A novel entropy-based fault diagnosis and inconsistency evaluation approach for lithium-ion battery energy storage systems
Introduction
In 2019, 83% of primary energy supplies still came from fossil fuels, namely, oil, nature gas and coal [1], which accelerated air pollution such as global warming by emitting tons of CO2. The desire to build a society with low-carbon or zero-carbon emission urges the intensified use of renewable energy sources including wind and solar energy. As volatile energy sources, wind energy and solar energy suffer from unbalance between electricity production and demand load. Therefore, for power plants with high shares of volatile renewable energy sources, energy storage at large scale for short or long term becomes one of the main solutions to enhance grid stability [2].
Comparing with other energy storage facilities, lithium-ion (Li-ion) battery (LIB) [3,4] has the advantages of higher energy density, higher efficiency, higher open circuit voltage (OCV), longer lifespan, lower self-discharge rate, and less pollution. And the cost of LIB has achieved a significant reduction. Thus, LIB becomes the first-choice candidate as principal or auxiliary power supply devices for electric vehicles (EVs), hybrid electric vehicles (HEVs), plug-in hybrid electric vehicles (PHEVs), telephone communication and portable appliances, as well as the second-choice candidate for energy storage systems (ESSs). To aid the transition to a renewable-based energy system, LIBs are increasingly installed in stationary battery ESSs [5] ranging from small (under 20 kWh of nominal energy) to large systems (over 1 MWh) [6]. The small ESSs are usually used for residential storage systems to store excess electricity from photovoltaic systems. And the large ESSs mainly act as grid ancillary services while the medium ESSs are often applied in local grid.
Currently, a main concern of the public about the widespread adoption of LIBs is their safety. As the popularization of LIBs, accidents regarding to LIBs occurred more frequently. On one hand, pursuing materials with higher energy density, such as the utilization of Ni-rich NCM as cathode, may lower thermal stability [7]. On the other hand, in order to achieve the required voltage and capacity, lots of battery cells are configured in complicated series and parallel connections. The more batteries installed in a system, the more likely accidents would happen since more batteries means more capacity and a system with more batteries more possibly incurs the initial internal resistance inconsistencies and contact resistance inconsistencies of battery cells, which are caused by manufacturing, design [8] or assembly issue, and would cause uneven temperature distribution among cells, further increasing inconsistencies of the internal resistances [9]. The existence of too large inconsistencies among battery cells in an ESS is thought to be a major factor causing faults or even safety accidents.
As a comprehensive electrochemical system, LIB has different types of faults. From the perspective of control, the faults can be generally classified into three categories [10]: battery faults, sensor faults [11], and actuator faults [12]. The battery faults can be further differentiated in three types, namely, mechanical abuse, electrical abuse, and thermal abuse from the view of abusive conditions [13]. Typical conditions for the mechanical abuse include collision, crushing or needling. External short circuit (ESC) [14], internal short circuit (ISC) [15], over-discharge [16], overcharge [17] are typical electrical abuse conditions while local overheat caused by contact loose and global heating due to high temperature ambient [13] are classic thermal abuse conditions. Moreover, different faults are intertwined. For example, the mechanical abuse can trigger ISC while ISC would cause local overheat or further arouse thermal runaway (TR), which may induce smoke, fire, and even explosion. In addition to battery faults, sensor faults can result in severe accidents if sensors cannot timely and correctly update parameters like currents, voltages, temperatures, which are the foundation of feedback-based algorithms in the battery management system (BMS) and battery thermal management system (BTMS). Compared with battery faults and sensor faults, actuator faults, like the cooling system fault and the fuse fault, have a more direct impact on the control system performance. For example, it may arouse overheat or even lead to TR if the cooling system fails. According to the time scale of fault occurrence and evolution, faults can be divided into two categories, i.e., the gradual faults and the sudden faults [18]. The gradual faults including capacity fade and power fade, mainly result from aging [4]. Sudden faults, like overcharge, ISC, ESC and TR, usually occur instantly and generate heat within the battery in a short time, which could cause severe damages if the heat is not timely removed.
Therefore, it is critical and meaningful to detect and diagnose faults early and accurately for providing safety alarms and conducting effective treatments to avert serious consequences like TR during actual operation. Considerable efforts have been dedicated to fault diagnosis methodologies for LIBs, which can be basically divided into two categories, i.e., the qualitative and quantitative analysis methods [19]. The qualitative methods are mainly knowledge-based methods, including graph theory-based methods, expert system [20], and fuzzy logic-based methods [21]. Fault tree [22] analysis is a typical graph theory-based method. Without needing mathematical models, the knowledge-based methods are suitable for complex nonlinear time-varying systems like LIBs [23]. However, the knowledge-based methods require further observation and knowledge on fault mechanism. The quantitative methods consist of model-based methods and data-driven methods. The model-based methods [18,[24], [25], [26], [27], [28]] usually obtain a residual by comparing the measurable signal, such as state of charge (SOC) [4] and state of health (SOH) [29], with the signal generated from high-fidelity battery models, such as the equivalent circuit model (ECM) [30], by utilizing a filter or an observer, such as Kalman filter (KF) [31], extended Kalman filter (EKF) [32], unscented Kalman filter [33], particle filter (PF) [34], Lunberger observer [35], and adaptive observer [36]. The data-driven methods contain machine learning methods and statistical analysis methods. Machine learning methods, such as the local outlier factor (LOF) algorithm [37], the clustering outlier diagnosis algorithm [37], the support vector machine (SVM) [38], the relevance vector machine (RVM) [39] and the long short-term memory (LSTM) recurrent neural network [40], are computation-intensive since a large amount of historical data is required to train a better model. Statistical analysis methods typically employ signal processing techniques to calculate parameters like standard deviation [37,41], z-score [19,42], Shannon entropy [43,44], sample entropy [45,46], Pearson product-moment correlation coefficient [28,47], interclass correlation coefficient (ICC) [48], and so on. Since statistical analysis methods neither depend on accurate analytical models and the experience of experts, nor account for the complex fault mechanism and system structure, they have gained a lot of attention, especially the Shannon entropy method.
Most of the studies [41], [42], [43], [44], [45] on the entropy method related to LIBs focus on fault diagnosis for EVs. In this work, the entropy method is proposed to conduct online fault diagnosis as well as inconsistency evaluation for LIB ESSs. In brief, a general entropy-based procedure is established, which uses the cell-level Shannon entropy algorithm for fault detection of battery cells and exploits the module-level and cluster-level Shannon entropy algorithms to assess the overall inconsistency of LIB cells in each module and in each cluster of ESS respectively. The capability and effectiveness of the multi-level Shannon entropy algorithms for fault diagnosis and inconsistency evaluation are demonstrated by applying the proposed procedure to a large-scale stationary LIB based ESS (1 MW/2 MWh) [49].
The remainder of this paper is organized as follows. In Section 2, different algorithms based on the Shannon entropy are firstly illustrated. Then, the general entropy-based procedure for fault detection and inconsistency evaluation is presented. Section 3 briefly introduces the physical description as well as the coupled model of the investigated LIB ESS. After that, the results of applying the proposed entropy-based algorithms in fault diagnosis as well as inconsistency evaluation are discussed and analyzed in Section 4. Concluding remarks are given in the last section, Section 5.
Section snippets
Definition of Shannon entropy
Entropy can be explained in three differentiated but semi-related ways, namely, a macroscopic viewpoint (classical thermodynamics), a microscopic viewpoint (statistical thermodynamics), and an information viewpoint (information theory). Information entropy was put forward by Shannon [50] and that is why it is also called Shannon entropy, which can be used to assess the degree of system disorders and has been successfully and popularly applied in many disciplines with various purposes like
Physical description
The investigated LIB ESS, as shown in Fig. 2, is a commercial in-service stationary battery ESS owned by State Grid Corporation of China (SGCC) with the size of 10.64 m (length) × 2.59 m (width) × 2.25 m (height). It has ten independent clusters in parallel connection. Every cluster contains 38 modules in series connection. Every module is made up of six series-connected submodules, each of which is composed of eight parallel-connected LIB cells. Therefore, each module has 48 LIB cells in
Decision of appropriate parameters for entropy
Before applying the proposed algorithms based on entropies in fault diagnosis for the LIBs in the ESS, it is necessary to determine appropriate user defined parameters, such as the width of the sliding window, W, and the number of reconstructed intervals, D, as mentioned in the Section 2.2.
According to Eq. (2), W actually means the number of data used to calculate one Shannon entropy. The Shannon entropy needs to calculate the probabilities or the frequencies of data in each reconstructed
Concluding remarks
In this work, a general entropy-based approach is put forward to conduct fault diagnosis as well as inconsistency evaluation for LIB ESSs. To be more specific, the cell-level Shannon entropy algorithm is employed for fault detection and diagnosis while the module-level Shannon entropy algorithm and the cluster-level Shannon entropy algorithm are proposed to assess inconsistencies of LIB cells in each module and in each cluster respectively. The way that the entropies are calculated by these
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This research is supported by the China National Key R&D Project (2018YFB0905300, 2018YFB0905303) and the Science and Technology Project of China Southern Power Grid (YNKJXM20180358). The authors wish to thank the China State Grid Jiangsu Electric Power Co. Ltd. Research Institute for providing the physical/structural data of the investigated LIB ESS.
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These authors contributed equally to this work and should be considered co-first author.