基于自适应无迹卡尔曼滤波和经济模型预测控制的全钒液流电池SOC/SOP联合估计方法

doi:10.19799/j.cnki.2095-4239.2024.0534

摘要/Abstract

摘要：

荷电状态(state of charge，SOC)和峰值功率(state of peak power，SOP)的精确估计对保障电池安全稳定运行具有重要意义。为解决传统估计算法误差高、鲁棒性差等问题，本文提出了一种基于自适应无迹卡尔曼滤波(adaptive unscented Kalman filtering，AUKF)和经济模型预测控制(economic model predictive control，EMPC)的全钒液流电池(all-vanadium redox batteries，VRB)SOC/SOP联合估计方法。首先，为了提高传统模型的建模精度，本文综合考虑了VRB的电化学场和流体力学场的耦合特性，建立了一个能够全面刻画VRB运行过程的综合等效电路模型，并采用人工蜂群算法(artificial bee colony algorithm，ABC)对模型参数进行离线辨识。随后，考虑到传统的UKF算法无法适应系统噪声，收敛性差，且忽略电池参数变化等缺点，本文提出了基于AUKF的在线参数辨识和SOC估计算法，通过自适应调整UKF算法的参数来提高模型的精度。结合SOC的估计结果，采用EMPC算法估计VRB的SOP，并综合考虑了电压、电流、SOC和电解液流速等约束条件。最后，设计了多种实验工况验证了本文提出的SOC/SOP联合估计算法的精度。文章研究内容能够为液流电池不同运行状态下峰值功率预测和储能电站的精准调度提供依据。

关键词: 全钒液流电池, 荷电状态, 峰值功率, 在线参数辨识, 自适应无迹卡尔曼滤波, 经济模型预测控制

Abstract:

Accurate estimation of the state of charge (SOC) and state of peak power (SOP) is crucial for ensuring the safe and stable operation of vanadium redox batteries (VRBs). To address the high errors and poor robustness associated with traditional estimation algorithms, this paper proposes a joint estimation method for SOC and SOP of VRBs based on adaptive unscented Kalman filtering (AUKF) and economic model predictive control (EMPC). First, considering the coupling characteristics of the electrochemical and fluid dynamics fields of VRBs, a comprehensive equivalent circuit model is developed to accurately represent the VRB operation. The artificial bee colony (ABC) algorithm is employed for offline identification of model parameters. Subsequently, given the limitations of the traditional unscented Kalman filter (UKF) algorithm, such as sensitivity to system noise, poor convergence, and neglect of dynamic battery parameters, an online parameter identification and SOC estimation algorithm based on AUKF is proposed. This approach enhances the model's accuracy by adaptively adjusting UKF parameters. Building on the SOC estimation results, the EMPC algorithm is utilized to estimate SOP, considering constraints including voltage, current, SOC, and electrolyte flow rate. The proposed SOC/SOP joint estimation algorithm's accuracy is validated under multiple experimental conditions. The findings of this research provide a reliable basis for predicting the peak power of VRBs under various operating conditions and for the precise scheduling of energy storage stations.

Key words: vanadium redox flow battery, state of charge, state of peak power, online model identification, adaptive unscented Kalman filter, economic model predictive control

中图分类号:

TM 911

张宇, 姚尧, 刘睿, 金雷, 薛斐, 周鹏, 熊斌宇. 基于自适应无迹卡尔曼滤波和经济模型预测控制的全钒液流电池SOC/SOP联合估计方法[J]. 储能科学与技术, 2024, 13(11): 4089-4101.

Yu ZHANG, Yao YAO, Rui LIU, Lei JIN, Fei XUE, Peng ZHOU, Binyu XIONG. A joint estimation method for SOC/SOP of all vanadium redox batteries based on online parameter identification and ensemble Kalman filtering[J]. Energy Storage Science and Technology, 2024, 13(11): 4089-4101.

图/表 14

图1

表1

UKF算法流程"

流程	UKF算法
系统初始化	$x ̂ 0 = E x 0 P 0 = E x 0 - x ̂ 0 x 0 - x ̂ 0 T$ (15)

时间更新(预测)	$χ k - 1 = x ̂ k - 1, x ̂ k - 1 + (n + λ) P k - 1 i, x ̂ k - 1 - (n + λ) P k - 1 i$ (16) $χ k \| k - 1 = f χ k - 1$ (17) $x ̂ k \| k - 1 = ∑ i = 0 2 n W i m χ i (k \| k - 1) P k \| k - 1 = ∑ i = 0 2 n W i c χ i (k \| k - 1) - x ̂ k \| k - 1 T χ i (k \| k - 1) - x ̂ k \| k - 1 + Q$ (18)

观测校正	$Y k \| k - 1 = h χ k \| k - 1$ (19) $z ̂ k \| k - 1 = ∑ i = 0 2 n W i (m) Y i (k \| k - 1) S k = ∑ i = 0 2 n W i (c) Y i (k \| k - 1) - z ̂ k \| k - 1 T Y i (k \| k - 1) - z ̂ k \| k - 1 + R P x z = ∑ i = 0 2 n W i (c) χ i (k \| k - 1) - x ̂ k \| k - 1 T Y i (k \| k - 1) - z ̂ k \| k - 1$ (20)

计算卡尔曼增益，更新状态估计和协方差	$K k = P x z S k - 1$ (21) $x ̂ k = x ̂ k \| k - 1 + K k z k - z ̂ k \| k - 1 P k = P k \| k - 1 - K k S k K k T$ (22)

表1

图2

图3

图4

表2

表3

图5

图6

表4

图7

图8

图9

图10

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参数	值
k₁	0.0042
k₂	1.3118
k₃	1.6930
E₀^T⁰/V	1.2887
R₀/Ω	0.1027
A_ed/m²	0.6363
R_act	0.0904
C_act	10000

模型参数	数值	模型参数	数值
η_pump	85%	μ	7×10^-3 Pa·s
ρ	1400 kg/m³	L_ed	0.24 m
A_p	1.28×10^-4 m²	d_f	3×10^-15 m
f_p	0.005	ε	0.54
L_p	0.48 m	K_ck	2
D_p	0.003 m	D_mc	8×10^-3 m
K_form	2.1

SOC₀	AUKF			UKF
SOC₀	MAE	RMSE	跟随系数	MAE	RMSE	跟随系数
0.8(恒流工况)	0.0018	0.0017	0.0216	0.01	0.023	0.0407
0.8(变流工况)	0.0083	0.0085	0.0074	0.0149	0.0167	0.0756

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