# 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 |

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**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% |

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## 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