From ROM of Electrochemistry to AI-Based Battery Digital and Hybrid Twin

Abstract

Lithium-ion batteries are widely used in the automobile industry (electric vehicles and hybrid electric vehicles) due to their high energy and power density. However, this raises new safety and reliability challenges which require development of novel sophisticated Battery Management Systems (BMS). A BMS ensures the safe and reliable operation of a battery pack and to realize it a model must be solved. However, current BMSs are not adapted to the specifications of the automotive industry, as they are unable to give accurate results at real-time rates and during a wide operation range. For this reason, the main focus of this work is to develop a Hybrid Twin, as introduced in Chinesta et al. (Arch Comput Methods Eng (in press), 2018. https://doi.org/10.1007/s11831-018-9301-4), so as to meet the requirements of the new generation of BMS. To achieve this, three reduced order model techniques are applied to the most commonly used physics-based models, each one for a different range of application. First, a POD model is used to greatly reduce the simulation time and the computational effort for the pseudo-2D model, while maintaining its accuracy. In this way, cell design, optimization of parameters, and simulation of battery packs can be done while saving time and computational resources. In addition, its real-time performance has been studied. Next, a regression model is constructed from data by using the sparse-Proper Generalized Decomposition (s-PGD). It is shown that it achieves real-time performance for the whole electric vehicle (EV) system with a battery pack. In addition, this regression model can be used in a BMS without issues because of the simple algebraic expression obtained. A simulation of the EV with the proposed approach is demonstrated using the system simulation tool SimulationX (ESI ITI GmbH. Dresden, Germany). Furthermore, the Digital Twin created using the s-PGD does not only allow for real-time simulations, but it can also adapt its predictions taking into consideration the real driving conditions and the real driving cycle to change the planning in real-time. Finally, a data-driven model based on the employment of Dynamic Mode Decomposition techniques is developed to extract an on-line model that corrects the gap between prediction and measurement, thus constructing the first (to our knowledge) hybrid twin of a Li-ion battery able to self-correct from data. In addition, thanks to this model, the above gap is corrected during the driving process, taking into consideration real-time restrictions.

Appendices

Appendices

Nomenclature Electrochemical Model

See Table 1.

Table 1 Nomenclature used

Cell Parameters and Additional Equations

See Table 2.

Table 2 Cell parameters

The units of the values shown in the table above are the same as those used in Table 1.

Additional equations:

$$\begin{aligned} \begin{array}{lll} D_e^{\mathrm{eff}} = \varepsilon _e^p \cdot D_e, &{} \ \ K^{\mathrm{eff}} = \varepsilon _e^p \cdot K, &{} \ \ K_D^{\mathrm{eff}} = \frac{2 \cdot R \cdot T \cdot K^{\mathrm{eff}}}{F} \cdot (t_+^0 - 1), \\ \sigma ^{\mathrm{eff}} = \varepsilon _s \cdot \sigma ,&{} \ \ a_s = \frac{3 \cdot \varepsilon _s}{R_s}. &{} \end{array} \end{aligned}$$

K, $U_n$ and $U_p$ are usually computed using empirical equations according to the simulated cell. The empirical equations for this cell are:

$$\begin{aligned} U_n(\theta _n)&= {} 0.7222 + 0.1387 \cdot \theta _n\\&+ 0.029 \cdot \theta _n^{0.5}-\frac{0.0172}{\theta _n} +\frac{0.0019}{\theta _n^{1.5}} \\&+ 0.2808 \cdot \exp (0.9 - 15 \cdot \theta _n) -0.7984 \cdot \exp (0.4465 \cdot \theta _n -0.4108),\\ U_p(\theta _p)&= {} \frac{-4.656+88.669 \cdot \theta _p^{2} -401.119 \cdot \theta _p^{4} +342.909 \cdot \theta _p^{6} -462.471 \cdot \theta _p^{8} +433.434 \cdot \theta _p^{10}}{-1+18.933 \cdot \theta _p^{2}-79.532 \cdot \theta _p^{4} +37.311 \cdot \theta _p^{6}-73.083 \cdot \theta _p^{8} +95.96 \cdot \theta _p^{10}},\\ K(c_e)&= {} 4.1253 \times 10^{-2}+ 5.007 \times 10^{-4} \cdot c_e - 4.7212 \times 10^{-7} \cdot c_e^2\\&+ 1.5094 \times 10^{-10} \cdot c_e^3 - 1.6018 \times 10^{-14} \cdot c_e^4 . \end{aligned}$$

Parameters Used in SimulationX Model

See Table 3.

Table 3 Main parameters

The parameters of the PI controller are assumed to have the following form:

$$\begin{aligned} G \cdot \left( 1+\frac{1}{Ti \cdot s}\right) . \end{aligned}$$

The parameters of the DC/DC converter are the default parameters in the SimulationX model described in [55]. The main forces considered for the linear movement of the vehicle are:

$$\begin{aligned} F_t = m \cdot a + R_{aero} + R_r + R_{grade} \end{aligned}$$

where $F_t$ is the tractive effort, and

$$\begin{aligned} R_{\mathrm{aero}} = \rho /2 \cdot A_{ref} \cdot C_w \cdot V^2 , \end{aligned}$$

represents the aerodynamic resistance. Likewise,

$$\begin{aligned} R_{r} = C_r \cdot m \cdot g \cdot \cos (\gamma ), \end{aligned}$$

represents the rolling resistance and, finally,

$$\begin{aligned} R_{\mathrm{grade}} = m \cdot g \cdot \sin (\gamma ), \end{aligned}$$

is the grade resistance.