A Fast Approach for In Situ SoC Estimation of a Hybrid Supercapacitor Based on GPR and EIS Measurements

A fast and accurate approach for the state-of-charge (SoC) estimation of a hybrid supercapacitor (HSC) is presented in this article. Electrochemical impedance spectroscopy (EIS) is performed with the HSC as the device under test (DUT). The EIS is initially performed at six different frequencies (0.05, 0.1, 0.5, 1, 5, and 10 Hz), collecting a dataset, including 6000 points describing SoC in the range from 100% to 0%. This collected dataset is then utilized for extensive training and testing of a Gaussian process regression (GPR) model with a nonisotropic exponential kernel and Bayesian optimization to accurately estimate the SoC of the HSC. To simplify the measurement setup and procedure, aiming at developing an in situ instrument for SoC evaluation, in the recognition process, a limited number of frequencies should be used. Moreover, special attention should be paid to the measurement time, leading to preferring higher frequencies over the lower ones. For this reason, a combination of only two frequency points (FPs) has been identified, for the best compromise between accuracy and timing, also considering the typical discharge curve of the HSC, which presents an abrupt decrease at low values of SoC. Data acquired at 0.1 Hz have been used to train the GPR model for SoC values within the range [30, 100], while the data acquired at 1 Hz have been exploited for SoC values within the range [0, 30]. Later, a postprocessing phase is applied, including a three-point linearization and an error calibration, which further improves the estimation accuracy. The resulting average root-mean-squared error (RMSE) for the proposed approach without and with the postprocessing phase came out to be 1.33 and 0.94, respectively, which are very good results compared with more complex approaches in the literature.