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

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.


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 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.

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, Cbus, with capacitance, Cbus, and battery capacitor, Cbat, with capacitance, Cbat), and an inductor (L1 with inductance L1). In addition, it can transfer the energy of

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 (S 1 , S 2 , S 3 , S 4 ), two filter capacitors (bus capacitor, C bus , with capacitance, C bus , and battery capacitor, C bat , with capacitance, Energies 2020, 13, 272 3 of 16 C bat ), and an inductor (L 1 with inductance L 1 ). In addition, it can transfer the energy of the DC bus (or battery) to the wireless charging load because L 1 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 (L 2 with inductance L 2 ) 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 (D 1 , D 2 ) and two doubler capacitors (C 1 with capacitance, C 1 , and C 2 with capacitance, C 2 ). L 1 and L 2 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 √ L 2 /L 1 , and L m = L 1 (Figure 2b).
Four switches achieve the ZVS turn-on by using the stored energy in L 1 . 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 D 1 and D 2 to WPT voltage, V wpt .
Energies 2020, 13, x 3 of 16 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, Cwpt, with capacitance, Cwpt), a resonant capacitor (Cr with capacitance, Cr), 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 (Llk with inductance, Llk), an effective turn ratio (Ne), and a magnetizing inductor (Lm with inductance, Lm), where Four switches achieve the ZVS turn-on by using the stored energy in L1. Llk resonates with Cr, and high voltage gain between the DC bus and wireless charging load is achieved by setting the switching frequency, fS, to the resonant frequency, fr, between Llk and Cr. 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, Vwpt.

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 S 1 , S 2 , S 3 , and S 4 ; the duty ratios of S 2 and S 3 are defined as D, and the duty ratios of S 1 and S 4 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) C 1 , C 2 , 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, t 0 ≤ t ≤ t 1 ): This mode starts at t = t 0 when S 2 and S 3 are turned on. At this time, S 2 and S 3 achieve ZVS turn-on because the body diodes, D S2 and D S3 , of S 2 and S 3 are turned on before t = t 0 . During this mode, the voltage, v m , of L m becomes V bus , and the current, i m , of L m is: where i m (t 0 ) = I bus + I bat − V bus DT S /(2L m ). C r has voltage v Cr = N e V bus − V C1 -v lk and current i Cr = i lk , and i Cr (t 0 ) = 0. Therefore: where v Cr (t 0 ) = −0.5T S I wpt /C r and ω r = 1/ √ L lk C r . The current, i D1 , of D 1 is equal to i Cr for t 0 ≤ t ≤ t 1 . Mode 2 (Figure 3b, t 1 ≤ t ≤ t 2 ): At t = t 1 , S 2 and S 3 are turned off, and S 1 and S 4 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 S 1 discharges from V bus to 0, and the output capacitance, C S2 , of S 2 charges from 0 to V bus . In addition, the output capacitance, C S4 , of S 4 discharges from V bat to 0, and the output capacitance, C S3 , of S 3 charges from 0 to V bat . Shortly after the discharging and charging processes are finished, the body diodes, D S1 and D S4 , of S 1 and S 4 are turned on.
Mode 3 (Figure 3c, t 2 ≤ t ≤ t 3 ): At t = t 2 , S 1 and S 4 are turned on under ZVS conditions because the body diodes, D S1 and D S4 , are turned on before t = t 2 . During this mode: because v m = −V bat . i Cr is obtained using v Cr = − N e V bat + V C2 − v lk and i Cr (t 2 ) = 0 as: where v Cr (t 2 ) = 0.5T S I wpt /C r . At t = t 2 , D 2 is turned on, and the current, i D2 , of D 2 is −i Cr . Mode 4 ( Figure 3d, t 3 ≤ t ≤ t 4 ): S 2 and S 3 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.

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, Gbb, between the DC bus and battery and (Equation (2)) a voltage gain, Gwb, between the DC bus and wireless charging load.
(1) Gbb = Vbat/Vbus For one TS, the average voltages of Cbus and Cbat are Vbus and Vbat, respectively. Then, the average voltage at node N1 between S1 and S2 is DVbus, and the average voltage at node N2 between S3 and S4 is given by (1-D) Vbat. 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 <iS2> = <iS3> = Ibus and <iS1> = <iS4> = −Ibat 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, RS, is the sum of RL1 and 2Ron, where RL1 and Ron are a winding resistance of L1 and on-resistance of a switch, respectively.

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 N 1 between S 1 and S 2 is DV bus , and the average voltage at node N 2 between S 3 and S 4 is given by (1-D) V bat . The average voltage of L 1 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 L 1 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: where R bat = V bat /I bat . In most cases, R bat >> R S , so: Energies 2020, 13, where bat bat bat . In most cases, (2) Gwb = Vwpt/Vbus 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, vac, between N1 and N2 is Vbus − (Ibus + Ibat)RS for DTS and − Vbat − (Ibus + Ibat)RS for (1-D)TS. Then, the current iac is iL1 − (Ibus + Ibat), and the square voltage, vac2, between N3 and N4 becomes Vwpt/2 for 0.5TS and −Vwpt/2 for the other 0.5TS. The current iac2 is given by iCr.
By applying fundamental harmonic approximation (FHA) to vac, iac, iac2, and vac2, the following root mean square (RMS) values are obtained ( Figure 6b); VL2,rms is the RMS value of the first harmonic component in the voltage, vL2, of L2, and it is given by: where: 2 / , 2 wpt rms ac and: (2) G wb = V wpt /V bus Based on the four nodes (N 1 , N 2 , N 3 , and N 4 ) in Figure 2a, the circuit of the proposed converter can be simplified (Figure 6a). Here, the square voltage, v ac , between N 1 and N 2 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 N 3 and N 4 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 L 2 , and it is given by: where: Energies 2020, 13, 272 9 of 16 and: are RMS values of the first harmonic components in i ac2 and v ac2 , respectively. Then, the equivalent resistance, R ac2 , between N 3 and N 4 is obtained using Equations (8) and (9) as: 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: where R L2 is a winding resistance of L 2 . Then, substituting Equations (7) and (9) into Equation (11) yields: If f r = f S , maximum G wb is obtained because ω S L lk = 1/(ω S C r ) at f r = f S (Figure 7), and it is given by: Energies 2020, 13, x 9 of 16 π / 2 , 2 wpt rms ac are RMS values of the first harmonic components in iac2 and vac2, respectively. Then, the equivalent resistance, Rac2, between N3 and N4 is obtained using Equations (8) and (9) where wpt wpt wpt . By applying KVL to the closed-loop in Figure 6b, the relation between VL2,rms and Vac2,rms is given by: where RL2 is a winding resistance of L2. Then, substituting Equations (7) and (9) into Equation (11) yields: If fr = fS, maximum Gwb is obtained because (Figure 7), and it is given by:

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 (BC) of the coil structure is given by: where µ0 is a vacuum permeability, = / 2 + is an effective relative permeability, N is the number of turns, im,peak is a peak value of im, lm is the mean magnetic path length, µr is a relative permeability, and lg is thee air-gap length.
Because the proposed converter has a DC bias current (=Ibus + Ibat) of L1, im,peak is given by: Magnetic saturation can be caused by this DC bias current because the DC bias current increases BC by increasing im,peak. There are two methods to solve the problem of the DC bias current [26,27]. First, decreasing N reduces BC. Second, increasing lg reduces BC by decreasing µe. However, lg is determined by a distance, ld, between L1 and L2. Therefore, the following condition for preventing magnetic saturation can be obtained using BC < Bsat, (Equation (14) and (15)) as: where Bsat is a saturation flux density of magnetic material.

Experimental Results
A prototype (Figure 8) of the proposed converter was fabricated using selected components and circuit parameters (Table 1), then tested to verify the operation of the proposed converter. Therefore, C r should be chosen to obtain the maximum voltage gain (G wb ) between V bus and V wpt . Because ω r = 1/ √ L lk C r and L lk = (1 − k 2 )L 2 , C r can be determined as:

Magnetic Saturation
The coil structure, which consists of a transmitting coil (L 1 ) and a receiving coil (L 2 ), 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: where µ 0 is a vacuum permeability, µ e = (µ r l m )/ 2l g µ r + l m 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 L 1 , i m,peak is given by: 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 L 1 and L 2 . Therefore, the following condition for preventing magnetic saturation can be obtained using B C < B sat , (Equations (14) and (15)) as: where B sat is a saturation flux density of magnetic material.

Experimental Results
A prototype (Figure 8) of the proposed converter was fabricated using selected components and circuit parameters (Table 1), then tested to verify the operation of the proposed converter.  The voltage and current waveforms of S1 and S2 were measured at Vbus = 400 V, Vbat = 400 V, fS = 400 kHz, and Pwpt (or Pbat) = 20 and 100 W (Figure 9). At both Pwpt = 20 W (Figure 9a) and Pwpt = 100 W (Figure 9b), the voltage stresses of S1 and S2 were measured as 400 V, which is equal to Vbus, and S1 and S2 achieved ZVS turn-on. In addition, S3 and S4 achieved ZVS turn-on at these conditions because iS1 = iS4 and iS2 = iS3. Even at both Pbat = 20 W (Figure 9c) and Pbat = 100 W (Figure 9d), all switches were turned on under the ZVS condition, which improves the power-conversion efficiency, ηe.  The voltage and current waveforms of S 1 and S 2 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 S 1 and S 2 were measured as 400 V, which is equal to V bus , and S 1 and S 2 achieved ZVS turn-on. In addition, S 3 and S 4 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 theoretical Vwpt obtained from Equation (13) was compared with the experimental Vwpt measured at Vbus = 400 V, Vbat = 400 V, and Pwpt = 20 W~100 W ( Figure 10). The theoretical Vwpt was higher than experimental Vwpt at all Pwpt, but the difference was <3%. This result shows that Equation The power-conversion efficiencies (ηe,wpt for the wireless charging load and ηe,bat for the battery load) were measured at Vbus = 400 V, Vbat = 400 V, fS = 400 kHz, and Pwpt (or Pbat) = 20 W~100 W ( Figure  11). The proposed converter had the highest ηe,wpt = 93.8% at Pwpt = 100 W (Figure 11a) and had the highest ηe,bat = 95.9% at Pbat = 100 W (Figure 11b). At low Pwpt = 20 W, the measured ηe,wpt was 82.5% (Figure 11a), and the measured ηe,bat was 83.5% at low Pbat = 20 W (Figure 11b). In addition, the measured ηe,bat was higher than the measured ηe,wpt because the wireless power loss during transfer  The theoretical Vwpt obtained from Equation (13) was compared with the experimental Vwpt measured at Vbus = 400 V, Vbat = 400 V, and Pwpt = 20 W~100 W ( Figure 10). The theoretical Vwpt was higher than experimental Vwpt at all Pwpt, but the difference was <3%. This result shows that Equation The power-conversion efficiencies (ηe,wpt for the wireless charging load and ηe,bat for the battery load) were measured at Vbus = 400 V, Vbat = 400 V, fS = 400 kHz, and Pwpt (or Pbat) = 20 W~100 W ( Figure  11). The proposed converter had the highest ηe,wpt = 93.8% at Pwpt = 100 W (Figure 11a) and had the highest ηe,bat = 95.9% at Pbat = 100 W (Figure 11b). At low Pwpt = 20 W, the measured ηe,wpt was 82.5% (Figure 11a), and the measured ηe,bat was 83.5% at low Pbat = 20 W (Figure 11b). In addition, the measured ηe,bat was higher than the measured ηe,wpt because the wireless power loss during transfer 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.
between two coils is included in ηe,wpt. These results show that the proposed converter had high ηe,wpt > 82% and high ηe,bat > 83% for all operating ranges due to the ZVS turn-on of all switches. The transient response of Vwpt was measured at Vbus = 400 V, Vbat = 400 V, and fS = 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 Vwpt was measured as 14 Vp.p, and Vwpt returned to the steady-state within 81 ms. In addition, the transient response of Vbat 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 Vbat was measured as 61 Vp.p when the load changed, and Vbat 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. 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.
Energies 2020, 13, x 13 of 16 between two coils is included in ηe,wpt. These results show that the proposed converter had high ηe,wpt > 82% and high ηe,bat > 83% for all operating ranges due to the ZVS turn-on of all switches. The transient response of Vwpt was measured at Vbus = 400 V, Vbat = 400 V, and fS = 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 Vwpt was measured as 14 Vp.p, and Vwpt returned to the steady-state within 81 ms. In addition, the transient response of Vbat 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 Vbat was measured as 61 Vp.p when the load changed, and Vbat 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. 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.
Energies 2020, 13, x 13 of 16 between two coils is included in ηe,wpt. These results show that the proposed converter had high ηe,wpt > 82% and high ηe,bat > 83% for all operating ranges due to the ZVS turn-on of all switches. The transient response of Vwpt was measured at Vbus = 400 V, Vbat = 400 V, and fS = 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 Vwpt was measured as 14 Vp.p, and Vwpt returned to the steady-state within 81 ms. In addition, the transient response of Vbat 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 Vbat was measured as 61 Vp.p when the load changed, and Vbat 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, 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 .  Figure 14 shows that Vwpt decreases and Vbat increases when the power (Pwpt, Pbat) increases. However, both Vwpt and Vbat maintained a near fixed value; Vwpt changed from 183.8 to 180.9 V, which is just a 1.58% change, and Vbat changed from 399.8 to 401 V, which is just a 0.3% change.
The measured Vwpt and Vbat are summarized in Table 2, and this experimental result shows that the proposed converter can operate in both charging the battery and charging wirelessly because both Vwpt and Vbat maintain a near fixed value regardless of Pwpt and Pbat.

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 ηe,wpt > 82% for 20 W ≤ Pwpt ≤ 100 W, and ηe,bat > 83% for Figure 14. The WPT voltage (V wpt ) and the battery voltage (V bat ) measured at (a) P wpt = 20 W and P bat = 20 W, (b) P wpt = 20 W and P bat = 100 W, (c) P wpt = 100 W and P bat = 20 W, and (d) P wpt = 100 W and P bat = 100 W.

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.