Review on reliability assessment of energy storage systems

Abstract

As renewable energy, characterised by its intermittent nature, increasingly penetrates the conventional power grid, the role of energy storage systems (ESS) in maintaining energy balance becomes paramount. This dynamic necessitates a rigorous reliability assessment of ESS to ensure consistent energy availability and system stability. The authors provide a review of the existing research on ESS reliability assessment, encompassing various methods, models, reliability indicators, and offers an analysis of future research trends in ESS reliability. Firstly, the authors summarise the different types of ESS and their characteristics, analysing the trends in ESS reliability research and the unique characteristics of ESS compared to conventional power systems. Secondly, the methods used for the assessment are reviewed, including Markov methods, generalised generating functions, Monte Carlo simulations etc. The shortcomings and characteristics of these methods are discussed. The key reliability indicators, such as Mean Time Between Failures and Mean Time to Repair are emphasised. The applied role of reliability studies is summarised. Finally, the perspective of new research trends in ESS reliability assessment are identified, especially the integration of artificial intelligence and machine learning, and emphasises their potential to further improve the robustness and effectiveness of ESS reliability.

INTRODUCTION

Energy storage systems (ESSs) have emerged as a cornerstone in the contemporary global energy paradigm, marking a transformative shift in how energy is managed, distributed, and utilised. The essence of ESS lies in their ability to store energy in various forms—chemical, electrical, mechanical, or thermal—providing a crucial bridge between fluctuating energy supply and the escalating demands of modern societies. These systems, with their diverse applications, have become integral in enhancing the efficiency and stability of energy infrastructures worldwide [1–3]. As of 2023, the global ESS market is witnessing unprecedented growth, driven by the increasing integration of renewable energy sources. According to recent statistics, the global energy storage market is expected to expand significantly, with projections estimating a total installed capacity of over 300 gigawatts (GW) by 2030, a substantial increase from approximately 27 GW in 2020. This surge is indicative of the critical role ESS plays in stabilising grids, particularly in harnessing intermittent renewable sources, such as solar and wind energy. For instance, in the United States alone, the energy storage market witnessed a remarkable annual growth rate, with a deployment of about 3.5 GW in 2021, a trend that is anticipated to accelerate in the coming years [4].

The technological landscape of ESS is diverse, spanning from traditional battery systems like lead-acid, which have been the mainstay of energy storage for decades, to advanced lithium-ion batteries that currently dominate the market due to their higher energy densities and efficiency. Lithium-ion battery technology, in particular, has seen a rapid decrease in costs, with prices falling by approximately 89% between 2010 and 2020, making them increasingly viable for large-scale energy storage solutions [3, 5]. Beyond batteries, mechanical storage solutions, such as pumped hydroelectric storage (PHS), flywheels, and compressed air energy storage (CAES) contribute significantly to the ESS market. PHS, for instance, accounts for a substantial portion of the installed storage capacity worldwide, with over 160 GW of capacity globally as of 2021. These technologies offer unique advantages in terms of scalability and longevity, making them suitable for different applications [1].

However, the ascent of ESS is not without challenges, the foremost being the issue of reliability. The reliability of ESS is multifaceted, encompassing their capability to provide uninterrupted power, perform optimally under various conditions, and maintain longevity. The importance of ESS reliability particularly shines in applications involving renewable energy sources. Reliable energy storage is essential to effectively manage and mitigate the inherent intermittency of renewable energies, ensuring a steady and dependable energy supply that promotes widespread adoption and trust in these sustainable technologies. Moreover, by maximising the efficiency of both generation and consumption patterns, reliable storage systems help reduce waste and the carbon footprint of energy systems, enabling a transition towards a more sustainable and less carbon-intensive future [6]. Reliability assessment in ESS, therefore, emerges as a strategic imperative.

As ESS technologies continue to evolve and diversify, the complexities in ensuring their reliability intensify, necessitating advanced and nuanced evaluation methodologies [7]. At present, research on the reliability assessment of ESS is extensive and diverse, covering various aspects in a scattered fashion. Some studies focus exclusively on the intrinsic reliability of the storage systems themselves, while others incorporate the reliability of distribution networks, integrated energy systems, or renewable energy stations, such as wind and solar, within which these storage systems operate. Therefore, it is necessary to comprehensively review and organise the existing research findings, summarising the strengths and weaknesses of current reliability assessment methods. However, there are fewer review studies on the reliability of ESS currently, and most of them focus on the impact of ESSs on the reliability of power systems [6–8]. The authors in ref. [9] review the reliability assessment specifically for supercapacitor storage systems. The authors in ref. [10] review the reliability assessment of ESSs combined with other grid flexibility measures. However, its focus is on the combination of ESS with flexibility measures, and the summary of reliability assessment methods is oriented towards power systems.

This review aims to provide an exhaustive exploration of the current state of ESS. Firstly, different types of ESSs and characteristics are introduced. Then, the current research trends, basic definitions, and the differences between the reliability assessment of ESS and electric power systems are introduced. After that, the models, methods, and indicators in the reliability assessment of ESS are reviewed, and the advantages and disadvantages of different methods are analysed in depth. Furthermore, the applications of reliability assessment of ESS are summarised, including the impacts on promoting renewable energy. Finally, the challenges and trends of research on reliability assessment of ESS are given, and the characteristics and technical details of different trends are analysed in depth.

The rest of the paper is organised as follows: Section 2 presents an overview of ESS technologies and their characters. Section 3 introduces the basics of reliability assessment of ESS, including the research trends, definition of ESS reliability, and differences with power system reliability. Section 4 provides an overview of the current models, reliability modelling methods, reliability assessment methods, and reliability indicators for ESS. Section 5 provides an overview of the applications of ESS reliability assessment. Section 6 analyses the challenges and future research trends in reliability assessment of ESS. Section 7 is the conclusion. The content outline of the article is shown in Figure 1.

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TYPES OF ESSs

The categorisation of ESS is multifaceted, encompassing electrical, mechanical, thermal, and chemical storage, each with distinct applications and advantages [1, 11]. This section conducts an in-depth discussion on the characteristics and composition of several different types of energy storage as shown in Figure 2.

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Battery energy storage systems (BESS): BESSs, characterised by their high energy density and efficiency in charge-discharge cycles, vary in lifespan based on the type of battery technology employed. A typical BESS comprises batteries such as lithium-ion or lead-acid, along with power conversion systems (inverters and converters) and management systems for effective monitoring and control. Reliability assessment in BESS is multi-faceted, often employing cycle life testing to determine battery endurance, thermal management analysis to ensure safe operation, state-of-health monitoring to track battery condition over time, and the use of Markov models to predict failure probabilities and degradation patterns. These methods are crucial in understanding the operational stability and lifespan of the batteries, which are core to the functioning of BESS [12, 13].

Supercapacitor-based energy storage (SBES): SBESs, known for their rapid charge and discharge capabilities, have a high power density but typically a shorter lifespan compared to batteries. The composition of these systems includes supercapacitors themselves, power electronics for energy conversion, and sophisticated control systems to manage the rapid energy flow. The reliability assessment of such systems focuses on endurance testing for their charge-discharge cycles, analysing the capacitance stability over time, and conducting electrochemical analysis to evaluate the supercapacitors' performance under various operational conditions. These assessments are critical in ensuring that supercapacitors can reliably deliver high power bursts, a key requirement in applications, such as regenerative braking systems in vehicles [14].

Hydrogen energy storage systems (HESS): HESSs are emerging as a key player in sustainable energy solutions, marked by their ability to store large amounts of energy over extended periods. HESS is particularly noted for its potential in bridging the gap between energy supply and demand, especially with fluctuating renewable energy sources. A typical HESS setup includes hydrogen production units (like electrolyzers), storage tanks for high-pressure hydrogen gas, and fuel cells or turbines for energy conversion back to electricity. The reliability assessment of HESS is complex and multifaceted. It involves evaluating the efficiency of hydrogen production, the integrity and safety of storage under high pressure, and the effectiveness of conversion systems. Techniques such as stress testing of storage vessels, performance analysis of electrolyzers and fuel cells, and the application of probabilistic models for system failure and efficiency degradation are critical. These assessment methods are essential to ensure the safe operation, longevity, and economic viability of HESS, addressing challenges in sustainable large-scale energy storage [15].

Flywheel energy storage systems (FESS): FESSs, offering high power density and quick response times, are best suited for short-term energy storage applications. These systems typically consist of a rotating flywheel, a motor/generator set for energy conversion, a bearing system to support the rotating mass, and control electronics to manage operations. Reliability assessment in flywheel systems involves rigorous mechanical stress testing to evaluate the structural integrity of the flywheel, analysis of rotational stability to ensure consistent performance, and the use of lifetime prediction models to anticipate the system's longevity. This comprehensive assessment ensures the flywheel's reliable performance in applications requiring rapid energy discharge, such as in grid frequency regulation [16, 17].

Pumped hydro storage systems (PHSS): PHSSs, ideal for large-scale energy storage, provide long discharge times and high durability. These systems involve two water reservoirs at different elevations, turbines for energy conversion, pumps to move water between the reservoirs, and control systems to manage the operation. Reliability assessment in PHS includes structural integrity assessments to ensure the durability of the reservoirs and associated infrastructure, efficiency testing of turbines and pumps to confirm optimal performance, and hydrological modelling to predict the system's behaviour under various environmental conditions. Such assessments are essential in ensuring the long-term reliability and efficiency of PHS, particularly in grid-scale energy balancing [18, 19].

Redox flow batteries (RFB): RFBs, known for their scalability and long discharge times, have a lower energy density compared to solid batteries. These systems consist of electrolyte tanks, pumps to circulate the electrolyte, cell stacks where the energy conversion occurs, power conversion equipment, and control systems. The reliability assessment of RFB focuses on evaluating the lifespan of the membrane, stability of the electrolyte, and overall system efficiency. This often involves flow and electrochemical modelling to understand the intricate interactions within the battery and to predict its performance over time. Such assessments are crucial for ensuring the reliability of RFB, particularly in grid storage applications where their modularity and prolonged discharge durations are advantageous [20, 21].

Carnot batteries (CB): A technology based on heat pumps and heat engines, consisting of pumps, compressors, expanders, turbines, and heat exchangers. These components are scalable, making CB a potential alternative to PHES and CAES. Unlike PHES and CAES, which depend on pre-existing reservoirs or caves, CB can be installed virtually anywhere due to their geographical independence. This advantage arises from the fact that, in contrast to CAES where energy is stored as pressure, CB store energy as heat. Although they might require slight pressurisation of the reservoirs, the operating pressures are generally low, enabling the artificial construction of thermal tanks at various locations [22, 23].

Compressed air energy storage (CAES): CAES systems store energy by compressing air in underground caverns or containers, which are later released to generate electricity. These systems include air compressors, storage vessels, and expansion turbines. Reliability assessment in CAES focuses on the integrity of storage vessels, the efficiency of compression and expansion cycles, and the system's ability to provide consistent energy output. CAES is particularly effective for large-scale storage and grid balancing [24, 25].

RELIABILITY IN ESS

In the dynamic and evolving field of ESS, understanding and ensuring reliability is of paramount importance. This section delves into the trends, definitions, and distinctions of reliability assessment within these systems. It starts with a review of recent research trends, highlighting shifts in publication focus and volume over the past decade. The chapter then explores the foundational aspects of reliability, including its definition, key components, and metrics that are vital for assessing and ensuring the operational integrity of ESS. Finally, it examines the unique challenges and methods in the reliability assessment of ESS compared to traditional power networks, underscoring the need for tailored approaches due to the complexities and technological diversities of ESS.

Research trends in reliability assessment of ESS

The last decade has seen a dynamic shift in the focus and volume of reliability research pertaining to ESS. As shown in Figure 3, a graph of scientific data from 2013 to 2023, as plotted by web of science search data, gives us a comprehensive view of publications in the field, including articles, conference proceedings (referred to as ‘conferences’ in the figure), and other forms of publication.

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A cursory glance at the chart reveals a progressive increase in the number of papers, which underscores the burgeoning interest and vital importance of reliability in ESS. In 2013, the total publications were just under a hundred, which has surged to over three hundred by 2023, with a notable rise in the percentage of articles. This steep climb reflects a consolidated effort in academic and industry circles to address the reliability concerns associated with the varied forms of ESS.

From the data, we also observe a discernible change in the proportion of articles to meeting publications. Initially, in 2013, the volume of conference proceedings constituted a larger portion of the total publications. As time passes, the ratio gradually shifts in favour of journal articles. This shift indicates a maturing of the field, as findings and innovations discussed in conferences begin to crystallise into more formalised research articles. This dynamic between ‘article’ and ‘meeting’ publications throughout the years not only highlights the evolution of research communication in the field, but also mirrors the development and consolidation of knowledge in ESS reliability.

Definition and basic aspects of reliability in ESS

In the realm of ESS, reliability is a multifaceted concept, essential not only for the system's performance, but also for its integration into the broader energy infrastructure. Understanding reliability in ESS involves more than just assessing the likelihood of system failure; it encompasses the system's ability to perform its required functions effectively and efficiently under stated conditions over a specified period. This definition of reliability is crucial in the context of ESS, as these systems often support critical applications ranging from grid stability to renewable energy integration and emergency backup power.

Delving deeper into the concept, reliability in ESS can be broken down into several key components. Availability, one of these components, refers to the system's readiness to perform its function whenever needed. Dependability emphasises the system's consistent performance over time, underlining the system's ability to deliver stable and predictable power. Maintainability, another crucial aspect, involves the ease and speed with which an ESS can be restored to its operational state following any downtime or malfunction. Durability then looks at the system's capacity to withstand operational stresses and environmental conditions over its lifespan. Each of these components plays a vital role in defining the overall reliability of ESS.

Reliability profoundly impacts the operational effectiveness of ESS. Systems with high reliability ensure improved energy efficiency, as they utilise energy resources effectively and minimise wastage due to downtime or suboptimal performance. The lifespan of ESS is also directly linked to their reliability—systems designed and maintained with a focus on reliability tend to have longer operational lives. Moreover, the aspect of safety, integral to ESS, especially those in residential or critical infrastructure, is closely tied to reliability. Ensuring high reliability is imperative to prevent hazardous situations and to maintain the integrity and trust in these systems.

In essence, the reliability of ESS is a comprehensive and critical concept, influencing every aspect of a system's operation, from its efficiency and lifespan to its safety and maintenance. As the world increasingly turns to ESS for sustainable and resilient energy solutions, understanding and enhancing the reliability of these systems remains a paramount concern.

Differences between reliability assessment of ESS and power networks

The reliability analysis of ESS is markedly different from that of power networks (such as distribution and transmission grids). These differences are evident in several aspects:

Focus of assessment: In power networks, the primary concern is the reliability of the grid structure and consistent electricity supply. ESS reliability, however, is akin to component-level evaluation, concentrating on the system's operational capability. As ESS complexity increases with multiple components, it becomes essential to consider not only individual component reliability but also their collective impact on the overall system.

Model detailing: Power networks, comprising numerous nodes and components, typically use simpler two-state models for ease of modelling and focus on overall electricity supply capability. ESS models, in contrast, tend to be more intricate, often considering multiple states to provide a detailed component-level assessment.

Assessment methods: Reliability assessment in power networks generally relies on Monte Carlo (MC) simulations, and sampling failure states of components to calculate indicators, such as expected energy not supplied etc. ESS reliability assessments, conversely, often utilise Markov processes and universal generating function (UGF) methods to address the system's various states [26].

The reliability assessment of ESS presents distinct challenges and requirements when compared to traditional distribution or power systems, primarily due to their variable nature, complexity, integration issues, and technological diversities. This comparison highlights key differences in how reliability is approached and managed in these two critical components of the energy infrastructure.

In contrast to the relatively stable operation of traditional power systems, ESS is characterised by their variable nature, exemplified by charging and discharging cycles and state of charge (SOC) management. These operational variabilities introduce unique reliability challenges. For instance, the frequency and depth of charge-discharge cycles in battery storage systems can significantly impact their lifespan and performance. This variable operational profile requires a more dynamic approach to reliability assessment, focusing on the endurance of components under fluctuating conditions and the system's ability to maintain optimal performance over time.

Further complexity in ESS reliability assessment arises from their integration into the power grid or operation as standalone systems. When integrated into the grid, ESS must seamlessly interact with existing infrastructure, managing not only their internal reliability concerns, but also contributing to the overall stability of the grid. This integration introduces challenges, such as managing bidirectional energy flows and ensuring compatibility with grid support functions. Standalone ESS, on the other hand, face challenges in maintaining reliability as independent power sources, often in remote or critical applications where failure can have significant consequences.

Additionally, the technological diversities within ESS call for tailored approaches to reliability assessment. Different ESS technologies, such as lithium-ion batteries, flow batteries, and flywheels, each have unique operational characteristics and failure modes. For example, the reliability assessment of lithium-ion batteries heavily focuses on aspects, such as thermal management and degradation over time, whereas for flow batteries, the emphasis might be on the integrity of the electrolyte and membrane systems. This diversity contrasts with more homogeneous traditional power systems, where reliability assessments can often follow a more standardised approach.

In summary, the reliability assessment of ESS requires a multifaceted and adaptive approach, reflecting the systems' variable nature, integration complexities, and diverse technologies. This approach is crucial in ensuring that ESS not only operates reliably as individual units but also contributes effectively to the broader energy system's stability and resilience. As ESS continues to evolve and play an increasingly prominent role in energy infrastructure, understanding and addressing these unique reliability challenges becomes ever more important.

RELIABILITY MODELS, METHODS, AND INDICATORS OF ESS

The reliability of ESS encompasses a complex spectrum, requiring an array of models, methods, and indicators to assess and ensure their dependable operation. This section explores the general processes, models, approaches, and indicators used in the reliability assessment of ESS as illustrated in Figure 4. It is important to note that most studies on the reliability assessment of ESS focus on distribution grids, microgrids, or renewable energy generation systems that include energy storage, taking into account the operational strategies of these storage systems. Therefore, the operation and control models of ESS are often referred to as reliability models in those research articles. In this section, we review the probabilistic models and modelling approaches used in the reliability assessment of ESS.

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General process to reliability assessment of ESS

The essence of reliability assessment in ESS revolves around ensuring that systems can consistently perform their intended function under specified conditions. The overall assessment process includes establishing state models, selecting appropriate assessment methods, and calculating reliability indicators.

At present, the models used for the reliability assessment of ESS can be categorised based on the level of detail in state division into two-state models and multi-state models. For reliability assessments involving ESS in power systems, distribution networks, or integrated energy systems, the two-state model of energy storage is commonly used. On the other hand, multi-state models are employed when focusing more on the reliability assessment of the ESS itself.

Reliability assessment approaches typically integrate both quantitative and qualitative analyses. In quantitative reliability assessment, statistical and probabilistic models are utilised to predict the likelihood of system failures and their impacts. This includes statistical analysis, which employs historical failure data to forecast future reliability, and probabilistic models such as MC Simulations and event tree analysis that map potential failure paths and their probabilities. Life cycle analysis is also pivotal, assessing the reliability over the entire lifespan of the ESS, considering factors, such as degradation, wear and tear, and maintenance schedules. Qualitative approaches, on the other hand, focus on non-quantifiable aspects such as design robustness, system redundancy, and quality control measures. Methods such as failure modes and effects analysis (FMEA) identify potential failure modes and their effects on system performance, while the root cause analysis determines the underlying causes of observed failures or performance issues. Expert judgement and the Delphi Method are also employed, leveraging expert opinions and consensus-building to assess reliability in scenarios with limited data.

The diversity in ESS technologies, from lithium-ion batteries to FESS, necessitates tailored approaches in reliability assessment. For BESS, emphasis is placed on evaluating lifespan and performance under different charge–discharge cycles, temperature conditions, and load scenarios. In FESS, the focus is on mechanical integrity, rotational stability, and bearing performance, using methods such as dynamic simulation and stress analysis. For supercapacitors, assessment centres around capacitance retention and thermal stability.

In summary, the reliability assessment of ESS is a comprehensive process integrating diverse methodologies tailored to specific system types and operational scenarios. By combining quantitative and qualitative approaches, along with continuous monitoring and robust metrics, the reliability of ESS can be effectively evaluated and enhanced, ensuring their pivotal role in modern energy systems is carried out with utmost dependability.

Reliability models of ESS

In the dynamic field of ESS, developing accurate and effective reliability models is crucial for predicting system behaviour, guiding maintenance strategies, and refining design methodologies. The complex and diverse nature of ESS demands a variety of modelling approaches, each tailored to specific characteristics and behaviours of these systems. These models range from simple binary state models to more complex multi-state representations, each providing unique insights into the system's reliability.

Two-state models

Representing the most fundamental approach, the Two-State Model simplifies the system's status into two distinct states: operational or failed [27]. This model is defined by Equations (1) and (2): 1 $$\begin{array}{c}G=\left\{{g}_{\text{operation}},{g}_{\text{fault}}\right\}\end{array}$$ 2 $$\begin{array}{c}P=\left\{{p}_{\text{operation}},{p}_{\text{fault}}\right\}\end{array}$$ where G is the set of all states, P is the set of all states probabilities, g_normal and g_fault represent the operation and fault state respectively, p_operation and p_fault represent the operation and fault state probability respectively, which can calculated by Markov method.

As the system only has two states, the probability of being in the normal state is considered the system's reliability at that moment [28]. 3 $$\begin{array}{c}R(t)={p}_{\text{operation},t}\end{array}$$

This model is particularly useful in assessments of simple ESS considered as a single component within distribution or power systems [29–32]. In broader system reliability assessments, the model is often used to provide sampling probabilities for MC simulations. Thus, the probabilities of operating and fault states are often more important to the model than the reliability results. However, it cannot capture complexities in systems that undergo gradual degradation or multiple performance states [27].

Multi-state model

Addressing the limitations of the Two-State Model, the Multi-State Model offers a more detailed perspective, accommodating ESS exhibiting a range of operational states. This model is particularly apt for systems where performance can degrade over time or operate under partially functional conditions [33, 34].

The n states model can defined by the Equations (4) and (5): 4 $$\begin{array}{c}G=\left\{{g}_{1},{g}_{2},{g}_{3},\text{\ldots },{g}_{i},\text{\ldots },{g}_{n}\right\}\end{array}$$ 5 $$\begin{array}{c}P=\left\{{p}_{1},{p}_{2},{p}_{3},\text{\ldots },{p}_{i},\text{\ldots },{p}_{n}\right\}\end{array}$$ where g_i is the i th state, p_i is the ith state probability, and n is the number of the state.

This model is crucial for sophisticated ESS such as advanced battery systems and flywheels, where performance can vary significantly. The formation of multi-state models can be differentiated into two types: (1) Combination of two-state components: Here, each component fundamentally follows a Two-State Model, but their combinations lead to a system exhibiting multiple states. This model often employs Markov methods to combine the states of components [35]. These are solved by analysing the transition relationships between states, leading to the listing of state transition matrices as shown in Figure 5. (2) Inherent multi-state components: This approach considers multiple states within each component, and thus, the system as a whole is multi-state. In this case, the general generating function is often used to handle multiple states [36–38]. When there are few states, the Markov process can also be used to handle it [39].

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For example, in BESS, multi-state classification at the component level might focus on the degradation and ageing of individual cells, categorised by State of Health (SOH), charge capacity, or internal resistance [36, 40]. At the system level, BESS might be classified based on overall energy capacity or power output efficiency [40]. In FESS, component-level states could be defined by rotational stability or wear levels of bearings, while system-level states might include overall energy storage capacity or system efficiency under different operational conditions. Supercapacitor-based systems might have states determined by capacitance levels and electrochemical stability at the component level, and power delivery efficiency at the system level [9].

In a multi-state model, determining the probabilities of various states is a critical task. This is done based on historical data, degradation models, or stress analysis. In situations where sufficient historical data is not available, statistical distributions like the normal distribution are utilised to estimate these probabilities. For instance, in BESS, battery SOH degradation under various conditions can be used to estimate state probabilities, while in flywheel systems, historical performance under comparable stress conditions can inform the likelihood of different states. In supercapacitor-based systems, cycle life tests and capacitance stability analyses contribute to the probability estimation of each state.

In multi-state models, a minimum acceptable system state threshold is often defined, and reliability is based on this threshold [36]: 6 $$\begin{array}{c}R(t)=\sum\limits _{i\in \left\{i\vert {g}_{i} > \gamma \right\}}{p}_{i,t}\end{array}$$ where R(t) denotes the system's reliability at time t, p_i represents the probability of being in the state g_i, γ is the status threshold, indicating the worst state of the system that can be introduced, and {i|g_i > γ} is the set consisting of all states greater than the state threshold γ.

This model allows for a more detailed and realistic analysis of the system's behaviour over time, considering the varying likelihoods and impacts of different operational states. Advanced battery storage systems, particularly those with capabilities for partial-state operation, are prime candidates for Multi-State Modelling. This is because their performance can degrade predictably over time, transitioning through multiple states before reaching complete failure. Similarly, newer flywheel designs, which might operate at different efficiency levels depending on the state of components like bearings or rotors, also benefit from this modelling approach. The application of multi-state models in current ESS technologies is increasingly important as these systems become more sophisticated. The ability to accurately predict and analyse the reliability of systems across various operational states not only aids in optimising performance but also plays a crucial role in maintenance scheduling and lifecycle management. This model provides a more realistic representation of ESS operation, essential for ensuring the longevity and efficiency of these advanced energy storage solutions.

The reliability models for ESS, from the two-state to the multi-state, provide a comprehensive framework to assess and predict the performance of these crucial systems. Each model plays a specific role, from offering a basic understanding of system reliability to providing an in-depth analysis of performance under varying conditions, ensuring the long-term efficiency and viability of ESS technologies.

Reliability modelling methods of ESS

Reliability modelling for ESS is essentially a method of calculating the probability of different states of ESS, thus also known as probabilistic modelling. Reliability modelling is the basis for conducting reliability assessment, and this section reviews various modelling approaches oriented to state modelling of ESS.

Directly calculate probability based on distribution

This method primarily relies on the assumption that failure times of ESS follow a specific statistical distribution, where the exponential distribution is often used due to its simplicity and the memoryless property, which states that the future probability of failure does not depend on how long the system has already been functioning. Thus, in the context of ESS, reliability calculations based on distribution are used to estimate the likelihood that the system will perform without failure over a given period. Reliability is usually calculated based on this distribution [36], given by: 7 $$\begin{array}{c}R(t)=\mathit{Pr}\,(T > t)={e}^{-\lambda t}\end{array}$$ where R(t) is the reliability at time t and λ is the constant failure rate. It provides an estimate of the average time a system is expected to operate without failure.

Additionally, considering different failure rates for various states in an ESS [41], a simplified approach for estimating multi-state system reliability is defined as follows: 8 $$\begin{array}{c}R(t)=\sum \nolimits_{i=1}^{n}{p}_{i}{e}^{-{\lambda }_{i}t}\end{array}$$ where, n represents the number of states, p_i is the probability of being in state i, and λ_i is the failure rate for state i.

To implement this method, data on the historical failure rates of ESS is required. This data is used to estimate the parameter λ, which is crucial for calculating the reliability function. This method is especially effective for ESS components that are expected to have constant failure rates over their operational lifetime, such as inverters and power electronics.

While useful, this method has limitations, particularly in handling systems or components with non-constant failure rates, which can occur due to ageing or environmental factors affecting the components over time. Additionally, the simplicity of the exponential distribution may not accurately represent the actual behaviour of more complex or new types of ESS technologies, such as those involving advanced battery chemistries that might exhibit variable degradation patterns. What's more, as the capacity of the ESS continues to increase, for which the battery degradation will be more obvious, different performance degradation will also affect the reliability, only assuming that the ESS obeys a certain distribution ignores the impact of battery performance.

Markov method

The Markov method is grounded in the theory of stochastic processes, specifically designed to model systems that undergo transitions from one state to another in a probabilistic manner. The core principle of this method is that the future state of the system depends only on its current state and not on how it arrived there (the Markov property). In the context of ESS, the Markov method is adept at capturing the dynamic behaviour of systems, particularly those involving components such as batteries whose performance and reliability deteriorate over time. Markov models can be constructed to represent various states of ESS health, such as different levels of battery degradation, and to simulate transitions between these states based on probabilities that can be derived from empirical data or predictive models. This method is effective for assessing the reliability of ESS by predicting the likelihood of remaining in operational states versus transitioning into failed or degraded states [42, 43].

Markov methods can be divided into discrete-time Markov processes (state transitions occur at a fixed time node) and continuous-time Markov processes (state transitions can occur at any time), based on whether the occurrence time of state transitions is continuous. But the prerequisite for both processes is to build the state transition matrix P of the system [35, 44–47]. 9 $$\begin{array}{c}P=\left[\begin{array}{@{}ccc@{}}{p}_{1}& {\cdots}& 0\\ {\vdots}& {\ddots}& {\vdots}\\ 0& {\cdots}& p\end{array}\right]\end{array}$$ where the p_n is the transition probability which usually use the failure rate and repair rate of the component.

In discrete-time Markov models, system transitions occur at fixed time intervals, making them apt for scenarios where changes are periodic. The state probabilities in these models can be calculated using the formula [48]: 10 $$\begin{array}{c}P(t)=P(0)\ast {P}^{t}\end{array}$$ where P^t is the tth power of the transition probability matrix P, P(t) is the state probability at time t, and P(0) is the initial state probability.

Continuous-time Markov models, on the other hand, are used when transitions can happen at any continuous time point. They are more suitable for physical systems such as ESS, where changes can occur unpredictably. The key component of continuous-time models is the rate matrix Q, and the state probabilities are generally determined by solving differential equations or through exponential matrices. A typical formulation for the continuous-time state probabilities involves solving [49]: 11 $$\begin{array}{c}\frac{dP(t)}{dt}=P(t)\ast Q\end{array}$$ where Q is the rate matrix.

While powerful, the Markov method has some limitations: (1) Estimating accurate transition probabilities requires extensive data, which may not be available for newer or less-studied ESS technologies. (2) The complexity of the model increases significantly with the number of states, which can make the analysis computationally intensive and difficult to manage. (3) Simplifying assumptions about state transitions may not capture all real-world complexities, especially in hybrid systems with interactions between different types of components [42].

Universal generating function (UGF)

The UGF is a probabilistic method extensively utilised in systems reliability analysis, especially suitable for complex and multi-component systems. The UGF integrates performance distributions of system components into a single function, allowing for the computation of the combined system reliability and performance levels. It is particularly useful for systems where component performance can be quantitatively expressed and where these performances contribute to the overall system behaviour. [36–38, 47]. The UGF of a component is expressed in the form: 12 $$\begin{array}{c}U(s)=\sum {p}_{k}{s}^{{q}_{k}}\end{array}$$ where p_k is the probability of the component being in state k and q_k is the performance level in that state.

The core principle of UGF lies in its use of polynomial algebra to depict a system's probabilistic performance, taking into account the different states and the probabilities associated with them. This approach is particularly useful in hybrid ESS, where diverse technologies are involved, as it allows for a seamless aggregation of the performance probabilities of the various components within the system [43].

As the complexity of the system increases, involving a variety of components each with its probability distribution and performance level, directly calculating the entire system's UGF becomes impractical. In this scenario, the recursive algorithm in UGF computation becomes critically important. It systematically constructs the UGF by progressively combining the generating functions of smaller subsets of the system as shown in Figure 6. This method not only simplifies the computational process, but also ensures accuracy in the assessment [39].

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First, the system needs to be divided into smaller subsystems or components. The UGF for each component should then be calculated using Equation (12).

Then, these individual UGFs should be combined step by step. At each step, the algorithm merges similar items—terms in the generating functions with the same power of s. For instance, if two components have generating functions U₁(s) and U₂(s), their combined UGF, representing the joint system, would be calculated by multiplying these functions and then merging terms with the same power of s. 13 $$\begin{array}{c}{U}_{\text{combine}}(s)={U}_{1}(s)\bigotimes{U}_{2}(s)\end{array}$$ where U_combine(s) is the combined UGF function and ⨂ is the defined operation rule, which is generally defined as follows according to the series and parallel connection relationship of the system: 14 $$\bigotimes\left({q}_{1},{q}_{2}\right)=\left\{\begin{array}{@{}l@{}}\max \left({q}_{1},{q}_{2}\right),\text{parallel}\\ \min \left({q}_{1},{q}_{2}\right),\text{series}\end{array}\right.$$

The process repeats, the process repeats, progressively combining the UGFs of additional components or subsystems until the generating function for the entire system is constructed.

However, one notable challenge in applying UGF is the need for detailed probabilistic information about each component within the system. This requirement can sometimes be complex, especially in systems with a large number of components or with components that have intricate performance characteristics. Additionally, UGF assumes independence or specific dependency forms between components which may not always capture complex real-world interactions within ESS [50].

Furthermore, the UGF method can be effectively combined with stochastic processes to enhance its predictive power in ESS reliability assessment.

This approach is represented by a generalised function 15 $$\begin{array}{c}G(x,t)=\sum {p}_{i}(t){x}^{{q}_{i}(t)}\end{array}$$ where p_i(t) and q_i(t) are the probability and performance level of state i at time t, respectively.

By integrating stochastic models, the approach accommodates dynamic changes and probabilistic transitions between different states of system components over time. This extension allows the UGF to not only assess the static probability distributions of system outcomes, but also to capture the temporal evolution of system reliability as influenced by external conditions and internal degradation processes. For instance, stochastic models can simulate random fluctuations in usage patterns, environmental conditions, and maintenance schedules, providing a more dynamic and realistic assessment of ESS reliability [51–53].

This advanced integration is particularly effective in scenarios involving ESS with complex operational conditions and where reliability needs to be forecasted over longer periods under variable conditions. It is also valuable in research and development settings where new ESS technologies are being tested for their robustness in fluctuating operational environments. While offering a more comprehensive analysis, the integration of UGF with stochastic processes also introduces greater complexity in terms of data requirements and computational intensity. Accurate modelling of stochastic processes demands extensive data and sophisticated analysis techniques, which may pose challenges in practical applications.

In addition to the above general modelling approaches for probabilistic modelling of ESS, there are a variety of other theoretical approaches that are often combined in the reliability modelling process, such as fuzzy theory, Bayesian network (BN) approaches, and so on. They are usually not used directly as a modelling method, but in combination with the modelling methods described above.

Application of fuzzy theory in ESS reliability assessment

In the reliability assessment of ESS, the application of fuzzy theory offers a nuanced approach to handle uncertainties and imprecise information [54–58]. This method is particularly relevant when dealing with systems where traditional statistical data is either unavailable or not wholly reliable [59, 60].

The application of fuzzy theory in ESS is conducted through fuzzy rules and inference systems. These rules use linguistic variables, enabling the system to infer the reliability of an ESS based on the fuzzy sets defined for its components. For example, if the SOH of a battery is ‘low’, and the operating temperature is ‘high’, a fuzzy rule might infer that the reliability of the battery is ‘moderately low’ [61–63]. So, Fuzzy theory is most effective in ESS reliability assessment scenarios where: (1) Data is uncertain or incomplete, or it is derived from subjective assessments. For instance, a membership function could be used to describe SOH of a battery in an ESS, where the SOH might not be precisely known [61]. (2) Traditional probabilistic models are inadequate because they cannot accommodate the vagueness or ambiguity inherent in system inputs. (3) Decisions need to accommodate human-like reasoning to assess complex scenarios that do not lend themselves to precise mathematical models.

However, fuzzy theory also presents challenges [54]. Its subjective nature can lead to less precise outcomes compared to quantitative methods. Accurate definition and interpretation of fuzzy sets and rules are crucial for effective reliability assessment.

Application of Bayesian network (BN) in ESS reliability assessment

Bayesian Networks are particularly valued for their ability to handle uncertainty and to model complex systems where interactions between variables are not straightforwardly additive or linear.

In the context of ESS, BN is applied to model the complex interactions between various components and environmental factors that affect system reliability. It provides a comprehensive view of how these factors collectively influence the probability of system failure or degradation, allowing for more nuanced reliability predictions and system diagnostics. For instance, BNs are capable of taking into account the probabilistic dependencies between variables such as battery wear, temperature effects, charge cycles, and maintenance schedules. Implementing BNs in ESS reliability assessment involves several key steps: Variable Identification: Determine the key variables that impact the reliability of the ESS, including both observable parameters (e.g. battery voltage, temperature) and latent factors (e.g. material fatigue). Structure definition: Define the structure of the BN, that is, how variables are conditionally dependent on each other. This is often based on expert knowledge or derived from data analysis. Parameter estimation: Assign probabilities to the transitions between different states of each variable, which can be based on historical data, experimental data, or expert estimates. Inference: Use inference algorithms to update the belief about the system's state as new data becomes available, which helps in predictive maintenance and risk assessment.

BNs are particularly effective in ESS reliability assessment in scenarios where: (1) There is complex interdependency between various system components and external factors. (2) There is a need to integrate different types of data, including subjective expert opinions and objective measurements. (3) Systems are dynamic, and continuous learning from new data is crucial for maintaining reliability [64–66].

However, BNs also have some limitations: (1) The accuracy of the results heavily depends on the quality and completeness of the data used for parameter estimation. (2) Scalability can be an issue as the complexity of the network grows, potentially leading to increased computational demands for inference.

Reliability assessment methods of ESS

Reliability assessment methods are in the utilisation of probabilistic models for energy storage. This section summarises the current stage of reliability assessment methods for ESS.

Directly calculate reliability by definition

The research focuses on the reliability of ESS itself, their purpose is to construct a more refined and accurate reliability model of ESS. So, in most of the research, after constructing the reliability model of ESS based on the method mentioned in part 4.3 and obtaining the state probability, the reliability is obtained directly based on Equations (3) or Equation (6).

Application of sampling simulation methods in ESS reliability assessment

Sampling methods, represented by MC simulation, Markov Chain Monte Carlo simulation, and Latin hypercubic sampling, are typical choices when assessing the reliability of ESS. These methods are grounded in statistical theory and provide ways to model the probability of different outcomes in complex systems, which are difficult to predict due to the intervention of random variables.

Implementing these simulations in ESS reliability assessment involves: Defining a model of the system that includes all relevant components and their interactions; Identifying the probability distributions for each uncertain parameter (e.g. failure rates, repair times, load demands); Randomly sampling from these distributions to simulate different scenarios of system operation; Repeating the simulations a large number of times to obtain a statistical distribution of the system's reliability.

The simulations are most effective in scenarios where detailed probabilistic assessment is needed to inform planning and decision-making processes, particularly for systems that incorporate ESS within a larger energy infrastructure. Therefore, in practice, this type of sampling method is applied to the reliability assessment of the ESS itself less, only in the case of extremely complex ESS, such as large-scale battery storage systems containing a large number of batteries, based on MC simulation to extract faulty batteries to form different scenarios [67]. The primary applications of this method are found in microgrids, distribution networks, integrated energy systems, or wind and solar storage stations that include ESSs. Here, the energy storage is considered as a component or part, and is involved in simulation sampling based on established two-state or multi-state models. At this point, a crucial consideration for the ESS is its dispatch operation strategy. Regulatory or configurational measures related to energy storage, which take into account demand response, flexibility standby, peak shaving, valley filling, and the promotion of new energy consumption, are often integrated into the reliability assessment. Thus, in these cases, less attention is paid to the reliability of the energy storage itself, and more emphasis is placed on the operational reliability of the storage system. These methods are used to assess the reliability of these systems by simulating thousands of possible scenarios, considering the randomness and variability of factors, such as load demands, component failures, weather conditions, and operational strategies [35, 68–73].

While these simulations are versatile and capable of modelling a wide range of situations, they are computationally demanding, requiring multiple iterations to obtain accurate results. Moreover, the computational complexity increases with the number of variables and the complexity of the system, and the results depend heavily on the quality of the probability distribution chosen [74].

Application of analytical methods in ESS reliability assessment

Typical analytical methods, such as fault tree analysis (FTA), reliability block diagram, and system efficiency analysis, rely on accurate mathematical models to predict system behaviour without the need for large-scale stochastic sample simulations. As the scale and complexity of ESS increase, traditional analytical methods are often difficult to adapt to the dynamic changes and variability of modern ESS operations, and their use in reliability assessment is gradually decreasing. However, these methods show high efficiency and accuracy when dealing with conventional systems that do not involve random variable disturbances. That is why analytical methods are still valuable in certain situations, such as when the operating environment is stable and predictable, or when regulatory standards require a detailed failure mode analysis.

At this stage, most of the research on the use of analytical methods in ESS involves BESS or HESS []. For applications in BESS, the focus is generally on specific novel topologies and the design of a novel analytical method. For applications in HESS, an example is the FTA method, which uses logic diagrams to map the relationships between hydrogen storage system failures and their root causes [75–77].

In general, though, the focus has shifted to more flexible and adaptable assessment techniques as ESS technology advances and becomes more closely integrated with variable renewable energy and smart grid technologies. The trend of these methods has been to integrate and adapt them with more modern technologies, resulting in a more holistic approach to ESS reliability that balances rigour and flexibility [78–81].

comprehensive assessment of reliability based on indicators

In addition, some studies have assessed the reliability of ESS directly based on indicators. The comprehensive assessment of reliability is carried out by establishing a few relevant indicators and using the corresponding comprehensive assessment method. One of the main advantages of this approach is its simplicity and clarity, as it provides clear indices for measuring system performance. However, the validity of the method is limited by the choice of indices; if the indices do not adequately reflect the complexity of the ESS or the environment in which it operates, the assessment may not provide a full picture of the system's reliability. In addition, the methodology requires accurate and continuous data collection [57, 82].

Comparative analysis of reliability methods for ESS

To compare different reliability assessment methods more intuitively, a comparison is made between the various reliability assessment methods mentioned in terms of the following criteria: Applicability: Whether the method is widely applicable across various types of ESS. A comparison of the various reliability assessment methods mentioned is presented in Table 1. The meanings of the criteria for each assessment are as follows:

• Applicability: Whether the method is widely applicable across various types of ESS.

• Ease of use: User-friendliness and the learning curve associated with the method.

• Accuracy: The precision and reliability of the method in assessing system reliability.

• Scalability: How well the method can be applied to larger and more complex systems.

• Data requirements: The amount and type of data necessary for the method to be effective.

• Real-time capability: Whether the method can be used for real-time reliability assessments.

• Probabilistic/deterministic: Whether the method primarily uses probabilistic models to deal with uncertainties or deterministic models for fixed outcomes.

TABLE 1 Comparison of different reliability assessment methods of ESS.

Reliability methods	Applicability	Ease of use	Accuracy	Scalability	Data requirements	Real-time capability	Probabilistic/deterministic
Modelling methods	Exponential distribution model		✔			✔		Probabilistic
Markov model	✔		✔	✔	✔		Probabilistic
UGF	✔		✔	✔	✔	✔	Probabilistic
UGF with stochastic processes	✔		✔	✔	✔	✔	Probabilistic
Assessment methods	Calculate by definition	–	✔			✔		Deterministic
Simulation methods	MC	–	✔		✔		✔	Probabilistic
MCMC	–		✔	✔		✔	Probabilistic
LHS	–		✔	✔		✔	Probabilistic
Analytical methods	FTA	–		✔		✔		Deterministic
RBD	–		✔		✔		Deterministic
SEA	–		✔		✔		Deterministic

Table 2 provides a comprehensive overview that combines the various ESS techniques with the most effective reliability assessment techniques to statistically characterise the types of energy storage for which the various methods are applicable at this stage of research.

TABLE 2 Suitability of reliability assessment methods for different types of ESSs.

Reliability modelling method	Suitable types of energy storage systems	Ref
Modelling methods	Exponential distribution models	Traditional battery systems, mechanical storage systems	[29, 30, 38, 46]
Markov models	Advanced lithium-ion batteries, flywheel storage systems	[37, 42, 49, 51]
Universal generating function (UGF)	Hybrid storage systems combining different technologies	[38–41]
Generalised generating functions	ESS with non-linear behaviours or performance variations over time	[67–69]
Assessment methods	Calculate by definition	Assessing the reliability of ESS itself alone, without considering operational impacts	[78, 79]
Simulation methods	ESS integrated with fluctuating renewable energy sources	[37, 71–75]
Analytical methods	Complex ESS for identifying potential failure modes and causes	[82–86]

Exponential distribution models, with their simplicity, are best suited for traditional battery systems and mechanical storage where changes are abrupt and predictable. They offer a quick way to estimate reliability but may not capture the nuances of complex systems.

Markov models excel in dynamic environments, such as advanced lithium-ion batteries or systems with clear operational phases like some flywheel storage systems. They can accurately represent state transitions but require precise data about these transitions, making them less suitable for systems without well-defined states or insufficient operational data. UGF is particularly advantageous for hybrid storage systems combining different technologies. It provides a detailed aggregation of individual component performances. However, its effectiveness hinges on the availability of comprehensive probabilistic data for each component, which might be challenging to gather, especially for newer or less-studied technologies.

Monte Carlo simulations stand out in scenarios with high variability and uncertainty. They are ideal for ESS integrated with fluctuating renewable energy sources, such as solar or wind. The method's strength lies in its ability to simulate a wide range of scenarios, although it requires significant computational power and numerous iterations for accuracy. Bayesian networks are superb for complex ESS with interdependent factors, such as systems combining various types of energy storage or those with intricate control mechanisms. They offer a profound understanding of probabilistic relationships within the system but necessitate a detailed understanding of these relationships and can be complex to construct. Generalised generating functions with stochastic processes are suitable for ESS exhibiting non-linear behaviours or performance variations over time, like certain types of thermal storage systems or advanced battery chemistries. These models provide a dynamic view of system performance over time but are mathematically complex and need time-dependent probabilistic data. FTA is most effective for complex ESS where identifying potential failure modes and their root causes is crucial. This method offers a clear visualisation of failure paths but can become unwieldy for large systems with numerous components.

In conclusion, the selection of a reliability evaluation methodology for ESS should be based on the specific characteristics of the storage system, the nature of its operation, and the availability of data. Simpler methods such as exponential distribution models are suitable for less complex systems, while methods such as Markov models, UGF, and Bayesian networks are better for more complex systems with detailed operational data. Monte Carlo simulations and FTA provide comprehensive insights but require significant computational efforts and accurate data. Understanding the strengths and limitations of each method is key to effectively assessing and enhancing the reliability of diverse ESS technologies.

Fault modelling methods for ESS

At present, there are numerous fault-based analysis methods for assessing the reliability of power networks, such as FMEA, FTA, and Simulation-Based Fault Modelling. However, in the current reliability assessment of ESS, faults are often assessed as a singular state. Detailed fault analysis and related models are primarily considered in BESS, specifically focussing on thermal runaway (TR) faults in batteries [37, 83].

In the assessment of the reliability of BESS considering battery thermal failure models, advanced thermal modelling is integrated to evaluate the risks associated with TR. This involves using the heat generation model, which accounts for heat produced due to internal resistance and changes in the SOC 16 $$\begin{array}{c}{Q}_{\text{gen}}={I}^{2}\ast {R}_{\mathrm{int}}+{\increment}H\frac{d\text{SOC}}{dt}\end{array}$$ where Q_gen represents the heat generated within the battery, I is the current flowing through the battery, R_int is the internal resistance of the battery, ∆H is the heat generated or absorbed per unit change in SOC, and $$\frac{d\text{SOC}}{dt}$$ is the rate of SOC.

Additionally, TR risk is evaluated using the function (17), linking risk to temperature, SOC, and current. 17 $$\begin{array}{c}TRR=f(T,\text{SOC},I)\end{array}$$ where TRR is TR risk and T is the temperature of the battery.

The battery life degradation is modelled by Equation (18) considering the impact of temperature on the SOH of the battery. 18 $$\begin{array}{c}\frac{d\text{SOH}}{dt}=-k\ast \text{SOH}\ast {e}^{-\tfrac{{E}_{a}}{RT}}\end{array}$$ where $$\frac{d\text{SOH}}{dt}$$ is the rate of SOH degradation, k is a constant, E_a is the activation energy, R is the universal gas constant, and T is the temperature.

These models collectively offer a nuanced understanding of thermal risks in battery systems, allowing for the development of mitigation strategies to enhance safety and reliability. The comprehensive nature of this approach necessitates detailed data on battery properties and operational conditions, making it a complex yet thorough method for reliability assessment.

Reliability indicators of ESS

Reliability assessment in ESS encompasses a range of indicators, essential for determining the robustness and dependability of these systems. Traditional, universal indicators used across various types of ESS include mean time between failures (MTBF), mean time to repair (MTTR), and failure rate. These indicators offer insights into system performance, longevity, and overall reliability [10].

The MTBF is represented as follows: 19 $$\begin{array}{c}\text{MTBF}=\frac{\sum \nolimits_{i=1}^{n}{T}_{i}}{n-1}\end{array}$$ where T_i is the operational time between the (i-1)th and ith failure and N is the total number of failures, providing a measure of the expected operational time between failures. This indicator helps predict the average time an ESS is likely to function without interruption.

MTTR is calculated as follows: 20 $$\begin{array}{c}\text{MTTR}=\frac{\sum \nolimits_{i=1}^{n}{R}_{i}}{n}\end{array}$$ where r_I is the repair time for the ith failure, which measures the average time required to repair and restore the system. This encompasses the time taken to diagnose a problem, implement a fix, and return the system to operational status.

The failure rate (λ) is another critical indicator, formulated as Equation (21). It quantifies the frequency of system failures over a given operational period 21 $$\begin{array}{c}\lambda =\frac{n}{\sum \nolimits_{i=1}^{n}{T}_{i}^{\text{all}}}\end{array}$$ where λ is the rate at which failures occur in a system, n is the total number of observed failures, $${T}_{i}^{\text{all}}$$ is the total operational time.

In the modelling of multi-state systems for ESS, besides reliability, common metrics like performance expectation, importance, and contribution are also applicable for assessing the reliability of ESS [36, 84].

Performance Expectation: This metric evaluates the expected performance of a system in its various states. The performance expectation is a weighted average of the performance levels in each state, taking into account the probability of being in each state. The formula can be represented as follows: 22 $$\begin{array}{c}E(X)=\sum \nolimits_{i=1}^{n}{P}_{i}{x}_{i}\end{array}$$ where E(X) is the performance expectation, p_i is the probability of the system being in state i, and x_i is the performance level in state i.

Importance: This metric measures the significance of each state or component in contributing to the overall system's performance. It can be quantified by analysing how changes in a particular state or component affect the system's overall performance. The formula for calculating the importance of state i can be defined as follows: 23 $$\begin{array}{c}{I}_{i}=\frac{\partial E(X)}{\partial {p}_{i}}\end{array}$$ where I_i is the performance importance of state i.

Contribution: This index assesses the contribution of each state or component to the overall performance or reliability of the system. It can be represented as the incremental change in system performance or reliability due to a specific state or component. The formula for the contribution of state i can be defined as follows: 24 $$\begin{array}{c}{C}_{i}={\increment}E(X){\vert }_{\text{change}\,\text{in}\,\text{state}\,i}\end{array}$$ where C_i is the contribution of state i and ∆E is the change in performance expectation due to a change in state i.

Specifically for BESS, more nuanced indicators are employed to assess the unique aspects of battery performance and health. This includes SOH-based indicators, such as the reliability probability sensitivity I_Rp,k, which measures the effect of SOH changes on system reliability. And SOH probability sensitivity I_Ep,k is used to assess the criticality and impact of SOH changes on overall system reliability and expected performance [38]. 25 $$\begin{array}{c}{I}_{Rp,k}=\frac{\partial {R}_{BES}}{\partial \text{SO}{\mathrm{H}}_{k}}\end{array}$$ 26 $$\begin{array}{c}{I}_{Ep,k}=\frac{\partial {E}_{BES}}{\partial \text{SO}{\mathrm{H}}_{k}}\end{array}$$ where R_BES is the reliability of BESS, E_BES is the performance expectation of BEES, and SOH_k is the SOH of kth battery cell.

Furthermore, $${I}_{Rcon,k}$$ and $${I}_{Econ,k}$$, for the contribution to overall system reliability, provide a detailed view of battery health and its impact on system robustness. 27 $$\begin{array}{c}{I}_{Rcon,k}=\frac{{\Delta }{R}_{BES}\left({\Gamma }\left({\Delta }\text{SO}{\mathrm{H}}_{k}\vert {\Psi }(\text{SOH})\right)\right)}{{\Delta }{R}_{BES}}\end{array}$$ 28 $$\begin{array}{c}{I}_{Econ,k}=\frac{{\Delta }{E}_{BES}\left({\Gamma }\left({\Delta }\text{SO}{\mathrm{H}}_{k}\vert {\Psi }(\text{SOH})\right)\right)}{{\Delta }{E}_{BES}}\end{array}$$ where Γ(ΔSOH_k∣Ψ(SOH)) refers to the battery SOH set if the kth battery SOH is increased by ΔSOH_k.

This comprehensive approach to reliability assessment in BESS is crucial for maintaining system performance and prolonging lifespan.

APPLICATION OF ESS RELIABILITY ASSESSMENT

In the realm of ESS, real-world applications and case studies offer invaluable insights into the practicalities of reliability assessment and implementation. This section aims to synthesise key findings from various case studies, examining their implications for the design, operation, and regulatory compliance of ESS.

Reliability assessment of ESS under different configuration schemes

The configuration of ESS significantly impacts their reliability assessment. In standalone systems, often used in remote or off-grid applications, the focus is on ensuring long-term energy storage and minimal maintenance needs. These systems must be robust and autonomous, with design considerations prioritising longevity and fault tolerance [10].

Grid-integrated ESS, conversely, require reliability assessments that emphasise responsiveness to load changes and support for grid stability. This includes evaluating the system's ability to handle bidirectional energy flows and its compatibility with grid dynamics. Such systems play a vital role in smoothing out energy supply fluctuations, especially with renewable energy integration.

Hybrid systems, which combine ESS with renewable sources such as solar or wind power, present unique challenges for reliability assessment. These systems must address the intermittency of renewable energy sources, requiring sophisticated control and management strategies. Reliability assessments in this context focus on the system's ability to maintain consistent energy output and support grid demands despite variable renewable inputs.

Case studies exemplify these differences. For instance, a standalone solar-plus-storage system in a remote Australian community would prioritise storage capacity and resistance to environmental wear [85]. In contrast, a grid-integrated ESS in an urban smart grid project would focus on rapid response and seamless integration with existing infrastructure.

Reliability assessment of ESS under different regulation objectives

The evaluation of energy storage reliability under different scheduling and control objectives is a complex task that requires a nuanced understanding of operational goals and their impact on the system. Operational goals, ranging from peak load management to frequency regulation, directly influence the criteria used for assessing reliability [86, 87].

Peak Shaving involves using ESS to alleviate peak loads on the grid. This strategy often requires frequent and intense charge-discharge cycles, which can accelerate battery degradation. Consequently, while peak shaving is effective in reducing energy costs and easing grid stress, it poses a challenge to the longevity of ESS. Studies have shown a correlation between intense cyclic usage and accelerated ageing in battery cells, leading to reduced storage capacity and efficiency over time.

Load levelling, on the other hand, aims to distribute energy demand evenly over time. ESS under this strategy undergo more consistent, yet prolonged operational periods. This can lead to a more balanced use of the system but does not eliminate the risk of degradation. Continuous cycling, even at lower intensities, gradually impacts battery health, manifesting in reduced capacity and potential thermal management issues. However, compared to peak shaving, load levelling generally presents a less severe impact on battery life, as evidenced by various lifecycle analysis studies.

Demand response requires ESS to adjust its operations in response to real-time electricity market signals or grid conditions. This approach demands high responsiveness and flexibility from the ESS, leading to irregular operational patterns. Such patterns can induce varying levels of thermal and mechanical stress, especially in battery and mechanical storage systems. The irregular usage associated with demand response can result in unpredictable degradation patterns, challenging traditional predictive maintenance strategies.

Customised approaches are necessary for different scheduling objectives. Each scheduling objective, be it load levelling, demand response, or integration with renewable sources, imposes unique demands on the ESS. Reliability assessments must therefore be tailored to evaluate how well an ESS can meet these specific demands under varying conditions. This includes assessing the system's capacity to handle fluctuating loads, its resilience to external disturbances, and its ability to maintain performance over time.

Adaptive control mechanisms are crucial for meeting varied operational demands. These mechanisms allow the ESS to dynamically adjust its behaviour based on external conditions and internal state. For example, an ESS with adaptive controls can modulate its charging and discharging rates to extend battery life or to respond more effectively to grid demands, thereby enhancing overall reliability.

Bridging reliability and sustainability in ESS

Understanding the reliability of ESS is fundamentally about ensuring consistent performance and minimising system failures, but its implications stretch far beyond these technical dimensions. Reliability in ESS is intrinsically linked to the broader objective of energy sustainability, especially vital in the context of integrating renewable energy sources.

Reliable ESS are indispensable in managing the intermittency and variability of renewable energy sources such as wind and solar power. By ensuring that these systems can effectively store and dispatch energy, they stabilise the grid and maximise the utilisation of renewable sources. This capability allows for a greater penetration of renewable energy, reducing the reliance on fossil fuels and enhancing the carbon efficiency of the energy grid, thereby contributing to the broader goal of sustainable energy utilisation.

Furthermore, advancements in the reliability assessment of ESS directly improve operational standards and extend the lifespan of these systems. Sophisticated diagnostic and prognostic tools enable continuous monitoring and optimisation of ESS, facilitating proactive maintenance that reduces the frequency of component replacements. This not only conserves resources, but also minimises waste and energy consumption, further promoting sustainable energy practices.

Additionally, enhancing the reliability of ESS leads to improvements in system efficiency, economic viability, stability, resilience, and flexibility. These improvements are crucial for efficiently managing load and generation variability, which is common in grids with high levels of renewable integration. By improving system reliability, ESS contribute to more efficient energy use, reduced operational costs, and a smoother integration into the energy market, supporting the transition to a sustainable energy future.

In conclusion, strengthening the reliability of ESS aligns directly with the objectives of advancing sustainable energy systems. It enhances performance, extends system lifespan, and ensures that ESS contribute positively to environmental sustainability.

Impact of reliability assessment on ESS design and operation

The application of reliability assessment in ESS significantly influences their design and operational strategies. Reliability assessment provides critical insights that guide engineers and designers in making informed decisions about the construction, materials, and components of ESS. This process ensures that each design element contributes to the overall durability and efficiency of the system [88, 89].

In the design phase, reliability assessment helps identify potential failure modes and their impact on the system's performance. By understanding these risks, designers can incorporate features that enhance the system's resilience to operational stresses and environmental factors. For instance, thermal management systems in battery storage are optimised based on reliability assessments to prevent overheating and prolong battery life [90].

Furthermore, reliability assessment plays a pivotal role in the operational phase of ESS. It informs maintenance schedules and operational protocols, aiming to maximise uptime while minimising risks and maintenance costs. Data derived from reliability assessments enable predictive maintenance, a proactive approach that addresses potential issues before they escalate into significant failures. This strategy not only extends the lifespan of the system but also ensures consistent performance and safety.

Additionally, the integration of reliability assessment into ESS operation contributes to the optimisation of energy management strategies. By accurately predicting the lifespan and degradation patterns of storage components, operators can make more efficient use of the stored energy, thereby enhancing the overall value proposition of ESS.

In summary, the impact of reliability assessment on ESS extends beyond mere risk mitigation. It is a foundational element that shapes the design, enhances the operational efficiency, and guarantees the long-term sustainability of ESS. As the demand and reliance on ESS grow, the role of thorough and advanced reliability assessments will become increasingly critical in steering the future of energy storage technologies.

CHALLENGES AND FUTURE TRENDS IN RELIABILITY ASSESSMENT OF ESS

Challenges in reliability assessment of ESS

The current landscape of reliability assessment in ESS is shaped by a blend of established practices, evolving methodologies, and emerging challenges. This landscape is continually adapting to accommodate technological advances, expanding ESS capacities, and shifting regulatory environments [7, 91–93]. The main challenges for the reliability assessment of ESS come from two aspects: 1. The increasing complexity of the system structure and more diverse control strategies lead to the difficulty of reliability modelling. 2. How to obtain, filter, and utilise the large amount of data in high quality brought by the larger scale of energy storage installations.

Challenge 1 is primarily driven by rapid technological advancements and increasing ESS capacities. As ESS technologies evolve, with advancements in battery chemistries and hybrid storage solutions, the complexity of reliability assessment escalates [94]. These advancements necessitate more sophisticated assessment tools and techniques capable of addressing the nuanced behaviours and failure modes of modern ESS. Additionally, the scaling up of ESS capacities to meet growing energy demands introduces challenges in maintaining system reliability at larger scales, where the impact of failures can be significantly magnified. Therefore, modelling faults is also challenging.

Data availability and quality are crucial for effective reliability analysis, yet they pose significant challenges in the current ESS landscape. The need for comprehensive and high-quality data is paramount, as it underpins all aspects of reliability assessment. The integration of real-time data monitoring systems, advanced data analytics, and the burgeoning role of artificial intelligence (AI) in predictive maintenance is becoming increasingly important. These technologies enable more accurate, timely, and proactive reliability assessments, allowing for quicker responses to potential issues and more effective maintenance strategies [12, 13, 95].

Future trends in reliability assessment of ESS

The landscape of ESS is on the cusp of a significant evolution, with reliability assessment at its core. The following sections delve into this transformation, starting with more refined reliability modelling. Here, we explore how the integration of machine learning (ML), AI, and enhanced data analytics is revolutionising ESS reliability assessment. This shift towards advanced modelling techniques marks a pivotal point in ensuring the efficiency, safety, and longevity of ESS, paving the way for a new era in energy storage solutions.

More refined reliability modelling

In the evolving landscape of ESS, the shift towards more refined reliability modelling signifies a pivotal transformation. This advancement is predominantly driven by the incorporation of ML and AI.

ML models, such as neural networks and decision trees, are now at the forefront of predictive maintenance. These models are trained on vast datasets comprising historical operation data, environmental conditions, and system performance metrics, enabling them to detect subtle patterns and anomalies that indicate potential system failures. These models excel at detecting subtle patterns and anomalies indicative of potential system failures, which is critical in ESS where early fault detection can significantly enhance system longevity and safety.

For instance, neural networks have shown exceptional capability in identifying degradation trends in battery life, which is vital for predicting and mitigating failures before they lead to critical system downtimes. The feasibility of implementing these models in ESS is supported by their ability to process and learn from time-series data, a common data type in ESS monitoring. Recurrent neural networks, and specifically long short-term memory networks, are particularly effective due to their capability to remember previous inputs—a crucial feature for anticipating future system behaviours.

The accuracy of reliability modelling can be further improved by utilising ML and AI methods, especially for the state transfer process and the formulation of reliability metrics that are more difficult to express through explicit mathematical name models.

However, the application of such advanced models in ESS requires careful consideration of computational demands and the need for ongoing model tuning to adapt to changing operational conditions. This is essential for maintaining the effectiveness of the models under real-world conditions. Moreover, these systems must be designed with robustness in mind, capable of handling the diverse and variable nature of ESS operations without compromising on performance.

Parallel to the integration of AI and ML, Enhanced Data Analytics plays a crucial role in elevating the reliability modelling of ESS. The ability to process and analyse vast volumes of data empowers analysts to gain deeper insights into the performance and degradation patterns of ESS. This analytical approach transcends traditional methods by unveiling intricate correlations that are often missed in more straightforward analyses. Enhanced Data Analytics allows for a more comprehensive understanding of various factors affecting ESS performance, including environmental impacts, usage patterns, and component wear and tear. Such detailed insights are vital for developing strategies to enhance the longevity and efficiency of ESS [96].

Advanced fault modelling and simulation in ESS reliability assessment

Enhancing fault modelling and simulation within ESS reliability assessments significantly elevates the precision with which these systems are evaluated. By integrating detailed models of specific faults—such as thermal dynamics in battery cells and mechanical stresses in CAES systems—into the assessment process, we achieve a more accurate prediction of potential failures and their implications.

Incorporating advanced simulations that utilise heat transfer equations coupled with reaction kinetics allows for a thorough examination of thermal faults, particularly TR in battery systems. These models are critical for simulating various failure scenarios and understanding how they propagate within a battery pack. This level of detail is essential for devising effective preventive measures and enhancing system resilience. Similarly, modelling mechanical faults through simulations that predict stress and wear over time enables more precise maintenance scheduling and system adjustments. This not only helps in mitigating the immediate risks but also extends the overall lifespan of the components.

The practicality of integrating these fault models into reliability assessments hinges on their ability to replicate real-world conditions accurately and predict the outcomes of potential faults. Important considerations for implementing these models include their computational efficiency and the ability to adapt to new data and changing operational conditions seamlessly.

By refining the fault predictions, these integrated simulations significantly enhance the reliability assessments of ESS. Such improvements lead to more proactive maintenance strategies and optimised system management, thereby ensuring that ESS operates with increased safety, efficiency, and resilience. This integration of sophisticated fault modelling and simulation into reliability assessments not only bolsters the accuracy of these evaluations but also fortifies the reliability of ESS, supporting their crucial role in sustainable energy infrastructure.

Advancements in diagnostic and prognostic tools

In the realm of ESS, recent advancements in diagnostic and prognostic tools are playing a crucial role in elevating the standards of reliability assessment. These modern tools have revolutionised the way ESS health and performance are monitored and predicted. Sophisticated diagnostic technologies such as thermal imaging, acoustic monitoring, and impedance spectroscopy are now integral in early fault detection. Thermal imaging allows for the non-invasive monitoring of temperature anomalies, a key indicator of potential failures, particularly in battery cells. Acoustic monitoring provides insights into mechanical and electrical components' health by detecting noise signatures that precede failures. Impedance spectroscopy, on the other hand, offers valuable data on the internal conditions of batteries, helping in assessing their SOH and efficiency. Data is the most important part of the reliability assessment process, and the need for data is reflected in the aforementioned models and methods. More advanced testing and evaluation techniques can provide more accurate data support for reliability, and never further improve the accuracy and authenticity of reliability.

Complementing these diagnostic advancements, prognostic health management (PHM) systems are becoming increasingly important. These systems utilise data from various sensors and historical performance metrics to not only assess the current state of ESS components but also to predict their future condition. This predictive capability is pivotal in scheduling maintenance activities, optimising system operation, and preventing unexpected downtimes. The integration of PHM systems in ESS ensures a more proactive approach to reliability, focussing on foreseeing and mitigating issues before they escalate into critical problems. Together, these advanced diagnostic and prognostic tools represent a significant leap forward in maintaining and enhancing the reliability of ESS, ensuring their safe, efficient, and long-lasting operation.

Development of customised reliability indicators for ESS

The development of customised reliability indicators for ESS represents a pivotal advancement, aiming to capture the unique operational dynamics and challenges inherent to these systems. These indicators are crafted to reflect critical aspects such as cyclic stress from charging and discharging, the impact of environmental conditions on material degradation, and responses to grid fluctuations, which are unique to the domain of energy storage.

To effectively measure and enhance the reliability of ESS, indicators can be developed from various key aspects:

• Operational performance: Indicators that measure the efficiency and stability of ESS operations under different load and environmental conditions.

• Component health: Metrics designed to monitor the wear and tear of critical components, predicting their end of life based on actual usage patterns.

• System resilience: Indicators that evaluate the system's ability to recover from operational stresses or external disruptions, ensuring continuity of service.

• Safety and risk management: Metrics that assess the potential risks associated with system operations, including the likelihood and impact of system failures.

The feasibility of implementing these customised indicators in reliability assessments is supported by their ability to provide targeted insights that are directly relevant to the operational conditions and failure risks specific to ESS. Critical considerations include ensuring the indicators are robust enough to handle diverse data types and scalable across different ESS technologies and configurations.

Future research and development efforts are likely to focus on harnessing advanced data analytics and ML techniques to refine these indicators continually. This will involve integrating real-time operational data to adapt and optimise the reliability assessments dynamically, ensuring that they remain aligned with evolving technological advancements and operational practices.

CONCLUSION

As ESS technologies become increasingly complex and integral to energy infrastructure, the need for robust, tailored evaluation methods has never been more apparent.

Existing reliability evaluation methodologies face significant challenges, including data quality variability and the rapid pace of technological advancements. Furthermore, critical areas such as environmental impacts and broader research opportunities are frequently overlooked, necessitating a focused discussion on these gaps. Advanced techniques such as ML, AI, and enhanced data analytics are revolutionising reliability modelling. These methodologies enhance our understanding of performance degradation patterns and facilitate more accurate predictions of system failures. They also enable the optimisation of maintenance schedules and extend the operational lifespans of ESS, thereby supporting the seamless integration of renewable energy sources into the global energy matrix.

This paper provides a thorough review of the reliability assessment research for ESS, highlighting the evolving evaluation methodologies and pinpointing emerging research directions. By underpinning subsequent research into ESS reliability, it ensures the capability of systems to support the increasing renewable energy sources effectively.

AUTHOR CONTRIBUTIONS

Xiaohe Yan: Conceptualization, formal analysis, supervision, writing – review & editing. Jialiang Li: Formal analysis, investigation, writing – original draft, writing – review & editing. Pengfei Zhao: Supervision, writing – review & editing. Nian Liu: Project administration, resources, supervision. Liangyou Wang: Resources. Bo Yue: Project administration, resources. Yanchao Liu: Investigation.

ACKNOWLEDGEMENTS

This work was supported by the National Key R&D Program of China (No. 2021YFB2400700) and the Science and Technology Research Institute of China Three Gorges Corporation (No. 202303140).

CONFLICT OF INTEREST STATEMENT

All authors disclosed no relevant relationships.

DATA AVAILABILITY STATEMENT

Data sharing is not applicable to this article as no new data were created or analysed in this study.

PERMISSION TO REPRODUCE MATERIALS FROM OTHER SOURCES

None.

References

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