This paper proposes a co-estimation scheme of the state of charge (SOC) and the state of power (SOP) for lithium-ion batteries in electric vehicles based on a fractional-order model (FOM). First, a series of FOMs and integer-order models (IOMs) is constructed using fractional- and integer-order calculus. The model parameters are then identified using particle swarm optimization over the whole SOC range, and the complexity and accuracy of the resulting models are evaluated. Second, a fractional-order extended Kalman filter-based SOC estimator is developed. Third, the co-estimation of SOC and SOP is formulated, and an SOP estimation method based on three restrictions and a correction method from constant-current to constant-power are proposed. Finally, the proposed model and method are verified by experiments. The main results are as follows: (1) The FOMs achieve better accuracy than IOMs over the whole SOC range (especially in the low SOC range), and the FOM with a pair of resistance-constant phase elements and one Warburg element (FO-2RCW) producing the best performance. (2) The SOC estimation accuracy based on the FO-2RCW with variable parameters and orders is less than 2% over the whole SOC range. (3) The proposed co-estimation method is validated to be effective under the dynamic operating conditions and shows high accuracy.

提出了一种基于分数阶模型（FOM）的电动汽车锂离子电池充电状态（SOC）和功率状态（SOP）的联合估计方案。首先，使用分数阶和整数阶演算来构造一系列FOM和整数阶模型（IOM）。然后使用粒子群优化在整个SOC范围内识别模型参数，并评估所得模型的复杂性和准确性。其次，开发了基于分数阶扩展卡尔曼滤波器的SOC估计器。第三，提出了SOC和SOP的协估计，提出了基于三个约束的SOP估计方法和从恒流到恒功率的校正方法。最后，通过实验验证了所提出的模型和方法。主要结果如下：（1）在整个SOC范围内（特别是在低SOC范围内），FOM的精度都优于IOM，并且具有一对电阻恒定相元件和一个Warburg元件（FO-2RCW）的FOM表现出最佳性能。（2）基于FO-2RCW的可变参数和阶数的SOC估计准确度在整个SOC范围内均小于2％。（3）所提出的协估计方法在动态工作条件下被证明是有效的，并且具有很高的精度。