Adaptive state of energy evaluation for supercapacitor in hybrid electric vehicle applications considering non-integer order impedance

For a hybrid electric vehicle with a supercapacitor pack, accurate state of energy (SOE) evaluation of the supercapacitor is very crucial for energy management and optimization of its power supply system. However, the non-integer impedance of the supercapacitor would affect the model accuracy, posing challenges for accurate SOE evaluation. Herein, this study introduces an adaptive SOE evaluation method that incorporates the non-integer order characteristics of supercapacitors. Specifically, the proposed method can adaptively estimate the fractional order model parameters in real time using an improved sliding mode observer and evaluate the SOE by accounting for the supercapacitor's inherent energy loss. We begin by establishing a fractional order equivalent circuit model that employs a constant phase angle element to capture the non-integer order impedance with higher fidelity. Based on this model, an improved sliding mode observer with a switchable reaching law is developed to track model parameter variations in real time. This enables the model parameter to remain accurate even as the supercapacitor's internal characteristics continue to evolve during operation. Using the real-time estimated parameters, an adaptive SOE evaluation method is then designed that incorporates the supercapacitor's inherent energy losses. Finally, both experimental and simulation results confirm the effectiveness of the proposed method. Under the Urban Dynamometer Driving Schedule (UDDS) and New European Driving Cycle (NEDC) operating conditions, the adaptive SOE evaluation method achieves estimation accuracies of 0.55% and 0.64%, respectively. Even under varying temperature conditions, the method maintains high accuracy, with estimation errors limited to 1.57% and 1.51%, respectively. • An adaptive SOE evaluation method was proposed for the supercapacitor in HEV applications. • A fractional order model of the supercapacitor was designed considering non-integer order impedance. • An improved sliding mode observer was developed to estimate the real-time parameters of the supercapacitor model. • Adaptive SOE evaluation for the supercapacitor can be achieved based on the real-time estimated parameters.