A Multi-Objective PSO-GWO Approach for Smart Grid Reconfiguration with Renewable Energy and Electric Vehicles

Abstract

In the contemporary landscape of power systems, the escalating integration of renewable energy resources and electric vehicle infrastructures into distribution networks has intensified the imperative to ensure power quality, operational optimization, and system reliability. Distribution network reconfiguration emerges as a pivotal strategy to mitigate power losses, facilitate the seamless assimilation of renewable generation, and regulate the charging and discharging dynamics of EVs, thereby constituting a critical endeavor in modern electrical engineering. While the Particle Swarm Optimization algorithm is renowned for its rapid convergence and effective exploitation of solution spaces, its capacity to thoroughly explore complex search domains remains limited, particularly in multifaceted optimization challenges. Conversely, the Grey Wolf Optimization algorithm excels in global exploration, offering robust mechanisms to circumvent local optima traps. Leveraging the complementary strengths of these approaches, this study proposes a hybrid PSO-GWO framework to address the distribution network reconfiguration problem, explicitly accounting for the integration of renewable energy sources and EV systems. Empirical validation, conducted on the IEEE 33-bus test system across diverse operational scenarios, underscores the efficacy of the proposed methodology, revealing exceptional precision and dependability. Notably, the approach achieves substantial reductions in power losses during peak demand periods with distributed generation incorporation while maintaining voltage profiles within the stringent operational bounds of 0.94 to 1.0 per unit, thus ensuring stability amidst variable load conditions. Comparative analyses further demonstrate that the hybrid method surpasses conventional optimization techniques, as evidenced by enhanced convergence rates and superior objective function outcomes. These findings affirm the proposed strategy as a potent tool for advancing the resilience and efficiency of next-generation distribution networks.

1. Introduction

The accelerating proliferation of electric vehicles (EVs) and renewable energy sources, notably photovoltaic (PV) solar and wind turbines (WT), presents formidable challenges to conventional distribution power systems. The integration of distributed generation (DG)—characterized by inherent variability and weather-dependent intermittency—coupled with the heterogeneous expansion of EV loads markedly amplifies the complexity of managing and operating distribution networks. Consequently, the task of distribution network reconfiguration has gained unprecedented urgency as it seeks to optimize system performance under these dynamic conditions.

Distribution network reconfiguration (DRN) constitutes a sophisticated optimization challenge, entailing the strategic adjustment of switch states to minimize power losses, enhance voltage profiles, and achieve load balancing, particularly amidst the stochastic fluctuations introduced by DG units and EV charging demands [1]. The global shift toward increased reliance on renewable energy and EV adoption not only imposes significant technical demands but also catalyzes the advancement of sophisticated optimization methodologies essential for ensuring the stability and efficiency of modern power systems.

Extensive research has explored diverse objective functions in distribution network reconfiguration incorporating DGs and EVs. Carpaneto and Chicco [2] employed a Genetic Algorithm (GA) to optimize network reconfiguration, targeting power loss minimization and voltage profile enhancement; however, their findings highlighted GA’s susceptibility to local optima and protracted convergence times. Wang et al. [3] leveraged the Differential Evolution (DE) algorithm to bolster system stability in the presence of DGs and EVs, achieving notable improvements, albeit with increased computational overhead. Kavousi-Fard et al. [4] proposed a stochastic framework integrating wind power management, optimizing system costs and reliability through reconfiguration. Meanwhile, Li et al. [5] applied the Particle Swarm Optimization algorithm (PSO), demonstrating faster convergence relative to GA, though limitations persisted in navigating complex search spaces. Duan et al. [6] utilized GA to enhance reliability and minimize losses in networks with EVs and demand response programs, underscoring its efficacy in specific contexts. Linh et al. [7,8,9] investigated a hybrid Crow Search Algorithm (CSA) and PSO approach for reconfiguration with PV, WT, and EVs, yet their analysis relied on average daily power profiles, neglecting diurnal variations critical to real-time operations. Geleta et al. [10] adopted the Artificial Bee Colony (ABC) algorithm, yielding significant reductions in power losses and improved system performance in renewable and EV-integrated networks. Chakma et al. [11] explored reconfiguration alongside EV charging infrastructure to augment load capacity and reliability, while Yousefi et al. [12] combined PSO with reconfiguration to optimize EV charging, enhancing system scalability for large EV penetrations.

Optimization techniques such as GA, Ant Colony Optimization (ACO), DE, PSO, and ABC have been widely deployed in reconfiguration problems involving DGs and EVs. GA and ACO excel in broad search exploration but falter in rapid convergence and frequently encounter local optima traps [13,14,15]. DE and ABC enhance solution precision, yet their computational complexity and prolonged execution times render them less viable for large-scale networks. PSO distinguishes itself with rapid convergence and implementation simplicity; however, its efficacy diminishes in intricate search domains with multiple local optima.

The study by J. Zhang et al. [16] focuses on predicting EV charging demand using multi-task learning (MTL), an approach distinct from the optimization methods employed in our research. While MTL provides accurate forecasts of charging demand, our study integrates prediction with optimization to not only predict but also optimize system operations in real time, thereby enhancing overall efficiency. On the other hand, the study by S. Wang et al. [17] addresses the restoration of multi-energy distribution systems through distributed stochastic programming. Although this study shares the goal of system optimization, our approach specifically focuses on the integration of EVs and renewable energy, balancing multiple objectives such as reducing power losses, maintaining voltage stability, and enhancing system resilience. Compared to these studies, our method comprehensively combines prediction and optimization, offering a more tailored solution to the challenges of modern power systems.

To summon these limitations, this study proposes a hybrid PSO-Grey Wolf Optimization (GWO) methodology. This approach synergistically harnesses PSO’s expeditious solution exploitation and GWO’s robust global search capabilities, which are adept at circumventing local optima and yielding a potent optimization framework. The hybrid method is particularly adept at addressing expansive solution spaces and accommodating the temporal and environmental uncertainties inherent in PV, WT, and EV integration. Validation results demonstrate its capacity to empower distribution network operators with precise, actionable insights for optimal system management, fostering enhanced operational efficiency and resilience in contemporary power grids.

The paper is structured as follows: Section 1 introduces the research context and significance; Section 2 constructs the mathematical model and delineates the associated constraints; Section 3 elucidates the proposed hybrid PSO-GWO methodology; Section 4 presents simulation results on the IEEE test grid, evaluating performance across diverse scenarios; and Section 5 concludes with key findings and future research directions.

2. Optimization Model Including Objective Function and Constraints

This section delineates the mathematical formulation and associated constraints governing the optimization of distribution network reconfiguration, incorporating the integration of DGs and EVs.

2.1. Optimal Objective Function

• The function power loss

Reconfiguration of the distribution network is a challenging combinatorial optimization problem. When considering multiple objective functions, the network’s various performance metrics include minimizing load deviation, voltage deviation, and system power losses [6].

$$F_1=min\sum _{i=1}^n{k}_i{R}_i{\displaystyle \frac{P_i^2+Q_i^2}{U_i^2}}$$

(1)

where n represents the aggregate number of branches; k_i denotes the switch position (with k_i = 0 indicating open and 1 indicating closed); R_i is the overall resistance of the ith branch; and P_i, Q_i, and U_i correspond to the terminal active power, reactive power, and node voltage at the termination of branch i, respectively.

• The function voltage deviation

$$F_2=min\sum _{j=1}^n{({\displaystyle \frac{U_j-U_{js}}{U_{js}}})}^2$$

(2)

where n is the total number of nodes; U_j is the actual voltage of node j; U_js is the rated voltage of node j.

• The variance of the function load

$$F_3=min\sum _{i=1}^m{({\displaystyle \frac{S_i}{S_{imax}}})}^2$$

(3)

where m is the total number of closed branches; S_i and S_imax respectively represent the actual value and the maximum value of the complex power on branch i.

• Objective function normalization

The method of random weight allocation has been employed to normalize the objective function.

$${\omega }_i={\displaystyle \frac{{rand}_i}{\sum _{i=1}^n{rand}_i}}$$

(4)

$$F=min({\omega }_1{\displaystyle \frac{F1}{f_1}}+{\omega }_2{\displaystyle \frac{F2}{f_2}}+{\omega }_3{\displaystyle \frac{F3}{f_3}})$$

(5)

where ω_i represents the random weight coefficient assigned to the ith objective function, rand generates random numbers within the interval [0, 1], and f_i is the minimum value achieved by the ith objective function in each iteration.

• The DG mathematical model

  ✓

  Solar photovoltaic modeling

The following formula can be used to calculate solar power output power [8]:

$$P_{PV}={\eta ·P}_{rate}{\displaystyle \frac{A}{A_s}}\left[1+\alpha p\left(T-T_{STC}\right)\right]$$

(6)

where η denotes the power factor, P_rate refers to the rated power, A indicates the actual light intensity, A_s is the light intensity in standard test conditions, α_p represents the power temperature coefficient, T is the present surface temperature of the photovoltaic cell, and T_STC is the temperature of the photovoltaic cell during standard test conditions.

• ✓

  Wind turbine modeling

The main factor influencing wind energy’s output power is wind speed, which is best explained as follows:

$$P_t(v)=\left\{\begin{array}{c}0,\hspace{1em}\hspace{1em}\hspace{1em}0\le v\le V_{ci}\\ a{v}^3-b{P}_{r,\hspace{1em}}{v}_{ci}\le v\le v_r\\ P_{r,}{\hspace{1em}\hspace{1em}\hspace{1em}v}_r\le v\le v_{co}\\ 0,{\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}v}_{co}\le v\end{array}\right.$$

(7)

where P_r represents the rated power, and v_ci, v_r, and v_co denote the minimum, rated, and maximum wind speeds for power generation, respectively, while v stands for the current wind speed. The output from distributed generation is often simplified and handled as a ’negative load’, being treated as a series of continuous variables. When the active power and power factor of a DG are known, it can be considered as a P, Q node.

$$\left\{\begin{array}{c}P=-P_s\\ Q=-Q_s\end{array}\right.$$

(8)

where P_s and Q_s indicate, respectively, active power and reactive power of DG.

• ✓

  EV Charging/Discharging Constraints

$$\mathrm{EV}\mathrm{battery}\mathrm{state}\mathrm{of}\mathrm{charge}\left(\mathit{SOC}\right):{SOC}_{k,min}\le {SOC}_{k,t}\le {SOC}_{k,max}$$

(9)

where: ${SOC}_{k,min}$: State of charge of EV k at time t

$$\mathrm{EV}\mathrm{charging}/\mathrm{discharging}\mathrm{power}\mathrm{limits}:P_{EV,k,min}\le P_{EV,k,t}\le P_{EV,k,max}\forall k\in N_{EV}$$

(10)

EV energy balance:

$${SOC}_{k,t}={SOC}_{k,t-1}+{\eta }_{ch}·P_{EV,k,t}^{ch}-{\displaystyle \frac{P_{EV,k,t}^{dis}}{{\eta }_{dis}}}$$

(11)

where: ${\eta }_{ch},{\eta }_{dis}:$Charging and discharging efficiencies.

$P_{EV,k,t}^{ch},P_{EV,k,t}^{dis}:$Charging and discharging power of EV k at time t.

2.2. Technical Binding Conditions

The optimization problem in the electrical distribution system involves constraints on power balance and operation. The power balance constraint (Equation (12)) requires that the active and reactive power at the nodes of the system must balance with the total power injected from DG sources and consumed by the loads. Specifically, the active and reactive power at each node are calculated based on voltage and phase angles, as well as the components of the system’s admittance matrix. The operational constraints (Equation (13)) set limits on the voltage at the nodes, the current through the branches, and the complex power that each branch can handle. Voltage and current limits ensure that the system operates within safe ranges, preventing issues such as overloads or unstable voltage levels. These constraints are necessary to maintain efficiency and stability in the electrical distribution system.

• Power balance restrictions [8]

$$\left\{\begin{array}{c}{P}_G-P_i-U_i{\displaystyle \sum _{j=1}^n}{U}_i\left(G_{i-j}{cos\theta }_{i-j}+B_{i-j}{sin\theta }_{i-j}\right)=0\\ Q_G-Q_i-Q_i{\displaystyle \sum _{j=1}^n}{U}_i\left(G_{i-j}{cos\theta }_{i-j}+B_{i-j}{sin\theta }_{i-j}\right)=0\end{array}\right.$$

(12)

where P_G and Q_G refer to the active and reactive power injected at the DG node, respectively, while P_i and Q_i indicate the active and reactive power at the load node.

• Operational constraints [18]

$$\left\{\begin{array}{c}{U}_{min}\le U_i\le U_{max}\\ I_{min}\le I_i\le I_{max}\\ S_i\le S_{imax}\\ P_G\le P_{Gmax}\end{array}\right.$$

(13)

where U_min and U_max represent the voltage limits at node i, setting the minimum and maximum thresholds, respectively. I_min and I_max define the lowest and highest current limits for branch i. S_i refers to the complex power on branch i, while P_Gmax indicates the highest output power that branch i can accommodate in the power distribution system.

3. Proposed Optimization Methodology for Distribution Network Reconfiguration

In the problem of distribution network reconfiguration integrated with renewable energy and electric vehicles, multi-objective optimization demands algorithms capable of balancing exploration and exploitation within the search space. PSO and GWO are two advanced algorithms, each with distinct strengths: PSO excels in rapid convergence due to its position-updating mechanism based on individual and global best solutions, while GWO mimics the hunting behavior of grey wolves, offering superior exploration capabilities and robustness against local optima. However, PSO is prone to getting trapped in local optima in complex search spaces, and GWO may exhibit slower convergence in certain scenarios.

The integration of PSO and GWO leverages the advantages of both algorithms: PSO accelerates convergence, while GWO ensures comprehensive exploration of the search space [19,20]. This hybrid approach is particularly suitable for distribution network reconfiguration, which is inherently nonlinear, multi-objective, and constrained by the integration of renewable energy and EVs. The expected outcome is a globally optimal solution with high precision, addressing technical requirements such as minimizing power losses, balancing load distribution, improving voltage profiles, and enhancing power supply reliability.

3.1. Overview Particle Swarm Optimization

Particle Swarm Optimization is a population-based meta-heuristic algorithm inspired by the social behavior of bird flocking and fish schooling [20]. It uses particles to explore a search space, updating their positions based on individual and global best solutions to solve optimization problems. The particle (X_i) is the position representation of everyone with N-dimensional search space, which is described using Equation (14)

$$X_i=(X_{i1},X_{i2},X_{i3}\dots .,X_{in})$$

(14)

Then, each particle moves to become a new particle position $X_i^{(t+1)}$ by updating the velocity through a new speed variable $V_i^{(t+1)}$ with the following Equation:

$$X_i^{t+1}=X_i^t+V_i^{t+1}$$

(15)

$$V_i^{t+1}={\omega ·V}_i^t+c_1·r_1\left(P_{best}^t+X_i^t\right)+c_2·r_2(g_{best}^t+X_i^t)$$

(16)

In PSO, each particle i within the swarm updates its position and velocity at each iteration. Here, n denotes the current iteration, while r₁ and r₂ are random values between 0 and 1. The parameter ω controls the inertia weight, which influences the particle’s tendency to continue in its current direction. The coefficients c₁ and c₂ are acceleration factors that guide the optimization, with x representing the particle’s position and v its velocity p_i is the best position found by particle i, and p_g is the best-known position among all particles in the swarm.

In each iteration, particles update their positions and velocities based on individual and global best solutions. To escape the local minimum, particles are reassigned to random positions, preventing stagnation. The process repeats until an optimal solution is found or the maximum iterations are reached.

3.2. Overview Grey Wolf Optimizer

The Grey Wolf Optimizer is a meta-heuristic algorithm inspired by the social hierarchy and hunting behavior of grey wolves. It employs alpha, beta, and delta wolves to guide the search, balancing exploration, and exploitation to efficiently solve complex optimization problems [20,21]. Grey wolves’ hunting includes the following three main parts:

(1)

Tracking, chasing, and approaching the prey;

(2)

Pursuing, encircling, and harassing the prey till it stops moving;

(3)

Attacking the prey.

Encircling the prey is modeled mathematically in the following Equations:

$$D=|C\times X_p\left(t\right)-X\left(t\right)|$$

(17)

$$X\left(t+1\right)=X_p\left(t\right)-A\times D$$

(18)

Here, t is the number of instantaneous iterations, X_p is the position of the prey, X is the location of grey wolves, and A and C are the coefficients for the vectors. The coefficients A and C are calculated as shown below:

$$A=a\times (2\times r_1-1)$$

(19)

$$C=2\times r_2$$

(20)

Here, the number of a is linearly decreasing from 2 to 0, as the number of iterations decreases r₁ and r₂ represent uniformly selected random numbers between [0, 1].

Grey wolves are led by alpha wolves to locate prey, with beta and delta wolves assisting. In GWO, the best solution is the alpha wolf, while the second and third best are beta and delta wolves. Other wolves follow these leaders, guiding the search process mathematically:

$$D_{\propto }=\left|C_{1\times }{X}_{\propto }-X\left(t\right)\right|;D_{\beta }=|C_{2\times }{X}_{\beta }-X\left(t\right)|;D_{\delta }=|C_{3\times }{X}_{\delta }-X\left(t\right)|$$

(21)

where X_∝, X_β and X_δ represent the best three wolves in each iteration, respectively

$$X_1=\left|X_{\propto }-a_1\times D_{\alpha }\right|;X_2=\left|X_{\beta }-a_2\times D_{\beta }\right|;X_3=\left|X_{\delta }-a_3\times D_{\delta }\right|$$

(22)

$$X_p\left(t+1\right)={\displaystyle \frac{X_1+X_2{+X}_3}{3}}$$

(23)

Here, the new position of the prey is expressed as X_p(t+1) as the meaning of the positions of three best wolves in the population.

Grey wolves attack prey by closing in, guided by parameter ranging from [−2a, 2a] where a decreases from 2 to 0. If $\left|A\right|\ge 1$ wolves abandon hunting to explore better solutions, if $\left|A\right|<1$ they attack. This prevents local minimum, and the search ends after reaching the maximum iterations.

3.3. A Combined PSO-GWO Approach to Distribution Network Reconfiguration

The hybrid integration of PSO and GWO synergistically combines their complementary strengths to enhance optimization efficiency. PSO excels in rapid exploitation, refining solutions locally through velocity-driven dynamics, but is prone to premature convergence to local optima, limiting its global search capabilities [5,20]. In contrast, GWO leverages a hierarchical search strategy inspired by grey wolf social behavior, enabling robust exploration of expansive search spaces and reducing the risk of suboptimal stagnation [22]. By merging PSO’s exploitation efficiency with GWO’s exploration robustness, the PSO-GWO framework achieves a balanced approach that accelerates convergence and mitigates local optima risks. This hybrid method effectively addresses complex, non-linear optimization problems, consistently achieving global optima with high precision [23,24]. The proposed PSO-GWO framework is particularly well-suited for resolving the stochastic complexities of distribution network reconfiguration, especially in systems integrating DGs and EVs. PSO’s ability to rapidly refine solutions within localized regions, guided by individual and swarm-wide best-known positions, is complemented by GWO’s systematic exploration of uncharted regions. This synergy not only enhances optimization performance but also increases the likelihood of identifying superior solutions in multi-modal and intricate search spaces. The adaptability and robustness of the PSO-GWO hybrid make it a powerful tool for addressing the dynamic challenges posed by modern power systems, ensuring efficient and reliable network reconfiguration in the presence of renewable energy and EV integration.

To delineate the operational mechanics of this hybrid methodology, Figure 1 presents the algorithmic flowchart, which illustrates the iterative interplay between PSO and GWO phases. The process initiates with the random generation of a population of candidate solutions—representing potential switch configurations in the distribution network. PSO then drives the exploitation phase, updating particle positions based on personal and global best metrics to refine solutions locally. Subsequently, GWO enhances exploration by repositioning solutions according to its hierarchical leadership structure, diversifying the search trajectory and mitigating the risk of local optima convergence. This cyclical alteration ensures a dynamic balance, with PSO focusing on localized optimization and GWO broadening the global perspective, thereby enabling the algorithm to navigate complex search domains effectively.

Further elucidating this approach, Figure 2 provides the pseudocode implementation, offering a detailed procedural representation of the hybrid algorithm’s logic. The pseudocode outlines the initialization of the swarm, followed by PSO’s velocity-based updates to particle positions and the subsequent adjustment via GWO’s structured exploration mechanism, inspired by a wolf pack hunting behavior [17]. This orchestrated integration maximizes the interaction between PSO’s momentum-driven search and GWO’s adaptive exploration strategy, facilitating efficient traversal of expansive search spaces while preventing stagnation. By synergistically harnessing PSO’s rapid convergence and GWO’s robust global search capabilities, the hybrid method demonstrably improves optimization outcomes, as evidenced by its proficiency in addressing multi-modal problems and consistently achieving global optima with enhanced precision and computational efficiency.

4. Results and Discussion

The proposed methodology was implemented on a personal computer equipped with an Intel CPU operating at 1.90 GHz and 16 GB of RAM. Optimal parameter settings were determined as follows: weights w₁ = 0.5, w₂ = 0.4, and w₃ = 0.1 alongside cognitive (c₁ = 2) and social (c₂ = 2) coefficients, yielding a minimized objective function value. The proposed methodology was rigorously evaluated using the IEEE 33-node test system, a widely recognized radial distribution network model. Figure 3 illustrates the system consists of 33 nodes, 37 branches, 32 sectionalizing switches, and 5 tie switches, operating at a nominal voltage of 10 kV. The IEEE 33-node system serves as a benchmark for assessing the performance of optimization techniques in distribution network reconfiguration, providing a robust platform to validate the effectiveness of the proposed approach under realistic operating conditions. The system supports a total user load of 4165 kW and 2300 kVar [24,25]. Over a 24-h period, the network integrates DG sources with fluctuating capacities: nodes 4 and 20 host EV charging stations; nodes 10, 13, and 27 are connected to wind turbine generators; and nodes 16, 24, and 31 are linked to PV units, reflecting the stochastic nature of renewable energy and EV integration.

Figure 4 illustrates the hourly output PV, WT and charging profiles of EVs, integrated into the distribution network over a 24-h period, providing a temporal representation of their dynamic interactions [26].

The results, as illustrated in Figure 5, provide a comprehensive evaluation of the proposed methodology applied to the IEEE 33-bus radial distribution network under two distinct operational scenarios: one incorporating PV and WT and the other excluding DG integration. A comparative analysis of total power losses between these scenarios unequivocally highlights the significant advantages of DG connectivity in mitigating power dissipation and enhancing system efficiency.

Throughout most operational hours, power losses in the scenario without DG integration are substantially higher compared to the scenario with DG integration. This trend is particularly pronounced during peak demand periods, such as at hours 9, 14, and 21, where power losses in the absence of DG exceed 340 kW. In contrast, the integration of DG reduces these losses to below 250 kW during the same periods, demonstrating the critical role of DG in alleviating system load and optimizing power distribution. The reduction in power losses during peak hours underscores the ability of DG to provide localized generation, thereby reducing the strain on the grid and minimizing transmission losses. During off-peak hours, such as at hours 4, 6, and 17, power losses in both scenarios are relatively lower. However, the presence of DG continues to contribute to system stability and further reduces losses, albeit to a lesser extent. This consistent performance across both peak and off-peak periods highlights the versatility and reliability of DG in enhancing grid operations under varying load conditions.

The integration of PV and WT systems not only reduces power losses but also enhances the overall resilience and efficiency of the distribution network. By generating power closer to the point of consumption, DG minimizes the need for long-distance power transmission, thereby reducing associated losses and improving voltage profiles. Furthermore, the ability of DG to dynamically respond to load variations ensures a more stable and efficient power system, particularly during periods of high demand.

In conclusion, the findings affirm that the integration of DGs, particularly PV and WT systems, is a highly effective strategy for optimizing the performance of distribution networks. By significantly reducing power losses, especially during high-load intervals, DG integration contributes to a more efficient, reliable, and sustainable power system. These results underscore the importance of adopting advanced optimization techniques and renewable energy integration to address the evolving challenges of modern power grids.

Figure 6 illustrates the temporal dynamics of voltage profiles, expressed in “per unit” (p.u.), across the 33 nodes of the IEEE 33-bus radial distribution network over a 24-h period. The voltage profiles exhibit fluctuations ranging from 0.94 to 1.0 p.u., signifying robust system stability and the absence of significant voltage deviations, thereby affirming compliance with operational safety thresholds [27]. Inter-nodal variations reveal differential voltage behaviors, with certain nodes demonstrating pronounced fluctuations, necessitating vigilant monitoring to safeguard system performance and reliability. Notably, between hours 0 and 10, voltage oscillations are more pronounced, potentially attributable to elevated load demands during peak periods, such as those induced by EV charging or DG intermittency [28]. Post-15 h, these fluctuations attenuate, suggesting enhanced system stability during off-peak conditions. While the voltage profiles consistently remain within the permissible range of 0.94 to 1.0 p.u., proactive surveillance and potential adjustment of nodes exhibiting significant variability are imperative to mitigate risks of substantial voltage excursions, particularly during high-load intervals.

In conclusion, the voltage stability of the distribution network is effectively maintained under the proposed framework. However, to ensure sustained operational integrity, particularly during high-demand scenarios involving DGs and EVs, continuous monitoring and targeted strategic interventions at nodes exhibiting elevated voltage fluctuations are imperative. These measures are crucial for mitigating potential risks and enhancing the resilience of the network under dynamic load conditions [29].

Figure 7 and

Table 1. Comparative Analysis of PSO, GWO, and PSO-GWO Algorithms.

Algorithm	Time Complexity	Space Complexity	Convergence Performance	Remarks
PSO	O (N xD xT)	O (N xD)	Slow convergence, reaching 0.006 after 20 iterations.	Simple and easy to implement but prone to getting stuck in local optima.
GWO	O (N xD xT)	O (N xD)	Fast initial convergence (reaching 0.007 after 3 iterations), but slower progress afterward.	Good exploration capability but weaker exploitation compared to PSO.
PSO & GWO	O (N xD xT)	O (N xD)	Fastest convergence, reaching 0.0054 after 7 iterations.	Combines the strengths of PSO (exploitation) and GWO (exploration), delivering superior performance in complex problems

compare the convergence performance of PSO, GWO, and the hybrid PSO-GWO algorithm [27,29]. PSO exhibits slow convergence, reaching an objective function value of 0.006 after 20 iterations, reflecting its strong exploitation but susceptibility to local optima. GWO achieves rapid initial convergence (0.007 in 3 iterations) due to its exploration strength but slows afterward, indicating weaker exploitation. In contrast, the hybrid PSO-GWO algorithm demonstrates superior performance, reaching 0.0054 in just 7 iterations by effectively balancing PSO’s exploitation and GWO’s exploration. While PSO-GWO incurs higher computational costs, its ability to achieve global optima efficiently makes it ideal for complex optimization problems. Standalone PSO and GWO remain suitable for simpler tasks or resource-constrained scenarios.

Collectively, these findings affirm that PSO-GWO represents the most efficacious optimization strategy, characterized by its accelerated convergence and attainment of the lowest objective function value. This superiority stems from the hybrid algorithm’s ability to transcend the inherent constraints of PSO and GWO, offering a robust solution for navigating the multifaceted optimization landscape of distribution networks integrated with DGs and EVs. While PSO delivers satisfactory outcomes, its slower convergence underscores its limitations, and GWO, despite its initial promise, proves less effective in securing the global optimum [30,31].

5. Conclusions

This study introduces a novel hybrid optimization framework that synergistically integrates Particle Swarm Optimization and Grey Wolf Optimization to address the intricate challenges of distribution network reconfiguration, with a particular focus on minimizing power losses, enhancing system reliability, and optimizing economic efficiency. The proposed PSO-GWO methodology demonstrates superior convergence characteristics and effectively circumvents local optima, thereby offering a robust solution for the complex, non-linear optimization problems inherent in modern power systems [31,32].

Empirical validation conducted on the IEEE 33-bus radial distribution network underscores the efficacy of the proposed approach across diverse operational scenarios, incorporating renewable energy sources—specifically photovoltaic and wind turbine units—and electric vehicles. The results highlight the critical importance of dynamic network reconfiguration in optimizing system performance, particularly in the context of fluctuating DG outputs and EV charging/discharging dynamics. Notably, the integration of DGs significantly reduces power losses during peak demand periods and enhances system stability during off-peak intervals, thereby affirming its pivotal role in improving operational efficiency [33].

Furthermore, the strategic incorporation of PV and WT into the distribution network, facilitated by the proposed optimization strategy, not only augments system performance but also enhances the operational efficiency of EV charging infrastructure, yielding substantial economic benefits. This approach provides transformative opportunities for smart grid implementations and underpins the sustainability of power system operations.

Future research directions could explore the stochastic uncertainties associated with supply and demand dynamics, as well as investigate advanced optimization paradigms tailored to larger-scale distribution networks. Additionally, the integration of real-time data analytics and machine learning techniques could further enhance the adaptability and resilience of the proposed framework, paving the way for more intelligent and autonomous power systems [34].