基于数据-模型驱动的锂离子电池健康状态估计*
方德宇, 楚潇, 刘涛, 李俊夫

Research on Health Assessment Method of Lithium-ion Battery Based on Data-model Hybrid Drive
FANG Deyu, CHU Xiao, LIU Tao, LI Junfu
表1 SP+模型
相应过程描述 模型方程
固相离子扩散 ${{y}_{\mathrm{surf}}}(t)={{y}_{\mathrm{avg}}}(t)+\Delta y(t)$
${{x}_{\mathrm{surf}}}(t)={{x}_{\mathrm{avg}}}(t)-\Delta x(t)$
$\Delta y\left( t \right)=\Delta {{y}_{1}}\left( t \right)+\frac{2}{7}\frac{{{\tau }_{\mathrm{p}}}}{{{Q}_{\mathrm{p}}}}\cdot I\left( t \right)$
$\Delta x\left( t \right)=\Delta {{x}_{1}}\left( t \right)+\frac{2}{7}\frac{{{\tau }_{\mathrm{n}}}}{{{Q}_{\mathrm{n}}}}\cdot I\left( t \right)$
正负集流体处
液相锂离子
浓度差
$\begin{matrix} \Delta c({{t}_{\mathrm{k}+1}})=\Delta c({{t}_{\mathrm{k}}})+ \\ \frac{1}{{{\tau }_{\mathrm{e}}}}\cdot \left[ {{P}_{\mathrm{con}}}\cdot I({{t}_{\mathrm{k}}})-\Delta c({{t}_{\mathrm{k}}}) \right]\cdot ({{t}_{\mathrm{k}+1}}-{{t}_{\mathrm{k}}}) \\ \end{matrix}$
浓差极化过
电势
${{\eta }_{\mathrm{con}}}=\frac{2RT}{F}\left( 1-{{t}_{+}} \right)\cdot \left( \ln \frac{{{c}_{0}}+\Delta {{c}_{0}}(t)}{{{c}_{0}}-\Delta {{c}_{0}}(t)} \right)$
反应极化
过电势
${{\eta }_{\mathrm{act}}}=\frac{2RT}{F}\cdot \left[ \ln \left( \sqrt{m_{\mathrm{n}}^{2}+1}+{{m}_{\mathrm{n}}} \right)+\ln \left( \sqrt{m_{\mathrm{p}}^{2}+1}+{{m}_{\mathrm{p}}} \right) \right]$
${{m}_{\mathrm{n}}}\left( t \right)=\frac{1}{6\cdot {{Q}_{\mathrm{n}}}{{\left( 1-{{x}_{\mathrm{surf}}} \right)}^{0.5}}{{\left( {{x}_{\mathrm{surf}}} \right)}^{0.5}}c_{0}^{0.5}}\cdot {{P}_{\mathrm{act}}}\cdot I\left( t \right)$
${{m}_{\mathrm{p}}}\left( t \right)=\frac{1}{6\cdot {{Q}_{\mathrm{p}}}{{\left( 1-{{y}_{\mathrm{surf}}} \right)}^{0.5}}{{\left( {{y}_{\mathrm{surf}}} \right)}^{0.5}}c_{0}^{0.5}}\cdot {{P}_{\mathrm{act}}}\cdot I\left( t \right)$
欧姆极化过
电势
${{\eta }_{\mathrm{ohm}}}={{R}_{\mathrm{ohm}}}\cdot I\left( t \right)$
端电压 $\begin{matrix} & {{U}_{\mathrm{OCV}}}\left( t \right)={{U}_{\mathrm{p}}}\left( {{y}_{\text{surf}}} \right)-{{U}_{\mathrm{n}}}\left( {{x}_{\text{surf}}} \right)- \\ & \ \ \ {{\eta }_{\text{con}}}\left( t \right)-{{\eta }_{\text{act}}}\left( t \right)-{{\eta }_{\text{ohm}}}\left( t \right) \\ \end{matrix}$