4.1. Simulation Results
Figure 12 shows the structure of the WPT coils designed using an electromagnetic (EM) field simulator. The contents proposed in this paper were verified using the coil in
Figure 12. The design specifications of the coils on the Tx and Rx sides are the same. The structural information of the coil and the wire is specified in
Table 3. In addition, the simulation results are shown in
Table 4. The resonance frequency was selected to be 60 kHz, and the mutual inductance values and coupling coefficient according to the air gap are listed in
Table A2 in
Appendix B.
First, the magnitude of the input impedance according to the coupling coefficient analysis was analyzed. The circuit simulation was conducted with the configuration shown in
Figure 1, and the magnitude of the input impedance was analyzed as the coupling coefficient (k) changed. Information on the detailed setup of the circuit simulation is shown in
Table 5.
Figure 13 shows the changes in the magnitude and phase of the input impedance, respectively. As expected in
Section 2.3, as the coupling coefficient increases, the slope of the input impedance decreases. Since the slope of the input impedance decreases, the magnitude of the input impedance also decreases in the harmonic components. This is shown in
Figure 13a. In addition, as expected in previous studies, as the coupling coefficient increases, the ZPA gradually moves away from the original resonance frequency of 60 kHz. This is shown in
Figure 13b. Note that the critical coupling coefficient (k
critical) obtained using Equation (10) is 0.176.
Next, the effect on the WPT system with series inductors was analyzed. As mentioned above, the calculation of the inductor is divided into a method using calculation [
27,
28] and an analysis method using an EM solver [
29]. In this paper, the inductor was designed using a toroidal core, and the inductance and resistance values of the inductor were calculated using an EM solver. Detailed design information about the inductors is presented in
Appendix C.
As described in
Section 3, not only the inductance of the series inductor, but also the resistance of the series inductor is very important, and the calculation results are shown in
Table A4. The circuit simulation was configured as shown in
Figure 7 and the basic circuit simulation setup is shown in
Table 6 and
Table 7. The coupling coefficient was selected to be 0.37 for a 30 mm air gap in
Table A2. The capacitance of the compensation circuits (
,
) was calculated by considering the resonance frequency and the equivalent inductance of each Tx and Rx (
,
and is calculated through Equations (25) and (26).
Figure 14 shows the change in the input impedance as the series inductance changes.
Figure 14a shows the magnitude of the input impedance. As expected from Equation (24), as the inductance value of the series inductors increases, the input impedance at the frequency of the harmonic component increases. Since L
add−tx, L
add−rx are increased in units of 10
, the slope of the input impedance increased very regularly, as expected in Equation (24). In addition, as can be seen from
Figure 14b, as the value of the series inductance increases, the ZPA frequencies (
converge to the original resonance frequency (
) of the system. Particularly, as described in
Section 3, when the WPT system is over-coupled and a frequency splitting phenomenon occurs,
is used as the operating frequency. It has been determined that
is the frequency of the MPT. On the other hand, as described in
Section 3, the frequency of the maximum PTE is the original resonant frequency (
) of the system. Therefore,
getting closer to
means that the frequency of maximum PTE and the frequency of MPT are getting closer, which can improve the disadvantages of the conventional over-coupled WPT system. In an over-coupled WPT system, the difference between the frequency of maximum PTE
) and the frequency of MPT
) is defined as follows:
Figure 15 shows the PTE and the relative power transferred to the load as a function of the additional series inductance. Here, PTE is the ratio of the power delivered to the equivalent load (R
L) to the power supplied from the power source (
Vin), and the power transfer capacity is the relative amount of power transferred to the equivalent load (R
L) in the setup in
Figure 7. The relative amount of transferred power means the ratio when the maximum transferred power is set to unity. As shown in
Figure 15a, it always has the maximum efficiency at the resonant frequency regardless of the inductance value of L
add. This is what was expected in Equation (17). As the value of L
add is increased, the overall efficiency decreases due to the parasitic resistance (R
add−tx, R
add−rx) of L
add.
Figure 15b shows the relative power transfer capacity according to series inductance. As expected from the impedance phase in
Figure 14b, the frequency (
,
) of MPT gradually approaches
as the series inductance increases. Note that the relative MPT gradually decreases as series inductance increases. This is a reasonable result considering that all parasitic resistance values are located in the denominator in Equation (18).
Figure 16a shows the difference between the maximum PTE frequency in
Figure 15a and the MPT frequency in
Figure 15b. As previously analyzed, the difference between the two frequencies decreases as the series inductance value increases. Meanwhile,
Figure 16b shows that the power transfer efficiency decreases as the series inductor increases.
Additionally,
Figure 17 shows the fast Fourier transform (FFT) results at the fundamental frequencies of the Tx current and Rx current and the third, fifth, and seventh harmonic frequencies when the circuit simulation of the 30 W class WPT system was conducted. As expected from
Section 2, the input impedance increased as the inductance of the series inductor increased, so that the current in the harmonic frequency component decreased. As the series inductance increases, the magnitude of the current decreases at the frequencies of all harmonics except the fundamental component. Meanwhile, as the series inductance increases, the MPT decreases slightly, as shown in
Figure 15b, so in order to transfer the same power (30 W), the fundamental component of the Tx current must increase slightly, which is shown in
Figure 17a. Since the output power is all the same at 30 W, the fundamental of the Rx current is the same, which is also shown in
Figure 17a.
In this paper, the additional series inductor was selected to be 30 . The PTE of the WPT system decreases by 2% or less compared to when the series inductor is not added. It is up to the WPT system designer to choose whether to focus on efficiency or EMI in a WPT system.
In order to analyze the components of the current harmonics of the WPT system including the designed L
add, a power transfer circuit simulation setup was constructed, as shown in
Figure 18. All circuit simulation parameters except the load resistance were configured as shown in
Table 4 and
Table 5. The load resistance was set to 3 ohms so that the input resistance considering the rectifier was equivalent to 2.4 ohms, as shown in
Figure 18 [
21]. The input power P
in is the real power output from the inverter, and the output power P
out is the real power input to the rectifier, as also shown in
Figure 18.
Table 8 shows the simulation results when operating a 30 W class WPT system. As previously targeted, it can be seen that the PTE of the WPT system with the series inductor added is 2% lower than that of the system without the series inductor added.
4.2. Experiment Results
For the measurement, WPT coils to be used in the WPT system are fabricated. The manufactured coil has design specifications as shown in
Figure 12 and
Table 3 and
Table 4, and the actual shape is shown in
Figure 19, and the measured electrical data are shown in
Table 9.
In addition,
Table 10 shows the mutual inductance and the coupling coefficient at each air gap of the coils of the WPT system.
Next, toroidal inductors were fabricated for the series inductors. The toroidal cores had the design specifications shown in
Table A3 in
Appendix C. The shape of the actual fabricated core is shown in
Figure 20, and the calculated resistance values and measured resistance values at each inductance are shown in
Table 11. The toroidal inductances for the experiments were produced by selecting three representative values (30
, 60
, 90
) from the series inductance values (10 to 90
) used in the simulation in
Table 7. Although there was a difference of up to 30% between the measured resistance value of the inductor and the resistance value calculated by the EM solver, it can be concluded that the calculation of the resistance value by the EM solver is reliable enough to design an actual WPT system.
Meanwhile,
Table 12 shows the value of the compensation capacitance selected using (25) and (26) according to the inductance value of the coil and the inductance value of the series inductors.
Using the fabricated and measured WPT coils, series inductors, and compensation capacitors, the setup was constructed as shown in
Figure 7 and the input impedance was measured. The load resistance (R
L) was selected to be 2.4 ohms as in the simulation, and the inductance of the load resistor was less than 10 nH, so it had little effect on the resonance of the WPT system. The input impedance was measured as shown in
Figure 21; an impedance analyzer (Keysight E4990A) was used for the measurement.
First, the slope and phase of the input impedance change were measured according to the coupling coefficient. The input impedance was measured by changing the air gap between the WPT coils to 30, 60, and 90 mm, and the result is shown in
Figure 22. As in the simulation conducted above, it can be seen from
Figure 22a that the smaller the air gap between the coils (the larger the coupling coefficient of the coils), the smaller the slope of the input impedance and the smaller the magnitude of the input impedance in the harmonic components. In addition, it can be seen from
Figure 22b that as the coupling coefficient increases, the ZPA frequencies
gradually become farther from the original resonant frequency (
Figure 23 shows the change in the input impedance when the series inductors were added to the WPT system. As in the simulation, as the series inductance value increased, both the slope of the magnitude of input impedance and the magnitude of impedance at the harmonic component frequency increased, as shown in
Figure 23a. Likewise, it can be seen from
Figure 23b that as the series inductance increased, the frequencies of ZPA
rather than the resonant frequency gradually approach the original resonant frequency
.
Figure 24 shows the experimental setup used for measuring the current harmonics and transferred power of a WPT system. Measurements were performed using an oscilloscope (Keysight MSO-X4154A) and a power analyzer (YOKOGAWA WT1802E). Input and output power were measured based on
Figure 18, from the output of the inverter (P
in) to the input of the rectifier (P
out).
Table 13 shows the voltage, current, and power of the input, output, respectively, with and without series inductance when performing a 30 W class WPT experiments. Compared to the WPT in the previous simulation, the PTE decreased by 4.5% both with and without the series inductance. For that reason, first, the resistance of the compensation capacitor was ignored in the simulation, but the parasitic resistance of the actual compensation capacitor was about 20 to 40
, which cannot be ignored, compared to the resistance of the WPT coils (about 50
). The second reason is that the resistance of the fabricated coil and the series inductor was measured to be slightly higher than that of the simulation. However, as in the simulation, the difference between the measured PTE with and without the series inductor was less than 2%, so it can be concluded that the design considerations of the WPT system with the series inductor analyzed in this paper are valid.
Table 14 shows the peak values of the fundamental components among the current components of the Tx and Rx coils. As in the previous simulation, the fundamental component of the Tx coil current when the series inductance was applied is higher than when the series inductance was not applied.
Figure 25 shows the current in the odd harmonic components of each coil with and without series inductors, when conducting a 30 W class WPT experiment. As in the simulation, the current of the odd harmonic component when the series inductance was applied was reduced by a minimum of 35% to a maximum of 73% compared to when the series inductance was not applied.
Finally, the EMI was measured at a distance of 3 m in accordance with CISPR 14-1 standard [
30], while the 30 W class WPT system was operating.
Figure 26 shows the measurement setup.
Table 15 shows the measured EMI data of the WPT system, and when the series inductance was applied. When the series inductance was applied, it reduced from 3.42
to a maximum of 9.02
compared to when it was not applied.
Meanwhile,
Table A5 of
Appendix D shows the standard of radiation emission defined in CISPR 14-1. Comparing the EMI measurement results of
Table 15 with the EMI limit specifications of
Table A5, it can be seen that all measurement results, whether the series inductor is added or not, do not exceed the limit specifications. This is because the power transfer capacity is relatively low (30 W class), and if the power transfer capacity is increased, the measured EMI results may exceed the limit standard. Although there is a difference between the limit standard and the measured EMI values, it can be said that the WPT design with the additional series inductors has proved sufficiently effective because it effectively reduced EMI (maximum −9.02
).