Three-Port Converter for Integrating Energy Storage and Wireless Power Transfer Systems in Future Residential Applications

Abstract

This paper presents a highly efficient three-port converter to integrate energy storage (ES) and wireless power transfer (WPT) systems. The proposed converter consists of a bidirectional DC-DC converter and an AC-DC converter with a resonant capacitor. By sharing an inductor and four switches in the bidirectional DC-DC converter, the bidirectional DC-DC converter operates as a DC-DC converter for ES systems and simultaneously as a DC-AC converter for WPT systems. Here, four switches are turned on under the zero voltage switching conditions. The AC-DC converter for WPT system achieves high voltage gain by using a resonance between the resonant capacitor and the leakage inductance of a receiving coil. A 100-W prototype was built and tested to verify the effectiveness of the converter; it had a maximum power-conversion efficiency of 95.9% for the battery load and of 93.8% for the wireless charging load.

1. Introduction

Photovoltaics (PVs) constitute a promising alternative energy source due to diverse applications and the ubiquity of sunlight [1,2,3,4]. Residential PV systems consist of a PV module and a PV inverter, and it converts sunlight into electricity. However, energy output by PV systems is not constant because it is affected by weather conditions and the day/night cycle. Therefore, energy storage (ES) systems are used to efficiently manage the PV energy. They consist of a battery and a bidirectional DC-DC converter that connects to the PV system [5,6,7]. Besides, in the near future, the wireless power transfer (WPT) systems will be widely used to wirelessly charge laptops as well as cell phones in many households [8,9,10,11]. Therefore, future PV energy delivery and management infrastructure for residential applications will consist of PV systems, ES systems, and WPT systems (Figure 1a).

Three-port converters have been used to reduce the cost and size of infrastructure, such as micro-grids and smart grids [12,13,14,15,16,17,18]. The infrastructure consists of several systems, so its cost and size increase in proportion to the number of systems. To alleviate this problem, two systems are integrated through on a three-port converter. The three-port converters usually add a port to a typical converter that has two ports, either by using a three-winding transformer instead of a two-winding transformer [13,14,15] or by using the storage capacitor in the typical converter as a third port [16,17,18].

Many three-port converters have been introduced to integrate renewable energy sources (e.g., PV, fuel cell, wind turbine) with ES systems, but a three-port converter to integrate ES and WPT systems has not been considered. Therefore, this paper presents a three-port converter that can integrate the ES and WPT systems that will be used in future PV energy delivery and management infrastructure for residential applications (Figure 1b). The proposed three-port converter consists of a bidirectional DC-DC converter for an ES system and an AC-DC converter with a resonant capacitor. The bidirectional DC-DC converter can also operate as a DC-AC converter of the WPT system because the inductor in the bidirectional DC-DC converter is also used as a transmitting coil for a WPT system. With these few components, the proposed converter can store energy for the ES system and simultaneously transfer the energy by using a WPT system. The proposed converter has a high power-conversion efficiency by achieving zero voltage switching (ZVS) turn-on for switches, and has high voltage gain for WPT by using a resonance between a resonant capacitor and a leakage inductance of a receiving coil.

Section 2 describes the circuit structure and operating principles of the proposed converter. Section 3 presents experimental results, and Section 4 concludes the paper.

2. Proposed Three-Port Converter

2.1. Circuit Structure

The proposed converter (Figure 2a) combines the structures of a bidirectional DC-DC converter and an AC-DC converter.

The bidirectional DC-DC converter is located between a DC bus and a battery to transfer the energy in both directions (DC bus ↔ battery). This converter consists of four switches (S₁, S₂, S₃, S₄), two filter capacitors (bus capacitor, C_bus, with capacitance, C_bus, and battery capacitor, C_bat, with capacitance, C_bat), and an inductor (L₁ with inductance L₁). In addition, it can transfer the energy of the DC bus (or battery) to the wireless charging load because L₁ also acts as a transmitting coil for WPT.

The AC-DC converter is connected to a wireless charging load, such as a cell phone or laptop, and it has a receiving coil (L₂ with inductance L₂) for WPT, a filter capacitor (WPT capacitor, C_wpt, with capacitance, C_wpt), a resonant capacitor (C_r with capacitance, C_r), and a voltage doubler rectifier that consists of two diodes (D₁, D₂) and two doubler capacitors (C₁ with capacitance, C₁, and C₂ with capacitance, C₂).

L₁ and L₂ are parts of the two-coil structure; they are coupled magnetically with a coupling coefficient, k, to transfer the energy wirelessly. Based on [19,20], the two-coil structure can be represented as a transformer with a leakage inductor (L_lk with inductance, L_lk), an effective turn ratio (N_e), and a magnetizing inductor (L_m with inductance, L_m), where $L_{lk}=(1-k^2)L_2$, $N_e=k\sqrt{L_2/L_1}$, and $L_m=L_1$ (Figure 2b).

Four switches achieve the ZVS turn-on by using the stored energy in L₁. L_lk resonates with C_r, and high voltage gain between the DC bus and wireless charging load is achieved by setting the switching frequency, f_S, to the resonant frequency, f_r, between L_lk and C_r. The voltage doubler rectifier converts AC voltage to DC voltage for wireless charging load, and clamps the reverse voltages of D₁ and D₂ to WPT voltage, V_wpt.

2.2. Principle of Operation

The proposed converter operates at a fixed switching frequency (f_S = 1/T_S), where T_S is a switching period, and it controls the voltage gain between the DC bus voltage, V_bus, and battery voltage, V_bat, by changing the duty ratios of S₁, S₂, S₃, and S₄; the duty ratios of S₂ and S₃ are defined as D, and the duty ratios of S₁ and S₄ are defined as 1–D. In addition, the voltage gain between V_bus and V_wpt is adjusted by using N_e.

The equivalent circuits (Figure 3) and operating waveforms (Figure 4) were obtained under the following assumptions and conditions: (1) All components are lossless, (2) C₁, C₂, C_bus, C_bat, and C_wpt are large enough to assume that V_C1, V_C2, V_bus, V_bat, and V_wpt are constant voltage sources, (3) f_r = f_S, and (4) the converter operates in a steady state. The converter operates in four modes.

Mode 1 (Figure 3a, t₀ ≤ t ≤ t₁): This mode starts at t = t₀ when S₂ and S₃ are turned on. At this time, S₂ and S₃ achieve ZVS turn-on because the body diodes, D_S2 and D_S3, of S₂ and S₃ are turned on before t = t₀. During this mode, the voltage, v_m, of L_m becomes V_bus, and the current, i_m, of L_m is:

$$i_m\left(t\right)=i_m\left(t_0\right)+\left(V_{bus}/L_m\right)\left(t-t_0\right),$$

(1)

where $i_m(t_0)=I_{bus}+I_{bat}-V_{bus}D{T}_S/\left(2L_m\right)$. C_r has voltage v_Cr = N_eV_bus − V_C1–v_lk and current i_Cr = i_lk, and i_Cr(t₀) = 0. Therefore:

$$i_{Cr}(t)=\frac{N_e{V}_{bus}-V_{wpt}/2-v_{Cr}(t_0)}{\sqrt{L_{lk}/C_r}}\sin \left[{\omega }_r(t-t_0)\right],$$

(2)

where $v_{Cr}(t_0)=-0.5T_S{I}_{wpt}/C_r$ and ${\omega }_r=1/\sqrt{L_{lk}{C}_r}$. The current, i_D1, of D₁ is equal to i_Cr for t₀ ≤ t ≤ t₁.

Mode 2 (Figure 3b, t₁ ≤ t ≤ t₂): At t = t₁, S₂ and S₃ are turned off, and S₁ and S₄ remain in the off-states to prevent a shoot-through problem. This mode is known as dead time. During this mode, the output capacitance, C_S1, of S₁ discharges from V_bus to 0, and the output capacitance, C_S2, of S₂ charges from 0 to V_bus. In addition, the output capacitance, C_S4, of S₄ discharges from V_bat to 0, and the output capacitance, C_S3, of S₃ charges from 0 to V_bat. Shortly after the discharging and charging processes are finished, the body diodes, D_S1 and D_S4, of S₁ and S₄ are turned on.

Mode 3 (Figure 3c, t₂ ≤ t ≤ t₃): At t = t₂, S₁ and S₄ are turned on under ZVS conditions because the body diodes, D_S1 and D_S4, are turned on before t = t₂. During this mode:

$$i_m\left(t\right)=i_m\left(t_2\right)-\left(V_{bat}/L_m\right)\left(t-t_2\right),$$

(3)

because v_m = −V_bat. i_Cr is obtained using v_Cr = − N_eV_bat + V_C2 − v_lk and i_Cr(t₂) = 0 as:

$$i_{Cr}(t)=-\frac{N_e{V}_{bat}-V_{wpt}/2+v_{Cr}(t_2)}{\sqrt{L_{lk}/C_r}}\sin \left[{\omega }_r(t-t_2)\right],$$

(4)

where $v_{Cr}(t_2)=0.5T_S{I}_{wpt}/C_r$. At t = t₂, D₂ is turned on, and the current, i_D2, of D₂ is −i_Cr.

Mode 4 (Figure 3d, t₃ ≤ t ≤ t₄): S₂ and S₃ remain in the off-states because this mode is the dead time interval. During this mode, C_S2 discharges from V_bus to 0, and C_S1 charges from 0 to V_bus. In addition, C_S3 discharges from V_bat to 0, and C_S4 charges from 0 to V_bat. Shortly after the discharging and charging processes are finished, D_S2 and D_S3 are turned on.

2.3. Voltage Gain

The proposed converter has one input port (DC bus) and two output ports (battery and wireless charging load). Therefore, it has (Equation (1)) a voltage gain, G_bb, between the DC bus and battery and (Equation (2)) a voltage gain, G_wb, between the DC bus and wireless charging load.

(1) G_bb = V_bat/V_bus

For one T_S, the average voltages of C_bus and C_bat are V_bus and V_bat, respectively. Then, the average voltage at node N₁ between S₁ and S₂ is DV_bus, and the average voltage at node N₂ between S₃ and S₄ is given by (1-D) V_bat. The average voltage of L₁ is zero due to the volt-second balance law for the inductor, and the average currents of switches are given by <i_S2> = <i_S3> = I_bus and <i_S1> = <i_S4> = −I_bat because the average current of the capacitor is zero by the charge balance law. Therefore, the average model of the circuit can be obtained (Figure 5). In this average model, the series resistance, R_S, is the sum of R_L1 and 2R_on, where R_L1 and R_on are a winding resistance of L₁ and on-resistance of a switch, respectively.

By applying Kirchhoff’s voltage law (KVL) to the closed-loop that contains DV_bus, R_S, and (1-D) V_bat, the voltage gain G_bb ( = V_bat/V_bus) is obtained as:

$$G_{bb}=-\frac{1}{2}\left\{\left[\frac{\left(1-D\right)R_{bat}}{R_S}+1\right]+\sqrt{{\left[\frac{\left(1-D\right)R_{bat}}{R_S}+1\right]}^2+\frac{4D{R}_{bat}}{R_S}}\right\},$$

(5)

where $R_{bat}=V_{bat}/I_{bat}$. In most cases, $R_{bat}>>R_S$, so:

$$G_{bb}\approx D/\left(1-D\right).$$

(6)

(2) G_wb = V_wpt/V_bus

Based on the four nodes (N₁, N₂, N₃, and N₄) in Figure 2a, the circuit of the proposed converter can be simplified (Figure 6a). Here, the square voltage, v_ac, between N₁ and N₂ is V_bus − (I_bus + I_bat)R_S for DT_S and − V_bat − (I_bus + I_bat)R_S for (1-D)T_S. Then, the current i_ac is i_L1 − (I_bus + I_bat), and the square voltage, v_ac2, between N₃ and N₄ becomes V_wpt/2 for 0.5T_S and −V_wpt/2 for the other 0.5T_S. The current i_ac2 is given by i_Cr.

By applying fundamental harmonic approximation (FHA) to v_ac, i_ac, i_ac2, and v_ac2, the following root mean square (RMS) values are obtained (Figure 6b); V_L2,rms is the RMS value of the first harmonic component in the voltage, v_L2, of L₂, and it is given by:

$$V_{L2,rms}=-\frac{N_e{}^2\pi V_{wpt}{R}_S}{\sqrt{2}{R}_{wpt}}+\frac{N_e{V}_{bus}}{\sqrt{2}}\left(\frac{2\left(1+G_{bb}\right)}{\pi }\sin (D\pi )-\frac{T_S{R}_S}{{\pi }^2\left(1-D\right)L_m}\right),$$

(7)

where:

$$I_{ac2,rms}=\pi I_{wpt}/\sqrt{2},$$

(8)

and:

$$V_{ac2,rms}=\sqrt{2}{V}_{wpt}/\pi ,$$

(9)

are RMS values of the first harmonic components in i_ac2 and v_ac2, respectively. Then, the equivalent resistance, R_ac2, between N₃ and N₄ is obtained using Equations (8) and (9) as:

$$R_{ac2}=V_{ac2,rms}/I_{ac2,rms}=2R_{wpt}/{\pi }^2,$$

(10)

where $R_{wpt}=V_{wpt}/I_{wpt}$. By applying KVL to the closed-loop in Figure 6b, the relation between V_L2,rms and V_ac2,rms is given by:

$$\frac{V_{L2,rms}}{V_{ac2,rms}}=\frac{1}{R_{ac2}}\left[j\left({\omega }_S{L}_{lk}-\frac{1}{{\omega }_S{C}_r}\right)+R_{L2}\right]+1,$$

(11)

where R_L2 is a winding resistance of L₂. Then, substituting Equations (7) and (9) into Equation (11) yields:

$$\begin{array}{c}{G}_{wb}=\left|\frac{V_{wpt}}{V_{bus}}\right|=\frac{N_e}{2}\left(2\left(1+G_{bb}\right)\sin (D\pi )-\frac{T_S{R}_S}{\pi \left(1-D\right)L_m}\right)\\ /\sqrt{\frac{1}{R_{ac2}{}^2}{\left({\omega }_S{L}_{lk}-\frac{1}{{\omega }_S{C}_r}\right)}^2+{\left(\frac{{\pi }^2{R}_{L2}}{2R_{wpt}}+1+\frac{N_e{}^2{\pi }^2{R}_S}{2R_{wpt}}\right)}^2}.\end{array}$$

(12)

If f_r = f_S, maximum G_wb is obtained because ${\omega }_S{L}_{lk}=1/\left({\omega }_S{C}_r\right)$ at f_r = f_S (Figure 7), and it is given by:

$${G_{wb}|}_{f_r=f_S}=\frac{N_e}{2}\left(2\left(1+G_{bb}\right)\sin (D\pi )-\frac{T_S{R}_S}{\pi \left(1-D\right)L_m}\right)/\left(\frac{{\pi }^2{R}_{L2}}{2R_{wpt}}+1+\frac{N_e{}^2{\pi }^2{R}_S}{2R_{wpt}}\right).$$

(13)

Therefore, C_r should be chosen to obtain the maximum voltage gain (G_wb) between V_bus and V_wpt. Because ${\omega }_r=1/\sqrt{L_{lk}{C}_r}$ and $L_{lk}=(1-k^2)L_2$, C_r can be determined as:

$$C_r=\frac{1}{4{\pi }^2{f}_S{}^2\left(1-k^2\right)L_2}.$$

2.4. Magnetic Saturation

The coil structure, which consists of a transmitting coil (L₁) and a receiving coil (L₂), can use magnetic bars to increase efficiency and reduce magnetic fields that can interfere with nearby electronics [21,22,23]. Based on [24,25], the magnetic flux density (B_C) of the coil structure is given by:

$$B_C=\frac{{\mu }_0{\mu }_{e}N{i}_{m,peak}}{l_m},$$

(14)

where µ₀ is a vacuum permeability, ${\mu }_e=\left({\mu }_r{l}_m\right)/\left(2l_g{\mu }_r+l_m\right)$ is an effective relative permeability, N is the number of turns, i_m,peak is a peak value of i_m, l_m is the mean magnetic path length, µ_r is a relative permeability, and l_g is thee air-gap length.

Because the proposed converter has a DC bias current (=I_bus + I_bat) of L₁, i_m,peak is given by:

$$i_{m,peak}=I_{bus}+I_{bat}+\frac{V_{bus}D{T}_S}{2L_m}.$$

(15)

Magnetic saturation can be caused by this DC bias current because the DC bias current increases B_C by increasing i_m,peak. There are two methods to solve the problem of the DC bias current [26,27]. First, decreasing N reduces B_C. Second, increasing l_g reduces B_C by decreasing µ_e. However, l_g is determined by a distance, l_d, between L₁ and L₂. Therefore, the following condition for preventing magnetic saturation can be obtained using B_C < B_sat, (Equations (14) and (15)) as:

$$N<\frac{l_m{B}_{sat}}{{\mu }_0{\mu }_e\left[I_{bus}+I_{bat}+V_{bus}D{T}_S/\left(2L_m\right)\right]},$$

(16)

where B_sat is a saturation flux density of magnetic material.

3. Experimental Results

A prototype (Figure 8) of the proposed converter was fabricated using selected components and circuit parameters (

Table 1. Values of the components used for the prototype.

Components			Values
2-coil structure	Winding type		Spiral
	Distance between two coils		5 cm
	Coupling coefficient (k)		0.227
	Equivalent turn ratio (Ne)		0.226
	Primary winding	Inductance (L1)	117.5 µH
		Resistance (RL1)	0.43 Ω
		Turn number (N1)	28 T
	Secondary winding	Inductance (L2)	116.5 µH
		Resistance (RL2)	0.4 Ω
		Turn number (N2)	28 T
Resonant capacitor (Cr)			1.43 nF
Doubler capacitors (C1, C2)			2.2 µF
Switches (S1~S4)			FCP099N60E (Ron = 99 mΩ)
Diodes (D1, D2)			BYV29-500

), then tested to verify the operation of the proposed converter.

The voltage and current waveforms of S₁ and S₂ were measured at V_bus = 400 V, V_bat = 400 V, f_S = 400 kHz, and P_wpt (or P_bat) = 20 and 100 W (Figure 9). At both P_wpt = 20 W (Figure 9a) and P_wpt = 100 W (Figure 9b), the voltage stresses of S₁ and S₂ were measured as 400 V, which is equal to V_bus, and S₁ and S₂ achieved ZVS turn-on. In addition, S₃ and S₄ achieved ZVS turn-on at these conditions because i_S1 = i_S4 and i_S2 = i_S3. Even at both P_bat = 20 W (Figure 9c) and P_bat = 100 W (Figure 9d), all switches were turned on under the ZVS condition, which improves the power-conversion efficiency, η_e.

The theoretical V_wpt obtained from Equation (13) was compared with the experimental V_wpt measured at V_bus = 400 V, V_bat = 400 V, and P_wpt = 20 W~100 W (Figure 10). The theoretical V_wpt was higher than experimental V_wpt at all P_wpt, but the difference was <3%. This result shows that Equation (13) predicts the experimental V_wpt with little error. In addition, V_wpt was almost constant regardless of P_wpt.

The power-conversion efficiencies (η_e,wpt for the wireless charging load and η_e,bat for the battery load) were measured at V_bus = 400 V, V_bat = 400 V, f_S = 400 kHz, and P_wpt (or P_bat) = 20 W~100 W (Figure 11). The proposed converter had the highest η_e,wpt = 93.8% at P_wpt = 100 W (Figure 11a) and had the highest η_e,bat = 95.9% at P_bat = 100 W (Figure 11b). At low P_wpt = 20 W, the measured η_e,wpt was 82.5% (Figure 11a), and the measured η_e,bat was 83.5% at low P_bat = 20 W (Figure 11b). In addition, the measured η_e,bat was higher than the measured η_e,wpt because the wireless power loss during transfer between two coils is included in η_e,wpt. These results show that the proposed converter had high η_e,wpt > 82% and high η_e,bat > 83% for all operating ranges due to the ZVS turn-on of all switches.

The transient response of V_wpt was measured at V_bus = 400 V, V_bat = 400 V, and f_S = 400 kHz, while changing the wireless charging load from 20% to 100% and from 100% to 20% (Figure 12). At the load transition, the maximum voltage spike of V_wpt was measured as 14 V_p.p, and V_wpt returned to the steady-state within 81 ms.

In addition, the transient response of V_bat was measured while changing the battery load from 20% to 100% and from 100% to 20% under the same conditions as in Figure 12 (Figure 13). The maximum voltage spike of V_bat was measured as 61 V_p.p when the load changed, and V_bat returned to the steady state within 125 ms. These experiment results of the transient response show that the proposed converter can operate properly despite sudden load changes.

To show that the proposed converter can operate both when charging the battery and when charging wirelessly, V_wpt and V_bat of the proposed converter were measured under the following four conditions (Figure 14): (1) P_wpt = 20 W and P_bat = 20 W, (2) P_wpt = 20 W and P_bat = 100 W, (3) P_wpt = 100 W and P_bat = 20 W, and (4) P_wpt = 100 W and P_bat = 100 W. Figure 14 shows that V_wpt decreases and V_bat increases when the power (P_wpt, P_bat) increases. However, both V_wpt and V_bat maintained a near fixed value; V_wpt changed from 183.8 to 180.9 V, which is just a 1.58% change, and V_bat changed from 399.8 to 401 V, which is just a 0.3% change.

The measured V_wpt and V_bat are summarized in

Table 2. WPT and battery voltages according to the WPT and battery powers.

Power	WPT Power (Pwpt)	20 W	20 W	100 W	100 W
	Battery Power (Pwpt)	20 W	100 W	20 W	100 W
WPT voltage (Vwpt)		183.8 V	183.6 V	182.7 V	180.9 V
Battery voltage (Vbat)		399.8 V	399.9 V	400.6 V	401 V

, and this experimental result shows that the proposed converter can operate in both charging the battery and charging wirelessly because both V_wpt and V_bat maintain a near fixed value regardless of P_wpt and P_bat.

4. Conclusions

This paper presented a three-port converter to integrate an ES system with a WPT system. If the ES and WPT systems are used separately, many converters are needed. However, these ES and WPT systems can be integrated through only one proposed converter because the proposed converter can use an inductor in the bidirectional DC-DC converter as a transmitting coil for the WPT system. Therefore, the proposed converter consists only of a bidirectional DC-DC converter and an AC-DC converter, and an ES-WPT system that uses the proposed converter can minimize the cost and circuit size. The operation of the proposed converter was verified by theoretical analysis and experimental results, and the proposed converter had high η_e,wpt > 82% for 20 W ≤ P_wpt ≤ 100 W, and η_e,bat > 83% for 20 W ≤ P_bat ≤ 100 W, due to the ZVS turn-on of all switches. These results show that the proposed converter is suitable for the ES-WPT system that is part of future PV energy delivery and management infrastructure for residential applications.