Study of a Bidirectional Power Converter Integrated with Battery/Ultracapacitor Dual-Energy Storage

Abstract

A patented bidirectional power converter was studied as an interface to connect the DC-bus of driving inverter, battery energy storage (BES), and ultracapacitor (UC) to solve the problem that the driving motor damages the battery life during acceleration and deceleration in electric vehicles (EVs). The proposed concept was to adopt a multiport switch to control the power flow and achieve the different operating mode transitions for the better utilization of energy. In addition, in order to improve the conversion efficiency, the proposed converter used a coupled inductor and interleaved-pulse-width-modulation (IPWM) control to achieve a high voltage conversion ratio (i.e., bidirectional high step-up/down conversion characteristics). This study discussed the steady-state operation and characteristic analysis of the proposed converter. Finally, a 500 W power converter prototype with specifications of 72 V DC-bus, 24 V BES, and 48 V UC was built, and the feasibility was verified by simulation and experiment results. The highest efficiency points of the realized prototype were 97.4%, 95.5%, 97.2%, 97.1%, and 95.3% for the UC charge, battery charge, UC discharge, the dual-energy in series discharge, and battery discharge modes, respectively.

1. Introduction

Electric vehicle (EV) technologies are currently being developed to lessen environmental impact and overcome shortages of fossil fuel [1,2,3,4,5,6,7,8,9,10]. The typical power configuration of pure electric vehicle (EV) contains four major parts: the battery energy storage (BES), the power converter, the driving inverter of motor, and the energy management system (EMS) [6,8,10]. Among them, BES is the most critical component, which can directly affect the life and endurance of the EV, driving efficiency, and system performance. In general, the power will be drawn rapidly from the BES during the vehicle acceleration, subsequently causing BES output current and temperature to rise quickly. Moreover, the driving inverter is prone to generate less stable pulse currents for the BES during deceleration [9]. Such long-term use not only causes damage to the external body of the battery but also excessively charges and discharges the BES, which eventually will shorten the lifespan of the BES, specifically in high power applications. Although it is feasible to size up the BES for high power demands, the high price of the overall system still remains an issue. Possible solutions may be to select an ultracapacitor (UC), to assist BES, forming a “hybrid energy” system as shown in Figure 1 for EVs [11,12].

UC has high-power density, long cycle life, quick dynamic response, but low-energy-density, which are opposite toward BES. Hence, it should exploit the complementary properties of both the UC and the BES [12]. Several conventional schemes integrating both the BES and UC are shown in Figure 1. These schemes have all been designed to control power flows, supply specific voltages to loads, and to reduce design cost, mass, and power consumptions [12,13,14,15].

Figure 1a shows the most basic parallel scheme of the BES and UC, with the latter serving as the low-pass filter [16]. Although simple, the energy stored in the UC is not utilized effectively due to the absence of power converters. The slightly more robust Figure 1b shows that a power converter is added in between the BES and UC [17,18,19,20]. In this scheme, the BES is connected directly to the DC-bus instead of the UC. The power output of the UC is controlled by the power converter, and this enables the UC to operate over a wider voltage range than in Figure 1a. Due to this, the power rating of the converter has to be sufficiently large to handle high surges of power demands from the UC. The purpose of the power converter is also to maintain a constant voltage value on the DC-bus during the operation of the motor. The drawback of this scheme is that the BES is exposed to large fluctuations of high charging and discharging current, resulting in its reduced lifetime. Figure 1c is similar to Figure 1b except that the positions of the BES and UC have been swapped [21]. Due to this, the BES is no longer exposed to the large current fluctuations. The power output from the BES is now controlled by the power converter. The main disadvantage of this scheme is that the DC-bus voltage is exposed to large voltages as it is directly connected to the UC. As a result, the power converter is exposed to a high risk of suffering adverse losses, especially in harsh driving conditions.

All the schemes in Figure 1a–c clearly demonstrate that it is insufficient to use only one or no power converter. Hence, cascaded schemes using two power converters, as shown in Figure 1d,e, have also been considered before [22,23]. In these two schemes, two converters decouple the BES and UC from the DC-bus. The circuit, in Figure 1d, is also known as the “type-I scheme” where an extra power converter is added in between the UC and the DC-bus. The converter that is located in between the BES and UC is rated according to the power rating of the BES. This scheme creates more losses for the higher rated converter that is located in between the UC and the DC-bus due to the fluctuations of the UC output voltage. In order to overcome this problem, the positions of the BES and UC are swapped, as shown in Figure 1e (type-II scheme). However, it is difficult to balance the BES cell due to it now being located at the higher voltage terminal. Although both the type-I and type-II schemes are more robust than all the previous designs that use only one or no power converter, the power losses and design costs of the schemes are increased substantially owing to the multi-stage energy conversion processes in the vehicular power train. Besides that, only one power converter is connected to the DC-bus in both of these schemes. An outage in one of the power converters will lead to the loss of the power-control function. An alternative is to employ the scheme in Figure 1f, where the power converters are connected in parallel and directly to the DC-bus [13,24,25,26,27,28]. In this scheme, the power converters have the same output voltage, and the power flow of both the energy sources (BES and UC) are not affected by the output of the other converter. Consequently, this scheme can operate in various modes [28]. But, the fully power-rated converters are needed, and the cost of this scheme is higher than all the aforementioned schemes.

In order to reduce the overall system cost, a multi-input power converter scheme is studied, as shown in Figure 2, into the EV system [29,30,31,32,33].

Multi-input power converters are potential solutions when multiple energy sources with different voltage levels (battery voltage ≠ UC voltage ≠ DC-bus voltage) and/or power capabilities are to be combined and yet maintain a regulated output load voltage across them.

Using multi-input power converters, it is possible to apply a different power control command for each input source. In order to reduce the cost and weight and enhance the overall performance of the hybrid energy storage system, the multi-input power converter scheme was chosen in this paper and further investigated.

In [29], a multi-input power converter topology has been proposed to combine various input energy sources in parallel by using a single-pole triple-throw switch. The major limitations of parallel-connected source topologies are: input source voltage should be asymmetric, and only one input source can supply power to the load at a time to avoid the power coupling effect.

In [30], a single-inductor unidirectional multi-input power converter has been presented, which can operate in buck, boost, or buck-boost modes. To realize the bidirectional power flow mode, all the diodes must be replaced by unidirectional switches, which increase the number of switches.

In [31], a DC-bus interfacing three-port converter with a simple topology and no electrical isolation has been proposed, but it cannot cope with a wide operating voltage ratio; energy storage devices connected to different ports must have a similar operating voltage, and this constricts the application.

In [32], a modular multi-input power converter has been presented to integrate the basic buck-boost circuit and a shared DC-bus. It is a very simple approach to integrate multiple converters into a single unit. However, it has limited static voltage gains, resulting in a narrow voltage range and a low voltage difference between the high- and low-side ports. Besides, since only a few circuit elements are shared among multiple converters, the benefits of the integration are limited.

In [33], a two-phase multi-input converter with a high voltage conversion ratio has been proposed as an interface between dual-energy storage sources. Due to the intrinsic automatic current balance characteristic, the currents of two energy sources are theoretically identical; it indicates that the high power capability of UC cannot be utilized, and the applications of the proposed converter would be limited.

By conducting a research literature review of [29,30,31,32,33,34,35,36], in this paper, a bidirectional power converter integrated BES/UC dual-energy storage was proposed, which had the capability to perform forward power transmission and reverse energy recovery.

First, the proposed converter used a multiport switch to change the different operating modes and to improve the energy utilization of UC and increase battery life.

Second, it was also integrated with interleaved-pulse-width-modulation (IPWM) control to increase power density and reduce bidirectional current ripples, which makes power delivery more reliable.

Third, the proposed converter also used a coupled inductor technique instead of a general single-winding inductor to achieve high voltage conversion ratio and high power density for bidirectional power conversion.

Finally, the steady-state operation and characteristic analysis of the proposed converter were described, validated using simulation and experimentation of a 500 W power converter prototype with specifications of 72 V DC-bus, 24 V BES, and 48 V UC.

The summarized main features of the proposed converter were its ability to:

(1)

interface more than two energy sources of different voltage levels,

(2)

control power flow between the DC-bus and the two low-voltage energy sources,

(3)

control power flow from either the UC or BES or both,

(4)

enhance static voltage gain and reduce switch voltage stress, and

(5)

possess a reasonable duty cycle and produce a wide voltage difference between its high- and low-side ports.

2. Converter Operating Principles

Figure 3 shows the architecture of the proposed converter integrated with dual-energy storage. The power devices (S₁~S₄) are the multiport switch used to control the power flow between the battery/UC dual-energy and DC-bus. To achieve the high conversion efficiency, the design concept for the converter are based on multi-phase operation and switch stress reduction as (1) the power devices (Q₁~Q₄) are designed to use IPWM control to reduce current stress and ripple on the switch, (2) two-phase coupled inductors T₁ and T₂ are integrated into the bidirectional power converter with high turns ratio to reduce the undesirable duty ratio and conduction loss of metal-oxide-semiconductor field-effect transistors (MOSFETs).

2.1. Multiport Switch

Figure 4 shows the equivalent circuits of the multiport switch of the proposed converter under different operating modes. For the converter operating in the UC charge or discharge mode, the multiport switches S₁, S₄ are turned on, and S₂, S₃ are turned off. The equivalent circuit of this condition is shown in Figure 4a. It is shown that the bidirectional energy delivery between the UC and the DC-bus can be achieved. For the converter operating under the battery charge mode or discharge mode, the multiport switches S₂, S₃ are turned on, and S₁, S₄ are turned off. Under this condition, the corresponding equivalent circuit is shown in Figure 4b. The figure shows that the bidirectional energy delivery between the battery and the DC-bus can be achieved. For the converter operating under the dual-energy in series discharge mode, the multiport switches S₁, S₃ are turned on, and S₂, S₄ are turned off. The battery/UC dual-energy delivers the energy to DC-bus, and its equivalent circuit is shown in Figure 4c.

2.2. Operating Principle of the Proposed Converter

Figure 5 shows the equivalent circuits of the different states for the proposed converter, where V_H represents the high-side voltage for the DC-bus, and V_L represents low-side voltage for UC, battery, or battery/UC dual-energy in series modes.

The assumptions are made in analyzing the proposed converter:

(1)

the converter operates in continuous conduction mode (CCM);

(2)

characteristic of the two-phase coupled inductors T₁ and T₂ are the same, i.e., L_m1 = L_m2, i_m1 = i_m2 and n = N₂/N₁ = N₄/N₃;

(3)

all voltages and currents in the circuits are periodic in steady-state condition; for simplicity, it is assumed that all the components in Figure 3 are idealized.

State 1. The equivalent circuit of this state is shown in Figure 5a. The power switches Q₂ and Q₄ are turned on, and Q₁ and Q₃ are turned off. During this state, the high-side voltage V_H stores energy to the magnetizing inductance L_m1 and L_m2, and then the magnetizing currents i_m1, i_m2 increase linearly. The circuit equations are expressed as follows,

$$v_{N1}=L_{m1}\frac{d{i}_{m1}}{dt}=V_H-v_{N2}-V_L$$

(1)

$$v_{N3}=L_{m2}\frac{d{i}_{m2}}{dt}=V_H-v_{N4}-V_L$$

(2)

$$i_H=i_{N2}+i_{N4}$$

(3)

$$i_{T1}=i_{N2}$$

(4)

$$i_{T2}=i_{N4}$$

(5)

$$i_T=i_{T1}+i_{T2}$$

(6)

State2. The equivalent circuit of this state is shown in Figure 5b. The power switches Q₂ and Q₃ are turned on, and Q₁ and Q₄ are turned off. At this time, the high-side voltage V_H continues to store energy to the magnetizing inductance L_m1, and the magnetizing current i_m1 increases linearly. The energy stored in the magnetizing inductor L_m2 is now released to the low-side energy device, and the magnetizing current i_m2 decreases linearly. The circuit equations are expressed as follows,

$$v_{N1}=V_H-v_{N2}-V_L$$

(7)

$$v_{N3}=-V_L$$

(8)

$$i_H=i_{N2}$$

(9)

$$i_{T1}=i_{N2}$$

(10)

$$i_{T2}=i_{m2}$$

(11)

State 3. The equivalent circuit of this state is shown in Figure 5c. The power switches Q₁ and Q₄ are turned on, and Q₂ and Q₃ are turned off. At this time, the energy stored in the magnetizing inductor L_m1 is now released to the low-side energy storage, and the magnetizing current i_m1 decreases linearly. The voltage across v_N1 of the magnetizing inductor L_m1 is negative of the low-side voltage V_L. The magnetizing inductor L_m2 draws the energy from the high-side voltage V_H, and the magnetizing current i_m2 increases linearly. The circuit equations are expressed as follows,

$$v_{N1}=-V_L$$

(12)

$$v_{N3}=V_H-v_{N4}-V_L$$

(13)

$$i_H=i_{N4}$$

(14)

$$i_{T1}=i_{m1}$$

(15)

$$i_{T2}=i_{N4}.$$

(16)

State 4. The equivalent circuit of this state is shown in Figure 5d. The power switches Q₁ and Q₃ are turned on, and Q₂ and Q₄ are turned off. At this time, the energy stored in the magnetizing inductor L_m1 and L_m2 is now released to the low-side energy storage, and the magnetizing currents i_m1 and i_m2 decrease linearly. The voltage across v_N1 and v_N3 of the magnetizing inductor L_m1 and L_m2 is negative of the low-side voltage V_L. The circuit equations are expressed as follows,

$$v_{N1}=-V_L$$

(17)

$$v_{N3}=-V_L$$

(18)

$$i_H=0$$

(19)

$$i_{T1}=i_{m1}$$

(20)

$$i_{T2}=i_{m2}$$

(21)

Considering the different duty ratio conditions in the charge mode and discharge mode, the operating state flow of each condition during a switching period is summarized as follows.

Charge Mode (D_c < 0.5)

State 2 → State 4 → State 3 → State 4

Charge Mode (D_c = 0.5)

State 2 → State 3

Charge Mode (D_c > 0.5)

State 2 → State 1 → State 3 → State 1

Discharge Mode (D_d < 0.5)

State 3 → State 1 → State 2 → State 1

Discharge Mode (D_d = 0.5)

State 3 → State 2

Discharge Mode (D_d > 0.5)

State 3 → State 4 → State 2 → State 4

As mentioned above, D_c is the duty ratio of switch Q₂ and Q₄ for the charge mode, and D_d is the duty ratio of switch Q₁ and Q₃ for the discharge mode.

When the proposed converter operates with the duty ratio of 0.5 in the charge or discharge mode (i.e., D_c = D_d = 0.5), the only two operating states of the proposed converter are produced.

When the proposed converter operates in the charge mode with duty ratio D_c > 0.5, the operation state in a switching period is the same as the discharge mode with D_d < 0.5, and only the reverse current direction is considered.

Similarly, when the proposed converter operates in the discharge mode with the duty ratio D_d > 0.5, the operation state in the switching period is the same as the charge mode with D_c < 0.5, and only the reverse current direction is considered. Figure 6 shows the key waveforms of the proposed converter in the charge mode with D_c < 0.5, and in the discharge mode with D_d < 0.5, respectively.

The time intervals of Figure 6 are described as

Charge Mode (D_c < 0.5)

[t₀ < t ≤ t₁]: state 2; [t₁ < t ≤ t₂]: state 4; [t₂ < t ≤ t₃]: state 3; [t₃ < t ≤ t₄]: state 4.

Discharge Mode (D_d < 0.5)

[t₀ < t ≤ t₁]: state 3; [t₁ < t ≤ t₂]: state 1; [t₂ < t ≤ t₃]: state 2; [t₃ < t ≤ t₄]: state 1.

3. Converter Steady-State Analyses

3.1. Static Voltage Conversion Ratio Analysis

Charge Mode (UC Charge; Battery Charge)

During steady-state operation and according to the volt-second balance principle of the magnetizing inductance operating in the charge mode, the static voltage conversion ratio M_c can be derived as from (22)–(25).

The voltage relationship between primary and secondary sides of the coupled inductor is shown as follows

$$v_{N2}=n{v}_{N1}$$

(22)

substituting (22) into (1), it can be rewritten as follows

$$v_{N1}=(V_H-V_L)\frac{1}{1+n}$$

(23)

By combining (23) and (12), the average voltage of the primary side for the coupled inductor during a switching period can be expressed as follows

$${\langle v_{N1}\rangle }_{T_s}={\displaystyle \underset{0}{\overset{D_c{T}_s}{\int }}\frac{V_H-V_L}{1+n}dt}+{\displaystyle \underset{D_c{T}_s}{\overset{T_s}{\int }}(-V_L)dt}=0$$

(24)

The static voltage conversion ratio of the proposed converter in the charge mode can be derived as follows

$$M_c=\frac{V_L}{V_H}=\frac{D_c}{1+n(1-D_c)}$$

(25)

Figure 7a shows the relationship between the coupled inductance with different turns ratio and the static voltage conversion ratio M_c of the proposed converter in the charge mode.

For simplicity, assuming that the turns ratio of the coupling inductance is n = 1, the relationship between M_c and D_c is shown in Figure 7b.

It can be seen that the static voltage conversion ratio of the proposed converter in the charge mode has a better performance, compared with the conventional buck converter.

Discharge Mode (UC Discharge; Battery Discharge; Dual-Energy in Series Discharge)

The static voltage conversion ratio M_d in the discharge mode can be derived from the average voltage of the magnetizing inductance. According to (23) and (12), and considering the duty ratio D_d of the switch Q₁ and Q₃, the average voltage of the primary side for the coupled inductor during a switching period can be expressed as follows

$${\langle -v_{N1}\rangle }_{T_s}={\displaystyle \underset{0}{\overset{D_d{T}_s}{\int }}(-V_L)dt}+{\displaystyle \underset{D_d{T}_s}{\overset{T_s}{\int }}\frac{V_H-V}{1+n}dt}=0$$

(26)

The static voltage conversion ratio of the converter in the discharge mode can be derived as follows

$$M_d=\frac{V_H}{V_L}=\frac{1+n{D}_d}{1-D_d}$$

(27)

Figure 8a shows the relationship between the coupled inductance with different turns ratios and the static voltage conversion ratio M_d of the proposed converter in the discharge mode. For simplicity, assuming that the turns ratio of the coupling inductance is n = 1, the relationship between M_d and D_d is shown in Figure 8b. It can be seen that the static voltage conversion ratio of the proposed converter in the discharge mode has a better performance, compared with the conventional boost converter.

3.2. Boundary Condition Analysis

Charge Mode (UC Charge; Battery Charge)

According to the ampere-second balance principle for the filter capacitor C_L on the low-voltage side, it means that the average current of the filter capacitor should be zero in steady-state, and the sum of the averaged currents I_T1 and I_T2 are equal to the low-side current I_L,BCM (i.e., UC current or battery current), as described below

$$I_{L,BCM}=\frac{V_L}{R_{L,BCM}}=I_{T1}+I_{T2}$$

(28)

$$I_{T1}=\frac{i_{mc1,pk}}{2(1+n)}{D}_c+\frac{i_{mc1,pk}}{2}(1-D_c)$$

(29)

$$I_{T1}=I_{T2}=i_{mc1,pk}(1-D_c)$$

(30)

In (28), R_L,BCM represents the low-side equivalent resistance under boundary-conduction-mode (BCM) condition.

Considering the low-side voltage V_L is constant, the peak value of the magnetizing current i_mc1,pk at BCM in the charge mode can be expressed as

$$i_{mc1,pk}=\frac{V_L}{L_m}(1-D_c)T_s$$

(31)

where T_s is the switching period.

Substituting (29), (30), and (31) into (28), the boundary magnetizing inductance L_mc,BCM in the charge mode can be derived as follows

$$L_{mc,BCM}=\frac{R_{L,BCM}(1-D_d)}{f_s}\left[\frac{1+n(1-D_c)}{1+n}\right]$$

(32)

The boundary time constant τ_c,BCM of the proposed converter in the charge mode can be derived as (33), and the corresponding relationship curve is depicted as shown in Figure 9.

$${\tau }_{c,BCM}=\frac{L_{mc,BCM}{f}_s}{R_{L,BCM}}=(1-D_c)\left[\frac{1+n(1-D_c)}{1+n}\right]$$

(33)

Discharge Mode (UC Discharge; Battery Discharge; Dual-Energy in Series Discharge)

According to the ampere-second balance principle of the filter capacitor C_H on the high-voltage side, it can be shown that the average current on the filter capacitor is zero in steady-state, and the sum of the averaged currents I_N2 and I_N4 are equal to the high-side current I_H,BCM (i.e., DC-bus current) as described below

$$I_{H,BCM}=\frac{V_H}{R_{H,BCM}}=I_{N2}+I_{N4}$$

(34)

$$I_{N2}=I_{N4}=\frac{i_{md1,pk}}{2(1+n)}(1-D_d)$$

(35)

where R_H,BCM represents the high-side equivalent resistance under BCM.

Considering the high-side voltage V_H is constant, the peak value of the magnetizing current i_md1,pk at BCM in the discharge mode can be expressed as follows

$$i_{md1,pk}=\frac{V_H{T}_s}{L_m}\frac{(1-D_d)D_d}{1+n{D}_d}$$

(36)

Substituting (35), (36) into (34) and simplifying it, the boundary magnetizing inductance in the discharge mode can be derived as follows

$$L_{md,BCM}=\frac{R_{H,BCM}}{f_s}\left[\frac{{(1-D_d)}^2{D}_d}{(1+n)(1+n{D}_d)}\right]$$

(37)

The boundary time constant τ_d,BCM of the converter in the discharge mode can be derived as (38), and the corresponding relationship curve is depicted as shown in Figure 10.

$${\tau }_{d,BCM}=\frac{L_{md,BCM}{f}_s}{R_{H,BCM}}=\frac{{(1-D_d)}^2{D}_d}{(1+n)(1+n{D}_d)}$$

(38)

3.3. Voltage and Current Stresses Analyses of Power Devices

3.3.1. Voltage Stress Derivations

The power switching device is the main design considerations when implementing the power converter. The voltage and current stresses of the power device for the converter circuit are analyzed, and then the appropriate components are selected as below.

The multiport switches S₁~S₄ are used as the pre-stage for the discharge mode or post-stage for the charge mode. The voltage stress of the multiport switches S₁ and S₂ is equal to the UC voltage V_U, and the voltage stress of S₃ and S₄ is equal to the battery voltage V_B, as follows

$$V_{S1,\max }=V_{S2,\max }=V_U$$

(39)

$$V_{S3,\max }=V_{S4,\max }=V_B$$

(40)

The voltage stress of the power switches Q₁ to Q₄ for the converter can be expressed as follows

$$V_{Q1,\max }=V_{Q3,\max }=V_H-v_{N2}=\frac{V_H+n{V}_L}{1+n}$$

(41)

$$V_{Q2,\max }=V_{Q4,\max }=V_H-v_{N2}=V_H+n{V}_L$$

(42)

3.3.2. Current Stress Derivations

The root mean square (RMS) current of the magnetizing inductances L_m1 and L_m2 are derived based on the operating state of the proposed converter, as follows

$$I_{m1,rms}=I_{m2,rms}=\sqrt{I_{m1}{}^2+{\left(\frac{\Delta i_{m1}}{2\sqrt{3}}\right)}^2}$$

(43)

where I_m1 and I_m2 are the DC value of the magnetizing current i_m1 and i_m2, respectively; Δi_m1 and Δi_m2 are the magnetizing ripple currents, as follows

$$I_{m1}=I_{m2}=\frac{I_L}{2}\cdot \frac{1+n}{1+n(1-D_c)}$$

(44)

$$\Delta i_{m1}=\Delta i_{m2}=\frac{V_L}{L_m}(1-D_c)T_s$$

(45)

The RMS current of the power switches Q₁~Q₄ of the proposed converter in the charge mode can be derived as follows

$$I_{Q1,rms}=I_{Q3,rms}=I_{m1,rms}\sqrt{1-D_c}$$

(46)

$$I_{Q2,rms}=I_{Q4,rms}=\frac{I_{m1,rms}}{1+n}\sqrt{D_c}$$

(47)

The RMS current of the filter capacitors C_L and C_H of the proposed converter in the charge mode can be derived as follows

$$I_{CL,rms}=\sqrt{I_{T1,rms}{}^2+I_{T2,rms}{}^2-I_L{}^2}$$

(48)

$$I_{CH,rms}=\sqrt{I_{Q2,rms}{}^2+I_{Q4,rms}{}^2-I_H{}^2}$$

(49)

where

$$I_{T1,rms}=I_{T2,rms}=I_{m1,rms}\sqrt{\frac{D_c}{{(1+n)}^2}+(1-D_c)}$$

(50)

4. Simulated and Experimented Results

The realized converter prototype is shown in Figure 11, and

Table 1. Specifications and circuit parameters of the realized power converter.

Symbol	Descriptions	Specifications
VH (Vbus)	high-side voltage (DC-bus voltage)	72 V
VL	low-side voltage
VB	battery voltage	20 V~26 V
VU	UC voltage	0 V~48 V
Po	rated output power	500 W
fs	switching frequency	20 kHz
Symbol	Descriptions	Parameters
Lm1, Lm2	magnetizing inductances of the coupled inductors	250 μH
n	turns ratio of the coupled inductors	1
CH	high-side capacitor	2400 μF
CL	low-side capacitor	800 μF

shows the electrical specifications and the circuit parameters of the realized power converter. For the convenience of the experiments, in the charge mode, the power supply (ITECH IT6726G) was used as the DC-bus on the high-voltage side, and the electronic load (ITECH IT8814B) was used as the UC or the battery on the low-voltage side. Conversely, in the discharge mode, the power supply was used as the UC, the battery, or the dual-energy storage in series.

UC Charge Mode

Figure 12 and Figure 13 show the waveforms of the gate signals of Q₂ and Q₄, the primary-side currents of the coupled inductor (i_T1, i_T2), the secondary-side currents of the coupled inductor (i_N2, i_N4), and the low-side voltage V_U in the UC charge mode with full load condition, respectively. In this mode, the UC voltage was about 48 V, the duty ratio of the switches Q₂ and Q₄ was set to 80% (i.e., D_c = 0.8), the DC values of the primary currents (i_T1, i_T2) and secondary currents (i_N2, i_N4) of the coupled inductance were about 5.2 A and 3.5 A, respectively.

Figure 14 shows the waveforms of the steady-state switching voltages across the power devices in the UC charge mode. The results showed that the steady-state switching voltages across the lower-leg MOSFETs Q₁ and Q₃ were about 60 V, and the steady-state switching voltages across the upper-leg MOSFETs Q₂ and Q₄ were about 120 V. It could be seen that in Figure 14, the simulation and the experimental results were consistent and corresponded to (41) and (42).

Battery Charge Mode

Figure 15 and Figure 16 show the waveforms of the gate signals of Q₂ and Q₄, the primary-side currents of the coupled inductor (i_T1, i_T2), the secondary-side currents of the coupled inductor (i_N2, i_N4), and the low-side voltage V_U in the battery charge mode with full load condition, respectively.

In this mode, the battery voltage was about 24 V, the duty ratio of the switches Q₂ and Q₄ was set to 50% (i.e., D_c = 0.5), and the DC values of the primary currents (i_T1, i_T2) and secondary currents (i_N2, i_N4) of the coupled inductance were about 10.4 A and 3.5 A, respectively. It could be seen that in Figure 15 and Figure 16, the simulation and the experimental results were consistent.

Figure 17 shows the waveforms of the steady-state switching voltages across the power devices in the battery charge mode. The results showed that the steady-state switching voltages across the lower-leg MOSFETs Q₁ and Q₃ were about 48 V, and the steady-state switching voltages across the upper-leg MOSFETs Q₂ and Q₄ were about 96 V. It could be seen that in Figure 17, the simulation and the experimental results were consistent and corresponded to (41) and (42).

UC Discharge Mode

Figure 18 and Figure 19 show the waveforms of the gate signals of Q₂ and Q₄, the primary-side currents of the coupled inductor (i_T1, i_T2), the secondary-side currents of the coupled inductor (i_N2, i_N4), and the high-side voltage V_H in the UC discharge mode with full load condition, respectively.

In this mode, the DC-bus voltage was about 72 V, the duty ratio of the switches Q₁ and Q₃ was set to 20% (i.e., D_d = 0.2), and the DC values of the primary currents (i_T1, i_T2) and secondary currents (i_N2, i_N4) of the coupled inductance were about 5.2 A and 3.5 A, respectively. It could be seen that in Figure 18 and Figure 19, the simulation and the experimental results were consistent.

Figure 20 shows the waveforms of the steady-state switching voltages across the power devices in the UC discharge mode. The results showed that the steady-state switching voltages across the lower-leg MOSFETs Q₁ and Q₃ were about 60 V, and the steady-state switching voltages across the upper-leg MOSFETs Q₂ and Q₄ were about 120 V. It could be seen that in Figure 20, the simulation and the experimental results were consistent and corresponded to (41) and (42).

Dual-Energy in Series Discharge Mode

Figure 21 and Figure 22 show the waveforms of the gate signals of Q₂ and Q₄, the primary-side currents of the coupled inductor (i_T1, i_T2), the secondary-side currents of the coupled inductor (i_N2, i_N4), and the high-side voltage V_H in the dual-energy discharge mode with full load condition, respectively.

In this mode, the DC-bus voltage was about 72 V, the low-side voltage V_L was 44 V, the duty ratio of the switches Q₁ and Q₃ was set to 25% (i.e., D_d = 0.25), and the DC values of the primary currents (i_T1, i_T2) and secondary currents (i_N2, i_N4) of the coupled inductance were about 5.8 A and 3.5 A, respectively. It could be seen that in Figure 21 and Figure 22, the simulation and the experimental results were consistent.

Figure 23 shows the waveforms of the steady-state switching voltages across the power devices in the dual-energy in series discharge mode. The results showed that the steady-state switching voltages across the lower-leg MOSFETs Q₁ and Q₃ were about 58 V, and the steady-state switching voltages across the upper-leg MOSFETs Q₂ and Q₄ were about 116 V. It could be seen that in Figure 23, the simulation and the experimental results were consistent and corresponded to (41) and (42).

Efficiency Measurement

The system used two power analyzers (YOKOGAWA WT310) connected to the input and output of the realized converter prototype. As could be seen in Figure 24, in the UC charge mode, the highest efficiency point was 97.4%; in the battery charge mode, the highest efficiency point was 95.5%; in the UC discharge mode, the highest efficiency point was 97.2%; in the dual-energy in series discharge mode, the highest efficiency point was 97.1%; in the battery discharge mode, the highest efficiency point was 95.3%.

5. Conclusions

This study proposed a patented bidirectional power converter that used dual-energy storage as input sources and incorporated a coupled inductor to obtain a higher voltage conversion ratio. The converter control used IPWM control to achieve low current ripple, dissipate low side current stress, and reduce the conduction loss of the power MOSFET. Moreover, the proposed bidirectional power converter in this study also discussed the steady-state operation in the charge mode and discharge mode, respectively. The voltage conversion ratio, boundary conditions, and voltage and current stress of each power component of the converter were analyzed. Finally, this study implemented a converter prototype with a 500 W power rating for verification. The simulation results and the experimental results were consistent; the highest efficiency points of the realized prototype were 97.4%, 95.5%, 97.2%, 97.1%, and 95.3% for the UC charge mode, battery charge mode, UC discharge mode, the dual-energy in series discharge mode, and battery discharge mode, respectively. In summary, this paper demonstrated that the proposed bidirectional power converter could be potentially applied to produce hybrid power architecture (has been patented [37]).