How determinate parameters for thermal-model battery (Advanced question about battery modelling)

Question

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.

Answer 1

Just a long comment....not an answer..

I don't have the patience to follow the thermal-chemical model when the author completely ignores the electric properties of all batteries and supercaps electrical double layer effects.

In the simple electrical model the battery has a low ESR1 capacitance, C1 in xx kFarads that is responsible for short term load voltage drops with high current e.g. CCA test which resumes to the previous voltage with charge transfer from the higher C2 value ( and higher ESR2) for slow 10h load tests (Ah rating)

The more complex model has more layers of n charge layers C not just 2 but usually adequate with expected tolerances of results.

^{simulate this circuit – Schematic created using CircuitLab}

The battery rises in ESR rapidly as SoC < 10% and increases >100x when dead with <1% of the Capacitance. ( which is why the battery voltage drops quickly when load on a dead cell, then restores back quickly after load removed)

Yet it is well known that batteries reduce ESR with rising temperature and deliver more current, at the expense of significantly more rapid aging which has also significant effects on plate sulphation at high temp or low SoC for extended periods causing >10X rise in ESR and leakage across cell.

It is also well known that SLA cells require a temperature compensated CV level after CC due to the thermal voltage coefficient, which you may look up.

Furthermore when 6x 2V cells in series come out of manufacturing with <<1% cell electrical properties, it can be measured in flooded cells by individual cell voltage under pulse and static load and also specific gravity , s.g.which correlates well with low s.g. and high ESR and low capacitance (Ah)

The effect of aging follows the weak link theory that the weakest cell reaches 0% and 100% Soc first and this ages the cell further. However brief high current pulses , low Pavg resonates plate suplation crystals to break down and flood cell short term cavitation of acid is used to rejuvenate plates from sulphation if the damage is short term.

SO knowing the above from personal experience of analysis and testing, I didn't have the patience to look at Electro-thermal only potentials. sawwie

Maxwell Supercap tests account for the above model in test plan to get equiv C using "rest times between discharges"
http://www.maxwell.com/images/documents/1007239-EN_test_procedures_technote.pdf

p.s. electrolytics and high Dk ceramics also have the "memory effect" from electrical double layers which is why non-NP0 ceramic caps should never be used in S&H circuits.