Enhancing Smart Microgrid Resilience Under Natural Disaster Conditions: Virtual Power Plant Allocation Using the Jellyfish Search Algorithm

Abstract

Electric power networks face critical challenges from extreme weather events and natural disasters, disrupting socioeconomic activities and jeopardizing energy security. This study presents an innovative approach incorporating virtual power plants (VPPs) within networked microgrids (MGs) to address these challenges. VPPs integrate diverse distributed energy resources such as solar- and wind-based generation, diesel generators, shunt capacitors, battery energy storage systems, and electric vehicles (EVs). These resources enhance MG autonomy during grid disruptions, ensuring uninterrupted power supply to critical services. EVs function as mobile energy storage units during emergencies, while shunt capacitors stabilize the system. Excess energy from distributed generation is stored in battery systems for future use. The seamless integration of VPPs and networked technologies enables MGs to operate independently under extreme weather conditions. Prosumers, acting as both energy producers and consumers, actively strengthen system resilience and efficiency. Energy management and VPP allocation are optimized using the jellyfish search optimization algorithm, enhancing resource scheduling during outages. This study evaluates the proposed approach’s resilience, reliability, stability, and emission reduction capabilities using real-world scenarios, including the IEEE 34-bus and Indian 52-bus radial distribution systems. Various weather conditions are analyzed, and a multi-objective function is employed to optimize system performance during disasters. The results demonstrate that networked microgrids with VPPs significantly enhance distribution grid resilience, offering a promising solution to mitigate the impacts of extreme weather events on energy infrastructure.

1. Introduction

In recent years, the intensity and frequency of natural disasters have increased, largely due to climate change. Events such as floods, hurricanes, earthquakes, and ice storms pose significant threats to human safety and infrastructure, highlighting weaknesses in traditional power system management. Extreme weather events, including storms and heatwaves, adversely affect microgrid (MG) resilience by increasing equipment failures, reducing the efficiency of renewable energy generation, and escalating power demand. Additionally, disruptions to communication and control systems exacerbate challenges in maintaining stable and reliable operations. Enhancing MG resilience under these conditions is essential to ensure a continuous and dependable power supply [1].

Recent research focuses on improving system resilience through adaptive planning, real-time monitoring, and advanced control techniques. Integrating distributed energy resources (DERs), fault location strategies, and risk mitigation measures strengthens the ability of power systems to withstand and recover from extreme events. Furthermore, advanced fault detection and location techniques are critical for minimizing outage durations and impacts, thereby enhancing stability and reliability during severe conditions. These strategies collectively highlight the necessity of fortifying power systems to address the increasing number of climate-related disruptions [2,3].

Historically, power system planning and operation focused on ensuring security and adequacy to maintain a stable electricity supply that reliably met customer demands over long periods. However, the rising frequency and severity of natural disasters have necessitated a re-evaluation of these traditional approaches. Recent studies highlight the importance of enhancing system resilience through advanced strategies such as microgrid integration, DERs, and prosumer-centric models. These approaches aim to improve system flexibility, expedite recovery, and enhance fault tolerance during extreme events. Moreover, incorporating real-time monitoring, adaptive control systems, and machine learning models has become critical for optimizing resilience and mitigating disaster impacts. Such advancements underscore the shift toward dynamic, responsive power system frameworks that prioritize resilience over static, conventional planning methods [4,5,6].

In light of these challenges, resilience has emerged as a key priority in power system management, emphasizing the ability to withstand, adapt to, and recover swiftly from disruptions. This proactive approach focuses on flexibility, adaptability, and risk mitigation to ensure uninterrupted service and minimize disruptions. Advanced technologies, including microgrids, DERs, and real-time monitoring systems, play a vital role in enhancing resilience. Additionally, emerging tools such as machine learning models and quantum computing are being utilized to optimize system responses, reduce recovery times, and improve stability during extreme weather events. This paradigm shift highlights the growing importance of resilience in creating sustainable and reliable energy systems [7,8].

Optimizing the performance of smart MGs during severe weather events requires consideration of factors beyond resilience alone. While resilience is essential, reliability is equally important for ensuring system effectiveness. Reliability analysis evaluates the system’s ability to withstand disruptions and provide an uninterrupted power supply to critical loads, minimizing downtime during adverse weather conditions [9,10]. In active distribution systems, resilience studies have primarily focused on MG formation, particularly the integration of grid-edge DERs [11]. Strategically placing DERs, such as distributed generators (DGs) and energy storage systems, enhances system stability, supports rapid load restoration, and reduces the risk of voltage collapse. These DERs help maintain voltage stability and minimize power losses, which are crucial for sustaining resilience during disruptions [12].

Furthermore, technological advancements have significantly bolstered the resilience of electrical distribution systems [13]. Innovations such as advanced control algorithms, smart grid technologies, and IoT-based monitoring systems have enabled more adaptive and flexible operations, enhancing overall resilience. These technologies facilitate the seamless integration of renewable energy sources (RESs) and DGs, improving fault recovery and reducing outage durations [14]. By addressing these factors alongside resilience strategies, microgrids can remain robust, reliable, and effective even under severe weather conditions. Leveraging these advancements ensures that microgrids can withstand and recover more effectively from extreme weather events, maintaining continuous and reliable electricity delivery to communities and critical infrastructure.

Virtual power plants (VPPs) have emerged as a promising solution for enhancing power system resilience through a decentralized and integrated operational framework. Leveraging advanced control algorithms and digital technologies, VPPs efficiently manage DERs, including RESs, energy storage systems, and demand response mechanisms. This approach ensures optimal resource utilization, enhances grid stability, and facilitates rapid responses to dynamic grid conditions. Consequently, VPPs mitigate disruptions while supporting sustainability goals. Their scalability and modularity enable deployment in diverse settings, from urban areas to remote regions. Recent studies highlight the critical role of VPPs in improving resilience during extreme weather events. Research demonstrates that strategically placed and sized VPPs within distribution networks can significantly enhance system performance under disruptive conditions. Furthermore, optimization algorithms have been shown to improve MG resilience, enabling better adaptation to changing grid conditions. Reliability-based bidding strategies for VPPs also ensure efficient operation and further strengthen resilience. Collectively, these advancements emphasize the pivotal role of VPPs in creating more resilient, sustainable, and adaptable energy systems [15,16,17].

Traditional energy management systems (EMSs) typically focus on optimizing isolated components, such as generators or storage systems, within centralized setups using methods like linear programming, mixed-integer linear programming, and genetic algorithms. These approaches are often single-objective and limited to localized systems. In contrast, our VPP-based EMS employs the jellyfish search optimization algorithm (JSOA) to optimize a network of decentralized DERs, including solar, wind, storage, and electric vehicles (EVs), across multiple microgrids. This method enables multi-objective optimization, addressing cost reduction, grid stability, resilience, and energy efficiency. Unlike a traditional EMS, which manages isolated system components, our approach ensures real-time coordination and fault tolerance, allowing VPPs to adapt to dynamic grid conditions and recover swiftly from disruptions [15,16,17].

Beyond resilience enhancement, VPPs address critical factors such as reliability, sustainability, and grid stability. With advanced control algorithms and real-time monitoring, VPPs optimize resource allocation, reducing outage risks and improving overall grid reliability. By integrating RESs, VPPs contribute to lowering carbon emissions and promoting environmental sustainability. Additionally, they strengthen grid stability by effectively managing fluctuations in supply and demand. The adoption of VPPs marks a significant step toward building more resilient and sustainable energy systems capable of meeting 21st-century challenges. By fostering flexibility, adaptability, and proactive risk management, VPPs empower grid operators to navigate disruptions effectively, ensuring a reliable energy supply for communities worldwide.

1.1. Literature Review on Resilience Improvement and VPP Allocation in Distribution Grid

This section provides a concise summary of existing research on VPP allocation, resilience enhancement, and their integration with RDSs. It lays the groundwork for the methodology adopted in this study, supporting advancements in energy infrastructure management under extreme weather conditions.

Several studies have proposed strategies to enhance the resilience of RDSs, focusing on infrastructure hardening, MG formation, and DG optimization to reduce network vulnerability. For instance, one study addressed a resilient distribution system planning problem by coordinating DG allocation to minimize network damage and improve stability [18]. Another investigation developed a resilience-oriented framework, effectively safeguarding RDSs against extreme weather through simulations on various network topologies [19]. A planning model was also proposed to minimize investment, operational, and resilience costs during natural disasters [20]. Additionally, a study explored optimizing system resilience through reconfiguration, avoiding the need for expensive construction measures [21].

The resilience of MGs under extreme conditions highlights the critical role of power electronics, energy storage systems, and DERs in improving supply reliability [22]. Furthermore, a multistage dynamic and resilience-based framework for RDS expansion planning has been developed to assess resilience metrics and optimize system performance during severe weather events [23]. These studies emphasize the need for advanced solutions, such as VPPs, to enhance RDS resilience. By deploying VPPs alongside DERs and energy storage, grid operators can optimize resource utilization, improve system stability, and better mitigate the impacts of extreme weather events.

Despite these promising results, the literature on VPPs and their integration into RDS resilience remains limited. Few studies explore the role of VPPs in strengthening RDS resilience. One study assessed the importance of nodes and lines, evaluating post-disaster recovery times through both pre- and post-event resilience assessments [24]. Another focused on resilient VPP operations during floods and earthquakes, using a hybrid metaheuristic optimization algorithm to minimize system damage costs during natural disasters [25]. Notably, results from the IEEE 69-bus RDS demonstrated the significant impact of VPPs in enhancing network resilience compared to traditional power flow analysis [25]. Additionally, research on optimizing VPP locations and sizes in RDSs, particularly under severe weather conditions, confirmed that VPPs play a crucial role in boosting resilience [26].

Recent studies highlight the role of VPPs in enhancing resilience during extreme weather events. One study utilized Monte Carlo simulations and Stackelberg games to optimize battery and electric vehicle (EV) resources, reducing costs and improving resilience. However, computational complexity and simplified models remain limitations, requiring further research to improve scalability [27]. Similarly, a framework designed to enhance the resilience of islanded microgrids (IMGs) against cyberattacks on critical loads integrated multiple techniques for improving resilience during the survive, sustain, and recovery phases. The absence of VPP integration and real-world testing, however, limited the scope of the findings [28].

Technological advancements in DERs have improved residential and commercial energy systems. VPPs enhance grid security and reliability by incorporating energy storage, flexible loads, and DERs. Recent studies propose VPP models to optimize energy management, focusing on maximizing operational profits through market participation. Despite this, challenges related to complex legislative frameworks and scalability remain [29]. Furthermore, a study reviewing VPP fundamentals emphasized the role of Vehicle-to-Grid (V2G) technology, which enhances resilience by allowing EV batteries to supply power during emergencies. While this improves grid stability and reduces costs, limited research on V2G integration into VPPs exists, especially concerning sociological, economic, and technical challenges [30].

The role of VPPs in competitive energy markets is crucial, providing solutions to social, economic, and environmental challenges through interconnected DERs. However, issues such as renewable energy unpredictability, market fluctuations, and communication security remain unresolved [31]. Moreover, floods, classified as high-impact low-probability (HILP) events, present substantial risks to power distribution systems. One study developed a risk-constrained bi-level model incorporating power-to-gas (P2G) and gas-to-power (G2P) units for energy sharing. The model showed a 35% improvement in resilience and a 25% reduction in power loss, emphasizing the importance of coordinated risk management during HILP events [32].

As energy demands rise, an enhanced supervisory control scheme (ESCS) for hybrid microgrids (HMGs) has been proposed, integrating both AC and DC grids within a VPP framework. The ESCS optimizes energy management and smart charging for EVs, facilitating V2G and Grid-to-Vehicle (G2V) interactions. The system improved power quality (PQ), demonstrating superior power management while adhering to IEEE 519 standards, as validated through simulations and Hardware-in-the-Loop testing [33]. Another study developed a framework for VPPs that aligns with market dynamics and integrates energy storage technologies to optimize new power systems. This integration enhances system stability, reduces overall production costs, and encourages the adoption of clean energy, contributing to environmental conservation [34].

As the integration of distributed clean energy sources increases, VPPs face challenges in coordinating resources such as EVs, energy storage, controlled loads, and DGs. A distributed control approach using a particle swarm optimization (PSO)-based reinforcement learning technique can optimize VPP performance by maximizing output and operational efficiency across various market scenarios. The potential of VPPs is highlighted, examining both their advantages and limitations in power management strategies [35]. Additionally, microgrids with RESs play a crucial role in enhancing power system resilience. Microgrids improve resilience by employing strategies for service restoration, network formation, and stability. Furthermore, integrating distributed generation and energy control helps reduce reliance on transmission lines and improves recovery times [36].

1.2. Literature Review on Application of JSOA in Energy Management

JSOA has become a prominent metaheuristic approach in energy management due to its effectiveness in solving complex optimization problems. Inspired by the foraging behavior of jellyfish, JSOA efficiently explores vast search spaces while balancing exploitation and exploration. Several studies have highlighted JSOA’s capabilities, often comparing its performance with other metaheuristic methods. One such study introduced the Artificial Jellyfish Optimization with a Deep Learning-Driven Decision Support System (AJODL-DSSEM) model for energy management in smart cities. This hybrid model integrated data preprocessing and an attention-based CNN-BLSTM for energy prediction, with hyperparameter optimization performed using JSOA. The results showed superior performance compared to other methods, underscoring JSOA’s capacity to manage large, complex datasets efficiently [37]. An enhanced version, EJSOA, was developed to address energy management in Multi-Microgrids (MMGs) within an 85-bus RDS. This version integrated Weibull flight motion and fitness distance balance (FDB) mechanisms, effectively mitigating stagnation issues in conventional JSOA and improving efficiency in large-scale systems [38].

JSOA has been successfully applied to the multi-area economic dispatch (MAED) problem, outperforming other algorithms in constraint handling and cost minimization, consistently demonstrating superior performance [39]. In distribution systems, JSOA optimized multi-type DG units using a leader-based mutation-selection approach, significantly reducing real power losses and improving voltage profiles [40]. Additionally, JSOA optimized Type I and Type III DG units within an RDS, enhancing voltage stability and reducing operating costs, particularly under nominal and peak demand conditions [41]. The Quasi-Reflection JSOA (QRJSOA) applied to OPF problems in large IEEE systems (57-bus, 118-bus) showed superior solution quality in terms of cost minimization and constraint handling [42]. Furthermore, JSOA’s application in isolated microgrids demonstrated its effectiveness in minimizing power losses and emissions, improving system performance under various operational scenarios [43]. These studies consistently validate JSOA’s ability to tackle energy management challenges, outperforming other metaheuristic methods in cost minimization, constraint handling, and system optimization. Its integration with advanced machine learning techniques further enhances its capabilities, yielding promising results in energy management.

1.3. Research Gaps

Traditional planning approaches in distribution networks have typically focused on optimizing the location and capacity of DGs and BESSs separately. While this simplifies the planning process, it overlooks the benefits of integrating these resources within VPPs. Coordinating DGs and BESSs as part of VPPs offers a more integrated approach, but it introduces additional complexity in decision-making. However, fostering collaboration between distributed energy sources and flexible loads in VPPs can enhance operational efficiency and improve both economic and technical outcomes.

Enhancing network resilience has traditionally involved costly measures, such as strengthening physical infrastructure or adding redundant systems. A more cost-effective strategy is to integrate local energy resources, such as DGs, BESSs, and demand response initiatives, as resilience measures. Deploying VPPs throughout the distribution network can improve reliability and mitigate the impact of outages by leveraging decentralized energy assets.

This process often requires solving complex optimization problems, such as mixed-integer nonlinear programming (MINLP). Advances in metaheuristic algorithms have shown promise in addressing these problems, improving both solution speed and reliability. VPPs, which combine RESs and EVs with practical modes, are key to strengthening the resilience of distribution networks. The mobility and battery capabilities of EVs provide a flexible solution to enhance power system adaptability and stability.

However, many existing studies fail to adequately consider crucial factors, such as varying weather scenarios, dynamic load factors, emission levels, system reliability, and critical load requirements, all of which are vital for optimizing VPP deployment in RDSs. By adopting a more comprehensive planning strategy, integrating VPPs can significantly enhance power system resilience and effectively utilize distributed energy resources [18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43].

1.4. Research Contribution

This paper makes several significant contributions to the field:

• The proposed research enhances resilience in VPP systems during cascade failure events, a critical aspect not adequately addressed by previous research.
• A novel Multi-Objective Framework (MOF) is introduced, incorporating reliability, stability, and emission indices along with the resilience index.
• The introduction of the JSOA enables optimal sizing and placement of VPP components, providing comprehensive solutions to resilience challenges in distribution systems.
• Various weather conditions (clear, cloudy, rainy) are considered, integrating technical, economic, and environmental parameters to improve the approach’s applicability with dynamic analysis.
• The integration of RESs, storage devices, and EVs in different modes enhances traditional VPP systems, boosting their potential for distribution system allocation.
• An innovative resilience measurement approach combined with a recovery timing strategy enables the development of post-disaster recovery plans to strengthen VPP resilience.
• New resilience indices are proposed to facilitate system resilience measurement across diverse scenarios, including varying weather conditions and damage severities.
• A comprehensive analysis of resilience metrics, integrating both technical and economic factors, highlights the benefits of managing VPPs within prosumer-centric networked MGs.
• The proposed method is rigorously tested on both standard and practical Indian bus systems, with a focus on critical loads, offering valuable insights into its real-world effectiveness and applicability.

1.5. Structure of This Paper

The organization of this paper is structured to ensure a logical flow of methodology and findings. Section 2 presents the system modeling, including the RDS, the VPP resources, and the objectives addressed in this study. In Section 3, the implementation of the JSOA within the proposed solution framework is outlined. The results of the case study, along with analysis and discussion of the findings, are provided in Section 4. Section 5 summarizes the key findings, discusses their implications, and highlights the limitations of this study. Finally, Section 6 offers recommendations for future research, exploring potential avenues for further investigation and development.

2. System Modeling

2.1. Modeling the Distribution Networks

The backward/forward sweep (BFS) approach is widely used in power flow analysis for RDSs due to its efficiency. This method is appreciated for its simplicity, speed, and low memory requirements, which make it highly suitable for processing. Additionally, BFS offers computational advantages and demonstrates robust convergence when solving power flow problems in RDSs [44].

Figure 1 illustrates a radial network model with VPPs integrated into the distribution system. In this model, each MG is optimized individually [45]. The impedance of the lines is represented as $r_i+j{x}_i$, where $r_i$ and $x_i$ are the resistance and reactance of the lines, respectively. The power flow equations for the ith bus of the RDS with VPP resources are linearized as follows:

$$P_{i+1}=P_i-r_i\ast \left({\displaystyle \frac{{\left(P_i\right)}^2+{\left(Q_i\right)}^2}{{\left(V_i\right)}^2}}\right)-P_{i+1}^{load}+P_{i+1}^{VPP}$$

(1)

$$Q_{i+1}=Q_i-x_i\ast \left({\displaystyle \frac{{\left(P_i\right)}^2+{\left(Q_i\right)}^2}{{\left(V_i\right)}^2}}\right)-Q_{i+1}^{load}+Q_{i+1}^{SC}$$

(2)

$${\left(U_{i+1}\right)}^2={\left(U_i\right)}^2-2\left(P_i{r}_i+Q_i{x}_i\right)+\left[{\left(r_i\right)}^2+{\left(x_i\right)}^2\right]\left({\displaystyle \frac{{\left(P_i\right)}^2+{\left(Q_i\right)}^2}{{\left(U_i\right)}^2}}\right)$$

(3)

$$\left(1-\delta \right)\le U_i\le \left(1+\delta \right)$$

(4)

In Equations (1)–(4), $P_{i+1}$ and $Q_{i+1}$ represent the active and reactive power flows from bus i. $U_i$ denotes the voltage magnitude at this bus, while $P_{i+1}^{load}$ and $Q_{i+1}^{load}$ indicate the active and reactive power loads at the same bus. $P_{i+1}^{VPP}$ refers to the real power contribution from the VPP, and $Q_{i+1}^{SC}$ represents the reactive power injected by shunt capacitors. The symbol $\delta$ signifies the maximum allowable voltage fluctuation.

2.2. Modeling of Various VPP Devices

Integrating various types of DERs within VPPs is crucial for enhancing grid flexibility and ensuring a reliable power supply. These DERs include non-renewable generators like diesel-based DGs, RESs such as solar and wind, BESSs, shunt capacitors, and EVs. Proper modeling of VPP components enables optimization of their operation, dynamic adaptation to changing grid conditions, and the development of control strategies that maximize energy efficiency and maintain grid stability. VPPs thus play a pivotal role in fostering a sustainable and resilient energy infrastructure. The power balance within a VPP can be expressed by an equation that considers the power generated by various DERs and the power consumed or stored, as shown in Equation (5).

$$P^{VPP}=P^{SDG}+P^{WDG}+{P^{DDG}+P}^{BESS}+P_{V2G}^{EV}+Q^{SC}-P^{Loss}$$

(5)

In the equation above, $P^{VPP}$ represents the total power balance of the VPP, measured in kW. This balance is influenced by multiple sources within the VPP. $P^{SDG}$ denotes the power generated by solar energy sources, while $P^{WDG}$ represents the power generated by wind energy sources, both measured in kW. Additionally, $P^{BESS}$ indicates the power stored or discharged by the BESS, and $P^{DDG}$ represents the power generated by diesel generators. $P_{V2G}^{EV}$ stands for the power injected by EVs in V2G mode, measured in kW. $Q^{SC}$ reflects the reactive power injected or absorbed by SCs, measured in kVAr. Finally, $P^{Loss}$ represents the total power loss in the system. The models for the various VPP devices are described below.

2.2.1. Modeling of Solar-Based DG

The output power of solar-based DG can be described using solar energy, which correlates solar irradiance S(t), temperature T(t), and panel specifications to power output [46]. The PV model equation, considering the impact of converter efficiency (${\eta }_{conv}$), is commonly expressed as

$$P^{SDG}\left(t\right)=a^{panel}\ast n^{panel}\ast p\left(t\right)\ast f\left[T\left(t\right)\right]\ast {\eta }_{conv}$$

(6)

Here, $a^{panel}$ represents the panel area, $n^{panel}$ denotes the efficiency of the solar panel, and $f\left[T\left(t\right)\right]$ stands for the temperature correction factor. The temperature correction factor is employed to compensate for the decrease in panel efficiency with increasing temperature, and it can be calculated using coefficients specified by the manufacturer.

2.2.2. Modeling of Wind-Energy-Based DG

The output power of the wind-based DG can be represented using the power curve model, which links wind speed $\left(N^{wind}\right)$ and turbine specifications to power output [46]. The power curve model equation is commonly expressed as

$$P^{WDG}\left(t\right)={\displaystyle \frac{1}{2}}\left[\epsilon \ast a^{rotor}\ast C_p\left(N^{wind}\left(t\right)\right)\ast {N^{wind}\left(t\right)}^3\right]\ast {\eta }_{conv}$$

(7)

In this equation, $\epsilon$ represents the air density, $a^{rotor}$ stands for the rotor-swept area, and $C_p$ signifies the power coefficient at wind speed $N^{wind}$.

2.2.3. Modeling of BESS

The energy stored in the battery ($P^{BESS}$) can be described using the state-of-charge (SoC) model. The SoC model equation is given as [46]

$$P^{BESS}\left(\mathrm{t}+1\right)=P^{BESS}\left(\mathrm{t}\right)+\left(P^{charge}\left(\mathrm{t}\right)\ast \nabla t\ast n^{charge}\ast {\eta }_{conv}\right)-\left({\displaystyle \frac{P^{discharge}\left(\mathrm{t}\right)\ast \nabla t}{n^{charge}}}\right)$$

(8)

Here, $P^{charge}\left(t\right)$ and $P^{discharge}\left(t\right)$ represent the charging and discharging powers of the battery at time t, respectively, with $\nabla t$ denoting the time step.

2.2.4. Modeling of Diesel-Based DG

The output power of the diesel-based DG can be depicted using the fuel consumption rate $e^{fuel}$ and generator efficiency $\left(n^{generator}\right)$. The output power is determined by the following equation [47]:

$$P^{DDG}\left(\mathrm{t}\right)={\displaystyle \frac{e^{fuel}\left(t\right)}{n^{generator}}}$$

(9)

2.2.5. Modeling of Shunt Capacitor

The placement of shunt capacitors within the MG is intended to offer reactive power support, voltage enhancement, and stability improvement, thereby ensuring the reliable and efficient operation of the microgrid under different operating conditions and load scenarios [48]. After injecting shunt capacitors at bus i within the MG, the net reactive power $Q_{NI}$ can be defined as

$$Q_{NI\left(i\right)}=Q_{i+1}-Q_{SC}$$

(10)

where $Q_{i+1}$ represents the reactive power at the bus adjacent to bus i within the MG (in kVAr). $Q_{SC}$ indicates the reactive power injected by the shunt capacitor within the MG (in kVAr). Increasing the number of shunt capacitor units within VPPs has the potential to enhance support for reactive power and stability within the MG, albeit within a defined threshold.

2.2.6. Modeling of Electric Vehicle

The charging process of EVs is governed by the battery’s SOC, which represents the ratio of the current charge level to the battery’s maximum capacity. SOC indicates how much charge the battery holds at any given time. This parameter provides crucial information on the required charging level, ensuring optimal performance and efficiency during the charging process. The power consumption of an EV is related to the battery’s capacity, SOC, and charging duration [49]. Furthermore, in V2G operation, the EV discharges power back into the grid.

$$P_{V2G}^{EV}={\displaystyle \frac{C_{EV}^{battery}\ast ({SOC}_{EV}^{max}-{SOC}_{EV}^{min})}{T^{discharge}}}\ast {\eta }_{conv}$$

(11)

In Equation (11), $P_{V2G}^{EV}$ represents the power injected by the EV into the grid during V2G operation, measured in kW. $C_{EV}^{battery}$ denotes the capacity of the EV battery, measured in kWh. ${SOC}_{EV}^{max}$ and ${SOC}_{EV}^{min}$ refer to the upper and lower SOC limits of the battery, respectively. $T^{discharge}$ indicates the time required for discharging the battery during V2G operation, measured in hrs.

Figure 2 illustrates the hourly contributions of various energy sources—RDS, PV, WT, and EV operating in G2V, V2G, and idle modes [50]. The RDS maintains a consistent load factor throughout the day, indicating stable performance. PV generation peaks during daylight hours, while WT output fluctuates due to changing wind conditions. The EV contributions vary based on their operating modes, showing distinct patterns of energy consumption and supply. This analysis underscores the need for JSOA testing across different scenarios, including diverse weather conditions and load profiles, to ensure its adaptability and robustness in various grid environments.

2.3. Formulation of the Objective Function

The objective function formulation for VPP planning focuses on enhancing resilience, reliability, and minimizing CO₂ emissions during natural events. Recognizing the significance of these factors in ensuring a robust and sustainable power system, the optimization model aims to maximize resilience and reliability while minimizing CO₂ emissions during such events. This multi-objective approach addresses the critical need for improved resilience and reliability, alongside environmental concerns, in the face of natural disasters. The model is designed to balance these aspects, contributing to the overall resilience and sustainability of the power infrastructure.

2.3.1. Formulation of Resilience Index

In the formulation of resilience indices, two main categories are considered:

(i)

Metrics for electrical utility resilience;

(ii)

Metrics for cost analysis resilience.

Each metric is calculated as follows.

(i) Metrics for Electrical Utility Resilience

(a) Total residence-hours during outage

$${\phi }_1=\sum _{i=1}^{nb}\left(R_i\ast t\right)$$

(12)

where ($R_i\ast t$) represents the total number of residence-hours during an outage, and nb stands for the number of buses in the RDS.

(b) Energy not delivered to residences

$${\phi }_2=\sum _{i=1}^{nb}\left({END}_i\ast t\right)$$

(13)

where (${END}_i\ast t$) denotes the amount of residence energy not delivered (END) during an outage.

(c) Total number of affected residences during an outage

$${\phi }_3=\sum _{c=1}^{c_T}\sum _{i=1}^{nb}{R}_{i,c}$$

(14)

where ${\phi }_3$ represents the total number of residences affected during outage case ‘c’, and ‘$c_T$’ is the total number of cases.

(d) Average number of affected residences during the outage

$${\phi }_4={\displaystyle \frac{\sum _{c=1}^{c_T}\sum _{i=1}^{nb}{R}_{i,c}}{c_T}}$$

(15)

where ${\phi }_4$ denotes the average number of residences affected during outage case ‘c’.

(ii) Metrics for Cost Analysis Resilience

(a) Total revenue loss from utilities during the outage

$${\partial }_1=C^{energy}\ast \left(\sum _{i=1}^{nb}\left({END}_i\ast t\right)\right)$$

(16)

Here, ${\partial }_1$ denotes the total revenue loss from utilities in dollars (USD), and $C^{energy}$ represents the cost of energy in ‘USD/kWh’.

(b) Total outage costs

$${\partial }_2=C^{out}\ast \left(\sum _{c=1}^{c_T}\sum _{i=1}^{nb}{R}_{i,c}\right)$$

(17)

where ${\partial }_2$ indicates the total outage cost in ‘USD’, and $C^{out}$ stands for the outage cost per hour in ‘USD/hr’.

(c) Total avoided outage cost

$${\partial }_3=C_{base}^{out}-{\partial }_2$$

(18)

Here, ${\partial }_3$ signifies the avoided cost in ‘USD’, and $C_{base}^{out}$ represents the total outage cost in ‘USD’ of the base case.

(d) Resilience index

The determination of resilience indices (RIs) for a system post-catastrophic event involves computing the reciprocal of the system’s loss performance.

$${Resilience}^{index}={\displaystyle \frac{1}{{∆P}_L}}$$

(19)

In this equation, ${∆P}_L$ denotes the amount of generated real power not available to the test system. Consequently, ${∆P}_L$ can be estimated as

$${∆P}_L={\displaystyle \frac{P_L^{total}-P_L^{active}}{P_L^{active}}}$$

(20)

Here, $P_L^{total}$ and $P_L^{active}$ represent the total load and active load in the system after the event occurs, respectively.

Resilience can be quantified along a theoretical continuum, ranging from zero to infinity. Perfect resilience is represented by infinity, indicating no performance degradation after an extreme event, while a lack of resilience is represented by zero, signifying an inability to withstand or an abrupt breakdown following the severe event. The first objective function (OF₁) in the proposed strategy, based on the resilience index, is expressed as follows:

$${OF}_1=Maximize \left({Resilience}^{index}\right)$$

(21)

2.3.2. Development of Reliability Index

In power system research, reliability indices are essential for evaluating a critical operational parameter: reliability. These indices provide quantitative measures to assess the performance and dependability of an RDS, offering key insights into the system’s ability to consistently deliver electricity and meet customer demands. Two commonly used reliability indices in RDSs are the System Average Interruption Duration Index (SAIDI) and the System Average Interruption Frequency Index (SAIFI) [9]. These indices offer utility companies and regulators valuable data for evaluating the effectiveness of the RDS, pinpointing areas for improvement, and comparing the reliability of different systems. By monitoring and enhancing these indices, utilities can improve customer satisfaction and optimize RDS performance. The key reliability indices, SAIDI and SAIFI, are represented by Equations (22) and (23).

$$SAIFI={\displaystyle \frac{\sum _i^{n^{load}}\left[f^{rate}\left(i\right){\ast n}^{customers}\left(i\right)\right]}{\sum _i^{n^{load}}\left[n_{total}^{customers}\left(i\right)\right]}}$$

(22)

$$SAIDI={\displaystyle \frac{\sum _i^{n^{load}}\left[{Out}^{period}\left(i\right){\ast n}^{customers}\left(i\right)\right]}{\sum _i^{n^{load}}\left[n_{total}^{customers}\left(i\right)\right]}}$$

(23)

Here, $f^{rate}\left(i\right)$ represents the failure rate of bus i, ${Out}^{period}\left(i\right)$ denotes the outage period of bus i, and $n^{customers}\left(i\right)$ stands for the number of customers associated with bus i. $n^{load}$ signifies the total number of load points. $n_{total}^{customers}\left(i\right)$ stands for the total number of customers in the RDS.

The various reliability indices for the objective function are given in Equation (24):

$${Reliability}^{index}={\alpha }_1\left({\displaystyle \frac{{SAIFI}_{VPP}^{after}}{{SAIFI}_{VPP}^{before}}}\right)+{\alpha }_2\left({\displaystyle \frac{{SAIDI}_{VPP}^{after}}{{SAIDI}_{VPP}^{before}}}\right)$$

(24)

In the above equation, ${SAIFI}_{VPP}^{before}$ and ${SAIFI}_{VPP}^{after}$ represent the SAIFI values before and after the optimal implementation of VPPs, respectively. Similarly, SAIDI follows the same convention. In Equation (24), the weights assigned to SAIFI and SAIDI are denoted as ${\alpha }_1$ and ${\alpha }_2$, respectively. The weightage factors assigned to ${\alpha }_1$ and ${\alpha }_2$ for the simulation are 0.5 and 0.5, respectively.

The second objective function (OF₂) of the proposed approach based on the reliability index can be expressed as follows:

$${OF}_2=Maximize\left[ {Reliability}^{index}\right]$$

(25)

2.3.3. Formulation of Emission Index

The objective function for reducing CO₂ emissions in an RDS with VPP resources during failures involves several key steps. First, it calculates the CO₂ emissions generated by grid electricity usage. Next, it evaluates the emission reductions achieved by integrating VPP resources during failure scenarios. Finally, the function aims to optimize system components by reducing the overall carbon footprint, thus promoting environmental sustainability and mitigating the impact of climate change. This is accomplished by leveraging RESs such as solar- and wind-based DGs, as well as BESSs, while optimizing EV processes to further minimize emissions. Among the VPP resources, diesel DGs are given the lowest priority due to their higher CO₂ emissions compared to other resources, especially during grid faults. This preference is driven by environmental considerations, as diesel DGs emit more CO₂ per unit of energy generated than renewable sources like solar DGs, wind DGs, and BESSs. By reducing reliance on diesel DGs and prioritizing cleaner energy sources, such as renewables and energy storage, the system can lower overall carbon emissions and support environmental sustainability.

$$Emission={Emission}^{factor}\ast \left[{\sum }_i^{nb}{\sum }_t^{24}{(P}^{grid}\left(i,t\right){{+P}^{DDG}\left(i,t\right))-(P}^{SDG}\left(i,t\right)+P^{WDG}\left(i,t\right)+P^{BESS}\left(i,t\right)+P_{V2G}^{EV}\left(i,t\right))\right]$$

(26)

In this scenario, various real power sources contribute to the RDS’s operation. These sources include power from the grid ($P^{grid}$), diesel DG ($P^{DDG}$), solar DG ($P^{SDG}$), wind DG ($P^{WDG})$, BESS ($P^{BESS}$), and EV operating in V2G mode ($P_{V2G}^{EV}$). The associated emissions per unit of real power production from the grid, denoted as ${Emission}^{factor}$, are crucial for evaluating the carbon footprint of the system. For this model, ${Emission}^{factor}$ is considered as 0.91 TonCO₂/kWh [51]. By assessing the real power contributions from these sources and applying the appropriate emission factors, the overall carbon emissions associated with the system’s operation can be accurately estimated, facilitating informed decision-making for emission reduction strategies and sustainable energy management.

$${Emission}^{index}=\left({\displaystyle \frac{{Emission}_{VPP}^{after}}{{Emission}_{VPP}^{before}}}\right)$$

(27)

The objective function (OF₃) aims to reduce overall CO₂ emissions by lowering grid emissions and optimizing the impact of VPPs, particularly those that use renewable-based DGs to reduce emissions. Equation (28) calculates the ${Emission}^{index}$, which compares CO₂ emissions before and after VPP allocation in the RDS. Reductions in the value of OF₃ lead to a decrease in CO₂ emissions for the system, indicating the success of emission reduction efforts.

$${OF}_3=Minimize\left[{Emission}^{index}\right]$$

(28)

2.3.4. Formulation of Stability Index

The presence of sensitive and nonlinear loads within the RDS requires immediate and robust reactive power support to maintain secure and stable network operation. Insufficient reactive power can lead to operational instabilities, potentially causing system outages. Ignoring voltage stability during optimization may worsen the system’s susceptibility to voltage-related issues. The implementation of SCs significantly improves the security of the RDS. To assess the network’s stability, the voltage stability index (VSI) [52] is calculated using Equation (29). This index is an important measure of system stability, with lower VSI values indicating higher vulnerability to voltage collapse, especially at buses with low VSI. Monitoring the VSI helps assess the power supply’s stability, and when the VSI is low, corrective actions can be taken to prevent instability.

$${Stability}^{index}=VSI\left(i+1\right)={\left|U_{i+1}\right|}^4-4\hspace{0.17em}{\left[P_{i,i+1}\ast x_{i,i+1}-Q_{i,i+1}\ast r_{i,i+1}\right]}^2-4\hspace{0.17em}\left[P_{i,i+1}\ast r_{i,i+1}+Q_{i,i+1}\ast x_{i,i+1}\right]\hspace{0.17em}{\left|U_{i+1}\right|}^2$$

(29)

As the VSI approaches unity, system stability improves, whereas a value approaching zero signals a vulnerable operational state. The critical bus, which has the lowest VSI in the RDS, plays a key role in stability assessment. To evaluate the impact of device allocation on stability margins, we formulate an objective function (OF₄) aimed at maximizing system voltage stability, as shown in Equation (30).

$${OF}_4=Maximize\left[ {Stability}^{index}\right]$$

(30)

The values of the OF₄ in Equation (30) may vary, either falling below, equaling, or surpassing unity. Allocating devices is considered beneficial when the OF₄ value is below unity. This condition indicates that the VSI of the critical bus approaches unity more closely with the presence of devices compared to when devices are absent in the RDS.

2.4. Multi-Objective Function

Previous studies have primarily focused on single objective functions and rarely addressed the VPP allocation problem in RDSs. Often, these objectives conflict, making simultaneous optimization challenging. The MOF includes multiple functions to be optimized simultaneously under operational constraints. The allocation of individual and combined devices can significantly improve the RDS’s performance by enhancing resilience and reliability and reducing CO₂ emissions. In a deregulated framework, device owners must also gain economic benefits, which incentivize investment in advanced devices. Therefore, careful consideration of device allocation is essential to ensure both technical and economic advantages. Thus, both technical and economic factors are integrated into the MOF, as presented in Equation (31).

$$MOF=Maximize\left[\left({\omega }_1\ast {OF}_1\right)+\left({\omega }_2\ast {OF}_2\right)+\left({\omega }_3\ast {({\displaystyle \frac{1}{OF}}}_3)\right)+\left({\omega }_4\ast {OF}_4\right)\right]$$

(31)

The constants ${\mathsf{\omega }}_1,{\mathsf{\omega }}_2,{\mathsf{\omega }}_3$, and ${\mathsf{\omega }}_4$ are adjustable to prioritize the impact of individual factors within the overall MOF. For the studied method, the weightage factors allocated to each individual objective function (OF₁ to OF₄) are 0.3, 0.3, 0.2, and 0.2, respectively.

2.5. Equality and Inequality Constraints

In the proposed work, both equality and inequality constraints are integrated to guide the optimization process and meet specific criteria. Particular attention is given to the limitations on the minimum and maximum real and reactive power outputs of various resources within the VPP. This includes solar-, wind-, and diesel-based DGs, as well as SCs, BESSs, and EVs operating in V2G mode. Constraints (32) to (37) are applied for each time period t within the MG to ensure the system’s proper functioning and operational efficiency.

$$P_{min}^{SDG}\left(t\right)\le P^{SDG}\left(t\right)\le P_{max}^{SDG}\left(t\right)$$

(32)

$$P_{min}^{WDG}\left(t\right)\le P^{WDG}\left(t\right)\le P_{max}^{WDG}\left(t\right)$$

(33)

$$P_{min}^{DDG}\left(t\right)\le P^{DDG}\left(t\right)\le P_{max}^{DDG}\left(t\right)$$

(34)

$$M{Q}_{min}^{SC}\left(t\right)\le P^{SC}\left(t\right)\le Q_{max}^{SC}\left(t\right)$$

(35)

$$P_{min}^{BESS}\left(t\right)\le P^{BESS}\left(t\right)\le P_{max}^{BESS}\left(t\right)$$

(36)

$$P_{min}^{EV\left(V2G\right)}\left(t\right)\le P^{EV\left(V2G\right)}\left(t\right)\le P_{max}^{EV\left(V2G\right)}\left(t\right)$$

(37)

2.6. Remaining Useful Life

The remaining useful life (RUL) of equipment is an essential metric for evaluating the long-term impact of operational strategies in power distribution systems. While optimization algorithms aim to enhance resilience, reliability, and emission reduction, they can also impose varying degrees of stress on the system components, ultimately affecting their lifespan. This section introduces the methodology for estimating RUL and demonstrates its application for three algorithms: JSOA, BESA, and SMA.

RUL estimation integrates two primary factors:

(i)

Utilization Factor (UF): Indicates the extent of equipment usage during system operations.

(ii)

Stress Factor (SF): Reflects the environmental and operational stresses, such as emissions, affecting equipment wear and tear.

The RUL is calculated using the following equation:

$$MRUL={\displaystyle \frac{T_{rated}}{1+k·(UF+SF)}}$$

(38)

where $T_{rated}$ is the rated lifetime of the equipment (assumed as 20,000 h in this study), k is the scaling factor (assumed as 0.5 for normalization), UF is the utilization factor derived from resilience metrics, and SF is the stress factor based on emissions.

In this study, it is assumed that the rated lifetime ($T_{rated}$) of all equipment is fixed at 20,000 h, providing a uniform baseline for comparison. The scaling factor (k) is kept constant across all cases to ensure fair evaluation of the algorithms. Additionally, the UF and SF values are normalized between 0 and 1 for consistency and comparability. It is further assumed that the operational impacts of each algorithm are directly proportional to the UF and SF values, reflecting their influence on equipment wear and tear over time.

3. Jellyfish Search Optimization Algorithm

The JSOA is a novel metaheuristic approach introduced by J. S. Chou and D.N. Truong in 2020 [53]. Inspired by the movement patterns of jellyfish in the ocean, JSOA integrates two key movement strategies: ocean current and swarm current. These methods are used to update solutions, enhancing performance compared to existing algorithms. The JSOA framework consists of three main steps that contribute to its effectiveness in optimization tasks.

3.1. Initialization of the Population

In the initialization phase, decision variables are defined to represent the parameters of the optimal solution. These variables form the basis for generating the initial population, ensuring a diverse set of potential solutions. These variables are constrained within a predefined upper bound ($b^{upper}$) and lower bound ($b^{lower}$) to ensure realistic and meaningful solutions. Each solution in the population is generated within these bounds.

$$x_i=b^{lower}+{\omega }_i\ast \left(b^{upper}-b^{lower}\right) with i=\mathrm{1,2},\dots {\dots ,n}_{pop}$$

(39)

3.2. Update Mechanisms for New Solutions

JSOA employs two update mechanisms: exploration and exploitation. At each iteration, one of these mechanisms is selected based on a balance factor ($B_{factor}=0.5)$ and a selection factor ($S_{Factor}$) that is computed as

$$S_{factor}=(2\ast rand-1)\left({\displaystyle \frac{{iter}^{max}-{iter}^{prst}}{{iter}^{max}}}\right)$$

(40)

• If $S_{Factor}\ge 0.5$, the ocean-current-based exploration phase is used.
• If $S_{Factor}<0.5$, the swarm-current-based exploitation phase is used.

3.2.1. Exploration Phase

The exploration phase updates solutions by focusing on the best and mean positions of the swarm:

$$x_i^{new}=x_i+rand\ast (x^{best}-3rand\ast x^{mean})$$

(41)

where $x_i^{new}$ represents the new location of the ith jellyfish, $x^{best}$ denotes the best present position in the entire swarm, and $x^{mean}$ signifies the mean position in the entire swarm, which is calculated as

$$x^{mean}={\displaystyle \frac{\sum _{i=1}^{n_{pop}}{x}_i}{n_{pop}}}$$

(42)

3.2.2. Exploitation Phase

The exploitation phase refines solutions by focusing on the distance between neighboring positions:

$$x_i^{new}=\left[\begin{array}{c}{x}_i+d^{int}, if rand\le (1-n_f)\\ x_i+0.1\ast {\omega }_i\ast \left(b^{upper}-b^{lower}\right), otherwise \end{array}\right.$$

(43)

In Equation (42), $d^{int}$ represents the increased interval between the present location of the ith and (i + 1)th jellyfish. This step can be calculated using the following formula:

$$d^{int}=\left|x_{i+1}-x_i\right|$$

(44)

where $x_{i+1}$ represents the present location of the (i + 1)th jellyfish in the swarm.

3.3. Selection Technique

After updating the positions, the fitness function evaluates each solution. Poor solutions are discarded, and high-quality solutions are selected for the next iteration:

$$x_i=\left[\begin{array}{c}{x}_i^{new} if z{x}_i^{new}<z{x}_i\\ x_i otherwise \end{array}\right.$$

(45)

$$z{x}_i=\left[\begin{array}{c}z{x}_i^{new} if z{x}_i^{new}<z{x}_i\\ z{x}_i otherwise \end{array}\right.$$

(46)

The best solution is retained if the maximum iteration is reached. If not, the iteration process continues until convergence. Figure 3 demonstrates the utilization of JSOA in a standard optimization scenario.

4. Case Study and Discussion

This section evaluates the effectiveness of the proposed microgrid formation approach using adaptations of the standard IEEE 34-bus and Indian practical 52-bus systems. The method employs a high-performance computational setup for accurate results, featuring an Intel Core i9-11900K processor (8 cores, 16 threads, up to 5.3 GHz), 64 GB DDR4 RAM, and a 1 TB SSD for fast data access. An NVIDIA RTX 3080 GPU accelerates parallel computations when needed. MATLAB R2023a, along with the parallel computing and optimization toolboxes, enables efficient task parallelization, reducing execution time for large-scale simulations.

Resilience, reliability, and emission indices are assessed over 24 h, including a simulated 5 h outage following a natural disaster. END costs are estimated using a fixed energy rate, while outage costs are based on a predetermined value per hour, assuming a 5 h repair time for lines. A simulated storm event causes severe damage, leading to a 5 h outage from 11 a.m. to 4 p.m. The sizing of VPP resources for microgrid installation is determined through JSOA. Systems are classified as severely damaged if over 80% of loads are un-serviced or as moderate disasters otherwise.

This study investigates resilience measures across two test systems under different weather conditions, including clear, cloudy, and rainy. Residential customers with rooftop solar DGs, wind turbines, EVs, diesel generators, shunt capacitors, and BESSs are included in the case studies. These resources are interconnected and controlled by VPPs within the microgrids to minimize emissions while enhancing RDS resilience and reliability during natural disasters. The primary goal of the VPP allocation process is to minimize emissions while boosting resilience and reliability in the RDS. Emphasis is placed on forming and reinforcing microgrids to enhance resilience, consistent with findings from existing literature. The optimization of the MOF focuses on minimizing END and optimizing load recovery during emergencies by optimally allocating VPP resources within the microgrids. The sizing of BESSs and diesel DGs is determined based on the projected surplus energy generated by each microgrid. For the case studies, the following assumptions are made:

• The expected time for line repairs is 5 h, from 11 a.m. to 4 p.m.
• All damaged lines are assumed to be repaired simultaneously, with sufficient repair crews available.
• Fault locations and MG formations remain consistent across all cases for comparative analysis.
• All DERs within VPPs remain operational post-event.
• Consumers/prosumers have a home energy management system connected and controlled by the VPP.
• Each prosumer is equipped with rooftop solar panels, wind turbines, BESSs, and EVs in the MGs.
• EVs operate in three distinct modes: G2V from 6 p.m. to 6 AM, V2G from 11 a.m. to 4 p.m., and idle from 7 a.m. to 10 a.m. and 5 p.m.
• During a power outage, priority is given to serving critical loads, presumed to be situated within the MGs.
• Shunt capacitors are installed to ensure power quality during faults.
• Diesel DGs within the VPP are given the least priority to reduce CO₂ emissions.
• The output power of SDG and WDG under various weather conditions is assumed as detailed in

  Table 1. Output power values of solar and wind DGs across different weather conditions [6].

  Types of Weather	Solar DG (%)	Wind DG (%)
  Clear day	100%	30%
  Cloudy day	50%	100%
  Rainy day	30%	50%

  .
• A dynamic load pattern is applied to all VPP resources and RDS loads across both test systems.

To demonstrate the effectiveness of the proposed method utilizing the JSOA, tests are conducted on both the standard IEEE 33-bus and practical Indian 52-bus RDS. These case studies are designed to evaluate the influence of VPPs on enhancing system resilience across different weather conditions, particularly under severe fault scenarios. Four different cases and weather conditions are examined across the standard IEEE 34-bus and Indian 52-bus RDS:

• Faulted system without VPP.
• Faulted system with VPP (clear day).
• Faulted system with VPP (cloudy day).
• Faulted system with VPP (rainy day).

4.1. IEEE 34-Bus RDS (Test System I)

The IEEE 34-bus system is a medium-voltage RDS with 34 nodes and 33 lines, operating at 11 kV. It has a total power consumption of 4636.50 + j2873.50 kVA, leading to active and reactive power losses of 221.75 kW and 65.12 kVAr, respectively. Data for this test feeder were adapted from [54]. A base-case load flow analysis using the BFS technique evaluates baseline performance. A dynamic 24 h load profile replicates realistic demand fluctuations driven by consumer behavior and environmental factors. This study applies JSOA in MATLAB for energy management and VPP resource allocation during fault conditions, assessing the impact of VPPs within MGs on RDS resilience, reliability, and emissions reduction during natural disasters. In a simulated storm, severe damage affects branches 1–34 and critical loads from 11 a.m. to 4 p.m. JSOA determines the optimal VPP size for MG installation to improve load recovery during emergencies, with BESS sizing based on projected surplus energy. This study covers 3085 residences across the RDS. Figure 4 highlights eight critical load-connected buses. Subsequent sections describe the cases studied for the 34-bus system.

Table 1 presents output power values of solar- and wind-based DGs under varying weather conditions for both case studies [6]. To assess JSOA effectiveness, its performance is tested across different scenarios, including varying weather conditions and load profiles for RDGs, EVs, and the RDS. This ensures robustness and adaptability to changing conditions. Based on the load factor shown in Figure 2,

Table 2. IEEE 34-bus simulation data.

MG	Prosumer/Consumer	Bus No.	Residences	Load (kW)	VPP Capacity
					Solar DG (kW)	Wind DG (kW)	Diesel DG (kW)	SC (kVAr)	EV (kW)	BESS (kW)
MG-1	C	13	48	66	-	-	-	-	-	-
	C	14	48	66	-	-	-	-	-	-
	P	15	48	66	60	30	133	166	44.76	166
	P	16	9	12	12	6	25	31	8.7	31
MG-2	C	17	153	212	-	-	-	-	-	-
	P	18	153	212	191	96	424	530	142.9	530
	C	19	153	212	-	-	-	-	-	-
	P	20	153	212	191	96	424	530	142.9	530
	C	21	153	212	-	-	-	-	-	-
	P	22	153	212	191	96	424	530	142.9	530
	C	23	153	212	-	-	-	-	-	-
	C	24	153	212	-	-	-	-	-	-
	P	25	153	212	191	96	424	530	142.9	530
	C	26	153	212	-	-	-	-	-	-
	P	27	91	126	114	57	253	316.14	85.17	316.14
MG-3	C	31	38	52.54	-	-	-	-	-	-
	P	32	38	52.54	47	24	105	131.8	35.44	131.8
	C	33	38	52.54	-	-	-	-	-	-
	P	34	38	52.54	47	24	105	131.8	35.44	131.8

summarizes key data from the case study, including residential areas, bus numbers, VPP capacities, and load values. The VPP incorporates various DGs, BESSs, EVs, and SC units, with corresponding load values provided in the table.

(i)

Faulted system without VPP

In the base-case scenario, the RDS operates without VPP connections. A storm causes major damage at bus 1 around 11 a.m., resulting in a 5 h outage that affects all 34 buses, including critical loads.

Table 3. Performance comparison of various indices across different cases in the IEEE 34-bus system.

Index	Metrics	Case I	Case II	Case III	Case IV
Resilience	Total residence-hours during outage (h)	14,250	4633	5101	6767
	END to residences (kWh)	21,367	6946	7647	10,146
	Total number and percentage of affected residences during the outage	2850 (100%)	926.67 (32.51%)	1020 (35.79%)	1353 (47.49%)
	Average number and percentage of affected residences during the outage	712.5 (25%)	231.67 (8.12%)	255.03 (8.94%)	338.37 (11.87%)
	Total revenue loss from utilities during the outage (USD/kWh)	12,991.32	15,299	15,187	14,787
	Total outage costs (USD/h)	72,675	23,630	26,013	34,515
	Total avoided outage cost (USD)	0	49,045	46,662	38,160
	Resilience	0	2.076	1.794	1.105
Reliability	SAIFI (failure/residence)	0.0400	0.0130	0.0143	0.0190
	SAIDI (h/residence)	5	1.6257	1.7897	2.3746
Emission	Emission (TonCO2/kWh)	3888.85	1376.35	1516.45	1935.95
Stability	VSI (p.u)	0	0.7863	0.7798	0.7719

compares performance metrics for different cases in the IEEE 34-bus system. In Case I, without VPP support, the outage disrupts 2850 residences, leading to a total of 14,250 residence-hours lost. Financially, utilities incur a revenue loss of USD 12,991.32, and total outage costs amount to USD 72,675. The system’s resilience metric of zero indicates its failure to recover from disruptions, as reflected in reliability indices such as SAIFI (0.0400 failures per residence) and SAIDI (5 h per residence). The emission rate of 3888.85 TonCO₂/kWh highlights the environmental impact of relying solely on traditional energy sources during outages. Additionally, the system’s VSI of zero signals inadequate stability measures, risking voltage collapse and underscoring the need for proactive stability enhancements.

(ii)

Faulted system with VPP (clear day)

Figure 5 illustrates the faulted IEEE 34-bus system, highlighting the integration of VPP to improve grid resilience and performance. The VPP comprises various distributed energy resources, including PV, WT, diesel-based DGs, capacitors, EVs in different modes, and BESSs. These resources are managed and allocated using the JSOA. In the faulted scenario, MGs and tie lines (TLs) are established to deliver energy across the RDS under varying weather conditions. Three MGs are formed: MG-1 (buses 13–16), MG-2 (buses 17–27), and MG-3 (buses 31–34). TLs are deployed to supply energy to loads outside these MGs.

During clear weather simulations, operational strategies account for varying weather conditions impacting energy generation from solar, wind, diesel generators, EVs, and BESSs. VPPs, managed by SCs, prioritize stability and reactive power support. Solar DGs operate at full capacity, while wind DGs run at 30%. In the absence of these resources, diesel DGs, EVs (in V2G mode), and BESSs supply power to MGs. CLs within MGs are prioritized during faults, while CLs outside MGs are restored via TLs.

In Case II, the introduction of VPPs results in significant improvements over Case I. The outage duration decreases to 4633 h, and energy supply restoration becomes more efficient, reducing END to 6946 kWh. The number of affected residences dropped to 926.67 (32.51%), with an average of 231.67 residences (8.12%) impacted. Despite a revenue loss of USD 15,299, total outage costs fall to USD 23,630, reflecting improved cost management. The resilience metric rises to 2.076, indicating a better ability to withstand and recover from disruptions. Reliability indices such as SAIFI and SAIDI show improvement, underscoring increased reliability. The emission rate decreases to 1376.35 TonCO₂/kWh, highlighting environmental benefits. Additionally, the VSI improves to 0.7863, signaling enhanced system stability due to VPP integration. These results demonstrate the effectiveness of VPPs in boosting system resilience, reliability, and stability and delivering significant economic and environmental advantages.

(iii)

Faulted system with VPP (cloudy day)

In addressing resilience improvement under cloudy weather, solar generation operates at 50% capacity and wind generation at full capacity. In Case III, which represents a faulted system with VPPs on a cloudy day, notable improvements are observed compared to Case I. The total residence-hours during the outage decrease to 5101, and END drops to 7647 kWh, reflecting more efficient energy restoration. The number of affected residences decreased to 1020 (35.79%), with an average of 255.03 residences (8.94%) impacted.

Financially, utilities incur a revenue loss of USD 15,187, while total outage costs fall to USD 26,013, indicating better cost management. The system’s resilience metric rises to 1.794, demonstrating the enhanced ability to withstand and recover from disruptions. Reliability indices such as SAIFI and SAIDI also improve, highlighting better system reliability. The emission rate decreases to 1516.45 TonCO₂/kWh, showcasing environmental benefits, and the VSI improves to 0.7798, signaling increased system stability. These results emphasize the effectiveness of VPPs in boosting system resilience, reliability, and stability, even in challenging weather conditions, while delivering significant economic and environmental advantages.

(iv)

Faulted system with VPP (rainy day)

In Case IV, which examines a faulted system equipped with VPPs during rainy weather, improvements in system resilience are observed compared to Case I, despite the challenges posed by adverse weather. With solar generation at 50% capacity and wind generation at full capacity, total residence-hours during the outage increase to 6767, and END rises to 10,146 kWh, indicating a moderate impact on energy supply.

The number of affected residences increased to 1353 (47.49%), with an average of 338.37 residences (11.87%) impacted. Financially, utilities incur a revenue loss of USD 14,787, while total outage costs amount to USD 34,515. Despite these challenges, the system’s resilience metric is 1.105, showing a reasonable ability to recover from disruptions. Reliability indices such as SAIFI (0.0190 failures per residence) and SAIDI (2.3746 h per residence) show slight increases, reflecting the impact of adverse weather on reliability. The emission rate rises to 1935.95 TonCO₂/kWh, highlighting environmental sustainability challenges in rainy conditions. The VSI remains stable at 0.7719, indicating satisfactory system stability. Overall, despite the challenges of rainy weather, the integration of VPPs continues to enhance system resilience and reliability, emphasizing their role in mitigating the impact of adverse weather on power distribution systems.

The comparative analysis of the four cases highlights the critical role of VPPs in enhancing the resilience, reliability, stability, and environmental sustainability of power distribution systems during faults. In Case I, without VPPs, the system faces severe disruptions, with substantial residence-hours lost, high financial losses, elevated emissions, and poor stability. In contrast, the introduction of VPPs (Cases II–IV) consistently improves performance across various weather conditions. On a clear day (Case II), the system achieves the highest resilience metric, lowest emissions, and reduced outage impacts, demonstrating optimal resource utilization. Under cloudy and rainy conditions (Cases III–IV), VPPs continue to reduce END, outage costs, and affected residences, despite weather-related challenges. Environmental benefits are evident in all VPP-supported scenarios, with significant reductions in CO₂ emissions compared to the base case. While performance varies with weather, VPPs consistently enhance system resilience and reliability, making them essential for modern power systems facing increasing challenges from natural disasters and sustainability concerns.

Figure 6 presents the END profile of the IEEE 34-bus system under faulted conditions, comparing the system’s performance with and without VPPs. The analysis focuses on energy restoration during faulted hours, utilizing VPP resources integrated into three MGs: MG-I (buses 13–16), MG-II (buses 17–27), and MG-III (buses 31–34). In Case I (without VPPs), END values remain high across all buses, as the system relies solely on traditional energy sources without localized generation or resilience measures, preventing power restoration to critical buses during the outage.

In Cases II–IV (with VPPs), significant reductions in END are observed across buses within the MGs. In Case II (clear day), solar DGs and other VPP resources operate near peak capacity, resulting in minimal END values, especially in MG-II and MG-III. Buses in these MGs, such as buses 13–16 and 31–34, show substantial improvements, with END values approaching zero for several buses.

In Case III (cloudy day), solar generation operates at reduced capacity (50%), with wind and other resources partially compensating. This leads to moderate increases in END values compared to Case II, though buses 13–16 and 31–34 still benefit from VPP support, resulting in only slightly higher END values. Case IV (rainy day) presents the most challenging conditions, with limited solar generation and increased reliance on other VPP resources, including wind and diesel DGs. END values increase compared to Cases II and III but remain significantly lower than Case I, illustrating the continued effectiveness of VPPs in mitigating outages. Notably, buses within MG-II (buses 17–27) show higher END values in Case IV, reflecting the difficulties in balancing the energy supply under adverse weather conditions.

The observed trend underscores the critical role of VPPs in ensuring energy delivery during faulted hours, particularly in MG zones, and highlights their resilience under varying weather conditions. The integration of VPP resources significantly improves energy restoration, as shown by the reduced END in all cases with VPPs compared to the base case. These findings emphasize the importance of VPP integration in enhancing the resilience and reliability of modern distribution systems.

Figure 7 compares key metrics—resilience, SAIFI, SAIDI, VSI, and emissions—across four cases of the IEEE 34-bus system, highlighting system performance and reliability under various scenarios. Case I, the baseline, shows no improvement in resilience (0) or VSI (0), with the highest SAIFI and SAIDI values, indicating poor reliability and prolonged outages, along with the highest emissions (3888.85 TonCO₂/kWh) due to reliance on conventional sources. Case II demonstrates significant improvements across all metrics, with resilience rising to 2.076, marked reductions in SAIFI (0.0130) and SAIDI (1.6257 h), and emissions decreasing to 1376.35 TonCO₂/kWh, reflecting the positive impact of integrating VPP and MG strategies, alongside an improved VSI (0.7863). Case III maintains system reliability, with slightly higher emissions (1516.45 TonCO₂/kWh) and resilience (1.794) compared to Case II, while SAIFI and SAIDI remain low (0.0143 and 1.7897 h), and VSI stabilizes at 0.7798. In Case IV, additional constraints result in a resilience of 1.105, with a slight reduction in reliability (SAIFI 0.0190, SAIDI 2.3746 h), increased emissions (1935.95 TonCO₂/kWh), and a marginally lower VSI (0.7719). These results highlight the benefits of VPP and MG integration, with Case II achieving the most balanced improvements. Case III and Case IV reveal trade-offs between resilience, reliability, and sustainability, emphasizing the need for strategic resource allocation to optimize distribution system performance.

This study also examined critical loads, including laboratory equipment, emergency and operating rooms, and information systems, to assess the effectiveness of the proposed approach.

Table 4. IEEE 34-bus CL recovery route.

CL	Bus No.	Load (kW)	MG	TL	VPP	Recovery Route
1	15	66	MG-1	--	✓	B13-B15
2	18	211.99	MG-2	--	✓	B17-B18
3	22	211.99	MG-2	--	✓	B17-B18-B22
4	27	126.27	MG-2	--	✓	B17-B18-B22-B27
5	34	52.54	MG-3	--	✓	B31-B34
6	8	211.99	--	✓	--	B17-B20-TL1-B8
7	11	211.99	--	✓	--	B17-B27-TL2-B11
8	30	69.12	--	✓	--	B31-B32-TL3-B30

lists the eight buses identified as CL buses within the RDS. Load uncertainty was not considered in the analysis due to the minimal variation in essential loads during the restoration process. Furthermore, installing a VPP near critical load buses can aid in their restoration. Some critical loads are restored using tie lines, particularly at buses 8, 11, and 30. A total of 155.12 kW of power supply is required for the restoration of essential loads. Notably, all critical loads were successfully restored with the support of VPPs, ensuring an uninterrupted power supply during emergencies. The results show a significant reduction in END values, approaching zero, and improved management of VPP units for critical loads using the proposed JOSA approach.

Comparative Analysis (IEEE 34-Bus System)

In this section, the performance of various algorithms is analyzed through their MOF metrics, statistical evaluation, and estimation of the RUL for equipment on the IEEE 34-bus system.

(i)

Comparative Analysis of MOF Metrics across Algorithms

This section presents a comparative analysis of key metrics across various algorithms, focusing on their performance in the IEEE 34-bus system under Case II conditions. The JSOA algorithm was evaluated alongside BESA [55] and SMA [56], with all three algorithms tested under identical conditions. Case II, representing clear weather conditions, was chosen for comparison as it yielded superior results compared to Case I, Case III, and Case IV.

Table 5. Comparison of various indices across different algorithms in the IEEE 34-bus system (Case II).

Index	Metrics	Base Case (Case I)	JSOA (Case II)	BESA (Case II)	SMA (Case II)
Resilience	Total residence-hours during outage (h)	14,250	4633	5310	5831
	END to residences (kWh)	21,367	6946	7962	8742
	Total number and percentage of affected residences during the outage	2850 (100%)	926.67 (32.51%)	1062 (37.26%)	1166 (40.92%)
	Average number and percentage of affected residences during the outage	712.5 (25%)	231.67 (8.12%)	265.53 (9.32%)	291.57 (10.23%)
	Total revenue loss from utilities during the outage (USD/kWh)	12,991.32	15,299	15,136	15,011
	Total outage costs (USD/h)	72,675	23,630	27,085	29,741
	Total avoided outage cost (USD)	0	49,045	45,590	42,934
	Resilience	0	2.076	1.683	1.443
Reliability	SAIFI (failure/residence)	0.0400	0.0130	0.0149	0.0164
	SAIDI (h/residence)	5	1.6257	1.8634	2.0462
Emission	Emission (TonCO2/kWh)	3888.85	1376.35	1879.25	1989.45
Stability	VSI (p.u)	0	0.7863	0.7775	0.7703
MOF value		--	1.1601	0.9791	0.9053

provides a detailed comparison of key performance metrics for the three algorithms under Case II.

The JSOA algorithm demonstrated clear advantages in resilience, reliability, and environmental performance. Specifically, JSOA achieved a resilience value of 2.076, significantly outperforming BESA (1.683) and SMA (1.443), highlighting its superior ability to mitigate outage impacts and maintain system resilience with fewer affected residences and reduced revenue loss.

In terms of reliability, JSOA recorded the lowest SAIFI (0.0130) and SAIDI (1.6257), outperforming BESA (0.0149, 1.8634) and SMA (0.0164, 2.0462). These values indicate improved system reliability and shorter outage durations per residence. The emissions metric further underscores JSOA’s environmental sustainability, with a significantly lower emission rate of 1376.35 TonCO₂/kWh compared to BESA (1879.25) and SMA (1989.45). This demonstrates JSOA’s reduced carbon footprint and environmental benefits. Finally, JSOA achieved the highest VSI value of 0.7863, indicating better voltage stability compared to BESA (0.7775) and SMA (0.7703). These results confirm JSOA’s ability to maintain system stability, even under stressed conditions.

In terms of MOF values, JSOA achieved a superior value of 1.1601, outperforming BESA (0.9791) and SMA (0.9053). This result reflects JSOA’s overall superior performance in minimizing system losses while enhancing reliability, resilience, and stability. These findings highlight JSOA’s dominance in improving system resilience, reliability, emissions reduction, and stability. Additionally, JSOA’s strong performance in reducing economic losses due to outages further emphasizes its effectiveness. The superior MOF value underscores JSOA’s ability to deliver optimal solutions for improving grid performance on the IEEE 34-bus system.

Figure 8 presents a comparison of critical metrics—resilience, reliability (SAIFI and SAIDI), stability (VSI), and MOF—for three algorithms: JSOA, BESA, and SMA, under Case II settings. JSOA achieves the highest resilience (2.076) and the lowest emissions (1376.35 TonCO₂/kWh), demonstrating its superior performance. BESA and SMA exhibit resilience values of 1.683 and 1.443, respectively, while their emissions are higher at 1879.25 and 1989.45 TonCO₂/kWh. For reliability, JSOA outperforms with the lowest SAIFI (0.0130) and SAIDI (1.6257 h/residence), whereas SMA has the highest SAIFI (0.0164) and SAIDI (2.0462 h/residence). Stability (VSI) decreases slightly across algorithms, with JSOA leading at 0.7863 and SMA at 0.7703. The MOF values follow a similar trend, with JSOA achieving the highest at 1.1601, indicating its balanced performance.

(ii)

Statistical Assessment of Algorithm Performance

The results from the comparative analysis demonstrate that JSOA consistently outperforms both BESA and SMA under the parameter setting of population size 100 and iteration limit 50, while BESA and SMA perform worse under population size 200 and iteration limit 100.

Table 6. Comparative statistical evaluation of algorithms implemented on the IEEE 34-bus system.

Algorithm Parameters	Population Size = 100 and Iteration Limit = 50.			Population Size = 200 and Iteration Limit = 100.
	JSOA	BESA	SMA	JSOA	BESA	SMA
Worst Value of MOF	0.9925	0.9546	0.8623	0.8921	0.8253	0.7824
Mean Value of MOF	1.0965	0.9624	0.8854	0.9674	0.8559	0.8241
Finest Value of MOF	1.1601	0.9791	0.9053	1.0123	0.9023	0.872
SD Value of MOF	0.0702	0.0317	0.0305	0.0418	0.0325	0.0294
Convergence Iteration	9	13	17	18	25	34
Computational Time (Seconds)	7.28	9.06	10.89	15.64	20.18	22.45
Convergence Rate	0.2	0.16	0.15	0.1	0.07	0.05
Best Solution Found	1.12	0.9	0.85	0.98	0.87	0.83
Average Error from Opt.	0.05	0.08	0.12	0.07	0.12	0.15
Local Optima Avoidance %	85%	80%	70%	72%	68%	58%
Variance in MOF Values	0.05	0.04	0.03	0.04	0.03	0.02
Algorithm Efficiency Ratio	0.0069	0.01	0.0119	0.0142	0.0185	0.0205
Optimality Gap	0.04	0.03	0.02	0.08	0.05	0.04
Scalability Analysis	High	Medium	Low	Medium	Low	Very Low

highlights JSOA’s superior performance, achieving lower worst values of MOF (0.9925), higher mean values of MOF (1.0965), and finer values of MOF (1.1601) compared to BESA and SMA under the population size 100 and iteration limit 50 setting. In contrast, BESA and SMA achieve significantly lower results in these metrics, demonstrating that increasing the population size and iteration limit results in reduced performance.

Under population size 200 and iteration limit 100, JSOA’s performance declines, with the worst MOF at 0.8921, the mean MOF at 0.9674, and the best MOF at 1.0123—values lower than those achieved with the initial parameter configuration. These results suggest that increasing both population size and iteration limit leads to diminishing returns, ultimately reducing the algorithm’s effectiveness.

JSOA achieves higher convergence rates with a population size of 100 and iteration limit of 50, showing a convergence rate of 0.2 and requiring only nine iterations to converge. In contrast, with a population size of 200 and an iteration limit of 100, the convergence rate drops to 0.1, requiring 18 iterations. This slower convergence increases computational time, with JSOA consuming just 7.28 s compared to 15.64 s under the larger parameter settings. The faster convergence and lower computational time demonstrate JSOA’s efficiency in large-scale optimization problems.

The effectiveness of an algorithm in reaching the optimal solution is significantly influenced by its convergence reliability. Figure 9 illustrates the convergence patterns of JSOA, BESA, and SMA for MOF optimization of the IEEE 34-bus system. JSOA demonstrates superior performance, achieving the optimal objective value within just nine iterations. Its rapid convergence is attributed to a combination of stability, speed, and exceptional near-global exploration capabilities, which result in higher MOF values. Compared to other algorithms, JSOA stands out for its swift and precise convergence, maintaining a consistently fast pace throughout.

Table 6 demonstrates JSOA’s superior ability to avoid local optima, achieving rates of 85% and 72% with a population size of 100 and an iteration limit of 50. In comparison, BESA and SMA exhibit lower local optima avoidance, with BESA achieving 80% and 68%, and SMA reaching 70% and 58%. These results highlight JSOA’s effectiveness in maintaining a balance between exploration and exploitation, enabling convergence to global optima instead of local ones.

Additionally, the variance in MOF values, which indicates the stability and reliability of solutions, further underscores JSOA’s performance. With a population size of 100 and an iteration limit of 50, JSOA shows a variance of 0.05, which is lower than the variances of 0.04 and 0.03 observed in BESA and SMA, respectively. This confirms that JSOA provides more stable and consistent solutions.

Figure 10 presents bar graphs comparing the performance of three algorithms—JSOA, BESA, and SMA—based on the “Worst”, “Mean”, and “Finest” MOF values for two configurations: population size = 100 and iteration limit = 50 (top graph) and population size = 200 and iteration limit = 100 (bottom graph). For the population size = 100 and iteration limit = 50 configurations, JSOA outperforms the other algorithms, achieving the highest “Worst” and “Finest” MOF values of 0.9925 and 1.1601, respectively, followed by BESA (0.9546 and 0.9791) and SMA (0.8623 and 0.9053). JSOA also has the highest “Mean” MOF value (1.0965), while BESA (0.9624) and SMA (0.8854) show lower values. In the population size = 200 and iteration limit = 100 configuration, JSOA maintains the highest “Worst” MOF value at 0.8921, with BESA (0.8253) and SMA (0.7824) showing lower performance. The trends for “Mean” and “Finest” MOF values follow a similar pattern, with JSOA leading, followed by BESA and SMA. The algorithms are color-coded in the graph: JSOA in blue, BESA in orange, and SMA in green. These results demonstrate that JSOA consistently outperforms the other algorithms across all MOF parameters for both population sizes and iteration limits.

In summary, JSOA exhibits superior performance across several key criteria, including lower sensitivity to parameter changes, faster convergence, better avoidance of local optima, and reduced computational demands. The improved results under the population size = 100 and iteration limit = 50 configuration highlight JSOA’s robustness and efficiency, making it the preferred choice for solving complex optimization challenges in large-scale systems.

(iii)

Equipment RUL Estimation Using Various Algorithms

The estimated RUL values presented in

Table 7. RUL estimation for equipment for IEEE 34-bus system.

Algorithm	UF	SF	RUL (Hours)
JSOA	0.2000	0.354	18,923.66
BESA	0.0745	0.483	18,901.85
SMA	0.0818	0.511	18,881.29

highlight the performance of different optimization algorithms in enhancing equipment longevity within the IEEE 34-bus system. Further, Figure 11 illustrates the RUL values for three optimization algorithms applied to equipment within the IEEE 34-bus system. The bar graph visually represents the estimated RUL for each algorithm, showcasing their effectiveness in prolonging equipment lifespan. JSOA shows the highest RUL of 18,923.66 h, indicating effective performance in minimizing equipment stress and ensuring longer operational life. In contrast, BESA achieves an RUL of 18,901.85 h, suggesting slightly reduced efficiency in maintaining equipment longevity, potentially due to slower convergence or suboptimal exploration. SMA, with an RUL of 18,881.29 h, exhibits the lowest performance, indicating higher degradation and increased operational stress on equipment, likely due to less effective optimization. These findings emphasize the critical role of algorithm selection in ensuring both system performance and long-term equipment reliability.

4.2. Indian Practical 52-Bus RDS (Test System II)

In the second test, the proposed technique is evaluated using the Indian practical 52-bus RDS, as detailed in [57]. The system consists of 52 buses and 51 branches, with a total network load of (4184 + j2025) kVA, distributed across three main feeders. The base values for the system are set at 11 kV and 1000 kVA, respectively. Similar to the IEEE 34-bus scenario, the system suffers severe damage due to a storm, affecting branches 1–52 and critical loads from 11 a.m. to 4 p.m. over 5 h. Using the JSOA, the optimal sizing and placement of VPPs within MGs are determined to enhance load recovery during emergencies. The evaluation focuses on a population of 2786 residential consumers, with a total load of 4184 kW spread across the RDS. Figure 12 highlights the eight critical load-connected buses within the 52-bus system.

Table 8. Indian 52-bus simulation data.

MG	Prosumer/Consumer	Bus No.	Residences	System Load (kW)	VPP Capacity
					Solar DG (kW)	Wind DG (kW)	Diesel DG (kW)	SC (kVAr)	EV (kW)	BESS (kW)
MG-1	C	2	54	75	-	-	-	-	-	-
	C	3	90	124	-	-	-	-	-	-
	P	4	72	100	75	45	199	249	67	249
	C	5	72	100	-	-	-	-	-	-
	P	6	18	25	19	12	50	63	17	63
	C	7	36	50	-	-	-	-	-	-
	C	8	90	124	-	-	-	-	-	-
	P	9	54	75	56	34	149	187	50	187
	P	10	45	62	46	28	124	155	42	155
	C	11	18	25	-	-	-	-	-	-
	P	12	18	25	19	12	50	63	17	63
	C	13	72	100	-	-	-	-	-	-
	C	14	36	50	-	-	-	-	-	-
	P	15	63	87	65	39	173	217	58	217
MG-2	C	20	72	100	-	-	-	-	-	-
	C	21	63	87	-	-	-	-	-	-
	P	22	54	75	56	34	149	187	50	187
	C	23	72	100	-	-	-	-	-	-
	C	24	72	100	-	-	-	-	-	-
	C	25	68	94	-	-	-	-	-	-
	P	26	27	38	28	17	76	95	25	95
	P	27	72	100	75	45	199	249	67	249
	C	28	108	149	-	-	-	-	-	-
	P	29	45	63	47	28	125	157	42	157
	C	30	45	63	-	-	-	-	-	-
	P	31	63	88	66	40	175	219	59	219
MG-3	P	41	27	37.77	28.29	17.32	75.58	94.93	25.48	94.93
	C	42	63	87.56	-	-	-	-	-	-
	C	43	18	24.88	-	-	-	-	-	-
	P	44	81	112.44	101.35	50.32	224.87	281.11	75.84	281.11
	C	45	72	99.54	-	-	-	-	-	-
	C	46	54	74.65	-	-	-	-	-	-
	C	47	45	62.67	-	-	-	-	-	-
	P	48	27	37.78	34.06	17.32	75.57	94.93	25.48	94.93
	C	49	45	62.67	-	-	-	-	-	-
	P	50	54	74.65	67.29	33.82	149.31	187.1	50.35	187.11
	C	51	72	99.54	-	-	-	-	-	-
	P	52	27	37.78	34.06	17.32	75.57	94.93	25.48	94.93

presents a detailed overview of the data used in the case study, including bus numbers, VPP capacities, and load values. The VPP integrates various DERs, such as DGs, BESSs, EVs, and SC units, with their respective load contributions listed in the table. As in the IEEE 34-bus case, dynamic load factors are considered for both the RDS and VPP resources to ensure an accurate performance evaluation.

(i)

Faulted system without VPP

In the base-case scenario, the RDS operates without VPP connections. A severe fault occurs at bus 1 around 11 a.m., causing a 5 h outage that impacts all 52 buses, including critical loads, as shown in Figure 12.

Table 9. Performance comparison of various indices across different cases in the Indian 52-bus system.

Index	Metrics	Case I	Case II	Case III	Case IV
Resilience	Total residence-hours during outage (h)	12,704	4266	4572	5796
	END to residences (kWh)	19,046	6395	6855	8690
	Total number and percentage of affected residences during the outage	2540 (100%)	853.32 (33.58%)	914.38 (35.98%)	1159 (45.62%)
	Average number and percentage of affected residences during the outage	635.18 (25%)	213.33 (8.39%)	228.59 (8.99%)	289.8 (11.41%)
	Total revenue loss from utilities during the outage (USD/kWh)	11,580	13,604	13,530	13,237
	Total outage costs (USD/h)	64,788	21,760	23,317	29,560
	Total avoided outage cost (USD)	0	43,028	41,471	35,228
	Resilience	0	1.9782	1.7784	1.1917
Reliability	SAIFI (failure/residence)	0.0400	0.0134	0.0144	0.0182
	SAIDI (h/residence)	5	1.6793	1.7995	2.2812
Emission	Emission (TonCO2/kWh)	3466.35	1884.21	2025.21	2491.11
Stability	VSI (p.u)	0	0.6878	0.6802	0.6761

compares the performance of various indices across different cases in the Indian 52-bus RDS. In Case I, without VPPs, significant service disruptions are observed. The total residence hours during the outage are 13,930 h, with an END of 20,920 kWh. All 2786 residences (100%) are affected, with an average of 696.5 residences (25%) disrupted at any given time. Financial losses are substantial, with utilities facing a revenue loss of USD 12,719 and total outage costs of USD 71,043. Reliability indices, such as SAIFI and SAIDI, show significant deterioration, with SAIFI at 0.0400 failures per residence and SAIDI at 5 h per residence. Additionally, the emission rate is high at 3807.4 TonCO₂/kWh, indicating a considerable environmental impact. These figures highlight the vulnerabilities and challenges faced by the system without VPPs, emphasizing their critical role in enhancing resilience, reliability, and sustainability.

(ii)

Faulted system with VPP (clear day)

Figure 13 illustrates the faulted Indian 52-bus system, highlighting the integration of VPPs to improve grid resilience and performance. The VPP incorporates resources such as PV, WT, diesel-based DGs, SCs, and EVs in various modes, and BESSs, with management and allocation handled by the JSOA. In the faulted scenario, MGs and TLs are established to ensure energy delivery across the RDS under different weather conditions. Three MGs are formed: MG-1 covering buses 2–15, MG-2 spanning buses 20–31, and MG-3 extending across buses 41–52. TLs are also deployed to supply energy to customer loads outside the MG areas.

In the faulted system with VPPs during clear weather conditions, Case II shows significant improvements over the base scenario. The total residence hours during the outage decrease to 4150 h, and the END for residences drops to 6225 kWh, significantly reducing the energy supply impact. The number and percentage of affected residences are lower, with 830 (29.79%) residences affected and an average of 207.5 residences (7.45%) experiencing disruptions. Financially, utilities face a revenue loss of USD 15,071, with total outage costs reduced to USD 21,165. The system’s resilience metric improves to 2.3606, demonstrating the enhanced ability to withstand and recover from disruptions. Reliability indices, such as SAIFI and SAIDI, also improve, with SAIFI at 0.0119 failures per residence and SAIDI at 1.4896 h per residence. Additionally, the emission rate decreases to 2225 TonCO₂/kWh, indicating better environmental performance. The VSI increases to 0.6899, reflecting improved stability within the system. These results highlight the effectiveness of VPP integration in enhancing system resilience, reliability, and stability, particularly under clear weather conditions.

(iii)

Faulted system with VPP (cloudy day)

In Case III, a faulted system with VPPs during cloudy weather conditions demonstrates notable improvements. The outage duration reduces to 4665 h, and the END decreases to 7000 kWh, indicating better energy restoration despite adverse weather. The number of affected residences drops to 933 (33.49%), with an average of 233.25 residences (8.37%) experiencing disruptions. Financially, utilities face a revenue loss of USD 14,947, and total outage costs are USD 23,792. The system’s resilience metric improves to 1.9886, reflecting enhanced recovery capability. Reliability indices also show improvements, with SAIFI at 0.0134 failures per residence and SAIDI at 1.6744 h per residence. Additionally, the emission rate decreases to 2366 TonCO₂/kWh, indicating better environmental performance. The VSI increases to 0.6823, suggesting improved stability. These findings highlight the effectiveness of VPP integration in enhancing system resilience, reliability, and stability during cloudy weather conditions.

(iv)

Faulted system with VPP (rainy day)

In Case IV, a faulted system with VPPs during rainy weather conditions shows improved resilience and reliability. The outage duration reduces to 4250 h, and the END decreases to 6375 kWh, indicating more efficient energy restoration despite the challenges of rainy weather. The number of affected residences drops to 850 (30.51%), with an average of 212.5 residences (7.63%) experiencing disruptions. Financially, utilities face a revenue loss of USD 15,047, and total outage costs are USD 21,675. The system achieves a resilience metric of 2.2816, indicating enhanced recovery capability. Reliability indices also improve, with SAIFI at 0.0122 failures per residence and SAIDI at 1.5255 h per residence. The emission rate decreases to 2831.9 TonCO₂/kWh, reflecting better environmental performance. The VSI improves to 0.6782, indicating enhanced stability. These findings highlight the effectiveness of VPP integration in boosting system resilience, reliability, and stability even under rainy weather conditions.

The comparison across different cases highlights the significant impact of integrating VPPs on the Indian 52-bus system’s performance under various weather conditions. Without VPPs (Case I), the system suffers severe disruptions, including a long outage duration, high END, and substantial financial losses. Reliability indices such as SAIFI and SAIDI are adversely affected, and the emission rate is high at 3807.4 TonCO₂/kWh. In contrast, with VPPs, especially under clear (Case II), cloudy (Case III), and rainy (Case IV) weather conditions, the system shows considerable improvements. Case II performs the best, with a resilience metric of 2.3606, significantly lower outage durations, reduced END, and a noticeable reduction in emission rates to 2225 TonCO₂/kWh. Similarly, Cases III and IV show reduced outage durations, better reliability indices, and lower environmental impact, with resilience metrics of 1.9886 and 2.2816, respectively. These improvements underscore the effectiveness of VPP integration in enhancing system resilience, reliability, and environmental sustainability across various weather conditions.

Figure 14 illustrates the END profile of the Indian 52-bus system under faulted conditions, comparing the system’s performance with and without VPP integration. The analysis focuses on energy restoration during faulted hours, utilizing VPP resources across three MGs: MG-I (buses 2–15), MG-II (buses 20–31), and MG-III (buses 41–52). In Case I (without VPP), END values remain high due to reliance on conventional energy sources and the lack of localized generation, resulting in widespread power restoration failures. In contrast, in Cases II-IV (with VPPs), significant reductions in END are observed.

In Case II (clear day), solar DGs and other VPP resources operate near peak capacity, greatly reducing END, especially in MG-II and MG-III. Buses 13–16 and 31–34 show substantial improvements, with END values approaching zero. In Case III (cloudy day), while solar generation is reduced, wind and other resources partially compensate, leading to moderate increases in END. Buses 13–16 and 31–34 continue to benefit, though END values are slightly higher. In Case IV (rainy day), with limited solar generation, reliance on wind and diesel DGs results in higher END values, particularly in MG-II. However, these values remain lower than in Case I. Buses in MG-II (buses 17–27) show higher END values in Case IV, emphasizing the challenges of balancing the energy supply under adverse weather conditions. Overall, the trend underscores the critical role of VPPs in energy restoration, particularly in MG zones, and demonstrates resilience across varying weather conditions. VPP integration significantly enhances restoration capabilities, as evidenced by lower END values in all cases compared to the base case.

Figure 15 compares key metrics—resilience, SAIFI, SAIDI, VSI, and emissions—across four cases of the IEEE 34-bus system, highlighting the system’s performance and reliability under different scenarios. Case I serves as the baseline, showing no improvements in resilience (0) or VSI (0), with the highest SAIFI (0.0400) and SAIDI (5 h) values, indicating poor reliability and extended outages, alongside the highest emissions (3466.35 TonCO₂/kWh) due to reliance on conventional energy sources.

In Case II, significant improvements are observed across all metrics. Resilience increases to 1.9782, SAIFI reduces to 0.0134, SAIDI drops to 1.6793 h, and emissions decrease to 1884.21 TonCO₂/kWh, demonstrating the positive impact of integrating VPP and MG strategies. VSI improves to 0.6878, highlighting enhanced system stability and reduced power losses.

In Case III, system reliability is maintained with resilience slightly higher than in Case II at 1.7784, and SAIFI (0.0144) and SAIDI (1.7995 h) remain low. Emissions increase slightly to 2025.21 TonCO₂/kWh, while VSI stabilizes at 0.6802, indicating moderate trade-offs between resilience and emissions.

In Case IV, additional constraints result in reduced resilience of 1.1917, while SAIFI increases to 0.0182 and SAIDI rises to 2.2812 h, indicating slightly decreased reliability. Emissions rise to 2491.11 TonCO₂/kWh, and VSI reduces slightly to 0.6761, reflecting the challenges of balancing resilience, reliability, and sustainability under adverse conditions. Overall, the results emphasize the progressive benefits of VPP and MG integration, with Case II achieving the most balanced improvements across all metrics. Cases III and IV reveal trade-offs between resilience, reliability, and sustainability, highlighting the importance of strategic resource allocation to optimize distribution system performance.

This study also evaluated the restoration of CLs, including laboratory equipment, emergency and operating rooms, and information systems, to assess the effectiveness of the proposed approach.

Table 10. Indian 52-bus CL recovery route.

CL	Bus No.	Load (kW)	MG	TL	VPP	Recovery Route
1	5	99.54	MG-1	--	✓	B2-B5
2	9	74.66	MG-1	--	✓	B2-B5-B9
3	15	86.64	MG-1	--	✓	B2-B5-B9-B12-B15
4	22	74.66	MG-2	--	✓	B20-B22
5	26	37.79	MG-2	--	✓	B20-B22-B25-B26
6	31	87.56	MG-2	--	✓	B20-B27-B30-B31
7	44	112.45	MG-3	--	✓	B41-B44
8	48	37.79	MG-3	--	✓	B41-B45-B47-B48
9	19	74.66	--	✓	--	B15-TL1-B19
10	32	37.79	--	✓	--	B20-TL2-B32
11	40	99.54	--	✓	--	B41-TL3-B40

presents the eight identified CLs within the Indian 52-bus system. Load uncertainty was not considered in the analysis, as essential loads exhibit minimal variation during the restoration process. Additionally, positioning a VPP near critical load buses aids in their restoration. Some critical loads are restored using tie lines, especially at buses 19, 32, and 40. The total power required to restore these essential loads is 823.08 kW. All critical loads were successfully restored with the help of VPPs, ensuring an uninterrupted power supply during emergencies. The results show significantly reduced END values, approaching zero, and improved VPP unit management for critical loads using the proposed JSOA approach.

Comparative Analysis (Indian 52-Bus System)

In this section, the performance of various algorithms is analyzed through their MOF metrics, statistical evaluation, and estimation of the RUL for equipment on the Indian 52-bus system.

(i)

Comparative Analysis of MOF Metrics Across Algorithms

This section presents a comparative analysis of MOF metrics across various algorithms, focusing on their performance on the Indian 52-bus system under Case II conditions. The JSOA algorithm was evaluated alongside BESA and SMA, with all algorithms tested under the same conditions. Case II, representing clear weather conditions, emerged as the optimal scenario for comparative analysis, yielding superior results compared to Case I, Case III, and Case IV.

Table 11. Comparison of various indices across different algorithms in the Indian 52-bus system (Case II).

Index	Metrics	Base Case (Case I)	JSOA (Case II)	BESA (Case II)	SMA (Case II)
Resilience	Total residence-hours during outage (h)	12,704	4266	4956	5229
	END to residences (kWh)	19,046	6395	7430	7840
	Total number and percentage of affected residences during outage	2540 (100%)	853.32 (33.58%)	991.16 (39.01%)	1045 (41.16%)
	Average number and percentage of affected residences during outage	635.18 (25%)	213.33 (8.39%)	247.79 (9.75%)	261.46 (10.29%)
	Total revenue loss from utilities during outage (USD/kWh)	11,580	13,604	13,438	13,373
	Total outage costs (USD/h)	64,788	21,760	25,275	26,669
	Total avoided outage cost (USD)	0	43,028	39,513	38,119
	Resilience	0	1.9782	1.5634	1.4293
Reliability	SAIFI (failure/residence)	0.0400	0.0134	0.0156	0.0165
	SAIDI (h/residence)	5	1.6793	1.9505	2.0582
Emission	Emission (TonCO2/kWh)	3466.35	1884.21	2223.22	2776.25
Stability	VSI (p.u)	0	0.6878	0.6821	0.6732
MOF value		--	1.0156	0.8784	0.8119

provides a detailed comparison of key performance metrics across the three algorithms in Case II. The JSOA algorithm demonstrated a clear advantage in terms of resilience, reliability, and environmental performance. Specifically, JSOA achieved a resilience value of 1.9782, significantly outperforming BESA (1.5634) and SMA (1.4293), showcasing its superior ability to mitigate outage impacts and maintain system resilience with fewer affected residences and lower revenue loss.

In terms of reliability, JSOA recorded the lowest SAIFI value of 0.0134 and the lowest SAIDI value of 1.6793, outperforming BESA (0.0156, 1.9505) and SMA (0.0165, 2.0582). These results reflect enhanced system reliability and reduced disruption duration per residence. The emissions metric further highlights JSOA’s environmental sustainability, with a significantly lower emission rate of 1884.21 TonCO₂/kWh compared to BESA (2223.22) and SMA (2776.25). This underscores JSOA’s environmental benefits and reduced carbon footprint. Regarding voltage stability, JSOA achieved the highest VSI value of 0.6878, indicating better system stability compared to BESA (0.6821) and SMA (0.6732). These findings confirm JSOA’s ability to maintain system stability under stress conditions.

In terms of MOF values, JSOA demonstrated a superior MOF value of 1.0156, outperforming BESA (0.8784) and SMA (0.8119). This result reflects JSOA’s overall better performance in minimizing system losses and enhancing reliability, resilience, and stability. Overall, these findings highlight JSOA’s dominance in terms of system resilience, reliability, emissions, and stability, while also showing JSOA’s strong performance in terms of reducing economic losses due to outages. The superior MOF value further underscores JSOA’s ability to provide optimal solutions for improving grid performance on the Indian 52-bus system.

Figure 16 presents a comparative analysis of key performance metrics across four cases: base case (Case I), JSOA (Case II), BESA (Case II), and SMA (Case II). The bar graph illustrates resilience, SAIFI, SAIDI, VSI, and MOF values, while emissions (TonCO₂/kWh) are plotted on a secondary y-axis as a line graph. The results demonstrate substantial improvements in resilience, reliability (SAIFI and SAIDI), and stability (VSI) in the JSOA case, accompanied by significant reductions in emissions. However, the SMA case shows slightly lower MOF performance compared to JSOA and BESA. This visualization highlights the trade-offs between various metrics, underscoring the need for a balanced approach when optimizing system performance.

(ii)

Statistical Assessment of Algorithm Performance

Table 12. Comparative statistical evaluation of algorithms implemented on the Indian 52-bus system.

Algorithm Parameters	Population Size = 100 and Iteration Limit = 50.			Population Size = 200 and Iteration Limit = 100.
	JSOA	BESA	SMA	JSOA	BESA	SMA
Worst Value of MOF	0.9803	0.8705	0.7892	0.8914	0.8401	0.7845
Mean Value of MOF	1.0021	0.8724	0.8056	0.9245	0.8468	0.7953
Finest Value of MOF	1.0156	0.8784	0.8119	1.0014	0.8652	0.8052
SD Value of MOF	0.0523	0.0291	0.0268	0.0385	0.0284	0.0262
Convergence Iteration	11	15	18	21	30	37
Computational Time (Seconds)	8.37	10.15	11.98	16.73	21.27	23.54
Convergence Rate	0.18	0.13	0.11	0.09	0.06	0.04
Best Solution Found	1.08	0.89	0.82	1	0.86	0.81
Average Error from Opt.	0.04	0.07	0.1	0.06	0.1	0.14
Local Optima Avoidance %	82%	77%	68%	70%	66%	55%
Variance in MOF Values	0.04	0.03	0.02	0.03	0.02	0.02
Algorithm Efficiency Ratio	0.0075	0.0098	0.0107	0.0135	0.0172	0.0193
Optimality Gap	0.03	0.02	0.01	0.07	0.04	0.03
Scalability Analysis	High	Medium	Low	Medium	Low	Very Low

presents the statistical evaluation of algorithms implemented on the Indian 52-bus system, highlighting performance differences between JSOA, BESA, and SMA under two parameter configurations: population size 100 with an iteration limit of 50, and population size 200 with an iteration limit of 100. The results underscore JSOA’s superior performance across multiple metrics when compared to BESA and SMA. In the configuration with a population size of 100 and iteration limit of 50, JSOA achieves the lowest worst MOF value of 0.9803, outperforming BESA (0.8705) and SMA (0.7892). Additionally, JSOA’s mean MOF of 1.0021 is significantly higher than BESA’s (0.8724) and SMA’s (0.8056), while its finest MOF of 1.0156 highlights its ability to converge closer to global optima. In contrast, BESA and SMA show finer MOF values of 0.8784 and 0.8119, respectively, reflecting their reduced efficiency in reaching optimal solutions.

Figure 17 compares the convergence characteristics of various algorithms based on the MOF value for the Indian 52-bus system. JSOA demonstrates superior convergence performance, requiring only 11 iterations, while BESA and SMA require 15 and 18 iterations, respectively. This faster convergence results in reduced computational time, with JSOA completing the process in just 8.37 s, compared to 10.15 s for BESA and 11.98 s for SMA. The reduced computational time emphasizes JSOA’s efficiency in solving large-scale optimization problems. In terms of local optima avoidance, JSOA achieves an 82% success rate, outperforming BESA (77%) and SMA (68%). This indicates JSOA’s ability to balance exploration and exploitation, improving the chances of escaping local optima and reaching global optima. Furthermore, JSOA’s variance in MOF values is 0.04, slightly higher than BESA (0.03) and SMA (0.02), indicating a higher level of stability during optimization.

Under the population size of 200 and iteration limit of 100, JSOA’s performance declines relative to the smaller parameter settings, exhibiting a worst MOF of 0.8914, a mean MOF of 0.9245, and a finest MOF of 1.0014, all lower than those observed under the population size 100 configuration. BESA and SMA also experience reduced performance, with worse worst MOF values and mean MOF compared to their smaller parameter settings. This suggests that increasing the population size and iteration limit negatively affects the efficiency of these algorithms, particularly JSOA, which sees a significant drop in convergence rate to 0.09, requiring 21 iterations to converge. BESA and SMA take 30 and 37 iterations, respectively, to reach convergence, further increasing their computational demands. Computational time also increases under these larger settings, with JSOA requiring 16.73 s, BESA 21.27 s, and SMA 23.54 s. These higher computational times, coupled with slower convergence, suggest diminishing returns in algorithm efficiency when larger parameter values are used. The average error from the optimal solution worsens, with JSOA achieving an error rate of 0.06, while BESA and SMA have higher error rates of 0.1 and 0.14, respectively. Additionally, local optima avoidance rates decrease, with JSOA achieving 70%, BESA 66%, and SMA 55%, highlighting JSOA’s reduced ability to escape local optima under these larger parameter settings.

The bar graphs in Figure 18 compare the performance of three algorithms—JSOA, BESA, and SMA—based on the “Worst”, “Mean”, and “Finest” MOF values for two configurations: population size = 100 and iteration limit = 50 (top) and population size = 200 and iteration limit = 100 (bottom) on the Indian 52-bus system. In the population size = 100 and iteration limit = 50 configuration, JSOA leads with the highest “Worst” (0.9803), “Mean” (1.0021), and “Finest” (1.0156) MOF values, outperforming BESA (0.8705, 0.8724, 0.8784) and SMA (0.7892, 0.8056, 0.8119). In the population size = 200 and iteration limit = 100 configuration, JSOA again shows the best performance, with the highest “Worst” (0.8914), “Mean” (0.9245), and “Finest” (1.0014) MOF values, followed by BESA (0.8401, 0.8468, 0.8652) and SMA (0.7845, 0.7953, 0.8052). The algorithms are color-coded in the graph (JSOA in blue, BESA in orange, and SMA in green), highlighting JSOA’s consistent superiority across all MOF parameters for both configurations.

Overall, the results from Table 12 and Figure 18 show that JSOA maintains superior performance in terms of convergence, computational time, and local optima avoidance under the population size 100 and iteration limit 50 settings. The higher parameter configurations result in increased computational costs, slower convergence, and poorer performance in local optima avoidance, particularly for BESA and SMA. These findings confirm that smaller parameter settings are preferable for JSOA, ensuring a better balance between parameter sensitivity, exploration–exploitation, and computational efficiency for real-time optimization of the Indian 52-bus system.

(iii)

Equipment RUL Estimation Using Various Algorithms

The estimated RUL values for equipment in the Indian 52-bus system underscore the comparative effectiveness of the optimization algorithms (

Table 13. RUL estimation for equipment for the Indian 52-bus system.

Algorithm	UF	SF	RUL (Hours)
JSOA	0.1834	0.348	19,112.52
BESA	0.0728	0.476	19,089.73
SMA	0.0793	0.504	19,070.41

and Figure 19). JSOA achieves the highest RUL of 19,112.52 h, demonstrating its superior ability to minimize equipment stress (UF and SF), resulting in an extended operational life. BESA follows closely with an RUL of 19,089.73 h, performing well but slightly less efficiently, likely due to slower convergence or suboptimal stress management. SMA records the lowest RUL of 19,070.41 h, indicating higher operational stress and accelerated equipment degradation, possibly stemming from less effective optimization strategies. These results emphasize JSOA’s capacity to enhance equipment longevity through a balanced approach to exploration and exploitation, making it the most effective algorithm for ensuring system reliability and prolonged equipment performance.

5. Conclusions

This study highlighted the potential of prosumer-centric microgrids in enhancing distribution grid performance, particularly under challenging weather conditions. By integrating VPPs into networked microgrids, the research demonstrated the feasibility of developing resilient energy infrastructures capable of withstanding severe weather events. Analyses of the IEEE 34-bus and Indian 52-bus RDSs under various weather scenarios emphasized the approach’s effectiveness, utilizing a 24 h dynamic load pattern for realistic power demand and resource availability. The findings emphasized VPPs’ role in meeting electricity demand, especially in clear weather, while microgrids dynamically adapted to adverse conditions, ensuring continuous power supply to critical loads. EVs proved to be valuable assets for backup power and grid stability. Reliability improved significantly, with notable reductions in SAIFI and SAIDI indices, while stability was enhanced through the deployment of SC. Additionally, emissions were reduced via RDGs, EVs, and BESSs. These findings are critical for policymakers and stakeholders working on the development of resilient, sustainable energy systems. The analysis of MOF values confirmed the superiority of the JSOA algorithm. For the IEEE 34-bus RDS, JSOA achieved a MOF value of 1.1601, outperforming BESA (0.9791) and SMA (0.9053). Similarly, for the Indian 52-bus RDS, JSOA recorded an MOF of 1.0156, surpassing BESA (0.8784) and SMA (0.8119). These results validate JSOA’s ability to minimize system losses and improve reliability, resilience, and stability, making it an optimal solution for enhancing grid performance.

As technology advances and prosumer engagement increases, the vision of a resilient, clean, and community-driven energy future becomes increasingly achievable. However, the large-scale implementation of VPPs faces significant challenges. Key barriers include high infrastructure costs, the need for supportive regulatory frameworks, and the complexities involved in integrating diverse energy resources. Scalability is largely determined by factors such as the availability of reliable communication networks, regulatory incentives for decentralized systems, and the adoption of advanced control and optimization algorithms. Additionally, interoperability issues between DERs, EVs, and storage systems present further challenges, as seamless integration and robust communication protocols are essential. Overcoming these barriers will require ongoing research to develop scalable and cost-effective solutions. Furthermore, collaboration among utilities, policymakers, and technology providers will be essential for enabling broader deployment and ensuring the successful adoption of VPPs, ultimately contributing to a more resilient, sustainable, and reliable energy grid.

6. Suggestions for Future Research

While this study provides valuable insights into the integration of VPPs in microgrids, there are several avenues for future research. One key area is optimizing VPPs for more complex grid structures, including hybrid microgrids that combine RESs with traditional power systems. Future research could focus on developing advanced algorithms to enhance VPP performance in real-time applications, particularly in areas like dynamic demand response, grid stability, and energy storage management.

Additionally, exploring trading mechanisms within VPPs, such as energy markets and peer-to-peer energy trading, could unlock significant value. This research could focus on how VPPs optimize energy exchanges, minimize costs, and provide economic benefits for prosumers. Furthermore, integrating emerging technologies like blockchain for secure, transparent, and decentralized energy trading within VPPs could enhance market efficiency and encourage broader participation.

Furthermore, examining the socioeconomic impacts of widespread VPP adoption—including consumer participation models, regulatory frameworks, and cost–benefit analyses—will be crucial for guiding policymakers. Finally, addressing the interoperability of diverse energy resources and the scalability of VPPs will be essential to their successful deployment at larger scales.