State of charge estimation of Li-ion battery for underwater vehicles based on EKF–RELM under temperature-varying conditions

Abstract

Underwater vehicles are important mobile platforms used for ocean exploration. However, temperature changes along the ocean depth are rapid and complex, making it difficult to estimate the SOC (state of charge). Besides, the EKF method, which is used widely for SOC estimation, ignores the higher-order terms of Taylor expansion, which may produce large truncation errors. To address this problem, this paper proposed a SOC estimation method based on the extended Kalman filter and regularised extreme learning machine (EKF–RELM). First, the relationship between model parameters and temperature is explored. Then the EKF is applied to estimate the value of SOC and the RELM is used ultimately to revise the estimated value. Offline experiments were conducted to assess the performance of the EKF–RELM method compared with the EKF method under different conditions. The estimation error of EKF–RELM was less than that of EKF under variable temperature and load conditions. Finally, trials were performed in Qiandao Lake, and the maximum error (ME) in the SOC estimation was found to be less than 1.67%.

Introduction

Underwater vehicles can freely move underwater and can use the sensors they carry to observe the ocean. Their comprehensive technology has matured, and various types of underwater vehicles, such as autonomous underwater vehicles (AUVs) (Zhang et al., 2020), gliders (Tian et al., 2021), floats (Petzrick et al., 2013) and profilers (Zhou et al., 2020), have been developed. Typically, an underwater vehicle carries a limited number of batteries. In addition, replacing the battery underwater is nearly impossible (Rudnick, 2016, Haavisto et al., 2018). Thus, if the energy of an underwater vehicle is depleted, it will be lost, which is a huge financial loss (Xue, 2020). Therefore, estimating the state of charge (SOC) of a battery is critical. The existing SOC estimation methods are focused on electric vehicle research (Vasebi et al., 2008). However, electrical energy management systems can be applied in the field of underwater vehicles. The technical status of fuel cell power systems of autonomous underwater profilers was reported in the literature (Dai et al., 2016). Niankai Yang reported a novel model predictive control framework for energy-optimal point-to-point motion control of an AUV (Yang et al., 2018). Alejandro Mendez investigated the current state of the technology of fuel cell power systems for AUVs (Mendez et al., 2014). Additionally, other energy management systems have been used to study the hybrid energy underwater profilers (Claus and Bachmayer, 2016).

Currently, SOC estimation methods are based on the traditional current integration method and mainly include the Kalman filter and neural network methods. The Kalman filtering recursion method is used to estimate SOC based on Kalman optimal filtering theory (Campestrini et al., 2016, Yu et al., 2015). The improved Kalman filter algorithm has attracted considerable attention because of its good performance. In one study (Luo et al., 2019), SOC was estimated online in real time using a cubature Kalman filter (CKF). In another study (Baccouche et al., 2017), Ines Baccouche et al. have used an extended Kalman filter (EKF) algorithm based on an improved open-circuit voltage (OCV) model to estimate SOC, showing a clear effect that the SOC estimation error was reduced to 3%. Moreover, due to the EKF method's ability to estimate nonlinear models, it is‌ ‌widely‌ ‌used for SOC estimation (Sun et al., 2021, Ling and Wei, 2021, Park et al., 2020). However, these studies did not focus on the problem that the EKF method ignores the higher-order terms of the Taylor expansion. Shunli Wang et al. (Wang et al., 2020) put forward an improved composite equivalent modeling method and proposed a novel splice Kalman filtering algorithm for charged state prediction of the lithium-ion battery packs. The experimental results show that the proposed method exhibits satisfactory robustness. Maofei Tian et al. (Maofei et al., 2019) have used an adaptive EKF algorithm to estimate the SOC of lead–acid batteries. Zhigang He et al. (Zhigang et al., 2016) have used the Thevenin model and untracked Kalman filter algorithm to estimate the SOC of a lead–acid battery. This study suggested that combining these two models resulted in high estimation accuracy. In addition, some scholars used the artificial neural network method to estimate the residual electric power for modelling complex nonlinear systems, which greatly improved the estimation of residual electric quantity (Shi et al., 2005, Liu et al., 2015). Yifeng Guo et al. (Guo et al., 2017) used a neural network strategy to divide the SOC of the system into different levels. Neural networks can be combined with optimisation and evolution algorithms to further improve the estimation accuracy. In study (Li and Liu, 2018), a full-parallel nonlinear autoregressive neural network with external inputs was used to obtain a SOC estimation for lithium batteries. In this study, the number of network nodes was relatively large with slow training speed. Yanqing Shen (Shen, 2010) proposed a novel approach using an adaptive artificial neural network-based model and a neuro-controller for online cell SOC determination in lead–acid batteries, resulting in a SOC estimation error of ±1.

In this study, the extended Kalman filter–regularised extreme learning machine (EKF–RELM) method was applied on the profiler called ZJU-HUP, which was developed by our team for monitoring a designed area of the ocean (Zhou et al., 2020) as shown in Figure 1. It is crucial to estimate correctly the power of the lithium battery in ZJU-HUP in order for the profiler to detect when power is insufficient and perform float to avoid‌ ‌its‌ ‌loss. Unlike electric vehicles on land, underwater vehicles are subjected to large temperature differences at different water depths, which affect the discharge curve of lithium batteries. This adds to the difficulties of SOC estimation.

It is difficult to set the parameters for the Kalman filtering method in the complicate environmental‌ ‌conditions, and it depends on the battery model (Yu et al., 2015). The estimation accuracy was improved to a certain extent using the neural network method; however, it did not consider the impact of the initial weights and thresholds of the network on its performance, resulting in an increase in the prediction error and prediction time of the network (Liu et al., 2015). Therefore, studying a new method for SOC estimation in real time with high precision is important to monitor the energy of underwater vehicles under temperature-varying conditions.

In this study, an improved SOC estimation method (EKF–RELM) based on EKF and RELM was proposed and validated using ZJU-HUP in Qiandao Lake, China. This paper is organised as follows: Section 2 introduces the mathematical model of the lithium battery and SOC estimation model. Section 3 discusses the SOC estimation method based on EKF and RELM. Section 4 presents the parameter identification and the offline simulation experiments for SOC estimation under different conditions. Finally, the lake trials and the corresponding results are presented.