New Characteristics Analysis Considering Transmission Distance and Load Variation in Wireless Power Transfer via Magnetic Resonant Coupling

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1 New Characteristics nalysis Considering Transission Distance and oad Variation in Wireless Power Transfer via Magnetic Resonant Coupling Masaki Kato, Takehiro ura, Yoichi Hori The Departent of dvanced Energy, the University of Tokyo Kashiwa, Chiba, JPN bstract - Wireless power transfer (WPT) via agnetic resonant coupling has been attracting research attention for various applications. Conventionally, load is assued to be constant and only transfer efficiency is studied. n actual WPT applications, the load and transfer distance change frequently. Furtherore, inforation such as ratio of input voltage to output voltage, ratio of input current to output current, and input ipedance are needed for understanding and constructing the power transfer syste. n this paper, not only the transfer efficiency but also the three paraeters entioned are studied. These paraeters are then analyzed for changing load and changing transfer distance conditions using actual antennas paraeters. Fro the analysis results, the load resistance value for axiu efficiency exists. Secondly, iproving efficiency by changing load resistance for sall utual inductance case has larger effect. The optiu load resistance also changes according to transission distance and also the consued power peak ay not correspond to axiu efficiency. Finally, fault protection ay also be necessary for the cases when the load resistance is extreely high and when the receiver antenna is not present causing high supply current.. NTRODUCTON Wireless Power Transfer (WPT) via agnetic resonant coupling which was first introduced in year 6 has been receiving uch attention fro researchers and copanies []. With this ethod high transfer efficiency is obtainable over relatively larger gap copared to induction ethod. Potential application includes charging electric vehicles [] (Fig.). Moreover the agnetic field in this power transfer ethod is non-radiative type and therefore is safe for the huan body [3]. The resonant antennas used in wireless power transfer consist of coils and capacitors. ntenna design with Series- Series(SS) configuration where the coils and capacitors are connected in series is preferred in recent research [9]. Conventional studies assue the load is always constant and discussed the transfer efficiency only in ters of input power and output power [4]-[6] but not in ters of voltage and input ipedance. Furtherore, the effects of changing load and changing transfer distant were not discussed [7]. However, in actual wireless power transission applications, load and transitting distance change frequently. nforation such as the ratio of input to output voltage, the ratio of input to output current and input ipedance seen fro high frequency power supply are needed to understand and construct the power transfer syste [8]. This paper presents not only the atheatical expression for transfer efficiency in SS-type agnetic resonant coupling but also the voltage ratio, current ratio and input ipedance in ters of load and transitting distance change. The derived equations are investigated using siulations. Fro these atheatical expressions, iportant inforation for wireless power transfer design such as voltage across the load and load ipedance values during axiu efficiency are obtainable. Fig.. Wireless power transfer for electric vehicle.. CHRCTERSTCS OF SEF RESONNT FREQUENCY. Equivalent Circuit The resonant antennas used in WPT consist of coils and capacitors. ntenna design with SS configuration where the coils and capacitors are connected in series is preferred in recent research [9]. The equivalent circuit of agnetic resonance coupling ethod with SS configuration has already been proved in the past research [9], and is illustrated in Fig.. and represent the inductances of the coils. C and C represent the capacitances that are connected to coils in series. R and R are the antennas internal losses. is utual inductance which is related to transfer distance. Transitting antenna and receiving antenna satisfy (). Ter ω in () is the self resonant frequency. The equivalent circuit of the wireless power transfer syste is shown in Fig..

2 ir gap ω () C C Receiving ntenna Transitting ntenna R C C R Transitting ntenna Receiving ntenna Fig.. Equivalent circuit of agnetic resonant coupling with SS configuration. B. Definition of the Four Characteristics n this section, the four characteristics used to study the phenoena of agnetic resonant coupling are defined. Fig. 3 shows T-type equivalent circuit of the wireless power transfer, and is terinated by a load and a power source on each side. Properties to be defined are V,, P, in. Where V is ratio of output to input voltage and is ratio of output to input current as shown by () and (3). P is the ratio of output to input power as shown in (4). P is the sae as transitting efficiency. Power ratio is the product of V and coplex conjugate of. in is the input ipedance seen fro the power source as shown in (5). Fro ()-(5), the relation of power supply s voltage and power supply s current can be known. V V () V (3) V V P V V V (4) V in (5) V (6) + R j ω (7) ωc jω (8) R + R + j ω (9) ωc The supply frequency is usually the sae as antenna s selfresonant frequency given by (). Substituting the selfresonant frequency, ()-(5) becoe ()-(3). V ω ω ωr j R R + R R + ω ω R + R P ω ω ω j ( ω ) ( ω ) R ( R + R ) RR + R R + ( ω ) V ( ω ) R + in ω ω R + R ( ) () () () (3) Equation () and () contain only iaginary coponent. This shows that voltage and current are phase shifted by 9 degree fro input to output regardless of the load ipedance and transitting distance. On the other hand, () contains only real coponent. This shows that power wavefor does not shift phase fro input to output. Equation (3) also contains only real coponent showing that power factor is %. NYSS OF CHNGNG OD VUE ND TRNSMTTNG DSTNCE. nalysis Method Using the derived equations, the change of each characteristic corresponding to load, R and transitting distance (which affects utual inductance ) is calculated. The antennas paraeters are set to be the sae as the actual antennas. and are 8 uh, C and C are pf and R and R are. Ω. Table shows the values of a few transitting distances. Fig. 3. Equivalent circuit of wireless power transfer syste terinated by power supply and load at each side. C. Equations of the Characteristics in Self Resonance Next, each characteristics of SS-type agnetic resonant coupling is described. Equation (6) is derived fro the equivalent circuit in Fig. 3. The eleents in the atrix are described by (7), (8), and (9). 44c Fig. 4. The actual antenna with the paraeters used in calculation.

3 Table vs transfer distance [uh] Transfer distance [c] B. nalysis Result of Changing R Fig. 5, Fig. 6, Fig. 7 and Fig. 8 show the plot of P, V, and in correspondings to changing R. Fig. 8. in when R changes. Fig. 5 shows P peaks at certain R values. Transitting efficiency is affected by load resistance. Therefore optiizing load value for high efficiency is iportant. Moreover wavefor of P is precipitous eaning that optiizing load resistance has larger effect when the transfer distance is far. Equation (4) describes R _Pax, and (5) describes Pax. R _Pax is the load resistance during axiu efficiency. Pax is axia eficiency when R is optiized. Fig. 5. P when R changes. (a) logarithic plot (b)linear plot Fig. 6. V when R changes. R R ( ) _ P ax P ax ω + R (4) R ( ω ) R( P ax) ( ω ) + R R ) + R ( ω ) ( + R ) R (5) Fig. 6 shows that V is increasing with increasing R and becoes saturated when R reaches a certain value. When the priary side is powered, the voltage at the secondary side increases with the load resistance. This voltage ay increase to a dangerous level without proper control. V_sat which is the saturation voltage ratio when R is infinite is expressed in (6). ω V _ sat (6) R (a) logarithic plot (b)linear plot Fig. 7. when R changes. Fig. 7 shows that decreases with increasing R. Fro (4), P is the product of V and. Furtherore, fro Fig. 5 and Fig. 7, P decreases due to decreasing when R is high whereas V is saturated at this point. On the other hand, efficiency declines when R is extreely low due to decreasing V. Fig. 8 shows that in decreases when R increases. The input ipedance is low when R increases and no load condition occur. Power supply current, increases. Result of Fig. 6 and Fig. 8 shows that no load (R is infinite) ay caused daage to both the load and the power supply.

4 C. nalysis Results of Changing Fig. 9, Fig., Fig., and Fig. show the plot of P, V,, in respectively when changes. Fig.. in when R changes Fig. 9. P when changes. Fig. 9 shows that P is large if is large regardless of the value of R. This eans that for sall transfer distance, the efficiency is always high. Fig. shows that V peaks at a certain value of. n other words, secondary side s voltage is axiized at a fixed transfer distance. n this condition, the power consuption is axiized but not the transfer efficiency. _ V ax V ax ( R + R ) R ω R R R ( R + ) (7) (8) Fig.. V when changes. Fig.. when changes. Fig. shows that is large when is large. When the transission distance is near, efficiency increases due to increasing current. Fig. shows that input ipedance, in decreases with lower. For further transission distance, the input ipedance is low as if the receiver antenna does not exist. Therefore, the power supply current ( ) ay increase to a dangerous level if there is no fault protection circuit. V. CONCUSON The characteristics of wireless power transfer which are the voltage ratio, current ratio, and input ipedance and transfer efficiency are studied atheatically. The analysis is perfored not only for constant load case, but also for changing load and changing transfer distant using the paraeters of actual antennas. Fro the analysis results, the optial load resistance value for axiu efficiency exists. Secondly iproving efficiency by changing load resistance for sall utual inductance case has larger effect. The optiu load resistance also changes according to transission distance and also the consued power peak ay not correspond to axiu efficiency. Finally fault protection ay also be necessary for the cases when the load resistance is extreely high and when the receiver antenna is not present causing high supply current. Future work will include perforing experients to verify the atheatical analysis in this paper.

5 REFERENCES [] ndre Kurs, risteidis Karalis, Robert Moffatt, J. D. Joannopoulos, Peter Fisher, MarinSoljacic, WPT via Strongly Coupled Magnetic Resonances,Science,Express, Vol.37, No.5834, pp.83-86, 7 June 7 [] Hori, Y.;, "Novel EV society based on otor/ capacitor/ wireless pplication of electric otor, supercapacitors, and wireless power transfer to enhance operation of future vehicles," Microwave Workshop Series on nnovative Wireless Power Transission: Technologies, Systes, and pplications (MWS), EEE MTT-S nternational, vol., no., pp.3-8, - May [3] risteidis Karalis, J.D. Joannopoulos and Marin Soljačić, Efficient wireless non-radiative id-range energy transfer, nnals of Physics, Volue 33, ssue, January 8, Pages 34-48, January Special ssue 8. [4] hen Ning ow; Chinga, R..; Tseng, R.; Jenshan in;, "Design and Test of a High-Power High-Efficiency oosely Coupled Planar Wireless Power Transfer Syste," ndustrial Electronics, EEE Transactions on, vol.56, no.5, pp.8-8, May 9 [5] Saple,.P.; Meyer, D..; Sith, J.R.;, "nalysis, Experiental Results, and Range daptation of Magnetically Coupled Resonators for Wireless Power Transfer," ndustrial Electronics, EEE Transactions on, vol.58, no., pp , Feb. [6] ura, T.; Hori, Y.;, "Maxiizing ir Gap and Efficiency of Magnetic Resonant Coupling for Wireless Power Transfer Using Equivalent Circuit and Neuann Forula," ndustrial Electronics, EEE Transactions on, vol.58, no., pp , Oct. [7] Hosotani, T.; wai,.;, " novel analysis of VS wireless power transfer syste using coupled resonators," Microwave Workshop Series on nnovative Wireless Power Transission: Technologies, Systes, and pplications (MWS), EEE MTT-S nternational, vol., no., pp.35-38, - May [8] Moriwaki, Y.; ura, T.; Hori, Y.;, "Basic study on reduction of reflected power using DC/DC converters in wireless power transfer syste via agnetic resonant coupling," Telecounications Energy Conference (NTEEC), EEE 33rd nternational, vol., no., pp.-5, 9-3 Oct. [9] ura et al.:"wpt during Displaceent Using Electroagnetic Coupling in Resonance -Magnetic versus Electric Type ntennas-", EEJ Trans., Vol. 3, No., pp ()(in Japanese)

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