Supercapacitor State of Health Estimation for Vehicular Applications
Authors: Hammou Abdelilah , Chaoui Hicham , Gualous Hamid 
Published: July 2022

The transportation electrification requires an energy storage system that can absorb and deliver high amounts of energy during short periods of time, such us acceleration and breaking phases. One of the solutions applied is the using of electrical double layer capacitors (ELDC) or supercapacitors, due to their higher power density. However, the performance and the safety of these components depend on their state of health (SoH). Therefore, the health monitoring of supercpacitor cells is necessary to assure their integration and their safety in vehicular application. The aging of supercapacitors is usually correlated with the decreasing of their capacitance end the increasing of their internal resistance. Thus, the monitoring of these two parameters is necessary for the diagnosis of the state of heath. The measuring of these two parameters cannot be performed directly during the working conditions of supercapacitors in electrical vehicles. Therefore, an online estimation approach of these parameters is needed to enable the diagnosis of supercapacitors.
This paper proposes a model-based method for supercapacitors state of health estimation. The approach uses the high gain observer to estimate the parameters of the equivalent RC network. The high gain observer, is one of the observers used for the system identification, it has shown its accuracy and robustness for dealing with nonlinear systems. The equivalent RC network used for modeling the system, simulates the energy and the electrical behavior of supercapacitors, it also presents a best tradeoff between accuracy and complexity. This approach enables the estimation of supercapacitors capacitance and internal resistance from current and voltage measurements.
In order to test the proposed method, an experimental test was realized to validate this method. During this test two supercapacitors cells were cycled, in a climate chamber at high temperature T=45°C, in order to accelerate their aging. After each number of cycles, the supercapacitors cells are discharged using WLTC current profile (World harmonized Light-duty vehicles Test Cycle) presented in figure 1. Then, the capacitance and the internal resistance were measured to calculate their state of health.
The WLTC current profiles is a dynamic current profile composed of charge and discharge current which allow to test the performance and the diagnosis method in conditions close to real electrical vehicles conditions.
Since the aging of supercpacitor is correlated with the evolution of their capacitance and their internal resistance, then the state of health of these components is defined based on these two parameters using these two equations:
and are the resistance and the capacitance measured at the beginning of life, and and and are and the resistance the capacitance measured at the end of each state of health k.
After each number of cycles, the parameters of the RC equivalent circuit model were estimated, using the high gain observer, from the voltage and current measured during WLTC current profile. In order to compare results, the Root mean square error (RMSE) is calculated between the measured and the estimated SoHr and SoHc.
The results presented in figure 2 and figure 3 and table I, show that the high gain observer presents a good accuracy for the state of health estimation, with an RMSE less than 0.77% for the SoHc and less than 1.58% for SoHr estimation. These results, indicate to robustness and the accuracy of this approach to estimate the supercpacitor parameters from a dynamic current profile such as WLTC, which make the used approach a good candidate for on board diagnosis in vehicular applications. The future work of this study is to implement this algorithm in microprocessor in order to test its performance in a real time.
References

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Saha, P. Saha and M. Khanra, "Performance Comparison of Nonlinear State Estimators for State-of-Charge Estimation of Supercapacitor," 2021 IEEE Second International Conference on Control, Measurement and Instrumentation (CMI), 2021, pp. 105-109, doi: 10.1109/CMI50323.2021.9362850.

El Mejdoubi, H. Chaoui, H. Gualous and J. Sabor, "Online Parameter Identification for Supercapacitor State-of-Health Diagnosis for Vehicular Applications," in IEEE Transactions on Power Electronics, vol. 32, no. 12, pp. 9355-9363, Dec. 2017, doi: 10.1109/TPEL.2017.2655578.

Figure 1