# Bi-Directional Cuk Equalizer-Based Li-Ion Battery Pack Equalization Control Strategy Research

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Functioning of the Equalization Circuit

#### 2.1. BCEQ System Structure

#### 2.2. Working Principle of BCEQ

#### 2.2.1. Battery Selection Network

#### 2.2.2. Analysis of the Operating State of BCEQ

## 3. Phased VFPID Equilibrium Strategy Design

#### 3.1. Control Scheme for Phased Equalization

#### 3.2. Equilibrium Strategy Based on VFPID Algorithm

#### 3.2.1. Control Rule Design

- When both $\overline{SOC}$ and $\Delta SOC$ are larger, to prevent the battery pack from overcharging, use the middle current value for equalization;
- When $\overline{SOC}$ is large and $\Delta SOC$ is small, a small current equalization can be used;
- When $\overline{SOC}$ is small and $\Delta SOC$ is large, high current equalization can be used to increase the equalization speed.

- When there is a great disparity between $\overline{SOC}$ and $\Delta SOC$, utilize the higher $\Delta {k}_{p}$, the smaller $\Delta {k}_{i}$, and the smaller $\Delta {k}_{d}$;
- When the values of $\overline{SOC}$ and $\Delta SOC$ are close, use the smaller $\Delta {k}_{p}$; $\Delta {k}_{i}$ should be smaller or take zero, the larger $\Delta {k}_{d}$;
- When the values of $\overline{SOC}$ and $\Delta SOC$ are large, in order to avoid excessive equalization current, use the appropriate size of $\Delta {k}_{p}$, the larger $\Delta {k}_{d}$.

#### 3.2.2. Scaling Factor Design

## 4. Simulation Experiment Verification and Analysis

#### 4.1. Equilibrium Topology Validation

#### 4.2. Equalization Control Strategy Verification

#### 4.3. Verification of the Equalization Scheme under Dynamic DST Conditions

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

BCEQ | Bidirectional Cuk Equalizer |

VFPID | Variable-domain fuzzy PID |

FPID | Fuzzy PID |

DST | Dynamic Stress Test |

SOC | State of Charge |

PWM | Pulse Width Modulation |

CCM | Continuous Conduction Mode |

UKF | Unscented Kalman Filter |

## References

- Chen, Z.; Liao, W.; Li, P.; Tan, J.; Chen, Y. Simple and high-performance cell balancing control strategy. Energy Sci. Eng.
**2022**, 10, 3592–3601. [Google Scholar] [CrossRef] - Wu, L.; Pang, K.; Zheng, Y.J.; Huang, P.; Chen, Y. A multi-module equalization system for lithium-ion battery packs. Int. J. Energy Res.
**2022**, 46, 2771–2782. [Google Scholar] [CrossRef] - Du, G.; Zhang, G.; Yu, S.S.; Iu, H.H.; Lin, W.; Le, W.; Zhang, Y. An any-unit-to-any-unit method for hybrid-structured voltage equalizer in series-connected battery/super-capacitor strings. Int. J. Circuit Theory Appl.
**2022**, 50, 2016–2034. [Google Scholar] [CrossRef] - Cui, H.; Wei, Z.; He, H.; Li, J. Novel reconfigurable topology-enabled hierarchical equalization of lithium-ion battery for maximum capacity utilization. IEEE Trans. Ind. Electron.
**2023**, 70, 396–406. [Google Scholar] [CrossRef] - Geethanjali, S.; Vijayakumar, K. Testing and implementation of dual way DC-DC converter for electric vehicle power train system. IEICE Electron. Express
**2022**, 19, 20220343. [Google Scholar] [CrossRef] - Fesenko, A.; Matiushkin, O.; Husev, O.; Vinnikov, D.; Strzelecki, R.; Kołodziejek, P. Design and Experimental Validation of a Single-Stage PV String Inverter with Optimal Number of Interleaved Buck-Boost Cells. Energies
**2021**, 14, 2448. [Google Scholar] [CrossRef] - Liao, L.; Chen, H. Research on two-stage equalization strategy based on fuzzy logic control for lithium-ion battery packs. J. Energy Storage
**2022**, 50, 104321. [Google Scholar] [CrossRef] - Li, Y.; Yin, P.; Chen, J. Active Equalization of Lithium-Ion Battery Based on Reconfigurable Topology. Appl. Sci.
**2023**, 13, 1154. [Google Scholar] [CrossRef] - Ye, Y.; Cheng, K.W.E.; Fong, Y.C.; Xue, X.; Lin, J. Topology, modeling, and design of switched-capacitor-based cell balancing systems and their balancing exploration. IEEE Trans. Power Electron.
**2016**, 32, 4444–4454. [Google Scholar] [CrossRef] - Miao, J.; Shen, C.; Bao, Y. Research on Bidirectional Active Equalization Control Strategy of Lithium Battery Pack for Energy Storage. In Proceedings of the 2019 IEEE 3rd International Electrical and Energy Conference (CIEEC), Beijing, China, 7–9 September 2019; pp. 658–661. [Google Scholar]
- Wei, Z.; Wang, H.; Lu, Y.; Shu, D.; Ning, G.; Fu, M. Bidirectional Constant Current String-to-Cell Battery Equalizer Based on L2C3 Resonant Topology. IEEE Trans. Power Electron.
**2022**, 38, 666–677. [Google Scholar] [CrossRef] - Turksoy, A.; Teke, A. A fast and energy-efficient nonnegative least square-based optimal active battery balancing control strategy for electric vehicle applications. Energy
**2023**, 262, 125409. [Google Scholar] [CrossRef] - Habib, A.A.; Hasan, M.K.; Islam, S.; Ahmed, M.M.; Aman, A.H.M.; Bagwari, A.; Khan, S. Voltage equalization circuit for retired batteries for energy storage applications. Energy Rep.
**2022**, 8, 367–374. [Google Scholar] [CrossRef] - Dam, S.K.; John, V. Low-frequency selection switch based cell-to-cell battery voltage equalizer with reduced switch count. IEEE Trans. Ind. Appl.
**2021**, 14, 2448. [Google Scholar] [CrossRef] - Xiong, H.; Song, D.; Shi, F.; Wei, Y.; Jinzhen, L. Novel voltage equalisation circuit of the lithium battery pack based on bidirectional flyback converter. IET Power Electron.
**2020**, 13, 2194–2200. [Google Scholar] [CrossRef] - Liao, L.; Chen, H.; Sun, S.; Li, H.; Jiang, J.; Wu, T. Research on Equalization Strategy Based on Credibility Factor Inference for Lithium-Ion Battery Packs. IEEE Access
**2022**, 10, 107980–107992. [Google Scholar] [CrossRef] - Feng, F.; Song, B.; Xu, J.; Na, W.; Zhang, K.; Chai, Y. Multiple time scale state-of-charge and capacity-based equalisation strategy for lithium-ion battery pack with passive equaliser. J. Energy Storage
**2022**, 53, 105196. [Google Scholar] [CrossRef] - Li, P.; Liu, J.; Deng, Z.; Yang, Y.; Lin, X.; Couture, J.; Hu, X. Increasing energy utilization of battery energy storage via active multivariable fusion-driven balancing. Energy
**2022**, 243, 122772. [Google Scholar] [CrossRef] - Kamel, M.; Sankaranarayanan, V.; Zane, R.; Maksimović, D. State-of-charge balancing with parallel and series output connected battery power modules. IEEE Trans. Power Electron.
**2022**, 37, 6669–6677. [Google Scholar] [CrossRef] - Cui, X. Online temperature distribution estimation of lithium-ion battery considering non-uniform heat generation characteristics under boundary cooling. Appl. Therm. Eng.
**2023**, 225, 120206. [Google Scholar] [CrossRef] - Galvão, J.R.; Calligaris, L.B.; de Souza, K.M.; Gotz, J.D.; Junior, P.B.; Corrêa, F.C. Hybrid Equalization Topology for Battery Management Systems Applied to an Electric Vehicle Model. Batteries
**2022**, 8, 178. [Google Scholar] [CrossRef] - Barreras, J.V.; de Castro, R.; Wan, Y.; Dragicevic, T. A consensus algorithm for multi-objective battery balancing. Energies
**2021**, 14, 4279. [Google Scholar] [CrossRef] - Ouyang, Q.; Zhang, Y.; Ghaeminezhad, N.; Chen, J.; Wang, Z.; Hu, X.; Li, J. Module-based active equalization for battery packs: A two-layer model predictive control strategy. IEEE Trans. Transp. Electrif.
**2021**, 8, 149–159. [Google Scholar] [CrossRef] - Lin, J.; Yang, X.; Zhou, J.; Wang, G.; Liu, J.; Yuan, Y. Algorithm of BPNN-UKF based on a fusion model for SOC estimation in lithium-ion batteries. IET Power Electron.
**2022**, 1–12. [Google Scholar] [CrossRef] - Zhang, X.; Zhang, R. Estimation of Lithium Battery SOC Based on Fuzzy Unscented Kalman Filter Algorithm. In Proceedings of the 2021 IEEE/IAS Industrial and Commercial Power System Asia (ICPS Asia), Chengdu, China, 18–21 July 2021; pp. 200–204. [Google Scholar]
- Wu, T.; Qi, Y.; Liao, L.; Ji, F.; Chen, H. Research on equalization strategy of lithium-ion batteries based on fuzzy logic control. J. Energy Storage
**2021**, 40, 102722. [Google Scholar] [CrossRef] - Yang, D.; Wang, F.; Qian, K.; Jiao, Z. Research on charge-discharge equalization strategy of aviation battery based on Gaussian variation function. In Proceedings of the 2021 IEEE 2nd International Conference on Information Technology, Big Data and Artificial Intelligence (ICIBA), Chongqing, China, 17–19 December 2021; pp. 819–822. [Google Scholar]
- Nie, W.; Chen, Z. Composite Active Equilibrium Method for Lithium Ion Battery Pack. In Proceedings of the 2019 IEEE 3rd International Electrical and Energy Conference (CIEEC), Beijing, China, 7–9 September 2019; pp. 1071–1075. [Google Scholar]
- Farzan Moghaddam, A.; Van den Bossche, A. A Ćuk converter cell balancing technique by using coupled inductors for lithium-based batteries. Energies
**2019**, 12, 2881. [Google Scholar] [CrossRef] [Green Version]

**Figure 4.**(

**a**) Bidirectional Cuk converter; (

**b**) simplified circuit; (

**c**) Stage 1 operating state; and (

**d**) Stage 2 operating state.

**Figure 5.**(

**a**) Physical circuit diagram and (

**b**) waveforms of switching control signal and inductor current.

**Figure 8.**(

**a**) Affiliation function of $SO{C}_{ave}$; (

**b**) Affiliation function of $SO{C}_{dif}$; (

**c**) Affiliation function of I.

**Figure 10.**Equilibrium process of the four circuits in the static state: (

**a**) Pattern 1; (

**b**) Pattern 2; (

**c**) Pattern 3; and (

**d**) Pattern 4.

**Figure 11.**Equalization process of four circuits in charging state: (

**a**) Pattern 1; (

**b**) Pattern 2; (

**c**) Pattern 3; and (

**d**) Pattern 4.

**Figure 12.**Equalization process of the four circuits in the discharged state: (

**a**) Pattern 1; (

**b**) Pattern 2; (

**c**) Pattern 3; and (

**d**) Pattern 4.

**Figure 13.**Comparison of equilibrium results: (

**a**) Battery SOC values at the end of equilibrium for the four patterns; (

**b**) Energy Losses.

**Figure 18.**Comparison of equilibrium results: (

**a**) Equalization time and SOC polarization value; (

**b**) Energy Losses.

**Figure 20.**Discharge equalization process under dynamic DST condition: (

**a**) Pattern 1; (

**b**) Pattern 2; (

**c**) Pattern 3; and (

**d**) Pattern 4.

I | $\Delta \mathit{SOC}$ | |||||
---|---|---|---|---|---|---|

XS | S | M | L | VL | ||

$\overline{SOC}$ | S | XS | XS | M | L | VL |

M | XS | S | M | M | L | |

L | S | S | S | M | M |

**Table 2.**Values for parameter adjustments $\Delta {k}_{p}$, $\Delta {k}_{i}$, and $\Delta {k}_{d}$ fuzzy rules.

$\Delta {\mathit{k}}_{\mathit{p}}$/$\Delta {\mathit{k}}_{\mathit{i}}$/$\Delta {\mathit{k}}_{\mathit{d}}$ | $\Delta \mathit{SOC}$ | |||||
---|---|---|---|---|---|---|

XS | S | M | L | VL | ||

$\overline{SOC}$ | S | XS/S/VL | S/S/VL | M/M/VL | L/L/VL | VL/VL/VL |

M | S/L/L | S/VL/M | VL/VL/VL | VL/VL/M | L/VL/M | |

L | M/S/S | M/S/S | VL/S/S | VL/M/S | L/M/S |

Parameters | Values |
---|---|

Nominal battery voltage | 3.7 V |

Battery Capacity | 50 Ah |

Inductor ${L}_{1a}$, ${L}_{1b}$,${L}_{2a}$, ${L}_{2b}$ | 100 μH |

Capacitor ${C}_{1a}$, ${C}_{1b}$ | 20 μF |

Turn on the balanced SOC value | 2% |

Battery Serial Number | Pattern 1 | Pattern 2 | Pattern 3 | Pattern 4 |
---|---|---|---|---|

B1 | 70.83% | 70.74% | 70.85% | 70.83% |

B2 | 70.87% | 70.81% | 70.89% | 70.76% |

B3 | 70.73% | 70.75% | 70.84% | 70.81% |

B4 | 70.71% | 70.83% | 70.75% | 70.74% |

B5 | 70.63% | 70.85% | 70.78% | 70.80% |

B6 | 70.67% | 70.72% | 70.71% | 70.77% |

Battery Serial Number | Pattern 1 | Pattern 2 | Pattern 3 | Pattern 4 |
---|---|---|---|---|

B1 | 60.63% | 60.65% | 60.64% | 61.61% |

B2 | 60.54% | 60.66% | 60.67% | 60.55% |

B3 | 60.68% | 60.63% | 60.57% | 60.57% |

B4 | 60.60% | 60.59% | 60.53% | 61.66% |

B5 | 60.57% | 60.55% | 60.49% | 61.64% |

B6 | 60.47% | 60.51% | 60.48% | 61.50% |

Battery Serial Number | Pattern 1 | Pattern 2 | Pattern 3 | Pattern 4 |
---|---|---|---|---|

B1 | 55.95% | 55.94% | 55.91% | 55.90% |

B2 | 55.99% | 55.91% | 55.89% | 55.91% |

B3 | 55.91% | 55.90% | 55.85% | 55.89% |

B4 | 55.86% | 55.86% | 55.93% | 55.85% |

B5 | 55.79% | 55.84% | 55.79% | 55.87% |

B6 | 55.77% | 55.80% | 55.75% | 55.81% |

Component Number | Pattern 1 | Pattern 2 | Pattern 3 | Pattern 4 |
---|---|---|---|---|

Inductors | 48 | 48 | 20 | 8 |

Capacitors | 48 | 48 | 16 | 16 |

Switch | 48 | 64 | 32 | 128 |

Establishment Costs(USD) | 3335.4 | 3337.4 | 3189 | 3174.8 |

Battery Number | FPID | VFPID | ||||
---|---|---|---|---|---|---|

Static | Charge | Discharge | Static | Charge | Discharge | |

B1 | 71.45% | 52.53% | 70.31% | 71.38% | 52.34% | 76.17% |

B2 | 71.39% | 52.51% | 76.27% | 71.33% | 52.32% | 76.15% |

B3 | 71.32% | 52.47% | 76.25% | 71.28% | 52.30% | 76.14% |

B4 | 71.27% | 52.36% | 76.21% | 71.25% | 52.27% | 76.11% |

B5 | 71.21% | 52.29% | 76.14% | 71.19% | 52.24% | 76.09% |

B6 | 71.12% | 52.25% | 76.07% | 71.16% | 52.23% | 76.08% |

Battery Serial Number | Pattern 1 | Pattern 2 | Pattern 3 | Pattern 4 |
---|---|---|---|---|

B1 | 55.87% | 55.85% | 55.86% | 55.78% |

B2 | 55.85% | 55.82% | 55.84% | 55.75% |

B3 | 55.77% | 55.80% | 55.73% | 55.73% |

B4 | 55.69% | 55.76% | 55.66% | 55.71% |

B5 | 55.65% | 55.68% | 55.59% | 55.64% |

B6 | 55.52% | 55.58% | 55.55% | 55.60% |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, X.; Tan, Z.; Cai, L.; Lei, G.; Dai, N.
Bi-Directional Cuk Equalizer-Based Li-Ion Battery Pack Equalization Control Strategy Research. *World Electr. Veh. J.* **2023**, *14*, 86.
https://doi.org/10.3390/wevj14040086

**AMA Style**

Wang X, Tan Z, Cai L, Lei G, Dai N.
Bi-Directional Cuk Equalizer-Based Li-Ion Battery Pack Equalization Control Strategy Research. *World Electric Vehicle Journal*. 2023; 14(4):86.
https://doi.org/10.3390/wevj14040086

**Chicago/Turabian Style**

Wang, Xiaolu, Zefu Tan, Li Cai, Guoping Lei, and Nina Dai.
2023. "Bi-Directional Cuk Equalizer-Based Li-Ion Battery Pack Equalization Control Strategy Research" *World Electric Vehicle Journal* 14, no. 4: 86.
https://doi.org/10.3390/wevj14040086