I'm trying to simulate an electrical model based on Ceraolo battery model for lead-acid battery. The challenge in this model is to determine the parameters that describe it.
I can understand and estimate most of the parameters. However, it is still unclear to me how the parameters \$Ke\$ described in the paper.
The problem in this case is that the equation used to define \$Ke\$ uses the value of \$Em\$ which is not a value obtained via lab tests.
For those who know and understand the model, it is known that \$Em\$ is the voltage source responsible for emf at the "beginning" of the circuit in question, while Figure 4 represents the voltage at the battery terminals (i.e at the "end" of the circuit). It is for this reason that I believe that it is not possible to use the test values to set the \$Em\$, since the test values already show the terminal voltage of the battery.
The equation I'm talking about:
\$E_m=E_{m0}-K_E(273+\theta)(1-SOC)\$
Figure 4
The table with the voltage values corresponding to Figure 4
\begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline Battery & V_0[V] & V_1[V] & V_2[V] & V_3[V] & V_4[V] & \theta_{end} & I[A] & t[h] \\ \hline Battery\ 1 & 2.165 & 1.965 & 2.06 & 1.790 & 1.890 & 26 & 58 & 8.494\\ \hline Battery\ 2 & 2.115 & 1.995 & 2.01 & 1.788 & 1.905 & 26 & 63 & 7.197\\ \hline \end{array}
The parameters that Ceraolo obtained from these data were
\begin{array}{|c|c|c|} \hline Battery & E_{m0}[V] & K_E[mV/°C] \\ \hline Battery\ 1 & 2.165 & 0.782 \\ \hline Battery\ 2 & 2.115 & 0.832 \\ \hline \end{array}
It is easy to realize that the value of \$E_{m0}\$ can be obtained directly from the tests, but for those who will have patience, how will I get the value of \$Ke\$ if it is not possible to get \$E_m\$ through test labs ?
I think I have provided all the necessary information for the doubt. If you need anything else please let me know. The article is attached at the beginning of the post.
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