Energy awareness for supercapacitors using Kalman filter state-of-charge tracking

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-mean-square error for predicting usable buffered energy.