# A High-Gain Reflex-Based Bidirectional DC Charger with Efficient Energy Recycling for Low-Voltage Battery Charging-Discharging Power Control

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## Abstract

**:**

## 1. Introduction

## 2. Operation Principles of the Proposed High-Gain RC-BDC

_{bus}and V

_{bat}are the DC-bus voltage and battery voltage on the high and low sides, respectively; i

_{L}

_{1}and i

_{L}

_{2}are the phase currents of the interleaved charge-pump converter (IBCPC), and i

_{Lt}is the sum of i

_{L}

_{1}and i

_{L}

_{2}; C

_{B}is the charge-pump capacitance; C

_{H}and C

_{L}denote the capacitance on the high and low sides, respectively; Q

_{1}–Q

_{4}and S

_{1}–S

_{4}are the power switches of the IBCPC and the unregulated level converter (ULC), respectively; D denotes the active switch duty cycle of the charging and discharging states; L

_{a}and L

_{b}are the high-frequency filtering inductance; and, C

_{M}

_{1}, C

_{M}

_{2}are DC-link capacitors. The ULC charges and discharges the battery with a conversion ratio of 2:1 (voltage-dividing) and 1:2 (voltage doubling). The IBCPC is used for bidirectional power flow control at high voltage conversion ratios (i.e., high-voltage 380 ± 20 V; low-voltage: 44–56 V).

**Mode 1 (t**Q

_{0}< t ≤ t_{1}):_{1}and Q

_{3}are turned on, whereas Q

_{2}and Q

_{4}are turned turn off; S

_{1}and S

_{3}are turned on, whereas S

_{2}and S

_{4}are turned off. The voltage across inductor L

_{1}is negative, and i

_{L}

_{1}linearly decreases. The voltage across inductor L

_{2}can be obtained by subtracting the charge-pump voltage V

_{CB}and V

_{M}from the high-side voltage V

_{bus}, and its slope is expressed as (V

_{bus}/2 − V

_{M})/L

_{2}.

**Mode 2 (t**Q

_{1}< t ≤ t_{2}):_{3}and Q

_{4}are turned on, whereas Q

_{1}and Q

_{2}are turned off; S

_{1}and S

_{3}are turned on, whereas S

_{2}and S

_{4}are turned off. The voltage across inductors L

_{1}and L

_{2}are negative, and thus, both i

_{L}

_{1}and i

_{L}

_{2}linearly decrease. Their current slopes are expressed as (−V

_{M})/L

_{1}and (−V

_{M})/L

_{2}, respectively.

**Mode 3 (t**Q

_{2}< t ≤ t_{3}]:_{2}and Q

_{4}are turned on, whereas Q

_{1}and Q

_{3}are turned off; S

_{1}and S

_{3}are turned on, whereas S

_{2}and S

_{4}are turned off. The voltage across inductor L

_{1}is equal to the difference between the charge-pump voltage V

_{CB}and V

_{M}, and its slope is (V

_{bus}/2 − V

_{M})/L

_{1}.

**Mode 4 (t**The state of the converter is the same as that of Mode 2.

_{3}< t ≤ t_{4}):_{bat}can be expressed as

**Mode 1 (t**Under this mode, Q

_{5}< t ≤ t_{6}):_{3}and Q

_{4}are open, whereas Q

_{1}and Q

_{2}are closed; S

_{2}and S

_{4}are open, whereas S

_{1}and S

_{3}are closed.

_{1}and L

_{2}linearly increase, which is representative of energy storage. Their current slopes are expressed as (−V

_{M})/L

_{1}and (−V

_{M})/L

_{2}, respectively.

**Mode 2 (t**Under this mode, Q

_{6}< t ≤ t_{7}):_{1}and Q

_{3}are open, whereas Q

_{2}and Q

_{4}are closed; S

_{2}and S

_{4}are open, whereas S

_{1}and S

_{3}are closed. The period of this mode is (1 − D

_{b})T

_{SW}.

_{1}is positive, and i

_{L}

_{1}linearly increases. The voltage across inductor L

_{2}can be obtained by subtracting the charge pump voltage V

_{CB}and V

_{M}from the high-side voltage V

_{H}, and its slope is expressed as (V

_{H}/2 − V

_{M})/L

_{2}.

**Mode 3 (t**Under this mode, the converter works in the same way as in Mode 1.

_{7}< t ≤ t_{8}):**Mode 4 (t**Under this mode, Q

_{8}< t ≤ t_{9}):_{1}and Q

_{3}are open, whereas Q

_{2}and Q

_{4}are closed; S

_{2}and S

_{4}are open, whereas S

_{1}and S

_{3}are closed.

_{2}. The voltage across inductor L

_{1}is equal to the difference between the charge pump voltage V

_{CB}and V

_{M}, and its slope is (V

_{CB}− V

_{M})/L

_{1}.

## 3. Controller Descriptions of the Proposed High-Gain RC-BDC

- (1)
- power switches and diodes are ideal;
- (2)
- equivalent series resistances (ESRs) of all the inductors and capacitors of the converter have precise dynamic model; and,
- (3)
- the converter works under continuous conduction mode (CCM) and ESRs (r
_{L}_{1}= r_{L}_{2}= 180 mΩ; r_{C}_{H}= r_{C}_{L}= r_{CB}= 60 mΩ). The circuit parameters for 500 W rating are L_{1}= L_{2}= 800 μH, C_{L}= C_{H}= 100 μF, C_{B}= 10 μF.

_{bus}), battery current (i

_{bat}) and battery voltage (V

_{bat}) are monitored to determine the converter operating mode.

_{Lt}

_{,}

_{ref}) for the entire system. The equal current sharing between the two interleaved phases are also obtained here. During the system startup, soft start (V

_{conss}) is used to avoid capacitor charge surge that can produce the current that damage the converter components.

_{M}is the constant gain of the PWM generator; G

_{iLtd}is the transfer function from the duty ratio to the total inductor current (i

_{Lt}); C

_{i}indicates the transfer function of current controllers; and, H

_{i}is the sensing gain of the current sensor. In the outer voltage control loop, G

_{vd}is the transfer function from the duty ratio to the middle-link voltage (V

_{M}); C

_{v}indicates the transfer function of output voltage controller; and, H

_{v}indicates the sensing gain of the voltage sensor.

_{M}= 1/100, H

_{i}= H

_{v}= 1.

_{iLtd}is given by Equation (4) and the duty ratio to middle-link voltage G

_{vMd}is given by Equation (5).

_{M}= 1/100, H

_{i}= H

_{v}= 1.

## 4. System Design and Implementations

## 5. Experimental Results

_{bat}rises from 5 A to 10 A and the total inductor current i

_{Lt}rises from 2.5 A to 5 A (100% load). Figure 9 shows the converter waveform in the charging state. The positive charging current i

_{bat}= 10 A, whereas the negative discharging current i

_{bat}= −10 A. During PPP, the total inductor current i

_{Lt}is 5 A, and it becomes −5 A during NPP. The reflex charging frequency is 5-Hz and the corresponding duty cycles for PPP and NPP are about 70% and 15%, respectively. Notably, a lot of methods [25,26,27] can be referred to adjust the reflex charging pattern (such as duty or frequency, etc.) for improving the charging efficiencies in future work.

_{bat}is −12 A and the total inductor current i

_{Lt}is −6 A. Figure 11 shows the charging curve of lead-acid batteries, which shows the reflex charging and constant-voltage charging stages. Reflex charging begins at 46 V and constant-voltage charging begins at 52 V. The charging process ends when the battery current drops to 2 A (about 0.1 C-rate). By recording the charging voltage and current of the battery every minute using the recorder, it is determined that the full charging time is 111 min.

_{bat}and the increased battery temperature curves with respect to the charging time. From Figure 12a, it is clear that the charging time of the proposed RC-BDC and the typical BDC with CC/CV charging profile are about 1.85 h and 2.12 h, respectively. The charging speed of the proposed RC-BDC has been increased by about 12.7% as compared to the typical BDC. According to Figure 12b, the maximum increased in the battery temperature of the proposed RC-BDC and the typical BDC are 5.6 °C and 7 °C, respectively. The results also demonstrated that the maximum battery temperature of the proposed RC-BDC can be reduced by about 25%. This means that the thermal deterioration effect is improved by about 25% with the proposed RC-BDC.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Hatziargyriou, N.; Asano, H.; Iravani, R.; Marnay, C. Microgrids. IEEE Power Energy Mag.
**2007**, 5, 78–94. [Google Scholar] [CrossRef] - Pan, C.T.; Lai, C.M.; Cheng, M.C.; Hsu, L.T. A Low Switch Voltage Stress Interleaved Boost Converter for Power Factor Correction. In Proceedings of the IEEE International Conference on Power Electronics and Drive Systems Conference, Taipei, Taiwan, 2–5 November 2009; pp. 49–54. [Google Scholar]
- Lai, C.M.; Pan, C.T.; Cheng, M.C. High-efficiency modular high step-up interleaved boost converter for dc-microgrid applications. IEEE Trans. Ind. Appl.
**2012**, 48, 161–171. [Google Scholar] [CrossRef] - Chukwu, U.C.; Mahajan, S.M. Real-time management of power systems with V2G facility for smart-grid applications. IEEE Trans. Sustain. Energy
**2014**, 5, 558–566. [Google Scholar] [CrossRef] - Yilmaz, M.; Krein, P.T. Review of the impact of vehicle-to-grid technologies on distribution systems and utility interfaces. IEEE Trans. Power Electron.
**2013**, 28, 5673–5689. [Google Scholar] [CrossRef] - Carrasco, J.M.; Franquelo, L.G.; Bialasiewicz, J.T.; Galván, E.; Guisado, R.C.P.; Prats, M.Á.M.; Leon, J.I.; Moreno-Alfonso, N. Power-electronic systems for the grid integration of renewable energy sources: A survey. IEEE Trans. Ind. Electron.
**2006**, 53, 1002–1016. [Google Scholar] [CrossRef] - Guerrero, J.M.; Blaabjerg, F.; Zhelev, T.; Hemmes, K.; Monmasson, E.; Jemei, S.; Comech, M.P.; Granadino, R.; Frau, J.I. Distributed generation: Toward a new energy paradigm. IEEE Ind. Electron. Mag.
**2010**, 4, 52–64. [Google Scholar] [CrossRef] - Pan, C.T.; Lai, C.M.; Cheng, M.C. A novel integrated single-phase inverter with auxiliary step-up circuit for low-voltage alternative energy source applications. IEEE Trans. Power Electron.
**2010**, 25, 2234–2241. [Google Scholar] [CrossRef] - Vilathgamuwa, D.M.; Gajanayake, C.J.; Loh, P.C. Modulation and control of three-phase paralleled Z-source inverters for distributed generation applications. IEEE Trans. Energy Convers.
**2009**, 24, 173–183. [Google Scholar] [CrossRef] - Lee, J.Y.; Yoon, Y.D.; Kang, J.W. A single-phase battery charger design for LEV based on DC-SRC with resonant valley-fill circuit. IEEE Trans Ind. Electron.
**2015**, 62, 2195–2205. [Google Scholar] [CrossRef] - Lai, C.M.; Lin, Y.C.; Lee, D.S. Study and implementation of a two-phase interleaved bidirectional DC/DC converter for vehicle and dc-microgrid systems. Energies
**2015**, 8, 9969–9991. [Google Scholar] [CrossRef] - Hu, K.W.; Liaw, C.M. Incorporated operation control of DC microgrid and electric vehicle. IEEE Trans. Ind. Electron.
**2016**, 63, 202–215. [Google Scholar] [CrossRef] - Lin, F.J.; Hung, Y.C.; Hwang, J.C.; Chang, I.P.; Tsai, M.T. Digital signal processor-based probabilistic fuzzy neural network control of in-wheel motor drive for light electric vehicle. IET Electr. Power Appl.
**2012**, 6, 47–61. [Google Scholar] [CrossRef] - Ke, Y.L.; Chuang, Y.C.; Kang, M.S.; Wu, Y.K.; Lai, C.M.; Yu, C.C. Solar Power Battery Charger with a Parallel-Load Resonant Converter. In Proceedings of the IEEE Industry Applications Society Annual Meeting, Orlando, FL, USA, 9–13 October 2011. [Google Scholar]
- Liang, T.J.; Wen, T.; Tseng, K.C.; Chen, J.F. Implementation of a regenerative pulse charger using hybrid buck-boost converter. In Proceedings of the IEEE International Conference on Power Electronics and Drive Systems, Denpasar, Indonesia, 25 October 2001; pp. 437–442. [Google Scholar]
- Hua, C.C.; Lin, M.Y. A study of charging control of lead-acid battery for electric vehicles. In Proceedings of the IEEE International Symposium on Industrial Electronics, Cholula, Puebla, Mexico, 4–8 December 2000. [Google Scholar]
- Chen, L.R.; Chu, N.Y.; Wang, C.S.; Liang, R.H. Design of a reflex-based bidirectional converter with the energy recovery function. IEEE Trans. Ind. Electron.
**2008**, 55, 3022–3029. [Google Scholar] [CrossRef] - Wang, T.W.; Yang, M.J.; Shyu, K.K.; Lai, C.M. Design Fuzzy SOC Estimation for Sealed Lead-Acid Batteries of Electric Vehicle in Reflex
^{TM}. In Proceedings of the IEEE International Symposium on Industrial Electronics, Vigo, Spain, 4–7 June 2007; pp. 95–99. [Google Scholar] - Tsai, C.T.; Kuo, Y.C.; Kuo, Y.P.; Hsieh, C.T. A Reflex Charger with ZVS and Non-Dissipative Cells for Photovoltaic Energy Conversion. Energies
**2015**, 8, 1373–1389. [Google Scholar] [CrossRef] - Lai, C.M. Development of a novel bidirectional DC/DC converter topology with high voltage conversion ratio for electric vehicles and DC-microgrids. Energies
**2016**, 9, 410. [Google Scholar] [CrossRef] - Lai, C.M.; Cheng, Y.H.; Li, Y.S.; Li, J.T.; Lin, Y.C. A Reflex-Charging Based Bidirectional DC Charger for Light Electric Vehicle and DC-Microgrid. In Proceedings of the IEEE Region 10 Conference, Penang, Malaysia, 5–8 November 2017; pp. 280–284. [Google Scholar]
- Micro Hybrid & Hybrid Vehicles Explained-Yuasa. Available online: https://www.yuasa.co.uk/info/technical/micro-hybrid-hybrid-vehicles-explained (accessed on 12 February 2018).
- Schaeck, S.; Stoermer, A.O.; Hockgeiger, E. Micro-hybrid electric vehicle application of valve-regulated lead-acid batteries in absorbent glass mat technology: Testing a partial-state-of-charge operation strategy. J. Power Sources
**2009**, 190, 173–183. [Google Scholar] [CrossRef] - Valenciano, J.; Fernndez, M.; Trinidad, F.; Sanz, L. Lead-acid batteries for micro- and mild-hybrid applications. J. Power Sources
**2009**, 187, 599–604. [Google Scholar] [CrossRef] - Chen, L.R. A design of an optimal battery pulse charge system by frequency-varied technique. IEEE Trans. Ind. Electron.
**2007**, 54, 398–405. [Google Scholar] [CrossRef] - Chen, J.H.; Yau, H.T.; Lu, J.H. Chaos embedded particle swarm optimization algorithm-based solar optimal Reflex
^{TM}frequency charge. J. Appl. Res. Technol.**2015**, 13, 321–327. [Google Scholar] [CrossRef] - Wang, Z.; Wang, Y.; Rong, Y.; Li, Z.; Fantao, L. Study on the Optimal Charring Method for Lithium-ion Batteries Used in Electric Vehicles. Energy Procedia
**2016**, 88, 1013–1017. [Google Scholar] [CrossRef]

**Figure 1.**The proposed high-gain reflex-charging-based bidirectional DC charger (RC-BDC): (

**a**) circuit topology [20], (

**b**) battery current waveforms in charging and discharging states.

**Figure 5.**Frequency responses of the loop gain: (

**a**) compensated current loop and (

**b**) compensated voltage loop.

**Figure 12.**The comparison between the proposed RC-BDC and the conventional BDC with the CC/CV charging profile: (

**a**) the battery charging current and (

**b**) the increased battery temperature.

**Figure 13.**Conversion efficiency curves of the developed system for nominal voltage V

_{bat}= 48 V and DC-bus voltage V

_{bus}= 400 V under different loads.

**Figure 14.**The extended galvanic isolated configuration based on the proposed high-gain RC-BDC for safety insulation requirement and higher voltage conversion ratio applications.

Specifications | |

V_{H} (DC-bus Voltage) | 380–410 V |

V_{L} (Battery Voltage) | 44–56 V Nominal: 48 V (four 12 V cells in series) |

Power rating | P_{o}: 500-W |

Switching frequency | f_{s}: 20 kHz |

Parameters | |

Capacitors | C_{H} = C_{L} = 400 μF, C_{M}_{1} = C_{M}_{2} = 100 μF, C _{B} = 10 = 0 μF; |

Inductors | L_{1} = L_{2} = L_{s} = 800 μH; L _{a} = L_{b} = 1.5 μH |

MOSFET | S_{1}–S_{4}: IXFH160N15T2, Q _{1}–Q_{4}: W25NM60 |

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## Share and Cite

**MDPI and ACS Style**

Lai, C.-M.; Li, Y.-H.; Cheng, Y.-H.; Teh, J.
A High-Gain Reflex-Based Bidirectional DC Charger with Efficient Energy Recycling for Low-Voltage Battery Charging-Discharging Power Control. *Energies* **2018**, *11*, 623.
https://doi.org/10.3390/en11030623

**AMA Style**

Lai C-M, Li Y-H, Cheng Y-H, Teh J.
A High-Gain Reflex-Based Bidirectional DC Charger with Efficient Energy Recycling for Low-Voltage Battery Charging-Discharging Power Control. *Energies*. 2018; 11(3):623.
https://doi.org/10.3390/en11030623

**Chicago/Turabian Style**

Lai, Ching-Ming, Yun-Hsiu Li, Yu-Huei Cheng, and Jiashen Teh.
2018. "A High-Gain Reflex-Based Bidirectional DC Charger with Efficient Energy Recycling for Low-Voltage Battery Charging-Discharging Power Control" *Energies* 11, no. 3: 623.
https://doi.org/10.3390/en11030623