Optimisation-driven technical,economic,and environmental enhancement of renewable and EVCS-integrated faulted Indian distribution networks using DFACTS devices

Abstract

The rising integration of renewable distributed generators (RDGs) and electric vehicle charging stations (EVCSs) in modern distribution networks introduces significant technical, economic, and environmental challenges, particularly under faulted operating conditions. The converter-interfaced characteristics of these sources often reduce system fault current contribution and inertia, leading to degraded voltage and frequency stability. This study proposes an enhanced resilience framework for a faulted Indian 28-bus radial distribution system (RDS) integrated with RDGs and EVCSs through the optimal allocation of Distributed Flexible AC Transmission System (DFACTS) devices ‒ Distribution Static Synchronous Compensator (DSTATCOM), Unified Power Quality Conditioner (UPQC), Distributed Static Series Synchronous Compensator (DSSSC), Distributed Static VAR Compensator (DSVC), and Distributed Thyristor Controlled Series Capacitor (DTCSC). A bio-inspired Black Widow Optimisation (BWO) algorithm is utilised and evaluated against Genetic Algorithm (GA), Particle Swarm Optimisation (PSO), and Marine Predators Algorithm (MPA) for multi-objective optimisation. The combined objective is to get the best environmental performance while minimising technical and economic impacts. BWO consistently beats the other algorithms, with the lowest average total objective (0.487), maximum (0.505), and minimum (0.485) values. It also has a standard deviation of 0.012, an average convergence of 120 iterations, and a CPU time of 8.5 s. Compared to GA, these changes mean that optimisation works up to 16.2% better and calculations are up to 22% faster. The simulation results confirm the concept that the proposed BWO-based model performs well in improving voltage stability, reducing active power loss, improving frequency response, and reducing CO₂ emissions. This suggests that it is robust and can be used to improve supply systems that are rich in renewable resources and prone to breakdowns.

Introduction

The integration of renewable energy and electric vehicle charging systems creates both new opportunities and challenges for grid operators due to the evolving capacity of modern power grids. New sources such as inverter-based generators (solar PV, wind) are replacing conventional generators, which provide power systems with their usual stability. The evolution has seen significant changes in dynamic lightning, increasing power losses and limiting voltage fluctuations. Fault tolerance, all of which are crucial for the proper functioning of modern distribution networks (Escalera et al., 2018; Qays et al., 2022; Yuvaraj et al., 2024b). Solar power (PV) and catalytic converters are rapidly becoming available, and as electric vehicle charging stations (EVCS) become more widespread, the entire electricity grid is being regenerated. This is good for the environment and for business, but it is also very difficult for computers. The reason for this change is that conventional synchronous machines, which previously provided valuable setpoint characteristics such as slowness and false flicker, are increasingly being replaced by inverter-based relays (IBRs). IBRs are inherently electronic-interfaced (Aziz et al., 2023; Wu et al., 2017), but they are less susceptible to any slowness or false flicker (Aziz et al., 2023).

Weak setpoints, increased lightning surges, increased power losses, transient-temporal boundary instability and increased fault-tolerance can easily lead to proven failures. The stability instability of inverter-based synchronous machines is very severe, as the ripples are accelerated. The internal energy of the recovery team can be reduced by the duration of the outage events. In addition, the robust networks with the shortest surrounding flicker levels may not perform well in the first-generation path-cavalry schemes. In addition to the reliability and power density of modern distribution systems, the formation of these problems has severe impacts on the reliability of the grid, which is exacerbated by the occurrence of faults, unstable nature of the grid, and the increasing variability of the load and the increasing variability of the load (Kenyon et al., 2020; Moore et al., 2025). To address these new challenges, we need new approaches that can recover some or all of the lost structures of the system. Possible solutions include improving the robustness of the system, lightning protection, defining the boundary layer, and adding faults in a non-disruptive manner. Current research is needed to address solutions such as distributed discrete AC transformation (DFACTS) devices/devices, and future-proof controls that balance reliability with energy storage integration and energy efficiency growth. High-level, that is, DSTATCOMs, UPQCs, DSSSCs, DSVCs, and DTCSCs have the capabilities (Babu et al., 2025; Iswariya and Yuvaraj, 2022; Khalili et al., 2022; Thirumalai and Yuvaraj, 2021; Yuvaraj et al., 2023a).

DFACTS devices have obvious technical advantages (Suresh et al., 2024). Devices such as DSTATCOM and UPQCs which provide fast reactive power compensation are key to cope with voltage deviations a major concern in networks suffering high amount of variable renewable is penetration (Wu et al., 2017). DSSSCs and DTCSCs are employed to reduce the power losses, which are magnified by many folds in fault and EV charging system loaded to high degree with the help of optimal power flow control. Proper deployment of DFACTS also lead to significant improvements in metrics tied to system reliability (e.g., ENS during faults due to increased fault ride-through and reduced outage durations enabled by DFACTS), as these devices will increase the system level ability to recover from disturbances. Virtual Inertia the new requirement for sys norm operation; Frequency stability is an additional concern with low-inertia systems, and DSVCs as well other advanced compensators can help fit this bill. Last but not the least DFACTS device to the alertness of short circuit ratio (Escalera et al., 2018), which is a very basic measure of system strength and this value rapidly depletes in highly renewable grids (Alajrash et al., 2024; Huadong et al., 2021).

Economically, deployment of DFACTS devices must be considered with an eye to costs and benefits from all levels up to and including system. Although power electronic devices may incur high initial investment, their power loss reduction capability has a tremendous operation cost saving after a certain time in general. As the operation of distributed generator and EVCS by DFACTS control optimise will lower maintenance requirement, increasing equipment life also led to cheaper economic outcomes. The capital costs of the DFACTS devices need not be the only consideration for a cost-benefit analysis, it should also take into account how these will be integrated into a more efficient and reliable system. Using advanced optimisation methods makes it possible to find the best deployment strategies that give the most technical benefits and cost the least amount of money (Yuvaraj et al., 2024c).

Nowadays, with the public more conscious of the use of energy, the environmental implications of deploying DFACTS are more significant than ever. They call for deep reductions in carbon emissions to make space for renewable energy and move away from fossil fuel generation. These integrations help increase the Renewable Energy Utilisation Factor (REUF), meaning that fewer clean energy sources are disconnected and the available renewable assets operate more efficiently. In addition, DFACTS equipment has a longer lifespan, making power systems more resilient and less likely to fail due to increasingly extreme weather patterns caused by climate change. On the one hand, it protects against very small disruptions and on the other hand, stabilises the grid under stress conditions necessary for a broader transition to sustainable energy systems in the future (Aggarwal and Singh, 2023).

In summary, this paper addresses the compelling need for comprehensive multi-objective optimisation of DFACTS tools in distributed systems with a large number of RES and EVCS – an area still lacking in research. The proposed work differs from current work that focuses on single objectives or individual devices by integrating voltage stability, loss reduction, wasted energy, and environmental impacts into a unified optimisation framework, thus encompassing system performance under adverse conditions. This paper presents a Black Widow Optimisation (BWO) algorithm that outperforms traditional metaheuristics such as GA in convergence rate and solution quality for a complex spatial, quantitative problem of multiple DFACTS tools. The approach has been extensively tested under various fault conditions, including single and multiple line-to-ground faults, including dynamic fault ride-through capability and transient support. Also, a comprehensive financial analysis that considers operational costs and capital costs ensures the feasibility of the project. MATLAB simulations of an Indian 28-bus radial distribution network validate the approach and demonstrate that it has distinct technical, economic, and environmental benefits. This research differs from others because it addresses multiple objectives simultaneously, quantitatively compares advanced metaheuristic algorithms, and considers operational problems caused by faults in high-density renewable energy networks. It provides a more practical and robust planning approach for future distribution systems.

Literature review

Consequently, the integration of RESs such as PV systems and WTs with EVCSs in RDS has become one of the most significant research areas. This integration enhances system resilience, reduces operational costs, and supports the achievement of environmental sustainability standards. The deployment of DFACTS devices namely as DSTATCOM, DSVC, DSSSC, UPQC and DTCSC highly contributes to better voltage stability, power losses minimisation and system reliability. Because in distribution grids with high penetration levels of RESs and EVCSs, these devices are very crucial to address issues on power quality, energy delivery and grid stability. Nevertheless, the drawbacks are plenty that are some as configured optimal state, control measures and cost related with these devices. A major study in the field defines a power system resilience index that evaluates the effect of EVCS load on RDS. The issue was identified with power losses and stability issues due to EVCS integration and the mitigation method was proposed which includes using DSTATCOMs along with DG units on the proposed area. In the study, through an appropriate location and sizing by applying spotted hyena optimisation algorithm (SHOA) the integration of EVCS may be increased to reduce power losses as well as improve the system performance (Yuvaraj et al., 2024a). This brings a very useful tool to evaluate technical allowability of EVCS and DFACTS in Indian faulted distribution system with RESs. Intelligent EVCS placement and load management reduce grid stress (Aggarwal et al., 2020, 2024), while swarm and hybrid algorithms improve scheduling and DG–DSTATCOM allocation (Chandra et al., 2025; Vaigundamoorthi et al., 2025). IABC and PSO methods further minimise losses and strengthen voltage profiles (Dashtdar et al., 2022; Djidimbélé et al., 2022). Advanced metaheuristics ‒ including political, sine-cosine, forensic, wombat, and user-centric coordinated optimisation ‒ enhance multi-objective grid performance and EVCS scheduling (Dharavat et al., 2022; Karthik et al., 2024; Malika et al., 2024, 2025b; Nagarajan et al., 2025; Thirumalai et al., 2025). Recent studies also emphasise comprehensive planning through DG and energy-storage coordination (Malika et al., 2025a). Complementary algorithms such as adaptive salp swarm, crow search, and chaotic Bat optimisation further strengthen energy management and dynamic stability (Panda et al., 2024; Selvaraj et al., 2024; Tadj et al., 2024).

Recent research proposes an optimisation technique for selecting the location and size of RDGs, DSTATCOMs and battery energy storage systems (BESS) with that of EVCSs (Babu et al., 2025). Its intention in this research is to decrease the power losses in the RDS through arranging and sizing this equipment's. A study that uses the slime mould algorithm (SMA), compare optimisation results for six diverse scenarios on IEEE 33-bus and 69-bus RDS is presented using SMA. These results clearly show that SMA has more effect in EVCS features, when analysing the issue of EVCSs commissioning (Yuvaraj et al., 2023b) making compensator allocation a more profound challenge (Babu et al., 2025), and thus required efficient allocation methodologies. This is especially important specifically the cost-effective integration of RESs and EVCSs in faulted distribution networks. Moreover, another study investigate the integration of EVCSs and DSVCs with RESs as RDS. It facilitates both Grid-to-Vehicle (G2V) and Vehicle-to-Grid (V2G) modes, which ensure grid flexibility and security. Objective of the research: to minimise the power losses under normal operating state and to reduce energy not supplied (ENS) due fault cases, it optimisation algorithms SHOA along with Genetic Algorithm (GA). IEEE 34-bus RDS simulations confirm that SHOA outperforms GA producing 25% of power losses reduction than the fault conditions system resiliency and energy losses decrease (Babu et al., 2025). This shows the importance for development of reliable optimisation guidelines regarding technical, economic and environmental aspects in fault conditions.

The research on the SCOPE framework presents a multi-objective optimisation strategy aimed at minimising power losses, decreasing bus voltage fluctuations, improving system voltage stability, and reducing CO₂ emissions within the framework of EVCSs. This method uses the improved bald eagle search algorithm (IBESA) to take into account how people drive in the real world and find the best way to connect EVCSs and RESs over a 24-h period. This study uses IEEE 33-bus RDS as a test case to examine the effects of EVCS integration on grid performance, which is a smart Microsoft building. It shows a significant improvement, which requires better design guidelines to deal with the problems that may arise when connecting EVCS and RES. The study of the UPQC-EVCS system advances a novel approach to the degradation of EV grid. This study investigates the application of superconducting magnetic energy storage (SMES) in regulating power surges without DC-side lightning. Two control methods are tested to improve the protection of the fault path by improving the previous language: the fault phase lightning characteristics are controlled by using method 1 and reducing the VA export by using method 2. The results specifically show significant reduction in VA loading and grid current which serves as a potential solution to the integration of EVCSs and RESs in faulted power system (Jin et al., 2022a). This is very important to fulfil the power quality issues in Indian faulted distribution system.

A related work combines the Gradient Boosting Decision Tree (GBDT) algorithm with the jellyfish search (JS) to maximise EVCS embedding in a UPQC architecture. With the goal of enhancing power quality by ameliorating harmonic content or the errant voltage oscillations while embedding RESs (e.g., PV systems). This was numerically evaluated using MATLAB/Simulink to result in considerably less Total Harmonic Distortion (THD) across the total system performance enhancing. The hybrid AI as shown in Prasada Rao et al. (2024) is expected to lower the DERs, including RESs and EVCS integration into faulted distribution system. One of the most critical solutions to optimised solar-powered EVCS connected with grid is the UPQC. In another work, the researchers integrate the Honey Badger Algorithm (HBA) and composite order relation aware recurrent neural networks (MORARNN) for the optimisation of UPQC shunt and series APFs. To decrease overall THD, stabilise DC capacitance voltage and address power quality issues such as voltage sags and swells. Proposed THD 1.5%, as compared to normal methodologies and therefore able to confirm potentiality of this system for power quality improvements in the large demand side fluctuations (SivaramKrishnan et al., 2025).

Despite the developments in bringing together DFACTS devices, EVs, and DERs, there exists a huge gap in research touching on the proper configuration and control schemes that realise the maximum efficiency of the system and the lack of seamless coordination between EVs and the distribution grid. Past research has concentrated on individual aspects of DFACTS or EV integration but not the holistic study that incorporates conventional and innovative techniques for raising efficiency and flexibility in faulted distribution networks. Further, the optimisation of using the flexibility of EVs as reversible loads with DFACTS control systems for augmenting resilience during power system disturbances is an area that requires more research (Mousaei et al., 2023). An investigation proposed the use of SSSC for best location and reference set point placement in certain DFACTS device integration in order to minimise power loss and improve system reliability. Considering the static nature of the operational controls and the system, this research uses the basic principles of the multi-channel bus (MOBBO) approach. The design of the IEEE 57-pass system has shown that the addition of SSSC to the faulted system reduces the computational cost and eliminates the need for maintenance (Galvani et al., 2021). This is an example of the need to integrate improved fault-tolerant methods to meet the technical-economic-aesthetic-cyclic trade-offs in fault-tolerant networks. In addition, a method for interfacing EVCS to UPQC systems using RERNN-SCSO techniques has been proposed. This approach has been used to solve electrical problems such as unbalanced sums, harmonic flicker, and flicker changes. The design results indicated that RERNN-SCSO performs better than conventional approaches due to its low THD under low-voltage and high-surge conditions. This research (Rao et al., 2024a) also confirms the need for innovative power solutions to connect EVCS to faulty distribution systems. When power from RES is not available, when EVCS is required, BESSs have a significant impact on maintaining crit. It is essential to consider how to integrate energy storage systems with the grid. By combining BESSs, RESs, and EVCSs to the extent possible, the grid will be able to manage load changes more effectively, be more dependable in general, and produce less impact on voltage instability during peak load or fault. Tests have revealed that BESS and RESs are more effective together than separately. They not only enhance energy storage, but they also stabilise the grid by offering dispatchable power in real time, particularly during crises (Jin et al., 2022b).

Furthermore, new ways of locating, isolating, and restoring systems following a fault are required in order to make RDS more robust, particularly where there is an issue. Research within the field has been successful due to automated restoration techniques and state-of-the-art fault detection software. Such technologies can assist in maintaining the grid's stability by rapidly identifying issues, which can reduce the duration of power cuts and minimise their detrimental impact. Applying machine learning-oriented approaches can enable it to detect defects in a more rapid and correct manner, which will enable it to recover from system faults easily (Pal et al., 2024). The latest developments in IoT technology and smart grid technology also enable the enhancement of the integration optimisation of DFACTS, RESs, and EVCSs. IoT sensors that enable real-time monitoring and control can be incorporated into EVCSs and RESs to enable them to operate more efficiently with the grid. This enables better management of the energy flow, perform preventive maintenance, and increase the grid's ability to handle changes in load. IoT sensors may also provide real-time feedback regarding the performance of DFACTS devices to ensure their optimisation always aligns with changing grid needs (Rao et al., 2024b).

Recent advances in predictive and adaptive control for real-time coordination of DFACTS–DER have demonstrated considerable potential for enhancing the stability and resilience of the grid when it is running in a faulty and dynamic manner. Model Predictive Control (MPC) and adaptive distributed controllers based on phasor measurement unit (PMU) feedback enable taking corrective action in advance and coordinating the regulation of set points for STATCOMs, SSSCs, and other DFACTS devices. This effectively reduces settling time and lowers post-fault oscillations. Event-driven and time-delays-aware distributed control architectures make systems even more resilient against communication delays and network issues, ensuring that coordinated DFACTS and DER devices operate reliably. Learning-based controllers, such as reinforcement learning and neural-adaptive controllers, have also proved very versatile by enabling online gain adjustment to address operating points with changing conditions as well as huge variability in renewable energy. These approaches interact to enable easier collaboration between DFACTS, DERs, and EVCSs in real-time, accelerating restoration, maintaining voltage and frequency stability, and enhancing the cyber-resilience of renewable-integrated distribution networks (Ge et al., 2021; Liu et al., 2023; Nawaz et al., 2025; Razmi et al., 2022).

In summary, tremendous progress has been achieved in interconnecting EVCSs and RESs to DFACTS devices. Further work is required, however, to identify the optimal configuration and control techniques that consider technological, financial, and environmental constraints. The current gap is intended to be bridged in this research with a consideration of innovative strategies of integrating DFACTS, EVCS, and RESs in faulty Indian distribution systems. The emphasis is on optimisation techniques which minimise power loss, make systems more robust, and facilitate sustainability. If all these technologies ‒ EVCSs, RESs, DFACTS, energy storage, and improved fault management ‒ are brought together, power distribution networks would look very different. To ensure integration effectively, you must understand a great deal about system dynamics, optimisation techniques, and how system components interact with each other. The future of grid resilience will be based on our ability to continually come up with new solutions to technical, financial, and environmental issues. This project seeks to stabilise and make more efficient Indian distribution networks that are not functioning effectively by refining existing models and algorithms. This will enable all customers to obtain a consistent, long-lasting, and affordable power supply.

Research gaps

Since RES and EVCS are always on and off, their rapid integration into RDS has created a lot of problems in their mode of operation. Because of this, the system is now vulnerable and prone to failure due to low fault current levels and low inertia. Although DFACTS devices such as DSTATCOMs, UPQCs have proven to be good options for making systems more resilient, there are still some key areas that are lacking in research. This is being looked at for the first time because most of the research that came before it focused on EVCS and DG integration, with little to no work on EVCS and DFACTS integrated systems. This study examines the enhancement of grid performance through the integration of DFACTS devices with EVCS and RESs, particularly in faulted scenarios. Second, the current methods do not have any systematic multi-objective planning frameworks (MOFs) that take into account the technical, financial, and environmental effects of deploying DFACTS. Most of the methods we currently use do not take into account important factors such as the lack of isolation of these objectives. All of these are important to ensure that the system is working properly and that the error is increased in the system that is not working properly. This difference is especially evident in settings with a large number of EVCS and renewable energy sources.

In addition, recent research shows that when planning DFACTS settings for faulty structures, the full life cycle cost (including capital expenditure (CAPEX) and operating expenditure (OPEX)) is not taken into account. The previous solutions are not very useful because they do not take into account how they affect the economy. All optimisation methods, such as GA and PSO, are complex in terms of DFACTS space and dimensions, and are stuck in a linear or local optimisation when used to solve non-native problems. There is room for new, biologically inspired metaheuristics, such as the Spade Hyena Optimiser Algorithm (SHOA), which strikes a fine balance between testing and validation. Finally, studies have not investigated how DFACTS devices can work in conjunction with advanced technologies such as BESS, RESs, and EVCS, so this system still seems to be a work in progress. Furthermore, the use of AI-driven prediction and adaptive control structures for DFACTS in dynamic load management has not been widely explored. This gap highlights the need for more research to address the increasingly complex challenges posed by the increasing integration of EVCS and RES in distributed networks.

Research contributions

The main contribution of this work is the development and validation of a novel optimisation framework for DFACTS device strategic planning for enhancing system robustness, resilience, and economic efficiency for integrated renewable weak distribution networks. The precise contributions are as follows:

Proposed a multi-objective planning framework that optimises voltage stability, power loss reduction, ENS, and environmental impacts, ensuring a holistic system enhancement under faulted conditions.

Developed the BWO algorithm to address the complex issue of determining optimum locations and sizes for the DFACTS devices, demonstrating that it converges quicker and presents optimum solutions compared to other algorithms.

Evaluated the DFACTS deployment strategy in a variety of fault conditions, including single and multiple line-to-ground faults, to determine how well it would perform dynamic fault ride-through and supply temporary system support.

Incorporated a comprehensive cost analysis involving both capital and operational expenditures, ensuring economically viable planning throughout the lifecycle of DFACTS devices.

Validated the proposed approach on the Indian 28-bus radial distribution system using MATLAB-based simulations, confirming its applicability and robustness in realistic operating conditions.

Compared BWO to GA, PSO, and MPA to show how well it works to improve voltage stability, lower losses, and make the system more resilient when the grid is under stress, especially in systems with a lot of RDGs and EVCSs.

Mathematical modelling of post-fault RDS parameters

After a major fault that disconnects the main grid, only DERs such as compensation from the Indian 28-bus RDS, PV systems, WT, EVCSs, and DFACTS devices can be used. In this case, the performance of the grid is closely monitored in three key areas: technical, economic, and environmental. These metrics are mathematically defined to optimise system performance and fully evaluate solutions. The technical aspect is to ensure that the grid is stable, minimise power losses, and ensure that the grid is reliable. The economic aspect examines how much it costs to operate DERs and DFACTS devices and how these affect the operation of the grid. The last part, the environmental part, is about reducing carbon emissions, using more renewable energy, and using renewable resources in a smart way. These formulations make it possible to improve the performance of the grid in a complete way when there are problems. Figure 1 shows the overall layout of the proposed distribution network, which includes DGs, EVCS, and DFACTS devices.

Figure 1.

Single line diagram of proposed work.

Technical parameters

Voltage profile improvement

Voltage profile improvement is an important parameter for evaluating the overall performance of an RDS, especially under fault conditions. Instability in the system is caused by voltage deviation from the nominal voltage, and it may result in equipment malfunction, voltage dips, or over-voltage conditions. Voltage profile improvement here is considered as the summation of the absolute voltage differences between the voltage at each bus and the reference voltage. This deviation needs to be kept to a minimum so that the system is within the acceptable voltage limits for both system reliability and effective power delivery. The voltage profile improvement equation is as follows:

$$V_{dev}=\sum _{i=1}^N|V_i-V_{ref}|$$

(1)

Where, $V_i$ is the voltage magnitude at bus i, $V_{ref}$ is the reference voltage (usually 1.0 p.u.) and N is the total number of buses in the system.

Power loss minimisation

Power losses in the RDS are caused by the intrinsic resistance in the transmission lines. Reduction of these losses is essential for minimising the cost of operation and improving energy efficiency in the system. The active power loss overall can be expressed as the total of losses at all buses taking into account the active and reactive power and line resistance. The objective is to reduce these losses using optimal placement of EVCS, DGs and DFACTS devices. The power loss minimisation equation is:

$$P_{loss}=\sum _{i=1}^N\sum _{j=1}^N{R}_{ij}\cdot {\displaystyle \frac{P_i^2+Q_i^2}{V_i^2}}$$

(2)

Where, $R_{ij}$ is the resistance between buses i and j, $P_i$ and $Q_i$ are the active and reactive power at bus i and $V_i$ is the voltage at bus i.

ENS

ENS is a measure of the amount of energy that is curtailed or not supplied during a fault condition in the system. This is an important parameter to evaluate how resilient the RDS is to disruptions caused by faults. It has a direct effect on how happy customers are and how well the business runs. To get the ENS, you multiply the load that was cut off by the time the system was down:

$$ENS=\sum _{i=1}^N{L}_i\cdot t_i$$

(3)

Where, $L_i$ is the load curtailed at bus i and $t_i$ is the duration of outage at bus i.

Frequency regulation

Frequency regulation ensures that the system operates at a constant frequency, which is usually around the nominal frequency (50 Hz). Frequency fluctuations can occur after a fault when generation and load are unbalanced. DERs or DFACTS devices help bring the system frequency back to a normal value. The formula for frequency deviation is:

$$\mathrm{\Delta }f=f_{nom}-f_{meas}$$

(4)

Where, $f_{nom}$ is the nominal frequency (50 Hz) and $f_{meas}$ is the measured frequency during operation.

Short circuit ratio (SCR)

SCR is a way of measuring how robust a system is; it shows how well it can handle faults without creating large transient changes. A more robust building has a higher SCR. In this study, we will use SCR to test how stable it is after a fault, especially when it comes to renewables and DERs. You can define SCR as:

$$SCR={\displaystyle \frac{S_{SC}}{P_{load}}}$$

(5)

Where, $S_{SC}$ is the short-circuit capacity at the bus and $P_{load}$ is the active power demand at the bus.

Economic parameters

Cost of energy losses

The economic cost of energy loss is an important factor in determining how well an electricity distribution system operates. To find the cost of energy loss, you multiply the total amount of energy lost by the cost per unit of energy. The formula to find the amount of energy loss is:

$$C_{loss}=P_{loss}\cdot T\cdot C_{unit}$$

(6)

Where, T is the duration in hours and $C_{unit}$ is the cost per unit energy lost (USD/kWh).

DG and EVCS operational cost

The operating cost of DGs and EVCSs includes the cost of fuel for DGs and the cost of charging and discharging EVs. This cost is usually determined by the number of devices in the system, the time they are used, and the fuel and operating costs of each device. The formula to find out how much it costs to run DGs and EVCS is:

$$C_{DG\mathrm{\&}EVCS}=\sum _{t=1}^T\left(\sum _{i=1}^{N_{DG}}{C}_{DG,i}(t)+\sum _{j=1}^{N_{EV}}{C}_{EV,j}(t)\right)$$

(7)

Where, $C_{DG,i}$ and $C_{EV,j}$ are the operational costs for DGs and EVCSs at time t.

DFACTS device cost

DFACTS devices are more durable, but they have their own costs for installation and use. If you think using these devices makes sense, you should think about these costs. The total cost of DFACTS devices is the sum of the costs of installing each device over time:

$$C_{DFACTS}=\sum _{l=1}^{N_{DFACTS}}(C_{install,l}+C_{oper,l}\cdot T)$$

(8)

Where, $C_{install,l}$ is the installation cost of DFACTS device l and $C_{install,l}$ is the operational cost per hour for DFACTS device l.

Environmental parameters

Carbon emission reduction

When RES is added, the carbon footprint is a major environmental factor. It is the difference between the carbon emissions from conventional generation and the emissions from renewable generation that are reduced. The formula for carbon footprint reduction:

$$E_{C{O}_2}=\sum _{i=1}^N{E}_{conv,i}-OF{F}_{RES,i}$$

(9)

Where, $E_{conv,i}$ is the emission from conventional supply and $OF{F}_{RES,i}$ is the emission offset by RES generation.

Renewable penetration index (RPI)

RPI shows how much of the total energy supplied to the system comes from renewable sources. The higher the RPI, the more the elements that are interesting to build, the more RPI is calculated, and the more the following:

$$RPI={\displaystyle \frac{E_{RES}}{E_{total}}}$$

(10)

Where, $E_{RES}$ is the energy supplied from renewable sources and $E_{total}$ is the total energy supplied to the system.

REUF

REUF shows how well the available renewable energy is being used. This factor is used to see how well renewable energy is being used, especially in organisations that do not always operate. To find the REUF, use this formula:

$$REUF={\displaystyle \frac{E_{RES-utilized}}{E_{RES-available}}}$$

(11)

Where, $E_{RES-utilized}$ and $E_{RES-available}$ are the utilised and available the energy supplied from renewable sources respectively.

DFACTS modelling

DFACTS devices are very important to make the system more stable, especially when faults occur or when RES and EVCS are added. They help to keep the lightning levels stable, control the lightning flow, keep the boundary layer stable, and also prevent small outages. RES, such as solar and wind, reduces the voltage drop by changing the voltage and current. DFACTS devices, such as DSTATCOM and DTCSC, help to reduce these effects by maintaining the voltage and current. EVCSs allow power to flow in both directions, but the DFACTS devices handle these changes in the structure of the device. To strengthen the grid, DFACTS devices are needed to address the issues that come with a large amount of renewable energy and EV integration.

DSTATCOM

DSTATCOM is used in RDS to improve voltage stability and compensate for reactive power. It gives reactive power injection to help keep the voltage stable, especially in places where the voltage profile is weak. DSTATCOM gives off reactive power in the following way:

$$Q_{inj}={\displaystyle \frac{V_i^2}{X_{DSTATCOM}}}$$

(12)

Where, $X_{DSTATCOM}$ is the equivalent reactance of the DSTATCOM device.

UPQC

UPQC combines series and shunt power quality conditioning to fix problems with power quality like voltage sags, harmonics, and others. The UPQC operates by injecting series voltage and shunt current to stabilise the system's voltage and current profiles. The model can be simplified as:

$$Q_{v,i}^{UPQC}=V_{inj}^{series}+I_{inj}^{shunt}$$

(13)

Where, $Q_{v,i}^{UPQC}$ is the voltage and current control using UPQC.

DSSSC

DSSSC is a series-connected device that provides compensation for reactive power and helps control power flow in transmission lines. The power flow is modified by injecting a compensating voltage in series with the transmission line:

$$P_{flow}={\displaystyle \frac{V_i.V_j}{X_{line}}\sin (\delta +{\delta }_{DSSSC})}$$

(14)

Where, $V_i$ and $V_j$ are the voltages at buses i and j, $X_{line}$ is the line reactance and ${\delta }_{DSSSC}$ is the phase angle injected by the DSSSC.

DSVC

DSVC helps in controlling the voltage by adjusting the shunt reactive power compensation. It improves system voltage profile and reduces voltage fluctuations by controlling the voltage through variable shunt admittance:

$$Q_{comp}^{DSVC}=V^2\cdot Y_{DSVC}$$

(15)

Where, $Y_{DSVC}$ is the variable shunt admittance of the DSVC.

DTCSC

DTCSC changes the line reactance in real time to make the power flow better and the voltage more stable. To lower gearbox losses and make the line more loadable, the effective reactance is changed:

$$Q_{eff}^{DTCSC}=X_{line}-X_{DTCSC}$$

(16)

Where, $X_{DTCSC}$ is the reactance introduced by the DTCSC device.

These DFACTS devices are important parts of making the RDS work better technically, economically, and environmentally, especially after a fault. These devices can greatly improve the grid's resilience, efficiency, and stability by regulating voltage, reducing losses, and improving power flow during faults.

Objective function formulation

This study formulates a multi-objective optimisation problem with three main domains: technology, economics, and environment. The goal is to make the post-fault RDS more resilient and better at what it does. A sub-objective function for each domain contributes to the overall performance of the system. The main objective is to minimise the weighted sum of the total objective function F_total. This makes the grid more stable, lowers operating costs, and makes it more stable under fault conditions.

Technical objective function – minimisation

The technical performance of the RDS after the fault is assessed using parameters such as voltage deviation, power loss, ENS, frequency deviation, and SCR. The parameters represent the reliability, efficiency, and toughness of the grid after faults. Reducing the technical objective function $F_{tech}$ guarantees better voltage profiles, loss reduction in the system, increase in load-serving capability, and stable dynamic performance under contingency conditions.

$$min{F}_{tech}={\omega }_1\cdot V_{dev}+{\omega }_2\cdot P_{loss}+{\omega }_3\cdot ENS+{\omega }_4\cdot f_{dev}+{\omega }_5\cdot \left({\displaystyle \frac{1}{SCR}}\right)$$

(17)

Economic objective function – minimisation

The economic objective ( $F_{econ}$ ) deals with the requirement for the cost-efficient operation of the distribution system in faulted conditions as well as in post-fault conditions. It encompasses minimizing cost of power loss, DER and EVCS operation costs, as well as the investment cost and operating cost of DFACTS devices. Reduction of these costs makes the financially viable operation of the resilient system and supports efficient use of the available infrastructure.

$$min{F}_{econ}={\omega }_6\cdot C_{loss}+{\omega }_7\cdot C_{DG\mathrm{\&}EVCS}+{\omega }_8\cdot C_{DFACTS}$$

(18)

Environmental objective function – minimization

The environmental goal aims at encouraging sustainable and environmentally friendly operation of the post-fault RDS through enhancement of the contribution and optimal utilization of RESs. Three such key indicators: carbon emission reduction, renewable penetration, and renewable utilization, are used in combination to evaluate the system's environmental performance. Optimization of these parameters facilitates reducing the reliance on fossil fuels, the minimization of greenhouse gas emissions, and enhancing the overall ecological footprint of the grid under resilient mode. The environmental objective function $F_{env}$ is defined as:

$$max{F}_{env}={\omega }_9\cdot E_{C{O}_2}+{\omega }_{10}\cdot RPI+{\omega }_{11}\cdot REUF$$

(19)

Main objective function – aggregated minimization

To maximize the post-fault resilience, sustainability, and operational efficiency of the RDS, this research develops a composite multi-objective function. The primary aim is to reduce the total technical and economic effects while maximizing the environmental gains such that the optimum grid performance in and after severe conditions is assured. The aggregate objective function $F_{total}$ is expressed as:

$$min{F}_{total}=\alpha \cdot F_{tech}+\beta \cdot F_{econ}-\gamma \cdot F_{env}$$

(20)

The letters α, β, and γ stand for the main weights given to the technical, economic, and environmental goals, respectively. The letters ${\omega }_1$ to ${\omega }_{11}$ stand for the secondary weights within each sub-objective domain. In this study, all three main goals are equally important, with α = β = γ = 1/3. This shows that technical performance, cost-effectiveness, and environmental sustainability are all equally important. This equal weighting approach makes sure that the optimisation process gives each domain the same level of importance. This leads to a general improvement in voltage stability, lower operating costs, and more use of renewable energy in the resilient distribution system.

Solution technique using black widow optimizer

Overview of BWO

The BWO, a powerful and modern evolutionary algorithm, is used in this research for optimal positioning and dimensioning of DFACTS devices in an RDS. The central aim is enhancing the overall performance of the grid by reducing technical losses, decreasing operational expenses, and reducing environmental factors such as CO₂ emissions. BWO is founded on the peculiar biological habits of black widows, particularly how they mate and whom they eat. It utilizes these habits as means of selecting, reproducing, mutating, and survival of the fittest. These processes enable an adaptive and fair trade-off between exploration (finding new regions) and exploitation (improving already working solutions), preventing premature convergence and improving the quality of solutions in complex, multi-objective optimisation problems such as DFACTS allocation (Hayyolalam and Kazem, 2020).

Justification for choosing BWO

• Improved optimisation performance: According to research, BWO always achieves a faster convergence rate, improved global optimum, and reduced solution variance compared to most classical meta-heuristics. For example, BWO has been proved to outperform common algorithms in engineering optimisation problems (Hayyolalam and Kazem, 2020; Velasco et al., 2024).

• Robust against local minima: The cannibalism-inspired approach ensures that poorer solutions are eliminated, which enhances population diversity and lessens the chances that individuals will be trapped in local optima (Velasco et al., 2024; Wei et al., 2025).

• Efficient and flexible with parameters: BWO requires fewer control parameters than certain other swarm-based algorithms, which simplifies the tuning in engineering applications (Velasco et al., 2024).

• Efficient for multi-dimensional problems with many objectives: Its reported application on a wide range of fields ‒ including power-system optimization ‒ indicates its versatility and adaptability under multiple constraints and dual criteria (Wadhwa and Gupta, 2023).

BWO is employed here to enhance voltage profiles, reduce power losses, reduce yearly energy expenses, and reduce carbon emissions through the integration of varying types of DFACTS devices. This makes power-distribution networks more sustainable and resilient.

BWO implementation for DFACTS device optimized allocation in RDS

The implementation of the BWO algorithm for allocating DFACTS devices follows the steps below and is represented in the flowchart presented in Figure 2:

Figure 2.

Flowchart for allocation of DFACTS.

Step 1 ‒ Data Input, Initialization, and Parameter Sensitivity:

Input RDS's line and load data, operational constraints, DFACTS device specifications, and BWO parameters, including:

The population size (N = 40).

Most iterations (iter_max = 100)

The sizes of control variables (D) vary with the number and type of DFACTS devices being considered.

A base-case power flow is performed to obtain the reference performance indices, including system loss, voltage deviation, Voltage Profile Index (VPI), Voltage Stability Index (VSI), operating cost, and CO₂ emissions. At the time of algorithm development, parameter sensitivity and convergence diagnostics were performed to ensure that the algorithm was robust and reliable. On running it several times, population size and maximum number of iterations were selected to optimize a trade-off between precision and speed of convergence. A population size in excess of 40 did little to improve it while increasing CPU time, while populations that were too small sometimes led to premature convergence. Similarly, the limit of 100 iterations ensured that objective function values remained constant over several trials, resulting in global convergence.

To maintain diversity in the search space and prevent it from converging prematurely, the mutation and crossover chances within BWO were fixed between 0.2 and 0.4. Diagnostic results on convergence indicated that BWO achieved stable objective values in 70–80% of all iterations. This indicated that it possessed a robust and adaptive balance of exploration and exploitation in comparison to other algorithms such as MPA, PSO, and GA. All the configurations combined ensured that the system performed optimally, could be replicated, and was stable in all the tests.

Step 2 ‒ Population Initialization:

Each candidate solution (black widow) represents a potential allocation plan of DFACTS devices and is composed of:

Lo.DFACTS: Bus locations for DFACTS installation (excluding slack bus)

Size.DFACTS: Device sizes (within min–max operational reactive power limits)

Initialization is done using:

$$Lo.DFACT{S}_i=round[L{o}_{lb}+rand(0,1)\times (L{o}_{ub}-L{o}_{lb})]$$

(21)

$$Size.DFACT{S}_i=round[Siz{e}_{lb}+rand(0,1)\times (Siz{e}_{ub}-Siz{e}_{lb})]$$

(22)

Step 3 ‒ Objective Function Evaluation:

Evaluate each candidate using a multi-objective fitness function in equation (20) that combines:

Technical: Total real power loss minimization

Economic: Reduction in total annualized cost of losses and device deployment

Environmental: Minimization of CO₂ emissions due to loss-related generation

Step 4 ‒ Selection:

Select top-performing solutions based on fitness scores to act as parents.

Step 5 ‒ Procreation and Cannibalism:

Perform crossover to generate offspring. The fitter parent (mother) survives, while the weaker one (father) is eliminated. A portion of the least-fit offspring is also removed based on a cannibalism rate to retain only the most competitive solutions.

Step 6 ‒ Mutation:

Random mutations are applied to a subset of solutions to maintain diversity and improve exploration capability.

Step 7 ‒ Population Update:

The new generation of solutions is formed by combining the elite survivors and mutated offspring:

$$W_{pop}=W_{pop2}+W_{pop3}$$

(23)

Step 8 ‒ Convergence Check:

If convergence criteria are met (e.g., no significant improvement over several generations), stop; otherwise, return to Step 3.

Step 9 ‒ Output Best Solution:

Identify and store the best solution based on the overall fitness score. Calculate detailed performance indices such as:

Lowered real and reactive power losses

Better voltage profiles and stability indices

Lower costs for energy and CO₂ emissions

Step 10 ‒ Termination:

Stop the algorithm and report the best DFACTS allocation configuration along with its measured benefits.

Results and discussion

Basic system and description

The Indian 28-bus RDS is a widely used benchmark model for testing how well optimisation, control, and planning strategies work in distribution networks. The system was first made to work like Indian urban and semi-urban feeders. It has 28 buses and 27 branches, and it can handle a total real and reactive power demand of about 2.445 MW and 1.232 MVAR, respectively (Thangaraj, 2019). It works at a nominal voltage of 11 kV and a system base of 10 MVA. This makes it good for analysing networks with a high resistance-to-reactance (R/X) ratio, which is a common feature of Indian distribution systems. Indian 28-bus RDS was selected as it is representative, dependable, and applicable to a wide variety of analyses. The radial structure, natural loading pattern, and middle-sized network provide the ability to properly test DG integration, voltage control, and robustness enhancement. It has been extensively tested in other research and effectively displays actual-world issues such as high R/X ratios, voltage sag, and losses typical of developing distribution systems. This research employs a marginally modified version of the Indian 28-bus RDS with the nominal system frequency kept at 50 Hz to align with regional grid standards. The modifications facilitate the introduction of DERs, energy storage, and elements that enhance the system's resilience without affecting the operation of the benchmark system.

Faulted Indian 28-bus RDS without DFACTS

The Indian 28-bus RDS has strategically integrated renewable DGs such as PV arrays and WTs with EVCSs to increase the sustainability of the system and promote the consumption of green energy. Table 1 provides much information regarding where these devices are being installed, how many, and how much power they can consume. Five PV-based DG units have been installed on buses 5, 8, 12, 17, and 21. Each unit has an addition of 50 kW, totaling 250 kW of PV power. Five WT-based DG units have also been installed on buses 6, 10, 15, 20, and 26. Each unit has an addition of 60 kW, giving a total of 300 kW of wind power. There are also five EVCSs installed on the network at buses 7, 11, 16, 22, and 25. The load on each of these charging stations is 50 kW, so the total load on the EVCSs is 250 kW. Sensitivity analysis of voltage deviation and line loading indices was employed to determine where to install and how many DFACTS units to install. This ensured that the technical effect was as great as could be while installation costs were as minimal as could be. Buses that experienced large voltage drops and traffic congestion in their branches when there was a fault or excessive load were prioritized. In the process of siting, practical constraints such as accessibility, space available close to substations, and feasibility of realistic implementation were also considered.

Table 1.

Deployed RDGs and EVCS devices.

Devices	Units deployed	Locations (bus no.)	Total capacity installed (kW)
PV DG	5	5, 8, 12, 17, 21	250 (5 × 50 kW)
WT DG	5	6, 10, 15, 20, 26	300 (5 × 60 kW)
EVCS	5	7, 11, 16, 22, 25	250 (5 × 50 kW)

Although there are obvious advantages to bringing together RDGs and EVCSs, such as reducing carbon emissions, adding more sources of energy, and enhancing electric mobility, it also makes the grid much more challenging to operate. The variable and shifting charging requirements of EVCSs combined with the intermittent output of renewables expose the system to more vulnerabilities. This can result in power losses, voltage instability, and potential reliability issues if something fails. This research considers the reduced performance of the Indian 28-bus RDS under such disturbances and emphasizes the need for advanced grid-support solutions, like DFACTS devices. These devices are highly critical to minimize the voltage fluctuation, enhance reactive power management, and restore the network to a normal state. When a fault occurs, impacted buses are isolated to form microgrids (MGs), which allow local RDGs to maintain power supply to critical loads. This fault-ride-through approach not only makes the system more robust, but it also ensures that renewable sources are utilized to their maximum and service disruptions are as minimal as possible when faults occur.

Figure 3 shows the Indian 28-bus RDS scenario, where bus 1 has a 24-h fault, which disconnects the entire structure from the grid. In this case, the important sums are transferred to the network MG operation. In the islanded mode, the RDGs such as PV arrays, catalase visas, and EVCSs that are available for maintenance support, support the sums of the organization, ensuring continuity within the service range and working together. Even if the configuration can be changed, its technical, economic and environmental performance shows a big drop when the fault occurs without DFACTS support. The entire configuration has a lightning discharge of 0.084 p.u. 185.6 kW active power. The total ENS is 128.5 kWh, which means that there are many service interruptions. The boundary deviation (Δf) is 0.36 Hz, and the SCR drops by 2.8, which shows the weakening of the system strength and stability.

Figure 3.

Faulted Indian 28-bus RDS without DFACTS.

The cost of power losses rises to USD 29.70 per kWh, and the total operational costs for the deployed DGs and EVCSs rise to USD 82.3 per kWh during the faulted state. This is a big financial burden. The inefficiency during the fault causes CO₂ emissions to rise, and the amount recorded was 72.5 tonnes. The RPI is 32.8%, and the REUF is 78.4%. This shows that renewable resources are not being used enough during contingency operations. These results clearly show that MG formation can help lessen the effects of system faults to some extent, but without DFACTS devices, voltage profiles are poor, losses are higher, and the system as a whole is less resilient.

Faulted Indian 28-bus RDS with DFACTS

Figure 4 shows the broken Indian 28-bus RDS that works with DFACTS devices. In this study, several commonly used DFACTS devices, such as DSTATCOM, UPQC, DSSSC, DSVC, and DTCSC, are used in a planned way to improve grid performance when there are faults. We chose these devices because they help reduce voltage instability, reduce power losses, and make the system more reliable overall. This study is divided into five different cases that examine how different DFACTS devices affect performance.

Figure 4.

Faulted Indian 28-bus RDS with DFACTS.

Table 2 shows a summary of the deployment details, including the type of device, where it will be installed, and the maximum number of users it can handle. In all cases, DFACTS devices are always placed on Bus 14 and Bus 18, which maintains the same installation sites and ensures that the evaluation framework is fair and consistent. The number of units and their positions are the same in all comparisons. However, the optimisation algorithms within the specified maximum capacity limits determine the best size (capacity) for each DFACTS device. The BWO algorithm is used to test the proposed method's effectiveness, and its performance is compared to that of the traditional GA. This comparative analysis shows that the BWO approach works better than the other DFACTS scenarios in terms of technical, economic, and environmental outcomes. The proposed methodology shows that it can greatly improve the resilience and efficiency of the faulty distribution system by optimising the allocation of capacity based on the changing needs of the system.

Case 1: Faulted RDS with DSTATCOM

Table 2.

Total capacity installed DFACTS devices in the RDS.

Case	DFACTS type	Locations (bus no.)	Total capacity installed (kW/kVAr) per device
Case 1	DSTATCOM	14, 18	150 kVAr
Case 2	UPQC	14, 18	100 kW/100 kVAr
Case 3	DSSSC	14, 18	±50 kVAr
Case 4	DSVC	14, 18	150 kVAr
Case 5	DTCSC	14, 18	±40 kVAr

In this case, the performance of the faulty Indian 28-bus RDS is tested by adding DSTATCOM devices. As we talked about before, the best place to put the items is at Buses 14 and 18. The performance comparison is conducted among the system devoid of DSTATCOM, the system with DSTATCOM optimised by GA, and the system with DSTATCOM optimised by the proposed BWO algorithm. Table 3 shows the numbers for technical, economic, and environmental factors in different situations. Figure 5(a)–(c) also shows how the system's performance gets better with and without DSTATCOM.

Technical Performance: As seen in Figure 5(a), the incorporation of DSTATCOM considerably enhances important technical parameters. Improved voltage profiles are indicated by a decrease in voltage deviation from 0.084 p.u. (without DSTATCOM) to 0.032 p.u. with BWO optimisation and to 0.028 p.u. with GA. Higher load reliability is ensured as ENS drops from 128.5 kWh to 62.3 kWh (BWO) and 65.1 kWh (GA), and power loss drops from 185.6 kW to 94.8 kW (BWO) and 98.5 kW (GA). System stability is improved as the frequency deviation (Δf) drops from 0.36 Hz to 0.18 Hz (BWO) and 0.21 Hz (GA). Stronger fault ride-through capability is indicated by an improvement in SCR from 2.8 to 4.1 (BWO) and 4.0 (GA).

Economic Performance: As seen in Figure 5(b), the implementation of DSTATCOM results in a thorough cost reduction. While the operational costs of DG and EVCS decrease from 82.3 USD/kWh to 80.1 USD/kWh (BWO) and 81.2 USD/kWh (GA), the power loss cost drops from 29.70 USD/kWh (without DSTATCOM) to 13.73 USD/kWh (BWO) and 14.14 USD/kWh (GA). Combined with the capital cost of using DSTATCOM (0.18 USD/kWh for BWO and 0.20 USD/kWh for GA), this is the lowest cost of public finance. Furthermore, the scenario analysis reveals that BWO continues to pay for itself with low overall operating and investment costs under various fault conditions, while reducing energy losses and demonstrating a low cost-effectiveness in terms of the use of ancillary equipment and the risk of equipment failure. In terms of cost-benefit balance, this extensive economic analysis suggests that BWO provides a very useful allocation incentive.

Environmental Performance: Figure 5(c) shows that total CO₂ emissions decreased from 72.5 tonnes (without DSTATCOM) to 38.4 tonnes (BWO) and 40.2 tonnes (GA). As a result of increased environmental sustainability and better use of renewable resources, RPI rises from 32.8% to 58.7% (BWO) and 57.1% (GA), while REUF increases from 78.4% to 87.5% (BWO) and 85.9% (GA).

Figure 5.

Comparison of system performance with/without DSTATCOM (Case 1): (a) technical parameters, (b) economic parameters and (c) environmental parameters.

Table 3.

Comparison of various parameters with and without DSTATCOM under various algorithms.

Parameters	Metrics	Without DSTATCOM	With DSTATCOM (BWO)	With DSTATCOM (GA)
Technical	$V_{dev}$ in p.u	0.084	0.032	0.028
	$P_{loss}$ in kW	185.6	94.8	98.5
	ENS in kWh	128.5	62.3	65.1
	Δf in Hz	0.36	0.18	0.21
	SCR	2.8	4.1	4.0
Economic	$C_{loss}$ in USD/kWh	29.70	13.73	14.14
	$C_{DG\mathrm{\&}EVCS}$ in USD/kWh	82.3	80.1	81.2
	$C_{DFACTS}$ in USD/kWh	0	0.18	0.20
Environmental	$E_{C{O}_2}$ in tons	72.5	38.4	40.2
	RPI in %	32.8	58.7	57.1
	REUF in %	78.4	87.5	85.9

When compared to the system without DSTATCOM, both GA and BWO optimisation greatly improve technical, economic, and environmental performance. BWO's superior voltage profile improvement, increased reliability, and improved environmental results validate its efficacy in boosting resilience and sustainability in faulted distribution networks.

(ii) Case 2: Faulted RDS with UPQC

In this instance, UPQC devices are integrated and the performance of the malfunctioning Indian 28-bus RDS is evaluated. As was previously mentioned, Buses 14 and 18 are the best locations for the UPQCs. Three scenarios ‒ without UPQC, with UPQC optimised by GA, and with UPQC optimised by the suggested BWO algorithm ‒ are used to compare the system's performance. Table 4 presents the detailed results, and Figure 6(a)–(c) shows the improvement trends graphically.

Technical Performance: After the deployment of UPQC, the technical performance measures reflect significant improvement, as evident from Figure 6(a). Improved voltage stability is observed from the reduction in voltage deviation from 0.084 p.u. (without UPQC) to 0.035 p.u. (BWO) and 0.038 p.u. (GA). Due to improved load reliability, the loss of power lowers considerably from 185.6 kW to 95.1 kW (BWO) and 98.7 kW (GA), and the ENS lowers from 128.5 kWh to 61.5 kWh (BWO) and 64.8 kWh (GA). SCR improves from 2.8 to 4.2 (BWO) and 4.1 (GA), and frequency deviation (Δf) is enhanced from 0.36 Hz to 0.15 Hz and 0.17 Hz (BWO) and GA, representing enhanced system resiliency and fault ride-through.

Economic Performance: As indicated in Figure 6(b), financial benefits to UPQC integration are substantial. Power loss cost reduces from 29.70 USD/kWh (without UPQC) to 12.80 USD/kWh (BWO) and 13.30 USD/kWh (GA). The cost of operation of EVCS and DG reduced from 82.3 USD/kWh to 80.4 USD/kWh (GA) and 79.0 USD/kWh (BWO). UPQC is found to have negligible incremental installation cost (0.20 USD/kWh for BWO and 0.22 USD/kWh for GA). Total cost saving is significant, implying that BWO ensures cost-efficient use of resources under a variety of faulted conditions apart from reducing energy losses. The superior economic operation of BWO over GA is substantiated by the fact that it continues to attain lowest combined operation and investment expenses.

(c)Environmental Performance: Overall CO₂ emissions fall from 72.5 tonnes (UPQC-less) to 36.7 tonnes (BWO) and 39.0 tonnes (GA) as evident in Figure 6(c). REUF improves from 78.4% to 88.0% (BWO) and 86.5% (GA), whereas RPI improves from 32.8% to 58.1% (BWO) and 56.3% (GA), reflecting improved utilization of renewable resources and enhanced environmental sustainability.

Figure 6.

Comparison of system performance with/without UPQC (Case 2): (a) technical parameters, (b) economic parameters and (c) environmental parameters.

Table 4.

Comparison of various parameters with and without UPQC under various algorithms.

Parameters	Metrics	Without UPQC	With UPQC (BWO)	With UPQC (GA)
Technical	$V_{dev}$ in p.u	0.084	0.035	0.038
	$P_{loss}$ in kW	185.6	95.1	98.7
	ENS in kWh	128.5	61.5	64.8
	Δf in Hz	0.36	0.15	0.17
	SCR	2.8	4.2	4.1
Economic	$C_{loss}$ in USD/kWh	29.70	12.80	13.30
	$C_{DG\mathrm{\&}EVCS}$ in USD/kWh	82.3	79.0	80.4
	$C_{DFACTS}$ in USD/kWh	0	0.20	0.22
Environmental	$E_{C{O}_2}$ in tons	72.5	36.7	39.0
	RPI in %	32.8	58.1	56.3
	REUF in %	78.4	88.0	86.5

Technical, economic, and environmental parameters are all significantly enhanced by GA and BWO compared to the UPQC-free system. The performance of the proposed BWO algorithm in enhancing resilience and sustainability in faulty distribution networks is also validated by its outstanding robustness, which ensures a balance between enhanced economic and environmental performances and maximum technical operation.

(iii) Case 3: Faulty RDS with DSSSC

In this case, the application of DSSSC devices is employed for testing the improvement in performance of the faulty Indian 28-bus RDS. Buses 14 and 18 possess the optimal DSSSC installations. Three scenarios ‒ without DSSSC, with DSSSC optimised through GA, and with DSSSC optimised through the proposed BWO algorithm ‒ are employed to test and compare the system performance. Table 5 presents the results of the detailed comparison, and Figure 7(a)–(c) depicts the trends.

Technical Performance: Following DSSSC deployment, the technical parameters show notable improvements, as shown in Figure 7(a). Improved voltage stability is shown by the voltage deviation, which drops from 0.084 p.u. (without DSSSC) to 0.042 p.u. (BWO) and 0.045 p.u. (GA). Effective loss minimisation is demonstrated by the power loss decreasing from 185.6 kW to 92.7 kW (BWO) and 96.1 kW (GA). ENS improves load reliability by dropping from 128.5 kWh to 60.1 kWh (BWO) and 63.2 kWh (GA). As a result of improved fault ride-through capability and system resilience, frequency deviation is reduced from 0.36 Hz to 0.16 Hz (BWO) and 0.19 Hz (GA), and SCR increases from 2.8 to 4.4 (BWO) and 4.3 (GA).

Economic Performance: Figure 7(b) makes clear the financial advantages of DSSSC implementation. The cost of power outages decreases from 29.70 USD/kWh to 12.45 USD/kWh (BWO) and 12.99 USD/kWh (GA). Operating costs for DG and EVCS drop from 82.3 USD/kWh to 79.4 USD/kWh (BWO) and 80.7 USD/kWh (GA). The cost of installing and running a DSSSC is very low (0.19 USD/kWh for BWO and 0.21 USD/kWh for GA). The economic feasibility of the suggested BWO-based DSSSC allocation is highlighted by the significant overall cost savings guaranteed by the combined effect of loss reduction and low deployment costs.

Environmental Performance: CO₂ emissions drop dramatically from 72.5 tonnes to 35.2 tonnes (BWO) and 37.5 tonnes (GA) as shown in Figure 7(c). Better use of renewable resources and enhanced environmental performance are demonstrated by the increases in RPI from 32.8% to 59.2% (BWO) and 57.7% (GA) and REUF from 78.4% to 86.2% (BWO) and 84.8% (GA).

Figure 7.

Comparison of system performance with/without DSSSC (Case 3): (a) technical parameters, (b) economic parameters and (c) environmental parameters.

Table 5.

Comparison of various parameters with and without DSSSC under various algorithms.

Parameters	Metrics	Without DSSSC	With DSSSC (BWO)	With DSSSC (GA)
Technical	$V_{dev}$ in p.u	0.084	0.042	0.045
	$P_{loss}$ in kW	185.6	92.7	96.1
	ENS in kWh	128.5	60.1	63.2
	Δf in Hz	0.36	0.16	0.19
	SCR	2.8	4.4	4.3
Economic	$C_{loss}$ in USD/kWh	29.70	12.45	12.99
	$C_{DG\mathrm{\&}EVCS}$ in USD/kWh	82.3	79.4	80.7
	$C_{DFACTS}$ in USD/kWh	0	0.19	0.21
Environmental	$E_{C{O}_2}$ in tons	72.5	35.2	37.5
	RPI in %	32.8	59.2	57.7
	REUF in %	78.4	86.2	84.8

The deployment of DSSSC improves the faulted RDS's technical, financial, and environmental metrics. Significant improvements are made by both GA and BWO, but the suggested BWO algorithm performs as well as or better, especially when it comes to striking a balance between cost reductions, dependability, and environmental benefits. This demonstrates that BWO works well for placing and sizing DFACTS in faulted distribution networks that are rich in renewable energy.

(iv) Case 4: Faulted RDS with DSVC

In Case 4, the integration of DSVC devices is used to analyse the performance of the malfunctioning Indian 28-bus RDS. At Buses 14 and 18, the DSVC devices are positioned thoughtfully. Three scenarios ‒ without DSVC, with DSVC optimised using GA, and with DSVC optimised using the suggested BWO algorithm ‒ are used to compare the system performance. Table 6 offers the specific performance metrics, and Figure 8(a)–(c) shows the trends.

Technical Performance: As evident from Figure 8(a), the inclusion of DSVC leads to significant improvements in technical performance. Enhanced voltage stability is reflected through the reduction in voltage deviation from 0.084 p.u. (base case) to 0.045 p.u. (BWO) and 0.048 p.u. (GA). Efficient loss minimization is reflected through the reduction in active power loss from 185.6 kW to 97.2 kW (BWO) and 100.2 kW (GA). ENS enhances load reliability from 128.5 kWh to 61.2 kWh (BWO) and 64.0 kWh (GA). SCR improves from 2.8 to 4.3 (BWO) and 4.2 (GA), and frequency deviation reduces from 0.36 Hz to 0.18 Hz (BWO) and 0.20 Hz (GA), enhancing the firmness of the system.

Economic Performance: From the economic analysis, cost savings are evident, as indicated from Figure 8(b). Huge operating savings are indicated by the reduction in the cost of power loss from 29.70 USD/kWh to 12.95 USD/kWh (BWO) and 13.60 USD/kWh (GA). Operating costs of DG and EVCS reduce from 82.3 USD/kWh to 79.9 USD/kWh (BWO) and 81.0 USD/kWh (GA). The cost-effectiveness of proposed BWO-based placement is also assured by low deployment expenditures of DSVC devices, that is, 0.21 USD/kWh (BWO) and 0.22 USD/kWh (GA). In general, economic analysis indicates that BWO maintains long-term financial sustainability by providing a balanced trade-off between investment expenditure and operational savings.

Environmental Performance: The advantages for the environment are also evident in Figure 8(c). Sustainability is improved as CO₂ emissions decrease from 72.5 tonnes to 36.3 tonnes (BWO) and 38.1 tonnes (GA). Higher use of renewable energy is indicated by the RPI rising from 32.8% to 58.8% (BWO) and 57.2% (GA), and the REUF rising from 78.4% to 87.2% (BWO) and 85.6% (GA).

Figure 8.

Comparison of system performance with/without DSVC (Case 4): (a) technical parameters, (b) economic parameters and (c) environmental parameters.

Table 6.

Comparison of various parameters with and without DSVC under various algorithms.

Parameters	Metrics	Without DSVC	With DSVC (BWO)	With DSVC (GA)
Technical	$V_{dev}$ in p.u	0.084	0.045	0.048
	$P_{loss}$ in kW	185.6	97.2	100.2
	ENS in kWh	128.5	61.2	64.0
	Δf in Hz	0.36	0.18	0.20
	SCR	2.8	4.3	4.2
Economic	$C_{loss}$ in USD/kWh	29.70	12.95	13.60
	$C_{DG\mathrm{\&}EVCS}$ in USD/kWh	82.3	79.9	81.0
	$C_{DFACTS}$ in USD/kWh	0	0.21	0.22
Environmental	$E_{C{O}_2}$ in tons	72.5	36.3	38.1
	RPI in %	32.8	58.8	57.2
	REUF in %	78.4	87.2	85.6

The faulted RDS's technical, financial, and environmental performance is greatly improved by DSVC deployment. The BWO algorithm consistently produces better or competitive results, guaranteeing balanced gains across all metrics, even though both GA and BWO produce improvements. This demonstrates how effective BWO is at allocating DSVC in faulted, renewable-rich distribution systems.

(v) Case 5: Faulted RDS with DTCSC

In Case 5, the integration of DTCSC devices is used to assess the performance of the malfunctioning Indian 28-bus RDS. Three scenarios ‒ without DTCSC, with DTCSC optimised using GA, and with DTCSC optimised using the suggested BWO algorithm ‒ are used for the analysis, just like in the earlier cases. Table 7 provides a summary of the findings, and Figure 9(a)–(c) displays the comparative trends.

Technical performance: Figure 9(a) shows that the use of DTCSC leads to significant technical improvements. The voltage variation is 0.084 p.u. (without DTCSC) to 0.050 p.u. (BWO) and 0.052 p.u. As (GA) decreases and the voltage stability improves. Although slightly higher than other DFACTS devices, the active power loss decreases from 185.6 kW to 98.4 kW (BWO) and 101.0 kW (GA), indicating significant loss reduction. With improved system reliability, ENS decreases from 128.5 kWh to 63.1 kWh (BWO) and 65.5 kWh (GA). Reduced frequency deviation from 0.36 Hz to 0.20 Hz (BWO) and 0.21 Hz (GA) and improved SCR from 2.8 to 4.3 (BWO) and 4.1 (GA) demonstrate robustness and fault riding capability of the system.

Economical Performance: Figure 9(b) shows that there are significant financial benefits. Significant operational savings are evident by reducing power loss costs from 29.70 USD/kWh to 13.07 USD/kWh (BWO) and 13.83 USD/kWh (GA). DG, EVCS operating costs remain unchanged at 80.2 USD/kWh (BWO) and 81.4 USD/kWh (GA), showing little impact on distributed resource operations. Low DTCSC application costs (0.20 USD/kWh for BWO and 0.22 USD/kWh for GA) demonstrate cost-effective planning. All things considered, BWO creates a balanced financial performance that guarantees long-term cost savings while preserving operational efficiency.

Environmental performance: Figure 9(c) shows significant improvement in environmental parameters. CO₂ emissions decrease from 72.5 tonnes to 37.0 tonnes (BWO) and 39.2 tonnes (GA). While REUF increases from 78.4% to 86.4% (BWO) and 85.0% (GA), RPI increases from 32.8% to 58.1% (BWO) and 56.6% (GA), indicating improved sustainability and increased use of renewable energy.

Figure 9.

Comparison of system performance with/without DTCSC (Case 5): (a) technical parameters, (b) economic parameters and (c) environmental parameters.

Table 7.

Comparison of various parameters with and without DTCSC under various algorithms.

Parameters	Metrics	Without DTCSC	With DTCSC (BWO)	With DTCSC (GA)
Technical	$V_{dev}$ in p.u	0.084	0.050	0.052
	$P_{loss}$ in kW	185.6	98.4	101.0
	ENS in kWh	128.5	63.1	65.5
	Δf in Hz	0.36	0.20	0.21
	SCR	2.8	4.3	4.1
Economic	$C_{loss}$ in USD/kWh	29.70	13.07	13.83
	$C_{DG\mathrm{\&}EVCS}$ in USD/kWh	82.3	80.2	81.4
	$C_{DFACTS}$ in USD/kWh	0	0.20	0.22
Environmental	$E_{C{O}_2}$ in tons	72.5	37.0	39.2
	RPI in %	32.8	58.1	56.6
	REUF in %	78.4	86.4	85.0

Faulty RDS performs better technically, economically and environmentally when combined with DTCSC devices. The BWO algorithm performs competitively in all indices, but GA gives marginally better results in some metrics. This shows how well the proposed BWO algorithm performs in optimal DTCSC allocation, which ensures increased environmental sustainability, economic efficiency, and system resilience. Figure 10 illustrates a comprehensive comparison of various performance parameters under BWO and GA.

Overall comparative analysis

• Technical Factors: The main objective here is to reduce computer losses and uncertainty. In all cases, Case 3 (BWO) is significantly more advantageous in terms of ENS (53.2%) and Min Loss (50.1%). The System Criticality Rating (SCR) shows the largest improvement by 57.1%. It also shows a significant improvement. In addition, the CO2 emissions of Case 3 (BWO) which is an important measure of environmental performance have increased by 51.4%. However, with an improvement of 66.7%, Case 1 (GA) performs better in terms of reducing lightning strikes. However, considering the overall balance of technical performance in all the metrics, Case 3 (BWO) is the best.

• Economic Factors: Table 8 shows that apart from the total operational cost, Case 3 (BWO) shows the greatest advantages in economic cost metrics. Due to the losses in some operations, the mean loss cost is reduced by 58.1%, indicating a significant operational savings. Under the additional penetration of RDGs and EVCS, this reduction directly translates into lower electricity generation and distribution costs. As a result of improved DFACTS control, distributed resources are dispatched and coordinated more effectively, resulting in a slight decrease in the operational cost of DG and EVCS in Case 3 (BWO) of about 3.5% to 4.0%. The investment is financially feasible even though the capital expenditure for DFACTS deployment (C_DFACTS) is marginally higher than in the base case due to long-term operational cost savings. Furthermore, in terms of lifecycle cost benefits, Case 3 (BWO) outperforms other cases in terms of combined economic efficiency by providing the best balance between upfront capital costs and operational savings. The overall economic gain from Case 3 (BWO) is higher because of the simultaneous optimisation of power loss, reliability-related costs, and minimal additional investment for DFACTS, but Case 2 (BWO) is more advantageous for DG and EVCS costs specifically (4.0% reduction).

• Environmental Factors: With a 51.4% improvement in CO2 emissions, Case 3 (BWO) performs exceptionally well, demonstrating the system's improved environmental performance. With an improvement of 80.5%, this case also yields the highest renewable penetration index (RPI), demonstrating a notable rise in the grid's use of renewable energy. Furthermore, with a 9.9% increase, Case 3 (BWO) shows a significant improvement in REUF. Because of this, Case 3 (BWO) is the most ecologically friendly choice for enhancing grid performance during fault situations.

Case 3 (BWO) is the best overall DFACTS case after weighing all technical, financial, and environmental factors. It offers the greatest gains in cost effectiveness, CO₂ emissions, power loss reduction, energy supply dependability, and integration of renewable energy. Because of this, Case 3 (BWO) is the best option for improving grid performance when EVCS and RDGs are installed, especially during fault events. It is the best option for maximising grid performance since it not only reduces losses and improves system stability but also guarantees substantial economic and environmental advantages.

Table 8.

Overall comparison of various parameters under various cases using BWO and GA in %.

Parameters	Metrics	Objective type	Case 1 (BWO)	Case 1 (GA)	Case 2 (BWO)	Case 2 (GA)	Case 3 (BWO)	Case 3 (GA)	Case 4 (BWO)	Case 4 (GA)	Case 5 (BWO)	Case-5 (GA)	Best DFACTS case
Technical	$V_{dev}$ in p.u	Minimize	61.9% ↓	66.7% ↓	58.3% ↓	54.8% ↓	50.0% ↓	46.4% ↓	46.4% ↓	42.9% ↓	40.5% ↓	38.1% ↓	Case 1 (GA)
	$P_{loss}$ in kW	Minimize	48.9% ↓	46.9% ↓	48.8% ↓	46.8% ↓	50.1% ↓	48.2% ↓	47.6% ↓	46.0% ↓	47.0% ↓	45.6% ↓	Case 3 (BWO)
	ENS in kWh	Minimize	51.5% ↓	49.3% ↓	52.1% ↓	49.6% ↓	53.2% ↓	50.8% ↓	52.4% ↓	50.2% ↓	50.9% ↓	49.0% ↓	Case 3 (BWO)
	Δf in Hz	Minimize	50.0% ↓	41.7% ↓	58.3% ↓	52.8% ↓	55.6% ↓	47.2% ↓	50.0% ↓	44.4% ↓	44.4% ↓	41.7% ↓	Case 2 (BWO)
	SCR	Maximize	46.4% ↑	42.9% ↑	50.0% ↑	46.4% ↑	57.1% ↑	53.6% ↑	53.6% ↑	50.0% ↑	53.6% ↑	46.4% ↑	Case 3 (BWO)
Economic	$C_{loss}$ in USD/kWh	Minimize	53.8% ↓	52.4% ↓	56.9% ↓	55.2% ↓	58.1% ↓	56.3% ↓	56.4% ↓	54.2% ↓	56.0% ↓	53.4% ↓	Case 3 (BWO)
	$C_{DG\mathrm{\&}EVCS}$ in USD/kWh	Minimize	2.7% ↓	1.3% ↓	4.0% ↓	2.3% ↓	3.5% ↓	1.9% ↓	2.9% ↓	1.6% ↓	2.6% ↓	1.1% ↓	Case 2 (BWO)
	$C_{DFACTS}$ in USD/kWh	Minimize	11.1%↓	-	10.0%↓	-	10.5%↓	-	4.8%↓	-	10.0%↓	-	Case 4 (BWO)
Environmental	$E_{C{O}_2}$ in tons	Maximize	47.0% ↓	44.6% ↓	49.4% ↓	46.2% ↓	51.4% ↓	48.3% ↓	49.9% ↓	47.4% ↓	49.0% ↓	45.9% ↓	Case 3 (BWO)
	RPI in %	Maximize	79.0% ↑	74.1% ↑	77.1% ↑	71.6% ↑	80.5% ↑	75.9% ↑	79.3% ↑	74.4% ↑	77.1% ↑	72.6% ↑	Case 3 (BWO)
	REUF in %	Maximize	11.6% ↑	9.6% ↑	12.2% ↑	10.3% ↑	9.9% ↑	8.2% ↑	11.2% ↑	9.2% ↑	10.2% ↑	8.4% ↑	Case 2 (BWO)

Using the BWO and GA algorithms, the overall comparison chart shows how well various distribution system controllers perform in five different scenarios. Regarding the technical parameters, the GA algorithm in Case 1 reduces voltage deviation the most (66.7%), while BWO in Case 3 minimises line losses and ENS the most (50.1% and 53.2%, respectively). The SCR, which represents network stability, increases maximally by 57.1% in Case 3 BWO, while the frequency deviation is best improved by 58.3% in Case 2 under BWO. While the combined cost of DG and EVCS shows a modest improvement of 4.0% in Case 2 with BWO, the cost of losses achieves the highest reduction of 58.1% in Case 3 using BWO. The efficiency of this controller in reducing device-related costs is demonstrated by the fact that the cost of DFACTS devices is reduced by 11.1% in Case 1 under BWO. In terms of environmental parameters, Case 3 shows the greatest environmental benefits, with carbon emissions reduced by 51.4% according to BWO. While REUF reaches its highest improvement of 12.2% in Case 2 BWO, the same case and algorithm see a large increase in RPI of 80.5%, indicating better integration of renewable resources.

Cases 2 (UPQC) and 3 (DSSSC) show the most significant improvements in technical, economic, and environmental indices where the BWO algorithm generally outperforms the GA in most parameters. In Case 1 (DSTATCOM) a significant reduction in voltage variation and costs associated with DFACTS can be achieved. By showing the relative performance of various controllers and optimization techniques in improving smart grid resilience, efficiency, and environmental performance, the chart's vertical bars and visible grid lines make it easy to compare performance across scenarios and algorithms.

Comparison of convergence of objective functions

The operational evaluation of the means-of-use values in various UCAP proposals, their performance in improving the distribution organization back-end structure, and their performance in improving the four guidelines - GA, Particle Swarm Optimization (PSO), Marine Predator Optimization (MPA) and BWO - are presented using Table 9, which shows the technology (F_tech), economic (F_econ), environmental (F_env) and combined total externality (F_total) values for five representative programs.

Table 9.

Objective function values for different cases and algorithms.

Case	DFACTS	Algorithm	Technical	Economic	Environmental	Total
			$F_{tech}$	$F_{econ}$	$F_{env}$	$F_{total}$
Case 1	DSTATCOM	GA	0.421	0.735	0.58	0.576
		PSO	0.41	0.725	0.585	0.55
		MPA	0.395	0.712	0.596	0.511
		BWO	0.385	0.705	0.605	0.485
Case 2	UPQC	GA	0.426	0.728	0.575	0.579
		PSO	0.412	0.719	0.581	0.55
		MPA	0.397	0.707	0.592	0.512
		BWO	0.388	0.7	0.602	0.486
Case 3	DSSSC	GA	0.415	0.724	0.585	0.554
		PSO	0.403	0.717	0.591	0.529
		MPA	0.389	0.705	0.602	0.492
		BWO	0.379	0.698	0.611	0.466
Case 4	DSVC	GA	0.432	0.73	0.572	0.59
		PSO	0.418	0.722	0.579	0.561
		MPA	0.401	0.709	0.589	0.521
		BWO	0.392	0.701	0.598	0.495
Case 5	DTCSC	GA	0.438	0.737	0.57	0.605
		PSO	0.423	0.728	0.576	0.575
		MPA	0.405	0.713	0.587	0.531
		BWO	0.396	0.705	0.596	0.505

All algorithms perform admirably for the technical goal, but BWO and MPA routinely produce lower values than GA and PSO, suggesting more efficient reduction of power loss and voltage deviation. The better adaptive search ability of the more recent metaheuristics in preserving system stability under emergency circumstances is demonstrated by Case 1, where Ftech is 0.421 for GA, 0.410 for PSO, 0.395 for MPA, and 0.385 for BWO. Similarly, BWO and MPA perform better than GA and PSO in the economic objective, which quantifies the minimisation of operational and investment costs. Case 5 values for BWO and MPA are 0.705 and 0.713, respectively, whereas GA and PSO's values are 0.737 and 0.728, respectively. This indicates improved cost efficiency through improved convergence behaviour and search diversity. BWO continuously achieves the highest values for the environmental objective, which is a maximisation criterion. Its superior capacity to lower CO₂ emissions and boost the use of renewable resources is demonstrated by its 0.611 score in Case 3, which is followed by 0.602 for MPA, 0.591 for PSO, and 0.585 for GA. Overall, the integrated total objective values confirm that BWO provides a very balanced optimization at technical, economic, and environmental levels, performing about 10–16% better than other methods, thereby providing a robust, stable, and efficient solution for post-fault distribution system optimization.

The integration behaviour of the four proposed approaches for technical, economic, environmental, and overall performance – GA, PSO, MPA, and the proposed BWO – is shown in Figure 11. The five DFACTS (DSTATCOM, UPQC, DSSSC, DSVC, and DTCSC) are shown in the figure when the appropriate structure is approached. The convergence ratio between the approaches, the combination of the differences between the stability and the final primitive values are clearly visible from the curves. The technical halo approach obtains the lowest BWO values (0.385–0.396), which are followed by GA (0.421–0.438), MPA (0.395–0.405), and PSO (0.410–0.423). This shows that BWO significantly reduces the losses and improves the lightning protection. Similarly, BWO again records the lowest values (0.698–0.705) in the financial objective, demonstrating its capacity to improve the organization's cost-effectiveness. Based on its cost-benefit analysis, BWO reveals a better financial side, with an average improvement of about 4% when GA is signed. On the other hand, in terms of environmental performance, BWO performs better in terms of GA (0.570–0.585), PSO (0.576–0.591) and MPA (0.587–0.602), achieving a maximum score of 0.596–0.611. This demonstrates that BWO provides greater environmental benefits due to the application of renewable energy sources and the reduction of CO2 emissions. The overall average values still support this trend, with average values of 0.581 for GA, 0.553 for PSO, 0.513 for MPA, and 0.487 for BWO. As the accumulation curves progress, BWO gradually and systematically approaches the global optimum, while GA and PSO converge rapidly, but remain in the local optimum. BWO outperforms all other algorithms by roughly 10–16% in terms of overall optimisation performance, exhibiting better multi-objective trade-offs, lower objective values, and superior convergence stability.

Figure 10.

Overall comparison of various parameters under BWO and GA.

Figure 11.

Convergence of objective functions for GA, PSO, MPA and BWO.

Performance metrics and statistical analysis of algorithms

The convergence behaviour and statistical features of GA, PSO, MPA, and the suggested BWO are examined in five DFACTS cases to offer a thorough comparison. The average total objective (F_total), maximum and minimum total objectives, standard deviation, average iterations, and CPU time for each algorithm are compiled in Table 10. The proposed BWO's superior ability to balance technical, economic, and environmental objectives is confirmed by its consistent achievement of the lowest average total objective of 0.487, followed by MPA (0.513), PSO (0.553), and GA (0.581). The maximum and minimum total objective values ranging from 0.485 to 0.505 demonstrate the robustness of BWO and are smaller than those of MPA (0.492–0.531), PSO (0.529–0.575), and GA (0.554–0.605). This low variability is reflected by the very low standard deviation of 0.012 for BWO, showing very stable convergence and reliable performance in all cases. BWO has faster convergence and better optimization quality. It requires an average of 120 iterations and 8.5 s of CPU time, which is slightly less than MPA (125 iterations, 9.2 s), PSO (130 iterations, 10 s), and GA (135 iterations, 10.8 s). These findings show that BWO combines accuracy and efficiency to produce better results with less computational effort. Overall, the statistical analysis demonstrates that the proposed BWO not only minimizes the total objective, but also provides better stability, faster convergence, and lower computational cost compared to state-of-the-art metaheuristics. BWO is an excellent algorithm for multi-objective optimization of post-fault distribution systems due to its low mean values, low variance, and effective computational efficiency.

Table 10.

Performance metrics of optimization algorithms (superiority order).

Algorithm	Total objective			SD	Average iterations	Average CPU time(s)
	Average	Max	Min
BWO	0.487	0.505	0.485	0.012	120	8.5
MPA	0.513	0.531	0.492	0.014	125	9.2
PSO	0.553	0.575	0.529	0.017	130	10.0
GA	0.581	0.605	0.554	0.020	135	10.8

Two complementary visualizations have been produced using Table 10 to provide a comprehensive and comprehensible comparison of the optimisation algorithms. A two-panel configuration is adopted by the first visualization in Figure 12, whose top panel provides grouped bars for each algorithm's average, maximum, and minimum total objective values (Ftotal). The proposed BWO always has the least average total objective (0.487), then MPA (0.513), PSO (0.553), and GA (0.581) that reflect the optimisation quality in this panel. Standard deviation, average iterations, and CPU time line plots of each algorithm are presented in the bottom panel, scaled for visibility. Besides having larger objective values, this plot emphasizes computational efficiency and convergence stability. It indicates that BWO converges faster (average of 120 iterations) and with minimum computational effort (8.5 s), followed in decreasing order of efficiency by MPA, PSO, and GA.

Figure 12.

Convergence of objective functions for GA, PSO, MPA and BWO.

Each cell in the second visualisation in Figure 13 is represented by an algorithm's normalised performance measures, like average, maximum, and minimum total objective, standard deviation, average iterations, and CPU time, which constitute a heatmap. Greener colours show superior outcomes, and colour gradients visually equate relative performance. It is easy for readers to immediately discern the general superiority of the algorithm due to this presentation, as it reveals that BWO excels at everything, MPA does well but less so, and PSO and GA lag behind. These visualizations complement each other nicely: the heatmap gives a clear, simple summary of performance on a variety of criteria, and the grouped bar and line plots present precise quantitative comparisons.

Figure 13.

Algorithm performance metrics heatmap (normalized).

Justification and quantitative comparison of optimization techniques

The improvement behind the failure of distribution systems is to choose the right U-Kappa technique. The concerns of the valuers regarding the algorithm selection were compared with the proposed BWO ‒ four modern metaheuristics ‒ GA, PSO, MPA ‒ and the proposed BWO ‒ in terms of the metrics. As shown in Table 9 and summarized in Table 10, the evaluation of U-Kappa type performance was done by considering various metrics such as technical objective (F_tech), economic objective (F_econ), environmental objective (F_env) and overall objective (F_total).

The main findings of the competition are as follows:

Optimization Quality (Total Objective F_total): BWO performs well overall, as evidenced by the fact that it consistently achieves the lowest total objective values (0.466 to 0.485) in all five test cases. With values ranging from 0.492 to 0.531, MPA comes second, followed by GA (0.554–0.605) and PSO (0.529–0.575).

Case wise performance: BWO achieves F_total = 0.485 in Case 1 (DSTATCOM) which outperforms GA (0.576), PSO (0.55) and MPA (0.511). The remaining cases show similar patterns, demonstrating the resilience of BWO in minimizing technical and economic impacts while maximizing environmental benefits.

Convergence stability: BWO shows the lowest standard deviation (0.012) indicating stable convergence over multiple runs. While PSO (0.017) and GA (0.020) show the highest variance, MPA ranks second with a slightly higher standard deviation (0.014).

Computational efficiency: BWO converges very quickly with an average of 120 iterations and 8.5 CPU seconds. The iterations and computational effort are increasing for MPA, PSO, and GA (125–135 iterations and 9.2–10.8 s CPU time).

Overall superiority: BWO is the best optimization method for multi-objective posterior fault distribution system optimization due to low total objective values, good convergence stability, short computational time. While PSO and GA are relatively less effective in terms of both solution quality and efficiency, MPA is competitive but marginally less efficient.

In summary, the quantitative data presented in Tables 9 and 10 amply supports the selection of BWO as the optimal algorithm for the proposed study due to its balanced superiority in terms of optimisation quality, robustness, and computational efficiency.

Conclusion

The technical, financial, and environmental issues related to high RDG and EVCS penetration rates in shoddy distribution networks functioning in faulted environments were thoroughly covered in this study. Two metaheuristic algorithms, the GA and the BWO, were used to determine the best location and size for a variety of DFACTS devices, including DSTATCOM, UPQC, DSSSC, DSVC, and DTCSC. BWO consistently outperformed MPA (0.512), PSO (0.550), and GA (0.576), exhibiting the lowest total objective value of 0.485, according to comparative analyses. In particular, compared to the ideal infrastructure using GA, the BWO proposal generated significant improvements in the DSSSC interior (Case 3): 49.3% reduction in operating min loss, 52.6% reduction in ENS, and 56.8% improvement in SCR. Along with a 79.4% improvement in the RPI and a 9.5% improvement in the REUF, there was also a 57.3% decrease in the cost of power losses, a 10.6% decrease in overall operating costs, and a 50.6% decrease in CO₂ emissions. These enhancements demonstrate how well DFACTS integration works to reduce the negative effects of faults while boosting grid sustainability, efficiency, and resilience.

Despite the promising findings, some limitations remain. The present analysis excludes stochastic variation and dynamic behaviour in real time, making static load and generation assumptions. Furthermore, only single fault cases are examined within this research; cascading or probabilistic fault effects are not considered. To bridge these limitations, future studies will incorporate real-time renewable and load forecasts, cyber-physical security evaluations, and dynamic and uncertainty-driven fault modelling to better represent operational conditions.

It is important to identify potential risks with the extensive application of power-electronic-based DFACTS devices along with the limitations recognized. These include interoperability issues in mixed-vendor systems, cybersecurity risk introduced by real-time data communication and coordinated control structures, and challenges with societal acceptance introduced by perceived complexity and maintenance needs. To provide assurance of safe and reliable incorporation of new-age DFACTS technologies in emerging smart and resilient power grids, it will become crucial to mitigate these issues through secure communication infrastructures, control strategies with resilience, and stakeholder sensitization initiatives.