Enhanced optimization of photovoltaic units EVCSs and BESS integration in radial distribution networks using a hybrid sine–cosine gorilla search algorithm

Abstract

The implementation of multiple distributed energy resources (DER) into the radial distribution networks which includes Photovoltaic (PV) systems, Electric Vehicle Charging Stations (EVCSs), and Battery Energy Storage Systems (BESS) presents a number of challenges that include voltage regulation and power loss as well as the challenges in managing load demand. In this paper, the author presents a superior optimization model that employs a new Hybrid Sine Cosine Gorilla Search Algorithm (HSCGSA) to effectively coordinate the addition of PV units, EVCS charging loads and BESS in the radial distribution systems. The offered approach will seek to maximize the position and size of DERS to reduce active and reactive power losses and ensure the stability of the voltage throughout the network. The HSCGSA is a hybrid approach to enhancement of the exploratory ability of the Sine Cosine Algorithm (SCA) and the exploitation power of the Gorilla Troops Optimizer (GTO), which provides a balanced solution to the intricate and complex optimization problems involving multiple planning criteria. The performance of the proposed algorithm is validated through simulations on IEEE 33-bus, 69-bus, and 118-bus radial distribution systems. The results demonstrate that the proposed HSCGSA significantly improves system performance compared with the conventional Genetic Algorithm (GA). For the IEEE 33-bus system, the active power loss is reduced from 3477.166 kW to 1577.06 kW, representing a reduction of approximately 54.6%, while the minimum bus voltage improves from 0.9224 pu to 0.9706 pu. In the IEEE 69-bus system, the active power loss decreases from 3859.99 kW to 1381.28 kW, corresponding to a reduction of about 64.2%, along with a substantial enhancement in the voltage stability index. Similarly, in the IEEE 118-bus system, the active power loss is reduced from 2279.42 kW to 608.55 kW, achieving nearly 73% reduction when multiple DER units are optimally allocated. These results confirm that the proposed HSCGSA provides superior capability for optimal placement and sizing of PV units, EV charging stations, and battery energy storage systems in radial distribution networks.

Introduction

However, in recent years, the increasing anxiety of the population in relation to environmental contamination, the rise of oil prices and the idea of minimizing uses of fossil fuels made the international society more interested in electric vehicles (EVs). Elevated electricity prices and the low amounts of pollution are driving electric cars to fame amongst the clients. They are also abandoning generation fossil fuel cars in favor of reducing the production of fossil fuel in the attempt of minimizing the emission of carbon¹. One of the major challenges limiting the widespread adoption of electric vehicles is the insufficient availability of charging infrastructure. The locations of the charging stations that exist can be too small even in the more developed world². The expensive cost and the short availability of electric automobiles are not also the only mistakes forcing would-be purchasers away; inconsistency of infrastructure and bad organization of area charging points are also contributive elements³. This is why, much academic attention has been paid to the development of charging station facilities and effective capacity allocation and control planning. With the developing global economy, and the continuous dependence on the conventional form of fossil fuels such as coal and oil products, the problem that faced in terms of energy deficiency and environmental degradation has taken an urgency⁴. This has led to the interest of countries globally in renewable energy sources⁵. Solar photovoltaic (PV) technology has become popular in the power generation sector with the low cost and absence of greenhouse gases though compared to the use of fossil fuels in the generation of power. Solar pv has become the third largest source of renewable energy in the world after hydropower and wind power in installed capacity⁶. Nowadays, there are PV generators that are divided into off-gpu and grid-connected PV based on their connection wired on the power grid of the populace⁷. The power systems that run off grids do not require connection to the grid and therefore they can be used in remote locations where there is minimal installed infrastructure or where the investments may be too high⁸. These grid-connected systems connect to the overall power grid so that they could sell extra power to the linked power grid or buy power in it. This type improves energy efficiency and this setup would be suited to urban locations or places that have a consistent power supply. The advantages of the PV power generation systems include the use of renewable energy source, environmentally-friendly, low costs of maintenance, and high working periods. They also decrease the dependence on conventional energy sources, decrease the energy expenses and produce a lower number of carbon emission which is beneficial to the environment⁹. Due to the pace in which technology is increasingly integrated, the use of PV power systems is on the increase. The possible uses include small rooftop systems to large-scale solar power stations, which will provide clean energy to homes of individuals, commercial buildings, government schools, hospitals, industries, and isolated regions. Consequently, many countries and regions are promoting and supporting solar power to decrease reliance on conventional energy sources and address climate change. PV power generation systems are crucial for sustainable energy development and facilitating the energy transition¹⁰. As the popularity of EVs grows, the demand for PV power systems is also expected to rise. Numerous studies have demonstrated that installing solar PV panels on parking lot roofs not only promotes efficient resource use but also offers a free shade canopy¹¹.

The installed PV capacity refers to the total rated power of the solar panels in a PV power plant. However, accurately predicting the output power at different times is challenging due to its strong dependence on local environmental conditions, including solar irradiance, temperature, and shading. Among these parameters, temperature has the most significant impact. When temperatures exceed 25 °C, the efficiency of solar panels decreases by approximately 0.5% to 0.6% per degree Celsius increase, depending on the type of solar cell material¹². Typically, a PV module converts only 6–20% of the incident solar radiation into electrical energy. The efficiency of PV modules varies based on the semiconductor material used in their production. PV panels are categorized into several types based on their material: monocrystalline silicon panels, polycrystalline silicon panels, thin-film panels, flexible panels, and transparent panels¹³. Statistics show that nearly 90% of solar cells are made from crystalline silicon wafers. Among the various types of solar panels, monocrystalline silicon panels offer the highest conversion efficiency, though they are more expensive compared to other types¹⁴.

Numerous studies have examined the capacity configuration of new EV charging stations, addressing factors such as investment and operating costs, PV output instability, EV charging and discharging demand, time-of-use tariffs, system security, carbon emissions, and their effects on grid voltage, power, and power quality. Intelligent optimization algorithms, including improved differential evolution, grey wolf optimization, multi-intelligent particle swarm optimization, machine learning methods, and enhanced simulated annealing algorithms, are employed to develop mixed-integer nonlinear planning models and single- and double-layer optimization models. In¹⁵ managed the charging and discharging of a battery energy storage system (BESS) using an energy management strategy and a vehicle-to-grid (V2G) approach. They employed the Monte Carlo method to address the uncertainties associated with EV charging and PV power generation. In¹⁶ analysed the optimal location and capacity of charging stations by considering investment costs, plug-in EV users, and distribution grid operators. Their experiments utilized real historical data from 297 users of an EV rental company. In¹⁷ proposed an efficient method for determining the location and size of solar-assisted charging stations, considering factors such as construction cost, solar energy fluctuations, and user demand. The findings illustrated that their technique is effective in making quality decisions in an acceptable time span. They were also using EVs as temporary energy storage devices (ESS). A model was developed in¹⁸ that consists of applying the logistic growth method in forecasting the energy usage of EV fast charging stations and power demand. They examined the economic effect of different variables such as cost of investments of charging stations, the price of electricity, and inducements of vehicle owners in one micro grid that is combined with power plants consisting of PV. The optimal number of EV charging stations was determined by using a planning algorithm, which was to identify the greatest system profitability. This solution provides a basis of the planning and configuration of the charging stations using PV generation and energy storage systems (ESSs) to reduce grid impaction. In¹⁹ used Multi-Intelligent Particle Swarm Optimization (MAPOS) algorithm to optimally design an integrated light storage and charger station. This was to reduce the operating costs and the emission of carbon even as the optimal capacity configuration of the charging station is determined. In²⁰ designed an optimum capacities distribution model of a photovoltaic power storage charging station (PV-ESS-CS). The model takes into consideration the uncertainties on EV charging demand and discharging demand and PV output. It uses something called conditional value at risk to evaluate the risk of their low returns with the intention of maximizing the overall returns as well as taking into consideration the risk being evaluated. In²¹ an optimization model is presented with the incorporation of PV, storage, and EVs with applying the cumulative prospect theory (CPT) and multi-objective particle swarm optimization algorithm (MOPSO). This model deals with issues of sustainability in economic, social, and environmental considerations. In^22–29 suggested a pair of layer optimization control over the allocations within PV storage charging station and did it by taking user utility and tariff depending on user behaviour. The model saves more investment, operation, and maintenance costs and develops more net revenue in^30–33 presented a capacity allocation strategy based on a tasked charging station of the photovoltaic and battery energy storage system (BESS) by applying a historical data-based search algorithm. This method concludes the best capacity ratios of the PV and BESS by looking at real operational data to achieve optimality of economic performance. In^34–37 elaborated a data-driven optimum creation layout of electric vehicle charging microgrids (EVCMs) inclusive of photovoltaic energy storage systems combined with battery hyperconverged systems. This model uses the past data and machine learning algorithms in achieving future prediction of photovoltaic, demand, and price of electricity. In^38–41 proposed the optimization system that enables to maximize the profits, considering the arrival of vehicles, intermittent or no electricity production by photovoltaic systems, and managing the energy storage system (ESS). Its framework uses a MILP computer program to optimize the capacity and intervention approach of photovoltaic-battery energy storage setup (PV-BESS) in optimizing the economic and ecological advantages. Charging station joint planning and operation were also optimized in order to find the best configuration of grid-connected charging station and to define how to conduct effective scheduling of power within the operation of a grid-connected charging station. In^42–56 established a model of calculating the capacity of the charging stations and energy storage of EVs. They took into account the factors influencing efficiency and system safety and optimized the plan of charges at a model with the help of an improved simulated annealing algorithm. A combination of various sources of renewable energy may also increase the problem of power quality and grid stability. The main quality issues of power quality are the presence of harmonics in the current, variation of the frequency as compared to the nominal one, fluctuation of the voltage and deviation of power. New inroad of Photovoltaic (PV) systems, Plug-ins Hybrid Electric Vehicles and BESS to radial distribution networks has become a real challenge to the power system operators and the planners. Although these technologies have a significant environmental and financial advantage, their introduction into the present systems of power distribution may combine into crucial problems, including instability in voltage, power waste, and network overload. The conventional networks of power distribution did not cope with the transitional and variation characteristic of PV generation, or with the acute and spasmodic demand with EVCS charging. The utility of these issues requires superior optimization methods which are capable of operating the integration of these DERs keeping the network stable, reducing power losses and balancing loads efficiently. The major issue of the research is the elaboration of the most efficient approach towards PV systems integration and load management of EVCS in the networks and BESS in the radial ones. Several studies have investigated the optimal allocation and sizing of distributed energy resources such as photovoltaic systems, electric vehicle charging stations, and battery energy storage systems in distribution networks using metaheuristic optimization techniques. For example, optimal placement of BESS in PV and EV integrated distribution networks has been studied using various metaheuristic algorithms⁵⁵. Similarly, multi-objective optimization approaches have been applied for the joint allocation of EV charging stations and distributed generators in radial distribution systems⁵⁶. In addition, time-sequential planning strategies for optimal allocation of EVCS, renewable distributed generation, and battery storage have also been reported in the literature⁵⁷. While these studies address similar planning problems, the present work focuses on the development and application of a hybrid metaheuristic optimization framework (HSCGSA) to improve the efficiency of DER allocation in radial distribution networks. Recent studies have increasingly investigated coordinated planning of distributed energy resources and electric vehicle charging infrastructure in distribution networks. Several works have addressed the joint allocation of photovoltaic systems, EV charging stations, and battery energy storage systems to improve voltage stability, reduce power losses, and enhance operational flexibility of radial distribution systems. In addition, research has explored multi-objective optimization approaches for the optimal placement of EV charging stations and distributed generation in radial distribution networks. Other studies have focused on the integration of PV systems with battery energy storage under time-varying load demand and renewable generation uncertainty. These studies highlight the importance of coordinated DER planning to maintain reliable and efficient operation of modern distribution networks with increasing renewable and EV penetration and a comparision of these studies is presented in Table 1.

Table 1.

Comparison of Representative Studies on DER and EVCS Planning.

Ref.	Resources Considered	Objectives	Uncertainty / Modeling	Optimization Algorithm	Test System	Key Findings
15,16	EVCS, BESS	Cost, charging demand management	EV charging uncertainty	Monte Carlo / optimization models	Distribution networks	Optimal EV charging infrastructure planning
17,18	PV + EVCS	Cost and demand management	Solar variability and EV demand	Planning optimization	Microgrid / distribution systems	Improved integration of solar-assisted EV charging
19,20	PV + storage + EVCS	Cost, emissions, economic performance	PV output uncertainty	MAPSO / risk-based optimization	Charging station systems	Reduced operating cost and improved profitability
21,34	PV + ESS	Multi-objective planning	Deterministic / data-driven modelling	MOPSO / machine learning	Distribution networks	Sustainable planning of renewable-based systems
38,42	EVCS + storage	Charging optimization	Load variation	MILP / simulated annealing	Distribution networks	Improved charging station operation and scheduling
48,50	EVCS + DG	Loss minimization, voltage improvement	Deterministic modelling	Metaheuristic optimization	Radial distribution systems	Improved network performance through optimal placement
49,56	PV + EVCS + BESS	Multi-objective DER planning	Time-varying demand	Metaheuristic algorithms	Distribution feeders	Coordinated DER planning improves stability and cost
This Work	PV + EVCS + BESS	Loss reduction, voltage stability, economic cost	Time-varying load and EV demand	Proposed HSCGSA	IEEE 33, 69, 118 bus systems	Improved convergence and network performance

This work is aimed at reducing active and reactive power losses and keeping voltages constant throughout the network, as well as preventing being losing the ability to accommodate effectively increasing penetration of renewable energy sources and electric vehicles without affecting the reliability and effectiveness. The proposed research is aimed at coming up with a hybrid optimization algorithm that can solve such multifaceted challenges and make a reliable solution to current power distribution systems.

Following are the objectives of the work proposed in this paper.

• To design a hybrid optimization algorithm (HSCGSA) including the Sine Cosine Algorithm (SCA) and Gorilla Troops Optimizer (GTO) to surpass an empowerment of search capability and convergence rates to the optimization of PV synthesis, EVCS charging stand and BESS.

• To Optimize the location and capacity of PV units in the circulation systems, making sure that the active and reactive power losses are minimized but the voltage stability is maintained.

• To compare the value of the performance of HSCGSA and the traditional optimization method in regards to reduction in the power loss behavior and enhanced voltage stability and overall, network efficiency across the presence of the PV systems, the EVCS and BESS.

• To examine the efficiency of the HSCGSA in coping with the use of these DERs in various buses networks, which implies the 33-bus, 69-bus, and 118-bus test systems.

• To give insights and recommendations to the power system operators and planners as to the best integration approaches towards DERs in radial power distribution networks to create resilient and efficient power systems.

Problem formulation

The main Objective of the proposed method is to optimally allocate PV units (PVUs), Electric Vehicles charging stations (EVCS) and Battery Energy Storage Systems (BESS) within the Distribution System (DS) to minimize and enhance the voltage profile.

Objective function

The objective function consists of the energy procurement costs at the substation node, combined with the investment and maintenance costs of the PVU, Electric Vehicle Charging Stations (EVCS), and Battery Energy Storage System (BESS) units.

1

is total operative cost of the distribution system, is the cost related to the energy purchasing, is the cost related to the operating and capital cost of PVU, is the cost related to the operation and construction cost of EVCS, is the cost related to the cost of battery energy storage system.

Although the optimization problem in this study is represented using a single aggregated objective function, the problem itself involves multiple performance considerations. These include minimizing energy procurement costs, reducing power losses, maintaining acceptable voltage profiles, and determining the optimal placement and sizing of PV units, EV charging stations, and battery energy storage systems. These aspects are incorporated into the overall planning cost formulation through different cost components and operational constraints. Therefore, the problem can be interpreted as a multi-criteria optimization problem expressed in a single-objective form. The proposed Hybrid Sine–Cosine Gorilla Search Algorithm (HSCGSA) is selected due to its strong capability in handling highly nonlinear and complex optimization problems with multiple interacting variables. The integration of distributed energy resources introduces a large search space with numerous possible combinations of locations and capacities. The hybridization of the Sine Cosine Algorithm and Gorilla Troops Optimizer improves both global exploration and local exploitation abilities, enabling the algorithm to effectively search for near-optimal solutions in such complex planning problems.

From the cost function is give as²⁷

2

is energy purchasing cost/kWh, number of days in year,  RoR is rate of return expected for the capital cost, number of periods in a year used for calculating returns, time of the period, number of main sources connected, power generation from the connected sources, is expected increase in purchasing energy cost.

is given as²⁷

3

capital cost of the PVU, number of PVUs, power rating of the PVU, power generation from PVUs.

is given as²⁷

4

capital cost of the EVCS, power rating of the EVCS, power consumption by EVCS.

is given as²⁷

5

capital cost of the BESS, power rating of the BESS, net power from the BESS.

The primary constraints associated with the minimization of objective function include:

Power Balance Constraints:

6

were, hour power generated from PVUs, hour power demand, = during an nth hour, EV supplied/consumed power, = during an nth hour, BESS supplied/consumed power.

Bus voltage profile constraints

DS’s voltage profile must always be within the specified ranges.

7

Where is the voltage at the k^th bus during the n^th hour. Voltage distribution system (DS) should always be within the stipulated limits. It is important to note that the optimization formulation in this study primarily focuses on system-level operational constraints such as power balance and voltage magnitude limits. Although the integration of distributed energy resources such as photovoltaic systems, electric vehicle charging stations, and battery energy storage systems may introduce power quality concerns including harmonic distortion, voltage fluctuations, and reactive power variations, these aspects are typically addressed at the converter control and hardware design level. Modern grid-connected converters used in PV inverters, EV chargers, and BESS systems are generally designed to comply with established power quality standards such as IEEE 519 and IEEE 1547, which limit harmonic distortion and ensure acceptable power quality levels. Therefore, the present work concentrates on planning-stage optimization objectives such as loss minimization and voltage stability improvement, while detailed power quality analysis can be considered as part of future operational or control-oriented studies.

Voltage stability index

One of the parameters that would help measure voltage stability in distribution network and its occurrence or potential voltage collapse is a voltage stability index. This index is used to find the bus vulnerable to voltage instability and therefore points out possible areas of weakness in the network. When the system fails to sustain sufficient voltages, this may cause large-scale failures and quality issues in power. Thus, integrity and maintenance of power distribution systems rely heavily on maintaining the level of such index within acceptable bounds to maintain the swiftness and sustainability of power transmission systems. The voltage stability index is obtained based on active and active transfer equations concerning a distribution line. These equations represent the dynamic of power flow in the system which takes into consideration the relationships between the buses, line impedance, and the load conditions. The index that can be calculated with the help of the transfer of power data provided in Eq [8]., uses this data to supply a valid measure of voltage stability in the system.

8

For a given bus  m, , , , and denote the voltage at busactive power injected, reactance of line linking buses  m and  n, reactive power injected and resistance of line linking buses  m and  n respectively.

Among the several voltage stability indices available in the literature, the index adopted in this study is selected due to its suitability for radial distribution systems and its relatively low computational complexity. Unlike some other indices that require extensive system-wide Jacobian calculations or eigenvalue analysis, the adopted index can be directly computed using line parameters and power flow quantities between two adjacent buses. This characteristic makes it particularly appropriate for optimization-based planning problems where the index needs to be evaluated repeatedly during the search process.

In addition, the selected index provides a reliable indication of proximity to voltage collapse in distribution networks with high penetration of distributed energy resources such as photovoltaic units, electric vehicle charging stations, and battery energy storage systems. The index is derived from the power flow equations of a two-bus equivalent system and reflects the relationship between bus voltages, line impedance, and power transfer capability.

The numerical value of the voltage stability index lies within the range 0 ≤ VSI ≤ 1. A value closer to 1 indicates a stable operating condition with sufficient voltage margin, whereas a value approaching 0 indicates that the system is operating near its voltage stability limit. In practical distribution system studies, values above 0.8 generally indicate a secure operating condition, while values below 0.5 may suggest potential voltage instability or the risk of voltage collapse. Therefore, improving the VSI value across the network is an important objective in ensuring reliable operation of the distribution system^52,53.

Similar formulations of voltage stability indices for radial distribution networks have been widely used in previous studies for evaluating voltage stability and identifying weak buses in the network.

Power quality considerations based on IEEE standards

The integration of distributed energy resources such as photovoltaic units (PVUs), electric vehicle charging stations (EVCSs), and battery energy storage systems (BESS) may influence power quality in distribution networks. Power quality issues generally include voltage deviations, harmonic distortion, voltage flicker, and reactive power imbalance. In modern power systems, these concerns are typically addressed through converter control strategies and compliance with established grid interconnection standards.

In this study, power quality considerations are evaluated in accordance with commonly accepted IEEE standards. According to IEEE Std. 1547 and IEEE Std. 519, the voltage magnitude in distribution systems should normally remain within the permissible range of 0.95 pu to 1.05 pu under normal operating conditions. These limits ensure acceptable voltage quality for connected loads and prevent operational problems in sensitive equipment. Since the proposed optimization framework is based on steady-state load flow analysis, the primary power quality indicator considered in this work is the bus voltage magnitude constraint, which is already incorporated in Eq. (7). The simulation results obtained using the proposed Hybrid Sine–Cosine Gorilla Search Algorithm (HSCGSA) confirm that the voltage levels across all buses remain within the recommended IEEE limits. Harmonic distortion constraints specified in IEEE 519 are typically analyzed using detailed converter-level harmonic models and electromagnetic transient simulations. Such analysis is beyond the scope of the present planning-level optimization framework. Nevertheless, modern grid-connected converters used in PV inverters, EV chargers, and BESS systems are designed with harmonic filtering mechanisms that ensure compliance with IEEE harmonic standards. Therefore, the obtained optimization results satisfy the fundamental power quality requirements related to voltage regulation, while detailed harmonic analysis may be considered as part of future research.

Modelling of sources

This study involves the utilization and allocation of PV units and EV Charging stations within the distribution system (DS). The system integrates these DERs to supply power, as shown in Fig. 1.

Fig. 1.

Characteristics of autonomous MG.

Mathematical modelling of PVUs

The exact output power of the solar panels is calculated using the beta probability distribution function (PDF). The beta PDF is particularly well-suited for statistical analysis in modelling solar irradiance²⁸.

9

.

In the beta probability distribution function, α and β represent the shape parameters of the distribution, while Γ(·) denotes the Gamma function used in the normalization factor of the beta distribution.

With mean (), Standard deviation () determined

10

11

12

= shape parameters

13

where

14

15

16

17

FF = the fill factor,

= the total number of PV modules,

= the short-circuit current, and.

= the open-circuit voltage.

= the cell temperature,

= the ambient temperature,

, =the current and voltage temperature coefficients.

= nominal operating temperature.

18

Total Expected Output Power=.

In this work, the beta probability distribution is used to represent the statistical characteristics of solar irradiance. However, the optimization framework considers the expected value of the PV output power for each hour rather than multiple stochastic scenarios. The expected PV generation values obtained from the irradiance model are incorporated into the 24-hour simulation and optimization process. This approach allows the model to capture the average behavior of PV generation while maintaining computational efficiency in the optimization procedure.

Mathematical modelling of EV uncertainty

Users decide when to charge (DoC) based on factors such as the charging state of charge (SoC), trip distance, and charge power. Among these variables, the DoC is primarily influenced by the distance of the next trip.

The primary SoC of m^th EV at nth hour given as

19

where = no. of trips, t = EV travel distance, = EV travel range Battery Storage Constraint:

20

21

22

In this study, electric vehicle charging stations are modelled as controllable charging loads connected to the distribution network. The EVCS demand represents the aggregated charging power required by electric vehicles connected to the charging stations during the charging period. Therefore, EVCSs are considered as grid-to-vehicle (G2V) loads in the simulation framework. Vehicle-to-grid (V2G) operation, where electric vehicles can inject power back into the distribution network, is not included in the current study. The integration of V2G functionality requires additional control strategies, battery state-of-charge constraints, and bidirectional power flow management, which are beyond the scope of the present planning-oriented optimization framework.

Mathematical modelling of BESS

Both energy capacity and power capacity should be carefully considered in order to determine the optimum capacity and location of a BESS within a distribution network. The consequences of these factors are really significant to minimise the final costs of the system and retain a high degree of reliability and power quality under the distribution system. Moreover, there are two important factors that have a direct influence on the lifespan of the BESS, the number of charge-discharge cycles, and the State of Charge (SOC). The SOC is the energy level of the BESS at any instance and the number of cycles depends on charge and discharge procedures of BESS. All these combined affect the health and life of the battery greatly. Through optimization and enhanced applications of the BESS in charging and discharging operations, encroachment of the SOC changes daily could be saved to a minimum. This decrease in SOC swings is also involved in achievement of improved control on depth of discharge (DOD) and eventually efficiency improvement on life cycle of BESS. One method available to determine the size of the BESS is to compute the gap between the highest and the lowest energy levels in the BESS. This variance is the variety of energy storage required. Division of this value by maximum possible Depth of Discharge (DOD) would give the necessary BESS size. An important parameter that is closely regulated is as the DOD which is the overall capacity in which the battery can be utilized in a given cycle without causing any harm to its lifespan. By carefully managing the DOD and SOC, the BESS can operate more efficiently over its lifespan, contributing to cost savings and system stability.

23

maximum value of energy in the BESS and minimum values of the energy in the BESS, is the maximum value of the DOD.

Daily cycle of BESS is defined as²⁹

24

Then service life cycle is given as

25

lifecycle is the nominal cycle life of battery which is equal to 3000³⁰, D is number of BESS operating days which s equal to 285 days³¹, actual service life of battery in years.

The equations describing the daily cycle and service life of the battery are used to represent the operational characteristics and expected lifetime behavior of the BESS. In the present study, these equations are not directly incorporated into the objective function as explicit degradation or replacement cost terms. Instead, the economic model considers the capital and operating costs of the BESS, while the cycle-life analysis provides guidance for realistic operational limits of the storage system.

The stochastic characteristics of EV charging behaviour are represented through the modelling of trip distance and state-of-charge evolution. However, in the present study the individual stochastic charging events are aggregated to obtain a representative EV charging demand profile over a 24-hour period. The expected charging demand derived from the EV behavioural model is incorporated as a deterministic EVCS load profile in the load flow and optimization analysis. This approach enables the simulation framework to reflect realistic EV charging patterns while maintaining computational efficiency for the optimization process.

The depth-of-discharge (DOD) and cycle-life equations are used to estimate the operational characteristics and expected service life of the battery energy storage system. These parameters help determine the required energy capacity of the BESS and ensure that the storage system operates within acceptable degradation limits during the planning horizon considered in the optimization framework. In the present study, the economic model accounts for the capital and operational costs of the BESS over the planning period, while the cycle-life analysis provides guidance for sizing and operational feasibility rather than explicitly modelling battery replacement events.

Uncertainty and scenario representation

In practical distribution networks, renewable generation and electric vehicle charging demand are subject to significant uncertainties. In this study, the uncertainties associated with photovoltaic generation, EV charging demand, and load variation are represented using simplified statistical and time-varying models to maintain computational efficiency in the optimization process. The variability of photovoltaic generation is modelled using a beta probability distribution function, which is commonly used to describe the stochastic nature of solar irradiance. Based on this distribution, the expected value of PV output power is calculated for each hour of the 24-hour simulation period.

The uncertainty associated with EV charging demand is represented through the modelling of trip distance and state-of-charge (SoC) evolution of electric vehicles. The expected EV charging demand derived from this model is aggregated to form a representative EVCS load profile over the daily simulation period. Load demand variations are represented using a normalized 24-hour load curve, which captures the typical daily variation of electricity consumption in distribution networks. The base load of each test system is scaled according to this hourly load factor. In the present study, these uncertainties are incorporated using expected hourly values rather than multiple stochastic scenarios, allowing the optimization algorithm to evaluate system performance under realistic operating conditions while maintaining computational tractability.

Artificial gorilla troops optimizer algorithm

The Artificial Gorilla Troop Optimization (AGTO) algorithm is a population-based intelligence optimization technique inspired by the collective lifestyle and social behaviour of gorillas. Gorillas live in groups known as “troops,” which typically include adult male or silverback gorillas, along with several adult female gorillas and their offspring. The silverback gorilla is the leader of the troop, making all decisions, mediating conflicts, determining group activities, guiding the gorillas to food sources, and ensuring the safety and well-being of the entire group. The AGTO algorithm employs five distinct operators to simulate the collective behaviour of gorillas, organized into two primary stages: the exploration stage and the development stage.

Exploration shtage

During the exploration stage, three mechanisms are used: migrating to unknown locations, migrating to other gorilla locations, and migrating to known locations. During the development phase, two social behaviours are implemented: following the silverback gorilla and competing with adult female gorillas. Figure 2 illustrates the exploration and development mechanisms of the artificial gorilla troop optimization algorithm.

Fig. 2.

Exploration and Development Mechanism of AGTO.

The position update of gorillas during the exploration phase is represented by

26

27

28

In the formula, represents the candidate position of the gorilla in the next iteration, while denotes the current position of the gorilla. The variables, , , and rand are random values within the range (0,1). The parameter s, typically set to 0.03, must be defined before optimization begins, as it determines the likelihood of the gorilla migrating to an unknown location. In this context, ub and lb denote the upper and lower limits of the variables, respectively. and refer to the positions of individual gorillas randomly selected from the population. The parameters C, L, and H are defined by the formulas (29), (30), and (31) respectively.

29

30

31

In Eq. (22),  t represents the current iteration number, while  Maxt is the total number of iterations for the optimization process. is a random value within the range (0,1). In Eq. (30), l is a random value that falls within the range of (− 1, 1). In Eq. (31), the parameter  Z is a random value within the range [− C, C] for the problem’s dimensions. During the development phase, gorillas may opt to follow the silverback gorilla mechanism, as described by Eq. (32).

32

33

34

In Eq. (32), represents the position of the silverback gorilla (the best solution), and  L is a parameter set prior to the optimization process. It is used to toggle the development stage mechanism. The parameter  M is given by Eq. (33), where denotes the position of the i-th candidate gorilla at the t-th iteration, N is the total number of gorillas, and g is defined by Eq. (34).

Exploration stage

During the development phase, gorillas compete with adult female gorillas according to the mechanism described in Eq. (35).

35

36

37

38

In Eq. (35), the parameter  Q represents the impact force and is defined by Eq. (36). The parameter  A is the coefficient of the conflict’s intensity and is described by Eq. (37). In Eq. (36), is a random value between 0 and 1, while in Eq. (37), is a parameter value assigned before the optimization process begins. The parameter E is used to simulate the impact of violence on the solution dimensions, as shown in Eq. (38). If rand equals 0.5,  E will be set to the normal distribution value along with a random value in the problem dimension. Conversely, if rand is not 0.5, E will be set to a random value derived from the normal distribution. In this article, the enhancements made to the multi-objective gorilla troop optimization algorithm involve calculations for gorilla troop coding, population initialization, coding factors, and crowding distance, as illustrated in Fig. 2.

AGTO algorithm integrates sine and cosine and Cauchy mutation Refractive reverse learning strategy

To address the loss of population diversity in the AGTO algorithm during the later stages of optimization, which increases the likelihood of converging to local extrema and results in insufficient accuracy, this paper incorporates a refraction reverse learning mechanism to initialize the gorilla troop algorithm population. Reverse learning is an optimization strategy introduced by [33]. The core idea is to broaden the search space by calculating the reverse solution of the current solution, thereby finding potentially better alternatives for a given problem. Combining intelligent algorithms with reverse learning can significantly enhance the accuracy of the algorithm. While reverse learning can improve convergence in the early stages of optimization, it has limitations. It may cause the algorithm to prematurely converge in the later stages. To address the issue of premature convergence in the later stages of the search, a refraction principle is incorporated into the reverse learning strategy. The reverse learning formula:

39

Equation (36) when generalized to the high dimensional space of the Gorilla Force algorithm, making n = 1 gives

40

In Eq. (40), represents the position of the ith gorilla in the jth dimension of the population, where . Here, D denotes the number of dimensions in the solution space, and is the refracted position of . The parameters are the minimum and maximum values in the jth dimension of the search space, respectively.

AGTO algorithm optimization flowchart

Figure 3 presents the flowchart for applying the optimization algorithm to the gorilla unit³².

Fig. 3.

Exploration and Development Mechanism of AGTO.

The optimization process of the Artificial Gorilla Troops Optimizer (AGTO) begins with the initialization of the population, where each gorilla represents a potential solution to the optimization problem. In this stage, the search agents are randomly distributed within the defined solution space based on the upper and lower bounds of the decision variables. The fitness value of each gorilla is then evaluated using the objective function. After initialization, the algorithm identifies the best-performing gorilla, which is considered the silverback, representing the current optimal solution. The optimization process then proceeds through two main phases: exploration and exploitation. During the exploration phase, gorillas update their positions using different movement strategies such as migration to unknown areas and interaction with other gorillas. This phase allows the algorithm to explore the global search space and avoid premature convergence. In the exploitation phase, the search agents adjust their positions around the silverback solution to refine the search in promising regions of the solution space. This phase improves convergence by intensifying the search near the best solution found so far. The position update equations guide the movement of gorillas toward improved solutions while maintaining a balance between exploration and exploitation. The fitness of the updated solutions is evaluated in each iteration, and the silverback is updated whenever a better solution is found. This iterative process continues until the predefined stopping criterion, such as the maximum number of iterations, is reached. Finally, the algorithm outputs the optimal solution corresponding to the best fitness value obtained during the optimization process.

Sine–cosine strategy

Recently, hybrid metaheuristic algorithms combining multiple search strategies have been proposed to improve optimization performance. For instance, a hybrid Gorilla optimization approach integrating sine–cosine search mechanisms and additional variation strategies has been reported in the literature⁵⁶. While such approaches demonstrate strong performance on benchmark optimization problems, the present work focuses on the application of a hybrid optimization framework specifically for distributed energy resource planning in radial distribution networks, where the optimization problem includes technical constraints such as power loss minimization, voltage stability improvement, and economic cost reduction.

In gorilla predation, the location of the food source is crucial as it influences the direction of the entire gorilla population. If the food source discovered is a local optimum, many followers will converge on that location. In gorilla predation, the location of the food source greatly influences the entire gorilla population’s direction. When the food source is at a local optimum, many followers may converge at that point, causing the discoverer and the population to stagnate. This can lead to a loss of diversity and an increased risk of getting stuck in local optima. To address this, the paper introduces the Sine Cosine Algorithm (SCA) into the gorilla search algorithm. The SCA uses the oscillatory behaviour of sine and cosine functions to maintain diversity and enhance the global search ability of AGTO, aiming to improve the overall optimization process.

Traditional sine-cosine algorithm

In the traditional Sine Cosine Algorithm, adaptive sine and cosine parameters were first introduced into the position updating formula. The updated position formula is as follows³⁴:

41

Here, is a random variable within the range [0,2π], and is another random variable. The parameter determines the search path, either sine or cosine, based on different random values in Eq (41) represents the objective solution. is a value that decreases from mmm to 0 throughout the iterations to balance the search process of the algorithm. This is represented as follows:

42

where i is the present iteration, is the total number of iterations, and m > 0.

The pseudo code of SCA is shown as follows:

1. Initialize a set of search agents (solutions) (X).

2. repeat.

3. Evaluate each of the search agents by the objective function.

4. Update the best solution obtained so far .

5. Update the parameters .

6. Update the poison of search agents using Eq. (5.47)

7. until.

8. Return the best solution obtained so far as the global optimum.

Reference³⁴ demonstrates the excellent performance of the Sine Cosine Algorithm (SCA), which has been successfully applied to the air foil design problem. Compared to the traditional Sine Cosine Algorithm (SCA), the new search path retains the random selection of sine and cosine parameters and the dual path characteristics but eliminates the absolute value and modifies the definition of the convergence factor.

The path search expression is as follows:

43

where is the current location of the optimal solution, k is the current iteration number, and is the optimal solution. The parameter is known as the convergence factor. It is used to balance the exploration and exploitation processes. By combining the linear path with the original path, the search process becomes more thorough and better suited for complex optimization problems. This approach narrows down the search range, making it more effective at finding the global optimum.

To find this global optimum, the original SCA search path uses continuous oscillations to find the maximum. As the linear path is introduced the proposed advanced SCA has considerably lower oscillation than the conventional one leading to higher search speeds. As such, the suggested SCA is able to also find the global optimum effectively. In Eq. (44), is the convergence factor, is a random number in the [0,π/2], and is a random value used to determine whether to use sine or cosine paths. In the equation, and are adjustable constants based on the specific problem, EEE is an empirical parameter derived from previous iterations.There is a single optimal value, P.F, in the original SCA which can be not good enough to solve complicated problems. With the empirical parameters, the prior search knowledge and information can help get narrower search entries with a higher precision. Thus, an empirical parameter will be integrated in search path to increase the accuracy of searches. The optimization algorithm is made more efficient by adding a linear search to it. The use of the empirical parameter adds to search accuracy taking advantage of the past iteration data. A combination of such improvements allows the algorithm to achieve the global optimum faster and address more complicated optimization issues. The final path search expression is as follows:

44

Improved convergence factor

Moreover, it is a work connected with the change of the definitions of related parameters. This is because it is important to define a convergence factor with an enhanced performance to improve the optimization algorithm. In the Eq. (45), is defined as follows:

45

where , are constants, which can be set according to specific problem.

The Eq. (45) has more flexibility in the convergence factor with the adjustment of one parameter m. The algorithm can be customized to more optimization cases by simply defining rmax and r_min. An increased convergence factor, at the beginning of the iteration, increases the global search ability. With further steps the convergence factor is regularly brought down to a and smaller value, making the algorithm more focused towards local maximization. Using a smaller value and lower conversion factor is useful towards achieving the improved final optimization results due to the fact that more refined adjustments are able to be made at the end of the process. PVUs and EVCS are integrated in radial distribution networks in order to optimize the development of a HSCGSA algorithm. It starts with modelling of IEEE 33-bus, 69-bus and 118-bus radial disturbed systems in a simulation model. The selection of these systems was on the basis of their varying complexity and representative element of a typical distribution network. The simulation of these networks during both the sets of PVU and EVCS integration occurs next. This enables to derive all the effects of such technologies on the voltage profiles, active and reactive power losses within the distribution networks. The fundamental aspect of the methodology is that it has created the HSCGSA which is a combination of the SCA and GTO in order to optimize the search ability and speed of convergence of the optimisation process. The strength of the search space is being explored, The SCA, whereas exploitation and local minima avoidance are well done by the GTO. The combination of these algorithms entails a strong hybrid mechanism, balancing between exploration and exploitation, which guarantees the optimal placement of the PVU, EVCS and BESS in the network. The HSCGSA is used on the simulated systems of the infrastructures of the distribution to estimate the optimal (and ideal) deployment of PV units and the optimal (and ideal) VR of EV charging arrangements. The work has been optimized with relative network efficiency to the traditional optimization schemes due to reduction of active and reactive losses of power, enhancement of voltage stability and various others.

Metaheuristic optimization algorithms are often evaluated using standard mathematical benchmark functions such as Sphere, Rastrigin, and Rosenbrock to assess their general search capability. However, the primary objective of this work is to demonstrate the effectiveness of the proposed HSCGSA algorithm in solving practical power system planning problems involving the optimal allocation of distributed energy resources. Therefore, the algorithm is validated using widely adopted benchmark radial distribution networks, including the IEEE 33-bus, 69-bus, and 118-bus systems. These test systems provide a realistic platform for evaluating the performance of optimization algorithms in distribution network planning problems.

Simulation results

The simulation outcomes discussed in this section were obtained on the use of the HSCGSA on three engineered radial distribution networks namely the IEEE 33-bus, 69-bus, and 118-bus. The test cases were chosen to exhibit a variety of distribution network complexities such as those of simpler and less congested networks to larger and more complex networks of different degrees of load and generation diversity. Under the PVU, EVCS and BESS integration, this study seeks to show that the algorithm is capable of enhancing the critical values of operational indicators, including stability in voltage, active power losses and reactive power losses by applying the HSCGSA on such networks. Optimization of PVUs, EVCSs and BESS units placement and capacity of the distribution networks are one of the major goals of the given study. The location of these units also plays a very important role on their efficacy of reducing losses in power as well as in shaping better voltage profiles. The HSCGSA will determine the best placement of the DERs depending on the peculiarities and limitations of every network. The findings of the simulation will demonstrate how far optimized location of PV units can go in passive and reactive power loss reduction without interrupting or improving voltage stability throughout the network. The optimization process was implemented in MATLAB/SIMULINK, which is a widely used platform in electrical engineering for simulation and optimization studies. The use of MATLAB/SIMULINK tools was special because it was easy and very healthy to use when dealing with complex optimization process and load flow analysis. A flowchart and elaborate steps of optimization process have been described in the earlier section. A particle size of 50 was set in the HSCGSA that is tested in every instance of the optimization process. A total of 100 iterations were performed on the algorithm to have enough time to converted to the optimum solution. Such an iterative process allowed the algorithm to search a broad solution space and strike the trade-offs between the various goals and optimize the position and the size of PVU, EVCS and BESS to get the most optimal result. Total network power loss was obtained in an operation of 24 h to record dynamism of load variation during the day. This technique enabled better representation of network performance in real world which deterred changes in power demand due to different factors like moment of the day, weather and consumer behaviour among others. Another important aspect of the fitness function is the voltage stability index which gave an idea of how the network managed the stable voltage condition across all buses. The intent of the optimization process was to make sure that the establishment of EVCS in the chain of distribution was strategic and effective, that it is the one that will cover all the needs of the EV users but will lead to minimum consequences on the overall performance of the network. Furthermore, the optimized voltage magnitudes obtained in all test systems were verified to remain within the acceptable IEEE voltage regulation limits (0.95–1.05 pu), indicating that the integration of PVUs, EVCSs, and BESS does not violate fundamental power quality requirements. The economic parameters used in the objective function are summarized in Table 2, where the units of cost coefficients are expressed consistently with the corresponding power or energy decision variables.

Table 2.

Parameters needed in the computation of the fitness function.

Parameter	Description	Value	Unit
	Grid electricity purchasing cost	0.1390	$/kWh
	PV capital cost	1036.49	$/kWp
	EVCS installation cost	208.33	$/kW
	BESS capital cost	672	$/kWh
RoR	Rate of return	10	%
	Number of days per year	365	days
	Project lifetime	20	years
	Hours per year	8760	hours
	Energy escalation rate	2	%
	Rated PV capacity	2000	kW
	PV operating cost	0.0019	$/kWh
	Rated EVCS capacity	1000	kW
	EVCS operating cost	0.087	$/kWh
	Rated BESS capacity	1000	kWh
	BESS operating cost	0.087	$/kWh

Figure 4 illustrates the normalized 24-hour load curve used in the simulation analysis to represent the variation of power demand throughout a typical day. This load profile reflects the daily demand pattern commonly observed in distribution networks, where the load gradually increases during daytime hours and reaches its peak during evening periods. In this study, the same load curve is applied to the IEEE 33-bus, IEEE 69-bus, and IEEE 118-bus radial distribution test systems to represent time-varying load conditions during the 24-hour simulation period. The use of this load profile enables the proposed optimization method to evaluate system performance under realistic operating conditions with varying load demand.

Fig. 4.

Load curve for 24 h³⁵.

In this study, a normalized 24-hour load profile is used to represent the daily variation of demand in the distribution system as given in Table 3. The same load curve shown in Fig. 4 is applied to the IEEE 33-bus, IEEE 69-bus, and IEEE 118-bus radial distribution networks. For each system, the hourly load demand is obtained by multiplying the normalized load factor with the base load of the corresponding test system. This approach allows the proposed optimization algorithm to evaluate the performance of the distribution networks under realistic time-varying load conditions while maintaining consistency across the different test systems.

Table 3.

Normalized hourly load factors used for 24-hour simulation.

Hour	Load Factor
1	0.60
2	0.58
3	0.56
4	0.55
5	0.57
6	0.62
7	0.70
8	0.78
9	0.82
10	0.86
11	0.90
12	0.94
13	0.96
14	0.98
15	1.00
16	0.97
17	0.95
18	0.98
19	1.00
20	0.96
21	0.92
22	0.85
23	0.75
24	0.68

When EV charging stations are integrated into the distribution network, the total load demand consists of the base system load and the EV charging demand. The EVCS load is incorporated into the simulation by adding the charging power demand to the base load profile at the corresponding buses and time intervals. In practical scenarios, EV charging activity is typically concentrated during evening and night hours when vehicles return from daily usage. Therefore, the load curve with EVCS integration shows a noticeable increase in demand during these periods compared to the base load profile. The modified load curve representing the combined demand of the base load and EV charging load is illustrated in Fig. 5.

Fig. 5.

24-hour load curve including EVCS charging demand.

As observed in Fig. 5, the EVCS demand increases the total system load during peak charging hours, particularly between 18:00 and 22:00, reflecting typical EV charging behaviour in residential distribution networks. Load profile including EVCS charging demand is presented in Table 4.

Table 4.

Load profile including EVCS charging demand.

Hour	Base Load Factor	EVCS Load Factor	Total Load Factor
1	0.60	0.00	0.60
2	0.58	0.00	0.58
3	0.56	0.00	0.56
4	0.55	0.00	0.55
5	0.57	0.01	0.58
6	0.62	0.02	0.64
7	0.70	0.03	0.73
8	0.78	0.04	0.82
9	0.82	0.05	0.87
10	0.86	0.05	0.91
11	0.90	0.06	0.96
12	0.94	0.06	1.00
13	0.96	0.05	1.01
14	0.98	0.05	1.03
15	1.00	0.06	1.06
16	0.97	0.08	1.05
17	0.95	0.12	1.07
18	0.98	0.20	1.18
19	1.00	0.25	1.25
20	0.96	0.22	1.18
21	0.92	0.18	1.10
22	0.85	0.12	0.97
23	0.75	0.07	0.82
24	0.68	0.03	0.71

The EVCS charging demand is modelled according to typical daily EV charging behaviour is focused in this work. Electric vehicles are generally charged after returning from daily usage, which usually occurs during evening hours. Therefore, EVCS loads are considered primarily during the time interval between 16:00 and 23:00 h, when charging demand is expected to be highest. The charging demand gradually increases from late afternoon, reaches its peak during evening hours (approximately 18:00–21:00), and then decreases during late-night hours. During early morning and midday periods, EVCS demand is assumed to be minimal or negligible. This modelling approach enables the simulation to represent realistic EV charging patterns in distribution networks is given in Table 5.

Table 5.

EVCS charging time distribution.

Time Period	EV Charging Activity	Load Contribution
00:00–05:00	Very Low	Minimal
06:00–10:00	Low	Small
11:00–15:00	Moderate	Moderate
16:00–18:00	Increasing	Medium
18:00–21:00	Peak Charging	High
21:00–23:00	Decreasing	Moderate
23:00–24:00	Low	Small

33 bus radial distribution system

The IEEE 33-node and 32-branch Radial Distribution System (RDS) one-line diagram is shown in Fig. 6. This system is 12.66 kV operated with a total rated power capability of 100 M VA. The combined base load is 3.715 MW of active power with 2.3 MVAR of reactive power that has been linked to the distribution system. Figure 6 shows the load demand pattern over a 24-hour period which clearly shows the patterns in the power consumption over the day. Details associated with loads that use bus connections, the resistance and inductance values of branches were consulted as indicated in³⁶. On the basis of this data the load flow analysis of the 33-bus distribution system was carried out to determine how it performed in the base case scenario. It was found that the total active power loss in the system was equal to 3477.166 k W, and the total reactive power loss was equal to 2318.503 k VAR. The outcomes of the results form a baseline upon which additional gains can be assessed. Proposed HSCGSA has been introduced and intensively tested in case of an optimization of the system. This evolved algorithm was later tested against more traditional genetic algorithm (GA) in order to assess the effectiveness³⁷. The objective of the comparison was to give emphasis on the advancements in the reduction of power loss, stability of the voltage, and the general performance of the system made by the HSCGSA compared to the traditional method.

Fig. 6.

33 bus radial distribution system.

Table 6 has made the comparison of the simulation outcomes of IEEE 33-bus RDS at the condition of three separate scenarios: without integrating the accumulation of PVUs core, EVCS and BESS, with PVUs, EVCS units and BESS core in optimal position due to the help of the GA and with PVUs, EVCS units and BESS core in optimal position due to the help of the proposed HSCGSA. This comparison shows how a significant progress is made in terms of active and reactive power loss, stability in voltages, and improvement of the system in general. When the system in question has no DER units incorporated in the RDS, power losses and voltage problems are significant. In particular, the total active power loss is registered to be 3477.166 kW, and the reactive power loss is 2318.503kvar. The critical index of the volatility of the system is the tension stability index (volatility stability index), and this is calculated with a value of 0.6712 pu. Besides, minimum voltage is noticed in the system when one is in the buses, at the 18 th bus, the voltage drops to 0.9224 pu. These values can be used to compare against the enhancement made out of DERs integration optimization. In the second case, we discuss the effects of the introduction of the PVUs, EVCS, and BESS units into the RDS and their location and sizes have been optimized with the help of a conventional GA. Since the implementation of the GA-optimized configuration, the system is observed to have visible positives in respect to all key metrics of performances. The active power loss is decreased with the debate to 2975.36 kW which is a big cut when compared to basic case scenario. In a similar manner, the reactive power loss reduces to 1656.15 kV AR which makes the system even more efficient. The improvement of the voltage stability index is also enormous that the index drops to 0.8573 pu meaning a more stable voltage spot across the network. In addition, the lowest voltage in the system is also high to 0.9465 pu, which this time is noted at the 18 th bus. This means that the incorporation of well systems of DER units has robustified the overall voltage levels within the network limiting the chances of voltage sags and has enhanced reliability. In the GA-optimized scenario, the algorithm identifies the 11th bus as the optimal location for the placement of the PV unit and with a capacity of 1512.34 kVA. The most appropriate location in the case of the EVCS is identified as the 32th bus, which has a capacity of 185.65 kVA. In the case of BESS, the 12th bus is identified as the most appropriate point, having the capacity of 542.37 kVA. The choice of these placements was dependent on the capacity of the algorithm to avoid excess diminishment of power and increase operational stability of the voltage magnitude as well as the operational limitations of the RDS. In the last scenario, the efficiency of RDS is considered in the case of the positions and sizes of DER units which have been optimized with the help of the proposed HSCGSA. These findings show that the HSCGSA is better than the traditional Genetic Algorithm at every metric that is consulted that also delivers a larger reduction in power losses and further stability in voltages. In the optimized operating configuration, active power loss is greatly lowered to 1577.06 kW, and it is very large improvement compared to the base case and the optimization of GA. The reactive power loss is also reduced by a substantial margin, and it is reduced to 1076.43 kVAR. Such power losses reduction will lead to an efficient and cost-effective running of the distribution system. Of most importance is the index of voltage stability which is lowered further to a stable 0.9188 pu of every one of the constant voltage throughout the network. This implies there is a very steady voltage profile hence reducing the chances of voltage being fluctuated which can have an adverse effect on the grid and the consumers using it. The lowest voltage in the system is increased to 0.9706 pu in the 33rd bus, which shows the success of the HSCGSA in enhancing the voltage levels within the distribution system. Regarding the best location and size of the DER units, the HSCGSA determines the 10th bus as the best location where the PVU should be the best location with the capacity that was assigned at 1430.75kVA. In the case of the EVCS, the 32th of the bus will be chosen once again as the best place with a not very low capacity of 187.69 kVA compared to the GA-optimized alternative. For the BESS, the 9th bus is determined to be the most suitable location, with a capacity of 520.04 kVA These optimizations reflect the HSCGSA’s superior capability in balancing multiple objectives, such as minimizing power losses, enhancing voltage stability, and ensuring adequate EVCS coverage, all while adhering to the operational constraints of the RDS.

Table 6.

Results comparison of 33 bus radial distribution system.

	Real Power Loss(kW)	Reactive Power Loss (kVAR)	Voltage stability Index (pu)	Voltage Minimum and Location (at peak load)	Position and Size of PVU	Position and Size of EVCS	Position and Size of BESS	Cost ($/year)
Without	3477.166	2318.503	0.6712	0.9224 at 18th bus	-	-	-	3,857,507.19
GA	2975.36	1656.15	0.8573	0.9465 at 18th bus	1512.34 at 11th bus	185.65 at 32nd bus	542.37 at 12th bus	3,792,485.16
HSCGSA	1577.06	1076.43	0.9188	0.9706 at 33rd bus	1430.75 at 10th bus	187.69 at 32nd bus	520.04 at 9th bus	3,371,666.09

To evaluate the convergence behaviour of the optimization algorithm, the variation of the objective function value with respect to the number of iterations is illustrated in Fig. 7. The convergence curve demonstrates that the Genetic Algorithm progressively improves the objective function value during the search process and stabilizes after several iterations, indicating that the algorithm has reached a near-optimal solution.

Fig. 7.

Convergence plot of the Genetic Algorithm (GA).

The convergence behaviour of the proposed Hybrid Sine–Cosine Gorilla Search Algorithm (HSCGSA) showing the variation of the objective function value with respect to iteration number is presented in Fig. 8.

Fig. 8.

Convergence plot of the proposed HSCGSA algorithm.

The comparison illustrates that the proposed HSCGSA algorithm converges faster and achieves a lower objective function value than the conventional Genetic Algorithm, demonstrating improved optimization performance is presented in Fig. 9. To analyse the convergence performance of the optimization algorithms, convergence plots were generated for the Genetic Algorithm (GA) and the proposed Hybrid Sine–Cosine Gorilla Search Algorithm (HSCGSA). The convergence curves illustrate the variation of the objective function value with respect to the number of iterations. As observed from the Fig. 9, the proposed HSCGSA algorithm converges faster and reaches a lower objective function value compared with the conventional GA, demonstrating its superior search capability and optimization efficiency.

Fig. 9.

Comparison of convergence characteristics of GA and HSCGSA.

Figure 10 illustrates the comparison of voltage magnitudes between the base case scenario and the optimized scenario, where one PVU, one EVCS and one BESS are integrated into the system. These units have been strategically placed and sized using the proposed HSCGSA.

Fig. 10.

Voltage Magnitude comparison of 33 bus radial distribution system with and without PVU, EVCS and BESS.

Figure 11illustrates the comparison of voltage magnitudes between base case, with PVU, with PVU and EVCS and with PVU, EVCS and BESS.

Fig. 11.

Voltage Magnitude comparison of 33 bus radial distribution system between without, with PVU, with PVU and EVCS, with PVU, EVCS and BESS.

Fig. 13.

Reactive Power Loss comparison of 33 bus radial distribution system with and without PVU, EVCS and BESS at Peak Load.

Fig. 16.

Active Power Loss comparison of 33 bus radial distribution system with and without PVU, EVCS and BESS for 24 hours.

Fig. 17.

Reactive Power Loss comparison of 33 bus radial distribution system with and without PVU, EVCS and BESS for 24 hours.

14 and 15 provide a comparison of the total active and reactive power losses over a 24-hour period between base case, with PVU, with PVU and EVCS and with PVU, EVCS and BESS.

Fig. 14.

Active Power Loss comparison of 33 bus radial distribution system between without, with PVU, with PVU and EVCS, with PVU, EVCS and BESS.

Fig. 15.

Reactive Power Loss comparison of 33 bus radial distribution system between without, with PVU, with PVU and EVCS, with PVU, EVCS and BESS.

Figs. 18.

Active Power Loss comparison of 33 bus radial distribution system between without, with PVU, with PVU and EVCS, with PVU, EVCS and BESS.

Figures 12–19 illustrate the variations in active and reactive power losses as well as voltage magnitudes under different operating scenarios, including the base case and the optimized configurations with PVU, EVCS, and BESS integration. The graphical results clearly demonstrate that the optimized allocation of distributed energy resources using the proposed HSCGSA algorithm significantly improves the overall performance of the distribution network. In particular, the integration of PV units provides local power support that reduces the power flow through heavily loaded branches, thereby decreasing active power losses. Similarly, the coordinated operation of EVCS and BESS units helps maintain voltage levels within acceptable limits across the network. The voltage magnitude profiles show a noticeable improvement compared to the base case, indicating enhanced voltage stability and reduced voltage drops at critical buses. These trends confirm that the optimal placement and sizing of DERs effectively enhance both the technical and operational performance of the distribution system.

Fig. 12.

Active Power Loss comparison of 33 bus radial distribution system with and without PVU, EVCS and BESS at Peak Load.

Fig. 19.

Reactive Power Loss comparison of 33 bus radial distribution system between without, with PVU, with PVU and EVCS, with PVU, EVCS and BESS.

69 bus radial distribution system

The proposed optimization algorithm was rigorously tested on the IEEE-69 bus system, which is an extensive RDS consisting of 68 branches and 69 nodes. This system is powered by a typical power distribution network of this size of 12.66 kV with 100 MVA distributed between bases. The design is adequate to operate on high loads, with the active portion of the rated power load of 3,801.89 kW, and the reactive portion of the rated power load of 2,694.10 kVAR. These requirements highlight the high energy requirements with which the system would have to meet, which would be representative of the issues that modern distribution networks usually have to struggle with, in addition to managing the loads and the quality of power. In order to maintain a clear picture of the network structure and work out the most efficient strategies of optimization, Fig. 20 gives the detailed single-line diagram of IEEE-69 bus system. All the data used in the process of optimization such as extensive details of the network in terms of demand and branches contents can be found in³⁸. Figure 20 represents the load profile of the IEEE-69 bus system which indicates the change in energy demand within 24 h. The percentage of this profile is in relation to the rated load, and it gives a dynamic picture of how consumptions of energy change during a day. It is important to appreciate such differences to achieve optimization as it enables one to design strategies that can withstand peak loads to the minimum power loss, and voltage stability. The 24-hour load profile presents exceptional challenges to optimization algorithms since it demands that they be flexible and be able to deal with the time-varying loads and yet attain the intended results. However, the IEEE-69 bus network undergoes considerable power losses in the scenario of the absence of the integration of DERs in the system base case. Namely, an active power loss is recorded as 3,859.99 kW, a reactive power loss is recorded at 1,752.642 kVAR. This loss is a pointer to the inefficiencies in the network and points to the fact that an effective way of minimizing these values is by having an effectual way of optimization.

Fig. 20.

69 Bus radial distribution system.

Table 7 provides a comprehensive comparison of the simulation results for the IEEE-69 bus system under different configurations, focusing on the impact of integrating DERs into the distribution network. The analysis compares performance performance of the system in the absence and cases of optimal placement and sizing of the DER units in terms of a GA and the provide HSCGSA. Under the base case option, when the DERs are not installed, the IEEE-69 bus RDS has quite enormous inefficiencies. The active losses of power in the network are 3,859.99 kW and the reactive power losses are 1,752.64 kVAR. It is even higher in VSI at 0.6812 pu showing possible problems of instability of voltage. Minimum voltage value within the system is found to be 0.9092 pu and it is at the location of the 65 th bus which is less than the acceptable value in regards to optimal operating status indicating where in the system low voltage drops and poor power quality may occur. The first optimization scenario involves the use of the GA to meet the problem of where and how much a single PVU, a single EVCS, and a single BESS should be placed in the network. There are great results after such optimization optimization is done. The active power losses are minimized to 3,185.72 kW as compared to 3,859.99 kW, which is a significant energy wastage. Also like the reactive power losses are reduced to 1,596.53 k VAR instead of 1,752.64 k VAR and were used to enhance the power quality and efficiency. The VSI also has a significant improvement and it has risen by 0.6812 pu into 0.8965 pu. The decrease shows a more consistent voltage pattern throughout the network and contributes to better system overall reliability. The minimum level of voltage at the 65th bus changes to be more 0.9396 pu rather than still being 0.9092 pu, and it brings the voltage level a bit nearer to the desired level to diminish the chances of the under-voltage situation occurring. Genetic Algorithm has the optimum position of the PVU on the 69 th bus which has capacity of 1,437.68 kVA. The EVCS is best located on the 17th bus with its capacity standing at 457.34 kVA. The BESS fits best at the 68 th bus with a capacity of 859.47 kVA. The locations of these placements are done strategically in order to ensure the retention of power loss is as minimized as possible and in such a way that the voltage stability in the network is enhanced. The second circumstance is where the proposed HSCGSA is used to maximize the position and size of a single PVU and single EVCS as well as a single BESS. This new system of optimization brings even greater benefits on the performance of the system. Active power losses are further cut down to 1,884.58 kW and the reactive power losses are also cut down to 828.83 kVAR. These cuts prove the efficiency of the HSCGSA algorithm in reducing the losses of energy in the network. The VSI rises to 0.9483 pu indicating very stable voltage profile which is vital in maintaining integrity of the power distribution system at changing load conditions. Minimal voltage level of the 65 th bus increases to 0.9652 pu which is far nearer to the optimal voltage level and with reduced rise in the chances of a voltage sags likely to occur and compromise the sensitive equipment. Following this scenario of optimization, the HSCGSA algorithm puts the PVU in the 69 th bus with a capacity of 1,287.12 kVA, EVCS in the 17 th bus with a capacity of 324.52 kVA, and BESS in the 68 th bus with a capacity of 816.76 kVA. This is because these values represent a more sophisticated and effective distribution of the resources in contrast to the Genetic Algorithm which results into optimal performance of the system in general. In the last optimization process, HSCGSA algorithm is additionally used to find the optimal positioning and size of two PVUs, two EVCSs and two BESS in the network. This situation will be a more complex and distributed attitude to the allocation of resources which will seek to make even better improvements in system performance. Optimization give the activepower losses and it decreased to 1381.28 kW and the reactivepower losses became 589.19 kVAR. These values depict that a sharp decrease over the base case and even the former scenario, which portrays the HSCGSA algorithm as very efficient in addressing numerous distributed energy resources. VSI is also reduced to 0.9635 pu, thus, showing that the voltage profile of the network is very stable and resilient. The lowest voltage degree of the 65 th bus also goes to 0.9866 pu that almost comes to the optimum dissimilarity of voltage; in this case, all the shreads of the network can hold phenomenal power quality and dependability. The HSCGSA algorithm partitions the locations of the DERs to be optimum as follows in the given scenario: The 17 th bus has the first PVU placing it at it with a capacity of 712.55 kVA and the 69 th bus has the second PVU forming it with a capacity of 1,326.23 kVA. In the EVCSs, the algorithm suggests that the first unit, having the capacity of 165.21 kVA should be located in the 11 th bus and the second unit, having the capacity of 394.45 kVA should be located at the 17 th bus. In the case of the BESS, the algorithm suggests to install the first unit which will have a capacity of 483.75 kVA in the 16 th bus and the second unit with a capacity of 637.36kVA at a 68 th bus. This decentralized method of DER placement leads to a decentralization of the distribution that is more balanced and optimum with minimum power losses and improved voltage stability. It has been clearly shown that proposed HSCGSA algorithm is effective in finding the media to optimize the positioning and size of DERs in IEEE-69 bus system. The HSCGSA algorithm also manages to reduce, through a successively generated sequence of active and reactive power losses, better the stability of voltage and offers strategic placement of energy resources, which make it a potent venerable means of performing optimization in diversity of efficiency and dependability of radial distribution networks. Figure 21 explains a stepwise analysis of voltage magnitudes with a case on the IEEE-69 bus system comparing both the base case situation and the optimal configurations. One and two of the EVCSs and BESS are strategically put into the system in these optimized situations. These units were planned and their size was calculated independently with the proposed HSCGSA. The outcomes show that there is a significant increase of voltage stability and consistency throughout the network as compared to the base case scenario.

Table 7.

Comparison Results of 69 bus radial distribution system.

	Real Power Loss(kW)	Reactive Power Loss (kVAR)	Voltage stability Index (pu)	Voltage Minimum and Location (at peak load)	Position and Size of PVU	Position and Size of EVCS	Position and Size of BESS	Cost ($/year)
Without	3859.99	1752.64	0.6812	0.9092 at 65th bus	-	-		3,965,251.06
GA	3185.72	1596.53	0.8965	0.9396 at 65th bus	1437.68 at 69th bus	457.34 at 17th bus	859.47 at 68th bus	3,869,174.24
HSCGSA (1 PVU, 1 EVCS and 1BESS)	1884.58	828.83	0.9483	0.9652 at 65th bus	1287.12 at 69th bus	324.52 at 17th bus	816.76 at 68th bus	3,661,924.82
HSCGSA (2 PVU, 2 EVCS and 2BESS)	1381.28	589.19	0.9635	0.9866 at 65th bus	712.55 at 17th bus1326.23 at 69th bus	165.21 at 11th bus394.45 at 17th bus	483.75 at 16th bus637.36 at 68th bus	3,484,514.64

Fig. 21.

Voltage Magnitude comparison of 69 bus radial distribution system with and without PVU, EVCS and BESS.

Figure 22. illustrates the comparison of voltage magnitudes between base case, with PVU, with PVU and EVCS and with PVU, EVCS and BESS.

Fig. 22.

Voltage Magnitude comparison of 69 bus radial distribution system between without, with PVU, with PVU and EVCS, with PVU, EVCS and BESS.

Figures 23 and 24 illustrate the active and reactive power losses experienced at each branch of the distribution system. These figures provide a comparative analysis between the base case scenario and the outcomes derived from the HSCGSA-optimized placements. The comparison is particularly significant under peak load conditions, where the impact of the optimization is most evident. The reduction in both active and reactive power losses across various branches underscores the effectiveness of the HSCGSA in enhancing the system’s overall efficiency.

Fig. 23.

Active Power Loss comparison of 69 bus radial distribution system with and without PVU, EVCS and BESS with Peak Load.

Fig. 24.

Reactive Power Loss comparison of 69 bus radial distribution system with and without PVU, EVCS and BESS with Peak Load.

Figures 25 and 26 illustrate comparison of the active and reactive power losses experienced at each branch of the distribution system between base case, with PVU, with PVU and EVCS and with PVU, EVCS and BESS.

Fig. 25.

Active Power Loss comparison of 69 bus radial distribution system between without, with PVU, with PVU and EVCS, with PVU, EVCS and BESS.

Fig. 26.

Reactive Power Loss comparison of 69 bus radial distribution system between without, with PVU, with PVU and EVCS, with PVU, EVCS and BESS.

Figures 27 and 28 offer a comprehensive comparison of total active and reactive power losses over a 24-hour period. These figures highlight the performance improvements achieved through the application of the HSCGSA optimization approach. The reductions in power losses, as evidenced over the entire day, indicate the algorithm’s capability to optimize energy distribution, thereby ensuring a more efficient and stable power network.

Fig. 27.

Active Power Loss comparison of 69 bus radial distribution system with and without PVU, EVCS and BESS for 24 h.

Fig. 28.

Reactive Power Loss comparison of 69 bus radial distribution system with and without PVU, EVCS and BESS for 24 h.

Figures 29 and 30 offer a comparison of total active and reactive power losses over a 24-hour period between base case, with PVU, with PVU and EVCS and with PVU, EVCS and BESS.

Fig. 29.

Active Power Loss comparison of 69 bus radial distribution system between without, with PVU, with PVU and EVCS, with PVU, EVCS and BESS.

Fig. 30.

Reactive Power Loss comparison of 69 bus radial distribution system between without, with PVU, with PVU and EVCS, with PVU, EVCS and BESS.

118 Radial distribution system

The proposed optimization algorithm was rigorously tested on the IEEE-118 bus system, a complex and extensive network comprising 118 nodes interconnected by 186 branches is presented in Fig. 31³⁹. This system can work at a common voltage of 12.66 kV and is a system capable of bearing heavy electrical loads, with a base power rating of 100 MVA. The active power load of the system is rated at 22709.72 kW and reactive power load is also rated at 17041.067 kVAR which is a big requirement of energy within this network though not extremely high. The base case scenario involves no integration of the DERs into the network which has a big power loss. In particular, the active power loss is noted as 935.6724 kW where reactive power loss is extremely higher i.e. 707.7794 kVAR. These marginal losses are important in highlighting the significance of introducing resources of distributed energy as PVUs, EVCSs and BESS systems in the network. The proposed algorithm will minimize service not only by considering the location and size of these units, but also by ensuring that power losses are minimized to achieve better stability of the voltage between these points and to make the entire distribution network more efficient. The usefulness of the optimization plans is eventually calculated on the scale of the minimization of these power losses and the option of sustaining or even enhancing the quality of supplying power throughout the network.

Fig. 31.

118 Bus radial distribution system.

Table 8 discusses the application of simulation outcome of the IEEE 118-bus RDS in different situations prior to and after DERs integration. The system was studied on the influence of these distributed energy resources, on active and reactive power losses, voltage stability as well as the lowest voltage levels of various buses in the network. In the base case (i.e. none of the DERs are integrated into the system), the cumulative value of both the active and reactive power losses is 2279.420 kW and 535.7967 kVAR respectively. Voltage stability in this Winding brec setting is determined to have a Voltage Stability Index 0.6145 pu, or a fairly unstable system with poor voltage regulation. And the lowest voltage is available across the system accesses 0.9430 pu at the 76th bus. This performance base shows that improvement in the efficiency and stability of the network heavily depends on optimization of the network. In the former, GA was utilized to optimize the system parameter namely where and how large a single PVU, one EVCS and one BESS could be. In this case active power losses are reduced from 2279.420 kW to 1876.84 kW, reactive power losses are decreased from 535.7967 kVAR to 435.11 kVAR. VSI is Improved from 0.6145 pu to 0.7233 pu, indicating better voltage regulation and stability. And minimum voltage is Increased from 0.9430 pu to 0.9507 pu at the 76th bus, reflecting enhanced voltage levels across the network. The optimized sizes and locations of the PVU, EVCS and BESS were determined to be 1545.32 kVA at the 42nd bus for the PVU, 2259.65 kVA at the 44th bus for the EVCS and 936.32 kVA at the 41st bus for the BESS. These optimizations demonstrate the effectiveness of GA in improving the network’s performance, albeit with some limitations in achieving maximum possible reductions in power losses and improvements in voltage stability.

Table 8.

Comparison Results of 118 bus radial distribution system.

	Real Power Loss(kW)	Reactive Power Loss (kVAR)	Voltage stability Index (pu)	Voltage Minimum and Location (at peak load)	Position and Size of PVU	Position and Size of EVCS	Position and Size of BESS	Cost($/year)
Without	2279.420	535.7967	0.6145	0.9430 at 76th bus	-	-		22,491,120.13
GA	1876.84	435.11	0.7233	0.9507 at 76th bus	1545.32 at 42nd bus,	2259.65 at 44th bus	936.32 at 41st bus	22,426,351.24
HSCGSA (1 PVU, 1 EVCS and 1 BESS)	1163.356	262.41	0.8542	0.9724 at 76th bus	1137.85 at 42nd bus,	1712.41 at 44th bus	902.56 at 41st bus	22,360,967.39
HSCGSA (2 PVU, 2 EVCS and 2 BESS)	868.76	184.51	0.9276	0.9872 at 76th bus	584.12 at 42nd bus and 1277.21 at 77th bus	913.55 at 44th bus and 863.54 at 100th bus	338.56 at 41stbus568.27 at 76th bus	22,337,418.52
HSCGSA (3 PVU, 3 EVCS and 3 BESS)	608.55	129.50	0.9560	0.9949 at 76th bus	436.95 at 42nd bus, 853.28 at 77th bus and 654.57 at 100th bus	733.64 at 44th bus, 852.47 at 100th bus and 833.68 at 118th bus	357.63 at 41st bus405.11 at 76th bus423.96 at 99th bus	22,289,765.86

In the second scenario, the HSCGSA was applied to optimize the placement and sizing of one PVU, one EVCS and one BESS. In this case active power losses are reduced further to 1163.356 kW, marking a substantial decrease in power wastage and reactive power losses are decreased significantly to 269.41 kVAR, enhancing the efficiency of reactive power management. VSI improved to 0.8542 pu, indicating a more stable voltage profile. Minimum Voltage is increased to 0.9724 pu at the 76th bus, ensuring better voltage regulation across the system. The optimal positions and sizes determined by the HSCGSA were 1137.85 kVA for the PVU at the 42nd bus, 1712.41 kVA for the EVCS at the 44th bus and 902.56 kVA for the BESS at 41st bus. This scenario underscores the superior capability of the HSCGSA in minimizing power losses and enhancing voltage stability compared to the traditional GA.

In the third scenario, the optimization was extended to include two PVUs, two EVCSs and two BESS. In this case active power losses are reduced to 868.76 kW, reflecting a marked improvement in overall energy efficiency and reactive power losses are decreased to 184.51 kVAR, indicating efficient reactive power management and reduced losses. VSI is lowered to 0.9276 pu, signifying enhanced voltage stability. Minimum Voltage is improved to 0.9872 pu at the 76th bus, nearing optimal voltage levels for the system. The optimized placements and sizes for the PVUs were 584.12 kVA at the 42nd bus and 1277.21 kVA at the 77th bus. The EVCSs were optimally sized and located at 913.55 kVA at the 44th bus and 863.54 kVA at the 100th bus. The BESSs were optimally sized and located at 338.56 kVA at the 41st bus and 568.27 kVA at the 76th bus. This scenario illustrates the effectiveness of deploying multiple distributed energy resources in tandem, leading to significant gains in system efficiency and stability.

Finally, the fourth scenario further increased the number of distributed resources to three PVUs, three EVCSs and three BESS, optimized using the HSCGSA algorithm. In this case active power losses are reduced to an impressive 608.55 kW, marking a substantial reduction in energy losses and reactive power losses are minimized to 129.50 kVAR, indicating highly efficient reactive power management. VSI improved to 0.9560 pu, which, although slightly higher than in the previous scenario, still reflects significant enhancement in system stability. Minimum voltage is reached a high of 0.9949 pu at the 76th bus, indicating an optimal voltage profile across the network.

The optimal locations and capacities for the PVUs were determined to be 436.95 kVA at the 42nd bus, 853.28 kVA at the 77th bus, and 654.57 kVA at the 100th bus. The EVCSs were optimally placed and sized at 732.64 kVA at the 44th bus, 852.47 kVA at the 100th bus, and 833.68 kVA at the 118th bus. The BESSs were optimally placed and sized at 357.63 kVA at the 44th bus, 405.11 kVA at the 100th bus, and 423.96 kVA at the 118th bus. This scenario demonstrates the exceptional capability of the HSCGSA algorithm to maximize the efficiency of the IEEE 118-bus system through the strategic deployment of multiple DERs, achieving the lowest power losses and the most stable voltage profiles across all scenarios. The results clearly indicate that the HSCGSA outperforms traditional optimization methods in managing and optimizing complex electrical distribution networks.

In addition to improvements in power loss reduction and voltage stability, the proposed optimization approach also provides significant economic benefits. As shown in Tables 5, 6 and 7, the annual operating cost of the distribution system is reduced when distributed energy resources are optimally allocated using the proposed HSCGSA algorithm. For the IEEE 33-bus system, the annual cost decreases from $3,857,507.19 in the base case to $3,371,666.09 after optimization using HSCGSA, representing a substantial cost saving compared to both the base case and the GA-based solution. Similarly, for the IEEE 69-bus system, the optimized configuration reduces the annual operating cost to $3,484,514.64, while for the IEEE 118-bus system the cost decreases to $22,289,765.86 when multiple DER units are optimally integrated. These results demonstrate that the proposed HSCGSA algorithm not only enhances the technical performance of the distribution network but also improves the economic efficiency of system operation.

Figure 32 presents a comprehensive comparison of voltage magnitudes throughout the IEEE-118 bus system, showcasing the variations between the base case scenario and the optimized configurations with integrated DERs. Optimizations which were performed based on the suggested Hybrid Sine Cosine Gorilla Search Algorithm (HSCGSA) were launched with the variety of one, two, and three PVUs, EVCSs and BESS. The results indicate the presence of a large improvement in the voltage stability and consistency across the network in the optimized case compared to the case of the base case.

Fig. 32.

Comparison of 118 bus radial distribution system with voltage Magnitude voltages and without PVU, EVCS and BESS.

The comparison of the magnitude of voltages of base case, PVU, PVU and EVCS and PVU, EVCS and BESS is compared as shown in Fig. 33.

Fig. 33.

Comparison of Automatic Voltage Magnitude of 118 bus radial distribution system between without, without PVU, without PVU, without PVU and EVCS, without PVU, EVCS and BESS.

Figures 34 and 35 give an analysis of active and reactive losses of power at each branch of the distribution system. These graphs are comparing the initial situation with the performance of the optimizing settings with the HSCGSA and especially at peak load. These reductions in active and reactive power loss are construed side by side in the comparison indicating the ability of the HSCGSA to enhance the efficiency of the entire system. The optimization has resulted in a significant reduction of the power loss in different branches proving that the algorithm is able to reach higher performance under intense load.

Fig. 34.

Active Power Loss comparison of 118 bus radial distribution system with and without PVU, EVCS and BESS at Peak Load.

Fig. 35.

Reactive Power Loss comparison of 118 bus radial distribution system with and without PVU, EVCS and BESS at Peak Load.

Figures 36 and 37 illustrate comparison of the active and reactive power losses experienced at each branch of the distribution system between base case, with PVU, with PVU and EVCS and with PVU, EVCS and BESS.

Fig. 36.

Active Power Loss comparison of 118 bus radial distribution system between without, with PVU, with PVU and EVCS, with PVU, EVCS and BESS.

Fig. 37.

Reactive Power Loss comparison of 118 bus radial distribution system between without, with PVU, with PVU and EVCS, with PVU, EVCS and BESS.

Figures 38 and 39 offer a thorough comparison of total active and reactive power losses over a 24-hour period. These figures illustrate the improvements achieved through the application of the HSCGSA optimization approach throughout the entire day.

Fig. 38.

Active Power Loss comparison of 118 bus radial distribution system with and without PVU, EVCS and BESS for 24 h.

Fig. 39.

Reactive Power Loss comparison of 118 bus radial distribution system with and without PVU, EVCS and BESS for 24 h.

Figures 40 and 41 provide the comparative analysis of total active and reactive power loss values during 24 h of operation based on the case of base, PVU, PVU and EVCS, as well as based on PVU, EVCS and BESS. The mitigation of power losses realized over the 24-hour period depicts the performance adequacy of the algorithm in streamlining the energy dispersion and promoting the stability of the system. The regular recurring better as the day rises, and the better performance indicates the capability of the HSCGSA to keep the power network functional and stable, which confirms its leading position in having a workable complex distribution network.

Fig. 40.

Active Power Loss comparison of 118 bus radial distribution system between without, with PVU, with PVU and EVCS, with PVU, EVCS and BESS.

Fig. 41.

Reactive Power Loss comparison of 118 bus radial distribution system between without, with PVU, with PVU and EVCS, with PVU, EVCS and BESS.

In this study, the proposed HSCGSA algorithm is compared with the conventional Genetic Algorithm, which is widely used as a benchmark optimization technique in power system planning studies. Since the proposed method is developed by hybridizing the Sine Cosine Algorithm and the Gorilla Troops Optimizer, the algorithm inherently combines the exploration and exploitation capabilities of these two methods. A broader comparative analysis with additional metaheuristic algorithms can be considered as part of future research.

Conclusion

This paper presented a hybrid metaheuristic optimization framework, termed the Hybrid Sine–Cosine Gorilla Search Algorithm (HSCGSA), for the optimal placement and sizing of photovoltaic units (PVUs), electric vehicle charging stations (EVCSs), and battery energy storage systems (BESSs) in radial distribution networks. The proposed algorithm integrates the exploration capability of the Sine Cosine Algorithm with the exploitation mechanisms of the Artificial Gorilla Troops Optimizer to effectively address the complex planning problem associated with the integration of distributed energy resources and electric vehicle charging infrastructure. The effectiveness of the proposed method was evaluated using three benchmark radial distribution systems: the IEEE 33-bus, IEEE 69-bus, and IEEE 118-bus networks. Simulation results demonstrate that the coordinated allocation of PV units, EV charging stations, and battery energy storage systems using the proposed HSCGSA algorithm significantly improves the operational performance of the distribution network. In particular, the proposed approach reduces active and reactive power losses and improves the voltage stability index. The optimized VSI values reached 0.9188 p.u. for the IEEE 33-bus system, approximately 0.93 p.u. for the IEEE 69-bus system, and about 0.90 p.u. for the IEEE 118-bus system, indicating improved voltage stability and enhanced voltage profiles compared with the base case and conventional optimization approaches.

The proposed framework can support distribution system operators and power system planners in developing efficient strategies for integrating renewable energy resources and EV charging infrastructure in modern distribution networks. Future work may extend this study by incorporating scenario-based uncertainty modelling, demand response mechanisms, and large-scale smart grid environments, as well as exploring further improvements in hybrid optimization techniques for distribution system planning.

Author contributions

Author Contribution: Conceptualization, Investigation, Writing – Initial Draft, Writing – Review and editing; A.M., S.G., K.S.L., R.N.B., V.S.R., N.G.

Funding

Authors did not receive any funding for this work.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.