A Comparative Study on Open Circuit Voltage Models for Lithium-ion Batteries

Yu, Quan-Qing; Xiong, Rui; Wang, Le-Yi; Lin, Cheng

doi:10.1186/s10033-018-0268-8

Chinese Journal of Mechanical Engineering

Table 2 OCV models evaluated in this study

From: A Comparative Study on Open Circuit Voltage Models for Lithium-ion Batteries

Model	Reference	OCV model expression
1	[24,25,26]	\(U_{\text{oc}} = K_{0} + K_{1} s + K_{2} /s + K_{3} \ln \left( s \right) + K_{4} \ln \left( {1 - s} \right)\)
2	[27, 28]	\(\begin{aligned} U_{\text{oc}} & = K_{0} + K_{1} s + K_{2} s^{2} + K_{3} /s + K_{4} \ln \left( s \right) \\ & \, + K_{5} \ln \left( {1 - s} \right) \\ \end{aligned}\)
3	[11, 12]	\(\begin{aligned} U_{\text{oc}} & = K_{0} + K_{1} s + K_{2} s^{2} + K_{3} s^{3} + K_{4} /s + K_{5} \ln \left( s \right) \\ & \, + K_{6} \ln \left( {1 - s} \right) \\ \end{aligned}\)
4	[14]	\(U_{\text{oc}} = K_{0} + K_{1} s + K_{2} s^{2} + K_{3} s^{3} + K_{4} \ln \left( s \right) + K_{5} \ln \left( {1 - s} \right)\)
5	[29]	\(U_{\text{oc}} = K_{0} + K_{1} \ln \left( s \right) + K_{2} \ln \left( {1 - s} \right)\)
6	[16]	\(U_{\text{oc}} = K_{0} + K_{1} s + K_{2} s^{2} + K_{3} s^{3} + K_{4} \exp (K_{5} s)\)
7	[15]	\(U_{\text{oc}} = K_{0} + K_{1} s + K_{2} \left( {1 - \exp (\alpha s)} \right) + K_{3} (1 - exp(\beta \left( {1 - s} \right)^{ - 1} ))\)
8	[17]	\(\begin{aligned} U_{\text{oc}} & = K_{0} s + K_{1} \left( {1 + \exp (\alpha_{1} (s - \beta_{1} )} \right)^{ - 1} + K_{2} \left( {1 + \exp (\alpha_{2} s)} \right)^{ - 1} \\ & + K_{3} \left( {1 + \exp (\alpha_{3} (s - \beta_{2} )} \right)^{ - 1} + K_{4} \left( {1 + \exp (\alpha_{4} (s - 1)} \right)^{ - 1} + K_{5} \, \\ \end{aligned}\)
9	[18, 30]	\(U_{\text{oc}} = K_{0} + K_{1} s + K_{2} (1 - \ln ))^{m} + K_{3} \exp (n(s - 1))\)
10	[14, 31]	\(U_{\text{oc}} = K_{0} + K_{1} s + K_{2} s^{2}\)
11	[32]	\(U_{\text{oc}} = K_{0} + K_{1} s + K_{2} s^{2} + K_{3} s^{3}\)
12	[20]	\(U_{\text{oc}} = K_{0} + K_{1} s + K_{2} s^{2} + K_{3} s^{3} + K_{4} s^{4}\)
13	[33]	\(U_{\text{oc}} = K_{0} + K_{1} s + K_{2} s^{2} + K_{3} s^{3} + K_{4} s^{4} + K_{5} s^{5}\)
14	[34, 35]	\(U_{\text{oc}} = K_{0} + K_{1} s + K_{2} s^{2} + K_{3} s^{3} + K_{4} s^{4} + K_{5} s^{5} + K_{6} s^{6}\)
15	[36, 37]	\(U_{\text{oc}} = K_{0} + K_{1} s + K_{2} s^{2} + K_{3} s^{3} + K_{4} s^{4} + K_{5} s^{5} + K_{6} s^{6} + K_{7} s^{7}\)
16	[38]	\(\begin{aligned} U_{\text{oc}} & = K_{0} + K_{1} s + K_{2} s^{2} + K_{3} s^{3} + K_{4} s^{4} + K_{5} s^{5} + K_{6} s^{6} + K_{7} s^{7} \\ & \, + K_{8} s^{8} \\ \end{aligned}\)
17	[39, 40]	\(\begin{aligned} U_{\text{oc}} & = K_{0} + K_{1} s + K_{2} s^{2} + K_{3} s^{3} + K_{4} s^{4} + K_{5} s^{5} + K_{6} s^{6} + K_{7} s^{7} \\ & \, + K_{8} s^{8} + K_{9} s^{9} \\ \end{aligned}\)
18	[41]	\(\begin{aligned} U_{\text{oc}} & = K_{0} + K_{1} s + K_{2} s^{2} + K_{3} s^{3} + K_{4} s^{4} + K_{5} s^{5} + K_{6} s^{6} + K_{7} s^{7} \\ & \, + K_{8} s^{8} + K_{9} s^{9} + K_{10} s^{10} + K_{11} s^{11} + K_{12} s^{12} \\ \end{aligned}\)

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