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

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

- (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

_{1}~S

_{4}) 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 (Q

_{1}~Q

_{4}) are designed to use IPWM control to reduce current stress and ripple on the switch, (2) two-phase coupled inductors T

_{1}and T

_{2}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

_{1}, S

_{4}are turned on, and S

_{2}, S

_{3}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 S

_{2}, S

_{3}are turned on, and S

_{1}, S

_{4}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 S

_{1}, S

_{3}are turned on, and S

_{2}, S

_{4}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

_{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.

- (1)
- the converter operates in continuous conduction mode (CCM);
- (2)
- characteristic of the two-phase coupled inductors T
_{1}and T_{2}are the same, i.e., L_{m}_{1}= L_{m}_{2}, i_{m}_{1}= i_{m}_{2}and n = N_{2}/N_{1}= N_{4}/N_{3}; - (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 Q

_{2}and Q

_{4}are turned on, and Q

_{1}and Q

_{3}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,

**State**

**2.**The equivalent circuit of this state is shown in Figure 5b. The power switches Q

_{2}and Q

_{3}are turned on, and Q

_{1}and Q

_{4}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,

**State 3.**The equivalent circuit of this state is shown in Figure 5c. The power switches Q

_{1}and Q

_{4}are turned on, and Q

_{2}and Q

_{3}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,

**State 4.**The equivalent circuit of this state is shown in Figure 5d. The power switches Q

_{1}and Q

_{3}are turned on, and Q

_{2}and Q

_{4}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,

**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 |

_{c}is the duty ratio of switch Q

_{2}and Q

_{4}for the charge mode, and D

_{d}is the duty ratio of switch Q

_{1}and Q

_{3}for the discharge mode.

_{c}= D

_{d}= 0.5), the only two operating states of the proposed converter are produced.

_{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.

_{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.

**Charge Mode (D**

_{c}< 0.5)_{0}< t ≤ t

_{1}]: state 2; [t

_{1}< t ≤ t

_{2}]: state 4; [t

_{2}< t ≤ t

_{3}]: state 3; [t

_{3}< t ≤ t

_{4}]: state 4.

**Discharge Mode (D**

_{d}< 0.5)_{0}< t ≤ t

_{1}]: state 3; [t

_{1}< t ≤ t

_{2}]: state 1; [t

_{2}< t ≤ t

_{3}]: state 2; [t

_{3}< t ≤ t

_{4}]: state 1.

## 3. Converter Steady-State Analyses

#### 3.1. Static Voltage Conversion Ratio Analysis

**Charge Mode (UC Charge; Battery Charge)**

_{c}can be derived as from (22)–(25).

_{c}of the proposed converter in the charge mode.

_{c}and D

_{c}is shown in Figure 7b.

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

_{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 Q

_{1}and Q

_{3}, the average voltage of the primary side for the coupled inductor during a switching period can be expressed as follows

_{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)**

_{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

_{T}

_{1}and I

_{T}

_{2}are equal to the low-side current I

_{L,BCM}(i.e., UC current or battery current), as described below

_{L,BCM}represents the low-side equivalent resistance under boundary-conduction-mode (BCM) condition.

_{L}is constant, the peak value of the magnetizing current i

_{mc}

_{1,pk}at BCM in the charge mode can be expressed as

_{s}is the switching period.

_{mc,BCM}in the charge mode can be derived as follows

_{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.

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

_{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

_{N}

_{2}and I

_{N}

_{4}are equal to the high-side current I

_{H,BCM}(i.e., DC-bus current) as described below

_{H,BCM}represents the high-side equivalent resistance under BCM.

_{H}is constant, the peak value of the magnetizing current i

_{md}

_{1,pk}at BCM in the discharge mode can be expressed as follows

_{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.

#### 3.3. Voltage and Current Stresses Analyses of Power Devices

#### 3.3.1. Voltage Stress Derivations

_{1}~S

_{4}are used as the pre-stage for the discharge mode or post-stage for the charge mode. The voltage stress of the multiport switches S

_{1}and S

_{2}is equal to the UC voltage V

_{U}, and the voltage stress of S

_{3}and S

_{4}is equal to the battery voltage V

_{B}, as follows

_{1}to Q

_{4}for the converter can be expressed as follows

#### 3.3.2. Current Stress Derivations

_{m}

_{1}and L

_{m}

_{2}are derived based on the operating state of the proposed converter, as follows

_{m}

_{1}and I

_{m}

_{2}are the DC value of the magnetizing current i

_{m}

_{1}and i

_{m}

_{2}, respectively; Δi

_{m}

_{1}and Δi

_{m}

_{2}are the magnetizing ripple currents, as follows

_{1}~Q

_{4}of the proposed converter in the charge mode can be derived as follows

_{L}and C

_{H}of the proposed converter in the charge mode can be derived as follows

## 4. Simulated and Experimented Results

**UC Charge Mode**

_{2}and Q

_{4}, the primary-side currents of the coupled inductor (i

_{T}

_{1}, i

_{T}

_{2}), 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 Q

_{2}and Q

_{4}was set to 80% (i.e., D

_{c}= 0.8), the DC values of the primary currents (i

_{T}

_{1}, i

_{T}

_{2}) and secondary currents (i

_{N}

_{2}, i

_{N}

_{4}) of the coupled inductance were about 5.2 A and 3.5 A, respectively.

_{1}and Q

_{3}were about 60 V, and the steady-state switching voltages across the upper-leg MOSFETs Q

_{2}and Q

_{4}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**

_{2}and Q

_{4}, the primary-side currents of the coupled inductor (i

_{T}

_{1}, i

_{T}

_{2}), the secondary-side currents of the coupled inductor (i

_{N}

_{2}, i

_{N}

_{4}), and the low-side voltage V

_{U}in the battery charge mode with full load condition, respectively.

_{2}and Q

_{4}was set to 50% (i.e., D

_{c}= 0.5), and the DC values of the primary currents (i

_{T}

_{1}, i

_{T}

_{2}) and secondary currents (i

_{N}

_{2}, i

_{N}

_{4}) 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.

_{1}and Q

_{3}were about 48 V, and the steady-state switching voltages across the upper-leg MOSFETs Q

_{2}and Q

_{4}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**

_{2}and Q

_{4}, the primary-side currents of the coupled inductor (i

_{T}

_{1}, i

_{T}

_{2}), the secondary-side currents of the coupled inductor (i

_{N}

_{2}, i

_{N}

_{4}), and the high-side voltage V

_{H}in the UC discharge mode with full load condition, respectively.

_{1}and Q

_{3}was set to 20% (i.e., D

_{d}= 0.2), and the DC values of the primary currents (i

_{T}

_{1}, i

_{T}

_{2}) and secondary currents (i

_{N}

_{2}, i

_{N}

_{4}) 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.

_{1}and Q

_{3}were about 60 V, and the steady-state switching voltages across the upper-leg MOSFETs Q

_{2}and Q

_{4}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**

_{2}and Q

_{4}, 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.

_{L}was 44 V, the duty ratio of the switches Q

_{1}and Q

_{3}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.

_{1}and Q

_{3}were about 58 V, and the steady-state switching voltages across the upper-leg MOSFETs Q

_{2}and Q

_{4}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**

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

T_{1}, T_{2} | Two-phase coupled inductors |

L_{m1}, L_{m2} | Magnetizing inductors of the two-phase coupled inductors |

L_{mc,BCM} | Boundary magnetizing inductance in the charge mode |

L_{md,BCM} | Boundary magnetizing inductance in the discharge mode |

n | Turns ratio of the two-phase coupled inductors (n = N_{2}/N_{1} = N_{4}/N_{3}) |

N_{1} | Primary winding of T_{1} |

N_{2} | Secondary winding of T_{1} |

N_{3} | Primary winding of T_{2} |

N_{4} | Secondary winding of T_{2} |

k | Coupling coefficient |

C_{U} | Input capacitor paralleled with UC |

C_{B} | Input capacitor paralleled with BES |

S_{1}~S_{4} | Power devices of the multiport switch |

Q_{1}~Q_{4} | Power devices of the two-phase bidirectional power converter |

V_{H} | High-side voltage for the DC-bus |

V_{L} | Low-side voltage for UC, BES, or BES/UC dual-energy in series |

V_{U} | UC voltage |

V_{B} | BES voltage |

i_{Bus} | DC-bus current |

i_{Uc} | UC current |

i_{Bat} | BES current |

i_{H} | High voltage side current |

i_{L} | Low voltage side current |

I_{L,BCM} | Low voltage side current under BCM condition |

I_{H,BCM} | High voltage side current under BCM condition |

I_{m1,rms}, I_{m2,rms} | RMS value of the magnetizing currents of the coupled inductors |

I_{T1,rms}, I_{T2,rms} | RMS value of the primary-side currents of the coupled inductors |

v_{N1} | Voltage of the winding N_{1} of the T_{1} |

v_{N2} | Voltage of the winding N_{2} of the T_{1} |

v_{N3} | Voltage of the winding N_{3} of the T_{2} |

v_{N4} | Voltage of the winding N_{4} of the T_{2} |

V_{S1,max}~V_{S4,max} | Switch voltage stress of the multiport switch |

V_{Q1,max}~V_{Q4,max} | Switch voltage stress of the two-phase bidirectional power converter |

i_{T1}, i_{T2} | The primary-side currents of the two-phase coupled inductors |

i_{T} | The sum of the primary-side currents i_{T1} and i_{T2} |

i_{N2}, i_{N4} | The secondary-side currents of the two-phase coupled inductors |

i_{m1}, i_{m2} | Magnetizing inductor currents of the coupled inductors T_{1} and T_{2} |

I_{m1}, I_{m2} | DC value of the magnetizing currents |

i_{mc,pk} | peak value of the magnetizing inductor current under BCM in the charge mode |

i_{md,pk} | peak value of the magnetizing inductor current under BCM in the discharge mode |

Δi_{m1}, Δi_{m2} | Magnetizing ripple currents |

I_{Q1,rms}~I_{Q4,rms} | RMS current of the power switches Q_{1}~Q_{4} |

I_{CH,rms}~I_{CL,rms} | RMS current of the filter capacitors C_{L} and C_{H} |

D_{c}, D_{d} | Duty ratio of charge mode and discharge mode |

T_{s} | Switching period |

τ_{c,BCM} | Boundary time constant in the charge mode |

τ_{d,BCM} | Boundary time constant in the discharge mode |

R_{L,BCM} | Low-side equivalent resistance under BCM condition |

R_{H,BCM} | High-side equivalent resistance under BCM condition |

M_{c} | Static voltage conversion ratio in the charge mode |

M_{d} | Static voltage conversion ratio in the discharge mode |

## References

- Lai, J.S.; Nelson, D.J. Energy management power converters in hybrid electric and fuel cell vehicles. Proc. IEEE
**2007**, 95, 766–777. [Google Scholar] [CrossRef] - Bauman, J.; Kazerani, M. A comparative study of fuel-cell-battery, fuel-cell-ultracapacitor, and fuel-cell-battery-ultracapacitor vehicles. IEEE Trans. Veh. Technol.
**2008**, 57, 760–769. [Google Scholar] [CrossRef] - Khaligh, A.; Li, Z. Battery ultracapacitor fuel cell and hybrid energy storage systems for electric hybrid electric fuel cell and plug-in hybrid electric vehicles: State of the art. IEEE Trans. Veh. Technol.
**2010**, 59, 2806–2814. [Google Scholar] [CrossRef] - Chan, C.C.; Bouscayrol, A.; Chen, K. Electric, hybrid, and fuel-cell vehicles: Architectures and modeling. IEEE Trans. Veh. Technol.
**2010**, 59, 589–598. [Google Scholar] [CrossRef] - Rajashekara, K. Present status and future trends in electric vehicle propulsion technologies. IEEE J. Emerg. Sel. Top. Power Electron.
**2013**, 1, 3–10. [Google Scholar] [CrossRef] - Zhang, Y.; Meng, D.; Zhou, M.; Li, S. Energy management of an electric city bus with battery/ultra-capacitor HESS. In Proceedings of the 2016 IEEE Vehicle Power and Propulsion Conference (VPPC), Hangzhou, China, 17–20 October 2016. [Google Scholar]
- Cheng, Y.H.; Lai, C.M. Control strategy optimization for parallel hybrid electric vehicles using memetic algorithm. Energies
**2017**, 10, 305. [Google Scholar] [CrossRef] [Green Version] - Cheng, L.; Acuna, P.; Aguilera, R.P.; Jiang, J.; Flecther, J.; Baier, C. Model predictive control for energy management of a hybrid energy storage system in light rail vehicles. In Proceedings of the 2017 11th IEEE International Conference on Compatibility, Power Electronics and Power Engineering (CPE-POWERENG), Cadiz, Spain, 4–6 April 2017; pp. 683–688. [Google Scholar]
- Un-Noor, F.; Padmanaban, S.; Mihet-Popa, L.; Mollah, M.N.; Hossain, E.A. Comprehensive study of key electric vehicle (EV) components, technologies, challenges, impacts, and future direction of development. Energies
**2017**, 10, 1217. [Google Scholar] [CrossRef] [Green Version] - Serpi, A.; Porru, M. Modelling and design of real-time energy management systems for fuel cell/battery electric vehicles. Energies
**2019**, 12, 4260. [Google Scholar] [CrossRef] [Green Version] - Schaltz, E.; Khaligh, A.; Rasmussen, P.O. Influence of battery/ultracapacitor energy-storage sizing on battery lifetime in a fuel cell hybrid electric vehicle. IEEE Trans. Veh. Technol.
**2009**, 58, 3882–3891. [Google Scholar] [CrossRef] - Cao, J.; Emadi, A. A new battery/ultracapacitor hybrid energy storage system for electric, hybrid, and plug-in hybrid electric vehicles. IEEE Trans. Power Electron.
**2012**, 27, 122–132. [Google Scholar] - Momayyezan, M.; Hredzak, B.; Agelidis, V.G. A new multiple converter topology for battery/ultracapacitor hybrid energy system. In Proceedings of the Annual Conference of the IEEE Industrial Electronics Society, Yokohama, Japan, 9–12 November 2015; pp. 464–468. [Google Scholar]
- Juned, S.; Mohammad, S.; Bhanabhagvanwala, D. Simulation analysis of battery/ultracapacitor hybrid energy storage system for electric vehicle. In Proceedings of the International Conference on Intelligent Sustainable Systems, Palladam, India, 21–22 February 2019. [Google Scholar]
- Chakraborty, S.; Vu, H.-N.; Hasan, M.M.; Tran, D.-D.; Baghdadi, M.E.; Hegazy, O. DC-DC converter topologies for electric vehicles, plug-in hybrid electric vehicles and fast charging stations: State of the art and future trends. Energies
**2019**, 12, 1569. [Google Scholar] [CrossRef] [Green Version] - Ding, S.; Wei, B.; Hang, J.; Zhang, P.; Ding, M. A Multifunctional Interface Circuit for Battery-Ultracapacitor Hybrid Energy Storage System; NSW: Sydney, Australia, 2017. [Google Scholar]
- Ortúzar, M.; Moreno, J.; Dixon, J. Ultracapacitor-based auxiliary energy system for an electric vehicle: Implementation and evaluation. IEEE Trans. Ind. Electron.
**2007**, 54, 2147–2156. [Google Scholar] [CrossRef] - Machado, F.; Antunes, C.H.; Dubois, M.R.; Trovao, J.P. Semi-active hybrid topology with three-level DC-DC converter for electric vehicle application. In Proceedings of the 2015 IEEE Vehicle Power and Propulsion Conference (VPPC), Montreal, QC, Canada, 19–22 October 2015; pp. 1–6. [Google Scholar]
- Shen, J.; Khaligh, A. A supervisory energy management control strategy in a battery/ultracapacitor hybrid energy storage system. IEEE Trans. Transp. Electrif.
**2015**, 1, 223–231. [Google Scholar] [CrossRef] - Castaings, A.; Lhomme, W.; Trigui, R.; Bouscayrol, A. Practical control schemes of a battery/supercapacitor system for electric vehicle. IET Electr. Syst. Transp.
**2016**, 6, 20–26. [Google Scholar] [CrossRef] - Kuperman, A.; Aharon, I.; Malki, S.; Kara, A. Design of a semiactive battery-ultracapacitor hybrid energy source. IEEE Trans. Power Electron.
**2013**, 28, 806–815. [Google Scholar] [CrossRef] - Onar, O.; Khaligh, A. Dynamic modeling and control of a cascaded active battery/ultra-capacitor based vehicular power system. In Proceedings of the 2008 IEEE Vehicle Power and Propulsion Conference (VPPC), Harbin, China, 3–5 September 2008. [Google Scholar]
- Jing, W.; Lai, C.H.; Wong, S.H.W.; Wong, M.L.D. Battery-supercapacitor hybrid energy storage system in standalone DC microgrids: Areview. IET Renew. Power Gener.
**2017**, 11, 461–469. [Google Scholar] [CrossRef] - Allegre, A.L.; Bouscayrol, A.; Trigui, R. Flexible real-time control of a hybrid energy storage system for electric vehicles. IET Electr. Syst. Transp.
**2013**, 3, 79–85. [Google Scholar] [CrossRef] - Trovão, J.P.F.; Pereirinha, P.G. Control scheme for hybridised electric vehicles with an online power follower management strategy. IET Electr. Syst. Transp.
**2015**, 5, 12–23. [Google Scholar] [CrossRef] - Trovao, J.P.; Silva, M.A.; Dubois, M.R. Coupled energy management algorithm for MESS in urban EV. IET Electr. Syst. Transp.
**2017**, 7, 125–134. [Google Scholar] [CrossRef] - Livreri, P.; Castiglia, V.; Pellitteri, F.; Miceli, R. Design of a battery/ultracapacitor energy storage system for electric vehicle applications. In Proceedings of the IEEE International Forum on Research and Technologies for Society and Industry, Palermo, Italy, 10–13 September 2018; pp. 1–5. [Google Scholar]
- Lu, X.; Wang, H. Optimal sizing and energy management for cost-effective PEV hybrid energy storage systems. IEEE Trans. Ind. Inform.
**2020**, 16, 3407–3416. [Google Scholar] [CrossRef] - Gummi, K.; Ferdowsi, M. Double-input DC–DC power electronic converters for electric-drive vehicles-Topology exploration and synthesis using a single-pole triple-throw switch. IEEE Trans. Ind. Electron.
**2010**, 57, 617–623. [Google Scholar] [CrossRef] - Kumar, L.; Jain, S. Multiple-input DC/DC converter topology for hybrid energy system. IET Power Electron.
**2013**, 6, 1483–1501. [Google Scholar] [CrossRef] - Lai, C.M.; Yang, M.J. A high-gain three-port power converter with fuel cell, battery sources and stacked output for hybrid electric vehicles and DC-microgrids. Energies
**2016**, 9, 180. [Google Scholar] [CrossRef] [Green Version] - Hintz, A.; Prasanna, U.R.; Rajashekara, K. Novel modular multiple-input bidirectional DC-DC power converter (MIPC) for HEV/FCV application. IEEE Trans. Ind. Electron.
**2015**, 62, 3163–3172. [Google Scholar] [CrossRef] - Lai, C.M.; Cheng, Y.H.; Hsieh, M.H.; Lin, Y.C. Development of a bidirectional DC/DC converter with dual-battery energy storage for hybrid electric vehicle system. IEEE Trans. Veh. Technol.
**2018**, 67, 1036–1052. [Google Scholar] [CrossRef] - Hernándeza, J.C.; Ruiz-Rodriguezb, F.J.; Juradoc, F. Modelling and assessment of the combined technical impact of electric vehicles and photovoltaic generation in radial distribution systems. Energy
**2017**, 141, 316–332. [Google Scholar] [CrossRef] - Hernándeza, J.C.; Sanchez-Sutila, F.; Muñoz-Rodríguezb, F.J. Design criteria for the optimal sizing of a hybrid energy storage system in PV household-prosumers to maximize self-consumption and self-sufficiency. Energy
**2019**, 186, 115827. [Google Scholar] [CrossRef] - Gomez-Gonzaleza, M.; Hernandezb, J.C.; Veraa, D.; Juradoa, F. Optimal sizing and power schedule in PV household-prosumers for improving PV self-consumption and providing frequency containment reserve. Energy
**2020**, 191, 116554. [Google Scholar] [CrossRef] - Lai, C.-M.; Yang, C.-Y.; Cheng, Y.-H. Power Supply System and Power Supply Method for Electric Vehicle. Taiwan Patent No. I642575, 1 December 2018. [Google Scholar]

**Figure 1.**Several schemes of interfacing battery energy storage (BES) and ultracapacitor (UC) to the DC-bus in electric vehicle (EV) power train: (

**a**) Directly parallel hybrid scheme; (

**b**) UC/BES scheme; (

**c**) BES/UC scheme; (

**d**) type-I of cascaded scheme; (

**e**) type-II of cascaded scheme; (

**f**) multiple converter parallel scheme.

**Figure 4.**Equivalent circuits of the multiport switch under different operating modes. (

**a**) UC charge mode or discharge mode. (

**b**) Battery charge mode or discharge mode. (

**c**) Battery/UC dual-energy in series discharge mode.

**Figure 5.**Equivalent circuits of the proposed converter. (

**a**) State 1: Q

_{2}, Q

_{4}on, and Q

_{1}, Q

_{3}off. (

**b**) State 2: Q

_{2}, Q

_{3}on, and Q

_{1}, Q

_{4}off. (

**c**) State 3: Q

_{1}, Q

_{4}on, and Q

_{2}, Q

_{3}off. (

**d**) State 4: Q

_{1}, Q

_{3}on, and Q

_{2}, Q

_{4}off. (The arrows in

**green**indicate the charge mode, and the arrows in

**red**indicate the discharge mode.).

**Figure 7.**Converter characteristics in charge mode: (

**a**) relationship diagram of M

_{c}, D

_{c}, and n; (

**b**) relationship diagram of M

_{c}and D

_{c}(n = 1).

**Figure 8.**Converter characteristics in discharge mode: (

**a**) relationship diagram of M

_{d}, D

_{d}, and n; (

**b**) relationship diagram of M

_{d}and D

_{d}(n = 1).

**Figure 12.**Waveforms of the switching gate signals and the primary-side currents of the coupled inductor in the UC recharging mode with D

_{c}= 0.8: (

**a**) simulated and (

**b**) experimental.

**Figure 13.**The waveform of the secondary-side currents of the coupled inductor and UC voltage in the UC charge mode with D

_{c}= 0.8: (

**a**) simulated and (

**b**) experimental.

**Figure 14.**The waveform of switching voltage across the power devices in the UC charge mode with D

_{c}= 0.8: (

**a**) simulated and (

**b**) experimental.

**Figure 15.**Waveforms of the switching gate signals and the primary-side currents of the coupled inductor in the battery charge mode with D

_{c}= 0.5: (

**a**) simulated and (

**b**) experimental.

**Figure 16.**The waveform of the secondary-side currents of the coupled inductor and UC voltage in the battery charge mode with D

_{c}= 0.5: (

**a**) simulated and (

**b**) experimental.

**Figure 17.**The waveform of switching voltage across the power devices in the battery charge mode with D

_{c}= 0.5: (

**a**) simulated and (

**b**) experimental.

**Figure 18.**Waveforms of the switching gate signals and the primary-side currents of the coupled inductor in the UC discharging mode with D

_{d}= 0.2: (

**a**) simulated and (

**b**) experimental.

**Figure 19.**The waveform of the secondary-side currents of the coupled inductor and DC-bus voltage in the UC discharging mode with D

_{d}= 0.2: (

**a**) simulated and (

**b**) experimental.

**Figure 20.**The waveform of switching voltage across the power devices in the UC discharging mode with D

_{d}= 0.2: (

**a**) simulated and (

**b**) experimental.

**Figure 21.**Waveforms of the switching gate signals and the primary-side currents of the coupled inductor in the dual-energy in series discharge mode with D

_{d}= 0.25: (

**a**) simulated and (

**b**) experimental.

**Figure 22.**The waveform of the secondary-side currents of the coupled inductor and DC-bus voltage in the dual-energy in series discharge mode with D

_{d}= 0.25: (

**a**) simulated and (

**b**) experimental.

**Figure 23.**The waveform of switching voltage across the power devices in the dual-energy in series discharge mode with D

_{d}= 0.25: (

**a**) simulated and (

**b**) experimental.

Symbol | Descriptions | Specifications |

V_{H} (V_{bus}) | high-side voltage (DC-bus voltage) | 72 V |

V_{L} | low-side voltage | |

V_{B} | battery voltage | 20 V~26 V |

V_{U} | UC voltage | 0 V~48 V |

P_{o} | rated output power | 500 W |

f_{s} | switching frequency | 20 kHz |

Symbol | Descriptions | Parameters |

L_{m}_{1}, L_{m}_{2} | magnetizing inductances of the coupled inductors | 250 μH |

n | turns ratio of the coupled inductors | 1 |

C_{H} | high-side capacitor | 2400 μF |

C_{L} | low-side capacitor | 800 μF |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lai, C.-M.; Teh, J.; Lin, Y.-C.; Liu, Y.
Study of a Bidirectional Power Converter Integrated with Battery/Ultracapacitor Dual-Energy Storage. *Energies* **2020**, *13*, 1234.
https://doi.org/10.3390/en13051234

**AMA Style**

Lai C-M, Teh J, Lin Y-C, Liu Y.
Study of a Bidirectional Power Converter Integrated with Battery/Ultracapacitor Dual-Energy Storage. *Energies*. 2020; 13(5):1234.
https://doi.org/10.3390/en13051234

**Chicago/Turabian Style**

Lai, Ching-Ming, Jiashen Teh, Yuan-Chih Lin, and Yitao Liu.
2020. "Study of a Bidirectional Power Converter Integrated with Battery/Ultracapacitor Dual-Energy Storage" *Energies* 13, no. 5: 1234.
https://doi.org/10.3390/en13051234