IEEJ Journal of Industry Applications Vol.5 No.6 pp.429–438 DOI: 10.1541/ieejjia.5.429

Paper

Development of Design Methodology for 60 Hz Wireless System

∗ ∗∗ Hiroki Ishida Member, Hiroto Furukawa Member ∗∗∗ Tomoaki Kyoden Non-member

(Manuscript received Feb. 3, 2016, revised May 6, 2016)

We previously reported a 60 Hz wireless power transmission (WPT) system, which is a system that uses the com- mon utility . In the study reported in paper, we solved several issues in order to install this system in a small electric vehicle. First, an accelerated finite difference time domain (FDTD) method using a graphics processing unit was developed to solve the issue of computation time. Next, theoretical equations for the transmission efficiency (η) and power (Pout) that include the stray load loss were derived from an equivalent circuit analysis. A new device was designed based on these theoretical equations, where by η = 70% and Pout = 451 W were achieved for a transmission distance of 150 mm. Finally, we attempted to wirelessly charge of a lead storage battery. The overall efficiency of the wireless charging system was maintained at 60% during battery charging.

Keywords: wireless power transfer, magnetic resonance, utility frequency, wireless charging

proposed the use of low frequency such as the common utility 1. Introduction frequency to eliminate power loss in concrete (15). As another From the time that resonance wireless power transmission advantage, no high-frequency unit would be (WPT) was first developed by the WiTricity project (1),there required. There have been no attempts to use the common has been a great deal of research conducted using this and utility frequency after the development of the WiTricity sys- other approaches (2)–(4). In addition, the direction of research tem. We are aware of only one report from the University of has progressed towards the design of devices such as invert- California over 30 years ago, where an efficiency of 60% was ers and control techniques (5)–(8). Wireless charging of electric achieved over a distance of 100 mm using a 400 Hz power vehicles is a typical application of WPT (9) (10). supply (16). A large value for the product of the coupling coefficient In our previous report, we achieved a power efficiency of (k) and the quality factor (Q) yields a high transmission ef- 78% and 165 W at a distance of 100 mm (63% and 69 W at ficiency. Therefore, to obtain high efficiency, even when k 150 mm), and also confirmed that energy loss into the con- is small (i.e., transmission distance is long), a large Q is re- crete does not occur. Although optimization has not yet been quired. A high-frequency power supply is thus used; how- performed, the 60 Hz-WPT system is expected to have higher ever, it is necessary to consider the skin effect and proxim- potential. The design has not yet been optimized, because ity effect to reduce the winding resistance (11). The capabil- we have not completed a theoretical analysis of the common ity of the high-frequency system is very high and a total ef- utility frequency WPT system. The efficiency-equation in the ficiency of 77% at a distance of 300 mm in free space has case of high frequency does not require core loss to be con- been achieved (12) (efficiency between two coils is 95% at a sidered, because there is no advantage in using a magnetic distance of 300 mm (12) (13)). Wireless charging of electric ve- core. However, a magnetic core is a necessary component hicles could be achieved by embedding the transmitter coil for low frequency. In addition, although the stray load loss into paved roads or car parking areas. Omar et al. reported cannot be neglected, as with an having a gap successful 23 kHz WPT of over 2 kW with a dc-to-dc effi- between the rotor and stator, an equation that contains the ciency of over 75% at a transmission distance of 100 mm, and stray load loss has not been presented until now. also evaluated the power loss in concrete block (14).Wehave Although transmission efficiency is strongly dependent on the shape of the magnet pole piece, a simulator has not been ∗ Department of Applied Physics, Okayama University of Sci- developed to determine the optimal shape. Accurate predic- ence tions of the transmission efficiency and power become possi- 1-1, Ridai-cho, Kita-ku, Okayama 700-0005, Japan ble if these issues are solved, and indicate that a 60 Hz-WPT ∗∗ National Institute of Technology, Toyama college, Hongo Cam- system has high capability. pus 13, Hongo-machi, Toyoma city, Toyama 939-8630, Japan 2. Experimental Procedure ∗∗∗ National Institute of Technology, Toyama College, Imizu Cam- pus The 60 Hz-WPT devices were produced with different 1-2, Ebie-neriya, Imizu city, Toyama 933-0293, Japan magnet-pole shapes. The magnet-pole pieces were fabricated

c 2016 The Institute of Electrical Engineers of Japan. 429 60 Hz Wireless Power Transmission System（Hiroki Ishida et al.） from 0.35 mm thick silicon steel plates containing 3.5% sili- Table 1. Specifications and analysis conditions of the con. At a frequency of 60 Hz, no saturation of the pole pieces 60 Hz-WPT simulation was observed up to a flux density of 0.7 T. The coils were wound from single-strand enamel-covered copper wire with a diameter of 2 mm. Experimental results from four devices (P1-P4) are presented in this paper. Although experimental results for P1-P3 have already been published previously (15), they are presented here for comparison with the calculation results. The specifications for these three devices have been previously reported and are thus omitted in this paper. The transmission efficiency and power were predicted through analysis of the equivalent circuit for the 60 Hz-WPT system. The parameters of the equivalent circuit used in the calculation (i.e., the constants) were determined experimentally using an actual WPT device. The transformer constants were measured using a frequency response ana- lyzer (FRA5097, NF Co., Ltd.) and a programmable AC power source (EC1000SA, NF Co., Ltd.). To determine the magnetic permeability, an inductor with a closed-loop core was required, which was also fabricated in addition to the four WPT devices. 3. GPGPU-FDTD Simulation The finite element method (FEM) for frequency-domain of the analysis plane. analysis and the finite difference time domain (FDTD) Calculations using the actual size and frequency could thus method for time-domain analysis are often used for electro- be performed. 2D magnetic field is expressed as a contour magnetic field simulation (17)–(20). FEM is an indirect method graph of magnetic flux density (B). Figures 1(a)–(c) show for solving Maxwell equations that employs weighted resid- simulation results for the open state of the secondary coil for uals. In contrast, FDTD is a simple method for solving P1, P2, and P3 for a transmission distance (δ) of 100 mm. Maxwell equations by transforming them into difference The transmitter was placed on the lower side and the receiver equations. The FDTD method is used for numerical analy- on the upper side in the analysis plane. Specification of these sis of high-frequency WPT (21)–(23). However, Maxwell equa- devices have been shown in our previous paper (15).Themain tions and Berenger’s perfectly matched layer (PML) can also parameters used in the calculation are shown in Table 2. De- be used for low-frequency analysis (24). Therefore, in the tails of these parameters will be described later in next chap- case of a low-frequency WPT analysis, there is no theo- ter. The initial relative permeability of silicon steel was taken retical problem. We have previously reported the results to be 2000. The conductivity of the copper winding was of an electromagnetic field analysis using FDTD (15),where 59 × 106 S/m. The input current of the primary coil was 10 A typical computing using a single-threaded program was per- RMS. There are no needs to specify the self- and formed. The calculation could not be performed using the load resistance because these are estimated by the simulator. actual size, because a large computation time is necessary for These contour graphs were obtained at 1/4 periods low-frequency analysis using FDTD. Therefore, there was a (4.17 ms) after the power supply was turned on. We have con- significant gap between what was ideal and practically pos- firmed that the steady state was reached at 4.17 ms by com- sible. We therefore attempted to create a program using the parison with simulation results using the quasi-static FDTD parallel distribution processing method with general-purpose method (25). As an example, the results shown in Fig. 1(a) took computing on graphics processing units (GPGPU) to signifi- 79 of computation time. The field is not high, even at cantly increase the processing speed. the tip of the magnet-poles, which suggests that no abnor- Specifications and analysis conditions for the 60 Hz-WPT mally high core loss occurs. k was estimated from the ra- simulation are given in Table 1. We used a GeForce GTX tio of the magnetic flux Φ1 generated in the primary coil to 980 Ti (NVIDIA Co., Ltd.) as the GPU, and it was over- the interlinkage flux Φ2, which is directed into the secondary clocked at up to 1.418 GHz from 1.0 GHz using ASUS GPU coil. To compare the experimental and calculation results, Tweak software. The number of CUDA cores for this de- Fig. 2 shows the variation in k with transmission distance for vice is 2861. Therefore, the processing speed reached 8.0 the three devices. The experimental data for P1 to P3 have TFPOLS for single-precision floating point operations. Used already been published in a previous paper (15). Although the Visual C++ 2013 and Cuda Toolkit 6.5 as our simulator de- predicted k values are slightly different from the experimen- velopment environment. tal results, the magnitude relationship of the three devices is Yee cell sizes of the two dimensional (2D) analysis plane consistent with the experimental results. were Δx = 1.0mmand Δy = 1.0 mm. The time step was 4. Equivalent Circuit Analysis 2.35 × 10−13 s, which meets the Courant-Friedrichs-Lewy condition (26). Berenger’s perfectly matched layer (PML) was Condensers function to compensate leakage inductance. used for the absorption of electromagnetic waves at the end Three modes of connection were performed; the primary C1

430 IEEJ Journal IA, Vol.5, No.6, 2016 60 Hz Wireless Power Transmission System（Hiroki Ishida et al.）

(a)

(b)

(c) Fig. 1. FDTD simulation results for δ = 100 mm: (a) P1, (b) P2, and (c) P3

and secondary C2 condensers were connected in parallel with similar process was applied for the other modes. The equiv- the respective coils (PP mode), C1 was connected in parallel alent circuit for the PP mode is shown in Fig. 3. To derive while C2 was connected in series (PS mode), and C1 and C2 an equation for the theoretical transmission efficiency (η), an were both connected in series (SS mode) (27). The equivalent analysis method was constructed based on that of Tohi et al., circuit analysis process for the PP mode is given here, and a in which the copper loss of the WPT system is considered (28).

431 IEEJ Journal IA, Vol.5, No.6, 2016 60 Hz Wireless Power Transmission System（Hiroki Ishida et al.） Table 2. Parameters used in the 60Hz-WPT simulation 2 xL xL x1 + x1 x2 + x2 xL Z = RL + j ····· (2) xL + x2 xL + x2 Z ≡ R + jX

 When C1 is connected, the overall impedance Z is expressed as 2 2 xC1 R − j XxC1 (X − xC1) + xC1R Z = .········(3) 2 2 R + (X − xC1)  The condition of C1, for which the imaginary part of Z be- comes zero, is given by 2 2 xL 2 + RL R xL x2 x x + x x + x x x = + X = + L 1 1 2 2 L . C1 x x +x x +x x X L 1 1 2 2 L xL + x2 xL+x2 ·························(4)

The relationship between VL and V2 is expressed as

RL(xL + x2) VL = V2.···················· (5) RL xL + jx2(xL + x2)

The relationship between V2 and VIN is given as

2 RL xL + jxL x2 (xL + x2) (x + x )2 V = L 2 V .···············(6) 2 Z IN

Thus, the relationship between VL and VIN is expressed as

2 RL xL + jxL x2(xL+x2) R (x + x ) + 2 V R x V = L L 2 (xL x2) V = IN L L . L R x + jx (x + x ) Z IN Z x + x δ L L 2 L 2 L 2 Fig. 2. Dependence of k on . The theoretical curves ························· were estimated by FDTD simulation (7)

The relationship between I1 and IL is derived by dividing both sides of Eq. (7).

VL VIN xL xL = IL = = I1 , RL Z xL + x2 xL + x2 xL + x2 I1 = αIL, ≡ α, ······················· (8) xL Fig. 3. 60 Hz-WPT system equivalent circuit for the PP mode. r1 is the primary winding resistance, jx1 is the where I1 and IL are in phase. primary leakage inductance, − jx is the primary capac- C1 The relationship between IL and I2 is given as itance, r2 is the secondary winding resistance, rs is the 2 stray load loss resistance, jx2 is the secondary leakage x − jR x − I = c2 L c2 I .···························· inductance, jxC2 is the secondary capacitance, rc is the L 2 2 2 (9) RL + xc2 core loss resistance, jxL is the mutual inductance, and RL is the load resistance The absolute value of IL is expressed as The resistance r is a factor of the stray load loss connected in 2 2 2 s | | = xc2 + RL xc2 | | = xc2 | | , series to the secondary winding resistance r . This idea was IL I2 I2 2 R 2 + x 2 R 2 + x 2 2 + 2 inspired by literature on induction motors (29)–(31). L c2 L c2 RL xc2 2 When C2 is connected, the following equation holds for a ∴ | | = + RL | | .···························· resonance frequency ω0: I2 1 IL (10) xc2 1 ff xC2 = = xL + x2.··························(1) The phase di erence between I1 and I2 is given by ω0C2 2 1 xc2 − jRL xc2 The overall impedance for the circuit in the absence of C1 IL = I1 = I2, α 2 + 2 can be expressed using Eq. (2). Here, the resistance compo- RL xc2 2 − 2 nents r1, r2, rS ,andrc are sufficiently small compared to the xc2 jRL xc2 xc2 RL xc2 I1 = α I2 = α − j I2, 2 2 2 2 2 2 reactance components, so that they were neglected. RL + xc2 RL + xc2 RL + xc2

432 IEEJ Journal IA, Vol.5, No.6, 2016 60 Hz Wireless Power Transmission System（Hiroki Ishida et al.）

x ∴ cos φ = c2 . ·····························(11) Substituting Eq. (18) into Eq. (19) yields R 2 + x 2 L c2 1 η = . max The relationship between I , I ,andI is expressed as: α2+ + 1 Q2 − α 1 Q2 + 0 1 2 rc 2 2 2 rs 2 2 + 2 1 Q2 + + k Q1 + k Q1 1 2 1 Q2 k Q1 1 Q2 1 Q2 = − r2 Q2 +1 r2 Q2 +1 I0 I1 I2 k2 Q1 k2 Q1 |I |2 = |I |2 + |I |2 − 2 |I ||I | cos φ ························(20) 0 1 ⎡ 2 1 2 ⎤ ⎢ ⎥ ⎢ R 2 R 2 ⎥ Equation (21) is true under any conditions; therefore, Eq. (20) = 2 ⎢α2 + + L − α + L φ⎥ . IL ⎣⎢ 1 2 1 cos ⎦⎥ can be approximated as shown by Eq. (22) (28). xc2 xc2

··················· 1 Q2 (12) > 1, ··································· (21) k2 Q η 1 For the equivalent circuit shown in Fig. 3, , with considera- 1 tion of the copper, core, and stray load losses is given as: ηmax ≈ . 2 1 Q2 1 Q2 rc α +2+ −2α rs +2 √ 2 k2 Q1 k2Q1 2 1 + + + k Q1 Q2 1 Q2 1 Q2 RLIL r2 Q2 r2 Q2 η = k2 Q1 k2 Q1 2 + 2 + 2 + + 2 RLIL rcI0 r1I1 (r2 rs) I2 ··················· (22) RL = . 1 Q2 When Q1 and Q2 are almost the same, α ≈ and ≈ 1 2 2 2 k Q1 2 RL 2 RL RL RL + r1α + (r2 + rs) 1 + + rc α + 1 + − 2α 1 + cos φ xc2 xc2 xc2 hold, so that ···························(13) η ≈ 1 .····· max −1 −1 (23) 2rc(k+k −1) rs(2k+k ) 1 + √ 2 + + The value of RL for which the copper loss is minimized is k Q1 Q2 r2 Q2 r2 Q2 (32) given as ffi To estimate the stray load loss resistance (rs)isdi cult. r When δ is short, the stray load loss may be acceptably neg- = α2 1 + .···························· RL xc2 1 (14) ligible. The magnetic field surrounding the magnetic pole r2 expands into free space with increasing δ; therefore, rs can- ffi η Thus, the maximum transmission e ciency ( max) with con- not be ignored in this case, and rs will be strongly dependent sideration of the copper, core, and stray load losses is given on δ.Furthermore,rs will be dependent on the shape of the as magnet-pole pieces, but this has not yet been investigated. ff 1 We have assumed that rs is zero to investigate the e ects of η = . max stray load loss, and then compared the experimental and cal- α2 + r1 − α α2 r1 + φ+ α2 r1 + rc 1 r 2 r 2cos 2 rs r 2 1 + 2r2 α2 r1 + 1 + 2 2 + 2 culated results. Figure 4(a) shows the calculation results with xc2 r2 2 r1 2 r1 xc2 α +1 xc2 α +1 r2 r2 consideration of the copper and core losses. Experimental ························(15) data have already been published in previous paper (15). Here, the core loss resistance (rc) is a constant value and it can be Here, k and the quality factors for the two coils (Q1 and Q2) easily identified by employing a measurement method similar are defined as to that for a power transformer. In the region where δ is short, ω ω r = 0L1 , = 0L2 , = M , = xL . s can be ignored. The discrepancy between the two results Q1 Q2 k √ M L2 δ r1 r2 L L xL + x2 increases with increasing . Therefore, rs was calculated as 1 2 δ ··················· (16) function of to compensate for the discrepancy with a best- fit polynomial curve. However, only one term of fourth order The following relationship is derived from Eq. (16): could be fitted, and the results are shown in Fig. 4(b). There is good agreement between the experimental and calculated 2 α2 r1 = L2 r1 = L1L2 r1L2 = L1L2 Q2 = 1 Q2 . values in all regions. The following best-fitting functions of 2 2 2 2 r2 M r2 M r2L1 M Q1 k Q1 rs were obtained for the three devices: ··················· (17) 4 −9 P1 (rectangular): rs(δ) = 15 × δ (10 Ω), ········(24-1) ηmax in Eq. (15) can thus be rewritten using k and Q: 4 −9 P2 (double flare): rs(δ) = 4.5 × δ (10 Ω), ·······(24-2) δ = . × δ4 −9Ω . ········ η = 1 . P3 (single flare): rs( ) 0 9 (10 ) (24-3) max α2+ + 1 Q2 − α 1 Q2 + φ 1 Q2 + rc 2 2 Q 2 2 Q 2cos rs 2 Q 2 + 2r2 1 Q2 + + k 1 k 1 + k 1 δ 1 2 1 Here, the unit for is millimeters. In the case of an induc- xc2 k Q1 1 Q2 1 Q2 xc2 +1 xc2 +1 k2 Q1 k2 Q1 tion motor, rs is a constant value because the gap between the ························(18) stator and rotor is fixed. Identification of the rs value from theoretical calculation is difficult, even though it is a constant ff The phase di erence of Eq. (11) was also adopted the condi- value. Here, the stray load loss was estimated as the remain- tion of Eq. (14) for minimum copper loss: ing power loss after subtraction of the copper, core and me- (29) (30) x 1 chanical losses from the total power loss .Thers value is cos φ = c2 = , ············· (19) 2 equivalent to division of the stray load loss by the square of R + x 2 1 Q2 + L c2 2 2 k Q1 the load current. Thus, the method used here to identify the

433 IEEJ Journal IA, Vol.5, No.6, 2016 60 Hz Wireless Power Transmission System（Hiroki Ishida et al.）

(a) Fig. 6. Dependence of Pout on δ

 where VIN is 100 or 200 V in Japan. Z is the overall impedance of the equivalent circuit in the state with con- densers connected: x 2R Z = C1 ,························· (26) 2 2 R + (X − xC1) where 2 xL xL x1 + x1 x2 + x2 xL R ≡ RL, X ≡ . xL + x2 xL + x2

(b) Here, the RL value was entered for the optimal conditions Fig. 4. Dependence of η on δ, with consideration of (a) shown in Eq. (14). copper and core losses, and (b) copper, core, and stray r 1 load losses R = x α2 1 + ≈ x + .·············· L c2 1 c2 2 1 (27) r2 k

Furthermore, xc1 and xc2 fulfilled the respective resonance conditions of Eqs. (4) and (1). The difference between the ex- perimental and the calculated results is shown in Fig. 6. Ex- perimental data have already been previously published (15). There is good agreement in the long δ region. However, for the short distance region, there is poor agreement with the experimental results. The leakage x1 and x2 be- come small in the short δ region, so that the relative contri- bution of the winding resistance cannot be neglected. Having ignored the effect of the winding resistance in Eq. (26), Z is estimated to be larger than the true value in the short δ region. Fig. 5. Correlation between k and the δ4 coefficients To mitigate the mismatch, the equivalent circuit containing resistance components should be solved precisely; however, this has not yet been completed. The conclusion can be de- function of r did not depart from the general method (29) (30). s rived from Eq. (25), where the simple solution to obtain large From comparison of the of δ4 coefficients, it can concluded P is to apply a large input , because P is propor- that the single flare is the optimal shape for low stray load out out tional to the square of the input voltage. loss among the three prototype devices. The δ4 coefficients could be determined from the shape of magnet-pole piece, 5. Design and Fabrication but they cannot be estimated using the simulator. Figure 5 Our purpose is to achieve wireless charging for a small shows the correlation between the k values and the δ4 coeffi- electric vehicle (EV). The 60 Hz-WPT system is designed cients (data for P4, which will be described later, are included to allow wireless charging at home without the need for a in this graph). A scale law was identified that logarithmically high-frequency power supply. We have developed a small decreases with k for any δ. It was thus possible to estimate EV equipped with the 60 Hz-WPT, and photographs of the the coefficients of δ4 from k, which are estimated from the prototype are shown Fig. 7. The small EV has a 48 V elec- FDTD simulator, using this scale law. trical system by the in-series connection of four 12 V lead The transmission power (P )atmaximumefficiency in- out storage battery packs. Table 3 shows the requirements of the dicated in Eq. (25) is given as 60 Hz-WPT charging system. The device was designed in V 2 an attempt to satisfy these requirements and evaluation was P = R I 2 = IN η ,······················ (25) out L L Z max conducted using equivalent circuit analysis (PP and SS mode)

434 IEEJ Journal IA, Vol.5, No.6, 2016 60 Hz Wireless Power Transmission System（Hiroki Ishida et al.）

Table 4. Specifications for the P4 prototype

Fig. 7. Small EV equipped with the 60 Hz-WPT charg- ing system. (a) Back view, and (b) internal components

Table 3. Requirements of the 60 Hz-WPT system

magnetic pole area of 132 mm2 was necessary to obtain k = 0.22 at δ = 10 cm. In the experiment, a sliding resistance (DW series, Yam- abishi Electric Co., Ltd.) was used as an experimental load. For example, the inductance included in the winding of 6.3 Ω was 0.5 mH, which is negligibly small compared to the self- inductance of the primary and secondary coils. The resis- tance change due to temperature increase was adjusted man- ually to keep constant. The experimental results, where the efficiency and power output were 79% and 190 W, confirm that the P4 prototype exhibits the designed performance. Fig- ures 9(a) and (b) show the η and Pout characteristics for the P4 prototype, and the results for P3 are also presented for (a) (b) comparison. At δ = 100 mm, the difference between the two Fig. 8. (a) Front and (b) side views of the P4 prototype devices appears small; however, the difference increased with δ. At 150 mm, η wasimprovedby7%,andPout was increased and an FDTD simulator. by 44 W. However, the output power of the 60 Hz-WPT sys- Figure 8 shows a photograph of the P4 prototype, and the tem would be too small in consideration of applications such specifications for P4 are given in Table 4. P4 was designed as small electric vehicles. For example, the high-frequency to be 2 kg lighter than P3, and an efficiency of 80% was the- WPT system for the Nissan Leaf II has over 3 kW output oretically predicted with δ = 100 mm. Here, rc could not be at a transmission distance of 150 mm. Although the exact identified by calculation; therefore, the values measured for size and weight are not published, the latter system has over- P3 were used. whelming performance compared to the 60 Hz-WPT system. The size of the device was determined based on the de- If applied to a small electric vehicle, the 60 Hz-WPT system sign guidelines for a low-voltage transformer for converted would require 500 W or more (33). to resistance at 75◦C. According to the guidelines, the cross- We considered that high power can be obtained even at low sectional area required for a single-strand copper wire was input voltage by lowering the overall impedance. Thus, a over 3.0 mm2. Therefore, a polyvinyl-formal enamel-coated simple solution is to select the SS mode. Figure 10(a) shows copper wire with a diameter of 2.0 mm was selected. In a typ- a comparison of the output power with input voltage for the ical low-voltage transformer, the sectional area of the mag- three modes (PP, PS, and SS modes). For the SS mode, netic core is determined assuming a magnetic field of up to the output power reached 854 W at 100 V. We did not at- approximately B = 1.5 T. However, a larger cross-sectional tempt to increase the input voltage over 100 V, because this area was required to obtain a large Q. To obtain Q > 60, would exceed the rated current of the condenser. Figure 10(b) a cross-sectional area of at least 28 cm2 was necessary. A shows a comparison of the transmission efficiency for the

435 IEEJ Journal IA, Vol.5, No.6, 2016 60 Hz Wireless Power Transmission System（Hiroki Ishida et al.）

Fig. 11. 60 Hz wireless charging circuits for charging lead storage batteries

weight reduction is required by optimization of the design. (a) 6. Wireless Charging System Wireless charging of lead storage batteries was performed in anticipation of wireless charging for a small EV. Fig- ure 11 shows the wireless charging circuits. The experiment was performed using the P4 device with a transmission dis- tance of 15 cm. The capacitances of the condenser for res- onance (C1, C2) were given by the following equation from the equivalent circuit analysis: 1 1 C1 = , C2 = .·········(28) ω0(xL + x1) ω0(xL + x2) 60 μF film condensers were selected according to Eq. (28). (b) Two lead storage batteries (Type: 44B19R, 12 V, 34 Ah) con- Fig. 9. Characteristics of the P4 prototype. (a) Depen- nected in series were used as the load. The internal resistance dence of η on δ,and(b)ofPout on δ. Results for the P3 in a lead storage battery changes during charging, and it also prototype are also shown for comparison varies depending on the charge time. The amount of change in the battery used for the experiment was between 20 and 35 mΩ. A diode bridge (GBP2504) with a large internal resistance was selected for the rectifier. The internal resistance was 180 mΩ, which is the average dynamic resistance in the op- erating voltage region of VF from 0.0 V to 0.93 V. The total load resistance was approximately 400 mΩ when the line re- sistance of 10 mΩ was considered. Therefore, the variable ratio of the load resistance caused by the internal resistance of the battery would be only 1.8%. Therefore, control to track the load variation was not necessary (as shown in Fig. 7(b)). The output voltage of wireless charging system was 31 V (a) under 50 V of input voltage, which is reasonable because the typical charging voltage per battery pack is 15.5 V. The com- mon utility voltage in Japan is 100 V; therefore, the input voltage is just 100 V in the case of four battery packs con- nected in series. Our small electric vehicle has been devel- oped with four battery packs connected in series. Figure 12 shows a time course of the voltage and current during battery charging. The WPT system in the SS mode has immittance conversion characteristics (28). Common util- ity power acts roughly as a constant voltage supply, so that the WPT system in the SS mode acts almost as a constant current supply. Therefore, the charging current continues to (b) flow, even if a charging voltage of 31 V is reached, which Fig. 10. Comparison of the transmission performance takes approximately 2 h. for the three modes. (a) Pout,and(b)η as a function of the input voltage Figure 13 shows the time course of the transmission ef- ficiency during charging. Here, ηwpt is Pwpt/Pin (× 100%), which is the efficiency of the WPT system. ηtotal is Pout/Pin three modes. For the SS mode, the maximum efficiency of (× 100%), which is the efficiency including the power loss 70% was maintained until 451 W. The weight of 10 kg would in the rectification circuit. Although the circuit was uncon- be too heavy for small electric vehicle. Therefore, further trolled during charging, ηtotal was kept at 60%, which is

436 IEEJ Journal IA, Vol.5, No.6, 2016 60 Hz Wireless Power Transmission System（Hiroki Ishida et al.）

improvement in η and an increase of 382 W for Pout over our previous report. Even with a lead storage battery as a load, the decrease from the maximum efficiency is only 4%. The device proposed here is very simple and easily fab- ricated with only silicon steel plates, single-strand copper wire, and phase-advanced condensers. In addition, this sys- tem could be directly connected to a wall socket. The man- ufacturing cost of the P4 prototype was approximately 600 USD (silicon steel plates: 100 USD, copper wire: 100 USD, and condensers: 400 USD). Therefore we consider that the 60 Hz-WPT is suitable for wireless charging of small electric Fig. 12. Time course of battery voltage and current dur- vehicles. ing charging Acknowledgment This research is partially supported by the Japan Science and Technology Agency A-STEP, (Feasibility studies stage No.AS262Z00347L), and JSPS KAKENHI Grant Number 15K13934.

References

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437 IEEJ Journal IA, Vol.5, No.6, 2016 60 Hz Wireless Power Transmission System（Hiroki Ishida et al.）

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