*3.1.2 AEKF SOC estimator for ANFIS 3RC ECM SAFT Li-ion battery model: accuracy performance*

For simplification purpose and SOC and battery terminal voltage accuracy, as alternative Li-ion 3RC ECM structure required to implement the AEKF SOC estimator on a MATLAB R2021b platform is considered the ANFIS 3RC ECM SAFT Li-ion battery model consisting of Rint-3RC ECM dynamic part block, and second ANFIS model attached to OCV(SOC) nonlinear block. The overall simplified ANFIS 3RC ECM battery model structure is described by the following equations:

$$\text{soc}(k+1) = \text{soc}(k) - \frac{\eta T\_\iota u(k)}{C\_{\text{nom}}},\\\text{soc}(\mathbf{0}) = \text{SOCmi} \tag{19}$$

$$y(k) = V\_{OCV}(k) - V\_d(k) = \left(\frac{anf\text{fs}(soc(k))}{soc(k)}\right)soc(k) - anf\text{fs}(u(k))\tag{20}$$

In all the MATLAB simulations for implementing the AEKF SOC estimator are considered the following parameters values:

• SOC initial value = 0.4,

Covariance of estimated value of SOC, Phat = 1e-10,


The MATLAB simulations results are presented in **Figure 18a–c**. Similar to ARX model developed in previous chapter 2, in **Figure 18** the robustness of AEKF

#### **Figure 18.**

*(a) Robustness of ANFIS AEKF SOC estimator to changes in SOC initial values from SOCini = 0.7 to SOCini = 0.4; (b) the ANFIS 3RC ECM Li-ion battery OCV voltage accuracy.*

#### **Figure 19.**

*(a) The ANFIS 3RC ECM Li-ion battery SOC residual error; (b) the ANFIS 3RC ECM Li-ion battery terminal voltage residual error with respect with the battery terminal voltage estimated by AEKF.*

SOC estimator to changes in the battery SOC initial values from SOCini = 0.7 to SOCini = 0.4 is shown. In **Figure 18b** the predicted values of battery terminal and OCV voltages cell by AEKF and ANFIS are compared with 3RC ECM true values.

The battery SOC and terminal voltage accuracy are revealed in **Figure 19a** and **b**, respectively, based on SOC and battery terminal voltage residuals.

#### **3.2 Discussion: ANFIS models and AEKF SOC estimator performance analysis**

Based on the information accessible from the battery SOC and terminal voltage residual errors presented in the first two subsections of Section 3, more precisely the MATLAB simulation results and the statistics criteria values RMSE, RSE, MAE, MAPE, collected in **Table 2**, can be made a rigorous performance analysis of both ANFIS models and AEKF SOC estimator.

*Investigations of Using an Intelligent ANFIS Modeling Approach for a Li-Ion Battery… DOI: http://dx.doi.org/10.5772/intechopen.105529*
