DAB-Based Bidirectional Wireless Power Transfer System with LCC-S Compensation Network under Grid-Connected Application

Abstract

To realize two-way power transfer without physical connections under a grid-connected application, bidirectional wireless power transfer (BDWPT) is introduced. This paper proposes an LCC-S compensated BDWPT system based on dual-active-bridge (DAB) topology with the minimum component counts. LCC-S is designed to be a constant voltage (CV) network. To obtain the power transmission characteristics of the system, a mathematical model based on the fundamental harmonic approximation (FHA) method is established, and the result shows that the direction and amount of transfer power can be controlled by changing the magnitude of output voltages of either/both side of H-bridges. The reactive power of the system can be controlled to be zero when the output voltages of two H-bridges are in the same phase. Compared with DAB-based BDWPT systems with constant current (CC) compensation networks, the proposed structure has better transfer power regulation capability and easier control of the direction of power flow. A 1.1 kW experimental prototype is built in the laboratory to verify the characteristics of the proposed system. The results indicate that the power transfer characteristics of the proposed BDWPT system match its mathematical derivation results based on the FHA model.

1. Introduction

Wireless power transfer (WPT) technology can transfer power across a loosely coupled transformer without physical connections. It is safe in wet or dusty environments, and there is no need to constantly plug and unplug devices from the charging system. Thus, it has gained attention in the fields of consumer electronics [1,2], implanted biomedical devices (IMDs) [3,4], underwater equipment [5,6] and electric vehicle [7,8,9].

A WPT converter normally consists of four parts: a primary-side DC/AC converter, a secondary-side AC/DC rectifier, a resonance compensation circuit and a pair of coils. However, the coupling coefficient of the WPT system is much lower than that of a conventional transformer because the inductance of the primary and secondary sides are coupled to each other through the air, not through the magnetic core. Thus, in order to obtain the desired mutual inductance and enhance the power transmission capability of the WPT system, coils wound by long wires with large diameters are inevitable. However, the power loss generated by the unavoidable parasitic resistance of the coils largely reduces the overall efficiency. Therefore, it is important to reduce the reactive current flows through the coils to improve the overall efficiency of the system, especially in the scenario of high-power transmission.

In a unidirectional WPT (UDWPT) system, transfer power flows from the source to the load, and the compensation networks in UDWPT are configured as constant current (CC) networks or constant voltage (CV) networks to acquire load-independent constant current/voltage output [4,5]. The basic structure of a UDWPT system is shown in Figure 1a. Series–series (SS) [6,7], LCL-LCL [8,9] and LCC-LCC [10,11] are the most typical CC compensation structures that have been proposed, while the most popular CV compensation structure is LCC-S [5,12,13]. Additionally, with the resonant parameter configuration method proposed in [5,6,7,8,9,10,11], zero-phase-angle (ZPA) can be achieved to minimize the VA rating.

With the continuous improvement of battery capacity, electric vehicles are becoming high-quality mobile energy stations. Electric vehicles can provide high-power energy for people’s outdoor activities in the field of camping. Electric vehicles can also feedback excess energy to the power grid to help adjust the dynamic load of the power grid. Therefore, a bidirectional WPT (BDWPT) system is applied, which is designed on the basis of the CC/CV compensation network in the UDWPT system. For the topologies with CC compensation networks, the most straightforward method to construct BDWPT systems is replacing the uncontrolled diodes of the UDWPT topology (as shown in Figure 1a) with a full-bridge converter [6,7,8,9,10,11]. The full-bridge converters on both sides of the BDWPT system constitute a dual-active-bridge (DAB) structure, as shown in Figure 1b. The feature of these WPT structures with CC networks is that the output current of a H-bridge is independent of its output voltage. Usually, the regulation of the direction and amount of power flow is achieved by adjusting either the relative phase angle or the magnitude of output voltages of either/both sides of H-bridges [6]. The relative phase angle is set to be ±90° to control the direction of power flow while realizing the unit power factor at the same time.

In the scenario of EV charging, to obtain a wide range of charging power, there are normally two ways to adjust the magnitude of output voltages of H-bridges: (1) adjusting input DC-bus voltage with grid interface converter; (2) modulating the duty cycle of the output voltages of H-bridges with phase-shift modulation (PSM). With a boost-type PFC rectifier, the grid-rectified output DC voltage should be higher than 1.414 times the phase voltage, and it can be up to 800 V [14]. Therefore, the input DC voltage only varies within a limited range, and PSM is usually adopted for traditional BDWPT systems [14,15,16,17,18,19]. However, the traditional CC network compensated BDWPT (CC-BDWPT) systems with PSM have the following drawbacks: (1) The maximum power of the system is highly dependent on the hardware parameter configuration and the mutual inductance because the output current is dependent on the load once the hardware parameter is determined. (2) The phase-shift angle changes rapidly with the amount of transferred power, which brings about a large amount of switching losses; triple-phase-shift (TPS) control [16,18,19] is proposed to realize zero voltage switching (ZVS); however, reactive power and conduction losses will increase correspondingly. (3) The control of bidirectional power transferring is not consistent and more complex.

To solve the shortcomings of the CC compensation network, the LCC-S compensation network has also been widely studied. Besides uncontrolled rectifiers, LCC-S compensation topology with a semi-bridgeless active rectifier (S-BAR) has become popular in recent years [20,21,22,23]. S-BAR with pulse density modulation control is applied in [20] to modulate the transfer power, and the ZVS operation of the primary and secondary side switches is realized in a wide load range. However, excessive reactive power is introduced when the secondary-side switches are turned on. In [21], S-BAR is introduced for impedance tuning, and dual-side phase shift control is applied to realize ZVS. But, the actual expressions of the control signals are complex, and it is difficult to obtain real-time results in digital signal processors. In [22], an impedance tuning control is achieved by adjusting the turn-on point and duty of the S-BAR. However, hard switching occurs when high current flows through the switches, which causes huge switching losses of SBAR.

A BDWPT system based on an LCC-S compensation network and a bidirectional buck–boost is proposed by [13]. For the power flowing from the primary side to the secondary side (P2S), the secondary-side full-bridge converter operates as a diode rectifier, and for the power flowing from the secondary side to the primary side (S2P), the primary-side full-bridge converter operates as a diode rectifier. Additionally, a cascaded buck/boost converter is applied to realize the accurate control of the magnitude of the power flow. This LCC-S compensated topology has a more complex structure than the DAB-based BDWPT system with CC networks proposed by [14,15,16,17,18,19], and the additional power loss caused by the uncontrolled rectifier and the additional DCDC converter is inevitable. A DAB-based BDWPT system with CV compensation networks, as shown in Figure 1b, has not been proposed yet.

This paper proposes a DAB-based LCC-S compensated BDWPT system, which is a CV network-based BDWPT (CV-BDWPT) structure. The proposed topology has the minimum component counts and thus can realize high efficiency. In contrast to the LCC-S compensated systems reported in [13], the proposed DAB-based system is simple in design, implementation and control. A mathematical model is derived, which describes the behavior of the proposed BDWPT interface. The power characteristics of DAB-based CV-BDWPT systems can be deduced: (1) reactive power equals 0 when the phase difference between output voltages of H-bridges is zero; (2) primary side delivers power when secondary-side DC-bus voltage is lower than the CV output voltage in the UDWPT system; primary side receives power when secondary-side DC-bus voltage is higher than the CV output voltage. The validity of the mathematical model is verified by the results of a 1.1 kW experimental prototype.

2. Operation Principles of the Proposed BDWPT System

2.1. Proposed System and Its Mathematical Model

The schematic of the proposed DAB-based LCC-S compensated BDWPT system is shown in Figure 2a. On the primary side, a full-bridge converter H₁ is formed by switches S₁~S₄, which supplies an AC voltage to the compensation network from the DC-link voltage V_DC,P. V_DC,P is the DC voltage source, which represents the output voltage of the PFC rectifier connected to the grid [14,22] or the battery energy storage system (BESS) [24,25]. The secondary-side full-bridge converter H₂ is formed by switches Q₁~Q₄. These two H-bridges consist of a traditional DAB structure. The output voltage of H₂ is shown as V_DC,S, which normally represents an Evs battery. An LCC network consisting of C_p, C_f and L_f is placed on the primary side. C_s is the resonant capacitor at the secondary side. Two coils, L_p and L_s, are coupled through mutual inductance (M) and form a loosely coupled transformer. The coupling coefficient k is defined as $k=M/\sqrt{L_P{L}_S}$. The parasitic resistance of the two coils is R_p and R_s, respectively. R_f is the parasitic resistance of L_f. v_AB and v_CD are the output voltage chopped by full-bridges H₁ and H₂. i_p, i_s, i_f are the current flowing through the L_p, L_s and L_f, respectively. The LCC-S compensation structure is designed as a CV network. L_f resonant with C_f, L_s resonant with C_s, L_p resonant with C_f and C_p. The control scheme of the proposed converter switches and relevant waveforms are illustrated in Figure 2d. The parameter configuration follows the rules published in [5,12,13].

$${\omega }_0=2\pi f_0={\displaystyle \frac{1}{\sqrt{L_s{C}_s}}}={\displaystyle \frac{1}{\sqrt{L_f{C}_f}}}$$

(1)

$${\displaystyle \frac{1}{{\omega }_0{C}_p}}+{\displaystyle \frac{1}{{\omega }_0{C}_f}}={\omega }_0{L}_p$$

(2)

Because the network of C_f, L_f, C_p and L_p has filter characteristics, the harmonic component of the output current is small. The bode plot of the C_f, L_f, C_p and L_p networks is shown in Figure 2c; they have a good capability to suppress high- and low-frequency harmonics. The center frequency is the fundamental harmonic, while the other high-frequency and low-frequency harmonics are significantly suppressed. The power calculation is performed using the fundamental harmonic approximation (FHA) method to simplify the analysis. The FHA method is applied to analyze the power transfer ability of the proposed BDWPT system. A T-type equivalent circuit is depicted in Figure 2b, where L_rp and L_rs are the leakage inductance of two coils, respectively. v₁ and v₂ are the fundamental component of v_AB and v_CD, respectively, which can be derived by Fourier series:

$$v_1=V_1\angle 0^{\circ }={\displaystyle \frac{2\sqrt{2}}{\pi }}{V}_{DC,P}\sin \left({\displaystyle \frac{\alpha }{2}}\right)\angle 0$$

(3)

$$v_2=V_2\angle \theta ={\displaystyle \frac{2\sqrt{2}}{\pi }}{V}_{DC,S}\sin \left({\displaystyle \frac{\beta }{2}}\right)\angle \theta .$$

(4)

where α and β are the phase-shift angles of two H-bridges. θ is the relative phase angle between v₁ and v₂. V₁ and V₂ are the magnitudes of v₁ and v₂. The power transfer of the proposed control system has thus been controlled by v₁ and v₂.

According to Kirchhoff’s laws, the circuit can be represented by the following equation:

$$\left[\begin{array}{l}{v}_1\\ 0\\ -v_2\\ 0\\ 0\end{array}\right]=\left[\begin{array}{ccccc}{X}_A& X_B& 0& 0& 0\\ 0& -X_B & X_C& X_D& 0\\ 0& 0& 0& -X_D& X_E\\ 1& -1& -1& 0& 0\\ 0& 0& 1& -1& -1\end{array}\right] \left[\begin{array}{l}{i}_f\\ i_{Cf}\\ i_p\\ i_m\\ i_s\end{array}\right]$$

(5)

where X_A~X_E represents the equivalent impedance of each branch, $X_A=j\omega L_f+R_f$, $X_B=1/j\omega C_f$, $X_C=j\omega L_{rp}+1/j\omega C_p+R_p$, $X_D=j\omega M$, $X_E=j\omega L_s+1/j\omega C_s+R_s$. By solving the Equation (5), current flows through each branch can be calculated as follows:

$$\left[\begin{array}{l}{i}_f\\ i_p\\ i_s\\ i_{Cf}\\ i_m\end{array}\right]={\displaystyle \frac{1}{X_0}}\left[\begin{array}{l}{v}_1(X_B{X}_D+X_B{X}_E+X_C{X}_D+X_C{X}_E+X_D{X}_E)-v_2{X}_B{X}_D\\ v_1(X_B{X}_D+X_B{X}_E)-v_2(X_A{X}_D+X_B{X}_D)\\ v_1{X}_B{X}_D-v_2(X_A{X}_B+X_A{X}_C+X_A{X}_D+X_B{X}_C+X_B{X}_D)\\ v_1(X_C{X}_D+X_C{X}_E+X_D{X}_E)+v_2{X}_A{X}_D\\ v_1{X}_B{X}_E+v_2(X_A{X}_B+X_A{X}_C+X_B{X}_C)\end{array}\right]$$

$$\begin{array}{l}{X}_0=X_A{X}_B{X}_D+X_A{X}_B{X}_E+X_A{X}_C{X}_D+X_A{X}_C{X}_E\\ +X_B{X}_C{X}_D+X_B{X}_C{X}_E+X_A{X}_D{X}_E+X_B{X}_D{X}_E\end{array}$$

(6)

When considering the parasitic resistance of the inductor,

$$X_A+X_B={\displaystyle \frac{1}{j\omega C_P}}+j\omega L_{rP}+{j\omega M+R}_P\approx R_P$$

(7)

$$X_D+X_E={\displaystyle \frac{1}{j\omega C_f}}+j\omega L_f+R_f\approx R_f$$

(8)

where R_p and R_f are the parasitic resistances of X_A and X_E branches, respectively. In each branch, the parasitic resistance is much less than the total impedance value of the corresponding branch. Therefore, the quadratic terms of $X_A+X_B$ and $X_D+X_E$ is neglected in Equation (6).

With the parameter configuration rules according to Equations (1) and (2), input current i_f can be represented by

$$i_f={\displaystyle \frac{X_D(v_1{X}_E-v_2{X}_B)+v_1(X_B+X_C)R_f}{X_C{R}_p{R}_f+X_A{X}_B{R}_f+X_D{X}_E{R}_s}}$$

(9)

Coil resistances R_p and R_s are much smaller than other impedances. To simplify the expression of Equation (7), the higher-order terms of R_p and R_s in the numerator and denominator are ignored, and i_f can be expressed as

$$i_f={\displaystyle \frac{L_{f}M}{R_f{M}^2+R_s{L_f}^2}}({\displaystyle \frac{v_{1}M}{L_f}}-v_2).$$

(10)

With a similar simplification method, current flows through two coils, L_p and L_s, can be calculated and simplified as

$$i_{\mathrm{p}}=-{\displaystyle \frac{j(v_1{L}_f{R}_f+v_{2}M{R}_p)}{{\omega }_0(R_f{L_f}^2+R_p{M}^2)}}$$

(11)

$$i_s={\displaystyle \frac{{L_f}^2}{R_f{M}^2+R_s{L_f}^2}}({\displaystyle \frac{v_{1}M}{L_f}}-v_2).$$

(12)

Thus, the expressions for the active power P₁ and P₂ and the reactive power Q₁ and Q₂ on the primary and secondary sides of the BDWPT system can be obtained:

$$P_1=\mathrm{Re}\left\{v_1{i_f}^{\ast }\right\}={\displaystyle \frac{1}{2}}{\displaystyle \frac{L_{f}M{V}_1}{R_f{M}^2+R_s{L_f}^2}}({\displaystyle \frac{V_{1}M}{L_f}}\cos \theta -V_2).$$

(13)

$$Q_1=\mathrm{Im}\left\{v_1{i_f}^{\ast }\right\}={\displaystyle \frac{1}{2}}{\displaystyle \frac{L_{f}M{V}_1{V}_2\sin \theta }{R_f{M}^2+R_s{L_f}^2}}.$$

(14)

$$P_2=-\mathrm{Re}\left\{v_2{i_s}^{\ast }\right\}=-{\displaystyle \frac{1}{2}}{\displaystyle \frac{{L_f}^2{V}_2}{R_f{M}^2+R_s{L_f}^2}}({\displaystyle \frac{V_{1}M}{L_f}}-V_2\cos \theta )$$

(15)

$$Q_2=-\mathrm{Im}\left\{v_2{i_s}^{\ast }\right\}=-{\displaystyle \frac{1}{2}}{\displaystyle \frac{L_{f}M{V}_1{V}_2\sin \theta }{R_f{M}^2+R_s{L_f}^2}}.$$

(16)

Through the control of S₁–S₄ and Q₁–Q₄, the voltage v₁ and v₂ of the system can be changed, and the transmission power of the system can be changed.

2.2. Power Transmission Characteristics

From Equations (12) and (14), reactive power equals zero when θ is 0° or 180°. Apparently, transfer active power is positive when θ = 180°, which means the directional of power flow is fixed. Therefore, θ = 0° is applied to realize bidirectional power transfer. The direction of power flow is determined by the relative magnitude between $V_{1}M/L_f$ and V₂. When $V_{1}M/L_f>V_2$, power flows from the primary side to the secondary side. When $V_{1}M/L_f<V_2$, power flows from the secondary side to the primary side. Additionally, the amount of power flow is positively related to the difference between V₂ and $V_{1}M/L_f$. The power transmission of the system can be changed by changing the difference in voltage $V_{1}M/L_f$ and V₂.

The relative phase angle θ is essentially maintained constant at 0°, and therefore, the system operates at unity power factor. When θ is 0°, both the amount and direction of power flow can be regulated by controlling V₁ and V₂, which are determined by DC-bus voltages (V_DC,P and V_DC,S) and phase shift angles (α and β), as shown in Equations (3) and (4). When θ is 0°, a diagram depicts the phasor relationship between the variables of the FHA equivalent circuit of the proposed system, as shown in Figure 3.

The relationship between primary DC-bus voltage V_DC,P and transfer power of the proposed LCC-S system and typical CC-BDWPT systems is illustrated in Figure 4. The secondary DC-bus voltage V_DC,S is kept at 100 V to show the power transmission capability of the different circuits in a more direct way. The component parameters of the LCC-S circuit are shown in

Table 1. System parameters.

Symbol	Parameters	Values
Lp	primary-side coil inductance	121.34 μH
Ls	secondary-side coil inductance	121.56 μH
Lf	compensation inductance	36.175 μH
M	mutual inductance	29.0 μH
k	coupling coefficient	0.24
Cp	series compensation capacitor	29.34 nF
Cs	series compensation capacitor	41.71 nF
Cf	compensation capacitor	95.94 nF
Rp	parasitic resistance of Cp	0.179 Ω
Rf	parasitic resistance of Cf	0.049 Ω
Rs	parasitic resistance of Cs	0.182 Ω

. The CC-BDWPT models published in [14,16,18] are applied to calculate the relationship between system transmission power and DC-bus voltage. Mathematical expressions of the maximum transfer power of CC-BDWPT systems are listed in

Table 2. Transfer power comparison of DAB-based CC-BDWPT systems and proposed LCC-S compensated BDWPT system.

Structures	Mathematical Expression of Transfer Power	Max Powerin Theory
SS	${\displaystyle \frac{V_1{V}_2}{{\omega }_{0}M}}\sin \left({\displaystyle \frac{\alpha }{2}}\right)\sin \left({\displaystyle \frac{\beta }{2}}\right)$	${\displaystyle \frac{V_1{V}_2}{{\omega }_{0}M}}$
LCL-LCL	${\displaystyle \frac{V_1{V}_{2}M}{{\omega }_0{L}_p{L}_S}}\sin \left({\displaystyle \frac{\alpha }{2}}\right)\sin \left({\displaystyle \frac{\beta }{2}}\right)$	${\displaystyle \frac{V_1{V}_{2}M}{{\omega }_0{L}_p{L}_S}}$
LCC-LCC	${\displaystyle \frac{V_1{V}_{2}M}{{\omega }_0{L_f}^2}}\sin \left({\displaystyle \frac{\alpha }{2}}\right)\sin \left({\displaystyle \frac{\beta }{2}}\right)$	${\displaystyle \frac{V_1{V}_{2}M}{{\omega }_0{L_f}^2}}$
proposed S-LCC	${\displaystyle \frac{{L_f}^2{V}_1(V_1-V_{2}M\cos \theta /L_f)}{R_f{M}^2+R_p{L_f}^2}}$	${\displaystyle \frac{{L_f}^2{V_1}^2}{R_f{M}^2+R_p{L_f}^2}}$

. As illustrated by Figure 4, the power transmission capacity of the CC-BDWPT systems changes little with the bus voltage. Therefore, when the transmission power is away from the maximum power of the system, the DC-bus voltage needs to be adjusted in a large range. This means that the phase shift angle will change dramatically with PSM, which makes it hard to maintain low switching loss and low reactive power at the same time. Additionally, the proposed DAB-based LCC-S system is capable of operating over a wider range of transfer power with limited variation in V_DC,P. Although the sensitivity to V_DC,P enhances the transfer power regulation capability of the proposed system, it creates challenges in precisely controlling the full-bridge output voltages when the resistance of the coils is too small. In summary, WPT systems with CV compensation networks represented by LCC-S have higher power transmission capability than CC-BDWPT systems.

The WPT system is very similar to other isolated power electronic topologies. The only difference is that the transformers wound by magnetic core are replaced by two coils that are coupled with each other through air. In order to eliminate the impact of the inductance in traditional isolated DC-DC converters, the resonance concept of active components has already been widely studied, analyzed and applied [26,27,28]. For traditional isolated DC-DC converters, the magnetic core provides a sufficient coupling coefficient for the primary and secondary side coils, so the self-induction of the primary and secondary side coils does not need to be large enough to obtain the desired mutual inductance value. Traditional LLC converter [26] can be seen as a CV output circuit when the resonant capacitor C_r is resonant with primary-side inductance L_r1. The AC equivalent circuit of a traditional LLC converter is shown in Figure 5, where the mutual inductance M is much larger than the secondary-side leakage inductance L_r2. The transfer power of the LLC converter can be approximately expressed as

$$S_{LLC}={\displaystyle \frac{v_2(v_1-v_2)}{jw{L}_{r2}+R_2}}.$$

(17)

Due to the low resistance value provided by the transformer, the transfer power can be theoretically close to infinity when the AC equivalent voltage of two sides in the model is at an unbalanced state. Thus, it is difficult to precisely control the transmission power by controlling the difference between the primary and secondary voltages. While WPT is a type of isolated DC-DC converter with unavoidable coil resistance, the resistance of a few hundred milliohms makes the method of controlling the voltage difference to adjust the transmission power realistic.

3. Performance Comparison with CC-BDWPT Systems

3.1. Better Regulation Capability of Transfer Power

Mathematical expressions of the transfer power of CC-BDWPT systems are listed in Table 2. The relationship between primary side DC-bus voltage V_DC,P and maximum active power of different topologies under unit power factor conditions has been illustrated in Figure 4. The parameters of resonant components in CC-BDWPT systems are the same as that in [4,6,8]. It can be found that the maximum transfer power of CC-BDWPT systems is not sensitive to the V_DC,P and stays almost constant when primary DC-bus voltage varies. But, the transfer power of the proposed LCC-S can be modulated by changing the difference between $V_{1}M\cos \theta /L_f$ and V₂, which strengthens the power regulation capacity of the system. As illustrated by Figure 4, the proposed LCC-S system is capable of operating over a wider range of transfer power with the variation in V_DC,P. Additionally, the proposed LCC-S has extra control freedom of power regulation in both directions, which means that both the amount and the direction of the transfer power can be controlled by simply changing either side of the full-bridge output voltage.

Moreover, from the expressions in Table 2, for the SS-compensated BDWPT, since the mutual inductance M is in the denominator position of the transmitted power expression, high transmission power can be obtained by a small mutual inductance M design. The misalignment of the coils will sharply increase the transmission power of the system, which brings difficulties to stable power control. The LCL-LCL compensated BDWPT system has a limited power transfer capability. For high power transferring conditions, LCL-LCL topology should have a high value of M and a small value of L_p and L_s, which is difficult in practical design.

The operating waveforms of the PSM method under unit power factor conditions are presented in Figure 6. φ is the phase-shift angle of the primary-side voltage. The operation of PSM in one period can be divided into four modes:

Mode 1 [t₀–t₁]: At t₀, switch S₄ turns on. During this mode, the current i_f flows in the positive direction, V_DC,P supplies the power, and current i_f flows through S₁ and S₄.

Mode 2 [t₁–t₂]: During this interval, switch S₁ is OFF, S₂ is ON. Current i_f flows through S₂ and S₄.

Mode 3 [t₂–t₃]: At t₂, switch S₃ turns on. During this mode, the current i_f flows in the negative direction, V_DC,P supplies the power, and current i_f flows through S₂ and S₃.

Mode 4 [t₃–t₄]: During this interval, switch S₁ is OFF, S₂ is ON. Current i_f flows through S₁ and S₃.

During the period when the full-bridge output voltages are 0 V, current freewheels are outputted via the switches when the power source is in open-load condition and does not supply the energy to the system. However, due to the constant power losses caused by the freewheeling current via the switch, the losses are higher at a fixed transmitted power.

As analyzed before, SS and LCL-LCL topology is not suitable for high-transfer power situations. Although LCC-LCC topology can provide high transmission power, larger phase-shift angles are essential at the same time when the system operates under light load. From Figure 7, when the transfer power changes from full-load (1100 W) to half-load (550 W), the phase-shift angle changes from 180° to 60°.

Compared with CC-BDWPT systems, LCC-S topology can be easily applied for high-power applications at a wide range of loads with larger phase-shift angles. From Figure 7, when the transfer power changes from full-load to half-load, the phase-shift angle changes from 180° to 162°; thus, the current freewheeling time through the switches is largely reduced.

3.2. Reduced Switching Losses with PSM

The drain-to-source voltage V_ds and current I_ds transitions overlap over finite time and result in switching losses. The overlap areas of V_ds and I_ds can be estimated by using the area of a triangle, which can be expressed as:

$$P_{SW}=2\left(t_{on}+t_{off }\right)i_f(t_1)V_{DC,P }$$

(18)

where t_on and t_off are the overlapping times of V_ds and I_ds during turn-on transition and turn-off transition, respectively. $i_f\left(t_1\right)$ is calculated by the transfer power and phase-shift angle:

$$i_f(t_1)={\displaystyle \frac{\pi P}{2V_{DC,P }}}\cos ({\displaystyle \frac{\alpha }{2}}).$$

(19)

The variation in switching loss P_SW and phase-shift angle α with transfer power P is shown in Figure 8. As illustrated by Figure 8, the LCC-S system has much lower switching losses than CC-BDWPT systems over a full range of loads. The LCC-S system is capable of operating over a wide range of power with a smaller phase shift range. In CC-BDWPT systems, α changes within a large range, and switching losses are much larger when the system is not operating at the rated output power.

4. Hybrid Control Strategy for Proposed System

As discussed before, the LCC-S compensated BDWPT system can work in higher power situations with stronger power regulation capabilities than CC-BDWPT systems. Additionally, high transfer power output control can be achieved with a small variation in phase-shift angle. However, the superior performance depends on matching the full bridge output voltage of the primary and secondary sides. The difference between the voltage $V_{1}M/L_f$ and V₂ is desired to be controlled on a relatively small scale. Normally, a cascaded DC/DC converter can be applied to regulate the DC voltage source. However, the transfer power is really sensitive to the magnitude of the voltage source of the LCC-S compensated BDWPT system compared with the CC-BDWPT system or other resonant circuits. Therefore, a hybrid control method combining DC voltage control and PSM control is applied. Primary DC-bus voltage V_DC,P changes in a relatively large step each time. PSM is applied under different V_DC,P to control the transfer power in accuracy.

In general, ZVS conditions will be lost when PSM is employed. However, the LCC network can contribute high-order harmonic currents, and ZVS can still be realized within a small phase shift range. The proposed hybrid controlling strategy is also able to realize ZVS at a full range of loads while maintaining accurate transfer power control at the same time. The variation in V_DC,P and phase-shift angle α under different transfer power is shown in Figure 5; V_DC,P changes 1 V each time, and α changes within 15°.

5. Experimental Verification

To verify the characteristics of the proposed LCC-S compensated BDWPT system, a hardware prototype is built, as shown in Figure 9. Two simple circular pads are employed as the magnetic coupler. The inner and outer diameters of the pads are 241 mm and 332 mm, respectively, and the distance between the two pads is 105 mm. The distance between the inductances of the primary side and the secondary side in this experiment is about 112 mm. The coupling coefficient of the system is about 0.24. The detailed parameters measured by the LCR meter have been provided in Table 1.

The switching frequency is fixed at 85 kHz. The secondary DC-bus voltage is 100 V. The parameters of hardware components are listed in Table 2, where M/L_f is about 0.767. In this experiment, θ is controlled to be zero in order to achieve a unity power factor. Figure 10 shows the experimental waveforms of output voltages and currents of H-bridges when power flows from the primary side to the secondary side. Figure 11 shows the experimental waveforms when power flows from the secondary side to the primary side. For the waveforms in Figure 10a,b and Figure 11a,b, the power transfer is controlled by DC-bus voltage regulation ($V_{1}M/L_f-V_2$), while for the waveforms in Figure 10c and Figure 11c, the PSM is employed.

In Figure 10a, V_DC,P is 142 V, and $V_{1}M/L_f-V_2=11.4 \mathrm{V}$. The transfer power is 1.079 kW. When V_DC,P is reduced to 138 V, $V_{1}M/L_f-V_2=7.4 \mathrm{V}$. The transfer power dropped to 570.5 W, and the experimental waveforms are shown in Figure 10b. Compared with Figure 10a, the primary-side phase shift angle α is set to be 148.0° in Figure 10c, and the transfer power drops to 577.6 W. The phase-shift angle α changes by only 32.0°, which is much smaller than that in CC-BDWPT systems. Additionally, ZVS can still be realized within a small phase shift range.

In Figure 11a, V_DC,P is 120 V, $V_{1}M/L_f-V_2=-10.3 \mathrm{V}$. The transfer power is 1.108 kW. When V_DC,P is increased to 125 V, $V_{1}M/L_f-V_2=-5.2 \mathrm{V}$. The transfer power dropped to 489.3 W, and the experimental waveforms are shown in Figure 11b. Compared with Figure 11b, the primary-side phase shift angle α is set to be 149.8° in Figure 11c. The transfer power increases to 800.3 W, and α changes by only 30.2°. In Figure 11c, Q₂ and Q₄ cannot realize ZVS. Under this condition, the high-frequency harmonic current of i_s is not large enough to achieve ZVS. But the switching losses are quite low due to i_f (t₂) is only about 1.8 A.

The above experimental results clearly demonstrated that the amount of transfer power of the proposed LCC-S can be controlled by modulating primary DC-bus voltage V_DC,P or primary phase-shift angle α to control the amount of transfer power, respectively. A wide range of soft-switching can also be achieved.

6. Conclusions and Discussion

A CV-BDWPT system (LCC-S) to realize the two-way wireless power transfer has been proposed. A mathematical model has been presented to show that the reactive power can be controlled to be zero when the output voltages of H-bridges are in the same phase, and the direction and amount of power flow can be controlled by changing the difference between $V_{1}M/L_f$ and V₂. This topology can also be applied as a UDWPT system, which has the advantages of higher maximum transfer power and reduced switching losses. The advantage of the proposed design is that the system can transfer power that is not limited by the inductance of primary side and secondary side coils and their mutual inductance. In our system, the transfer power is sensitive to the output voltages of either side of H-bridges, so significant changes in the transmission of energy can be obtained by relatively small changes in phase-shift angles. While each coin has two sides, the disadvantage of the proposal is that the system is sensitive to the variation in DC-bus voltage. A 1.1 kW experiment is established to verify that a small change in phase-shift angle or DC-bus voltage can largely change the transfer power of the system while realizing the unit power factor at the same time.