Coordinated Allocation of Multi-Type DERs and EVCSs in Distribution Networks Using a Multi-Stage GSA Framework

Abstract

This study introduces a multi-stage, multi-objective optimization framework based on the Gravitational Search Algorithm (GSA) for determining the optimal sizing and placement of distributed energy resources (DERs) and associated infrastructure. The proposed approach considers solar distributed generation (DG) units with battery storage systems (BSSs), wind DGs, shunt capacitors (SCs) and electric vehicle charging stations (EVCSs). With the rapid adoption of electric vehicles as part of global decarbonization efforts, integrating EVCSs into already stressed distribution networks poses significant operational challenges, often requiring system reinforcement supported by renewable-based DGs. The uncoordinated deployment of EVCSs and DGs can exacerbate power losses and deteriorate voltage profiles. To address these issues, the first stage of the methodology employs GSA to optimally allocate solar DGs with BSSs, wind DGs and SCs, targeting objectives such as minimizing power losses, enhancing voltage stability and alleviating substation loading. The second stage identifies optimal locations and maximum feasible capacities for EVCS integration. Finally, the third stage upgrades the network to mitigate the impacts of EVCS integration. The effectiveness of the proposed approach is validated through simulations on a practical 52-bus, 11 kV distribution network under hourly varying load, solar irradiance and wind velocity conditions for all seasons. The simulation results show an 85% reduction in power losses during peak hours, with nodal voltages maintained above 0.95 p.u. under all scenarios. Additionally, net-zero grid power exchange during peak periods confirms the full islanded operation.

1. Introduction

Global electricity demand continues to rise, driven by economic growth, modernization, urbanization, and the expansion of infrastructure and industry. As a result, ensuring access to sustainable and affordable electric power has become a critical priority for many nations. Meeting this growing demand requires not only an increase in generation capacity but also enhancements to transmission infrastructure—an option that is often constrained by existing installations and geographical limitations. Even when feasible, long-distance transmission introduces significant power losses due to line resistance, increasing operational costs and causing under-voltage conditions for consumers. High distribution losses also place additional stress on central power sources and escalate energy costs.

A practical and effective solution is to promote localized power generation through the deployment of distributed generation (DG) units and shunt capacitors (SCs). These resources improve system capacity and reliability, reduce transmission burdens, minimize network losses, and enhance the overall power quality.

To address environmental concerns such as greenhouse gas emissions and global warming, renewable energy-based DGs—particularly solar PV systems, including rooftop installations and wind DGs—have gained widespread adoption in recent years. This trend is supported by technological advancements and declining module costs, enabling compact and efficient configurations. Furthermore, the depletion of fossil fuel reserves and rising oil prices have accelerated the growth of the electric vehicle (EV) market, which has expanded rapidly due to modern technological breakthroughs. Consequently, there is an increasing need for the extensive deployment of electric vehicle charging stations (EVCSs).

However, the effective integration of DGs, SCs, and EVCSs requires careful planning and configuration. Overloading a node with DGs and SCs can lead to overvoltage conditions, increased power losses, and potential under-voltage issues at downstream nodes. Similarly, the improper placement of EVCSs may degrade voltage profiles and further exacerbate network losses. Therefore, the strategic optimization of these resources is essential to ensure system stability, efficiency, and reliability.

Extensive research has been conducted on the optimal sizing and placement of DGs—including solar, wind and other DGs—along with SCs and EVCSs, either individually or in combination, to enhance distribution network performance. Gümüş et al. [1] introduced a Thevenin-based stability index for DG allocation using a mixed-integer genetic algorithm. Sellami et al. [2] proposed an enhanced Particle Swarm Optimization (PSO) technique for simultaneous DG placement and sizing. Kashyap et al. [3] employed an analytical approach to determine the optimal capacity and location of DGs and SCs under varying load conditions. Nguyen et al. [4] utilized a hybrid neural network algorithm for the multi-objective optimization of DG and SC placement in distribution systems. Rekha and Byalihal [5] applied PSO for siting and sizing solar–wind hybrid systems to minimize power losses. Vempalle and Dhal [6] developed a hybrid optimization method for integrating solar and wind DGs under time-varying load scenarios. Fathy et al. [7] introduced a capuchin search algorithm to identify optimal locations, sizes, and power factors for biomass DG units. Argüello et al. [8] proposed a methodology for deploying rooftop solar PV systems across all consumers in a distribution network and evaluated its performance benefits. Roy et al. [9] presented an integrated approach combining rooftop solar PV systems with optimal DG and SC placement to improve the performance of a practical distribution network across different seasons.

Goli et al. [10] proposed a two-stage methodology to enhance distribution system performance. In the first stage, annual energy losses were minimized through optimal network reconductoring using the Flower Pollination Algorithm. The second stage involved allocating EV charging loads across the distribution nodes. Ferraz et al. [11] formulated a two-stage optimization approach, beginning with strategic planning for EVCS placement and sizing, followed by optimal DG allocation to improve voltage profiles and reduce power losses. Bhadoriya et al. [12] applied a transient search optimization-based multi-objective function for determining the optimal siting of EVCSs and DGs. Mehroliya et al. [13] utilized a whale optimization algorithm within a multi-objective framework for the simultaneous placement of EVCSs, DGs, and SCs to achieve power loss reduction and voltage profile enhancement. Salkuti [14] provided a comprehensive review of smart energy system designs incorporating renewable energy sources, electric vehicles, and energy storage technologies, highlighting applications, challenges, and advancements enabled by artificial intelligence, machine learning, big data analytics, and IoT. In a related study, Salkuti [15] examined the economic integration of renewable energy systems, EVs, and energy storage within modern hybrid grids to address generation–demand fluctuations and improve grid stability. Jung et al. [16] evaluated the techno-economic aspects of modeling renewable energy systems, EVs, and battery storage solutions to mitigate the variability of renewable generation and enhance grid interoperability. Babu et al. [17] presented an integrated framework incorporating EVCSs, distribution static VAR compensators (DSVCs) and renewable energy sources (solar and wind) into radial distribution systems. By enabling both grid-to-vehicle (G2V) and vehicle-to-grid (V2G) operation, the proposed approach minimizes power and energy losses while enhancing system flexibility and resilience under diverse weather conditions. Vaigundamoorthi et al. [18] proposed an enhanced Black Widow Optimization Algorithm (BWOA) framework and compare its performance with the Slime Mould Algorithm (SMA). The proposed approach jointly optimizes the placement and sizing of PV-based distributed generators, distribution static compensators, and EV charging stations by minimizing a normalized multi-objective function incorporating power losses, voltage indices, and total installation and operational cost. Çeçen et al. [19] investigated optimal allocation strategies for EVCSs with and without DG in renewable-supported multi-energy systems. A hybrid optimization framework combining Grey Wolf Optimization (GWO) and Dynamic Fitness–Distance Balance (dFDB) is developed to minimize active power losses and voltage deviations.

The application of rooftop photovoltaic (PV) systems spans from small-scale installations on individual buildings to large-scale deployments in both off-grid and grid-connected configurations, as documented in numerous studies worldwide. Yao and Zhou [20] conducted a comprehensive survey of rooftop PV systems integrated with battery storage, ranging from standalone buildings to city-wide implementations, and performed micro-level comparative analyses considering lifecycle, installation angle, mechanical and tracking systems, as well as indoor and shading effects. Ren et al. [21] focused on optimizing space utilization for irregularly shaped rooftops while minimizing shading impacts to enable large-scale PV deployment in Hong Kong. Barbon et al. [22] developed a generalized algorithm that accounts for irregular flat rooftop geometries, PV module mounting arrangements, and self-shading effects to maximize rooftop space utilization. Alharbi et al. [23] employed mixed-integer programming to optimize grid-connected rooftop PV layouts, incorporating constraints such as inverter type and self-shading limitations. Sujon et al. [24] proposed a sustainable solution for powering household loads using rooftop PV systems by integrating dynamic programming (DP) with Internet of Things (IoT) technologies. Pérez et al. [25] investigated rooftop utilization strategies in Spain, considering obstacles and shaded areas, and validated their approach through simulations and experiments, achieving a 48% utilization. Additionally, the computation of solar radiation variability over time and location is discussed in [26].

Table 1 indicates that numerous studies have explored the integration of solar PV systems—including rooftop PVs—alongside wind DGs, SCs and EVCSs. However, a comprehensive approach that simultaneously considers all four systems, specifically incorporating solar DGs and wind DGs rather than generic DGs and optimizes their allocation, remains insufficiently addressed in the literature. Such an integrated strategy is crucial to enable the distribution system to manage time-varying power demands internally while adhering to network constraints.

Table 1. Literature analysis.

References	Rooftop Solar PV	Solar DGs	Wind DGs	Other/ General DGs	SCs	Fast EVCSs	Load Variations	Complete Internal Power Generation Capability
[1,2,7]	No	No	No	Yes	No	No	No	No
[4]	No	No	No	Yes	Yes	No	Yes	No
[5,6]	No	Yes	Yes	No	No	No	No	No
[8]	Yes	No	No	No	No	No	Yes	No
[9]	Yes	No	No	Yes	Yes	No	Yes	No
[11,12]	No	No	No	Yes	No	Yes	Yes	No
[13]	No	No	No	Yes	Yes	Yes	No	No
Proposed methodology	Yes	Yes	Yes	No	Yes	Yes	Yes	Yes

Solar radiation is inherently variable, fluctuating seasonally and throughout the day, and is completely unavailable during the nighttime. To ensure continuous clean energy generation, the system can be complemented with wind DGs. Since both solar and wind DGs produce intermittent and variable outputs, the inclusion of appropriately sized energy storage systems becomes essential. Furthermore, deploying shunt capacitors within the network helps to meet reactive power requirements and enhances overall system performance.

While the optimal allocation of DGs and SCs significantly reduces power losses, the integration of EVCSs tends to increase losses. Therefore, the present study adopts a three-stage optimization framework. In the first stage, the GSA is applied to determine the optimal sizing and placement of solar DGs, wind DGs, battery storage units and SCs, addressing multiple objectives such as minimizing real and reactive power losses, improving voltage profiles, and minimizing the source substation loading to near zero. Once the network is upgraded, the second stage involves strategically locating fast EVCSs while ensuring that node voltages remain above the minimum permissible threshold. In the third and final stage, the system is further optimized to mitigate the impact of integrated EVCSs while satisfying the same multi-objective criteria and achieving the desired level of EVCS integration.

In the past ten years, many researchers have proposed several metaheuristic optimization techniques based on swarm optimization and evolutionary based concepts. Each of these algorithms has its own importance depending on the application and nature of the problem, and all the algorithms are not suitable for all the solutions. GSA is an optimization method indifferent to the earlier metaheuristic techniques, inspired by the theory of Newtonian gravity in physics. In GSA, the equations developed for updating next-generation solution parameters depend on the fitness values, unlike other algorithms like PSO and GA, whereas the parameter update only depends on the previous best solutions. Many authors effectively used GSA for the past years for solving various complex problems related to electrical engineering. Hence, in the present case, GSA is used for obtaining the optimum planning of the distribution system upgrade with renewable energy resources.

Novelty and Contribution of the Work

• The time-dependent power output of rooftop PV systems is assessed using a solar insolation-based mathematical model.
• Wind turbine power generation is evaluated using reference data for time-varying conditions.
• The Gravitational Search Algorithm (GSA) is employed to determine the optimal sizing and placement of solar DGs, wind DGs, SCs, and fast EVCSs through a multi-stage, multi-objective optimization framework.
• The multi-objective optimization aims to minimize real and reactive power losses, enhance voltage profiles and minimize the source substation loading to near zero.
• Solar DG outputs are computed based on hourly average insolation values.
• Ratings for the battery storage systems, which are fed from the solar DGs, are calculated in accordance with IEEE 485 standards to ensure an adequate capacity for meeting time-varying load demands.
• The high penetration of the EVCSs is considered.
• Fixed ratings for solar DGs are determined to satisfy load requirements and recharge battery storage units.
• A practical 52-bus distribution system is analyzed as the test case.
• Performance evaluation is conducted for summer, rainy and winter seasons, each with a corresponding 24 h load schedule.
• The distribution network is upgraded to work as a microgrid with net metering capability.

For this work, in Section 2, a modified American Society of Heating Refrigeration and Air-conditioning Engineers (ASHRAE) model is discussed for calculating the solar insolation based on geographic location and time. The calculation steps for the solar DG and wind DG power generation capacity are presented in Section 3 and Section 4, respectively, and are used to calculate the time-varying output seasonally. The types/ranges of battery chargers and ratings of some practical EV batteries are presented in Section 5. The battery charging load demand model for lithium-ion batteries is presented in Section 6. The multi-objective function formulation to improve the performance of the distribution system is described in Section 7, and the methodology for the optimum allocation of solar DGs with battery storage systems, SCs, EVCSs and roof top solar PV systems using GSA is presented in Section 8. In Section 9, the simulation results are tabulated and explained, followed by a comparison with other studies in Section 10 and a comparison of the three stages of the optimization work in Section 11. Subsequently, the conclusions of the observations are presented in Section 12.

2. Solar Radiation Assessment via Enhanced ASHRAE Model

In this research, a modified ASHRAE approach [26,27] has been employed to compute hourly average solar radiation tailored to Indian climatic conditions. The following set of mathematical expressions describes the estimation of solar radiation (I) at any given time for a specific geographic location.

$$I=I_b+I_d$$

(1)

$$I_b=A I_N\cos {\theta }_z+\mathrm{B}$$

(2)

$$I_d=E I_N+F$$

(3)

$$I_N=C\exp \left[-{\displaystyle \frac{D}{\cos {\theta }_z}}\right]$$

(4)

The term $I$ represents the hourly total global solar radiation, which is composed of two components: $I_b$ (beam radiation) and $I_d$ (diffuse radiation). Additionally, $I_N$ denotes the portion of $I_b$ aligned with the direction of the sun’s rays. The constants $A, B, C, D, E$ and $F$ used in these calculations are specified in reference [26] and detailed in Table A1 within Appendix A.

$$\cos {\theta }_z=\sin \varnothing \sin \delta +\cos \varnothing \cos \delta \cos \omega$$

(5)

$$\delta =23.45\sin \left[360(284+n)/365\right]$$

(6)

$$\omega =15\left(12-\mathrm{L}\mathrm{A}\mathrm{T}\right)$$

(7)

$$\mathrm{L}\mathrm{A}\mathrm{T}=\mathrm{S}\mathrm{T}+\mathrm{E}\mathrm{T}\pm 4\left(\mathrm{S}\mathrm{T}\mathrm{L}-\propto \right)$$

(8)

$$\mathrm{E}\mathrm{T}=229.2(0.000075+0.001868\cos \beta -0.032077\sin \beta -0.014615\cos 2\beta -0.04089\sin 2\beta )$$

(9)

$$\beta =\left(n-1\right) 360/365$$

(10)

In these equations, ${\theta }_z$ denotes the solar zenith angle, while $\varphi$ and $\alpha$ represent the latitude and longitude of the location, respectively. The parameter $\delta$ corresponds to the solar declination angle, and $\omega$ is the hour angle. Furthermore, ST refers to the standard time, LAT indicates the local apparent solar time at noon, ET is the equation of time correction, STL represents the standard meridian for the local time zone, and $n$ signifies the day number within the year.

3. Assessment of Solar Power Production

This section determines the rooftop solar PV capacity (SPVC) [28] for each node within the distribution network, as computed using Equation (11).

$$\mathrm{S}\mathrm{P}\mathrm{V}\mathrm{C}=\mathrm{S}\mathrm{P}\mathrm{V}\mathrm{A}\times \mathrm{I}\times {\mathrm{E}}_{\mathrm{P}\mathrm{V}}\times \mathrm{P}\mathrm{R}$$

(11)

The parameter SPVA denotes the rooftop area available for installing solar PV modules, while $\mathrm{I}$ represents solar insolation. ${\mathrm{E}}_{\mathrm{P}\mathrm{V}}$ refers to the efficiency of the PV module and PR indicates its performance ratio. In this study, ${\mathrm{E}}_{\mathrm{P}\mathrm{V}}$ is assumed to be 0.20 [29], and PR is taken as 0.75 [28]. As outlined earlier, the SPVA at the jth node of the distribution network is determined using Equation (12).

$$\mathrm{S}\mathrm{P}\mathrm{V}\mathrm{A}={\mathrm{R}\mathrm{L}}_{\mathrm{j}}^{\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}\times \mathrm{A}\mathrm{r}\mathrm{e}{\mathrm{a}}^{\mathrm{S}\mathrm{H}}\times \mathrm{A}\mathrm{F}$$

(12)

The term $\mathrm{R}{\mathrm{L}}_j^{\mathrm{Total}}$ refers to the total number of houses connected to the jth node of the distribution network. ${\mathrm{Area}}^{\mathrm{S}\mathrm{H}}$ represents the average house area, while AF is the area factor, indicating the proportion of rooftop space available for solar PV installation. In this study, ${\mathrm{Area}}^{\mathrm{S}\mathrm{H}}$ is assumed to be 1000 sq. ft., and AF is taken as 30%, reflecting a conservative feasibility estimate [25]. The value of $\mathrm{R}{\mathrm{L}}_j^{\mathrm{Total}}$, as noted earlier, is computed using Equation (13).

$${\mathrm{R}\mathrm{L}}_j^{\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}\approx {\displaystyle \frac{{\mathrm{R}\mathrm{P}\mathrm{L}}_j^{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}}{{\mathrm{R}\mathrm{P}\mathrm{L}}_{\mathrm{s}\mathrm{h}}^{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}}}$$

(13)

The parameter $\mathrm{R}\mathrm{P}{\mathrm{L}}_j^{\mathrm{peak}}$ denotes the peak real power load at the jth node of the distribution network, while $\mathrm{R}\mathrm{P}{\mathrm{L}}_{\mathrm{s}\mathrm{h}}^{\mathrm{peak}}$ represents the peak real power demand for a single household, which is approximately 3.54 kW [9].

4. Assessment of Wind Power Production

Wind energy conversion results in wind power generation, which is influenced by several key parameters. Figure 1 shows a typical simplified structure of a wind turbine.

Figure 1. Simplified structure of wind turbine.

The output power from a wind turbine can be expressed using the following equation:

$$P_w={\displaystyle \frac{1}{2}}\rho A{v}^3{C}_p$$

(14)

$P_w$ denotes the power output of the wind turbine, $\rho$ refers to the air density, ‘$A$’ represents the swept area, ‘$v$’ is the wind speed, and $C_p$ denotes the power coefficient. Table 2 presents the turbine dimensions and parameters used in this analysis.

Table 2. Turbine parameters [6].

Parameters	Values
Turbine blade length ($r$)	52 m
Swept area ($A=\pi r^2$)	8495 m2
Air density ($\rho$)	1.23 kg/m3
Power coefficient ($C_p$)	0.4

5. Levels of EV Battery Charging and Ratings of Charging Stations

EV batteries can be charged using either alternating current (AC) or direct current (DC). In AC charging setups, the onboard charger within the EV handles the conversion from AC to DC, as batteries require DC for storage. Conversely, in DC charging systems, the conversion occurs within the external charging station, delivering DC directly to the battery.

For high-speed or fast charging, DC charging is the only practical solution. This is because the power rating and physical size of fast chargers are too large to be integrated into the vehicle without significantly increasing the cost and complexity. Therefore, fast chargers are always part of the external charging infrastructure. Table 3 outlines the standardized charging levels, categorized by power capacity and the corresponding type of charging equipment.

Table 3. Charging power level [30].

Charging Level	AC/DC	Power
Level 1	AC and DC	0–10 kW
Level 2	AC and DC	10–50 kW
Level 3 (Fast charging)	Only DC	>50 kW (up to 350 kW)

Rating of EVCSs at Strategic Locations

Fast-charging stations should be strategically positioned within the distribution network to maximize coverage and operational efficiency while adhering to network constraints. Table 4 provides examples of various EV categories—such as two-wheelers, three-wheelers, rickshaws, and passenger cars—along with their typical battery capacities and the corresponding travel range per full charge. Based on these vehicle profiles, installing charging ports rated at 10 kW, 50 kW, and 100 kW at key locations is recommended to meet fast-charging demands effectively.

Table 4. Charging characteristics of EVs.

S. No.	2-Wheeler EV Model [31]	Power	Battery Capacity	Range/Charge
1	Bajaj Chetak	4.2 kW	2.9 kWh	108 km
2	TVS iQube	4.4 kW	4.56 kWh	100–145 km
3	Hero Electric Optima CX	1.2 kW	2 kWh	89 km
4	Revolt RV 400	3 kW	3.24 kWh	180 km
5	Ampere Nexus	4 kW	3 kWh	136 km
S. No.	E Rickshaw EV Model [32]	Power	Battery Capacity	Range/Charge
1	Bajaj RE E TEC 9	-	8.9 kWh	178 km
2	Mahindra Treo Yaari	-	12 kWh	80 km
3	Saarthi DLX	-	8.9 kWh	120 km
4	Atul Elite Plus	-	3.69 kWh	125 km
5	E-Ashwa	-	9 kWh	125 km
S. No.	EV Cars Model [33]	Power	Battery Capacity	Range/Charge
1	MG Comet EV	3.3 kW	17.3 kWh	230 km
2	Tata Tigor	25 kW	26 kWh	315 km
3	Tata Nexon	50 kW	30–40.5 kWh	325–465 km
4	Mahindra XUV400	50 kW	34.5–39.4 kWh	375–456 km
5	Hyundai Ioniq 5	350 kW	72.6 kWh	631 km

Smart charging strategies should be employed to dynamically allocate charging ports based on the power ratings of EVs arriving at the station. This ensures that the aggregate load at any given station does not exceed 300 kW. The overall capacity of the charging station must be carefully determined so that the additional demand does not negatively impact other consumers connected to the same distribution network.

6. Modeling of EV Battery Charging Load Demand

Lithium-ion batteries (LIBs) are highly efficient and well suited for electric vehicle applications. Figure 2 illustrates a typical charging profile for an LIB operating under constant-power and constant-voltage modes. From this characteristic curve, the following equations can be derived to perform load-flow analysis for the battery during charging.

$${EV}^{CP}\left(t\right)={EV}_{max}^{CP}\hspace{1em} for T_a \le t\le T_b$$

(15)

$${EV}^{CV}\left(t\right)={EV}_{max}^{CV}\left({\displaystyle \frac{T_{max}-t}{T_{max}-T_b}}\right)\hspace{1em}for T_b \le t\le T_{max}$$

(16)

Figure 2. Charging characteristics of lithium-ion battery [10].

${EV}_{max}^{CP}$ and ${EV}_{max}^{CV}$ denote the maximum electric vehicle load demands during the constant-power and constant-voltage charging phases, respectively.

The energy storage capacity of a battery (BES) during the charging process can be quantified through its State of Charge (SOC), which is expressed using the following equations:

$$\mathrm{B}\mathrm{E}\mathrm{S}\left(t+1\right)=\mathrm{B}\mathrm{E}\mathrm{S}\left(t\right)+\mathrm{E}\mathrm{V}\left(t\right)∆\left(t\right)\hspace{1em}$$

(17)

$$\mathrm{S}\mathrm{O}\mathrm{C}\left(t\right)={\displaystyle \frac{\mathrm{B}\mathrm{E}\mathrm{S}\left(t\right)}{{\mathrm{B}\mathrm{E}\mathrm{S}}_{max}}}\times 100\%\hspace{1em}$$

(18)

Once the SOC reaches 100%, the battery must be detached from the charging socket to prevent overcharging. Modern chargers incorporate advanced power factor correction techniques to minimize charging time. In this study, a lagging power factor of 0.95 has been assumed for the battery chargers. Consequently, the peak battery charging load demand at strategic locations can be expressed using the following equations:

$${PL}_{\mathrm{E}\mathrm{V}}\left(N_K\right)=\sum _{n=1}^{{NV}_K}{\mathrm{E}\mathrm{V}}_{max}^n$$

(19)

$${QL}_{\mathrm{E}\mathrm{V}}\left(N_K\right)=\sum _{n=1}^{{NV}_K}{\mathrm{E}\mathrm{V}}_{max}^n\mathrm{t}\mathrm{a}\mathrm{n}(\varnothing )$$

(20)

${PL}_{\mathrm{E}\mathrm{V}}\left(N_K\right)$ and ${QL}_{\mathrm{E}\mathrm{V}}\left(N_K\right)$ represent the active and reactive power demand of the EVCS for the Kth node, respectively, ${NV}_K$ denotes the number of EVs connected at that Kth node, ${\mathrm{E}\mathrm{V}}_{max}^n$ indicates the peak charging power of an individual EV, and $\mathrm{\varnothing }$ is the power factor angle.

7. Multi-Objective Function Formulation

This work proposes the optimal allocation of solar DGs, wind DGs, battery storage systems, SCs and fast EVCSs within a distribution network. The primary goal is to minimize both real and reactive power drawn from the source substation, ideally reducing it to near zero. Additional objectives include lowering active and reactive power losses across the network and simultaneously enhancing the voltage profile. These five objectives are formulated individually using mathematical models, and, finally, a combined multi-objective optimization function is developed to achieve the desired performance.

Real power drawn index (XPJ): This index aims to minimize the total real power drawn from the substation by optimally allocating solar DGs, wind DGs, battery storage systems and fast EVCSs (Equation (21)).

$$\mathrm{X}\mathrm{P}\mathrm{J}=\left|{\displaystyle \frac{\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{B}-({\sum }_{n=1}^{\mathrm{N}\mathrm{D}\mathrm{G}}{\mathrm{S}\mathrm{P}\mathrm{D}\mathrm{G}}_n+{\sum }_{n=1}^{\mathrm{N}\mathrm{D}\mathrm{G}}{\mathrm{W}\mathrm{P}\mathrm{D}\mathrm{G}}_n+{\sum }_{n=1}^{\mathrm{N}\mathrm{B}-1}{\mathrm{P}\mathrm{V}\mathrm{D}\mathrm{G}}_n)+{\sum }_{n=1}^{\mathrm{N}\mathrm{C}\mathrm{S}}{\mathrm{P}\mathrm{E}\mathrm{V}\mathrm{C}\mathrm{S}}_n}{\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{B}}}\right|$$

(21)

PSIB denotes the real power delivered from the source substation under the base configuration. PVDGn represents the real power generated by the rooftop PV system at the nth node of the distribution network having NB nodes. SPDGn and WPDGn refer to the real power generated by solar DGs with battery storage and wind DGs, respectively, at the NDG locations within the distribution network, where $\mathrm{N}\mathrm{D}\mathrm{G}$ is considered as 3 in this study. The PEVCSn indicates the real power consumption of the fast EVCSs at the NCS locations, with NCS taken as 10.

Reactive power drawn index (XQJ): This index aims to minimize the total reactive power drawn from the substation by optimally allocating solar DGs, wind DGs, battery storage systems and fast EVCSs (Equation (22)).

$$\mathrm{X}\mathrm{Q}\mathrm{J}=\left|{\displaystyle \frac{\mathrm{Q}\mathrm{S}\mathrm{I}\mathrm{B}-({\sum }_{n=1}^{\mathrm{N}\mathrm{D}\mathrm{G}}{\mathrm{S}\mathrm{Q}\mathrm{D}\mathrm{G}}_n+{\sum }_{n=1}^{\mathrm{N}\mathrm{D}\mathrm{G}}{\mathrm{W}\mathrm{Q}\mathrm{D}\mathrm{G}}_n+{\sum }_{n=1}^{\mathrm{N}\mathrm{S}\mathrm{C}}{\mathrm{S}\mathrm{C}}_n)+{\sum }_{n=1}^{\mathrm{N}\mathrm{C}\mathrm{S}}{\mathrm{Q}\mathrm{E}\mathrm{V}\mathrm{C}\mathrm{S}}_n}{\mathrm{Q}\mathrm{S}\mathrm{I}\mathrm{B}}}\right|$$

(22)

QSIB denotes the reactive power delivered from the source substation under the base configuration. SQDGn and WQDGn refer to the reactive power generations of solar DGs and wind DGs, respectively. SCn refers to the reactive power generations of the shunt capacitors at the NSC locations, where $\mathrm{N}\mathrm{S}\mathrm{C}$ is considered as 3 in this study. The QEVCSn indicates the reactive power consumption of the fast EVCSs.

Real power loss minimization index (XPLJ): This index is designed to minimize the total real power loss within the distribution network (Equation (23)).

$$\mathrm{X}\mathrm{P}\mathrm{L}\mathrm{J}={\displaystyle \frac{\mathrm{T}\mathrm{L}\mathrm{P}}{\mathrm{T}\mathrm{L}\mathrm{P}\mathrm{B}}}$$

(23)

TLPB represents the real power loss in the base configuration of the network, while $\mathrm{T}\mathrm{L}\mathrm{P}$ denotes the corresponding loss after implementing the proposed modifications.

Reactive power loss minimization index (XQLJ): This index is designed to minimize the total reactive power loss within the distribution network (Equation (24)).

$$\mathrm{X}\mathrm{Q}\mathrm{L}\mathrm{J}={\displaystyle \frac{\mathrm{T}\mathrm{L}\mathrm{Q}}{\mathrm{T}\mathrm{L}\mathrm{Q}\mathrm{B}}}$$

(24)

TLQB represents the reactive power loss in the base configuration of the network, while $\mathrm{T}\mathrm{L}\mathrm{Q}$ denotes the corresponding loss after implementing the proposed modifications.

Voltage profile index (XVPJ): This index is intended to enhance the voltage profile across all nodes of the distribution network, bringing them as close as possible to the nominal value of 1 p.u (Equation (25)).

$$\mathrm{X}\mathrm{V}\mathrm{P}\mathrm{J}=\sqrt{{\displaystyle \frac{{\sum }_{\mathrm{k}=1}^{\mathrm{N}\mathrm{B}-1}{(1-{\mathrm{V}}_{\mathrm{k}}^{\mathrm{M}})}^2}{{\sum }_{\mathrm{k}=1}^{\mathrm{N}\mathrm{B}-1}{(1-{\mathrm{V}}_{\mathrm{k}}^{\mathrm{B}\mathrm{a}\mathrm{s}\mathrm{e}})}^2}}}$$

(25)

${\mathrm{V}}_{\mathrm{k}}^{\mathrm{B}\mathrm{a}\mathrm{s}\mathrm{e}}$ represents the node voltages in the base configuration and ${\mathrm{V}}_{\mathrm{k}}^{\mathrm{M}}$ denotes the voltages in the modified network.

Multi-objective function (MOF): All five previously discussed objectives are integrated into a single formulation, which can be expressed through the following combined equation.

$$\mathrm{M}\mathrm{O}\mathrm{F}=\mathrm{X}\mathrm{P}\mathrm{J}+\mathrm{X}\mathrm{Q}\mathrm{J}+\mathrm{X}\mathrm{P}\mathrm{L}\mathrm{J}+\mathrm{X}\mathrm{Q}\mathrm{L}\mathrm{J}+\mathrm{X}\mathrm{V}\mathrm{P}\mathrm{J}$$

(26)

8. Gravitational Search Algorithm (GSA) for Optimum Allocation of Solar DGs with Battery Storage, Wind DGs, SCs and EVCSs

The Gravitational Search Algorithm (GSA) [34] is a metaheuristic optimization method inspired by Newton’s law of gravity and Newton’s law of motion.

According to Newton’s law of gravity, the gravitational force $F$ acting between two masses, $M_1$ and $M_2$, can be mathematically expressed as follows:

$$F=G{\displaystyle \frac{M_1{M}_2}{R_{12}^2}}$$

(27)

Here, $R_{12}$ denotes the distance between the two particles, and $G$ is the gravitational constant, which gradually decreases as the universe ages.

However, for implementation within the optimization framework, the $R^2$ term in Equation (27) was replaced with $R$ to achieve an improved experimental performance. The modified equation is therefore expressed as follows:

$$F=G{\displaystyle \frac{M_1{M}_2}{R_{12}}}$$

(28)

According to Newton’s law of motion, the acceleration of a particle under the influence of a force $F$ can be expressed mathematically as follows, where $a$ denotes the particle’s acceleration and $M$ represents its inertial mass.

$$a={\displaystyle \frac{F}{M}}$$

(29)

Based on Newton’s laws, the GSA models the solution space as a gravitational field, where particles (or masses) represent decision variables whose optimal values need to be determined. Initial masses are assigned by randomly generating fitness values within the search space. While all agents exert gravitational attraction on each other, heavier masses apply stronger forces, guiding lighter agents toward them over successive iterations to converge on optimal solutions. In this study, GSA is employed to determine the optimal placement and sizing of solar DGs with battery storage systems, wind DGs, SCs and EVCSs across different seasons. A multi-objective function, defined by Equation (26), serves as the fitness function to enhance the performance of the distribution system.

For an optimization problem with $N$ decision variables, each represented as a mass agent with $d$ dimensions in the search space, the position of the jth mass is expressed as follows:

$$X_j=\left(x_j^1, x_j^2, x_j^3,\dots ,x_j^d\right) for j=1, 2, 3,\dots ,N$$

(30)

In GSA, the force acting on the jth mass due to the kth mass at a given iteration ‘itrn’ is computed using the modified Newtonian gravitational law, as shown in Equation (28).

$$F_{jk}^d\left(itrn\right)=G\left(itrn\right){\displaystyle \frac{M_{pj}\left(itrn\right)\times M_{ak}\left(itrn\right)}{R_{jk}\left(itrn\right)+\epsilon }} (x_k^d\left(itrn\right)-x_j^d\left(itrn\right))$$

(31)

$M_{ak}$ and $M_{pj}$ represent the active and passive gravitational masses, $R_{jk}$ is the separation distance between those in the search space, and $\epsilon$ refers to a small constant. G denotes the gravitational constant that varies with each iteration, along with other parameters.

Considering the combined influence of all N masses, the resultant force on the jth mass is calculated by incorporating stochastic random numbers ($ran{d}_k$) within the interval [0, 1], which account for the weighted contribution of individual masses.

$$F_j^d\left(itrn\right)=\sum _{\begin{array}{c}k=1\\ k\ne j\end{array}}^N{rand}_k F_{jk}^d\left(itrn\right)$$

(32)

Based on this resultant force, the acceleration of the jth mass is determined, where $M_{jj}$ denotes its inertial mass.

$$a_j^d\left(itrn\right)={\displaystyle \frac{F_j^d\left(itrn\right)}{M_{jj}\left(itrn\right)}}$$

(33)

$M_{jj}$ is derived from the population fitness values as follows:

$$M_{jj}\left(itrn\right)=m_{jj}\left(itrn\right)/(\sum _{k=1}^N{m}_{jj}\left(itrn\right))$$

(34)

$$m_{jj}\left(itrn\right)={\displaystyle \frac{{fit}_{jj}\left(itrn\right)-worst\left({fit}_{jj}\left(itrn\right)\right)}{best\left({fit}_{jj}\left(itrn\right)\right)-worst\left({fit}_{jj}\left(itrn\right)\right)}}$$

(35)

${fit}_{jj}\left(itrn\right)$ is the fitness value of the jth mass, and $worst({fit}_{jj}\left(itrn\right))$ and $best({fit}_{jj}\left(itrn\right))$ represent the maximum and minimum fitness values, respectively.

Using the computed acceleration, the velocity and position of the jth mass for the next iteration are updated through the corresponding equations:

$$v_j^d\left(itrn+1\right)={rand}_j\times v_j^d\left(itrn\right)+a_j^d\left(itrn\right)$$

(36)

$$x_j^d\left(itrn+1\right)=x_j^d\left(itrn\right)+v_j^d\left(itrn+1\right)$$

(37)

A flowchart illustrating the optimal allocation and sizing of three solar DG units, three wind DG units, three SCs, and ten fast EVCSs using GSA is presented in Figure 3.

Figure 3. Flow chart for optimal allocation and sizing of solar and wind DG units, SCs and EVCSs using GSA.

9. Results and Discussions

In this study, a practical 11 kV, 52-bus, Indian distribution network [9], illustrated in Figure 4, is examined to improve its operational performance through the proposed multi-objective optimization framework. The system’s line and load parameters, sourced from [9], are presented in Table A2 within Appendix A.

Figure 4. Practical 52-bus rural distribution system.

Additionally, the seasonal hourly average load profile for this distribution network, located in Bengaluru, India, is provided in [9] and depicted in Figure 5.

Figure 5. Seasonal load schedule of the 52-bus distribution system.

The corresponding hourly average insolation profile season-wise has been assessed using the methodology outlined in Section 2, based on Bengaluru’s geographical coordinates, and is shown in Figure 6.

Figure 6. Seasonal hourly average insolation profile.

Furthermore, the rooftop solar PV generation capacity for the distribution system has been computed following the procedure described in Section 3, with the results summarized in Tables 5, 8 and 11.

The seasonal hourly average wind speed sourced from [6] is depicted in Figure 7, and the wind power generation capacity for the distribution system has been estimated following the formulation and assumptions described in Section 4, with the results summarized in Tables 5, 6, 8, 9, 11 and 12.

Figure 7. Seasonal hourly average wind speed profile.

9.1. Optimum Output and Location of Wind DGs, Solar DGs with Batteries, SCs and EVCSs Using GSA

In addition to rooftop solar PV installations, the optimal sizing and placement of wind-based DGs, solar DGs, battery storage, SCs and EVCSs have been determined using the GSA described in Section 7. These solutions satisfy multiple objectives simultaneously. The results for different seasons are summarized in Table 5, Table 6 and Table 7 for summer, Table 8, Table 9 and Table 10 for the rainy season and Table 11, Table 12 and Table 13 for winter.

Table 5. Solar DG output requirements for summer load (daytime only without battery charging).

Time	Load Factor	Rooftop PVDG (kW)	Solar DG-1 (kW)	Solar DG-2 (kW)	Solar DG-3 (kW)	Wind DG-1, 2, 3 (kW)	Total DG (kW)	Real Power Loss (kW)	Real Power Load (kW)	Real Power from Substation (Net Metering) (kW)
6~7 a.m.	0.7	879.0285	1447.3852	1072.1453	1667.7654	348.7772	6112.6560	177.6043	2928.8000	−6.2517
7~8 a.m.	0.7	1040.4890	1423.3550	1026.2304	1536.7220	356.4491	6096.1436	165.2838	2928.8000	−2.0598
8~9 a.m.	0.9	1834.6675	1395.4208	1079.7153	1505.4066	379.3543	6953.2731	186.2381	3765.6000	−1.4350
9~10 a.m.	0.9	2841.0529	981.7335	867.3797	954.4313	418.9041	6901.3098	130.0266	3765.6000	−5.6832
10~11 a.m.	1.0	3707.8841	769.9149	761.7652	675.0911	469.3065	7322.5748	131.8525	4184.0000	−6.7224
11~12 p.m.	1.0	4254.1760	432.3103	606.1042	409.4335	537.5111	7314.5574	130.1898	4184.0000	−0.3676
12~1 p.m.	1.0	4393.2925	325.7910	573.2610	311.1367	575.4520	7329.8372	133.0140	4184.0000	−12.8231
1~2 p.m.	1.0	4105.4870	458.5258	633.4723	439.8354	562.3653	7324.4165	129.4284	4184.0000	−10.9881
2~3 p.m.	0.9	3432.9584	564.0432	671.6723	545.0195	557.0982	6884.9879	114.8972	3765.6000	−4.4907
3~4 p.m.	0.9	2490.5573	929.8698	913.1496	943.1049	541.9242	6902.4542	131.2204	3765.6000	−5.6338
4~5 p.m.	0.8	1505.4733	1215.4229	1027.8542	1315.0449	479.2053	6501.4111	148.9063	3347.2000	−5.3048
5~6 p.m.	0.8	899.2740	1449.1074	1197.6657	1771.0235	413.6774	6558.1028	198.2277	3347.2000	−12.6751

Table 6. Battery storage capacity requirements for summer load (nighttime).

Time	Load Factor	Battery1 Output (kW)	Battery2 Output (kW)	Battery3 Output (kW)	Wind DG-1, 2, 3 (kW)	Total DG (kW)	Real Power Loss (kW)	Real Power Load (kW)	Real Power from Substation (Net Metering) (kW)
6~7 p.m.	0.8	2005.5421	1450.5432	2104.0986	364.7440	6654.4159	302.7147	3347.2000	−4.5011
7~8 p.m.	0.8	2005.5421	1603.9490	2104.0986	318.8215	6670.0541	321.1976	3347.2000	−1.6566
8~9 p.m.	0.7	1839.7599	1421.1123	2093.6564	286.5230	6214.0976	274.9636	2928.8000	−10.3340
9~10 p.m.	0.7	1839.7599	1427.5927	2093.6564	282.2915	6207.8835	275.7377	2928.8000	−3.3459
10~11 p.m.	0.7	1839.7599	1395.1906	2093.6564	293.9814	6210.5511	272.1967	2928.8000	−9.5544
11~12 a.m.	0.7	1839.7599	1369.2690	2093.6564	301.6571	6207.6566	269.6273	2928.8000	−9.2292
12~1 a.m.	0.6	1636.3186	1217.7655	1951.0085	312.1881	5741.6569	219.4900	2510.4000	−11.7669
1~2 a.m.	0.6	1636.3186	1165.3217	1951.0085	325.5770	5729.3798	216.1983	2510.4000	−2.7815
2~3 a.m.	0.6	1636.3186	1165.3217	1916.6125	335.6546	5725.2166	213.2076	2510.4000	−1.6090
3~4 a.m.	0.6	1636.3186	1175.8105	1951.0085	323.1350	5732.5426	216.7758	2510.4000	−5.3668
4~5 a.m.	0.6	1636.3186	1191.5436	1951.0085	318.5034	5734.3809	217.7318	2510.4000	−6.2491
5~6 a.m.	0.6	1636.3186	1165.3217	1916.6125	338.4746	5733.6766	213.1556	2510.4000	−10.1210

Table 7. Shunt capacitor capacity requirements for summer load.

Time	Load Factor	SC-1 (kVAR)	SC-2 (kVAR)	SC-3 (kVAR)	Total SCs with DG Reactive Power (kVAR)	Reactive Power Loss (kVAR)	Reactive Power Load (kVAR)	Reactive Power from Substation (kVAR)
6~7 a.m.	0.7	247.4402	294.5729	225.2192	2487.5256	76.4112	1417.5000	−7.5145
7~8 a.m.	0.7	264.3727	310.2269	239.4704	2475.8636	71.1105	1417.5000	−1.1531
8~9 a.m.	0.9	360.1989	326.2847	521.1247	2890.0940	80.1257	1822.5000	−1.3683
9~10 a.m.	0.9	486.7859	514.9410	529.7602	2866.0935	55.9417	1822.5000	−1.5518
10~11 a.m.	1.0	643.7921	643.7921	607.8064	3083.5396	56.7272	2025.0000	−15.7123
11~12 p.m.	1.0	691.9261	691.9261	691.9261	3081.7257	56.0119	2025.0000	−14.6139
12~1 p.m.	1.0	709.4540	709.9765	692.6572	3077.3299	57.2270	2025.0000	−9.0029
1~2 p.m.	1.0	673.2782	679.8926	663.3227	3074.5556	55.6843	2025.0000	−7.7713
2~3 p.m.	0.9	579.0275	579.0275	579.0275	2871.7645	49.4325	1822.5000	−13.7320
3~4 p.m.	0.9	510.7313	461.8522	460.8229	2883.5969	56.4553	1822.5000	−18.5416
4~5 p.m.	0.8	312.8537	365.9935	356.7630	2677.7749	64.0643	1620.0000	−7.6106
5~6 p.m.	0.8	245.6957	308.4284	284.9469	2699.1281	85.2840	1620.0000	−7.7441
6~7 p.m.	0.8	249.0473	159.0588	143.8383	2739.2509	130.2377	1620.0000	−2.9132
7~8 p.m.	0.8	249.0473	159.0588	143.8383	2744.3912	138.1897	1620.0000	−0.1015
8~9 p.m.	0.7	170.7731	173.0958	136.8655	2523.3083	118.2983	1417.5000	−1.4100
9~10 p.m.	0.7	170.7731	173.0958	136.8655	2521.2657	118.6313	1417.5000	0.9656
10~11 p.m.	0.7	170.7731	173.0958	136.8655	2522.1426	117.1079	1417.5000	−1.4347
11~12 a.m.	0.7	170.7731	173.0958	136.8655	2521.1911	116.0025	1417.5000	−1.5887
12~1 a.m.	0.6	148.0110	107.7005	157.5025	2300.4966	94.4317	1215.0000	−4.9649
1~2 a.m.	0.6	148.0110	107.7005	157.5025	2296.4612	93.0155	1215.0000	−2.3456
2~3 a.m.	0.6	148.0110	107.7005	157.5025	2295.0927	91.7288	1215.0000	−2.2639
3~4 a.m.	0.6	148.0110	107.7005	157.5025	2297.5008	93.2640	1215.0000	−3.1368
4~5 a.m.	0.6	148.0110	107.7005	157.5025	2298.1050	93.6753	1215.0000	−3.3297
5~6 a.m.	0.6	148.0110	107.7005	157.5025	2297.8735	91.7065	1215.0000	−5.0671

Table 8. Solar DG output requirements for rainy season load (daytime only without battery charging).

Time	Load Factor	Rooftop PVDG (kW)	Solar DG-1 (kW)	Solar DG-2 (kW)	Solar DG-3 (kW)	Wind DG-1, 2, 3 (kW)	Total DG (kW)	Real Power Loss (kW)	Real Power Load (kW)	Real Power from Substation (Net Metering) (kW)
6~7 a.m.	0.66	546.6072	1257.2236	1057.7688	1203.6191	620.8212	5927.6823	152.3503	2761.4400	−13.8920
7~8 a.m.	0.66	737.7280	1387.4060	1052.2807	1410.3794	444.0078	5919.8176	156.6004	2761.4400	−1.7772
8~9 a.m.	0.79	1439.5609	1337.6753	1024.8286	1423.0918	416.3905	6474.3281	160.3455	3305.3600	−8.6227
9~10 a.m.	0.79	2180.9207	964.0508	855.2040	934.6955	498.6760	6430.8989	115.5295	3305.3600	−10.0095
10~11 a.m.	0.80	2758.6118	555.4026	743.6388	584.6399	604.7812	6456.6367	104.6444	3347.2000	−4.7923
11~12 p.m.	0.80	3095.6650	356.6122	610.1202	397.7439	727.4970	6642.6323	106.7889	3347.2000	−188.6434
12~1 p.m.	0.76	3160.8323	304.7957	531.3914	304.7074	792.8140	6680.1687	104.6247	3179.8400	−395.7040
1~2 p.m.	0.76	2949.5652	304.7554	576.3500	379.5138	769.3799	6518.3240	103.7799	3179.8400	−234.7041
2~3 p.m.	0.73	2481.8924	365.1731	646.9266	518.8374	747.9019	6256.5353	96.7080	3054.3200	−105.5072
3~4 p.m.	0.73	1811.6634	540.0042	797.8421	775.6060	747.6386	6168.0314	107.1152	3054.3200	−6.5963
4~5 p.m.	0.70	1068.2515	627.6085	927.2109	1009.1658	805.3561	6048.3050	115.9729	2928.8000	−3.5321
5~6 p.m.	0.70	573.4269	1042.8479	1061.2623	1282.8254	707.5170	6082.9135	143.2997	2928.8000	−10.8138

Table 9. Battery storage capacity requirements for rainy season load (nighttime).

Time	Load Factor	Battery1 Output (kW)	Battery2 Output (kW)	Battery3 Output (kW)	Wind DG-1, 2, 3 (kW)	Total DG (kW)	Real Power Loss (kW)	Real Power Load (kW)	Real Power from Substation (Net Metering) (kW)
6~7 p.m.	0.69	1567.6485	1235.9052	1750.0867	515.3075	6099.5629	207.5533	2886.9600	−5.0496
7~8 p.m.	0.69	1646.8765	1286.4947	1830.6470	450.4286	6115.3040	222.3622	2886.9600	−5.9819
8~9 p.m.	0.67	1780.0698	1234.9540	1811.2292	404.7975	6040.6455	230.5697	2803.2800	−6.7957
9~10 p.m.	0.67	1780.0698	1234.9540	1826.8088	398.8192	6038.2903	231.3935	2803.2800	−3.6168
10~11 p.m.	0.58	1566.0135	1122.9180	1688.1651	415.3346	5623.1005	187.7839	2426.7200	−8.5965
11~12 a.m.	0.58	1566.0135	1122.9180	1648.5032	426.1788	5615.9712	185.9941	2426.7200	−3.2571
12~1 a.m.	0.51	1376.1116	1026.1354	1565.2246	441.0569	5290.6423	153.9641	2133.8400	−2.8382
1~2 a.m.	0.51	1376.1116	1026.1354	1507.7144	459.9727	5289.8795	151.6458	2133.8400	−4.3937
2~3 a.m.	0.48	1297.9873	1010.5529	1420.3233	474.2103	5151.4944	139.2349	2008.3200	−3.9395
3~4 a.m.	0.48	1297.9873	1067.3971	1420.3233	456.5226	5155.2756	142.1523	2008.3200	−4.8032
4~5 a.m.	0.52	1357.3600	1044.9626	1584.5304	449.9791	5336.7903	155.6154	2175.6800	−5.4949
5~6 a.m.	0.52	1181.1333	1044.9626	1283.6494	602.1125	5316.0828	136.8573	2175.6800	−3.5455

Table 10. Shunt capacitor capacity requirements for rainy season load.

Time	Load Factor	SC-1 (kVAR)	SC-2 (kVAR)	SC-3 (kVAR)	Total SCs with DG Reactive Power (kVAR)	Reactive Power Loss (kVAR)	Reactive Power Load (kVAR)	Reactive Power from Substation (kVAR)
6~7 a.m.	0.66	201.6470	293.2582	138.9794	2402.6439	65.5461	1336.5000	−14.4978
7~8 a.m.	0.66	262.8766	270.3828	159.6745	2396.2867	67.3746	1336.5000	−6.3121
8~9 a.m.	0.79	311.6762	340.0887	353.1568	2659.8496	68.9859	1599.7500	−5.0137
9~10 a.m.	0.79	424.7848	477.2918	343.1965	2642.2410	49.7046	1599.7500	−6.6865
10~11 a.m.	0.80	468.1644	493.5250	479.5438	2656.7740	45.0214	1620.0000	−5.6526
11~12 p.m.	0.80	516.3734	516.3734	516.3734	2715.0083	45.9441	1620.0000	−62.9642
12~1 p.m.	0.76	512.2173	512.2173	512.2173	2693.4578	45.0130	1539.0000	−123.3448
1~2 p.m.	0.76	494.9999	494.9999	494.9999	2658.0507	44.6495	1539.0000	−88.3012
2~3 p.m.	0.73	484.8942	434.1970	387.9225	2547.7389	41.6069	1478.2500	−41.7819
3~4 p.m.	0.73	358.7742	331.0822	403.3517	2525.1463	46.0844	1478.2500	−14.7118
4~5 p.m.	0.70	252.1508	284.1608	293.5694	2466.8246	49.8953	1417.5000	−13.3293
5~6 p.m.	0.70	252.3305	207.9336	211.0212	2482.2536	61.6522	1417.5000	−17.0014
6~7 p.m.	0.69	112.2621	171.9893	184.5202	2473.6979	89.2962	1397.2500	−1.0517
7~8 p.m.	0.69	112.2621	171.9893	184.5202	2478.8720	95.6674	1397.2500	0.1454
8~9 p.m.	0.67	130.5476	185.8611	141.6149	2443.5839	99.1986	1356.7500	−1.5352
9~10 p.m.	0.67	130.5476	185.8611	141.6149	2442.8097	99.5530	1356.7500	−0.4067
10~11 p.m.	0.58	180.7429	152.6701	64.6002	2246.3262	80.7908	1174.5000	−4.9355
11~12 a.m.	0.58	180.7429	152.6701	64.6002	2243.9828	80.0207	1174.5000	−3.3621
12~1 a.m.	0.51	105.2273	140.3323	101.3445	2085.9382	66.2404	1032.7500	−0.8479
1~2 a.m.	0.51	105.2273	140.3323	101.3445	2085.6875	65.2430	1032.7500	−1.5945
2~3 a.m.	0.48	109.1923	152.9474	71.7008	2027.1367	59.9034	972.0000	−9.1333
3~4 a.m.	0.48	109.1923	152.9474	71.7008	2028.3795	61.1586	972.0000	−9.1210
4~5 a.m.	0.52	132.2852	171.9993	56.9254	2115.4129	66.9508	1053.0000	−9.3621
5~6 a.m.	0.52	132.2852	171.9993	56.9254	2108.6063	58.8805	1053.0000	−10.6259

Table 11. Solar DG output requirements for winter load (daytime only without battery charging).

Time	Load Factor	Rooftop PVDG (kW)	Solar DG-1 (kW)	Solar DG-2 (kW)	Solar DG-3 (kW)	Wind DG-1, 2, 3 (kW)	Total DG (kW)	Real Power Loss (kW)	Real Power Load (kW)	Real Power from Substation (Net Metering) (kW)
6~7 a.m.	0.66	602.0017	1648.7683	1213.5390	1900.4779	208.7668	5991.0873	223.5199	2761.4400	−6.1275
7~8 a.m.	0.66	690.2384	1663.0864	1185.0815	1701.3754	246.7692	5980.0892	205.6062	2761.4400	−13.0431
8~9 a.m.	0.80	1368.8521	1435.6499	1133.2595	1659.1574	313.5392	6537.5365	185.4726	3347.2000	−4.8639
9~10 a.m.	0.80	2279.0046	1101.2234	883.7595	1122.3755	366.1955	6484.9495	128.0402	3347.2000	−9.7093
10~11 a.m.	0.82	3048.1032	741.5365	694.3711	772.2182	427.3378	6538.2424	103.5174	3430.8800	−3.8449
11~12 p.m.	0.82	3511.6798	512.6905	573.1784	479.9658	486.1674	6536.0166	100.0881	3430.8800	−5.0485
12~1 p.m.	0.77	3598.2295	355.4465	530.6880	339.5845	499.9031	6323.6578	94.5883	3221.6800	−7.3894
1~2 p.m.	0.77	3296.1237	476.4017	594.1593	480.9508	489.1089	6314.9622	92.0976	3221.6800	−1.1845
2~3 p.m.	0.72	2649.5679	773.8406	679.0255	669.8139	446.5874	6112.0100	92.8370	3012.4800	−6.6931
3~4 p.m.	0.72	1775.4628	1181.2680	947.4057	1285.3409	319.6475	6148.4198	131.7997	3012.4800	−4.1402
4~5 p.m.	0.69	931.2998	1602.5601	1161.8068	1645.3582	247.8458	6084.5622	196.4476	2886.9600	−1.1546
5~6 p.m.	0.69	600.7783	1747.3393	1149.5721	1806.4789	270.0045	6114.1821	220.4484	2886.9600	−6.7738

Table 12. Battery storage capacity requirements for winter load (nighttime).

Time	Load Factor	Battery1 Output (kW)	Battery2 Output (kW)	Battery3 Output (kW)	Wind DG-1, 2, 3 (kW)	Total DG (kW)	Real Power Loss (kW)	Real Power Load (kW)	Real Power from Substation (Net Metering) (kW)
6~7 p.m.	0.67	1857.9682	1346.0216	2077.2597	266.9559	6082.1172	268.9826	2803.2800	−9.8546
7~8 p.m.	0.67	1857.9682	1373.5485	2154.5318	233.3453	6086.0845	279.6899	2803.2800	−3.1145
8~9 p.m.	0.62	1906.2507	1325.9482	2012.6894	209.7060	5874.0063	265.7839	2594.0800	−14.1424
9~10 p.m.	0.62	1906.2507	1325.9482	2012.6894	206.6090	5864.7153	265.8575	2594.0800	−4.7777
10~11 p.m.	0.55	1799.2697	1232.0300	1861.7393	215.1648	5538.5333	230.6089	2301.2000	−6.7244
11~12 a.m.	0.55	1799.2697	1210.8475	1861.7393	220.7827	5534.2045	228.8217	2301.2000	−4.1828
12~1 a.m.	0.50	1693.1081	1204.0820	1718.3384	228.4903	5300.9994	205.0289	2092.0000	−3.9705
1~2 a.m.	0.50	1669.0890	1204.0820	1718.3384	238.2897	5306.3785	202.3718	2092.0000	−12.0067
2~3 a.m.	0.49	1572.3148	1180.0300	1759.1245	245.6654	5248.4655	193.2717	2050.1600	−5.0337
3~4 a.m.	0.49	1605.9231	1180.0300	1759.1245	236.5023	5254.5845	196.6353	2050.1600	−7.7892
4~5 a.m.	0.53	1679.5260	1184.1563	1891.4753	229.6533	5444.1175	215.9162	2217.5200	−10.6813
5~6 a.m.	0.53	1679.5260	1184.1563	1873.7923	233.1124	5436.8117	214.2948	2217.5200	−4.9970

Table 13. Shunt capacitor capacity requirements for winter load.

Time	Load Factor	SC-1 (kVAR)	SC-2 (kVAR)	SC-3 (kVAR)	Total SCs with DG Reactive Power (kVAR)	Reactive Power Loss (kVAR)	Reactive Power Load (kVAR)	Reactive Power from Substation (kVAR)
6~7 a.m.	0.66	165.4009	178.7169	304.2553	2419.7656	96.1655	1336.5000	−1.0001
7~8 a.m.	0.66	248.2302	213.3502	212.8432	2413.1976	88.4585	1336.5000	−2.1391
8~9 a.m.	0.80	415.8405	321.5590	248.7467	2685.0927	79.7964	1620.0000	0.8036
9~10 a.m.	0.80	403.7262	440.1997	440.7348	2667.1549	55.0871	1620.0000	−5.9678
10~11 a.m.	0.82	519.9483	492.3062	531.6393	2691.1025	44.5366	1660.5000	0.0340
11~12 p.m.	0.82	564.5728	564.5728	564.5728	2687.8178	43.0612	1660.5000	1.8434
12~1 p.m.	0.77	563.7428	563.7428	563.7428	2587.0766	40.6950	1559.2500	−1.0316
1~2 p.m.	0.77	533.1521	529.4205	528.1181	2582.9829	39.6234	1559.2500	1.9906
2~3 p.m.	0.72	464.7386	469.2136	417.2687	2489.3256	39.9415	1458.0000	−5.2842
3~4 p.m.	0.72	369.0102	408.2944	283.2708	2497.9664	56.7045	1458.0000	2.8382
4~5 p.m.	0.69	281.5332	240.9385	253.1550	2469.5042	84.5182	1397.2500	−1.6360
5~6 p.m.	0.69	312.1687	197.5768	156.4948	2478.4961	94.8441	1397.2500	−0.3020
6~7 p.m.	0.67	154.2479	212.5053	96.4905	2462.4355	115.7251	1356.7500	−3.8605
7~8 p.m.	0.67	154.2479	212.5053	96.4905	2463.7396	120.3317	1356.7500	−0.5579
8~9 p.m.	0.62	51.9258	167.2689	201.7112	2351.6917	114.3489	1255.5000	4.2571
9~10 p.m.	0.62	51.9258	167.2689	201.7112	2348.6378	114.3806	1255.5000	7.3428
10~11 p.m.	0.55	110.4982	145.0168	121.1445	2197.1754	99.2155	1113.7500	1.8900
11~12 a.m.	0.55	110.4982	145.0168	121.1445	2195.7526	98.4466	1113.7500	2.5440
12~1 a.m.	0.50	123.1191	139.4200	79.5874	2084.5651	88.2101	1012.5000	2.2451
1~2 a.m.	0.50	123.1191	139.4200	79.5874	2086.3332	87.0669	1012.5000	−0.6662
2~3 a.m.	0.49	144.2037	125.2957	63.0260	2057.6961	83.1518	992.2500	3.8057
3~4 a.m.	0.49	144.2037	125.2957	63.0260	2059.7074	84.5989	992.2500	3.2415
4~5 a.m.	0.53	136.3566	131.6589	94.8049	2152.3018	92.8942	1073.2500	−0.0577
5~6 a.m.	0.53	136.3566	131.6589	94.8049	2149.9004	92.1966	1073.2500	1.6462

The strategic locations were initially identified under peak load, insolation and wind speed conditions for the summer season using GSA and then applied across other seasonal scenarios and for successive stages. The optimal nodes are 2, 20 and 32 for wind DGs; 19, 29 and 41 for the solar DGs with battery storage systems; 23, 27 and 49 for the SCs; and 4, 7, 11, 19, 21, 29, 31, 33, 41 and 47 for the EVCSs.

The analysis of Table 5 and Table 7 reveals that, during summer peak hours (12–1 p.m.), the substation does not need to supply any real power to the distribution network. Instead, the network is capable of injecting approximately 12.8231 kW of active power and 9.0029 kVAR of reactive power back into the grid. Similarly, as shown in Table 8 and Table 10, during the rainy season peak hours (12–1 p.m.), the network can export about 395.7040 kW and 123.3448 kVAR to the grid. This surplus occurs because both wind DGs and solar DGs operate at their maximum output, exceeding the peak load demand at that time. The excess energy can alternatively be utilized for charging battery storage systems.

From the comprehensive results presented in Table 5, Table 6, Table 7, Table 8, Table 9, Table 10, Table 11, Table 12 and Table 13, it is evident that the distribution network has been optimized to achieve self-sufficiency in meeting its own power requirements. Furthermore, surplus generation enables net metering with the grid or substation across all seasons and load conditions considered. Therefore, net-zero power exchange with the utility grid during peak hours is attained, effectively demonstrating complete grid independence under islanded operation.

9.2. Sizing of Battery Storage

This section presents the battery storage capacity ratings calculated in accordance with [35,36], as summarized in Table 14. The ratings are based on the seasonal battery output requirements for a 12 h nighttime duration, which are detailed in Table 6, Table 9 and Table 12. These requirements were used as the basis for determining the battery sizes. To account for performance degradation over time, an aging factor of 1.25 has been applied, as recommended in [36]. Additionally, a design margin of 1.1 has been incorporated into the sizing process. The analysis of Table 14 indicates that batteries have their highest ratings during the winter season. Consequently, the selected capacities are 33,000 kVAH for Battery-1, 24,200 kVAH for Battery-2, and 36,300 kVAH for Battery-3.

Table 14. Battery Storage capacity rating for summer, rainy and winter seasons.

Season	Battery Storage	Battery Voltage (V)	Battery Rating (AH)	Battery Capacity (kVAH/kWH)
Summer	Battery-1	220	129,000	28,380
	Battery-2	220	100,000	22,000
	Battery-3	220	165,000	36,300
Rainy	Battery-1	220	116,000	25,520
	Battery-2	220	86,000	18,920
	Battery-3	220	129,000	28,380
Winter	Battery-1	220	150,000	33,000
	Battery-2	220	110,000	24,200
	Battery-3	220	165,000	36,300

9.3. Sizing of Solar DG

In this study, the DGs are designed not only to supply power during daytime operations but also to simultaneously charge the battery systems. A solar array-to-load ratio of 2.2 has been adopted and reflected in Table 15. For a 12 h daytime period, the seasonal solar DG output requirements and their respective durations are detailed in Table 5, Table 8 and Table 11. The maximum output values across these periods were used to determine the DG ratings. Specifically, Solar DG-1 exhibits its peak requirement of 1747.34 kW during winter (5–6 p.m.), while Solar DG-2 and DG-3 reach their highest demands of 1213.54 kW and 1900.48 kW, respectively, during winter (6–7 a.m.). Based on these observations, the selected average capacities for the solar DGs are 3700 kW for DG-1, 2900 kW for DG-2 and 4050 kW for DG-3, as summarized in Table 15. It is important to note that the actual DG output fluctuates throughout the 12 h daytime window due to variations in solar insolation; the corresponding hourly output values are provided in Table 16.

Table 15. Solar DG capacity rating.

Solar DG	Highest Capacity Requirements for Load (kW)	Solar Array-to-Load Ratio Estimated	Solar DG Capacity Estimated (kW)	Solar DG Capacity Selected (kW)
Solar DG-1	1747.3393	2.2	3844.14646	3700
Solar DG-2	1213.539	2.2	2669.7858	2900
Solar DG-3	1900.4779	2.2	4181.05138	4050

Table 16. Solar DG output calculation for summer.

Time	Solar DG-1 (kW)	Solar DG-2 (kW)	Solar DG-3 (kW)
6~7 a.m.	1243.5777	974.6960	1361.2134
7~8 a.m.	1471.9987	1153.7287	1611.2419
8~9 a.m.	2595.5377	2034.3403	2841.0615
9~10 a.m.	4019.2895	3150.2539	4399.4926
10~11 a.m.	5245.6114	4111.4252	5741.8179
11~12 p.m.	6018.4606	4717.1718	6587.7744
12~1 p.m.	6215.2712	4871.4288	6803.2022
1~2 p.m.	5808.1075	4552.3005	6357.5231
2~3 p.m.	4856.6689	3806.5784	5316.0836
3~4 p.m.	3523.4369	2761.6127	3856.7350
4~5 p.m.	2129.8205	1669.3188	2331.2900
5~6 p.m.	1272.2193	997.1449	1392.5644

9.4. Evaluation for Battery Recharging

This section validates that the excess energy generated by the solar DGs and wind DGs during the 12 h daytime period is adequate for recharging the batteries. The corresponding data for the summer season is presented in Table 17. The surplus energy from each solar DG is influenced by the load demand and the combined output from the solar DGs and wind DGs, which vary with insolation levels and wind speed throughout the day. Notably, the surplus becomes negative during the early morning (6–7 a.m.) and late evening (5–6 p.m.), indicating insufficient power generation due to low insolation and/or wind speed. During these intervals, the batteries supplement the load to maintain supply. This demonstrates that the integrated power system ensures a stable and reliable power supply, effectively mitigating the uncertainties associated with fluctuating load profiles and variable solar and wind power generations across different times and seasons. The estimated total surplus energies during the summer season are 33,007.1201 kW, 24,369.5848 kW and 36,525.9852 kW for Solar DG-1, DG-2, and DG-3, respectively, as shown in Table 17. These values exceed the corresponding battery capacities discussed in Section 9.2.

Table 17. Battery recharge calculation.

Time	Load to Be Fed by			Surplus Energy of Solar DGs
	Solar DG-1 (kW)	Solar DG-2 (kW)	Solar DG-3 (kW)	Solar DG-1 (kW)	Solar DG-2 (kW)	Solar DG-3 (kW)
6~7 a.m.	1447.3852	1072.1453	1667.7654	−203.8075	−97.4493	−306.5520
7~8 a.m.	1423.3550	1026.2304	1536.7220	48.6437	127.4983	74.5199
8~9 a.m.	1395.4208	1079.7153	1505.4066	1200.1169	954.6250	1335.6549
9~10 a.m.	981.7335	867.3797	954.4313	3037.5560	2282.8742	3445.0613
10~11 a.m.	769.9149	761.7652	675.0911	4475.6965	3349.6600	5066.7268
11~12 p.m.	432.3103	606.1042	409.4335	5586.1503	4111.0676	6178.3409
12~1 p.m.	325.7910	573.2610	311.1367	5889.4802	4298.1678	6492.0655
1~2 p.m.	458.5258	633.4723	439.8354	5349.5817	3918.8282	5917.6877
2~3 p.m.	564.0432	671.6723	545.0195	4292.6257	3134.9061	4771.0641
3~4 p.m.	929.8698	913.1496	943.1049	2593.5671	1848.4631	2913.6301
4~5 p.m.	1215.4229	1027.8542	1315.0449	914.3976	641.4646	1016.2451
5~6 p.m.	1449.1074	1197.6657	1771.0235	−176.8881	−200.5208	−378.4591
TOTAL (kVAH/kWH)				33,007.1201	24,369.5848	36,525.9852

9.5. Minimizing Power Loss

This section presents the seasonal reductions in real and reactive power losses over a 24 h period, as illustrated in Figure 8 and Figure 9 for summer, Figure 10 and Figure 11 for the rainy season, and Figure 12 and Figure 13 for winter. During the summer peak load interval (12–1 p.m.), Figure 8 shows that the real power loss decreases significantly—from 887.19 kW to 169.35 kW, and further to 133.01 kW—with the integration of wind DGs, representing reductions of approximately 81% and 85%, respectively. Similarly, Figure 9 indicates that the reactive power loss during the same period drops from 381.70 kVAr to 72.86 kVAr and then to 57.23 kVAr after adding wind DGs, corresponding to reductions of about 81% and 85%. These results highlight the substantial improvement in system efficiency achieved through the incorporation of wind DGs.

Figure 8. Real power loss comparison during summer.

Figure 9. Reactive power loss comparison during summer.

Figure 10. Real power loss comparison during rainy season.

Figure 11. Reactive power loss comparison during rainy season.

Figure 12. Real power loss comparison during winter.

Figure 13. Reactive power loss comparison during winter.

Comparable reductions in power losses are also evident during the rainy and winter seasons, as illustrated in Figure 10, Figure 11, Figure 12 and Figure 13. These improvements are achieved through the proposed multi-objective optimization framework based on the GSA, which determines the optimal placement and sizing of wind DGs, solar DGs, SCs and EVCSs. By strategically allocating these resources, the approach significantly enhances the overall performance of the distribution network, delivering substantial loss reductions across all seasons.

9.6. Enhancement of Voltage Profile

In addition to the substantial reductions in power losses, the voltage profiles also exhibit significant improvements across all three seasons throughout the 24 h period, as illustrated in Figure 14, Figure 15 and Figure 16.

Figure 14. Minimum voltage profile comparison during summer.

Figure 15. Minimum voltage profile comparison during rainy season.

Figure 16. Minimum voltage profile comparison during winter.

During the summer peak period (12–1 p.m.), the minimum voltage in the existing network was approximately 0.6844 p.u., which improved to 0.9515 p.u. after optimization—or 0.9330 p.u. when wind DGs were excluded (Figure 12). Similarly, for the rainy season, the minimum voltage increased from 0.7869 p.u. to 0.9517 p.u. (0.9182 p.u. without wind DGs), and during winter it improved from 0.7833 p.u. to 0.9562 p.u. (0.9403 p.u. without wind DGs), all measured during the same peak interval of 12–1 p.m. These results indicate that maintaining a minimum network voltage above 0.95 p.u. across all seasons is not achievable without the integration of wind DGs.

10. Comparative Analysis with Existing Literature

A comparative analysis of the proposed methodology against approaches reported in the existing literature is presented in Table 1, with the corresponding results summarized in Table 18.

Table 18. Literature analysis with comparison results.

Performance Parameter	Methodology DGs Only [1,8]	Methodology [DGs, SCs] [9,13]	Methodology [Solar DGs with More Rooftop Utilization, SCs]	Proposed Methodology [Wind DGs, Solar DGs, Batteries, SCs]
Real power from substation (kW)	5509.7055	5299.8591	1749.8711	−12.8231
Reactive power from substation (kVAR)	3043.6834	841.3130	574.0842	−9.0029
Overall real power loss (kW)	1000.3250	790.4787	169.3523	133.0140
Overall reactive power loss (kVAR)	430.3724	340.0897	72.8609	57.2270
Minimum voltage (p.u.)	0.6561	0.7477	0.9330	0.9515

The comparison is based on the summer peak scenario, which represents conditions of maximum solar insolation and peak system loading. From Table 18, it is obvious that the methodology introduced in this study outperforms conventional techniques that incorporate rooftop solar DGs, wind DGs, battery storage, and SCs while feeding existing loads and new EVCSs. The proposed approach delivers substantial improvements in distribution system performance, particularly in reducing power losses and enhancing minimum voltage levels, while simultaneously enabling the network to achieve self-sufficiency through internal power generation from renewable energy sources.

11. Comparative Analysis Across Three Stages of Optimization

The outcomes of the three stages in the multi-stage optimization process are summarized in Table 19, focusing on summer mornings (6–7 a.m.) for comparison. Stage 1 identifies the optimal placement of solar DGs, wind DGs and SCs to achieve multiple objectives: minimizing real and reactive power losses, enhancing voltage profiles and minimizing the load on the source substation to near zero.

Table 19. Comparison among three stages.

Performance Parameter	Stage-1 (No EVCS)	Stage-2			Stage-3 (Full EVCS Ratings)
		Case-1 (Full EVCS Ratings)	Case-2 (Partial EVCS Ratings)	Case-3 (Partial EVCS Ratings)
Solar DG1 (kW)	262.9424	Same Stage-1	Same Stage-1	Same Stage-1	1447.3852
Solar DG2 (kW)	326.6768	Same Stage-1	Same Stage-1	Same Stage-1	1072.1453
Solar DG3 (kW)	450.4617	Same Stage-1	Same Stage-1	Same Stage-1	1667.7654
Wind DG1 (kW)	348.7772	Same Stage-1	Same Stage-1	Same Stage-1	348.7772
Wind DG2 (kW)	348.7772	Same Stage-1	Same Stage-1	Same Stage-1	348.7772
Wind DG3 (kW)	348.7772	Same Stage-1	Same Stage-1	Same Stage-1	348.7772
SC-1 (kVAR)	242.0019	Same Stage-1	Same Stage-1	Same Stage-1	247.4402
SC-2 (kVAR)	288.0988	Same Stage-1	Same Stage-1	Same Stage-1	294.5729
SC-3 (kVAR)	220.2693	Same Stage-1	Same Stage-1	Same Stage-1	225.2192
Each EVCS (kW)	No	300	100	40	300
Real power from substation (kW)	−2.6365	3392.2396	1048.1890	410.2134	−6.2517
Reactive power from substation (kVAR)	−4.0440	1151.9446	346.5228	132.9645	−7.5145
Overall real power loss (kW)	34.0046	428.8807	84.8301	46.8544	177.6043
Overall reactive power loss (kVAR)	14.6299	184.5184	36.4967	20.1583	76.4112
Minimum voltage (p.u.)	0.9708	0.8149	0.9246	0.9528	0.9517

In Stage 2, case studies are conducted using the same DG and SC allocations from Stage 1. Among these, Case 3 indicates that the network can provisionally support EVCSs rated up to 40 kW. In contrast, Case 1 and Case 2 reveal under-voltage issues, with minimum voltages dropping to 0.8149 p.u. and 0.9246 p.u., respectively.

Finally, Stage 3 introduces an upgraded allocation of solar DGs, wind DGs and SCs to counteract the impact of EVCS integration as proposed in Stage 2, Case 1, while still meeting the original multi-objective optimization criteria. The initial rows of Table 5 and Table 7 present the final allocation corresponding to Stage 3 in Table 19.

12. Conclusions

This study develops and analyses a three-stage multi-objective optimization framework using the GSA for a loss-prone distribution network operating under a weak grid supply. The seasonal simulation results demonstrate that the proposed approach significantly enhances network performance by reducing real and reactive power losses, improving voltage profiles, and ensuring an optimal power quality. The methodology also maximizes internal renewable energy utilization through optimal fixed configurations of solar DGs with battery storage, wind DGs, and SCs, enabling the system to meet both its internal load demand and the additional demand from strategically located EVCSs. This fulfills all five objectives defined in the optimization process. In the first stage, solar DGs with battery storage, wind DGs, and SCs are optimally placed to upgrade the network and achieve the targeted objectives. During peak daytime hours, high insolation ensures maximum solar generation, maintaining load balance. Conversely, during nighttime, early morning, and evening periods, when insolation is low, battery storage and wind DGs compensate for the shortfall. The simulations incorporate hourly variations in insolation, wind speed, and load across all seasons to validate convergence under consistent optimal installations. Hourly solar insolation is computed using the modified ASHRAE model for accurate solar generation estimation. The second stage determines the strategic placement of fast EVCSs with maximum feasible ratings while ensuring that the network performance remains unaffected. In the third stage, the sizing of solar DGs, battery storage, and SCs is revisited to mitigate the impact of EVCS integration while maintaining compliance with the multi-objective criteria. Given the inherent unpredictability of load variations, wind speeds, and solar insolation, the system retains grid connectivity to manage uncertainties. The network operates as a microgrid with net metering capability, supplying existing loads and EVCSs at optimized locations.