A Statistical out-of-Sample Forecast to Estimate Lithium-Ion Parameters That Determine State of Charge
Authors: Khalid Asadullah , Sundararajan Aditya , Sarwat Arif 
Published: February 2020

Predicting state of charge (SOC) is crucial for an intelligent battery management system. Most of the existing SOC estimator models in literature use traditional methods such as bookkeeping and direct measurement, or rely on adaptive techniques such as neural networks. However, these models require the acquisition of significant experimental data on cell voltage and current, among others, to predict SOC with acceptable generalization performance. This paper proposes to compare two available statistical time-series forecasting methods, autoregressive integrated moving average (ARIMA) and Holt-Winters Exponential Smoothing (HWES), to forecast cell current and voltage of an actual 3.7V, 3.5Ah Lithium-ion battery for an unknown charging/discharging rate (C-rate) of C/10 using the values of the corresponding parameters from preceding C-rates of C/2, C/4, C/6, and C/8 obtained by performing lifecycle tests. The forecast values of current and voltage could, in practice, be used to calculate SOC using Coulomb-counting method [1]. The results are finally documented as a table in the attached figure.
Proposed Work:
Predicting the state of charge (SOC) of Lithium-ion batteries is critical for applications such as electric vehicles to determine the available capacity and function accordingly. Under scenarios where access to infrastructure and means to acquire experimental data on battery parameters is limited, the availability of an estimator model that is pre-trained for a given battery that can directly be used to predict SOC for any required C-rate is favorable. The paper proposes to use ARIMA and HWES algorithms to forecast current and voltage using historical time-series values of the same parameters obtained for C-rates C/2 to C/8. The voltage and current data are stationary as they both reject the null hypothesis in the Augmented Dickey-Fuller test [2] with a p-value of 0.01. Correlograms of the autocorrelation and partial autocorrelation functions for current and voltage are shown in Figure A in the attachment. The optimal values for the autoregressive integrative, and moving average terms are selected to be (34,1,4) such that their combination minimized the Akaike Information Criterion (AIC) [2]. The ACF and PACF plots for the fitted ARIMA model is illustrated in Figure B. The results of cell current and voltage predictions for C/10 made using the ARIMA model are shown in Figs. C and D, respectively, in the attachment.
Results and discussion:
The experimental setup comprised a 3.7V, 3.5Ah Li-ion battery that was subjected to different C-rates: C/2, C/4, C/6, C/8, and C/10, for 60 cycles each at discharging and charging currents of 850mAh and 2.6Ah for each test, respectively. The cell current and voltage values for C-rates C/2 through C/8 were augmented to form the time-series datasets to be used by ARIMA and HWES for model fitting. The corresponding datasets for C/10 were used solely during the forecasting phase, thereby making the forecasting process out-of-sample. For ARIMA, the mean squared error (MSE) between the forecast and observed values for C/10 voltage and current are 0.019 and 0.079, respectively. For HWES, the MSE values for C/10 voltage and current turned out to be higher, with 0.3996 and 1.6775, respectively. Besides MSE, three other errors, root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE), are also calculated for both models in predicting C/10 current and voltage. This table is also included in the attachment as Fig. G. It can be seen that ARIMA had a superior performance than HWES for this specific problem.
Conclusion and Future Work:
To develop a reliable SOC estimator model for intelligent battery management systems that are capable of predicting SOC for future, unseen C-rates using the available cell current and voltage data from previous C-rates, this paper proposes to use ARIMA. Results show that between ARIMA and HWES, the two most widely used statistical time-series forecasting methods, ARIMA shows superior performance. As a future work, artificial neural network-based SOC and voltage estimation techniques will be identified.
References:
[1] K.S. Ng, C.S. Moo, Y.P. Chen, Y.C. Hsieh, “Enhanced coulomb counting method for estimating state-of-charge and state-of-health of lithium-ion batteries,” Journal of Applied Energy, Vol. 86, No. 9, 2009
[2] M. Aritova, D. Fedorova, “Selection of Unit Root Test on the Basis of Length of the Time Series and Value of AR(1) Parameter,” Statistika, 2016
This work is a result of the research supported by the National Science Foundation (NSF) under grant number CNS-1553494.

Figure 1