# A Switching Observer for State-of-Charge Estimation of Reconfigurable Supercapacitors
## 1 Introduction  
Supercapacitors have emerged as promising energy storage devices due to their exceptional performance, finding applications in electric vehicles, renewable energy systems, and modern power grids [1], and research on it continues to be updated [2]. As a commonly used onboard power source for electric vehicles, the State of Charge (SOC) of supercapacitors is a key parameter that reflects the current charge storage level. Accurate SOC estimation is fundamental to energy control and management, ensuring the safe and reliable operation of the onboard power system, which is crucial for maintaining its operational efficiency and longevity [3]. At times we need to ensure that the SOC operates within a certain range to guarantee the system's proper functioning [4].  
Due to the importance of the SOC in supercapacitors, many methods for estimating the SOC have already been proposed [5]. While traditional Coulomb counting is straightforward, its accuracy diminishes under dynamic conditions due to the gradual accumulation of errors over time. Data-driven approaches for estimating battery SOC [6], like deep feedforward neural networks (DNNs) [7], Elman neural networks [8], and long short-term memory recurrent neural networks (LSTM RNNs) [9] provide greater accuracy but come with higher computational demands and a reliance on data quality. These methods often necessitate the frequent retraining of the model. In contrast, model-based techniques such as Luenberger observers, sliding-mode observers [10], Kalman Filters, and nonlinear observers [11] strike a balance between computational efficiency and accuracy. The Kalman Filter is one of the most widely used methods, and different types of Kalman Filters have already been applied to SOC estimation, including the Extended Kalman Filter (EKF) [12, 13], Adaptive Kalman Filter (AKF) [14], and Unscented Kalman Filter (UKF) [15, 16].  
However, most existing research primarily focuses on individual supercapacitor cells, utilizing cell current as input and cell voltage as output for observer design. In practicalapplications, supercapacitors are rarely used in isolation and are often integrated with balancing circuits [17; 18; 19]. Reconfigurable circuits have recently emerged as a promising solution to address balancing challenges in battery and supercapacitor applications [20]. These circuits enable dynamic reconfiguration to adjust voltage and current levels, optimize energy conversion efficiency, and isolate faulty cells, ultimately extending the lifespan of the energy storage system. However, the switching actions inherent in reconfigurable circuits introduce abrupt changes in the system model, rendering traditional observers ineffective.  
This paper proposes a novel SOC estimation method for supercapacitors integrated with reconfigurable circuits based on a switched systems approach. We develop a linear switched system model to capture the dynamic behavior of the system. A corresponding observer is designed, explicitly considering the impact of switching events on system dynamics. Experimental results validate the effectiveness of the proposed method.