h i g h l i g h t sThe energy stored in a supercapacitor cannot be determined by terminal voltage alone. Kalman state tracking with a three branch model improves stored energy awareness. A novel estimation technique enables in-situ estimation of required model parameters. The proposed method accurately determines the energy buffered in a supercapacitor.Keywords: Supercapacitor Three branch model State of charge Parameter estimation Kalman Energy awareness a b s t r a c t Among energy buffering alternatives, supercapacitors can provide unmatched efficiency and durability. Additionally, the direct relation between a supercapacitor's terminal voltage and stored energy can improve energy awareness. However, a simple capacitive approximation cannot adequately represent the stored energy in a supercapacitor. It is shown that the three branch equivalent circuit model provides more accurate energy awareness. This equivalent circuit uses three capacitances and associated resistances to represent the supercapacitor's internal SOC (state-of-charge). However, the SOC cannot be determined from one observation of the terminal voltage, and must be tracked over time using inexact measurements. We present: 1) a Kalman filtering solution for tracking the SOC; 2) an on-line system identification procedure to efficiently estimate the equivalent circuit's parameters; and 3) experimental validation of both parameter estimation and SOC tracking for 5 F, 10 F, 50 F, and 350 F supercapacitors. Validation is done within the operating range of a solar powered application and the associated power variability due to energy harvesting. The proposed techniques are benchmarked against the simple capacitive model and prior parameter estimation techniques, and provide a 67% reduction in root-meansquare error for predicting usable buffered energy.

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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.Index Terms-supercapacitor, ultracapacitor, electric double layer capacitor, solar energy, kalman filter, state of charge, energy awareness.

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