﻿ 基于可重构电路的电池组充电均衡方法
 上海理工大学学报  2023, Vol. 45 Issue (5): 468-476 PDF

1. 上海理工大学 光电信息与计算机工程学院，上海 200093;
2. 上海理工大学 理学院，上海 200093

Battery pack charging equalization method based on reconfigurable circuit
REN Zihao1, TIAN Engang1, WANG Licheng1, LIU Shuai2
1. School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China;
2. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
Abstract: An improved reconfigurable equalization circuit was proposed to solve the problem of battery voltage inconsistency caused by voltage drop after constant current charging. During the charging process of the battery pack, the improved reconfigurable equalization circuit can be equivalent to the traditional reconfigurable circuit, which controls the charging status of each battery through the reconfigurable circuit to achieve equalization during charging. After charging was completed and a certain period elapses, the Buck-Boost circuit in the improved reconfigurable circuit was used for rebalancing. The improved reconfigurable circuit can rebalance the battery pack voltage inconsistency caused by voltage drop while ensuring charging balance. Finally, a physical platform was built to verify the performance of the improved reconfigurable equalization circuit and compared it with the traditional reconfigurable circuit. The experimental results show that the equalization circuit has good performance.
Key words: lithium-ion battery pack     reconfigurable circuit     active equalization     voltage drop

1 锂电池建模及均衡电路拓扑 1.1 锂电池模型的建立

 图 1 锂离子电池一阶RC模型 Fig. 1 First-order RC model for lithium-ion batteries

 ${U_{\rm{t}}} = {U_{{\rm{OCV}}}} + {U_{\rm{p}}} + {I_0}{R_0}$ (1)

1.2 可重构均衡电路

 图 2 可重构均衡电路示意图 Fig. 2 Schematic diagram of reconfigurable equalization circuit

 图 3 可重构均衡电路 Fig. 3 Reconfigurable equalization circuit

1.3 改进后的可重构均衡电路

 图 4 改进后的可重构电路 Fig. 4 Improved reconfigurable circuit

 图 5 Buck-Boost电路 Fig. 5 Buck-Boost circuit

2 均衡策略 2.1 基于一致性的充电均衡方案

 ${\boldsymbol{L }}= {\boldsymbol{\varDelta}} - {\boldsymbol{A}}$ (2)

 ${\boldsymbol{K }}= {\rm{diag}}{({k_i})_n}$ (3)

a. 参考点至少要与一个节点相连接。

b.与参考点相连的节点必须为生成树的根。

 图 6 电池组通信拓扑图示 Fig. 6 Battery pack communication topology diagram

 ${e_i} = {k_i}({x_0} - {x_i}) + \sum\limits_{j \in {N_i}} {{a_{ij}}({x_j} - {x_i})}$ (4)

 ${q_i} = {\rm{sign}}({e_i})$ (5)

${q}_{i}$ =1时，开关 ${S}_{{\rm{a}},i}$ 断开， ${S}_{{\rm{b}},i}$ 闭合；当 ${q}_{i}$ =0时，开关 ${S}_{{\rm{a}},i}$ 闭合， ${S}_{{\rm{b}},i}$ 断开。

 ${\rm{sign}}({e_i}) = \left\{ \begin{gathered} 1,\qquad \forall {e_i} \leqslant 0 \\ 0 ,\qquad 其他 \\ \end{gathered} \right.$ (6)

${x}_{0}$ ${x}_{i}$ ${e}_{i}$ 进行增广，可得

 ${\boldsymbol{X}} = {[{x_1}{\text{ }}{x_2}{\text{ }} \cdots {\text{ }}{x_n}]^{\rm{T}}}$ (7)
 ${{\boldsymbol{X}}_0} = {[{x_0}{\text{ }}{x_0}{\text{ }} \cdots {\text{ }}{x_0}]^{\rm{T}}}$ (8)
 ${\boldsymbol{E }}= {[{e_1}{\text{ }}{e_2}{\text{ }} \cdots {\text{ }}{e_n}]^{\rm{T}}}$ (9)

 $\begin{split} {e_i} = &{k_i}{x_0} - {k_i}{x_i} + \sum\limits_{j \in {N_i}} {{a_{ij}}{x_j} - \sum\limits_{j \in {N_i}} {{a_{ij}}{x_i}} } = \\& - ({d_i} + {k_i}){x_i} + {k_i}{x_0} + \sum\limits_{j \in {N_i}} {{a_{ij}}{x_j}} \end{split}$ (10)

 $\begin{split} {\boldsymbol{E}} = &- ({\boldsymbol{\varDelta}} + {\boldsymbol{K}}){\boldsymbol{X}} + {\boldsymbol{K}}{{\boldsymbol{X}}_0} + {\boldsymbol{A}}{\boldsymbol{X}} {\text{=}} \\ &- ({\boldsymbol{\varDelta}} - {\boldsymbol{A}}){\boldsymbol{X}} + {\boldsymbol{K}}({{\boldsymbol{X}}_0} - {\boldsymbol{X}}) {\text{=}} \\ & - {\boldsymbol{L}}{\boldsymbol{X}} + {\boldsymbol{K}}({{\boldsymbol{X}}_0} - {\boldsymbol{X}}) \end{split}$ (11)

 $\begin{split} {\boldsymbol{E}} = &{\boldsymbol{L}}{{\boldsymbol{X}}_0} - {\boldsymbol{LX}} + {\boldsymbol{K}}({{\boldsymbol{X}}_0} - {\boldsymbol{X}}) {\text{=}}\\& ({\boldsymbol{L}} + {\boldsymbol{K}})({{\boldsymbol{X}}_0} - {\boldsymbol{X}}) \end{split}$ (12)

2.2 充电结束后再均衡方案

 图 7 电感电流的波形 Fig. 7 Operational waveforms of the inductor current

Buck-Boost均衡电路（图5）中， ${B}_{1}$ ${B}_{2}$ 表示锂电池， ${S}_{1}$ ${S}_{2}$ 表示开关， ${R}_{1}$ ${R}_{2}$ 都包含了电池、开关和电路的内阻，L表示电感。假设电池 ${B}_{1}$ 向电池 ${B}_{2}$ 转移能量，电池 ${B}_{1}$ ${B}_{2}$ 的电压可表示为 ${U}_{{{B}}_1}$ ${U}_{{{B}}_2}$ ，流经电池 ${B}_{1}$ 的电流为 ${i}_{1}\left(t\right)$ ，流经电池 ${B}_{2}$ 的电流为 ${i}_{2}\left(t\right)$

 $L\frac{{{\rm{d}}\;{i_1}(t)}}{{{\rm{d}}\;t}} + {i_1}(t){R_1} = {U_{{{B}}_1}}$ (13)
 $- L\frac{{{\rm{d}}\;{i_2}(t)}}{{{\rm{d}}\;t}} + {i_2}(t){R_2} = {U_{{{B}}_2}}$ (14)

 ${I_{L,\max }} = {i_1}(DT)$ (15)
 ${I_{L,\min }} = {i_2}(T)$ (16)

 ${I_{L,\max }} = \frac{{{U_{{B_1}}}{R_2}(1 - \alpha ) - {U_{{B_2}}}{R_1}(\alpha - \alpha \beta )}}{{{R_1}{R_2}(1 - \alpha \beta )}}$ (17)
 ${I_{L,\min }} = \frac{{{U_{B_1}}{R_2}(b - \alpha \beta ) - {U_{B_2}}{R_1}(1 - \beta )}}{{{R_1}{R_2}(1 - \alpha \beta )}}$ (18)

 ${D_L} = - \frac{L}{{RT}}\ln \frac{{{U_{B_1}} + {U_{B_2}}}}{{{U_{B_1}} + {U_{B_2}}{{\rm{e}}^{\frac{{RT}}{L}}}}}$ (19)

$D > {D}_{L}$ 时，电路将工作在CCM下。

3 实验验证

 图 8 实验验证平台 Fig. 8 Experimental verification platform

 图 9 均衡流程图 Fig. 9 Equalization flowchart

 图 10 恒流充电过程电池电压变化曲线 Fig. 10 Battery voltage change curve during constant current charging

 图 11 再均衡过程中电压变化曲线 Fig. 11 Voltage variation curve during rebalance process

 图 12 恒流恒压充电曲线 Fig. 12 Constant current and constant voltage charging curve

4 结　论

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