Single-Stage Wireless Battery Charging Circuit with Coupling Coefficient Prediction

Abstract

This paper proposes a single-stage wireless battery charging circuit with a coupling coefficient prediction method. The proposed circuit consists of only two stages: full bridge inverter with transmitter coil in the first stage and full bridge rectifier with receiver coil in the second stage. This circuit implements the constant current (CC) charging mode at the resonant frequency of two coils and the constant voltage (CV) charging mode at a specific frequency that is dependent on the coupling coefficient of two coils. The operation at a specific frequency guarantees the CV operation regardless of load condition and reduces the switching losses than the operation at the resonant frequency owing to a zero-voltage switching (ZVS) operation. In CC-CV modes, the phase-shift technique is additionally applied to improve the output voltage/current regulation. Unlike other approaches, the proposed single-stage wireless battery charging circuit does not require multiple stages of power conversion, or additional components, a pre-measured coupling coefficient or a complex control algorithm for CC-CV charging operation. The prototype proposed circuit was tested under various coil alignment conditions, and successfully implemented the CC-CV charging operation for a 36 V battery pack. The predicted coupling coefficient had an error of ≤0.62% in the coil alignment condition, and the circuit had errors of ≤0.32%, ≤0.1% in the output current and voltage regulation, respectively.

1. Introduction

In recent years, the use of wireless power transfer (WPT) systems has increased in the field of biomedical devices, electric vehicles (EVs) and all kinds of consumer electronics [1,2,3,4]. However, the power supply of these devices is not as stable as that of wired devices, so most adopt batteries to improve safety and convenience. As the air gap between the transmitter and receiver coil increases, the coupling coefficient decreases, and so increases the reactive power. Thus, many capacitor-compensated network structures have been proposed to solve this problem [5,6,7]. Among them, the series-series (S-S) compensated capacitors method has been widely adopted for low and middle power ranges, because the capacitance can be easily selected regardless of the load resistance and coupling coefficient [8,9].

To charge a battery using a WPT circuit, it must support the constant current (CC) and the constant voltage (CV) charging mode. Thus, there are multiple stages of power conversion, as shown in Figure 1a, which reduce the cost effectiveness and power density of the entire wireless battery charging circuit [8,9,10,11]. To solve this issue, the circuit stage can be simplified to a single stage, as shown in Figure 1b. The single-stage wireless battery charging circuit in [12] adopts a pulse frequency modulation (PFM) technique to obtain a CV output. Whenever the coil alignment changes, this system should change the operating frequency range. Thus, designing such a frequency limiter is a difficult task. The WPT circuit in [13] inserts two intermediate coils between transmitter and receiver coil to improve efficiency, and the system operates in two fixed frequencies for CC-CV charging modes. However, the resonant frequency of intermediate coils should be differently designed whenever the coupling coefficient is changed, and there is no way to know that according to the various coil alignments. The WPT circuits in [14,15,16] introduce the hybrid compensation network using active switches and auxiliary capacitors. This method changes the compensation network whenever charging modes are changed, and the additional components reduce power density. The simplest way to use the single-stage S-S- compensated wireless battery charging circuit is by adopting the phase shift control of a full-bridge inverter at the resonant frequency f = f_o of two coils as in Figure 2a,b. This method can attain high efficiency in the CC mode, because S-S-compensated two coils have an ideal output characteristic of CC regardless of load condition with a zero-phase angle (Figure 2a), so that the transmitter does not have a reactive power and soft switching condition is achieved. However, much phase should be shifted in the CV mode, and it causes a hard switching condition (Figure 2b).

This paper notes that the S-S-compensated two coils have a specific frequency related to the coupling coefficient f = f_CV, where the constant output voltage and zero voltage switching (ZVS) condition can be attained regardless of load condition (Figure 2c). In this paper, the proposed single-stage wireless battery charging circuit operates at the resonant frequency of two coils and predicts a coupling coefficient between the transmitter and receiver coil. Then, the predicted value is used to decide the operating frequency of the CV mode as f = f_CV. Thus, the proposed system attains the ZVS operation and does not require a multi-stage circuit, additional components, complex control algorithm or pre-measured coupling coefficient. In addition, the proposed circuit adopts a phase-shift control to complement the effects of parasitic elements in the regulation of CC and CV charging modes. In Section 2, the analysis of the single-stage wireless battery charging circuit with coupling coefficient prediction method is given based on the fundamental harmonic approximation (FHA), Experimental results are presented in Section 3, and a conclusion is given in Section 4.

2. Single-Stage Wireless Battery Charging Circuit

2.1. Circuit Structure and Analysis of Equivalent Circuit

The proposed single-stage wireless battery charging circuit (Figure 3a) consists of a full bridge inverter (S₁–S₄) with transmitter coil (L_p) in the primary side and full bridge rectifier (D₁–D₄) with receiver coil (L_s) in the secondary side. The two coils are serially compensated by the capacitors (C_p, C_s), and have a mutual inductance of $M_{ps}=k_{ps}\sqrt{L_p{L}_s}$, where k_ps is the coupling coefficient between two coils. To maximize the output power capability, two coils are designed to have the same resonant frequency as ω_o = 2π⸱f_o; L_pC_p = L_sC_s = 1/ω_o². The two complementary switch pairs (S₁, S_2′ and S₃, S_4′) operate at the switching frequency f_s = 1/T_s and are phase-shifted by an angle of α, so the output voltage of the full bridge inverter (v_p) can be expressed as in Figure 4, where V_DC is supplied DC voltage. Based on the FHA, the voltage and current of the proposed circuit in Figure 3 can be expressed as follows:

$$v_p(t)=V_p\sin (\omega t+\theta +\phi )=\frac{2V_{DC}}{\pi }(1+\cos \alpha )\sin (\omega t+\theta +\phi ),$$

(1)

$$i_p(t)=I_p\sin (\omega t+\theta ),$$

(2)

$$v_s(t)=V_s\sin \omega t=\frac{4V_{bat}}{\pi }\sin \omega t,$$

(3)

$$i_s(t)=I_s\sin \omega t=\frac{\pi I_{bat}}{2}\sin \omega t,$$

(4)

where the subscripts p and s stand for the primary and secondary, V_bat is the voltage of the battery pack and I_bat is the charging current of the battery pack. Then, an equivalent of the proposed circuit is shown in Figure 3b, where R_in, R_p and R_s are equivalent series resistance (ESR) of full bridge inverter, primary coil and secondary coil, respectively. R_bat,eq is the equivalent load resistance of the battery pack, which can be expressed as:

$$R_{bat,eq}=\frac{V_s}{I_s}=\frac{8}{{\pi }^2}\cdot R_{bat}.$$

(5)

If the Kirchhoff’s voltage law (KVL) is applied to the Figure 3b:

$$\overrightarrow{V_p}=(R_{in}+Z_p)\overrightarrow{I_p}-j\omega M_{ps}\overrightarrow{I_s},$$

(6)

$$j\omega M_{ps}\overrightarrow{I_p}=(Z_s+R_{bat,eq})\overrightarrow{I_s},$$

(7)

where Z_p and Z_s are impedance of the transmitter and receiver coil as Z_p = R_p + jωL_p + 1/jωC_p and Z_s = R_s + jωL_s + 1/jωC_s. From (6) and (7), amplitude of i_s, I_s (Figure 5a), voltage conversion ratio G (Figure 5c), and input impedance Z_in (Figure 5e) of the proposed circuit can be expressed as:

$$\left|\overrightarrow{I_s}\right|=\left|\frac{j\omega M_{ps}}{(R_{in}+Z_p)(Z_s+R_{bat,eq})+{\omega }^2{M}_{ps}{}^2}\right|\cdot \left|\overrightarrow{V_p}\right|.$$

(8)

$$G=\left|\frac{\overrightarrow{V_s}}{\overrightarrow{V_p}}\right|=\left|\frac{R_{bat,eq}\overrightarrow{I_s}}{\overrightarrow{V_p}}\right|=\left|\frac{j\omega M_{ps}{R}_{bat,eq}}{(R_{in}+Z_p)(Z_s+R_{bat,eq})+{\omega }^2{M}_{ps}{}^2}\right|,$$

(9)

$$Z_{in}=\frac{\overrightarrow{V_p}}{\overrightarrow{I_p}}=\frac{(R_{in}+Z_p)(Z_s+R_{bat,eq})+{\omega }^2{M}_{ps}{}^2}{Z_s+R_{bat,eq}},$$

(10)

2.2. Anlaysis of Circuit for CC-CV Charging Mode

Normally, a battery charger has a CC-CV charging profile. At first, the battery pack is charged by the CC mode. When the V_bat reaches the cut-off voltage (V_bat,cut), the charging mode is changed to the CV mode, and the I_bat gradually decreases. Finally, the charging operation is terminated when the I_bat tapers to the end of the charging current (I_end) [8,9,10,12,13]. To support both modes, the proposed WPT circuit adopts the S-S-compensated network as in Figure 1.

At f_s = f_o, Z_p = R_p and Z_s = R_s, so (8) can be represented as:

$$I_s={\frac{{\omega }_o{M}_{ps}{V}_p}{(R_{in}+R_p)(R_s+R_{bat,eq})+{\omega }_o{}^2{M}_{ps}{}^2}|}_{f_s=f_o}.$$

(11)

If ESRs are negligible, I_s = V_p/ω_oM_ps, which means the circuit operates in CC regardless of R_bat,eq. However, ESRs inevitably exist in the circuit, and they affect the CC regulation as in Figure 5b. Thus, the operation of circuit at f_s = f_o with phase-shift of α_CC guarantees the CC charging profile. From (1) and (11),

$${\alpha }_{CC}={\cos }^{-1}\left\{\frac{{\pi }^2}{4}\cdot \frac{I_{cc}\left[(R_{in}+R_p)(R_s+R_{bat,eq})+{\omega }_o{}^2{M}_{ps}{}^2\right]}{V_{DC}{\omega }_o{M}_{ps}}-1\right\},$$

(12)

where I_cc is the value of CC.

If the circuit still operates at f_s = f_o to get a CV, (9) can be arranged as

$$G={\frac{{\omega }_o{M}_{ps}{R}_{bat,eq}}{(R_{in}+R_p)(R_s+R_{bat,eq})+{\omega }_o{}^2{M}_{ps}{}^2}\cdot V_p|}_{f_s=f_o}.$$

(13)

When ESRs are negligible, G = R_bat,eq/ω_oM_ps, which means G depends on R_bat,eq, and the circuit cannot attain CV. Thus, the phase α_cv,o to be compensated in the full bridge inverter is derived from (1) and (13) as

$${\alpha }_{cv,o}={\cos }^{-1}\left\{\frac{2V_{cv}\left[(R_{in}+R_p)(R_s+R_{bat,eq})+{\omega }_o{}^2{M}_{ps}{}^2\right]}{V_{DC}{R}_{bat,eq}{\omega }_o{M}_{ps}}-1\right\},$$

(14)

where V_cv is the value of CV. However, α_cv,o is proportional to R_bat,eq, and it generates a hard switching condition because α_cv,o is larger than ∠Z_in at f_s = f_o (Figure 2b and Figure 6a).

To tackle this issue, the proposed circuit operates at a specific frequency f_CV, where CV and ZVS are secured regardless of R_bat,eq. When the circuit operates in the CV mode, G should have a constant value regardless of R_bat,eq. If ESRs are negligible at (9), G can be expressed as

$$G\approx \left|\frac{j\omega M_{ps}}{(j\omega L_p+1/j\omega C_p)+\beta /R_{bat,eq}}\right|,$$

(15)

where $\beta ={\omega }^2{C}_p{C}_s(M_{ps}{}^2-L_p{L}_s)+(C_p{L}_p+C_s{L}_s)-1/{\omega }^2$. If β is set to zero, the f_CV, which guarantees the CV, is derived as ${\omega }_{CV1}=2\pi f_{CV1}=2\pi f_o/\sqrt{1+k_{ps}}$ and ${\omega }_{CV2}=2\pi f_{CV2}=2\pi f_o/\sqrt{1-k_{ps}}$. To achieve the ZVS operation of S₁–S₄, ∠Z_in at f_s = f_CV should be larger than zero as in Figure 5e, so f_CV2 is desirable as f_CV. Consequently, the operation of the circuit at f_CV derives CV as $G\approx \sqrt{L_s/L_p}$. However, the inevitable ESRs affect the CV regulation as in Figure 5d, so the phase α_CV to be compensated is derived from (1), (3) and (9) as

$${\alpha }_{CV}={\cos }^{-1}\left\{\frac{2V_{CV}}{V_{DC}{\omega }_{CV}{M}_{ps}{R}_{bat,eq}}\cdot \sqrt{\begin{array}{l}{\left[(R_{in}+R_p)(R_s+R_{bat,eq})-({\omega }_{CVcv}{L}_p-1/{\omega }_{CV}{C}_p)\cdot ({\omega }_{CV}{L}_s-1/{\omega }_{CV}{C}_s)+{\omega }_{CV}{}^2{M}_{ps}{}^2\right]}^2\\ +{\left[(R_{in}+R_p)({\omega }_{CV}{L}_s-1/{\omega }_{CV}{C}_s)+(R_s+R_{bat,eq})\cdot ({\omega }_{CV}{L}_p-1/{\omega }_{CV}{C}_p)\right]}^2\end{array}}-1\right\}.$$

(16)

Because α_CV is larger than ∠Z_in at f_s = f_CV in whole range of R_bat,eq (Figure 6b), the ZVS operation is secured.

Finally, the proposed single-stage wireless battery charging circuit uses the proportional integral (PI) controller to track the α_CC for I_CC and α_CV for V_CV. The only issue is finding k_ps to operate the circuit at $f_{CV}=f_o/\sqrt{1-k_{ps}}$ in the CV mode. In the following section, the method to find k_ps and the composition of the controller will be presented.

2.3. Coupling Coefficient Prediction Method and Control of CC-CV Charging Mode

The output current and voltage regulation characteristics are affected by the ESRs, load resistance and operating frequency as expressed in the above section. Also, because k_ps is changed by variable coil alignment, the CV mode at f_s = f_CV has been unpractical. Therefore, additional circuits, complex control algorithms or pre-measured k_ps have been used to charge the battery pack [8,9,10,11,12,13,14,15,16]. We introduce the prediction method of k_ps, which can be used to calculate f_CV. Also, we incorporate this method to the phase-shift technique to charge a battery pack in CC-CV mode.

When the proposed WPT system operates in CC modes at f_o, I_bat can be expressed as follows by using (1), (4), (5), (11):

$$I_{bat}=\frac{4}{{\pi }^2}\cdot \frac{{\omega }_o{M}_{ps}{V}_{DC}(\cos {\alpha }_{CC}+1)}{(R_{in}+R_p)(R_s+8V_{bat}/{\pi }^2{I}_{bat})+{\omega }_o{}^2{M}_{ps}{}^2}.$$

(17)

It can be rearranged according to M_ps as:

$$\left({\pi }^4{\omega }_o{}^2{I}_{bat}{}^2\right)M_{ps}{}^2-4{\pi }^2{V}_{DC}{\omega }_o{I}_{bat}(\cos {\alpha }_{CC}+1)M_{ps}+{\pi }^2{I}_{bat}(R_{in}+R_p)({\pi }^2{R}_s{I}_{bat}+8V_{bat})=0$$

(18)

This equation has two solutions for M_ps, and the larger one is a reasonable value according to the calculation result, so

$$M_{ps}=\frac{-b+\sqrt{b^2-ac}}{a},$$

(19)

where $a={\pi }^4{\omega }_o{}^2{I}_{bat}{}^2$, $b=-2{\pi }^2{V}_{DC}{\omega }_o{I}_{bat}(\cos {\alpha }_{CC}+1)$, $c={\pi }^2{I}_{bat}(R_{in}+R_p)({\pi }^2{R}_s{I}_{bat}+8V_{bat})$.

Because the value of α_CC, ω_o, R_in, R_p and R_s is known, and the DC value of V_DC, V_bat and I_bat is easily sensed, k_ps can be predicted by $k_{ps,pd}=M_{ps,pd}/\sqrt{L_p\cdot L_s}$, where the subscript pd stands for prediction.

Finally, the controller for the proposed single-stage wireless battery charging circuit can be designed as in Figure 7, and it consists of an operating algorithm with k_ps prediction, PI control part for the α_CC and α_CV, CC and CV mode selector part, gate signal conditioning part and protection part for over-charging the voltage/current (V_oc, I_oc). The main controller is implemented by TMS320F28335, which has a 12-bit analog-to-digital converter. The gate signal block is modulated by an enhanced pulse width modulator (ePWM) module, and other parts including an algorithm, PI controller, mode selector and protection are operated by the interrupt function of ADC block. The operating algorithm consists of the following eight procedures:

(1)

If V_bat[n] < V_bat,cut, the circuit operates in the CC mode, otherwise the circuit terminates the charging operation.

(2)

To regulate the I_bat as I_CC, f_s is set to f_o, and the PI controller compensates the phase α_CC[n].

(3)

By using (18), k_ps,pd[n] is continuously updated to check the variation of coil alignment.

(4)

The algorithm repeats (2) and (3) until V_bat[n] = V_bat,cut.

(5)

At the instant of V_bat[n] = V_bat,cut, f_CV is calculated based on the final updated k_ps,pd[n].

(6)

The CC mode is changed to the CV mode. The transition mode consists of two sequences; (a) The transferred power is decreased to zero by gradually increasing α_CC[n] to π. (b) f_s is set to f_CV, and the circuit renews the CV mode.

(7)

To regulate the V_bat as V_CV, the PI controller compensates the phase α_CV[n].

(8)

If I_bat has tapper to I_end, the total charging operation for the battery pack is finished, otherwise it continuously operates the CV mode as in (7).

3. Experimental Results

The prototype (Figure 8) was built and tested to prove the proposed single-stage wireless battery charging circuit. The battery pack was emulated by an electrical load (PLZ1004WH; Kikusui, Co., Ltd.), and the voltage range of the emulated battery pack was set to 30~42 V; 10 serially connected Li-ion battery cells. The simulated battery pack of the equivalent (R_bat) was 13.04~18.26 Ω in the CC mode having I_CC = 2.3 A and 18.26~182.6 Ω in the CV mode having V_CV = 42 V and I_end = 0.23 A. The inner diameter of the transmitter and receiver coil was 100 mm, the outer diameter was 200 mm, and the f_o was set to 50 kHz.

The turns ratio of two coils was 1:1, so V_DC = 45 V from $V_s\approx V_p\cdot \sqrt{L_s/L_p}$. The values of circuit parameters and circuit components are given in

Table 1. Parameter values and components of the experimental circuit.

Symbol	Value/Model
Lp, Ls	201.89 μH, 202.9 μH
Cp, Cs	50.05 nF, 49.92 nF
Rin, Rp, Rs	13 mΩ, 242 mΩ, 210 mΩ
S1–S4	FDP075N15A
D1–D4	30ETH06
Controller	TMS320F28335

.

At first, the values of measured k_ps and M_ps were compared with the k_ps,pd and M_ps,pd in the alignment and misalignment conditions as in

Table 2. Prediction results of k_ps and M_ps in the range of V_bat = 30~42 V.

Alignment	Vbat [V]	kps	kps,pd (Error %)	Mps [μH]	Mps,pd [μH] (Error %)
x = 6 cm, y = 0 cm	30	0.2479	0.2465 (0.5508)	50.1795	49.8663 (0.6242)
	32		0.2463 (0.6211)		49.9073 (0.5424)
	34		0.2464 (0.6077)		49.9136 (0.5299)
	36		0.2467 (0.4744)		49.9645 (0.4284)
	38		0.2467 (0.4880)		49.9011 (0.5547)
	40		0.2468 (0.4256)		49.9305 (0.4963)
	42		0.2469 (0.4070)		49.9610 (0.4355)
x = 6 cm, y = 2 cm	30	0.2402	0.2363 (1.6304)	48.6187	47.7593 (1.7676)
	32		0.2359 (1.7761)		47.7291 (1.8298)
	34		0.2359 (1.7835)		47.7416 (1.8041)
	36		0.2360 (1.7497)		47.7314 (1.8250)
	38		0.2357 (1.8512)		47.7294 (1.8291)
	40		0.2359 (1.7823)		47.7272 (1.8336)
	42		0.2359 (1.7939)		47.7483 (1.7903)

. The location of two coils were set by using an orthogonal coordinate; the transmitter coil was located at x = 0 cm, y = 0 cm, and receiver coil was located at x = 6 cm, y = 0 cm in the alignment condition and x = 6 cm, y = 2cm in the misalignment condition. The k_ps and M_ps in the alignment condition were 0.2479 and 50.1795 μH, respectively. The prediction was implemented in the whole voltage range of V_bat, and k_ps,pd was in the range of 0.2463~0.2469; 0.41~0.62% errors. M_ps,pd was calculated based on $M_{ps,pd}=k_{ps,pd}\sqrt{L_p{L}_s}$, and in the range of 49.8663~49.9645 μH; 0.43~0.52% errors. When the coils were located in the misalignment condition, the k_ps and M_ps were 0.2402 and 48.6187 μH, respectively. The k_ps,pd was in the range of 0.2357~0.2363, and M_ps,pd was in the range of 47.7272~47.7593 μH; 1.63~1.85%, and 1.77~1.83% errors, respectively.

The regulation capability of the single-stage wireless battery charging circuit was tested at x = 6 cm, y = 0 cm as Figure 9a–c. When the circuit operates in f_s = f_o in the CC mode, I_bat was in the range of 2.32~2.358 A at 13.04 Ω < R_bat < 18.26 Ω. The variation of I_bat was 38 mA due to the effect of parasitic components as in (11). To complement this effect, the phase-shift technique was applied to the full bridge inverter. The compensated phase α was 32.58° at R_bat = 13.04 Ω and 28.8° at R_bat = 17.04 Ω as Figure 10. The regulated I_bat in the CC mode was in the range of 2.298~2.308 A (Figure 9c), and the variation of I_bat was improved from 38 mA to 10 mA owing to the phase-shift technique. When V_bat reached 42 V at R_bat = 18.26 Ω, the operational mode of the circuit was changed to CV mode. Because the circuit still operated at f_s = f_o, it is difficult to attain the CV characteristic regardless of R_bat as in Figure 5c. Thus, the circuit compensated α for maintaining V_bat was 37.62° at R_bat = 18.29 Ω and increased to 127.8° at R_bat = 41.53 Ω as in Figure 11. Consequently, V_bat was regulated in the range of 41.92~43 V, and variation of V_bat was 1.08 V as Figure 9b. However, the full bridge inverter operated in the hard switching condition across the whole range of R_bat as in Figure 10, and the power efficiency was measured at 86.65–60.35% in CV mode as in Figure 9d.

To improve the performance of the single-stage wireless battery charging circuit, the circuit can operate in f_s = f_CV, where the circuit has the CV characteristic and ZVS operating condition. Because k_ps,pd was 0.2469 at x = 6 cm and y = 0 cm, the f_CV was set to 57.616 kHz by using $f_{CV}=f_o/\sqrt{1-k_{ps}}$. As a result, the power efficiency was measured at 89.37–71.74% in CV mode as in Figure 9d, which was 2.72–11.39% higher than the operation at f_s = f_o with phase-shift technique. Even though the power efficiency increased owing to the ZVS operation, V_bat was regulated in the range of 42.54–44.22 V (Figure 9b). The variation of V_bat was 1.68 V, which was 0.6 V higher than the operation at f_s = f_o with phase-shift technique. This means that the parasitic components still influence the voltage regulation. To solve this issue, the phase-shift technique of the full bridge inverter was introduced to the circuit, the compensated α for maintaining V_bat was measured as 13.74° at R_bat = 18.29 Ω and increased to 36.83° at R_bat = 41.53 Ω as in Figure 12. Consequently, V_bat was regulated in the range of 41.96–42.02 V, and the variation of V_bat was only 6 mV as Figure 9b. In addition to the improved V_bat regulation, the waveforms in Figure 12 show that the circuit achieved ZVS operation condition across the whole range of R_bat. Therefore, the power efficiency was measured at 89.14–72.23% as in Figure 9d, which was 2.49–11.88% higher than the operation at f_s = f_o with the phase-shift technique.

4. Conclusions

In this paper, a single-stage wireless battery charging circuit is proposed. This circuit implements the CC charging mode at the resonant frequency of two coils and the CV charging mode based on the proposed coupling coefficient prediction method; the predicted value is used to calculate the operating frequency of the circuit, which stands for CV output characteristic and ZVS operating condition of the circuit. Additionally, the proposed circuit adopts the phase-shift technique at the full bridge inverter to improve the output current/voltage regulation capability in the CC/CV modes. The prototype was tested for its ability to charge a 36 V battery pack, and the resonant frequency of the transmitter/receiver coils was set to 50 kHz. The experimental circuit predicted a coupling coefficient within 0.62% error in the coil alignment condition. By incorporating this predicted value to the circuit with phase-shift technique, the experimental circuit successfully improved power efficiency using the ZVS operation in the CV mode, and achieved CC and CV regulation within 0.32% error in the CC mode and 0.1% error in the CV mode, respectively.