A Review of Reliability Research in Regional Integrated Energy System: Indicator, Modeling, and Assessment Methods

Abstract

The increasing complexity of integrated energy systems has made reliability assessment a critical challenge. This paper presents a comprehensive review of reliability assessment in Regional Integrated Energy Systems (RIES), focusing on key aspects such as reliability indicators, modeling approaches, and evaluation techniques. This study highlights the role of renewable energy sources and examines the coupling relationships within RIES. Energy hub models and complex network theory are identified as significant in RIES modeling, while probabilistic load flow analysis shows promise in handling renewable energy uncertainties. This paper also explores the potential of machine learning methods and multi-objective optimization approaches in enhancing system reliability. By proposing an integrated assessment framework, this study addresses this research gap in reliability evaluation under high renewable energy penetration scenarios. The findings contribute to the advancement of reliability assessment methodologies for integrated energy systems, supporting the development of more resilient and sustainable energy infrastructures.

1. Introduction

1.1. Background

Energy constitutes a fundamental material foundation for the sustenance and advancement of human civilization. The secure and consistent functioning of the energy system is connected to the advancement of the national economy and the steadiness of societal harmony. With the increasingly tense international relations, the issue concerning the correlation between supply and demand of conventional fossil fuels has become increasingly prominent. The supply mode relying on a single energy resource can no longer meet people’s growing living demands [1]. Decarbonization and terminal electrification based on the concept of carbon neutrality by 2050 are also placing higher demands on the energy system [2].

Therefore, the concept of integrated energy system (IES), as an essential carrier of energy Internet to integrate multiple types of energy resource supply, has been put forward [3]. IES is a system integrating the production, conversion, storage, and consumption of multiple energy sources [4]. Several agency reports [5,6,7] have noted the importance of IES in supporting grid stability, improving energy efficiency, and reducing carbon emissions, especially in integrating renewable and conventional energy sources. Considering the control capacity of a local system, the integrated energy system is often planned in a region or town as the coverage area, which is the regional integrated energy system (RIES).

1.2. Present Research Focus

There are several research fields contributing to this research of RIES. Currently, many scholars have conducted research on energy system optimization, reliability assessment, and advanced modeling methods.

Energy system optimization in RIES has seen significant advancements in recent years. A major focus has been on improving district heating and cooling systems (DHC), with researchers exploring optimization in energy generation, distribution, thermal substations, and end-user applications [8]. The concept of Energy Hubs (EH) has been introduced to enhance system optimization and management. EHs serve as integrated energy management centers, addressing key challenges in the consumer sector and facilitating the integration of various energy forms [9].

Building on this, the integration of microgrids into the EH framework has been a notable trend. Nikmehr (2020) [10] explores integrating microgrids into the EH framework to meet various energy demands while resolving power exchange conflicts. These developments have led to demonstrable economic and environmental benefits, particularly when combined with innovative energy storage schemes, as verified by Sameti (2018) [11].

The integration of renewable energy brings complexity and a series of related issues to the energy system. Recent research has focused on addressing the inherent uncertainties associated with renewable sources, particularly photovoltaic systems, and demand fluctuations. Taheri (2021) [12] considers the uncertainty of photovoltaic and demand fluctuations and uses First Order Reliability Method and Second Order Reliability However, there remains a gap in addressing highly complex uncertainty models with nonlinear relationships, presenting an opportunity for future research.

To provide a more precise evaluation of the system state, Heylen et al. (2021) [13] classify the reliability indicators of electric power systems and summarize in detail the characteristics and scope of the indicators currently used and available in the literature. The analysis of reliability in mixed energy output systems has led to the adoption of multifaceted approaches. Postnikov (2022) [14] combined reliability theory, Markov random process, graph theory, and other methods for analysis.

Advanced modeling and analysis methods have also been applied in RIES research. Fichera (2017) [15] builds models that incorporate complex network theoretical frameworks and energy distribution problems to optimize energy distribution between producers and consumers while minimizing energy supply from traditional power stations. Prusty (2017) [16] proposes a method based on a clustering distortion function to estimate the optimal number of clusters associated with multivariate data. This method is used to compute the distribution of multimodal expected random variables in probabilistic load flow. It offers advantages over traditional methods in terms of both accuracy and time scale. The application of machine learning techniques in reliability assessment represents a promising frontier in RIES research. Yang et al. (2022) [17] optimize the strategy for extracting optimal sample points using the Expected System Improvement (ESI) active learning function to predict the impact of component reliability updates on system reliability. This study employs the black-box model evidence network theory to investigate complex systems with common-cause failures and mixed deterministic elements. Li et al. [18] explore the modeling methods and application scenarios of the gray box model in the field of building energy efficiency simulation and demonstrate its limitations.

1.3. Research Challenges and Objectives

Despite the rapid development of Regional Integrated Energy Systems (RIES), several challenges remain. Energy dispatch and storage optimization need more effective integration within microgrids to resolve energy exchange conflicts. Ensuring reliability during actual operation still requires in-depth research. The uncertainties of renewable energy generation and demand fluctuations have not been fully addressed, with complex models and nonlinear relationships needing more study. Current reliability evaluation standards must be more generalized to fit various scenarios, and the transparency of these indicators needs improvement. Research on the coupling between supply and demand sides is incomplete, requiring a balance between model accuracy and computational efficiency. As new energy types and equipment are introduced, evolving research methods are necessary to reduce safety risks and enhance system efficiency.

This paper aims to provide a comprehensive review of the reliability research on RIES, with a focus on analyzing reliability indicators, modeling methods, and corresponding evaluation techniques to guide the reliability assessment of RIES. The specific research objectives are as follows:

To review the definition of RIES and its global application status by analyzing typical cases from different regions, demonstrating the diversity and flexibility of RIES in practical applications; to explore the reliability indicators of RIES by summarizing commonly used reliability indicators in power systems and extending them to integrated energy systems, with particular attention to the participation rate of renewable energy and its impact on system reliability; to analyze the modeling methods of RIES by introducing the energy hub model and complex network theory in the context of RIES, discussing how these models describe the production, conversion, storage, and consumption processes of various energy carriers; to evaluate the analysis methods for RIES by detailing various evaluation techniques used for RIES reliability assessment, including probabilistic methods, machine learning methods, and other advanced evaluation techniques, and validating the effectiveness of these methods through case studies; and to summarize the current challenges in RIES reliability research and future research directions, emphasizing the importance of further optimizing and improving RIES reliability assessment methods to provide references for future research.

In this paper, Section 2 provides the basic concepts of RIES. Section 3 introduces reliability indicators for IES based on power system reliability indicators. Section 4 discusses the modeling methods of RIES. Section 5 analyzes the methods used for RIES evaluation. Section 6 concludes this paper, summarizing the main findings, current challenges, and future research directions in RIES reliability research.

1.4. Review Methodology

This review employed a systematic approach to identify, analyze, and synthesize relevant literature on reliability research in Regional Integrated Energy Systems (RIES). The primary literature search was conducted using authoritative academic databases, including Web of Science, Scopus, and IEEE Xplore, supplemented by other scholarly search engines to ensure comprehensive coverage.

The main focus was on peer-reviewed articles published between 2010 and 2024. Key search terms included ‘integrated energy system’, ‘reliability’, ‘energy hub’, and ‘complex network theory’, along with their relevant variations and combinations. Additionally, we included several seminal works published before 2010 that are considered foundational to the field to provide historical context and theoretical grounding.

Articles were selected based on their relevance to RIES reliability, novelty of research content, and potential impact on the field. The review process involved careful reading and analysis of selected papers, with key information extracted and synthesized to form a comprehensive overview of the field’s development and current state.

While this approach allowed for a broad and authoritative coverage of the topic, including its historical foundations, it is important to note that it may not capture all relevant literature, particularly those not indexed in the searched databases or published in languages other than English. Despite these limitations, this review aims to provide a thorough, historically informed, and up-to-date analysis of reliability research in RIES.

2. Overview of Regional Integrated Energy System

2.1. Definition

RIES is a system integrating the production, conversion, storage, and consumption of multiple energy sources within a certain area. Since the RIES concept is still developing and completing, there is no fixed model or definition. Similar concepts include hybrid energy systems [19], energy system integration [20], universal energy networks, distributed energy Internet, energy bus networks, micro-energy grids, etc.

RIES optimize equipment scheduling and improve utilization efficiency by integrating multiple energy systems. By leveraging both renewable and traditional energy sources, IES enhances overall energy efficiency. Additionally, IES reduces carbon emissions through diverse energy substitutions, contributing to global warming mitigation. With its multi-input, multi-output energy supply, IES reduces dependence on a single energy source, ensuring energy security [21]. Within a specific region, RIES can prevent issues arising from cross-regional energy system integration. Additionally, by operating within a defined area, the system’s performance can be more effectively monitored and managed, ensuring optimized operational efficiency and reliability [22,23].

2.2. Framework

IES can meet the needs of different energy scenarios. The common classification is shown in Figure 1.

In regional integrated energy systems, this study of electricity, heat, and gas as independent systems is relatively complete. The integration of renewable energy introduces a significant amount of uncertainty [24]. Regarding energy conversion, there are various combinations of energy supply equipment and scheduling strategies to meet end-user loads. Economic factors, environmental factors, and reliability still need to be balanced according to the actual conditions of the area. In practical planning issues, community-based RIES often have better coordination capabilities and greater autonomy. The adaptability of RIES itself helps different types of industries meet their energy demands.

2.3. Coupling Relationship

The coupling relationship describes the mutual influence and collaborative working capacity between different energy devices [21]. Specifically, the coupling relationship reflects the interdependence and coordination among energy supply, conversion, and storage devices. In an integrated energy system, the coupling relationship involves not only physical connections and energy flows but also the coordination of information transmission and control strategies. Properly constructing the coupling relationship between subsystems can achieve optimal resource allocation. A schematic diagram of the energy-flow coupling relationship for a typical integrated energy system is given in Figure 2.

The coupling mode enhances the flexibility of integrated energy systems and promotes the integration of renewable energy. This flexibility allows integrated energy systems to better adapt to load variations and resource fluctuations, thereby improving energy utilization efficiency and supply adequacy. However, strongly coupled multi-energy systems may increase the risk of cascading failures; for instance, a fault in the power system may lead to interruptions in gas and heating supply. Integrating renewable energy sources with significant uncertainties further complicates the coupling relationship, posing greater challenges to system safety. By analyzing and optimizing the coupling relationships within the RIES, it can better meet current requirements for economic efficiency, environmental benefits, and reliability.

2.4. RIES Cases

The concept of Regional Integrated Energy Systems (RIES) is revolutionizing urban energy infrastructure globally, as illustrated in Figure 3. This comprehensive diagram showcases how various energy sources, distribution networks, and consumption points interconnect within a modern city ecosystem. Such integrated systems are being implemented and refined in different parts of the world, each with its own unique focus and challenges. The construction and completion of RIES projects worldwide demonstrate that it has become the focal point for the development of future energy-efficient technologies. Germany’s New 4.0 project is designed to meet the needs of the energy transition with zero net emissions. To meet intermittent, distributed generation and large-scale energy storage needs, Germany needs to redesign the original centralized grid. In the state of Schleswig-Holstein, the project makes flexible use of wind power peaks to avoid waste while promoting production efficiency in the local power to aluminum and power to steel industries. Ref. [25] At the Idaho National Laboratory (INL) in the United States, a multi-phase demonstration project is being developed to explore innovative applications of nuclear energy within regional integrated energy systems. Leveraging the National Reactor Innovation Center (NRIC) and the Crosscutting Technology Development Integrated Energy Systems (CTD IES) program, this initiative aims to address the demand for low-carbon energy in heavy industry and transportation sectors. The project also identifies potential applications in industries such as chemical processing, petrochemicals, and steel manufacturing [26]. In China, the Chinese and Singaporean governments have jointly initiated the Sino-Singapore Tianjin Eco-City project. The city extensively uses renewable energy, integrating smart grid and energy storage technologies. A 10 kV energy microgrid enables the complementary use of various distributed energy sources, while four independent photovoltaic storage microgrid systems at the building level enhance solar energy utilization. This clean energy production supports emerging industries, such as the new energy vehicle manufacturing sector [27].

3. Reliability Evaluation Indicator

The purpose of applying indicators is to characterize the operating principles of the system. Given the relative simplicity and scale of power systems, their reliability indicators can serve as a reference for evaluating the reliability of integrated energy systems. The associated concepts can also be applied to other energy supply systems. With the increasing penetration of renewable energy sources, relevant indicators have been developed to expand the reliability evaluation framework of RIES.

3.1. Power System Reliability Indicator

Reliability in power systems is generally defined as the ability of the electrical grid to provide uninterrupted electricity to customers [29]. The evaluation of power system reliability involves the quantitative assessment and analysis of the likelihood of power outages due to unforeseen events, as well as the quantitative description of the system’s ability to withstand various adverse random events through various measurement indicators. This process aims to identify weak links and assess the safety margin of the power system. Recent research on energy sustainability and smart grids has shown that decision-makers in the electricity market prioritize reliability as the primary factor influencing their behavior. Reliability also serves as a performance indicator for categorizing electric utilities [30,31].

Power system reliability indicator, as a measurement for system performance, can be measured by two types of indicators: system-level indicators and equipment-level indicators. For equipment-level indicators, reliability assessment research is focusing on the performance of specific mechanical components, which is discussed in [32,33,34] and will not be explained detailly in this article. For system-level reliability indicators, different classification standards are applied for further research. From the point of system structure, it can be classified into adequacy and safety [35]. Adequacy in power systems refers to the capacity of the system to supply uninterrupted power demand and total electrical energy to consumers, considering scheduled outages and foreseeable unplanned outages of system components. This is also known as static reliability. Safety of a power system refers to its ability to endure sudden disruptions, including unexpected short circuits or the loss of system components. This is also known as dynamic reliability. Reliability indicators can also be classified by energy source type, including electricity, heating, and gas, or by the energy flow, which can be separated as supply side and demand side [36].

The electric utility industry has distinguished the type of malfunctioning assessment indicator in the power system reliability context, including probabilities of outages, frequency of outages, mean duration, and expectations of malfunctioning [37].

The common reliability indicators of evaluation are listed in Table 1 [29,38,39].

By using indicators given in Table 1, research has been processed to evaluate power system reliability. AliJafar–Nowdeh [40] proposes an optimal reconfiguration approach for radial distribution systems that incorporate solar and wind renewable energy sources. The approach utilizes the weight factor method and takes into account reliability as a key factor in the decision-making process. Main objective functions contain minimizing power loss, enhancing voltage profile, and improving system stability. The expected energy not-supplied (EENS) indicator is used as a measure of reliability for end-users. Abdelsalam [41] utilizes the sine cosine algorithm (SCA) to optimize the performance of distributed energy resources and capacitor banks based on both reliability and economic benefits. The Energy Not Supplied (ENS) indicator serves as an indicator of system reliability. A non-parametric Wilcoxon statistical test is employed to compare the algorithm with alternative optimization techniques. SUN [42] proposes an optimum planning method for RIES with reliability verification model and hierarchical economic optimization model. Equivalent cost and EENS are used separately for the economic and reliability layer as cost functions.

Some coordinating organizations, including the European Network of Transmission System Operators for Electricity (ENTSO-E) and the North American Electric Reliability Corporation, are carrying forward this research of reliability standard management, and discussion is given in [14].

3.2. Integrated Energy System Reliability Indicators

For the concern of the implementation of renewable energy, a serval indicator can be used to represent the participation rate of renewable energy and hence a reflection of the system reliability. Energy penetration is an indicator that measures the proportion of electricity produced by a specific source. Furthermore, energy penetration potential is the ability of a distributed energy system to utilize renewable energy sources for consumption. The intermittency and uncertainty of renewable energy caused by multiple factors can be conducted by it in terms of the advancement of renewable energy system dependability [43]. Zhang et al. [44] aim to examine the desertion situation of renewable energy by evaluating the usage of wind and solar power in China and to provide recommendations for enhancing the renewable energy penetration rate (REPR). Other energy-related indicators, including primary energy factor and energy efficiency, can be used in the analysis of the energy flow characteristics of RIES.

In addition to indicators related to energy production, there are also indicator pertaining to energy conversion, storage, and utilization. For instance, Energy Conversion Efficiency is crucial for evaluating the effectiveness of energy conversion processes. Storage Capacity is an important measure related to energy storage [45]. Furthermore, Renewable Energy Forecast Accuracy is vital for optimizing energy utilization and planning. There are some indicators that are not computational and reflect level of interaction connecting the energy system and the demand side, including active peaking and valley filling load, peak-to-valley ratio of load, distributed energy interoperability (distributed energy access capability), smart meter popularity, etc. [46].

Indicators are quantitative or qualitative variables that represent phenomena or attributes of concepts that are challenging to measure directly. In monitoring the operational status of continuously running projects, the impact of minor fluctuations in a single indicator within a limited scope is intuitive and easily comprehensible. However, quantifying the system-level effects resulting from the coupling of multiple indicators becomes more complex, and unintegrated indicators often fail to identify incipient faults. This limitation affects the global reliability of integrated energy systems.

Several studies have consolidated measures and indicators to form indices and metrics, providing multidimensional frameworks for evaluating system design and operational status. The classification of reliability evaluation criteria and corresponding case studies are presented in Table 2.

The table illustrates a progressive increase in complexity of object-oriented approaches as concepts deepen. Evaluation methods at the indicator level can be expressed intuitively through formulas, representing system parameters. Indices tend to offer more macro-level assessments oriented towards end-users. Metric-level evaluation methods are less prevalent, primarily due to their need to address specific requirements of practical projects. Moreover, when reliability issues occur, their conclusions are strongly correlated with the emergency management capabilities of the operational department. Consequently, this aspect will not be elaborated further.

4. Modeling

In addressing the multi-objective optimization challenges of complex systems like RIES, hierarchical planning methods, particularly bi-level programming, have gained widespread adoption [53]. This approach typically employs a bi-level programming framework: the upper level comprises various iterative models, such as energy hub models, multi-agent systems, and graph-theoretic methods, for simulating and optimizing system operations; the lower level incorporates the results from the upper level into specific reliability indicators for evaluation. This bi-level structure facilitates a comprehensive analysis of both system performance and reliability. In this chapter, the upper-level modeling methods are introduced.

4.1. Energy Hub

An energy hub can be described as a comprehensive framework that facilitates the operations related to the production, conversion, storage, and consumption of diverse energy carriers [54]. In simpler terms, it refers to a device that can receive, convert, store, and distribute multiple types of energy [55]. By integrating multiple energy carriers and conversion technologies, energy hubs have the potential to enhance overall system reliability through diversification and redundancy. In the energy hub model, an integrated energy system can be divided into three components: the input side $L$, the coupling matrix $C$, and the output side $P$ and is shown in equation. $C_{\alpha \beta }$ is the conversion efficiency from energy source $\alpha$ to energy source $\beta$. This division facilitates the formation of matrices, which in turn enables more detailed analysis.

$\left[\begin{array}{c}{L}_{\alpha }\\ L_{\beta }\\ ⋮\\ L_{\varpi }\end{array}\right]=\left[\begin{array}{cccc}{c}_{\alpha \alpha }& c_{\beta \alpha }& \cdots & c_{\varpi \alpha }\\ c_{\alpha \beta }& c_{\beta \beta }& \cdots & ⋮\\ ⋮& ⋮& \ddots & ⋮\\ c_{\alpha \varpi }& c_{\beta \varpi }& \cdots & c_{\varpi \varpi }\end{array}\right]\left[\begin{array}{c}{P}_{\alpha }\\ P_{\beta }\\ ⋮\\ P_{\varpi }\end{array}\right]$

Energy hubs vary in scale, ranging from individual home energy systems to entire urban energy systems. They can be categorized into four types based on consumption sectors: residential, commercial, industrial, and agricultural. For small-scale energy hubs, customers primarily focus on energy cost, while large-scale hubs also consider load profile, peak load, and service quality [9]. The integration of diverse energy sources and storage systems in small-scale energy hubs can improve local energy reliability, reducing dependence on a single energy source or grid.

In small-scale energy hubs, factors contributing to energy losses include extensive distribution networks, inadequate demand-side management, and suboptimal equipment efficiency. The promotion of renewable energy resources (RES) faces challenges such as fluctuating natural conditions and unpredictable climate, leading to a high dependency on energy storage systems (ESS) and control systems [10]. Home Energy Management Systems (HEMS) are introduced to optimize energy production and consumption, enhancing efficiency within the energy hub [56,57,58].

For larger-scale energy hubs, sophisticated energy generation systems are essential. These systems accommodate diverse energy sources to meet the demands of commercial buildings, offering significant potential for optimizing energy efficiency [59,60]. Large-scale energy hubs, with their sophisticated energy generation and management systems, can significantly contribute to grid stability and reliability, especially when incorporating renewable energy sources and advanced control strategies. Building Energy Management Systems (BEMS) are implemented to manage the energy integration system effectively, including distributed generation units and renewable energy systems [60,61].

The concept of a macro energy hub involves the amalgamation of numerous discrete micro energy hubs. This approach allows for more options in peak shaving and considers the spatial determination of energy flow influenced by individual movements [62,63]. The interconnection of multiple micro-energy hubs in a macro-energy hub framework can enhance system-wide reliability through load balancing and mutual support during peak demands or unexpected outages. Optimization in macro-energy hubs occurs at both the micro and macro levels, focusing on the Optimal Energy Flow (OEF) problem [55,64,65]. Research has been conducted on solving multi-objective optimization problems in macro-energy hub systems using heuristic methods and genetic algorithms [66,67]. Long-term planning of energy hubs has also been studied, considering life-cycle operations and component interconnections [68].

The EH framework inherently possesses the flexibility to incorporate diverse models and methodologies. Beyond basic applications like energy conversion matrices, EH can integrate specialized analytical models tailored to specific requirements. These models span domains including time series analysis, probabilistic load flow, multi-objective optimization, complex network theory, and machine learning, addressing tasks such as energy demand forecasting, renewable energy uncertainty management, and operational strategy optimization. The subsequent sections will focus on three key research directions: Complex Network Theory, Load Flow Analysis, and Coupling Relationship Model. These areas represent the most challenging and promising frontiers in current EH analysis. Examining these models can enhance the EH framework’s capability to address specific issues in RIES, establishing it as a comprehensive analytical tool.

4.2. Complex Network Theory

When considering the energy consumption patterns of regional users, distributed energy systems are more adept at meeting the demands of IES. Extensive research has been conducted on optimization frameworks for these systems; however, such frameworks often rely on complex computations and equation solving. As the number of supply and demand sites scales to reflect real-world regional conditions, the computational complexity increases significantly, impeding the efficient attainment of optimal configurations that ensure both sufficient energy supply and network security. Furthermore, the spatial distribution and physical interconnections between producers and consumers are critical factors in the optimization process.

Complex networks are already used in many scientific fields, revealing crucial insights into the fundamental significance of interactions among the elements within a system [69], but little research results on RIES reliability. The system’s structure is gradually transitioning from the traditional bus integrated network to a complex network, characterized by the emergence of multi-node coupling phenomena. At present, the network characteristics of power systems have been deeply analyzed, and it is proved that there are complex network characteristics, including scale-free and small-world properties, within power systems [70], which can be estimated as real-world networks [71]. The implementation of complex network theory in weak link identification and risk assessment of power systems is explored in [72]. It can evaluate the risk of occurring a blackout or other failure to prevent huge revenue losses and serious damage to the life quality of residents and social production. An example of a 30-bus power system is given in Figure 4.

To evaluate complex networks, criteria including the average length path and clustering coefficient are used. A small-world network is an extension of the “Six Degrees of Separation” concept, wherein each node in the network is connected to another node through a maximum of six connections, allowing them to be in contact with one another. Nodes can become neighbors by connection. Consequently, low average path length and high clustering coefficient are the features of small-world networks [73].

Research has applied the complex network theory to study the reliability of power systems. In [74], the percentage of noncritical links (PNL) and the percentage of unserved nodes (PUN) are raised as indicators for evaluating the robustness and dependability of the power grid. The influence of generator location and network topology is discussed. The findings indicate that the majority of cascading failures in the power system are initiated by the malfunction of certain specific components. Subsequently, these failures propagate and lead to significant blackout events. Hence, it is of utmost significance to identify and continuously monitor the condition of specific critical nodes and branches to ensure the reliability of the power system. Literature [75] focuses on improving the analysis of fundamental properties of electrical power grids, particularly concerning failures that may occur due to power flow allocation governed by Kirchhoff’s laws. To assess the grid’s robustness, effective graph resistance is adopted as a key indicator representing the grid’s topology. Four tactics, centered on network characteristics, are explored to enhance the optimization of effective graph resistance, which serves as the cost function for enhancing reliability. These tactics are evaluated using a power grid model with low computational complexity. For integrated energy systems, researchers [76] modify the complex network indicator to accommodate the distinctive attributes of various energy sources within the transmission pipeline. A weighted complex network model is developed that incorporates relevant network characteristics. Based on network topology, a novel reliability evaluation indicator encompassing both individual nodes and the overall system is proposed. This approach allows for a holistic evaluation of the power system’s reliability, taking into account the specific attributes of different energy sources and their interactions within the network.

4.3. Load Flow Analysis

Load flow is an important analytical method in power system planning, operation, and control [77]. In deterministic load flow (DLF), the system conditions are characterized by input variables with specific, fixed values, leading to a unique solution for the system. It can be expressed as for an $n$ bus system with $k$ different load values and non-dispatchable renewable energy, $k^n$ load flows are needed for simulation [78]. The precision of DLF solutions depends on the information density of the input data, which can only be recognized with a certain degree of accuracy. In practice, input data were inherently subject to uncertainties, primarily due to inaccuracies in predictions or measurements, stochastic variations in input variables, and potential component failures [16]. Probabilistic Load Flow (PLF) offers a quantitative method to evaluate the reliability of energy systems by incorporating system randomness and uncertainties. The concept of PLF is to treat variables with stochastic attributes (renewable energy supply and demand load) as following certain probability distributions. In particular, PLF typically models renewable energy sources such as wind and solar power as random variables following specific probability distributions to account for their inherent variability and uncertainty. Its applications will be discussed in detail in the next chapter.

RIES usually contains systems including electric, natural gas, thermal energy, and their transmission network. However, the development level of each energy source varies greatly due to the various subject recognitions. Load flow in the electric system is quite complete, even for the smart grid, ac\dc hybrid system, and renewable energy access based on traditional power. This study of load flow in natural gas systems is emphasized in the 21st century. Load flow analysis for regional thermal systems is developed much later. This research is driven by completing the coupling of each energy system for comprehensive analysis with the advancement of RIES.

In the power system, load, flow function is usually expressed as the Linear constraint on node power balance. For the injection power $S_i$ of node $i$ is:

(1)$S_i\triangleq P_i+j{Q}_i=\dot{U_i}\overline{I_i}=\dot{U_i}\sum \overline{Y_{ij}}\overline{U_j}$

where $P_i$ and $Q_i$ are the active power and reactive power for node $i$; Node j is the node set connecting node $i$ through component in power system, including node $i$; $\dot{U_i}$ and $\dot{I_i}$ are voltage phasor and current phasor for node $i$; $Y_{ij}$ is the Node admittance matrix of power network; $\overline{I_i}$, $\overline{U_j}$ and $\overline{Y_{ij}}$ are the conjugate complex numbers for $\dot{I_i}$, $\dot{U_i}$, $Y_{ij}$;

For the natural gas system, the linear function of node power balance is given below. Detail discussion is given in [79].

(2)$\left(A_g+U\right)F+\omega -Z_C{F}_c=0$

where, $A_g$ is the node-branch incidence matrix, $U$ is the compressor-node incidence matrix, $F$ is the flow rate in the pipe; $\omega$ is the injection flow rate at the node, $Z_C$ is the vector of the compressor injection flow rate, $F_c$ is the compressor injection flow rate.

For a thermal system, it usually consists of a thermal source, load, supply network, return network, and regulating valve, which can be categorized into the thermal model and hydraulic model. By obtaining the data of flow rate in the pipe and supply and return temperature of each node, the load flow function set can be determined [80].

The hydraulic model includes a node net flow equation and a head loss equation. According to Kirchhoff’s First Law, the node net flow is calculated as follows:

(3)$m_q=\sum m_{in}-\sum m_{out}$

Which can be expressed in matrix:

(4)$A_s\dot{m}=\dot{m_q}$

where $m$ is the flow rate for each pipe, $m_q$ is the net flow rate, $A_s$ is incidence matrix of node and pipe.

For head loss in a thermal system, function can be established by that the sum of the head loss of the network loop $h_f$ is zero, hence:

(5)$\sum h_f=0$

where, head loss in pipe is given:

(6)$h_f=Km\left|m\right|$

where $K$ is the resistance coefficient of network loop.

Combining the above two functions, the head loss function in hydraulic system is:

(7)$B{h}_f=BK\dot{m}\left|\dot{m}\right|=0$

where $B$ is the incidence matrix of loop and branch.

A thermal model is employed to calculate the temperature of each node in the system, including supply temperature $T_s$, return temperature $T_r$ and outlet temperature $T_o$. The outlet temperature refers to the temperature of the flow before the mixing of each outlet node. According to the thermal power calculation, the thermal power supplied or consumed by a network node is given by:

(8)$\mathsf{\Phi }=C_p\dot{m_q}(T_s-T_o)$

where $C_p$ is the specific heat of water at constant pressure, $m_q$ is the net flow rate for each node.

Up to this point, numerous scholars have utilized power flow analysis in the reliability assessment of energy systems. In literature [79], following the reliability evaluation method of power systems, natural gas system nodes are categorized into known injected natural gas power nodes and known natural gas pressure nodes, and power flow equations are established. Through a comprehensive examination of power flow distribution within the natural gas system, the integration of said system into a unified assessment framework has been accomplished, facilitating comprehensive analysis. Liu (2013) [81] divides the district heating system into hydraulic model and thermal model by referring to the power flow analysis method. After setting the power flow calculating functions of hydraulic and thermodynamic models, respectively, the power flow is calculated by means of decomposition solution and joint solution. Considering the variations in time scale, load characteristics, and system composition among regional integrated energy systems, several scholars have investigated the concurrent calculation of multi-energy flows. In literature [60], the authors account for the time-scale characteristics of the electric/thermal integrated energy system and develop a power flow calculation model to evaluate its dynamic performance. By analyzing the dynamic propagation characteristics and time-scale differences among the main components, they categorize disturbance propagation into four quasi-stable processes. For each process, a power flow model is constructed to analyze the dynamic characteristics of disturbance propagation within the system.

Due to the continuous rise in load demand and the increasing intermittency of energy generation, driven by the influence of renewable energy sources, power systems are approaching their theoretical limits [60]. Reference [82] discusses various methods to identify a suitable solution that ensures the system’s voltage profile remains within proximity to the maximum loading point. An ill-conditioned power system is defined as a system whose topology often exhibits a tree-like structure with a high ratio of resistance to reactance (R/X) lines. This attribute can exert a substantial influence on the stability of both distribution and transmission systems [83]. Several methods, including State Space Search Methods and Path Following Methods, are verified to overcome the conventional method, which cannot converge or obtain an unreliable solution of load flow under an ill-conditioned system [84].

4.4. Coupling Relationship Model

The establishment of coupling relationships in RIES includes physical models, mathematical models, and information models. Physical models describe the actual operational processes of energy conversion devices, detailing the physical connections and energy flows between different energy carriers. For example, the thermoelectric coupling model in a CHP system accurately reflects the mutual conversion processes between electricity and heat. Mathematical models, on the other hand, quantitatively describe the coupling relationships between different energy subsystems by establishing a series of mathematical equations and constraints. These models typically encompass energy balance equations, power flow equations, and equipment characteristic curves, thereby enabling precise analysis of the overall system performance [85]. Additionally, information (digital) models integrate data from various sensors and controllers to monitor and adjust the system’s operational status in real-time, facilitating information exchange and coordinated control among subsystems.

In most research, coupling relationships are often used as the basis for modeling IES rather than as evaluation indicators. In literature [86], a game theory-based coupling weight method and the coupling coordination degree parameter are employed to quantitatively evaluate the coupling degree of complex systems. Building on this, Wang (2024) [53] made advancements specifically for integrated energy systems by clearly defining the coupling degree of the coupling model, the comprehensive evaluation indicator for system equipment combinations, and the calculation method for the overall system coupling coordination degree. Initially, this study integrated the conversion relationships of different energy flows during the energy transformation process, categorized as gas-to-electricity, gas-to-heat, and electricity-to-heat. These were uniformly organized into coupling degree parameters, as outlined below:

(9)$D_{a\to b}={\displaystyle \frac{{\beta }_{u,ab}}{{\eta }_{u,ab}}}{\displaystyle \frac{L_{u,ab}}{L_{u,max,ab}}}{\displaystyle \frac{P_{u,ab}}{C_{u,ab}}}\ast 100\%$

where, $D_{ab}$ is the coupling degree of the coupled systems, including gas-to-electricity, gas-to-heat, and electricity-to-heat (%); ${\beta }_{u,ab}$ is the actual conversion rate of the coupled unit (%); ${\eta }_{u,ab}$ is the rated conversion rate of the coupled unit (%); $L_{u,ab}$ is the output power of the coupled unit (%); $L_{u,max,ab}$ represents the output capacity of the coupling unit (%); $P_{u,ab}$ is the input power of the coupled unit (%); $C_{u,ab}$ is the input capacity of the coupled unit (%).

Extending the analysis of equipment combination schemes within the system, the coupling degree of the equipment combination scheme can be obtained by:

(10)$D={\displaystyle \frac{\sqrt[3]{D_{ge}\ast D_{gh}\ast D_{eh}}}{D_{ge}+D_{gh}+D_{eh}}}$

where $D_{ge},D_{gh},D_{eh}$ are the coupling degree of gas-to-electric, gas-to-heat, and electro-thermal systems, separately.$D$ represents the overall coupling degree of the system. In this context, a higher value of $D$ indicates a lower degree of discreteness between subsystems, signifying a higher level of system coupling. Conversely, a lower value of $D$ implies a greater degree of discreteness and a lower level of coupling.

To further balance the contributions of different subsystems, the literature employed an arithmetic weighting method. Consequently, the comprehensive evaluation indicator of the equipment combination scheme can be obtained, as given below:

(11)$\left\{\begin{array}{c}T=\alpha \ast D_{ge}+\beta \ast D_{gh}+\lambda \ast D_{eh}\\ \alpha +\beta +\lambda =1\end{array}\right.$

where $T$ is the comprehensive evaluation coupling degree (%); $\alpha ,\beta ,\lambda$ are the weights of the gas-to-electric, gas-to-heat, and electric-to-thermal coupling systems, separately.

To conclude, $C_{ous}$, the coupling coordination degree of the equipment combination scheme can be obtained by equation:

(12)$C_{ous}=D\ast T$

In the framework of this model, it is necessary to reduce the types of devices and simplify the device combination scheme to improve the coupling coordination degree.

4.5. Comparison of Modeling Approaches

To facilitate a comprehensive understanding of the modeling approaches discussed, Table 3 presents a comparative analysis of their respective strengths, limitations, and RIES application. This synthesis aims to guide researchers and practitioners in selecting appropriate methodologies for specific RIES applications.

As illustrated in Table 3, each modeling approach offers unique insights into RIES analysis. The selection of an appropriate combination of these methods should be based on the specific research requirements and objectives of the RIES study at hand.

5. Assessment Methods

This section examines the assessment methods for reliability evaluation in integrated energy systems. It covers three main categories: simulation, analytical, and approximate methods. The simulation methods, including Monte Carlo and state enumeration techniques, are discussed for their ability to handle complex systems. Analytical methods, such as conventional analytical methods and probabilistic load flow, are explored for their mathematical rigor. Approximate methods, which balance accuracy and computational efficiency, are also presented. Each subsection concludes with a summary table, presenting key characteristics, advantages, and limitations of the discussed methods. These tables serve to facilitate comparison and provide a concise overview of the diverse approaches available for reliability assessment in RIES.

5.1. Simulation Method

The simulation method can avoid complex modeling processes and improve computing efficiency by using computer simulation technology. The Monte Carlo simulation method and the State Enumeration method are two common reliability evaluation techniques for complex systems [87]. The Monte Carlo simulation method has better scalability and flexibility, which is more suitable for this study of the system with renewable energy, load uncertainty, and other factors. Monte Carlo simulation encompasses two main categories: sequential Monte Carlo simulation and non-sequential Monte Carlo simulation. In the sequential approach, the simulation records the state changes of the components in chronological order. Given sufficient simulation time, the reliability indicator can be computed by recording the system states and their respective durations. In the sequential method, the system’s evolution process is replicated, preserving time sequence, causation, and correlation. Conversely, the non-sequential method involves sampling states from the state space according to their respective probabilities [88]. When components are independent, the system state can be formed by directly sampling the state of each individual component. This procedure can be iterated until a satisfactory quantity of system state samples is achieved. It is crucial to note that within the non-sequential simulation approach, the sampled system states have no temporal interdependence or correlation with one another [89]. Monte Carlo simulations are often used to provide reference values for evaluating the accuracy of optimization models.

In order to reflect the random correlation of random faults of various equipment and ensure a certain computational efficiency, some researchers combine the Markov process with the Monte Carlo simulation method. While realizing dynamic simulation, the time sequence correlation of various equipment is considered, which is closer to the actual operation situation. Existing literature has shown that the Markov process is often applied in power grid chain fault prediction, wind power prediction, probabilistic safety assessment, and risk assessment [90]. In literature [91], the random characteristics of renewable energy are considered in system reliability assessment. Building upon this consideration, a general model of photovoltaic and wind power output outage meters is established. Within the all-encompassing energy system, the energy conversion apparatus is posited to exist in two distinct states: the normal state and the failure state [92]. Utilizing the fundamental principles of Markov processes, the state space of the energy hub is deduced and the availability rate in each state is computed. This methodology provides valuable insights into comprehending the repercussions of state transitions in energy conversion equipment on the reliability of the all-encompassing energy system. In literature [93], the reliability analysis was conducted using a Markov model to account for component failures, and the notion of “valve level” was proposed to assess the influence of various energy conversion equipment on the system’s reliability. In literature [94], the sequential Markov chain Monte Carlo method is used to evaluate the load loss risk of generators in distributed power systems. The preventive maintenance scheduling problem for generator sets is treated as a nonlinear stochastic optimization problem. To effectively solve this problem, a combination of genetic algorithm techniques and particle swarm optimization is utilized. In reference [95], the developed algorithm employs a combination of particle swarm optimization and interior point hybrid optimization methods to efficiently evaluate the system’s reliability. Through the synergistic utilization of particle swarm optimization and interior point techniques, an accurate quantification of the reliability indicator for the integrated energy system in the specified region has the capacity to be achieved. The reference [96] uses Monte Carlo simulation to address the decoupling issue between the combined energy system model and the optimal load reduction model of the distribution network within the integrated energy system. In literature [97], building upon the time-sequence model of state transition, a two-layer multi-objective optimization allocation model was developed, which integrates regional integrated energy system planning and operation. The model considers both economy and reliability as optimization objectives to achieve an effective allocation strategy.

Some scholars also use other proxy models to study the system reliability methods based on random sampling. In literature [98], the reliability assessment of a train auxiliary power supply system is analyzed by using the analytic hierarchy process (AHP) based on evidence network. Literature [17] used the Expected System Improvement (ESI) method, combined with Kriging model-based active learning function, to forecast the influence of component reliability update optimization on system reliability. Hawchar (2017) [99] explores the domain of time-varying reliability using chaotic polynomial expansion. Song (2013) [100] uses virtual support vector machines to optimize model accuracy and solve high-dimensional problems. Literature [18] discusses the utilization of the gray box model in the simulation of building energy supply networks. This paper [101] proposes a comprehensive regional energy reliability assessment method, utilizing the fault incidence matrix (FIM) as a foundation, and the influence of equipment failure on system functions is analyzed and demonstrated.

In order to alleviate the computational load associated with reliability assessment methods that rely on random sampling for complex systems, a number of investigations have tackled this challenge by negating the temporal interdependencies among system variables, consequently leading to reduced computation time. In literature [102], a novel approach is introduced for evaluating the ramifications of incorporating significant proportions of renewable energy, particularly wind energy. This method emphasizes the adverse effects on voltage magnitude and transient response during fault occurrences. In literature [103,104,105], the central moment method is introduced as an approach to improve computation efficiency with the objective function of reliability from first-order to fourth-order. The above method ignores the historical data, which is not capable of analyzing real-time reliability conditions. For the participation of time-series data in real-time reliability analyses, Chi (2021) [51] proposes a system framework that can dynamically analyze the real-time reliability of the system and carry out reliability assessment through the utilization of analytical methods to estimate the probability distribution of each functional state. By employing historical data of daily demand and predictions of renewable energy generation, this study [106] investigates the operational reliability and its impact on the power-to-gas system. In reference [107], the suggested model is employed to evaluate system reliability, considering the orchestrated operation of constrained electricity and natural gas networks. This involves integrating cost-effective and sustainable wind energy as a replacement for natural gas units. The simulation incorporates numerous Monte Carlo scenarios, simulating wind speed forecast inaccuracies through the utilization of the autoregressive moving average (ARMA) time-series model.

The summary of methods discussed in this part is given in Table 4.

5.2. Analytical Method

The analytical approach relies on the energy system’s structure, the condition of its components, and their logical interrelationships to establish a specific mathematical reliability model. The analytical methods mainly include the state space method, fault tree method, general generating function, decision graph, power flow analysis, and so on. For power systems, state analysis is the top priority of reliability evaluation, and power flow analysis serves as the foundation for conducting state analysis. In analytical methods, the complexity of models arises from various factors, including nonlinear relationships, coupling effects, interdependencies, multi-dimensional variable interactions, and dynamic changes. These complexity factors result in substantial computational demands, significantly impacting solution efficiency [112]. To address these challenges, researchers have incorporated various optimization strategies into basic analytical methods to enhance overall computational efficiency and model accuracy.

The conventional analytical methods (COM) are employed to simplify the primal problem, which includes linearizing the system model, treating components as independent entities, and assuming Gaussian input random variables. COM is employed on the linearized AC load flow model, and the precision of its outcomes is juxtaposed with those of deterministic load flow. Numerous convolution operations are required for COM of large systems, where the Laplace Transform is needed for convolution calculation. With increasing improvement, COM is still an option for energy system calculation [113,114,115].

The Gaussian mixture approximation provides an estimate for both non-Gaussian and discrete input random variables by representing them as a combination of Gaussian components with varying weights. Valverde (2012) [116] proposes a Gaussian mixture model as a reduction technique for the computational time of convolution operation, efficiently representing correlated non-Gaussian input variables. The primary benefit of the Gaussian components approach is its ability to directly obtain probability density functions for any variable. In literature [51], the uncertainty associated with photovoltaic generation and load demand is addressed through the utilization of the Gaussian Mixture Model-Hidden Markov Model.

Sequence operation theory is a novel and versatile mathematical theory expected to find widespread application in various fields, including the process of power energy system reliability evaluation. It can deal with power reliability assessment with integrated resource planning. Literature [117] proposed four types of discrete sequence operations called addition-type-convolution, subtraction-type-convolution, AND-type-product and OR-type-product. A particular form of discrete sequence called probabilistic sequence is explained in detail to solve the reliability evaluation problem under the condition of integrated resource planning or deregulation environment. To overcome the problem that sequency operation theory cannot handle correlation between input random variables, a copula function is incorporated with input correlation, which is called dependent discrete convolution [118].

The summary of methods discussed in this part is given in Table 5.

5.3. Approximate Methods

The approximate methods belong to the method approximating the input variable in the first place to reduce the computational burden. The point estimate method (PEM) deals with the statistical properties of input random variables without the help of a complete understanding of distribution. Literature [119] first uses PEM to pre-process Gaussian input random variables. It can ensure high computational efficiency and accuracy with a smaller input number [120]. In practical power systems, a huge amount of input variables is computationally burdensome. Several enhancement methods are given in [121,122,123]. The simplest method under the concept of PEM is a two-point estimate method, or 2m scheme. The proposed approach requires running 2m deterministic optimal power flow simulations for m uncertain variables to obtain the first three moments of their corresponding probability density functions [124]. For a high-dimension scheme, Perez-Ruiz (2007) [125] have tested four PEM on the problem of probability load flow. Among the four methods, the 2m+1 scheme shows superior effectiveness when dealing with a substantial quantity of input random variables. On the other hand, the 4m+1 scheme offers comparable results but entails increased computational complexity. For other schemes, the accuracy of the 2m scheme decreases as the input number increases; the 3m scheme usually provides useless complex concentration values under certain circumstances. Wang (2014) [126] uses the extend 2m+1 scheme with fuzzy satisfying decision method under the framework of clonal selection algorithm to solve the multi-objective regional carbon emission management problem.

For other approximate methods, Zou (2013) [127] uses the univariate dimension reduction method to enhance the accuracy of assessing the first moments of the output variable compared with PEM, especially in high-order moments. By using Taguchi’s orthogonal arrays, an approximate PLF solution is achieved, and an optimal experiment is specified [128].

The summary of methods discussed in this part is given in Table 6.

5.4. Case Summary

To elucidate the state-of-the-art applications of reliability assessment methods in RIES, a comprehensive literature review encompassing both previously discussed cases and recent advancements is conducted. Through systematic analysis and synthesis of these studies, a comprehensive table that delineates the prevalent methodologies employed at each stage of the reliability assessment process is developed. This Table 7 serves as a holistic and up-to-date synopsis of the current research landscape.

Energy system modeling and reliability assessment methodologies have evolved significantly, as evidenced by recent literature. The Energy Hub concept has emerged as a prevalent framework for system architecture. Integer programming, often built upon load flow analysis, remains a staple approach. Multi-objective optimization has become the dominant computational paradigm, while complex network theory has filled a crucial gap in node connectivity research. Machine learning algorithms and probability distribution functions (PDF) frequently appear as solution methods, demonstrating the field’s embrace of advanced computational techniques.

Despite the expansion from traditional power systems to IES encompassing electricity, gas, and heat, and even Renewable Energy (RE) sources, many studies still employ reliability indices originally developed for electrical grids. This trend underscores the robustness and adaptability of these metrics.

Uncertainty analysis in many studies considers load volatility, often limited to sensitivity analysis, which lacks generalizability and is thus marked as Not Applicable (NA) in the summary. Beyond NA cases, uncertainty is predominantly addressed through probability distribution functions and random fault generation, with fuzzy inference appearing in a minority of studies.

This evolution in methodologies reflects the increasing complexity of energy systems and the growing emphasis on holistic, robust reliability assessment techniques. However, the methods presented in Table 7, while sophisticated, often rely on complex simulations and theoretical models with numerous hyperparameters. This complexity, combined with the inherent intricacy of RIES, poses significant challenges in establishing a unified metric or normalized evaluation framework for comparative analysis.

It is crucial to note that most current studies in this field are largely detached from real-world projects and lack experimental validation. Consequently, the results tend to be overly idealized, potentially limiting their practical applicability. This disconnect between theoretical models and actual implementation underscores the need for future research to bridge this gap through empirical studies and project-based validations in operational environments.

6. Conclusions

Findings indicate that the energy hub model has emerged as the predominant framework for RIES architecture, facilitating effective multi-energy system integration. Complex network theory demonstrates unique advantages in analyzing RIES topological structures and node criticality. Probabilistic load flow analysis excels in addressing renewable energy uncertainties, though computational complexity remains a significant hurdle. Machine learning methods, particularly deep learning techniques, show remarkable potential in RIES reliability assessment, offering novel approaches to handle high-dimensional, large-scale data. Multi-objective optimization methods play a crucial role in balancing system economics, reliability, and environmental impact, providing decision-makers with comprehensive evaluation tools.

Compared to traditional single-energy system reliability studies, this research has made progress in multi-energy coupling and has explored various approaches to enhance the reliability assessment of RIES, particularly in the context of increasing renewable energy integration. This review and analysis of diverse assessment methodologies provides valuable guidance for researchers and practitioners in selecting appropriate method combinations for specific RIES reliability challenges. Notably, the proposed comprehensive evaluation framework addresses this research gap in system reliability assessment under high renewable energy penetration scenarios. These advancements have direct applications in RIES planning, design, and operational optimization, enhancing overall system performance and stability.

Nevertheless, several challenges persist. Further research is required in the deep integration of energy dispatch, storage optimization, and demand response. Highly integrated systems potentially increase cascading failure risks, necessitating more refined risk assessment models. The intermittentity and uncertainty of renewable energy sources continue to pose reliability challenges. Moreover, the universality of existing reliability assessment standards needs improvement, and supply-demand coupling studies must strike a balance between model accuracy and computational efficiency.

Based on the challenges and limitations identified in this comprehensive review, several areas warrant further investigation in the RIES reliability assessment. Future studies could benefit from focusing on enhancing integration strategies for energy systems, advancing risk assessment models for highly integrated networks, and refining methods to manage renewable energy uncertainties. There is also a need to standardize and optimize assessment frameworks, balancing accuracy and computational efficiency across diverse RIES configurations. Importantly, addressing the gap between theoretical models and practical applications through empirical studies and real-world validations appears crucial.

It is important to note that this study’s limitations lie in its reliance on literature review and theoretical analysis, lacking validation from large-scale practical systems.

In conclusion, this research systematically elucidates the current state of RIES reliability assessment and delineates critical future research trajectories. As renewable energy penetration deepens and energy systems grow increasingly complex, RIES reliability assessment remains a field replete with challenges and opportunities. It is posited that through sustained technological innovation and interdisciplinary collaboration, RIES will play an increasingly pivotal role in future energy systems, contributing significantly to the realization of clean, efficient, and reliable energy supply.

Data Availability Statement

No new data were created or analyzed in this study. Data sharing is not applicable to this article.

Conflicts of Interest

The authors declare no conflict of interest.

Abbreviations

AECM	Augmented Epsilon Constraint Method	ESS	Energy Storage System
AHP	Analytic Hierarchy Process	FLC	Load reduction frequency
APCU	Aggregate Power Conversion Unit	LOLP	Loss of Load Probability
ASAI	Average Service Availability Index	LOLH	Loss of Load hours
ASUI	Average Service Unavailability Index	MAIFI	Momentary Average Interruption Frequency Index
BEMS	Building Energy Management System	MFO	Moth-Flame Optimization
CAIDI	Customer Average Interruption Duration Index	MINLP	Mixed-Integer Nonlinear Programming
CAIFI	Customer Average Interruption Frequency Index	ML	Machine Learning
CE	Carbon Emission	MOO	Multi-Objective Optimization
COM	Conventional Analytical Methods	MOPSO	Multi-Objective Particle Swarm Optimization Algorithm
CTAIDI	Customer Total Average Interruption Duration Index	MTBF	Mean Time Between Failures
DHC	District Heating and Cooling Systems	MTTF	Mean Time to Failure
DLF	Deterministic Load Flow	OEF	Optimal Energy Flow
DR	Demand Response	PDF	Probability Distribution Function
DSM	Demand-Side Management	PEM	Point Estimate Method
EDLC	Expected Duration of Load Curtailment	PLF	Probabilistic Load Flow
EENS	Expected Energy Not Supplied	RE	Renewable Energy
EFLC	Expected Frequency of Load Curtailment	REPR	Renewable Energy Penetration Rate
EH	Energy Hub	RES	Renewable Energy Resource
ENS	Energy Not Supplied	RIES	Regional Integrated Energy System
HEMS	Home Energy Management System	SAIDI	System Average Interruption Duration Index
IES	Integrated Energy System	SAIFI	System Average Interruption Frequency Index
LOLE	Loss of Load Expectation	SCA	Sine Cosine Algorithm
ESI	Expected System Improvement

Footnotes

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Figures and Tables

Figure 1. Common Classification of IES. Source: Developed by the authors.

Figure 2. Energy-Flow Coupling Relationship for A Typical Integrated Energy System. Source: Developed by the authors.

Figure 3. Integrated Urban Energy Ecosystem: A Comprehensive View of Regional Integrated Energy Systems. Source: Adapted from IEEE Smart Cities. (March 2022) [28].

Figure 4. Example of 30 bus power system in complex network. Source: Developed by the authors.

Table 1

Definition and function of common reliability indicators.

Name	Function
SAIDI	$\mathrm{S}\mathrm{A}\mathrm{I}\mathrm{D}\mathrm{I}={\displaystyle \frac{\mathrm{s}\mathrm{u}\mathrm{m}\mathrm{o}\mathrm{f}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{u}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{d}}}$
SAIFI	$\mathrm{S}\mathrm{A}\mathrm{I}\mathrm{F}\mathrm{I}={\displaystyle \frac{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{u}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}}{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{d}}}$
CAIDI	$\mathrm{S}\mathrm{A}\mathrm{I}\mathrm{F}\mathrm{I}={\displaystyle \frac{\mathrm{s}\mathrm{u}\mathrm{m}\mathrm{o}\mathrm{f}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{u}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{d}}}={\displaystyle \frac{\mathrm{S}\mathrm{A}\mathrm{I}\mathrm{D}\mathrm{I}}{\mathrm{S}\mathrm{A}\mathrm{I}\mathrm{F}\mathrm{I}}}$
CAIFI	$\mathrm{C}\mathrm{A}\mathrm{I}\mathrm{F}\mathrm{I}={\displaystyle \frac{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{u}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}}{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{t}\mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{u}\mathrm{p}\mathrm{t}\mathrm{e}\mathrm{d}}}$
MAIFI	$\mathrm{C}\mathrm{A}\mathrm{I}\mathrm{F}\mathrm{I}={\displaystyle \frac{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{m}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{y}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{u}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}}{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{d}}}$
ASAI/ASUI	$\mathrm{A}\mathrm{S}\mathrm{A}\mathrm{I}=1-{\displaystyle \frac{\mathrm{S}\mathrm{A}\mathrm{I}\mathrm{D}\mathrm{I}}{8760}}\hspace{1em}\mathrm{A}\mathrm{S}\mathrm{U}\mathrm{I}={\displaystyle \frac{\mathrm{S}\mathrm{A}\mathrm{I}\mathrm{D}\mathrm{I}}{8760}}$
CTAIDI	$\mathrm{C}\mathrm{T}\mathrm{A}\mathrm{I}\mathrm{D}\mathrm{I}={\displaystyle \frac{\mathrm{s}\mathrm{u}\mathrm{m}\mathrm{o}\mathrm{f}\mathrm{d}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{u}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}}{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{t}\mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{u}\mathrm{p}\mathrm{t}\mathrm{e}\mathrm{d}}}$
LOLP	$\mathrm{L}\mathrm{O}\mathrm{L}\mathrm{P}=\mathrm{s}\mathrm{u}\mathrm{m}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{b}\mathrm{a}\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{t}\mathrm{h}\mathrm{a}\mathrm{t}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{m}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{c}\mathrm{a}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{o}\mathrm{n}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{d}\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{a}\mathrm{g}\mathrm{e}$
LOLE	$\mathrm{L}\mathrm{O}\mathrm{L}\mathrm{E}=\mathrm{L}\mathrm{O}\mathrm{L}\mathrm{P}\times \mathrm{N}$Where $\mathrm{N}$ is the total number of increments inside the long interval
LOLH	Loss of load hours, LOLE measured in hour
EENS	$\mathrm{E}\mathrm{E}\mathrm{N}\mathrm{S}=\left(\mathrm{E}\mathrm{D}\mathrm{L}\mathrm{C}\right)\times \mathrm{L}$Where $\mathrm{L}$ is the load curtailed at a considered load point
EFLC	$\mathrm{E}\mathrm{F}\mathrm{L}\mathrm{C}=\mathrm{s}\mathrm{u}\mathrm{m}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{f}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}$
EDLC	$\mathrm{E}\mathrm{D}\mathrm{L}\mathrm{C}=\mathrm{s}\mathrm{u}\mathrm{m}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{f}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{s}\mathrm{f}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}$

Source: Compiled by the authors based on [29,38,39].

Table 2

Representative reliability evaluation methodology of IES.

Classification	Definition	Example
MEASURE	Systematic value against established benchmarks.	Load, Frequency, Energy Flow, Cost
INDICATOR	Quantitative or qualitative manifestation of results.	EENS [40], SAIDI, LOLP [29], CAIDI, ECOST [47], REPR [44], Reliability Cost [48]
INDICES	Synthesized metrics enable hierarchical analysis and summation of observational data.	Integrated Reliability Index [14], Resilience Index [49], Network Redundancy [50], CDI [51]
METRIC	A comprehensive set of measures, indicators, or indices designed to assess specific attributes or properties.	Energy Trilemma Index [52]

Source: Synthesized by the authors from various sources.

Table 3

Strengths, Limitations and RIES Application of Modeling Approaches.

Approach	Strengths	Limitations	Ries Application
ENERGY HUB	Comprehensive multi-energy frameworkFacilitates conversion and storage analysisScalable from buildings to urban systems	Computationally intensive for large-scale systemsPotential oversimplification of complex interactionsRequires detailed conversion efficiency data	Can improve local energy reliabilityHelps optimize energy production and consumption
COMPLEX NETWORK THEORY	Effective for topological and critical analysisSuitable for cascading failure and robustness studiesEfficient for large-scale system analysis	May oversimplify physical constraintsLimited accuracy in detailed energy flow representationChallenges in time-dependent behavior incorporation	Analyzes network characteristics and node importance in RIESIdentifies system weak points
LOAD FLOW ANALYSIS	Detailed energy flow and system state analysisWell-established methodology with extensive toolsHigh accuracy for steady-state analysis	Computationally demanding for large systemsPotential issues with highly non-linear systemsLimited dynamic behavior representation	Applicable for coupled analysis of electricity, gas, and thermal systems in RIESAnalyzes impacts of renewable energy on the system
COUPLING RELATIONSHIP MODEL	Explicit inter-carrier interaction representationFacilitates multi-energy system optimizationIncorporates physical and operational constraints	Complex formulation and solution processesExtensive system interaction data requirementsChallenges in balancing complexity and efficiency	Analyzes coupling of different energy subsystems in RIESEvaluates coupling degree of equipment combination

Source: Authors’ compilation based on the main text.

Table 4

Simulation Method Summary.

Method	Description	Advantage	Limitations
MONTE CARLO SIMULATION	Uses random sampling to obtain numerical results	FlexibleScalableSuitable for complex systems	Computationally intensiveResults are approximate
MARKOV PROCESS + MONTE CARLO	Combines Markov process with Monte Carlo for dynamic simulation	Considers time sequence correlationCloser to actual operation	More complex to implement
ANALYTIC HIERARCHY PROCESS (AHP)	Uses pairwise comparisons to rank alternatives	Structured approachCan handle both qualitative and quantitative criteria	Subjective judgments can affect results
EXPECTED SYSTEM IMPROVEMENT (ESI)	Forecasts impact of component reliability updates	Optimizes system reliabilityUses active learning	Requires accurate initial models
GREY BOX MODEL	Combines theoretical and empirical modeling	Balances complexity and accuracyUseful for partially known systems	Requires both system knowledge and data

Source: Authors’ compilation based on the main text. Furthermore, the cost function utilized in the above reliability assessment relies on the component failure probability, which considers two functional states: functionality and failure. However, due to the high-dimensional data generated in the system coupling, system performance should be represented in multi-modal forms rather than binary values. The system’s functionality is influenced by real-time loads and renewable energy generation [108]. In some specific cases, the diagnosis of system performance and the analysis of its degradation are determined by process variables, such as nuclear reactors [109]. Literature [110] proposed an integrated safety prognosis model (ISPM) utilizing dynamic Bayesian networks to provide a comprehensive approach to assess current safety states, predict future degradation trends, and enhance long-term operational performance and reliability in complex industrial systems. To implement such methods, the determination of the functional state based on multiple process variables should be paid attention to [111].

Table 5

Analytical Method Summary.

Method	Description	Advantages	Disadvantages
CONVENTIONAL ANALYTICAL METHODS (COM)	Simplifies original problem, linearizes system model	Still applicable for energy system calculations	Requires numerous convolution operations for large systems
GAUSSIAN MIXTURE APPROXIMATION	Represents non-Gaussian and discrete inputs as Gaussian components	Directly obtains probability density functions	May require extensive data for accurate estimation
SEQUENCE OPERATION THEORY	Novel mathematical theory with four types of discrete sequence operations	Can handle reliability assessment with integrated resource planning	Original form cannot handle input variable correlations
DEPENDENT DISCRETE CONVOLUTION	Incorporates copula function with input correlation	Addresses correlations between input random variables	May increase computational complexity
PROBABILISTIC LOAD FLOW (PLF)	Accurately represents uncertainties in energy systems	Suitable for systems with significant renewable energy	Computationally complex, requires substantial resources
FUZZY LOGIC METHODS	Integrates expert knowledge, handles imprecise data	Highly adaptable	Can be subjective and complex in large-scale systems

Source: Authors’ compilation based on the main text. To conclude, the advantage of the PLF method lies in its ability to accurately represent uncertainties within energy systems, making it particularly suitable for integrated energy systems where renewable energy plays a significant role. However, PLF is computationally complex, potentially requiring substantial computational resources, and is highly dependent on accurate and comprehensive data. Fuzzy logic methods effectively integrate expert knowledge, are highly adaptable, and can handle imprecise and ambiguous data efficiently. Nevertheless, these methods can be subjective, potentially introducing bias, and can be complex to model and implement in large-scale systems. Bayesian networks excel in managing and representing uncertainties, leveraging prior knowledge to enhance the reliability of assessments. However, they require extensive data for accurate probability estimation and entail significant computational overhead, especially when dealing with large-scale networks.

Table 6

Approximate Method Summary.

Method	Description	Advantages	Limitations
POINT ESTIMATE METHOD (PEM)	Approximates statistical properties of input variables	Computationally efficient Does not require full distribution knowledge	Less accurate for highly nonlinear systems
2M SCHEME	Simplest PEM variant	Very efficient Good for low-dimensional problems	Accuracy decreases with more input variables
2M+1 SCHEME	Enhanced PEM for high-dimensional problems	Effective for many input variablesGood balance of accuracy and efficiency	More complex than basic 2m scheme
UNIVARIATE DIMENSION REDUCTION	Enhances accuracy of moment assessment	Improved accuracy over PEMGood for high-order moments	More complex implementation
TAGUCHI’S ORTHOGONAL ARRAYS	Achieves approximate PLF solution	Optimal experiment designEfficient for complex systems	May not capture all system interactions

Source: Authors’ compilation based on the main text.

Table 7

Examples of Reliability Assessment Methods Applied to Integrated Energy Systems.

Energy Type	Modelling	Assessment	Indicator	Uncertainty	Reference
IES, WIND, SOLAR	MINLP, MOO	Pareto Front	Cost, CE	PDF	[129]
IES, SOLAR	GMM-HMM	ML	FLC, CDI	PDF	[51]
POWER	Fuzzy Inference	heuristic algorithm	SAIFI, SAIDI, Cost	Fuzzy Inference	[130]
POWER	AHP	AHP	Cost, EENS	Expert grade	[131]
IES, WIND, SOLAR	Load flow	Cumulant method	PDF	Fuzzy integral	[132]
IES	MILP	AHP	SAIFI, SAIDI, EENS	NA	[96]
POWER	Fast Decoupled	Path Following Methods	Voltage Stability Index	NA	[82]
WIND, SOLAR	Markov process	Path Following Methods	Availability factor	PDF	[15]
WIND, SOLAR, BIOMASS, GEOTHERM, GAS	Bi-level program	MOPSO	Cost, CE, Threshold level of energy equipment	NA	[53]
POWER	Complex network	Linear program	fraction of activated links	NA	[13]
FOSSIL FUEL, NUCLEAR, RE	Multiregional physical supply usage table	Linear program	fraction of activated links	NA	[133]
IES	Energy hub	Alternating Direction Method of Multipliers	Cost, Load interruption	NA	[10]
THERMA AND RE	MILP, MOO	Heuristic Algorithms	Cost, Payback Period	NA	[8]
POWER AND HEAT	MOO, Reliable Energy Supply Interval Model	Non-dominated Sorting Genetic Algorithm II	EENS, Reliable Operating Distance	NA	[134]
FOSSIL FUEL, RE	Fuzzy System	Center of Gravity Defuzzification	LOLP	PDF	[32]
GENERAL	Kriging Model	Active Learning Method	System Failure Probability	PDF	[17]
IES, SOLAR	MILP	Bounded Objective Function	Cost, Energy Self-sufficiency Rate	NA	[11]
RE	MOO	MFO	EENS, FLC	NA	[40]
IES	Load flow	MILP	Cost, EENS	No liner relationship	[112]
IES	Load flow	MINLP, Improved Genetic Algorithm	Cost, Performance Factor Index, peak-to-valley ratio of load	Demand response	[21]
IES	Two-State model, smart agent model	Sequential Monte Carlo simulation	SAIFI, SAIDI, CAIDI, ASAI, EENS	Random fault	[135]
IES, BATTERY	Probabilistic model	Particle Swarm Optimization	SAIFI, SAIDI, ASAI, EENS, Expected Electric Vehicles Grid Dependency	PDF	[136]
IES	Probabilistic Model	Probability Transformation Method	Cost, FLC	PDF	[12]
SOLAR, BATTREY	Markov State Transition Diagram, Failure Rate Model	Chapman–Kolmogorov Equation	MTTF	Random fault	[101]
IES	Markov Two-State Model, Energy Hub, User Experience Model	Markov Chain Monte Carlo Method	Consumer-group-aware Factor	Random fault	[137]
SOLAR, WIND, BATTERY	Hybrid Renewable Energy System Model	MOO, Genetic Algorithm	Techno-Economic-Reliability Index	NA	[138]
POWER	Sequence Operation Theory	Sequence Operation	LOLP, LOLE	NA	[117]

Source: Compiled by the authors.

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