State-of-charge estimation for supercapacitors: A Kalman filtering formulation

Supercapacitors are an attractive option for energy buffering because of their high efficiency, durability, and low environmental impact. For energy-aware applications, it is desirable to accurately estimate the buffered energy. Under conditions of varying energy supply and demand, estimation of buffered energy by using only the supercapacitor terminal voltage is inaccurate because this does not fully comprehend the physical state of charge. To address this problem, we present a Kalman filtering formulation, using the accepted three-branch circuit model for supercapacitors. Compared with an ideal capacitor, the physically-motivated three-branch model provides a much more accurate representation of the state of charge via three internal state voltages associated with short, medium, and long term charging constants. The proposed Kalman formulation tracks these unobservable internal states. This methodology demonstrates a significantly more accurate estimate of the buffered energy as compared with the alternative models of ideal capacitance or a recursive computation of the stored energy. Simulations conducted with variations that approximate recorded solar intensity profiles, our proposed approach has an error of 1% compared with 31% and 85% for the respective alternative models.