Online state of charge and state of power co-estimation of lithium-ion batteries based on fractional-order calculus and model predictive control theory.

• Battery SOC and SOP are co-estimated by combining the fractional-order calculus and the model predictive control theory. • A fractional-order modified moving horizon estimation algorithm is proposed for online SOC estimation. • A fractional-order model predictive control algorithm is devised to optimize current sequences for online SOP estimation. • Different battery current–voltage behaviors in the prediction horizon are researched over a battery operating range. Accurate battery modelling is the cornerstone to state of charge (SOC) and state of power (SOP) co-estimation of lithium-ion batteries in electric vehicles. Due to strong battery nonlinearity over a broad frequency range, traditional integer-order models are incapable of capturing complex battery dynamics for SOC and SOP co-estimation. This paper proposes a fractional-order modified moving horizon estimation (FO-mMHE) algorithm and a fractional-order model predictive control (FO-MPC) algorithm. Firstly, a second-order FOM is constructed by performing a series of hybrid pulse tests at different SOC regions, and its model parameters are identified through a particle swarm optimization-genetic algorithm method. Secondly, online SOC estimation is converted into a constrained optimization problem in a past moving horizon and then solved by the FO-mMHE algorithm, which enables fast convergence speed and proactive smoothing of estimation outcomes. Thirdly, the FO-MPC algorithm is devised to manipulate the current sequence in a prediction horizon for maximizing discharge/charge power accumulation and determining battery SOP in real time. Moreover, different battery current–voltage behaviors are comprehensively researched in the prediction horizon over a whole battery operating range. The proposed co-estimation method is validated under different dynamic load profiles. The experimental results demonstrate a SOC estimation error reduction of up to 1.2 % compared with the commonly used fractional-order extended Kalman filter while the SOP estimation error could be limited below 0.35 W. [ABSTRACT FROM AUTHOR]