessos fo fuel cells I. INTRODUCTION The ai management in PEMFC (Poton Exchange Membane Fuel Cells) systems fo automotive applications plays an impotant ole fo the oveall pefomance of the entie vehicle since it absobs about % of the enegy povided by the fuel cell []. It is well known that the use of PEMFCs esults in the need of a lowe tempeatue than othe kinds of fuel cells, in highe powe density and a good tanktowheel efficiency. The liteatue lacks of pesenting guidelines fo the choice, on one hand of the compesso to be adopted, and on the othe hand of the electical dive which is most suitable as well as its contol stategy to be used fo optimising the pefomance []. As fo the ai compesso, the possibility of having high pessue ai esults in highe efficiency, lowe weight and lowe humidification wate fo the membane in the PEMFC stack [3]. Moeove, in geneal the liteatue gives expeimental esults as fo the efficiency of the system only fo one woking point, which is not the case in actual woking conditions whee diffeent woking points occu, depending on the path of the vehicle. Usually, centifugal compessos ae employed fo the ai management in PEMFC systems fo automotive applications because they have the wellknown advantage to be vey compact and light. Howeve, they have to wok at a vey high otation speed and need high tech beaings (magnetic o gas based). Centifugal compessos have also the disavantage to be efficient only fo a educed ange of mass flow and pessue. In medium powe PEMFC systems, centifugal compessos can be eplaced by positive displacement compessos like Scoll compessos, which pemit the system to wok at constant pessue and high efficiency ove a wide ange of mass flow. Moeove, thei much lowe otational speed allows the use of offtheshelf electical machines like induction machines o bushless IMPM (Intenal Mounted Pemanent Magnets) machines. This pape theefoe poposes a technological solution with a Scoll compesso diven by an induction machine dive. Futhemoe, the availability in the maket of low cost poweful DSPs as well as the educed cost of powe electonics devices esult in the possibility of adopting vaiable speed dive with high pefomance contol stategies. This pape pesents a solution fo the ai management of PEMFC systems which adopts, among othe possible solutions, a scoll compesso diven by an induction moto dive with a field oiented contol (FOC) []. The whole system is diven by a classic Euopean Diving Cycle (EEC Diective 9/C8/). An expeimental ig has been built fo testing the system. The toquespeed chaacteistics of a eal Scoll compesso have been fistly measued, then they have been emulated by a bushless IMPM contolled in toque. This emulated Scoll compesso has been diven by a FOC induction moto dive. The whole ca model, including the 9768/7/$. 7 IEEE

2 PEMFC, has been implemented by softwae on the same DSP whee the dive contol algoithm had been implemented; in this way, a hadwaeintheloop stuctue has been adopted to emulate the behaviou of the ca including the electical supply of the PEMFC. The pape is oganised as follows. Section II descibes Scoll compessos and justifies its use in this application. Section III descibes the vehicle model and its components. Section IV justifies the use of the induction moto dive fo the ai management. Section V descibes the expeimental ig. Section VI gives the simulation and expeimental esults. II. THE SCROLL COMPRESSOR SOLUTION The design and contol system fo managing the ai plays a key ole in a PEMFC system: some compaative studies have been caied out ove the past few yeas [4] [] [] and they show that seveal kinds of compessos can be employed, among which the tubocompessos (dynamical compessos) and the positive displacement compessos (Scoll compesso, lobe compesso, scew compesso, etc.). Fig. shows a compaison between seveal kinds of compessos accoding to thei equiements fo fuel cells systems in tanspotation, which ae: pessue atio: the pessue atio should be aound. 3 bas depending on the fuel cell stack; oil content: the oil has to be pohibited because it is detimental fo the fuel cell membane; pessue ipple: no pessue ipple geate than mbas is allowed. A geate pessue ipple would damage (pefoate) the membane; weight: weight should be as low as possible; volume: volume should be as small as possible. Othe equiements, which ae not witten hee, should be consideed like efficiency, pice and eliability. Most of the compessos given in Fig. meet the equiements, with the exception of piston compessos and membane compessos, which ae too bulky and heavy and also have a big pessue ipple. The blowes (low pessue) have to be chosen fo a low pessue fuel cell, which is not howeve the case hee. Positive displacement compessos with intenal compession have to be pefeed to those with extenal compession (isocoic compession) because they offe a bette efficiency. Centifugal compessos have the advantage of being vey compact and light (moe than any kind of positive displacement compesso as seen on Fig. ) as long as the otation speed is vey high ( kpm/min), which equies the use of oilfee magnetic o gas beaings and an adequate contol. Thei enegy efficiency is high but only in a educed ange of mass flow and pessue [] and they cannot wok at constant pessue, whateve the mass flow may be: actually at low values of mass flow the suge limit makes the compesso wok at quite low pessue with low efficiency. A lot of publications have been issued about centifugal compessos and thei contol in PEMFC systems [6]. On the othe hand, in the ange of medium powe PEMFC systems (below kw) the efficiency achieved by centifugal compessos is not so good, and positive displacement compessos with intenal compession (which ensues a good efficiency) like scoll compessos [7] ae to be pefeed, also because they allow the humidification to be embedded in the compession system [8] [9], esulting in the elimination of the humidifie and in a moe compact and efficient system. Unlike centifugal compessos, scoll compessos pemit the system to wok at constant pessue and high efficiency ove a wide ange of mass flow and do not have a zone of instability. Tests on oilfee ai compessos fo fuel cells have aleady been studied [] and have shown the advantages of thei use, without howeve testing them in a fuel cell system; moeove thei pefomance as been tested only in steady state at constant speed. III. VEHICLE SYSTEM MODEL As descibed on Fig. 4, the model contains thee main pats, that is the fuel cell system (stack) modelled by its static chaacteistic, the fuel cell auxiliaies (scoll compesso) and the ca. It is assumed hee that all the powe is deliveed by the fuel cell, also duing the tansients (no auxiliay powe souce). The fuel cell stack delives a goss powe (P goss )tothe ca and auxiliaies. It is calculated fom the equied electical powe of the ca P net (based on the diving cycle) and the auxiliaies powe (P aux ) of the fuel cell. The latte can be divided into two main contibutions: the electical compesso powe (P comp ) and the constant auxiliay powe (P const ) consumed mainly by the cooling system and the humidifie. P goss = P net P comp P const () The compesso powe P comp is measued: it is the electical powe of the induction machine. A. Fuel cell stack model It is assumed that the time constant of the compesso is geate than any othe time constant of the stack (i.e., the tempeatue and humidity ae pefectly egulated). The fuel cell is modelled and built fom a single cell static chaacteistic []: V c (j) =, 3, 4 4 j, 3 ln(j), exp ( 8 3 j ) () whee V c and j (ma/cm ) ae the cell voltage and the cuent density, espectively. The elation between the cuent density (j in A/cm ), the stack cuent (I in A), the numbe of cells (n c ) and the total suface active aea (S tot in cm ) is given by: j = In c (3) S tot The fuel cell powe is infeed fom () and (3). ( ) Inc P goss (I) =IV(I) =n c IV c (4) S tot The design paametes ae the numbe of cells n c fo minimum desied voltage and S tot fo the maximum powe.

3 Radial blowe Piston Centifugal Side Channel Scew Membane Rotay vane Lobe Scoll Claw Legend Pesseu atio Volume Oil? Vey bulky Volume Vey Compact Vey Heavy Weight Vey Light High ipple Pessue ipple No ipple Weight Pessue ipple Oil lubication Oil Oil fee Pessue atio Fig.. Compaison between seveal kinds of compessos Stack voltage (V) Stack powe (kw) Fig.. Stack cuent I (A) Numbe of cells : n c = Single cell active aea : S tot = 7 cm Stack minimum voltage Stack maximum powe (3 kw) Stack cuent I (A) Fuel cell stack chaacteistics The simulated fuel cell contains cells and a cell suface aea of 7 cm giving a maximal powe of 3 kw which meet the pefomance of the tested scoll compesso. The voltage and powe vs cuent chaacteistics of the stack ae given on Fig.. Because the voltage of fuel cells stack is low, a boost convete has to be added in ode incease the DC voltage to 7 volts. B. Ca model The scaled electical powe calculation of the ca P net takes into account the dynamics of the vehicle (dv/dt), its mass (M v ), the coefficient of fiction (C x ), the ca font suface (S), the olling coefficient (C ) and the dive tain efficiency (η d ). This model computes the electical powe necessay fo achieving the desied speed: P net = κ η d v ( dv M v dt ) ρ ai v SC x M v gc The powe is educed by a facto κ =/3 to adapt the powe to the maximum ai flow ate of the tested scoll compesso. C. Compesso model The compesso model is diectly based on the expeimental esults given by Fig. 3 and Fig. 7. The flow ate efeence q ai is calculated fom the goss powe demand of the fuel cell system [] on the basis of the following equation: q ai =3.7 7 λ P goss (6) V c (j) whee λ is the ai deliveing stoichiomety (λ =). The fuel cell cuent I (i.e., j) is obtained fom a D lookup table (P goss,i) and the single cell voltage V c (j) is calculated fom () and (3). ()

4 p, (ba) q (g/s) 9 Woking line Fig. 3. Electical powe contou lines (in watts) of the scoll compesso and woking pessue line Pcomp Fig. 4. Pconst contol H Induction machine Induction moto HARDWAREINTHELOOP scoll qai pai Paux efficiency: ηfc = Vfc/.48 Vfc Powe conditionning Pgoss Pnet not consideed Auxiliay powe souce valve Pext contol Block diagam of the vehicle system efficiency: ηt Electomechanical tansmission geas Pmech SIMULATED The compesso speed efeence is obtained fom the ai demand q ai and the intepolated data given on Fig. 7. The coesponding toque is computed fom Fig. 3 (taking into account the compesso mechanical efficiency). As seen on this figue the pessue is kept at bas duing all the test when it is possible: at low flow ates the scoll compesso cannot wok at bas and the pessue is maintained at its maximum value. IV. THE INDUCTION MOTOR DRIVE FOR THE AIR MANAGEMENT OF THE PEMFC SYSTEM Among the diffeent solutions, an induction machine dive has been chosen to dive the scoll compesso. The main altenative solution is a bushless pemanent magnet dive. With this egad, this choice has been made since induction motos have well known advantages in tems of highe eliability, highe obustness and lowe cost. On the contay, the dawbacks of such a solution ae: inceased volume occupied by the moto, educed toque/volume and toque/weight atios and inceased contol algoithm complexity. Nevetheless the availability in the maket of low cost high powe DSPs makes induction moto dives an inteesting altenative solution to pemanent magnet ones. In this pape, the induction moto solution has been chosen on the basis of the obustness, the eliability and the cost. Since the compesso dive must tack a speed efeence depending on the speed of the ca, a high pefomance contol technique has been chosen, the field oiented contol (FOC). Paticulaly, a diect otofluxoiented FOC scheme (Fig. ) has been adopted, whee the cuent contol is pefomed in the oto flux oiented efeence fame. In this case, the DC link is supplied by a PEMFC. On the diect axis, a flux contol loop commands the cuent loop and a voltage contol loop commands the flux loop to pemit the dive to wok automatically in the field weakening egion keeping the poduct between the oto flux amplitude and oto speed absolute value constant. On the quadatue axis, a speed loop contols the cuent loop. The speed efeence of the dive is computed in the hadwaeintheloop stuctue on the basis of the speed of an invese ca model based on the vehicle dynamics which takes into account its mass, the coefficient of fiction, the ca font suface and the dive tain efficiency (pat. III). A decoupling cicuit (Fig. ) has been used to coectly decouple the diect and quadatue cuent contols. All PI (Popotional Integal) contolles have been used in all the contol loops. An asynchonous space vecto modulation (SVM) with f PWM = khz has been used to command the invete. This modulation technique has been implemented by softwae in the same DSP whee the FOC algoithm has been implemented. The use of such a contol scheme pemits the dive to follow the speed efeence with high pefomance, to povide the load toque equied by the scoll compesso, which has a nonlinea law in espect with the speed of the dive itself, and finally to wok in the field weakening egion when the ca speed inceases. Since one of the most expensive pats of a high pefomance dive is the encode, a sensoless solution pemitting the dive to wok in a wide speed ange could be an inteesting pespective [9], [], [], [3]. In this case, a oto flux estimato based on the oto equations of the induction moto in the otofluxoiented efeence fame (the so called cuent model ), has been adopted. This choice has been done fo two easons: ) the cuent model is sensitive mainly to the oto esistance vaiation at inceasing slip speed of the machine caused by the load toque, diffeently fom the voltage model which is sensitive to the stato esistance vaiations at low speed. Many pats of the dive speed cycle ae at vey low speed and this justifies choice of the cuent model; ) the cuent model in the otofluxoiented efeence fame pefoms a closedloop integation, while the voltage model equies an openloop integation with consequent poblems that can be ovecome by suitable solution [4]. In this wok this solution has been tested expeimentally on a test ig with an induction moto to veify the goodness of the solution. Howeve, some impotant issues have still to be addessed, which ae not addesses by this wok, which ae: the choice of the moto in tems of size, powe and numbe of pole pais, the consequent choice of the DC link voltage to pemit the moto to wok in the whole speed ange equied by the vehicle at the maximum toque of the scoll compesso. V. EXPERIMENTAL RIG A expeimental ig has been devised fo the expeimental veification of the methodology. Fistly, a scoll compesso

5 u ef u I mef ef m i syef PI i sy i sxef PI i sy i sx m isx PI u sy u syef u sqef u dy j 3 DECOUPLING CIRCUIT u e dx u PI sx u u sdef sxef u saef u sbef u scef VECTOR MODULATION PEMFC VSI INVERTER INDUCTION MOTOR Scoll Compesso Encode ABS X m m i sy i sx FLUX MODEL i sd i sq Ud 3 A D i sa i sb i sc Ud Fig.. Block diagam of the FOC scheme fo diving the scoll compesso qai (g/s) Ω(q) =.37 q 3.94 q 4.34 q Ω(q ai ) Expeiment Ω (ad/s) Fig. 7. Relation between the speed and the ai mass flow ate Fig. 6. Photogaph of the scoll compesso test bench (UTBM Laboatoy, Fance) has been expeimentally chaacteized to etieve the speed vs toque cuve (extacted fom Fig. 3) and the ai mass flowate vs speed (Fig. 7). Fig. 6 shows a photogaph of the scoll compesso unde study. This expeimental ig has been built to test in an automated way the pefomance and contol laws of positive displacement compessos. Aftewads, the speed vs toque chaacteistics of the scoll compesso as well as the whole ca model including the PEMFC has been implemented by softwae on the same DSP whee the dive contol algoithm had been implemented; in this way, a hadwaeintheloop stuctue has been adopted to emulate the behaviou of the ca including the electical supply of the PEMFC. A static model of the PEMFC (see pat III) has been adopted fo the expeimental veification of the method. Howeve, since the vaying time constant of the PEMFC is much highe than that of the machine, it does not affect the goodness of the methodology. The dive test set up consists of [] [6]: A theephase induction moto with paametes shown in Table I; A fequency convete which consists of a theephase diode ectifie and a 7. kva, theephase VSI fo supplying the induction moto; A bushless Inteio Mounted Pemament Magnets (IMPM) machine dive fo loading the induction machine; A fequency convete which consists of a theephase diode ectifie and a 8 kva, theephase VSI fo supplying the IMPM; A dspace cad (DS3) with a PowePC 64e at 4 MHz and a floatingpoint DSP TMS3F4. Fig. 8 shows a photogaph of the test setup. The output DigitaltoAnalog channel of the DSP gives the toque efeence to the IMPM dive in eal time on the basis of the scoll compesso model implemented on the DSP itself. In this way, the IMPM dive behaves exactly as the scoll compesso in the whole speed ange. The flux estimato and the whole FOC contol algoithm have been implemented on the DSP at a sampling fequency of f c =khz. The ca model, the PEMFC model and the Scoll compesso model have been implemented at a lowe sampling fequency, which is in this case khz.

6 Rated powe P ated [kw]. Rated voltage U ated [V] Rated fequency f ated [Hz] Rated Speed [ad/s] 49.7 Polepais Stato esistance R s [Ω].9 Stato inductance L s [mh] 3 Roto esistance R [Ω]. Roto inductance L [mh] 9 3phase magnetizing inductance L m [mh] 7 Moment of inetia J [kg m ].48 TABLE I PARAMETERS OF THE INDUCTION MOTOR ca speed (m/s) Fig. 9. Ca speed duing the diving cycle (simulation). ψ (wb) Field weakening Fig. 8. Photogaph of the test setup (ISSIACNR Electical Dives Laboatoy, Italy) VI. RESULTS A. Simulation esults The poposed scoll compesso based system supplied by the PEMFC has been tested fistly in numeical simulation in MatlabSimulink envionment. The paametes of the simulated induction machine, VSI invete, Scoll compesso and PEMFC ae those of the expeimental ig descibed in pat V. The sampling fequency of the contol scheme has been set equal to khz fo both contol schemes. The models of the sensoless induction moto dive with its flux obseve, the PEMFC and the vehicle dynamics have been ceated fo this pupose (see pat. III). The Euopean Diving Cycle ( uban followed by extauban) has been adopted to test the behaviou of the dive. Since the adopted woking cycle makes the machine wok in the field weakening egion, the value of the load toque equied by the Scoll compesso has been limited to 4 Nm, which is close to the toque limit value which can be povided by the induction machine unde test at the maximum speed duing the above mentioned test cycle. Fig. 9 shows the ca speed in the Euopean Diving Cycle. This is vey challenging cycle fom the point of view of the compesso dive. As a matte of fact it can be obseved that the dive speed efeence anges fom zeo speed duing some time intevals to vey low speed (.97 ad/s) in othe time intevals up to 97 ad/s in field weakening egion. Fig.s and show wavefoms of the oto flux amplitude, the Scoll toque with the coesponding electomagnetic toque povided by the induction machine and finally the efeence and measued speed of the dive. They show that toque (Nm) 3 Scoll toque Electomagnetic toque Fig.. Roto flux amplitude, scoll compesso toque duing the diving cycle (simulation) above ad/s the contol system automatically educes the oto flux amplitude, as expected. The electomagnetic toque poduced by the induction machine is always equal to the scoll compesso toque excepted when a speed tansients equied by the machine. The speed cuves show that the dive coectly woks in the whole speed ange fom vey low speed up to the ad/s. Both in tansient and steadystate conditions the dynamics of the speed loop is high, with hadly distinguishable cuves of the efeence and measued speed; the dives thus woks coectly with the diving cycle. Fig. shows the net and goss powe P net, P goss, q ai and the PEMFC voltage povided by the fuel cells stack duing the same test. It also shows the global efficiency of the systems (tanktowheel efficiency). B. Expeimental esults The expeimental veification of the scoll compesso dive has been caied out on the test setup descibed in section V. As in the simulation test, the standad Euopean Diving Cycle has been adopted. Since this woking cycle makes the machine wok in the field weakening egion, also in this

7 Refeence Measued 9 ad/s ω (ad/s) ad/s zeo speed ca speed (m/s) Fig.. Refeence and measued dive speed duing the diving cycle (simulation) PEMFC voltage (V) q ai (g/s) Fig Ca speed in the standad diving cycle (expeiment) ψ (wb) Field weakening Goss and net powe (kw) P net P goss Tank to wheel efficency (%) Scoll toque (Nm) 4 3 Fig.. Net powe povided by the supply duing the diving cycle (simulation) case the value of the load toque has been limited to 4 Nm. Fig. 3 shows the ca speed in the Euopean Diving Cycle, as implemented on the DSP. Fig.s 3, 4 and show the coesponding wavefoms of the oto flux amplitude, the scoll toque (IMPM toque) and the efeence and measued speed of the dive. They show that above ad/s the contol system automatically educes the oto flux amplitude. The load toque poduced by the IMPM coesponds to that of the scoll compesso, with the above mentioned limit of 4 Nm in field weakening. The speed cuves show that the induction moto dive coectly woks in the whole speed ange fom vey low speed up to the ad/s. Both in tansient and steadystate conditions the speed loop dynamics is high, and the dives woks coectly with the Euopean Diving Cycle. This is paticulaly inteesting, since the dive cycle equies vaiying speed anging fom zeo up to ad/s at vaiying speed load toques Fig. 4. Roto flux amplitude, scoll compesso toque duing the Euopean Diving Cycle (expeiment) ω (ad/s) Refeence 9 ad/s Measued zeo speed.97 ad/s Fig.. Refeence and measued speed of the dive (expeiment) VII. CONCLUSION This pape pesents expeimentally the advantages of using a highpefomance induction moto dive connected to a scoll compesso fo the ai management of PEMFC (Poton Exchange Membane Fuel Cells) in automotive applications. The use of a scoll compesso has the advantage that it can be contolled at constant pessue. Unlike centifugal compessos. Moeove, the lowe otational speed of such compessos

8 makes the use of induction moto dive possible, which esults in highe obustness, lowe cost and highe eliability than those obtainable with othe technological solutions (fo example centifugal compessos plus pemanent magnet motos). The toquespeed chaacteistics of a eal scoll compesso have been measued and then emulated by a bushless IMPM (intenal Mounted Pemanent Magnets) machine contolled in toque. This emulated scoll compesso has been diven by a field oiented contolled (FOC) induction moto dive. The whole ca model as well as the PEMFC have been implemented by softwae on the same DSP which implements the dive contol algoithm; in this way the hadwaeintheloop stuctue has been employed fo emulating the behaviou of a eal ca including the electical supply of the PEMFC. The whole system has been tested with a classic Euopean diving cycle. The expeimental esults have shown that the speed efeence pofile anging fom zeo speed to vey low speed up to ad/s in field weakening egion, obtained duing a uban diving cycle, is followed coectly and that the tanktowheel efficiency emains at quite high values confiming the goodness of the poposed technological solution. Futue wok will deal with the application of intelligent sensoless techniques to impove the eliability and educe the cost of such this application. NOMENCLATURE Geek lettes η d Dive tain efficiency κ Scaling facto λ Ai deliveing stoichiomety ρ Roto fluxlinkage angle (ad) Ψ d, Ψ q Diect and quadatue component of the oto flux linkage in the stato efeence fame ω m Speed of the oto flux linkage space vecto ω m Mechanical oto speed Roman lettes C Ca olling coefficient C x Ca coefficient of fiction f PWM Invete modulation fequency I Fuel cell stack cuent (A) i s Space vecto of the stato cuents in the stato efeence fame i sd,i sq Diect and quadatue components of the stato cuents in the stato efeence fame j Fuel cell cuent density (ma/cm ) L m Total static magnetising inductance L Roto inductance L s Stato inductance M v Ca weight (kg) n c Stack cells numbe P aux Fuel cell auxiliaies powe (W) P comp Fuel cell compesso powe (W) P const Fuel cell constant auxiliaies powe (W) P goss Fuel cell goss powe (W) P net Fuel cell net (ca) powe (W) q ai Compesso ai mass flow ate (kg/s) Resistance of a oto phase winding R R s Resistance of a stato phase winding S Ca font suface (m ) S tot Fuel cell total active aea (cm ) U d DC link volatge (V) V Fuel cell stack voltage (V) v Ca speed (m/s) Single fuel cell voltage (V) V c REFERENCES [] S. 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