Multi-state joint estimation for a lithium-ion hybrid capacitor over a wide temperature range

Lithium-ion hybrid capacitors (LIHCs) have the advantages of high energy and power densities and long cycle life. This paper proposes a multi-state joint estimation method for LIHCs. The effects of temperature on the key LIHC parameters are analyzed. A first-order resistor-capacitor (RC) equivalent circuit model is used to characterize the LIHC dynamics. The coupling relationships among multiple states and LIHC parameters are derived. A recursive least squares algorithm with a variable forgetting factor (VFF-RLS) is employed to adaptively update model parameters at different temperatures. Subsequently, the online identified open-circuit voltage (OCV) is corrected by using a long short-term memory (LSTM) artificial neural network model and an ampere-hour integration method. With the corrected OCV curves and the other model parameters, the estimations of the state of charge (SOC), the remaining useful energy (RUE) and the state of energy (SOE) under dynamic operating conditions over a wide temperature range are achieved. The accuracy of the multi-state joint estimation is verified via the Federal Urban Driving Schedule (FUDS) test and the dynamic stress test (DST) at −10 °C, 25 °C and 50 °C. The root-mean-square errors (RMSEs) of the SOC, RUE and SOE estimations are 2.1%, 0.9 Wh, and 2.3%, respectively.