# Performance Analysis of a Novel High Frequency Self-Reconfigurable Battery

^{*}

## Abstract

**:**

## 1. Introduction

_{level}resulting in a staircase shape signal of period T and nominal root mean square voltage U

_{rms}, as shown in Figure 1. A cell insertion increases the output voltage of one cell voltage, we name that voltage increment a “Level”, Level 1 being the first step, and Level n, the nth step. A level is not attached to a particular cell, any cell of the battery pack can ensure that level. As shown on Figure 1, each level performs four switching operations within a sinusoidal period, while a H-bridge allows the voltage to be reversed by switching two times less. Therefore, in order to generate a 50-Hz sinusoidal waveform, the switching frequency of a level is 200 Hz when those of the H-bridge is 100 Hz. However, in order to generate an accurate waveform in its steepest part, it is necessary to respect a minimum time TimeStep

_{min}between two level changes. In the case of a sine wave, the minimum time step must be less than or equal to the period of the fundamental harmonic of the voltage over more than six times the number of levels N

_{max}. When taking EU electrical network voltage as an example, which is 230 V

_{RMS}+/− 10% with a frequency of 50 Hz, and using cells which the specified end of discharge threshold is 2800 mV, N

_{max}reaches 128 and the related minimum time step is then about 25 µs, which corresponds to an equivalent switching frequency of 40 kHz. This frequency can be reduced if more than one level can be switched at each control time step. Note that the battery pack could include additional cells that could be used to provide the maximum voltage output in case of cell failures; therefore, the number of cells could be greater than N

_{max}without affecting TimeStep

_{min}. Staircase shape waveform are usually generated from multilevel converters using carrier phase shift Pulse Width Modulation (PWM) or carrier cascaded PWM implemented on Field Programmable Gate Arrays (FPGA) and Digital Signal Processor (DSP) targets [8].

## 2. HF SRB Operating Principle

## 3. HF SRB Simulator

#### 3.1. Cell Selection

#### 3.2. Cell Model

_{0}and a single resistor-capacitor pair R

_{1}C

_{1}, the evolution equations are:

_{0}the cell internal resistance, R

_{1}and C

_{1}the resistor and capacitor values of the parallel circuit, i

_{R}

_{1}the current through the resistor R

_{1}. Cell parameters are identified on an Arbin test bench at some discrete breakpoints. Then it is necessary to interpolate each parameter at the SoC points of interest. To avoid interpolation computations at each time step, interpolated parameters are stored along a discretized SoC grid. The validity of this approach is confirmed in Section 4.1.

#### 3.3. Control Loop Function

#### 3.4. Measurement Error Models

#### 3.5. SoC Estimator

#### 3.6. Cell Balancing

#### 3.7. Implementation

## 4. Simulator Validation

#### 4.1. Arbitrary Waveform Generation Validation

#### 4.2. Comparison to a Real Battery

_{0}× I added to the OCV when a cell is connected). Thus, the unfiltered voltages reached 4 V, causing the BMS to stop charging the battery.

_{0}, R

_{1}, C

_{1}, R

_{2}, C

_{2}. This cell description allows us to compare the balancing dynamics of the simulated battery and the real one.

## 5. Simulations Results

#### 5.1. Application to the New European Driving Cycle (NEDC)

#### 5.2. Effect of the Balancing Criterion

#### 5.3. Cells Capacity Dispersion and Battery Lifetime Improvement over WLTC

_{1}where 2.208 Ah have been used when 2.22 Ah have been used for the HF SRB, which shows the similar use of both batteries with a difference of less than 0.5%.

_{2}with a total of 2.43 Ah provided with the charge balancing strategy and 2.505 Ah for the SoC balancing, which respectively represent 9.87 and 7.1% of unavailable capacity.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Lu, L.; Han, X.; Li, J.; Hua, J.; Ouyang, M. A review on the key issues for lithium-ion battery management in electric vehicles. J. Power Sources
**2013**, 226, 272–288. [Google Scholar] [CrossRef] - Ci, S.; Kin, N.; Wu, D. Reconfigurable battery techniques and systems: A survey. IEEE Access
**2016**, 4, 1175–1189. [Google Scholar] [CrossRef] - Bouchhima, N.; Schnierle, M.; Schulte, S.; Birke, K.P. Active model-based balancing strategy for self-reconfigurable batteries. J. Power Sources
**2016**, 322, 129–137. [Google Scholar] [CrossRef] - Bouchhima, N.; Schnierle, M.; Schulte, S.; Birke, K.P. Optimal energy management strategy for self-reconfigurable batteries. Energy
**2017**, 122, 560–569. [Google Scholar] - D’Arco, S.; Quraan, M.; Tricoli, P.; Piegari, L. Low frequency operation of Modular Multilevel Converters with embedded battery cells for traction drives. In Proceedings of the 2016 International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM), Anacapri, Italy, 22–24 June 2016; pp. 1375–1382. [Google Scholar]
- Simone, D.D.; Piegari, L. Integration of stationary batteries for fast charge EV charging stations. Energies
**2019**, 12, 4638. [Google Scholar] [CrossRef] [Green Version] - Akagi, H.; Maharjan, L. A battery energy storage system based on a multilevel cascade PWM converter. In Proceedings of the 2009 Brazilian Power Electronics Conference, Bonito-Mato Grosso do Sul, Brazil, 27 September–1 October 2009; pp. 9–18. [Google Scholar]
- Zheng, Z.; Wand, K.; Xu, L.; Li, Y. A hybrid cascaded multilevel converter for battery energy management applied in electric vehicles. IEEE Trans. Power Electron.
**2014**, 29, 3537–3546. [Google Scholar] [CrossRef] - Thomas, R.; Despesse, G.; Bacquet, S.; Fernandez, E.; Lopez, Y.; Ramahefa-andry, P.; Cassarino, L. A High Frequency Self-Reconfigurable Battery for Arbitrary Waveform Generation. World Electr. Veh. J.
**2020**, 12, 8. [Google Scholar] [CrossRef] - Despesse, G.; Sanjuan, S.; Gery, S. Battery Monitoring System using switching battery cells. In Proceedings of the RITF Research & Innovation for Transport Systems of the Future, Paris, France, 23 August 2012. [Google Scholar]
- Gao, F.; Gu, X.; Ma, Z.; Zhang, C. Redistributed Pulsewidth Modulation of MMC Battery Energy Storage System under Submodule Fault Condition. IEEE Trans. Power Electron.
**2020**, 35, 2284–2294. [Google Scholar] [CrossRef] - Plett, G.L. Battery Management Systems; Artech House: Norwood, MA, USA, 2015. [Google Scholar]
- Andrea, D. Battery Management Systems for Large Lithium-Ion Battery Packs; Artech House: Norwood, MA, USA, 2010. [Google Scholar]
- Buchmann, I. Battery University 803a: Cell Matching and Balancing. Available online: https://batteryuniversity.com/learn/article/bu_803a_cell_mismatch_balancing (accessed on 14 August 2019).
- Bentley, W.F. Cell balancing considerations for lithium-ion battery systems. In Proceedings of the Annual Battery Conference on Applications and Advances, Long Beach, CA, USA, 14–17 January 1997; pp. 223–226. [Google Scholar]

**Figure 5.**Mean error and maximal error between real and estimated SoC over 100 s of a normalized New European Driving Cycle (NEDC) profile with 20 NMC cells.

**Figure 8.**Simulated and experimental results of the HF SRB charging over the national power grid with a 56% initial State of Charge (SoC) unbalancing.

**Figure 11.**Comparison of charge dispersions between a static battery and a self-reconfiguring battery discharging with Worldwide harmonized Light vehicles Test Cycle (WLTC) vehicle cycles.

Values | Description | |
---|---|---|

${C}_{r}$ | 0.0111 | Rolling friction coefficient |

$g$ | 9.81 N/kg | Acceleration of gravity |

${\rho}_{air}$ | 1.225 kg/m^{3} | Air density |

${S}_{frontal}$ | 1.84 m^{2} | Aerodynamic frontal area |

${C}_{d}$ | 0.22 | Drag coefficient |

$m$ | 1425 kg | Vehicle masse |

${R}_{wheel}$ | 0.35 m | Wheel radius |

${J}_{motor}$ | 0.2 kg m^{2} | Motor inertia |

${J}_{gear}$ | 0.05 kg m^{2} | Gear inertia |

$N$ | 4 | Gear ratio |

${n}_{wheel}$ | 4 | Number of wheels |

${J}_{wheel}$ | 8 kg m^{2} | Wheel inertia |

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**MDPI and ACS Style**

Thomas, R.; Lehmann, F.; Blatter, J.; Despesse, G.; Heiries, V.
Performance Analysis of a Novel High Frequency Self-Reconfigurable Battery. *World Electr. Veh. J.* **2021**, *12*, 10.
https://doi.org/10.3390/wevj12010010

**AMA Style**

Thomas R, Lehmann F, Blatter J, Despesse G, Heiries V.
Performance Analysis of a Novel High Frequency Self-Reconfigurable Battery. *World Electric Vehicle Journal*. 2021; 12(1):10.
https://doi.org/10.3390/wevj12010010

**Chicago/Turabian Style**

Thomas, Rémy, Fanny Lehmann, Jérôme Blatter, Ghislain Despesse, and Vincent Heiries.
2021. "Performance Analysis of a Novel High Frequency Self-Reconfigurable Battery" *World Electric Vehicle Journal* 12, no. 1: 10.
https://doi.org/10.3390/wevj12010010