Wireless (power transfer) transmission of electrical energy (electricity) intended for consumer purposes up to 50 W

POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 |NUMBER: 1 |2016 |MARCH Wi eless (Powe T ans e ) T ansmission o Elec ical Ene gy (Elec ici y) In ended o Consume Pu poses up o 50 W Ma ek PIRI, Pa ol SPANIK, Michal FRIVALDSKY, Anna KONDELOVA Depa men o Mecha onics and Elec onics, Facul y o Elec ical Enginee ing, Uni e si y o Zilina, Uni e zi na 8215/1, 01026 Zilina, Slo ak Republic [email p o ec ed], pa [email p o ec ed], michal. i [email p o ec ed], anna.kondelo [email p o ec ed] DOI: 10.15598/aeee. 14i1.1573 Abs ac . This p ojec deals wi h Powe Semiconduc- o Sys ems PSS o wi eless ansmission o elec ici y o he powe o 50 W wi h ega d o he dis ance and ansmission e iciency. We decided o use elec omag- ne ic esonance o elec ical ene gy ansmission. Fo expe imen al e i ica ion, we ha e wound wo coils o iden ical dimensions. A a gi en powe ansmission solu ions, we ob ain he highes e iciency η= 70 %a a dis ance o 5 cm, whe e he ansmi ed powe was 48 W. Keywo ds Coil, equency, esonan , wi eless powe ans- e . 1. In oduc ion Wi eless ansmission o elec ici y is a ision ha ci - cula es in he minds o in en o s o o e 100 yea s. Disco e ing o magne ic esonance opened he way o sol ing he p oblem o e iciency o elec ici y ansmis- sion in he nea ield. Thanks o his phenomenon, i is possible o ans e a high powe capaci y a high e - iciency. The esul is a p ospec i e solu ion o many applica ions such as consume elec onics, au omo i e sys ems, medical equipmen and many mo e. The aim o he pape is o design a opology o PSS o wi eless ansmission o elec ici y wi h he powe up o 50 W wi h ega d o he dis ance and ansmission e iciency. Analysis o cu en s o main ci cui o he wi eless ans e sys em, has o help success ul implemen a ion o he ask. The choice o he op imal design o achie e he speci ied pa ame e s, he simula ion o he designed sys em and i s s uc u e is based on his analysis. The a icle consis s o se e al pa s. The i s is de o ed o analysis and he cu en s a e o sys em solu ions o he wi eless ansmission o elec ici y. The second pa o he a icle desc ibes he design o he main ci - cui o he wi eless ansmission. In he hi d pa o he pape he simula ion model is p o ided ha is based on an ea lie p oposal and desc ibes he beha io o he p oposed sys em. The expe imen al e i ica ion o he designed solu ion he aim o which is an e icien ansmission o elec ici y om he sou ce o he load wi hou he use o wi es is pe o med in he ou h pa o his wo k. 2. Applied Type o Coupling and i s Analysis When he mu ual induc ance o wo coils is low, he e- cei e coil induces he low ol age wi h a low e iciency. Acco ding o Eq. (1) we can see ha he low M alue may be compensa ed by an inc ease in he angula e- quency ω, o by an inc ease in he I1ampli ude o he ansmi ing coil. up( ) = dφ d =Mdi1( ) d =MωI1·cos(ω ).(1) The e a e wo ypes o powe sys ems o wi eless ansmission-di ec and indi ec powe supply (Fig. 1). A indi ec powe supply, ansmi ing and ecei ing coil is sepa a ed om he sou ce and load o achie e highe quali y ac o Qa he ansmi ing and e- cei ing pa , whe eby i is possible o achie e g ea e ansmission dis ance. Coils L1and L2se e as bind- ing coils, which ans o m he impedance o sou ce and load. Reaching he highe quali y ac o Qcan inc ease c 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 40 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 |NUMBER: 1 |2016 |MARCH Indi ec - ed Di ec - ed Induc ion Coupled Resonance Induc ion Coupled Resonance Fig. 1: Wi eless ansmission in di ec and indi ec powe sup- ply. ansmi ed dis ance. Howe e , he sys ems a e mo e sensi i e o he choice o pa ame e s such as he in- duc ance and he esonance equency. Di ec ype o powe supply indica es om he i le ha he sou ce is di ec ly connec ed o he ansmi e sec ion. A choice o his ype o powe supply is mo e sui able o p ac i- cal applica ions because o he simplici y o he design, cus omiza ion op ions, con ol and low cos . I s disad- an age is he educ ion o he quali y ac o Q[1], [2], [3], [4]. 3. Design o he Sys em o Selec ed T ansmission Me hod The usage o he esonan ci cui in he ecei e and ansmi e allows ansmi ing o he highes ans- mi ed capaci y a he highes possible dis ance. Fo his ype o ansmission, i is impo an o design a low-loss coils and pai ing ci cui s. Ful ilmen o he gi en condi ions in he design allows achie emen o he bes ansmission pa ame e s. Topology design is based on he p inciple diag am o he esonan wi e- less sys em o elec ici y ansmi ing (Fig. 2). Fig. 2: P inciples schema ic o he esonan wi eless sys em. DC ol age sou ce supplies powe ampli ie (DC/AC), which p oduces ec angula ol age wa e- o m. This ol age p oduces an al e na ing magne ic ield in a ansmission esonan ci cui . Recei ing esonan ci cui is uned o he same esonan e- quency as he sou ce equency. Magne ic ene gy induces a sinusoidal ol age a he ecei ing side. The AC ol age is hen ec i ied in a diode ec i ie and DC ol age is led o he load [5], [6]. Based on he p edic ed pe o mance, we se o he pa ame e s. Tab. 1: O he pa ame e s. Uin 100 V Pou 50 W Uou 20 V Iou 2.5 A RL8Ω SW 293 kHz 4. The Coil Design The coil design is one o he mos impo an ac o s in he design o a sys em o wi eless ansmission. Impo - an pa ame e s such as quali y ac o Qand mu ual induc ance ha de e mine he maximum ansmission e iciency, maximum ansmission dis ance and also he ansmission capaci y depends on he pa ame e s o ansmi e / ecei e coil. Induc ance calcula ion no - mally begins on he so-called pu e induc o , when i is assumed ha he solenoid coil is o med o in ini ely hin wi e wi hou gaps be ween conduc o s ( u ns o wi e a e elec ically isola ed). The main cha ac e is ic o his coil is ha a low equencies i adia es uni o m magne ic ield o e he whole leng h. As a as hese condi ions a e me , we can w i e: Ls=µπD2N2 4h,(2) whe e µis he ela i e pe meabili y o acuum, Dis he diame e o he coil, Nis he numbe o u ns and his he leng h o he coil Fig. 3. Pu e induc o is a he- o e ical model, bu we can use i a e a small modi ica- ion. The modi ica ion can be di ided in o wo pa s, equency-dependen and equency-independen . p h 2a D Fig. 3: Layou and dimensions o coil. A equency independen modi ica ion, coe icien kLdesc ibes he i egula i y o he ield and is ex- p essed in Eq. (3) [7], [8], [9], [10], [11]. c 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 41 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 |NUMBER: 1 |2016 |MARCH kL=2h D· ln 4D h−1 2·1+0.393901 ·h D+ 0.017108 ·h D4 1+0.258952 ·h D2 +0.093842 ·h D2+ 0.002029 ·h D4−0.000801 ·h D6. (3) Then, an equa ion o induc ance LScan be w i en acco ding o Eq. (2). LS=µπD2N2 4h.(4) Fo eal coils, i is needed o include he coe icien kS, which akes in o accoun ci cula conduc o c oss- sec ion and he coe icien km o he mu ual induc- ance be ween he u ns. ks=3 2−ln p a.(5) km= ln (2π)−3 2−ln (N) 6N−0.33084236 N −1 120N3+1 504N5−0.0011923 N7+0.0005068 N9. (6) L=Ls−µND 2 (ks+km).(7) Two o he pa asi ic elemen s: he skin e ec and p oximi y e ec should be aken in o conside a ion a high equencies, espec i ely a equency dependen modula ion. The so-called in e nal induc ion, which is an imagina y con a equi alen o he skin e ec , apidly dec eases wi h inc easing equency and is p o- po ional o he leng h o he conduc o , a ec s he calcula ion o he induc ion coil. The e ec o he in- e nal induc ance, howe e , can be used only o sho coils. Li= µ0δi  1−e(−"a 2δi#3,8)   1 3,8 4πa (1 −y)l, (8) whe e µ0is he pe meabili y o acuum, δi- dep h o pene a ion, a- he adius o he conduc o , l- o al leng h o he coil conduc o . y=0.0239 1+1.67 (z0.036 −z−0.72)24.(9) z=a 2.552δi .(10) l=q(πND)2+h2.(11) The inal o mula o calcula e he induc ance o coil wi h all co ec ions is as ollows: L=Ls−µND 2(ks+km) + Li,(12) whe e LSis induc ance o he pu e induc o , µ0is ac- uum pe meabili y, nis numbe o u ns, ks,kma e co ec ion ac o s and Liis in e nal coil induc ance. So called Li zwi e-high equency cable is used o sup- p ess he nega i e e ec s o equency dependen pa o esis ance o a coil conduc o in he high equency sys ems. I s ask is he supp ession o skin e ec and p oximi y e ec [12]. High- equency cable is made up o angled hin insula ed wi es, he ecommended di- ame e o which is: d≤2δ, (13) whe e dis he conduc o diame e and δi is he dep h o pene a ion. Li zwi e should be used only o e- quencies om 50 kHz o 3 MHz. I he wo coils ha e he same adius, he same numbe o u ns and a e held in he same axis, hei mu ual induc ance can be de e mined: M=µ0 D 2N2Zπ 0 cos x s2 (1 −cos (x)) + d D2dx. (14) Based on es ablished pa ame e s and ela ionships, he pa ame e s o he being designed coil a e calcula ed acco ding o Tab. 2. Tab. 2: Calcula ed pa ame e s o he designed coil. Pa . Value Uni Desc ibe D185 (mm) Coil a e age l60 (mm) Coil leng h a1.5 (mm) Wi e a e age N6 (-) Numb. u ns 300 (kHz) F equency used in design p10 (mm) Pi ch Φ1.06 (-) P oximi y ac o kL0.442 (-) C. . inequali ies ield ks-1.34 (-) C. . sel ind. O ound wi e km0.233 (-) C. . mu ual ind. O ound wi e l3486 (mm) Physical leng h o we e dmin <0.36 (mm) Recommended min. hickness cable wi e NLW 32 (-) Num. o cable o li z-wi e δl120 (µm) Pene a ion dep h L9.34 (µH) Induc ance R0.062 (Ω) Se ial AC esis ance C1020 (pF) Pa asi ic capaci ance Q174 (-) Quali y ac o ez 22.652 (MHz) Sel es. eq. o coil Fo he calcula ion o he mu ual induc ance M he Eq. (12) was used and he esul s a e shown in Tab. 3. c 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 42 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 |NUMBER: 1 |2016 |MARCH Tab. 3: Mu ual induc ance o wo symme ical coils. Dis ance (cm) 5 10 15 20 25 M(µ) 3.44 1.465 0.726 0.398 0.237 k(-) 0.368 0.157 0.078 0.043 0.025 Whe e kis he coupling ac o which is calcula ed by he ollowing o mula: k=M √L1L2 .(15) 5. Calcula ion o Pa ame e s and Ci cui Elemen s Fo he analysis o opologies, i has been chosen a sui able es opology wi h se ies se ial connec ion o he compensa ion capaci o , Fig. 4. He e he choice o opology de e mines he u he calcula ions o ele- men s and ci cui pa ame e s. DC C1L1 M L2C2 R Fig. 4: Se ial capaci i e compensa ing o capaci o . The ollowing equa ion was used o he calcula ion o he ans o ma ion a io: n=AV Uin 2 Uou = Uin 2 Uou |AV=1 = 2.5.(16) T ans o ma ion a io be ween p ima y and sec- onda y coil was chosen o 1 o simpli y he design and he desi ed ou pu ol age has been achie ed wi h a equency con ol [13]. Simila ly, his solu ion is p e- e ed in ligh o he coil s uc u e and u he design o he sys em. Value o compensa ion capaci y C2o he seconda y side is calcula ed om equa ion: C2=1 ω2 0L2 = 31.16 nF.(17) Nex , he alue o p ima y side compensa ion capac- i y C1was calcula ed: C1=L2C2 L1 = 31.16 nF.(18) Capaci y alues a e ounded o he nex highe p oduc ion se ies C1,C2= 33 nF. Nex , he e iciency o a gi en opology a a dis ance o 5 cm was calcula ed, whe e M= 3.44 µH. η=RL (RL+R2)1 + R1(R2+RL) ω2M2.(19) Then, he quali y ac o Qo ansmi e (p ima y side) and o he ecei e (seconda y side) may be cal- cula ed: Q1=L1RL ω0M2= 3.43.(20) Q2=ω0L2 RL = 2.15.(21) Calcula ed alues a e decisi e, bu hei alues a e only heo e ical. The main eason is ha he calcula- ion was p o ided only o he esis ance o he coils. Wi e esis ance, capaci o s esis ance and in luence o dis u bing elemen s ha e been neglec ed. 6. Time Dependen Analysis Mu ual induc ion was calcula ed o i e dis ances (Tab. 4) and used as a a iable pa ame e . The sim- ula ions we e sol ed o wo cases. The i s was he measu emen o ou pu ol age, cu en , and e i- ciency a a esonan equency. The second simula ion was aimed a changing he equency and he achie e- men o cons an ou pu pa ame e s Vou = 20 V and Iou = 2.5 A, in o de o achie e he desi ed ou pu powe o 50 W. Vol age and cu en wa e o ms a indi- idual componen s a e displayed o one selec ed alue o coils dis ance (5 cm). Tab. 4: The simula ion esul s o a cons an equency a A = 1 s. Equi alen ci cui K_linea Dis ance (cm) U (V) I (A) η (%) U (V) I (A) η (%) 5 42 4.84 80 46.7 5.5 83 10 33.6 3.95 56 34 4 56 15 27.8 3.26 26 30 3.5 26 20 19.5 2.35 10 18.5 2.1 9 25 12.8 1.42 3 10.8 1.25 3.5 The alue o esonance equency was 286 675 Hz. F om he p e ious simula ion and he ol age ans- mission cha ac e is ics, i is known ha a ol age gain is equal o 1 hen. Howe e , he ope a ion mode o swi ching ansis o s a his poin is no ideal and he sui able ope a ing mode o swi ching a ze o ol age (ZVS) is abo e he esonan equency. Fo bes esul s, he ange om 286 kHz o 296 kHz was chosen, which is close o he esonan equency and o he nine alues he pa ame ic simula ion was c 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 43 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 |NUMBER: 1 |2016 |MARCH 5 10 15 20 25 0 20 40 60 80 100 η = (D) D (cm) η (%) Equi alen ci cui K_linea Fig. 5: Dependence o e iciency on he dis ance o he cons an equency. 5 10 15 20 25 0 10 20 30 40 50 U = (D) D (cm) U (V) Equi alen ci cui K_linea Fig. 6: Dependence o seconda y ol age on he dis ance o he cons an equency. pe o med om which he mos sui able equency was de e mined in e ms o e iciency. I was 290 kHz. Max- imum e iciency was 83 % o he simula ion model using K_linea block. The di e ence be ween using a ans o me equi alen ci cui and K_linea block is minimal, so he esul s can be conside ed co ec . The ol age and cu en wa e o ms a each componen a e displayed o 5 cm alue. Fig. 7: The ime wa e o ms o he ol age Uds and cu en Id o ansis o T1 o 5 cm. Tab. 5: Simula ion esul s o he cons an Uou and Iou . ZVS ZCS Dis ance (cm) η(%) (Hz) η(%) (Hz) 5 73 326250 30.5 196078 10 53 305510 26 229357 15 26 294117 11.5 251889 20 8.7 289885 5.2 265252 25 3 287356 2.5 277777 Fig. 8: The ime wa e o ms o he ol age a esonan elemen s o ansmi ing side o 5 cm dis ance. Fig. 9: The ime wa e o ms o he ol age and cu en a he load wi hou a ec i ie b idge o 5 cm dis ance. 5 10 15 20 25 0 20 40 60 80 η = (D) D (cm) η (%) ZVS ZCS Fig. 10: Dependence o he e ec i eness on he dis ance o con- s an Uou and Iou . 5 10 15 20 25 150 200 250 300 350 = (D) D (cm) (kHz) ZVS ZCS Fig. 11: Dependence o Tws change on he dis ance o cons an Uou and Iou . c 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 44 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 |NUMBER: 1 |2016 |MARCH As he ans o ma ion a io o coils was 1:1, he change in he ou pu ol age and cu en was ensu ed wi h he change in swi ching equency. The Tab. 5 shows ha ze o ol age swi ching (ZVS) is mo e p e- e ed in e ms o e iciency han swi ching a ze o cu - en . F om he measu ed alues i is con i med ha he sys em is mo e sensi i e o changes o equency a a longe dis ance. The cha o equency dependence on he dis ance (Fig. 10) shows ha wi h he inc easing dis ance i is necessa y o app oach o he esonance equency o ob ain a su icien gain. 7. Expe imen al Ve i ica ion on Physical Model We ha e c ea ed a physical model o e i y he co ec - ness o he designed solu ions on he basis o heo e ical analysis and simula ion analysis in he p e ious chap- e s. Design o physical model is based on se e al pa s: on he choice o opology om heo e ical documen s, on he ype o ci cui powe supply, on choice o swi ch- ing ansis o s, sui able capaci o s, on cons uc ion o ansmi e and ecei e coils. The whole sys em is di- ided acco ding o he block diag am Fig. 7, which was c ea ed in he heo e ical design o he sys em. A hal b idge connec ion o ansis o s is used as a DC/AC in- e e simila ly o simula ion model. Fo his pu pose, he wi ing on he uni e sal boa d o a hal b idge ci - cui was used. T ansis o s FDPF17N60NT a e used o swi ching. Thei selec ion has been made on he ba- sis o simula ion analysis, om which we see ha he ansis o s cu en Ida lowe dis ances is 8 A and i is g owing wi h inc easing dis ance. The ansis o s a e sui able o he maximum allowable ol age. Tab. 6: Basic pa ame e s. Id17 A Uds 600 V Rds(on) 340 mΩ The physical model was powe ed by a DC sys em sou ce Agilen N5771A. Du ing he design, i was con- side ed a p oduc ion se ies o capaci o s MKP o MKT ha ing low ESR alues. As in he simula ions, in he expe imen al physical model 33 nF alue was used o he ansmi e and he ecei e side oo. To educe he ol age and cu en load, he capaci o o ans- mi ing (p ima y) side was made up o se ies pa allel capaci o s Fig. 12. Fo he p oposed sys em, wo iden ical coils we e made, he dimensions o which can be ound in Sec ion 5. The coil design. Wi e o coil is o med o 32 angled hin insula ed wi es wi h a diam- e e o 0.18 mm. A non-conduc i e ma e ial (ex uded polys y ene) was used as a ame o coil. The calcula ed induc ance alue in he design o coil a he designed equency o 100 kHz was L= 9.34 µH and i s quali y ac o Q= 94.7. The RLC me e was used o e i y he design. Following pa ame e s we e measu ed a he 100 kHz. L1= 9.57 µH, Q1= 69 and L2= 9.12 µH, Q2= 59. The esul ing alues a e in luenced mainly by ce ain cons uc ion elemen s such as cable leng hs, he endency o indi idual u ns, and by he ac ha he esul ing coil is no a pe ec ci cle. Howe e , he goal was achie ed and he di e ence be ween he cal- cula ed and measu ed induc ance is wi hin a s anda d. Fig. 12: View o he se ies-pa allel connec ion o capaci o s - 33 nF. Fig. 13: View on a designed coil. The ou pu ec i ie was connec ed as b idge ec i ie . I was designed om Scho ky diodes STPS10H100CT due o he high wo king equencies. Used load had only esis i e cha ac e . I was buil o ou non-induc i e esis o s connec ed in pa allel and i s esul ing alue was 8.25 Ω. c 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 45 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 |NUMBER: 1 |2016 |MARCH 8. Measu emen s on Physical Model C ea ed physical model o he wi eless ansmission o elec ical ene gy has been subjec ed o measu emen . Time cou ses we e eco ded on an oscilloscope Tek- onix TDS 3024B ha allows he s o age o scanned wa e o m in he da a ile. The cu en p obe Tek onix TCP A306 and he di e en ial ol age p obe HZ100 HAMEG we e applied o aking he ime wa e o ms o ol age and cu en on he load. The esul ing wa e- o ms we e p ocessed in a sp eadshee p og am and g aphically displayed. The esul ing measu ed alues o ol age and cu en on he load we e unca ed o one pe iod o g aphical ep esen a ion. The esul ing g aph was in e pola ed by end line o med wi h he polynomial o he six h deg ee because o a iabili y and la ge amoun s o da a. The equa ion o he end line is shown in he Fig. 14 whe e yUis an equa ion o ol age and yIis an equa ion o cu en . Fo each measu emen inpu , ou pu powe and e iciency we e hen calcula ed. An example calcula ion is measu ing o dis ance 5 cm be ween he coils. Fig. 14: Dependence o ou pu ol age and ou pu cu en o a dis ance o 5 cm a cons an swi ching equency. Tab. 7: Measu emen a a dis ance o 5 cm. Uin (V) Pin (W) IM (A) ϕ () Iin (A) UM (V) T (µs) η () 99.9 67.93 3.43 0 0.68 27.92 3.4388 Pou =1 TZT 0 UMsin(ω )·Imsin (ω +ϕ)d . (22) Pou =1 3.4388 ·10−6 ·ZT 0 27.92 ·sin (2π·290799 · ) ·3.43 ·sin (2π·290799 · )=4. (23) η=Pou Pin =47.88 67.93 = 0.705.(24) Tab. 8: Measu emen a a dis ance o 10 - 20 cm. Measu emen a a dis ance o 10 cm Uin (V) Pin (W) IM (A) ϕ () Iin (A) UM (V) T (µs) η () 99.9 63.94 1.83 13.49 0.64 14.74 3.43 0.21 Measu emen a a dis ance o 15 cm Uin (V) Pin (W) IM (A) ϕ () Iin (A) UM (V) T (µs) η () 99.9 62.94 1.05 4.22 0.63 8.04 3.43 0.08 Measu emen a a dis ance o 20 cm Uin (V) Pin (W) IM (A) ϕ () Iin (A) UM (V) T (µs) η () 99.9 62.94 0.63 1.51 0.63 4.8 3.43 0.02 9. Conclusions Design o sys ems o wi eless ansmission is cu en ly p omising a ea o esea ch and de elopmen , in espec o he wide ange o applica ions whe e i is possible o use his echnology. Fo he design and cons uc ion oday he e is s ill no s ic p ocedu e o achie ing he desi ed esul an pa ame e s, he e o e sol ing o he gi en issue is no uni o m, howe e , i is based on he phenomenon o magne ic esonance. In his pape we ha e se a a ge o design he PSS opology o wi eless ansmission o elec ici y wi h powe up o 50 W. In he p ocess solu ions, we di ided he wo k in o h ee pa s - heo e ical, heo e ical- p ac ical and p ac ical. In hem, we ocused on impo - an indi idual design analysis. In he heo e ical pa we wen in o he his o y o wi eless ansmission and we desc ibed he a ious op ions o wi eless ansmission o elec ici y. F om his ini ial heo e ical analysis, we decided o ansmission by means o elec omagne ic esonance. Explana ion o impo an ac o s ha en- e in o his ype o ansmission and in luence i was a con inua ion o heo e ical analysis. Theo e ical-p ac ical pa was used o summa izing o possible solu ions and o choosing o he app op ia e sys em opology o wi eless ansmission. We ha e c ea ed a block diag am o he ci cui and in he same pa we ha e made he design o sys em and design o he coil. In he p ac ical pa we ha e c ea ed he simula ion model i s , which we used o p edic he beha io o he designed sys em. I also ga e us he c 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 46 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 |NUMBER: 1 |2016 |MARCH esul s ha we hen compa ed wi h measu emen s on a physical model. We ha e spooled wo coils wi h iden ical dimensions o he expe imen al e i ica ion o he sys em. Com- pa ed o he heo e ical calcula ion, de ia ion o hei induc ance was 3 %, bu he quali y ac o was lowe han 38 %. We ha e hen c ea ed an expe imen al wi ing acco ding o he simula ion model and we pe - o med measu emen s o ou dis ances. The highes achie ed e iciency o 70 %was o 5 cm dis ance and he ansmi ed powe was 48 W. We ha e me he main aim o his pape We ha e designed PSS opol- ogy o wi eless ansmission o elec ic ene gy wi h powe up o 50 W and we ha e expe imen ally e i ied he solu ion’s co ec ness. Based on he knowledge ob- ained du ing pape solu ions we ha e w i en some ecommenda ions o u he de elopmen o he sys- em design o wi eless ansmission o elec ic ene gy. Acknowledgmen The au ho s wish o hank o Slo ak g an agency VEGA o p ojec no. 1/0184/13 - Resea ch o indi- ec compu ing algo i hms and ools o e alua ion o powe loss in powe elec onic de ice’s componen wi h suppo o physical model simula ion pos p ocesing. Re e ences [1] PANKRAC, V. The Algo i hm o Calcula ion o he Sel and Mu ual Induc ance o Thin- Walled Ai Coils o Gene al Shape Wi h Pa al- lel Axes. IEEE T ansac ions on Magne ics. 2012, ol. 48, iss. 5, pp. 1875–1889. ISSN 0018-9464. DOI: 10.1109/TMAG.2011.2177854. [2] WEISSTEIN, E. W. Ellip ic In eg al o he Thi d Kind. In: Ma hWo ld–A Wol- am Web Resou ce [online]. 2015. A ailable a : h p://ma hwo ld.wol am.com/Ellip icIn eg al o heThi dKind.h ml. [3] GLAD, M. Design o pho o ol aic sola cell model o s and-alone enewable sys em. In: ELEK- TRO. Rajecke Teplice: IEEE, 2014, pp. 285–288. ISBN 978-1-4799-3720-2. DOI: 10.1109/ELEK- TRO.2014.6848903. [4] TIRPAK, A. Elek omagne izmus. 1s ed. B a isla a: Polyg a ia SAV, 1999. 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Elek onika IR Elek- o echnika. 2011, ol. 110, no. 4, pp. 7–12. ISSN 2029-5731. DOI: 10.5755/j01.eee.110.4.276. Abou Au ho s Ma ek PIRI was bo n in Sahy, Slo ak Republic. He g adua ed s udy a Uni e si y o Zilina (2006). c 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 47 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 |NUMBER: 1 |2016 |MARCH Nowadays s udy a Ph.D. g ade a Depa men o Mecha onics and Elec onics a Uni e si y o Zilina. He is in e es ing in he ield o powe elec onics-swi ch mode powe supplies, simula ions, design o powe supplies. Pa ol SPANIK g adua ed a Uni e si y o T ans- po and Communica ions in Zilina (1978), in he ield o Elec ical ac ion and ene ge ics in anspo . Nowadays wo ks a Depa men o Mecha onics and Elec onics o Facul y o Elec o echnical Enginee ing a Uni e si y o Zilina. He is in e es ed in he ield o powe elec onics, mecha onics and con ol sys ems. Michal FRIVALDSKY was bo n in S a a Lubo na, Slo ak Republic. He g adua ed s udy a Uni e si y o Zilina (2006). He inished his Ph.D. S udy in he ield o powe elec onics a he Uni e si y o Zilina (2009) and became assoc. p o . in 2014. Nowadays he wo ks a he Depa men o Mecha onics and elec onics, Facul y o Elec ical Enginee ing, a he Uni e si y o Zilina. His esea ch in e es s include powe elec on- ics, simula ions (FEM, ime-domain, mul ile el) and powe con e e s op imiza ion, design and applica ion. Anna KONDELOVA was bo n in T s ena, Slo ak Republic. She g adua ed a Slo ak Technical Uni e si y in B a isla a (1983). She inished he Ph.D. s udy in he ield o P ocess Con ol a he Uni e si y o Zilina (2013). Nowadays she wo ks a he Depa men o Mecha onics and Elec onics, Facul y o Elec ical Enginee ing, a he Uni e si y o Zilina. He esea ch in e es s include p og ammable ci cui s, elec onics, and simula ions. c 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 48