Skip to main content

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] \(\begin{aligned} U_{\text{oc}} & = K_{0} + K_{1} s + K_{2} s^{2} + K_{3} s^{3} + K_{4} s^{4} + K_{5} s^{5} + K_{6} s^{6} + K_{7} s^{7} \\ & \, + K_{8} s^{8} + K_{9} s^{9} + K_{10} s^{10} + K_{11} s^{11} + K_{12} s^{12} \\ \end{aligned}\)