Comparison of winding topologies in a pot core rotating transformer Smeets, J.P.C.; Encica, L.; Lomonova, E.

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1 Compaison of winding topologies in a pot coe otating tansfome Smeets, J.P.C.; Encica, L.; Lomonova, E. Published in: Poceedings of the 2 2th Intenational Confeence on Optimiation of Electical and Electonic Equipment (OPTIM), 2-22 May 2, Basov DOI:.9/OPTIM Published: //2 Document Vesion Publishe s PDF, also known as Vesion of Recod (includes final page, issue and volume numbes) Please check the document vesion of this publication: A submitted manuscipt is the autho's vesion of the aticle upon submission and befoe pee-eview. Thee can be impotant diffeences between the submitted vesion and the official published vesion of ecod. People inteested in the eseach ae advised to contact the autho fo the final vesion of the publication, o visit the DOI to the publishe's website. The final autho vesion and the galley poof ae vesions of the publication afte pee eview. The final published vesion featues the final layout of the pape including the volume, issue and page numbes. Link to publication Citation fo published vesion (APA): Smeets, J. P. C., Encica, L., & Lomonova, E. (2). Compaison of winding topologies in a pot coe otating tansfome. In Poceedings of the 2 2th Intenational Confeence on Optimiation of Electical and Electonic Equipment (OPTIM), 2-22 May 2, Basov (pp. 3-). Piscataway: Institute of Electical and Electonics Enginees (IEEE). DOI:.9/OPTIM Geneal ights Copyight and moal ights fo the publications made accessible in the public potal ae etained by the authos and/o othe copyight ownes and it is a condition of accessing publications that uses ecognise and abide by the legal equiements associated with these ights. Uses may download and pint one copy of any publication fom the public potal fo the pupose of pivate study o eseach. You may not futhe distibute the mateial o use it fo any pofit-making activity o commecial gain You may feely distibute the URL identifying the publication in the public potal? Take down policy If you believe that this document beaches copyight please contact us poviding details, and we will emove access to the wok immediately and investigate you claim. Download date:. Oct. 28

2 Compaison of Winding Topologies in a Pot Coe Rotating Tansfome J.P.C. Smeets, L. Encica, E.A. Lomonova Depatment of Electical Engineeing, Electomechanics and Powe Electonics Eindhoven Univesity of Technology, Eindhoven, The Nethelands j.p.c.smeets@tue.nl Abstact This pape discusses the compaison of two winding topologies in a contactless enegy tansfe system fom the stationay to the otating pat of a device. A otating tansfome, based on a pot coe geomety, is poposed as a eplacement fo wies and slip ings. An electomagnetic and a themal model of the otating tansfome ae deived. The models ae combined and used in a multi-objective optimiation. A Paeto font, in tems of minimal volume and powe losses, is deived to compae both winding topologies. Finally, the optimiation algoithm is used to design a pototype tansfome fo each winding topology, which ae manufactued using a commecially available pot coe. Fig.. Axial and pot coe otating tansfomes. I. INTRODUCTION In many moden technetonic systems, the tansfe of powe to otating pats plays an impotant ole, fo example, in obotic applications [] and in industial electonics whit otating electonics. Nowadays, wies and slip ings ae used to tansfe powe to the otating pat. Disadvantages of wies ae a limited otation angle and an inceased stiffness. To ovecome the poblem of limited otation, slip ings ae used. Despite the significant amount of eseach and development of eliable and duable slip ings, the lifetime is limited by contact wea as well as vibation and fequent maintenance is equied [2]. A solution to ovecome the disadvantages of wies and slip ings is a contactless enegy tansfe (CET) system that uses a otating tansfome. That is a tansfome with an aigap between the pimay and seconday side, whee one side can otate with espect to the othe. An exta advantage could be the feedom in winding atio to tansfom the pimay voltage level to the equiements of the load. The axial and pot coe tansfome geometies, both shown in Fig., have the possibility to otate one side with espect to the othe side and, theefoe, can be used as a otating tansfome. Both geometies ae compaed in tems of optimal volume and efficiency in [3]. The pot coe tansfome geomety gives bette pefomance indices compaed to the axial geomety. Inside the pot coe otating tansfome two winding topologies can be used. The adjacent winding topology, shown in Fig. 2a, whee each winding is placed in an own coe half and the coaxial winding topology, shown in Fig. 2b, whee the seconday winding is place aound the pimay winding [4]. In this pape both winding topologies ae compaed in tems of minimal powe losses and volume using an optimiation algoithm. Fo this pupose, tansfome models ae deived N p N s Winding bobbin N p Ns Fig. 2. Winding topologies fo the pot coe otating tansfome, adjacent and coaxial. based on the electomagnetic and themal behavio and combined in a optimiation pocedue. A multi-objective optimiation is conducted to define the optimal winding topology [5]. Finally, fo each winding topology a otating tansfome with minimal powe losses is designed and manufactued using a commecially available pot coe. The pototypes ae used to veify the deived tansfome models. II. ROTATING POT CORE TRANSFORMER A detailed dawing of the geomety of the otating pot coe tansfome is shown in Fig. 3, the coesponding paametes ae listed in Table I. Based on Faaday s law of induction and Ampee s cicuital law, an initial design expession fo the powe tansfe in the tansfome can be given by P = πjsk f fb peak A e, () whee J is the cuent density, S is the winding aea, f is the fequency of the applied voltage, k f is the filling facto of the winding, B peak is the peak flux density and A e is the coss section of the inne coe. Equation () shows that the powe tansfe is depending on the geometic paametes, fequency and flux density //$26. '2 IEEE 3

3 θ R cb A e S R ca N p R cc lag R lkp hin R aga R agb c in cout hout hc R lks R ca N s R cc Fig. 3. Geomety of the pot coe otating tansfome, top view and coss section. TABLE I GEOMETRICAL PARAMETERS OF FIG. 2 AND FIG. 3 Paamete, 2, 3, 4 cin cout h out h in h c l ag A e S N p N s Desciption Radius of the diffeent coe pats Length of the inne coe pat Length of the oute coe pat Oute height of a coe half Height of the winding aea S Thickness of the hoiontal coe pat Length of the aigap Effective coe aea Winding suface Numbe of tuns on pimay side Numbe of tuns on seconday side The otating tansfome is pat of a dc-dc powe convesion system, which consists of a half bidge convete connected to the pimay side of the tansfome to ceate a high fequency voltage and a diode ectifie connected to the seconday side of the tansfome to ectify the voltage back to a dc-voltage. III. ANALYTICAL MODELS In this section the electomagnetic and themal model of the otating tansfome ae descibed. The models will be combined fo futhe analysis. A. Magnetic model A magnetic model is deived to calculate the inductances of the tansfome. The magnetiing inductance, L m, is calculated using a eluctance model. The model is shown in Fig. 4, whee R pesents the eluctance of the magnetic path and the subscipts c, ag and lk indicate the flux path in the coe, aigap and leakage, espectively. The magnetiing inductance is calculated by L m = N 2 p 2(R ca + R cb + R cc ) + R aga + R agb. (2) The leakage flux lines in the otating tansfome do not have an a pioi known path, theefoe, it is inaccuate to model them with a eluctance netwok as well. The leakage inductance, L lk, is calculated by the enegy of the magnetic field in the winding volume 2 L lki 2 = 2 v B Hdv, (3) R cb Fig. 4. Reluctance model of the otating tansfome with adjacent winding topology. V p I p Fig. 5. C p R p L lkp I m I s k I s L m N p N s L lks R s C s V s R load Electic equivalent cicuit of the otating tansfome. which is equal to the magnetic enegy of the leakage inductance [6]. An expession fo the magnetic field stength is found by the magnetic cicuit law. In the case of the adjacent winding topology, the magnetic field stength is expessed fo the pimay winding as function of the axial length H() = N pi p, (4) ( 3 2 ) h wp whee h wp is the height of the pimay winding. A simila expession can be deived along the seconday winding. In the aigap a unifom mmf is assumed, defining the magnetic field stength by H = N pi p l ag. (5) Combining (3)-(5), esults in an expession fo the total leakage inductance of the tansfome seen fom the pimay side ( ) L lk = µ Np 2 2π hwp + h ws + l ag. (6) ln( 3 / 2 ) 3 B. Electic model An electic equivalent cicuit of the otating tansfome is deived to calculate the powe losses in the tansfome. The model is shown in Fig. 5. In the cicuit the otating tansfome is epesented by the magnetiing and leakage inductances and a lossless tansfome with winding atio a = N p /N s and coupling facto, k. Futhemoe, winding esistance and esonance capacitances ae inseted. The cicuit is connected to a squae wave input voltage souce and an equivalent load esistance. 4

4 The winding esistance, R p, R s, consists of a dc and acesistance. An expession fo the winding esistance in case of non-sinusoidal wavefoms is deived in [7], based on Dowell s fomula fo AC-esistances. The effective winding esistance is calculated by R eff = R dc + Ψ ( ) I R ms dc, (7) 2πf I ms whee Ψ is a coection facto fo the numbe of layes, is the winding thickness of a laye when it is conveted to an equivalent foil-type winding divided by the skin depth, I ms is the ms-value of the deivative of the cuent wavefom and ω is the angula fequency. To impove the powe tansfe of the tansfome, esonant techniques ae used [8]. A esonant capacito is placed in seies on both sides of the tansfome: On the pimay side, to ceate a eo cossing esonance voltage and theeby allowing the use of a half bidge invete. On the seconday, to ovecome the voltage dop acoss the leakage inductance and theeby impoving the powe tansfe. Futhemoe, by a applying seies esonance on the seconday side, the pimay side is made unsensitive fo coupling changes, fo example caused by vibation duing otation. This can be illustated by calculating the value of the pimay esonance capacitance fo a seies and paallel esonance on the seconday side, espectively C p seies = C p paallel = ωes 2 (L p ), (8) ωes(l 2 lkp M 2 /L lks ), (9) whee L p (= L m /k) and L s (= L m /a 2 k) is the self inductance of the pimay side and seconday side of the otating tansfome, espectively, and M(= k L p L s ) is the mutual inductance of the otating tansfome. The esults of equation (8) and (9) is shown in Fig. 6 fo an inceasing magnetic coupling. A constant pimay esonance capacitance can be obtained by applying seies esonance on the seconday side, The esonance technique ceates a band pass filte aound the esonance fequency to filte-out unwanted hamonics and theeby deceasing the AC-losses in the windings. The quality of this filte depends on the esonance fequency, leakage inductance and load esistance of the tansfome and is defined by Q = 2πf esl lk R load. () Using esonance capacitos, the pimay voltage at esonance, V p, can be calculated with [9] V p = (R p + ω2 esm 2 ) I p, () R s + R load (2) Nomalied Cp Seies Seies esonance Seies Paallel esonance Magnetic coupling, k Fig. 6. Influence of the magnetic coupling on the pimay esonance capacitance. and the cuent density in the winding is calculated, based on () J n = I nn n Sk f. (3) The conduction and coe losses ae the main powe losses in the otating tansfome. The conduction losses, P cond, ae calculated by P cond = I 2 p ms R p + I 2 s ms R s, (4) whee I pms is the pimay ms-cuent, which consists of the magnetiing cuent and the eflected load cuent. The coe losses, P coe, ae calculated by the Steinmet equation P coe = C m C(T)f x esb y V coe, (5) whee C m, x and y ae mateial specified constants (fo example C m =7, x=.4 and y=2.5 fo the 3C8 coe mateial). C(T) is a tempeatue depending constant and is equal to if the coe tempeatue is ±2 aound the ideal woking tempeatue, which is 6 C fo the 3C8 coe mateial. Fo a constant powe tansfe, the flux density can be calculated as a function of fequency as indicated in (). By vaying the fequency an optimal woking point with minimal losses can be found (shown in Fig. 7). C. Themal model It is impotant to estimate the coe tempeatue since the coe and conduction losses cause a tempeatue ise in the coe mateial, which has an optimal woking tempeatue with minimal powe losses. A themal equivalent cicuit of the coe, shown in Fig. 8, is made using a finite-diffeence modeling technique, whee the themal esistance concept is used fo deiving the heat tansfe between the nodes []. The themal model is deived by dividing the uppe half of the geomety into six egions, whee egions I till V epesent the coe and egion V I epesents the tansfome winding. Five nodes ae defined fo each egion and the heat tansfe between the nodes is modeled by a themal esistance. Conduction esistances ae used to model heat tansfe inside 5

5 Powe loss (W) P coe P cond P total loss TABLE II LIMITS OF THE OPTIMIZATION VARIABLES. min va. max < 2 max 2 < 3 max < h in h max.5 mm l ag 2. mm N p N max N s N max kh f es 2 kh Fequency (kh) Fig. 7. a b c d e Fig. 8. I Powe losses as a function of the fequency. q II III IV q q q V I q a b c d e f g Conduction esistance Convection esistance q Heat souces: Coe o coppe losses Themal equivalent cicuit of the tansfome. the egions and convection esistances ae used to model the heat tansfe between the bode of the egions and the ai. The conductive themal esistance in - and - diection ae calculated by R th = π(o 2 i 2 (6) )k, R th = ln( o/ i ) 2πk, (7) whee k is the themal conductivity, equal to 4.25 and 394 Wm K fo the feite coe and coppe windings, espectively. The convective themal heat esistance is calculated by R h = ha, (8) whee h is the heat tansfe coefficient obtained fom the Nusselt-numbe, which is equal to 2.7 and 8.5 Wm 2 K fo the axial and adial boundaies of the pot coe. No heat tansfe is assumed at left and lowe bounday of the model, assuming a wost-case themal situation. The powe losses in each egion ae pesented by a heat souce and inseted in the middle node of egion. By calculating the heat tansfe between each node, the tempeatue in the middle V q of each egion is obtained. An ambient tempeatue of 2 C is assumed. IV. OPTIMIZATION ALGORITHM The analytical models ae implemented in MATLAB and used in an optimiation pocedue to find the optimal tansfome design in tems of both minimal volume and powe losses fo a constant powe tansfe of kw and a seconday voltage of 5 V. A sequential quadatic pogamming algoithm is used to find the minimal Paeto font of the two objective functions []. Theefoe, the weighted sum method fo multi-objective poblems is used min F(x) = N obj m= w mf m (x) m =,...,N obj g j (x) j =,...,J neq h k (x) = x lo i x i x up i k =,...,K eq i =,...,N va (9) The weights w m [,...,] ae selected such that the sum of the weighting coefficients is always N obj m= w m =. This function finds the minimum of the objective functions subjected to the unequality, g j, and equality constaints, h k, within the lowe and uppe boundaies of the vaiables x i. In the next sections the vaiables, constaints and objective functions ae explained in moe detail. A. Vaiables As shown in (), the coe dimensions, length of the aigap, numbe of tuns and fequency ae paametes which have influence on the design of the otating tansfome. The lowe and uppe value of those vaiables is specified in Table II. Whee N max is the maximum numbe of tuns, defined by N max = Sk f A wie. (2) Paametes max and h max limit the maximum coe dimensions and theeby, educe the calculation time. Futhemoe, the atio between the inne and oute adial length and the thickness of the hoiontal coe pat ae fixed, based on existing pot coes dimensions [2] cout =.55 cin, (2) h c =.65 cin, (22) = 2.7 mm. (23) With constaint (23) the inne adius of the coe is set to obtain a minimal hole in the middle of the tansfome to mount the coe. Othe geometic paametes such as coe 6

6 f 2 f 2n 25 Adjacent Coaxial 2 f 2 Paeto font Nomalied Paeto font Powe loss (W) 5 f f f n 5 Fig. 9. Paeto font befoe and afte nomaliation Volume (cm 3 ) mateial specifications and wie paametes ae given as input paametes fo the optimiation function. B. Constaints Fo the electomagnetic and themal popeties of the otating tansfome, a numbe of constaints is intoduced. Fistly, fom a magnetic point of view, satuation in the coe should be avoided and the coupling should be lage than 6%, i.e. B coe B sat, (24) k.6. (25) Secondly, fom an electical point of view, the input voltage is limited by the maximal output voltage of the dc-voltage souce, the maximal cuent density is limited by the wie popeties and the quality facto of the esonance cicuit should be lage than to filte-out highe hamonics V p V dcmax, (26) J n J nmax, (27) Q. (28) Finally, fom a themal point of view, the coe tempeatue should stay below C, because up to this tempeatue the coe losses ae almost constant, C. Objective functions T coe C. (29) The design optimiation is conducted in tems of minimal volume and powe losses, using the following objective functions f (x) = π 2 4 2h out (3) f 2 (x) = P cond + P coe. (3) Both objectives ae nomalied by defining the two limits of the Paeto font, esulting in paamete sets x and x 2 fo the individual minimiation of f (x) and f 2 (x), espectively [3] (see Fig. 9). The nomalied objective functions ae f n (x) = f (x) f (x ) f (x 2 ) f (x ), (32) f 2n (x) = f 2(x) f 2 (x 2 ) f 2 (x ) f 2 (x 2 ). (33) The nomaliation allows an equal compaison of both winding topologies. Fig.. Paeto font fo optimal design in tems of volume and powe losses. V. DISCUSSION OF THE OPTIMIZATION RESULT By applying diffeent combinations of weighing factos, a minimal Paeto font is found fo both topologies, shown in Fig.. The Paeto font shows that the adjacent winding topology obtains lowe powe losses fo the same coe volume compaed the coaxial winding topology. In the Paeto font two asymptotes can be obtained. A vetical asymptote fo the minimal equied coe volume, limited by the maximal allowable coe tempeatue, since the losses ae inceasing damatically fo a small coe with a high fequency and high magnetic flux density. And a hoiontal asymptote fo the minimal powe losses, which is based on an optimum in magnetic flux density, fequency and volume, compaable as shown in Fig. 7. Detailed tansfome paametes ae given fo two ealistic exteme optimiation cases fo the coaxial and adjacent winding topology in Table III and IV, espectively. The objective functions ae defined as 9%f n (x) + %f 2n (x) fo case and %f n (x) + 9%f 2n (x) fo case 2. In othe wods, the volume is minimied in case and the powe losses ae minimied in case 2. The lette A and C befoe the case numbes indicate the adjacent and coaxial winding topology, espectively. The uppe half of the coss section of two coaxial cases is shown in Fig.. The coe dimensions of the adjacent winding topology ae almost identical to the coaxial winding topology and theefoe not shown. Compaing the fou cases, the following obsevations ae made: In case C, a small coe adius with a elative lage winding aea is obtained and, in case C2, a lage coe adius and a smalle winding aea can be found. The total volume of the adjacent winding topology is slightly lowe, because the winding aea is used moe efficient. In all fou cases the aigap is minimied to the minimal ealiable mechanical aigap. The magnetiing inductances of both winding topologies ae compaable fo the diffeent cases. The leakage inductance of the coaxial winding topology is appoximately 5 times lowe compaed to the adjacent 7

7 (mm) (mm) (mm) (mm) Fig.. Optimied coe dimensions fo the coaxial winding topology, minimal volume and minimal losses. TABLE III TRANSFORMER PARAMETERS FOR TWO CASES WITH COAXIAL WINDING TOPOLOGY. Paamete Case: C Case: C2 Unit cin mm cout 3..5 mm mm h out mm l ag.5.5 mm S 3 95 mm 2 A e mm 2 V cm 3 N p tuns N s 6 tuns B coe mt f es kh L mp mh L Lkp.5.5 mh L lks µh k P loss.7 4. W T coe C winding topology. This is because both windings of the coaxial winding topology shae an identical magnetic flux path, which is not the case in the adjacent winding topology. Less leakage esult in a highe coupling coefficient, which is obtained fo the coaxial winding topology. The winding atio is the same in the fou cases, because of the fixed seconday voltage and the maximied pimay voltage. The optimiation algoithm maximies the pimay voltage, to educe the pimay cuent and theeby the losses. In case 2, a lowe fequency and magnetic flux density is obtained compaed to case, coesponding to the elation between the geomety, fequency and flux density as given in (). The powe losses in case A ae 2% highe as in case C, coesponding to a 2% smalle volume in case A compaed to case C. In case 2 both topologies have almost equal powe losses. The tempeatue is depending on the powe losses and coe volume and is thus highe in the adjacent winding topology compaed to the coaxial winding topology. TABLE IV TRANSFORMER PARAMETERS FOR TWO CASES WITH ADJACENT WINDING TOPOLOGY. Paamete Case: A Case: A2 Unit cin mm cout mm mm h out mm l ag.5.5 mm S mm 2 A e mm 2 V cm 3 N p 99 7 tuns N s 7 tuns B coe 37 3 mt f es 24.2 kh L mp mh L Lkp mh L lks µh k P loss W T coe C TABLE V P66/55 POT CORE DIMENSIONS. Paamete Dimension Unit cin.8 mm cout 5.9 mm mm h out 28.7 mm l ag.5 mm S 286 mm 2 A e 583 mm 2 V 99 cm 3 Oveall, minimal losses can be obtained in a elative lage coe. The adjacent winding topology is favoable because it uses the winding aea moe efficient, esulting in a lowe magnetiing cuent and theeby, lowe losses, as shown in the Paeto font. VI. EXPERIMENTAL VERIFICATION Fo each winding topology a otating tansfome is designed using the optimiation algoithm. The optimiation is conducted fo fixed powe tansfe of kw, obtaining minimal powe losses, using the commecially available P66/56 pot coe fom Feoxcube. Theeby, the coe dimensions ae fixed and they ae specified in Table V. The coe consist of the mateial 3C8 [2], a special developed Mann feite fo high powe applications below a fequency of 2 kh, with minimal powe losses aound 6 C. The mateial has a low satuation level, hence in this pape a satuation level of 35 mt is assumed. The manufactued otating tansfomes ae shown in Fig. 2. The coesponding paametes ae specified in Table VI and VII fo the adjacent and coaxial winding topology, espectively. The paametes ae compaed with FEM simulations [4] and inductances ae measued with the HP 494A impedance analye, a maximum eo of 8% is obtained. Compaison of the paametes of the pototype tansfomes shows that minimal losses ae obtained in the adjacent winding topology. This can be explained by the diffeent numbe of tuns which fit in the winding aea of both topologies. Since 8

8 TABLE VI OPTIMIZED TRANSFORMER PARAMETERS FOR THE ADJACENT WINDING TOPOLOGY. Paamete Optimiation FEM Measuement Unit N p - - tuns N s - - tuns l ag mm f es kh B coe mt L mp mh L Lkp mh L lks µh k P loss W T coe C TABLE VII OPTIMIZED TRANSFORMER PARAMETERS FOR THE COAXIAL WINDING TOPOLOGY. Paamete Optimiation FEM Measuement Unit N p tuns N s tuns l ag mm f es kh B coe mt L mp mh L Lkp.9.. mh L lks µh k P loss W T coe C the adjacent winding topology uses the winding aea moe efficiently, a highe numbe of tuns is obtained which inceases the magnetiing inductance and simultaneously deceases the magnetiing cuent. This esults in lowe conduction losses. Futhemoe, since moe tuns fit in the adjacent winding topology, a lowe fequency can be obtained which educes the coe losses. The stationay pefomance of the otating tansfomes is measued in an expeimental setup. A half bidge convete is connected to the pimay side of the tansfome and a diode ectifie is connected to the seconday side. Resonance capacitances ae connected on both sides of the tansfome. A 2 VDC input voltage is supplied to the half bidge and an equivalent esistance of 2.5 Ohm is connected to the diode ectifie. The pimay voltage wavefom is measued afte the half bidge and the seconday voltage wavefom is measued befoe the diode ectifie. The wavefoms ae shown in Fig. 3 fo a powe tansfe of 5 W, since the used half bidge limits the maximal input voltage. The figue shows the pimay voltage on the left axis of the gaphs. The axis on the ight indicates the seconday voltage, appoximately times lowe in amplitude due to the winding atio and vaies aound. The amplitude of the seconday voltage of the coaxial winding topology is lowe compaed to the adjacent winding topology because of the slightly highe winding atio. VII. CONCLUSION In this pape the adjacent and coaxial winding topologies in a otating pot coe tansfome have been compaed in tems of total coe volume and powe losses. A multi-objective Fig. 2. Manufactued tansfomes adjacent winding topology and coaxial winding topology. Pimay voltage (V) Pimay voltage (V) time (s) x Pimay voltage Pimay voltage Seconday voltage Seconday voltage time (s) x 4 Fig. 3. Measued pimay and seconday voltage wavefom of the otating tansfome with adjacent and coaxial winding topology. optimiation has been defined, using an electomagnetic and a themal model of the otating tansfome. The optimiation algoithm has been used to deive the minimal Paeto font, which showed that lowe powe losses could be obtained in the adjacent winding topology. Two pototype tansfomes have been designed and manufactued to veify the models. Oveall, the adjacent winding topology is favoable fo a fixed powe tansfe of kw. REFERENCES [] A. Esse and H.-C. Skudelny, A new appoach to powe supplies fo obots, IEEE Tansactions on Industy Applications, vol. 27, no. 5, pp , 99. [2] K. Papastegiou and D. Macpheson, Contact-less tansfe of enegy by means of a otating tansfome, Poc. ISIE, pp , June 25. [3] J. Legange, G. Fiedich, S. Vivie, and J. Mipo, Compaison of two optimal otay tansfome designs fo highly constained applications, Electical Machines & Dive Confeence, vol. 2, pp , May 27. [4] K. Papastegiou and D. Macpheson, An aibone ada powe supply with contactless tansfe of enegy - pat i: Rotating tansfome, IEEE Tans. Ind. Electon., vol. 54, no. 5, pp , Octobe Seconday voltage (V) Seconday voltage (V) 9

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