Optimizing Energy-Efficient Grid Performance: Integrating Electric Vehicles, DSTATCOM, and Renewable Sources using the Hippopotamus Optimization Algorithm

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A. Abdelaziz, A. A. Ali, R. A. Swief, Rasha Elazab This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4752135/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 22 Nov, 2024 Read the published version in Scientific Reports → Version 1 posted 15 You are reading this latest preprint version Abstract This study explores the intricate relationships among renewable energy integration, electric vehicle (EV) adoption, and their effects on power grid performance. The need for optimized integration of EV charging stations (EVCSs), Distribution Static Compensators (DSTATCOMs), and photovoltaic (PV) systems to enhance network efficiency and stability is addressed. Using the IEEE 69-bus system, this study evaluates four scenarios, each incorporating different combinations of EVCSs, PVs, and DSTATCOMs. Introducing the Renewable Distributed Generation Hosting Factor (RDG-HF) and Electric Vehicle Hosting Factor (EV-HF) as pivotal metrics, this research aims to optimize the placement and sizing of these components using the Hippopotamus Optimization Algorithm (HO). The integration of EVCSs, PVs, and DSTATCOMs significantly reduced the power loss (up to 31.5%) and reactive power loss (up to 29.2%), highlighting the technical benefits of optimized integration. Economically, the scenarios demonstrate varying payback periods (2.7 to 10.4 years) and substantial long-term profits (up to $ 1,052,365 over 25 years), emphasizing the importance of strategic integration for maximizing economic benefits alongside technical performance improvements. Physical sciences/Engineering/Energy infrastructure/Energy grids and networks Physical sciences/Engineering/Energy infrastructure/Power distribution Electric Vehicles Charging Stations Photovoltaic Integration DSTATCOM Voltage Stability Power Losses Economic analysis Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1. Introduction The increasing adoption of electric vehicles (EVs) necessitates the integration of electric vehicle charging stations (EVCSs) into distribution networks, which poses significant challenges. Extensive research has focused on optimizing EVCS placement from an operational perspective, considering factors such as waiting time, driving range, and user satisfaction. However, a critical gap remains in understanding the impact of the EV demand load on distribution networks. Efforts have aimed at minimizing power losses and voltage deviations while considering hosting factors (HFs). Notably, current research primarily focuses on EV hosting factors (EV-HF) and renewable distributed generation hosting factors (RDG-HF). This introduction highlights recent research efforts to optimize EVCSs within distribution networks and underscores the need for further exploration of the relationship between EV demand load and network performance. Considerable research has been devoted to optimizing EVCS placement, emphasizing factors such as waiting time, driving range, and user satisfaction [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ]. Despite this, there is a pressing need to examine the impact of the EV demand load on distribution networks, considering both EV-HF and RDG-HF. Previous studies have primarily concentrated on reducing active and reactive power losses for various EV-HF values. For instance, the Quantum-Behaved Gaussian Mutational Dragonfly Algorithm (QGDA) has been employed for optimization [ 6 ]. However, these studies often overlook the influence of RDG-HF. Algorithms such as Harmony Particle Swarm Optimization (PSO) have demonstrated improvements in voltage quality without accounting for RDG-HF [ 7 ]. Efforts to enhance the integration of EVCSs with other network components, such as Distributed Generators (DGs) and DSTATCOMs, aim to improve network efficiency and reliability [ 8 ], [ 9 ], [ 10 ], [ 11 ], [ 12 ], [ 13 ], [ 14 ]. Nonetheless, the limited consideration of EV-HF and RDG-HF complicates the evaluation of these efforts. For example, in [ 15 ], an RDG-HF exceeding 60% potentially surpassed the limits set by specific countries for Radial Distribution Networks (RDNs) [ 16 ]. A distinct research direction involves optimizing the power loss within distribution networks that incorporate both EVCSs and RDGs [ 8 ], [ 9 ], [ 10 ], [ 11 ], [ 12 ], [ 13 ], [ 14 ]. Techniques such as Particle Swarm Optimization (PSO), Modified Teaching-Learning-Based Optimization (TLBO), and Multi-Objective Particle Swarm Optimization (MOPSO) have been utilized. However, these studies lack a comprehensive investigation into the interaction and influence of hosting factors on network performance, highlighting a significant research gap. Several studies have explored minimizing energy loss and voltage deviation using various optimization techniques, including Differential Evolution (DE), Grey Wolf Optimizer (GWO), and Fuzzy Analytic Hierarchy Process (AHP) [ 17 ], [ 18 ], [ 19 ], [ 20 ], [ 21 ], [ 22 ]. Regrettably, these studies often neglect the proper use of RDG-HF, thereby limiting the scope of their findings. In [ 20 ], the EV-HF is assumed to be equal to the total demand load. In contrast, numerous studies addressing uncertainties in EV-HF through probabilistic modeling tend to overlook the role of RDG-HF [ 23 ], [ 24 ], [ 25 ], [ 26 ], [ 27 ]. Additionally, integrating renewable sources at charging stations, which reduces grid demand, frequently ignores RDG-HF [ 28 ], [ 29 ], [ 30 ], [ 31 ], [ 32 ]. This raises questions about its applicability in scenarios with high renewable energy penetration. Most studies focus on minimizing active power loss and voltage deviation using optimization algorithms such as GWO-PSO [ 26 ], [ 29 ], Chicken Swarm Optimization (CSO), and TLBO [ 30 ], a general algebraic modeling system [ 34 ], and a mixed optimization of Lazy Greedy with Direct Gain and Lazy Greedy with Effective Gain (LGEG) [ 32 ]. This emphasis might lead to the neglect of other critical network performance attributes under high RDG-HF conditions. Various optimization techniques have been employed to determine the optimal placement of EVCSs, aiming to minimize energy loss and enhance reliability. Methods include Mixed Integer Nonlinear Programming (MINLP) [ 33 ], Differential Evolution combined with Harris Hawks Optimization (DE-HHO) [ 34 ], the Binary Atom Search algorithm [ 35 ], and the BAT algorithm [ 36 ]. However, these approaches often disregard RDG-HF, limiting the optimization scope. Notably, EV-HF is typically presented with discrete values, such as 5%, 10%, 15%, and 20% [ 36 ]. While many studies acknowledge variations in EV-HF distribution [ 37 ], [ 38 ], [ 39 ], [ 40 ], they rarely specify the RDG-HF percentage, except in [ 41 ], where RDG-HF exceeded 40%. This highlights the need for more explicit consideration of RDG-HF in future research. In this study, the impact of EV-HF and Renewable Distributed Generation Hosting Factor RDG-HF is examined across five different scenarios involving the integration of EVCSs and DSTATCOMs. The summarization and all the scenarios of the study are shown in Fig. 1 . 2. Problem formulation The surge in EV consumption presents a critical challenge for both EV customers and Distribution Network Operators (DNOs). EV customers are concerned with the distance to charging stations (CSs), while DNOs face the impact of EV charging, which can lead to increased real and reactive power losses and voltage drops at the buses of radial distribution systems (RDSs). Proper positioning of EVCSs is vital for minimizing power losses and enhancing voltage stability by incorporating Renewable Distributed Generators (RDGs). This study proposes a novel approach for hosting renewable energy, such as solar energy, in the RDS with various hosting percentages. The RDG systems are paired with compensators (DSTATCOMs) to mitigate the effect of the EV hosting factor (HF-EV). The HF-RDG is a percentage of the maximum demand load of the RDS [ 16 ]. This study aims to evaluate the performance of the RDS under different HF-EV values, focusing on minimizing active and reactive power losses and boosting the voltage stability index. 3. Methodology 3.1 PV/DSTATCOM Technical Model RDG and DSTATCOMs are modeled by their respective contributions of injected active and reactive power to the electrical grid. The active power injected by RDGs, primarily photovoltaic PV systems, and DSTATCOMs are determined based on their respective capacities, which are established through a detailed sizing process, as discussed in [ 42 ], [ 43 ], [ 44 ]. 3.2 RDG and DSTATCOM sizing Through the utilization of RDGs and DSTATCOMs, grid stability is provided. The maximum capacity of RDGs must be within the given limit of the DNO [ 16 ], despite their high potential. The maximum capacity of the RDG in each zone ( \(\:{P}_{\text{m}\text{a}\text{x}\_zone}^{RDG}\) ) can be defined by multiplying the hosting factor ( \(\:HF\) ) by the cumulative power of the zone ( \(\:{P}_{Demand}^{Zone}\) ), as shown in Eq. ( 1 ) [ 16 ]. The Hosting Factor (HF) is the percentage of the total demand load of the radial distribution network that can be safely accommodated by the existing infrastructure without requiring significant upgrades or causing reliability issues. $$\:{P}_{\text{m}\text{a}\text{x}\_zone}^{RDG}=HF\times\:{P}_{Demand}^{Zone}$$ 1 Likewise, the varying effective ratings of RDGs ( \(\:{P}_{zone}^{RDG}\) ) should fall between the minimum ( \(\:{P}_{\text{m}\text{i}\text{n}\_zone}^{RDG}\) ) and maximum ( \(\:{P}_{\text{m}\text{a}\text{x}\_zone}^{RDG}\) ) ratings. Additionally, the reactive power ( \(\:{Q}^{DSTATCOM}\) ) should be kept within the working range of DSTATCOMs, where ( \(\:{Q}_{min}^{DSTATCOM}\) ) and ( \(\:{Q}_{max}^{DSTATCOM}\) ) are the upper and lower working ranges of DSTACOMs, respectively. Equations ( 2 ) and ( 3 ) illustrate the working ranges of RDGs and DSTATCOMs [ 42 ], [ 43 ], [ 44 ]. $$\:{P}_{\text{m}\text{i}\text{n}\_zone}^{RDG}\le\:{P}_{zone}^{RDG}\le\:\:{P}_{\text{m}\text{a}\text{x}\_zone}^{RDG}$$ 2 $$\:{Q}_{min}^{DSTATCOM}\le\:{Q}^{DSTATCOM}\le\:\:{Q}_{max}^{DSTATCOM}$$ 3 3.3 Cost analysis A- DSTATCOM Cost The annual investment cost ( \(\:{AC}_{DSTATCOM}\) ) of the DSTATCOM can be calculated using the formula provided in Eq. ( 4 ), where \(\:{C}_{DSTATCOM}\) ​ represents the cost of the DSTATCOM, \(\:{B}_{D}\) is the rate of return, and \(\:{n}_{D}\) is the operational lifetime of the DSTATCOM in years. For this analysis, we assume \(\:{C}_{DSTATCOM}\) ​=50 $ /kVAr, \(\:{n}_{D}\) =1 year, and \(\:{B}_{D}\) =0.1 [ 45 ]. $$\:{AC}_{DSTATCOM}={C}_{DSTATCOM}\frac{{\left(1+{B}_{D}\right)}^{{n}_{D}}\:\times\:\:{B}_{D}}{{\left(1+{B}_{D}\right)}^{{n}_{D}}-1}$$ 4 In this context, the total annual cost savings ( \(\:TACS\) ) are determined by considering the overall energy loss costs before and after the installation of the DSTATCOM. This can be calculated using Eq. ( 5 ), where \(\:{K}_{{P}_{loss}}\) is the energy cost of losses (given as 0.06 $ /kWh), \(\:T\) represents the total annual hours (8760 hours), and \(\:{P}_{loss}^{Before}\) ​ and \(\:{P}_{loss}^{After}\) ​ are the total active power losses before and after the installation of the DSTATCOM, respectively [ 45 ]. $$\:TACS={K}_{{P}_{loss}}\left(T\times\:{P}_{loss}^{Before}\right)-{K}_{{P}_{loss}}\left(T\times\:{P}_{loss}^{After}\right)-{AC}_{DSTATCOM}$$ 5 The total annual cost savings in the per-unit system can then be expressed through Eq. ( 6 ), incorporating the specifics of the power losses and energy costs into a comprehensive financial analysis [ 45 ]. $$\:{TACS}_{p.u}=\frac{TACS}{{K}_{{P}_{loss}}\left(T\times\:{P}_{loss}^{Before}\right)}$$ 6 These equations provide a structured method for evaluating the financial benefits of DSTATCOM implementation, allowing for an accurate assessment of both the initial investment and the potential cost savings over time. This methodology is crucial for ensuring the economic feasibility and justification of deploying DSTATCOMs in power systems. B- PV Cost The total cost of PV ( \(\:{PV}_{Total\_Cost}\) ) can be broken down into many costs, such as solar modules, solar inverters, structural balance of system (BOS), electrical balance of system (BOS), installation of labor and equipment, contractor overhead, sales tax, permitting, inspection and interconnection (PII), transmission line costs, developer overhead, contingency budget, and contractor and developer profit [ 46 ]. Therefore, the total cost of the PV distributed generator is calculated via Eq. ( 7 ). $$\:{PV}_{Total\_Cost}={C}_{PV/W}\times\:{PV}_{size}$$ 7 where \(\:{C}_{PV/W}\) is the total cost of PV per watt and \(\:{PV}_{size}\) is the size of the PV. 3.4 Technical modeling of the system The technical modeling sector can be divided into power balance, voltage limits, reactive power limitations of DSTATCOM, and real power limitations of RDG. The locations of the RDG and DSTATCOM are essential parameters in the power equations of the RDS. 1- Power balance The power balance constraints are expressed as follows: $$\:{P\:}_{Total\_Loss}+\:\sum\:{P}_{m}^{Demand}\:+\:\sum\:{P}_{m}^{EVCS}\:=\:\sum\:(\:{P}_{m}^{DSTATCOM}\:+\:{P}_{m}^{RDGs})$$ 8 The variables \(\:{P\:}_{Total\_Loss},\:{P}_{m}^{Demand},\:{{P}_{m}^{EVCS},\:P}_{m}^{DSTATCOM}\) and \(\:{P}_{m}^{RDGs}\) indicate the total power loss in the RDS, the total demand of the RDS, the total demand of the EVCSs, the power of the DSTATCOM, and the power injected by the RDGs, respectively. 2- Voltage limit The voltage limits at the m-th bus in the RDS are given by: 9 where \(\:{V}_{m}^{min}\) and \(\:\:{V}_{m}^{max}\) are the lower and upper limits of the bus voltage, respectively. \(\:{V}_{m}.\) 3- Reactive power compensation The limit of reactive power compensation DSTATCOM is denoted in Eq. ( 10 ), where \(\:{Q}_{DSTATCOM\left(m\right)}^{min}\) and \(\:{Q}_{DSTATCOM\left(m\right)}^{MAX}\) are the lower and upper limits of the DSTATCOM reactive power, respectively. $$\:{Q}_{DSTATCOM\left(m\right)}^{min}\le\:{Q}_{DSTATCOM\left(m\right)}\le\:\:{Q}_{DSTATCOM\left(m\right)}^{MAX}$$ 10 4- Real power compensation by RDG RDGs exhibit limits dictated by the RDS characteristics and the geographic region within each country. HF-RDGs vary across nations. For instance, in Egypt, the HF-RDG is established at 1.5% of the maximum demand load of the RDS. Conversely, in Portugal, the upper threshold for HF-RDG stands at 25%, while in South Africa, it is specified not to surpass 15% [ 16 ]. The RDG must ensure that the power injected at each optimized bus falls within the specified minimum and maximum limitations. The maximum RDG power of each zone is indicated in Eq. ( 1 ). Eq. ( 2 ) specifies the specific quantity of real power adjustment that RDG \(\:{P}_{RDG\left(zone\right)}\) provides for the system in each zone. 5- Voltage Deviation Index (VDI) One of the objectives is to minimize the voltage deviation index. Voltage deviation refers to the difference between the nominal voltage and the measured value. The closer the bus voltage is to the nominal voltage, the better the voltage condition of the system. The calculation of the VDI is displayed in Eq. ( 11 ) [ 47 ], where \(\:{V}_{i}\) and \(\:{V}_{Ni}\) are the voltage and nominal voltage at the \(\:{i}^{th}\) node, respectively. $$\:VDI=\sum\:_{i}^{Ni}\left|{V}_{n}-{V}_{i}\right|$$ 11 6- Voltage Stability Index (VSI) Various criteria are applied to evaluate the safety level of power systems. This research offers a Voltage Stability Index (VSI) designed for steady-state settings aimed at detecting nodes with heightened sensitivity to voltage collapse. Derived from power flow analysis, the index, abbreviated as VSI and expressed by Eq. ( 12 ) [ 48 ], serves to determine the stability of the voltage at each node. For stable operation of an RDS, the VSI should be equal to or greater than zero (m ≥ 0). Nodes with lower VSI values imply a greater need for compensators to provide voltage stability. $$\:VSI\left(m+1\right)={\left|{V}_{m+1}\right|}^{4}-4\:{\left[{P}_{m,m+1}\:{X}_{m,m+1}-{Q}_{m,m+1}\:{R}_{m,m+1}\right]}^{2}-4\left[{P}_{m,m+1}\:{R}_{m,m+1}+{Q}_{m,m+1}\:{X}_{m,m+1}\right]\:{\left|{V}_{m,m+1}\right|}^{2}$$ 12 \(\:{V}_{m+1}\:\) denotes the voltage magnitude at the \(\:{(m+1)}^{th}\) bus, while \(\:{X}_{m,m+1},\:\:{R}_{m,m+1},{Q}_{m,m+1}\) and \(\:\:{P}_{m,m+1}\) refer to the resistance, reactance, reactive power flow, and real power flow, respectively, of the line connecting the \(\:{m}^{th}\) and \(\:{(m+1)}^{th}\) buses. 7- The objective function The aim of this study is to determine the optimal locations of EVCSs, DSTATCOMs, and RDGs. The optimal locations are the locations that achieve the minimum active power loss (P loss ), reactive power loss (Q loss ), voltage deviation index (VDI), installation cost of PVs or DSTATCOMs (C instal ), and total annual savings (TAS) while improving the VSI. The following equation presents the weighted fitness function to determine the optimal solution. where \(\:{w}_{1}\) , \(\:{w}_{2}\) , \(\:{w}_{3}\) , \(\:\:{w}_{4}\) , \(\:{w}_{5}\) , and \(\:{w}_{6}\) are the weight factors used to equilibrate the fitness function. $$\:Fit\:fun={w}_{1}\:{P}_{loss}+{w}_{2}\:{Q}_{loss}+{w}_{3}\:\text{V}\text{D}-{w}_{4}\:{VSI}_{min}+{w}_{5}\:{C}_{install}+{w}_{6}\:TAS$$ 13 4. Hippopotamus optimization algorithm The Hippopotamus Optimization (HO) algorithm has been among the most frequently used and well-developed bioinspired metaheuristic optimization techniques used to solve complex optimization problems. This process is inspired by the social behavior and defense mechanisms of their herds. The HO algorithm consists of three phases: Phase 1: Hippopotamuses Position Update in the River or Pond (Exploration) This phase aims at exploring the search space similarly to how hippos go about their environment, the water. Therefore, the movement and location of individual males ( \(\:{{x}_{ij}}^{M\:hippo}\) ), females, and the dominant hippo ( \(\:{D}^{hippo}\) ) control the exploration process. From Eq. ( 14 ), the dominant hippo (representing the current best solution) moves other individuals in relation to its distance from it. This distance is, in turn, a function of not only the dominance of the hippo but also of a random vector ( \(\:{x}_{ij}\) ). ( \(\:{\chi\:}_{i}\) ), and ( \(\:{y}_{1}\) ) and an integer ( \(\:{I}_{1}\) ) representing inherent variability observed in exploration [ 49 ]. $$\:{{\chi\:}}_{i}^{M\:hippo}:{{x}_{ij}}^{M\:hippo}={x}_{ij}+{y}_{1}\cdot\:\left({D}^{hippo}-I1{x}_{ij}\right)$$ 14 If a male or female hippopotamus's position results in a superior objective function value compared to the current dominant hippopotamus, the dominant's position is then replaced with that individual's position. This mechanism ensures that the exploration process continuously seeks better solutions. Phase 2: The defense action of Hippopotamus against predators (exploration) The defense mode comes into play when something to defend against (e.g., crocodiles of the Nile) is detected by the herd. Immediate defense from the predator is undertaken, accompanied by loud vocalization. Eq. ( 15 ) can be used to model the rapid turn toward the threat. where the random movement of predators ( \(\:{\mathcal{P}\text{\:redator}}_{j}\) ) is denoted by a random vector ( \(\:{\overrightarrow{r}}_{8}\) ) ranging from zero to one within the upper ( \(\:{ub}_{j}\) ) and lower ( \(\:{ll}_{j}\) ) limits of the decision variables at ( \(\:{j}^{th}\) ). Additionally, Eq. ( 16 ) models the change in distance between predator and hippo after the defense response [ 49 ]. $$\:\text{Predator\::\:}{\mathcal{P}\text{\:redator}}_{j}\text{\:}={ll}_{j}+{\overrightarrow{r}}_{8}\cdot\:\left({ub}_{j}-{ll}_{j}\right),\:j=\text{1,2},\dots\:,m$$ 15 $$\:\overrightarrow{\mathcal{D}}=\left|{\mathcal{P}\text{\:redator}}_{j}\text{\:}-{x}_{i\varvec{j}}\right|$$ 16 Phase 3: Hippopotamus Escaping from the Predator (Exploitation) The hippos may escape overwhelming predator attacks or situations in which they cannot mount a sufficient defense to more protected areas. Mathematically, these stochastic refugia are modeled to simulate the unpredictability of escape routes. Since a new location provides a better objective function value (indicating a better solution), this would characterize how a hippo escapes, symbolizing a successful escape. The HO algorithm is a sophisticated method that considers the complexities of optimization problems and devises an efficient search strategy by mimicking the behavior of hippos. Throughout successive iterative phases simulating herd dynamics and defensive mechanisms, the algorithm proves to be robust and efficient for most optimization problems. The following is the pseudocode and flowchart describing the HO algorithm in Fig. 2 . Start 1 Define the optimization problem at hand. 2 Establish the maximum number of iterations (denoted as "it") and determine the quantity of hippopotamuses (referred to as "N"). 3 Generate the initial population of hippopotamuses and evaluate the objective function for this initial set. 4 For i = 1: it 5 Update the position of the dominant hippopotamus on the criterion of objective function value criterion 6 Phase 1: Updating the hippopotamus's position in the river or pond 7 For i = 1 : N/2 8 Calculate new position for \(\:{i}^{th}\) hippopotamus 9 Update position for \(\:{i}^{th}\) hippopotamus 10 End for 11 Phase 2: Hippopotamus defense against predators 12 For i = 1 + N/2:N 13 Generate random position for predator 14 Calculate new position for \(\:{i}^{th}\) hippopotamus 15 Update position for \(\:{i}^{th}\) hippopotamus 16 End for 17 Phase 3: Hippopotamus escaping from the predator 18 Calculate new bounds of variables decision 19 For i = 1:N 20 Calculate the new position for \(\:{i}^{th}\) hippopotamus 21 Update position for \(\:{i}^{th}\) hippopotamus 22 End for 23 Save the best candidate solution found thus far. 24 End for 25 Output the best solution of the objective function END 5. Results and Discussion This study investigates the impact of increasing electric vehicle (EV) adoption and renewable energy sources on the performance of a local power grid, specifically a Radial Distribution Network (RDN). The Renewable Distributed Generation Hosting Factor (RDG-HF) and the EV Hosting Factor (EV-HF) are used to represent these variables. The analysis is conducted using the IEEE 69-bus system, which represents a scenario with 3.80 MW of active power and 2.69 MVAR of reactive power, as shown in Fig. 1 a. Five distinct scenarios are explored to understand the effects of varying EV-HF and RDG-HF values, simulating the integration of the latest EV and renewable energy technologies into the RDN. The RDN is divided into four zones, each with a specific number of buses. The EV-HF in each zone is a ratio of the total demand within that zone, as detailed in Table 1 and Fig. 3. Figure 3: The clustering of the RDN. Table 1 The number of buses included in each zone and the sizes of EVCSs in each zone at different EV-HFs. Buses at each zone Total demand load EVCS demand load due to EV-HF 30% 40% 50% 60% Zone 1 2-3-4-5-6-7-8-9-10-11-12-51-52 510.1 153.03 204.04 255.05 306.06 Zone 2 28-29-30-31-32-33-34-35-53-54-55-56-57-58-59-60-61-62-63-64-65 1808.2 542.48 723.30 904.13 1084.95 Zone 3 36-37-38-39-40-41-42-43-44-45-46-47-48-49-50 1034 310.21 413.62 517.02 620.42 Zone 4 13-14-15-16-17-18-19-20-21-23-24-25-26-27-66-67-68-69 393.8 118.14 157.52 196.90 236.28 Scenario 1: Integrating EVCSs with the RDN In this scenario, the optimal placement of Electric Vehicle Charging Stations (EVCSs) in each zone is determined using the HO algorithm. The EV-HF values considered are 0.3, 0.4, 0.5, and 0.6. The size of each EVCS is calculated based on the EV-HF and the total demand load of each zone, as shown in Table 1 . The optimal locations for the EVCSs are at buses 2, 28, 36, and 66, as illustrated in Fig. 4 . As EV-HF increases, both the total active and reactive power increase, while the VSI, voltage deviation, and minimum voltage decrease compared to those in the base case, as shown in Table 4 . The voltage profile and power losses across buses for different EV-HF values are illustrated in Figs. 6 and 7 . Scenario 2: Integration of EVCS and DSTATCOM The HO algorithm is utilized to ascertain the optimal sizing and placement of DSTATCOMs in various zones, as well as the ideal locations for EVCSs. The integration of DSTATCOMs is intended to counteract the negative impacts of elevated EV-HF on power loss and voltage stability. The findings reveal significant reductions in active power losses (between 27% and 30%) and reactive power losses of 28% in comparison to the baseline scenario. Relative to the initial scenario, the reductions are approximately 31% for both active and reactive power losses. Additionally, there is a decrease in the voltage deviation index, while improvements are observed in the minimum voltage levels and the Voltage Stability Index (VSI) at all EV-HF levels. These effects are detailed in Table 2 , which highlights the impact of DSTATCOMs on these metrics. Figures 6 and 7 illustrate the voltage and power loss profiles of scenario 2, providing a comparison with the baseline case. Table 2 The impact of EV-HF on the objectives in scenario 2. Base Scenario 2 EVCSs & DSTATCOMs EV-HF - 30% 40% 50% 60% \(\:{P}_{loss}\) 225 155.44 156.54 158.46 162.97 \(\:{Q}_{loss}\) 102.2 72.17 72.83 73.65 75.63 \(\:{VSI}_{min}\) 0.6868 0.7449 0.7451 0.7443 0.7389 VDI 0.0993 0.0594 0.0593 0.0609 0.0652 \(\:{V}_{min}\) 0.9092 0.9279 0.9280 0.9277 0.9260 Table 3 outlines the results obtained through the HO algorithm, which identifies the optimal sizes and placements of DSTATCOMs across different zones. The sizes and locations of the DSTATCOMs vary due to the differing HFs in each zone. The average installation cost of DSTATCOMs across various EV-HF levels is estimated at $ 94,000, with annual savings fluctuating based on the EV-HF, as shown in Table 3 . Table 3 DSTATCOMs’ specifications in Scenario 2. zone Scenario 2 (EVCSs & DSTATCOM) EV-HF 0.3 0.4 0.5 0.6 DSTATCOM Size (KVAR) zone 1 303 549 433 0 zone 2 1000 1000 1000 1000 zone 3 0 0 0 0 zone 4 597 428 541 550 DSTATCOM Location (Bus) zone 1 8 11 9 - zone 2 61 61 61 61 zone 3 - - - - zone 4 16 20 17 21 Total DSTATCOMs cost ( $ ) 95050 99200 100450 80750 Annual Savings Costs ( $ ) 36560.6121 35983.66 34973.64 32600.68 Scenario 3: The Integration of EVCSs and RDGs This scenario maintains the same EVCS size and location as in Scenario 1. The HO algorithm is used to determine the optimal locations and sizes of Renewable Distributed Generators (RDGs) in the IEEE 69-bus RDN, considering the RDG-HF restricted limitations (not exceeding 25%) [ 16 ]. The optimal locations for RDGs in zone two are determined to be at bus number 64. The recommended sizes for this location are 349 kW, 369 kW, 380 kW, and 392 kW for EV-HF levels of 0.3, 0.4, 0.5, and 0.6, respectively, with no additional RDGs needed in other zones, as shown in Fig. 5 . This integration reduces active and reactive power losses by approximately 29% for all EV-HF values compared to the base case, resulting in an enhanced voltage profile, as illustrated in Fig. 6 . The voltage deviation index is reduced to approximately 0.075 in all cases, while the VSI and minimum voltage improve to approximately 0.74 and 0.928, respectively, as shown in Table 4 and Fig. 7 . The PV calculation parameters are based on the location of Cairo, Egypt, which is situated at 30.033° latitude and 31.562° longitude. Scenario 4: The Integration of EVCSs, DSTATCOMs, and RDGs By optimizing the locations of the EVCSs, DSTATCOMs, and RDGs, this scenario achieves the best performance outcomes. The active and reactive power losses decreased by approximately 30.4% and 27%, respectively, across all EV-HF values compared to those of the base case, as shown in Table 4 . The voltage deviation index decreases to approximately 0.073 for different EV-HF scenarios, while the VSI and minimum voltage increase to 0.7724 and 0.93, respectively. The best voltage and power loss profiles across all scenarios are achieved in this scenario, as illustrated in Figs. 6 and 7 . The optimal placement for the DSTATCOM and RDG was determined to be at bus 64. The sizing for the DSTATCOM is specified as 264 kVAR, 272 kVAR, 273 kVAR, and 278 kVAR for EV-HF values of 0.3, 0.4, 0.5, and 0.6, respectively. Correspondingly, the size of the RDG is equal to that of the DSTATCOM but measured in kW. In summary, the integration of EVCSs, DSTATCOMs, and RDGs significantly enhances the performance of the RDN by reducing power losses and improving voltage stability. These results underscore the importance of the optimal placement and sizing of these components in addressing the challenges posed by increasing EV and renewable energy integration in distribution networks. Table 4 The impact of EV-HF on the objectives in various scenarios. Scenario Base 1 2 3 4 P loss (kW) 225 230.88–237.28 155.45–162.98 159.85–159.89 154.11–156.5 Q loss (kVAR) 102.2 105.14–108.39 72.18–75.63 74.84–75.25 72.37–73.85 VSI min 0.6868 0.6845 − 0.6821 0.745 − 0.739 0.7363–0.7445 0.742–0.7421 VDI 0.0993 0.1034–0.1076 0.0594–0.0653 0.0723–0.0754 0.0738–0.0761 V min 0.9092 0.9085 − 0.9077 0.928 − 0.9261 0.9296 − 0.9286 0.9289 − 0.9287 Costs ($) - - $ 80,750 - $ 100,450 $ 365,310 - $ 388,080 $ 275,880 - $ 290,510 Annual saving Costs ($) - - $ 32,600.7 - $ 36,560.6121 $ 44915.1 - $ 39988.2204 $ 52,568- $ 53,495 Payback Period (Years) - - 2.7–3 8.7–9.4 9.8–10.4 Total Profit ($) $ 714,267.5 - $ 816,515 $ 747,877.5 - $ 999,705 $ 1,039,320 - $ 1,052,365 From a technical perspective, integrating EVCSs alone in Scenario 1 resulted in an increase in power loss from 225 kW to between 230.88 kW and 237.28 kW (2.6–5.4%) and an increase in reactive power loss from 102.2 kVAR to between 105.14 kVAR and 108.39 kVAR (2.9–6%). However, Scenario 2, which combines EVCSs with DSTATCOM, significantly reduces these losses, with the power loss decreasing to between 155.45 kW and 162.98 kW (31–27.6%) and the reactive power loss decreasing to between 72.18 kVAR and 75.63 kVAR (29.4–26%). PV integration alone in Scenario 3 maintains a stable reduction in power loss of approximately 159.85 kW to 159.89 kW (29%) and a decrease in reactive power loss of approximately 74.84 kVAR to 75.25 kVAR (26.8–26.1%). The combined integration of EVCSs, PVs, and DSTATCOMs in Scenario 4 shows the most significant improvements, with the power loss reduced to between 154.11 kW and 156.5 kW (31.5–30.5%) and the reactive power loss reduced to between 72.37 kVAR and 73.85 kVAR (29.2–27.8%). The voltage stability also improved across the scenarios. VSI min increases from 0.6868 to between 0.745 and 0.739 (8.5–7.6%) in Scenario 2. V min increases from 0.9092 p.u. to between 0.928 p.u. and 0.9261 p.u. (2.1–1.9%) in Scenario 2, indicating enhanced voltage stability. Furthermore, the VDI improved from 0.0993 to between 0.0594 and 0.0653 (40.2–34.2%) in Scenario 2. Economically, Scenario 2, which integrates EVCS and DSTATCOM, presents significant benefits, with total DSTATCOM costs ranging from $ 80,750 to $ 100,450 and annual savings between $ 32,600.7 and $ 36,560.6, resulting in a payback period of 2.7 to 3 years. Scenario 3, which focuses on PV integration, has installation costs ranging from $ 365,310 to $ 388,080, with a payback period of 8.7 to 9.4 years and a total profit over 25 years ranging from $ 747,877.5 to $ 999,705. Scenario 4, which combines EVCS, PV, and DSTATCOM, has total costs ranging from $ 275,880 to $ 290,510, with annual savings of $ 52,568 to $ 53,495, a payback period of 9.8 to 10.4 years, and a total profit over 25 years ranging from $ 1,039,320 to $ 1,052,365. 6. Conclusion The integration of EVCSs, PV systems, and DSTATCOMs significantly enhances power grid performance by reducing power and reactive power losses and improving voltage stability. The combined scenario (EVCS, PV, and DSTATCOM) demonstrated the most substantial improvements, with reductions in power loss of 31.5% and reactive power loss of 29.2%, alongside significant economic benefits, including a total profit of up to $ 1,052,365 over 25 years and a payback period of 9.8 to 10.4 years. The strategic deployment and optimization of these components using the Hippopotamus Optimization algorithm (HO) is essential for achieving an efficient, stable, and cost-effective power distribution network. The findings underscore the importance of optimizing the integration of EVCSs, PVs, and DSTATCOMs to maximize both technical performance and economic benefits. Declarations Competing interests: The authors declare no competing interests. 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Abdelaziz","email":"data:image/png;base64,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","orcid":"","institution":"Helwan University","correspondingAuthor":true,"prefix":"","firstName":"M.","middleName":"A.","lastName":"Abdelaziz","suffix":""},{"id":338449110,"identity":"4016e57e-3653-4dd6-b311-6230dd143dec","order_by":1,"name":"A. A. Ali","email":"","orcid":"","institution":"Helwan University","correspondingAuthor":false,"prefix":"","firstName":"A.","middleName":"A.","lastName":"Ali","suffix":""},{"id":338449111,"identity":"71deffa4-fdd7-470b-a41a-083b0e5e2143","order_by":2,"name":"R. A. Swief","email":"","orcid":"","institution":"Ain Shams University","correspondingAuthor":false,"prefix":"","firstName":"R.","middleName":"A.","lastName":"Swief","suffix":""},{"id":338449112,"identity":"d7605f5d-ab40-496a-ba13-65ac1e0f0014","order_by":3,"name":"Rasha Elazab","email":"","orcid":"","institution":"Helwan University","correspondingAuthor":false,"prefix":"","firstName":"Rasha","middleName":"","lastName":"Elazab","suffix":""}],"badges":[],"createdAt":"2024-07-16 19:44:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4752135/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4752135/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-024-79381-4","type":"published","date":"2024-11-22T15:57:39+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":62269679,"identity":"cc6815f9-768c-47d0-a3e9-1dd338a1e587","added_by":"auto","created_at":"2024-08-12 09:59:41","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":102883,"visible":true,"origin":"","legend":"\u003cp\u003eThe study graphical framework.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4752135/v1/d77f53eae6467f4310d55951.jpg"},{"id":62269677,"identity":"53bab1b6-64fb-4738-9ccb-1fffd0e2373e","added_by":"auto","created_at":"2024-08-12 09:59:41","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":244746,"visible":true,"origin":"","legend":"\u003cp\u003eThe flowchart of the HO algorithm.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4752135/v1/d8f8e24858319f27a0232d06.jpg"},{"id":62271082,"identity":"00360240-3834-4aac-95c8-78a2329faa46","added_by":"auto","created_at":"2024-08-12 10:15:41","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":305503,"visible":true,"origin":"","legend":"\u003cp\u003eThe clustering of the RDN.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4752135/v1/2edcfee5ccbedaa7e76824f0.png"},{"id":62269681,"identity":"a6a58d81-640d-4436-a822-af5894334d4b","added_by":"auto","created_at":"2024-08-12 09:59:41","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":262330,"visible":true,"origin":"","legend":"\u003cp\u003eThe optimal locations of EVCSs.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4752135/v1/c97534ae7a00ede356995ded.png"},{"id":62269682,"identity":"3b130b18-9797-4884-a1b5-091a23e0b384","added_by":"auto","created_at":"2024-08-12 09:59:41","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":73686,"visible":true,"origin":"","legend":"\u003cp\u003eThe proposed IEEE 69-bus as RDN in various conditions in scenario 3.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4752135/v1/6fbb6317ad0891b41778da5a.png"},{"id":62270360,"identity":"042017e1-d0b9-468a-83f7-43d92a52f1e9","added_by":"auto","created_at":"2024-08-12 10:07:41","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":108590,"visible":true,"origin":"","legend":"\u003cp\u003eThe impact of EV-HF on the voltage profile in various scenarios.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4752135/v1/de53bf508026ffc237524411.png"},{"id":62270362,"identity":"413868cc-79a1-4aa5-aa01-26e84156fcfa","added_by":"auto","created_at":"2024-08-12 10:07:41","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":105688,"visible":true,"origin":"","legend":"\u003cp\u003eThe impact of EV-HF on power loss profiles in various scenarios.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-4752135/v1/d170869f45a48f827cef4b31.png"},{"id":69835150,"identity":"5d340648-f57f-45e8-b07a-2cfc38ae10eb","added_by":"auto","created_at":"2024-11-25 16:12:25","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2123551,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4752135/v1/04eb74b2-a157-4b1f-ad50-3d6dec35ca14.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Optimizing Energy-Efficient Grid Performance: Integrating Electric Vehicles, DSTATCOM, and Renewable Sources using the Hippopotamus Optimization Algorithm","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe increasing adoption of electric vehicles (EVs) necessitates the integration of electric vehicle charging stations (EVCSs) into distribution networks, which poses significant challenges. Extensive research has focused on optimizing EVCS placement from an operational perspective, considering factors such as waiting time, driving range, and user satisfaction. However, a critical gap remains in understanding the impact of the EV demand load on distribution networks. Efforts have aimed at minimizing power losses and voltage deviations while considering hosting factors (HFs). Notably, current research primarily focuses on EV hosting factors (EV-HF) and renewable distributed generation hosting factors (RDG-HF). This introduction highlights recent research efforts to optimize EVCSs within distribution networks and underscores the need for further exploration of the relationship between EV demand load and network performance.\u003c/p\u003e \u003cp\u003eConsiderable research has been devoted to optimizing EVCS placement, emphasizing factors such as waiting time, driving range, and user satisfaction [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Despite this, there is a pressing need to examine the impact of the EV demand load on distribution networks, considering both EV-HF and RDG-HF.\u003c/p\u003e \u003cp\u003ePrevious studies have primarily concentrated on reducing active and reactive power losses for various EV-HF values. For instance, the Quantum-Behaved Gaussian Mutational Dragonfly Algorithm (QGDA) has been employed for optimization [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. However, these studies often overlook the influence of RDG-HF. Algorithms such as Harmony Particle Swarm Optimization (PSO) have demonstrated improvements in voltage quality without accounting for RDG-HF [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eEfforts to enhance the integration of EVCSs with other network components, such as Distributed Generators (DGs) and DSTATCOMs, aim to improve network efficiency and reliability [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Nonetheless, the limited consideration of EV-HF and RDG-HF complicates the evaluation of these efforts. For example, in [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], an RDG-HF exceeding 60% potentially surpassed the limits set by specific countries for Radial Distribution Networks (RDNs) [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eA distinct research direction involves optimizing the power loss within distribution networks that incorporate both EVCSs and RDGs [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Techniques such as Particle Swarm Optimization (PSO), Modified Teaching-Learning-Based Optimization (TLBO), and Multi-Objective Particle Swarm Optimization (MOPSO) have been utilized. However, these studies lack a comprehensive investigation into the interaction and influence of hosting factors on network performance, highlighting a significant research gap.\u003c/p\u003e \u003cp\u003eSeveral studies have explored minimizing energy loss and voltage deviation using various optimization techniques, including Differential Evolution (DE), Grey Wolf Optimizer (GWO), and Fuzzy Analytic Hierarchy Process (AHP) [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e], [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Regrettably, these studies often neglect the proper use of RDG-HF, thereby limiting the scope of their findings. In [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e], the EV-HF is assumed to be equal to the total demand load.\u003c/p\u003e \u003cp\u003eIn contrast, numerous studies addressing uncertainties in EV-HF through probabilistic modeling tend to overlook the role of RDG-HF [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e], [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e], [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Additionally, integrating renewable sources at charging stations, which reduces grid demand, frequently ignores RDG-HF [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e], [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e], [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. This raises questions about its applicability in scenarios with high renewable energy penetration. Most studies focus on minimizing active power loss and voltage deviation using optimization algorithms such as GWO-PSO [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], Chicken Swarm Optimization (CSO), and TLBO [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e], a general algebraic modeling system [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e], and a mixed optimization of Lazy Greedy with Direct Gain and Lazy Greedy with Effective Gain (LGEG) [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. This emphasis might lead to the neglect of other critical network performance attributes under high RDG-HF conditions.\u003c/p\u003e \u003cp\u003eVarious optimization techniques have been employed to determine the optimal placement of EVCSs, aiming to minimize energy loss and enhance reliability. Methods include Mixed Integer Nonlinear Programming (MINLP) [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e], Differential Evolution combined with Harris Hawks Optimization (DE-HHO) [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e], the Binary Atom Search algorithm [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e], and the BAT algorithm [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. However, these approaches often disregard RDG-HF, limiting the optimization scope. Notably, EV-HF is typically presented with discrete values, such as 5%, 10%, 15%, and 20% [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eWhile many studies acknowledge variations in EV-HF distribution [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e], [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e], [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e], [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e], they rarely specify the RDG-HF percentage, except in [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e], where RDG-HF exceeded 40%. This highlights the need for more explicit consideration of RDG-HF in future research. In this study, the impact of EV-HF and Renewable Distributed Generation Hosting Factor RDG-HF is examined across five different scenarios involving the integration of EVCSs and DSTATCOMs. The summarization and all the scenarios of the study are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"2. Problem formulation","content":"\u003cp\u003eThe surge in EV consumption presents a critical challenge for both EV customers and Distribution Network Operators (DNOs). EV customers are concerned with the distance to charging stations (CSs), while DNOs face the impact of EV charging, which can lead to increased real and reactive power losses and voltage drops at the buses of radial distribution systems (RDSs). Proper positioning of EVCSs is vital for minimizing power losses and enhancing voltage stability by incorporating Renewable Distributed Generators (RDGs).\u003c/p\u003e \u003cp\u003eThis study proposes a novel approach for hosting renewable energy, such as solar energy, in the RDS with various hosting percentages. The RDG systems are paired with compensators (DSTATCOMs) to mitigate the effect of the EV hosting factor (HF-EV). The HF-RDG is a percentage of the maximum demand load of the RDS [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. This study aims to evaluate the performance of the RDS under different HF-EV values, focusing on minimizing active and reactive power losses and boosting the voltage stability index.\u003c/p\u003e"},{"header":"3. Methodology","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 PV/DSTATCOM Technical Model\u003c/h2\u003e \u003cp\u003eRDG and DSTATCOMs are modeled by their respective contributions of injected active and reactive power to the electrical grid. The active power injected by RDGs, primarily photovoltaic PV systems, and DSTATCOMs are determined based on their respective capacities, which are established through a detailed sizing process, as discussed in [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e], [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e], [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 RDG and DSTATCOM sizing\u003c/h2\u003e \u003cp\u003eThrough the utilization of RDGs and DSTATCOMs, grid stability is provided. The maximum capacity of RDGs must be within the given limit of the DNO [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], despite their high potential. The maximum capacity of the RDG in each zone (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{P}_{\\text{m}\\text{a}\\text{x}\\_zone}^{RDG}\\)\u003c/span\u003e\u003c/span\u003e) can be defined by multiplying the hosting factor (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:HF\\)\u003c/span\u003e\u003c/span\u003e) by the cumulative power of the zone (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{P}_{Demand}^{Zone}\\)\u003c/span\u003e\u003c/span\u003e), as shown in Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe Hosting Factor (HF) is the percentage of the total demand load of the radial distribution network that can be safely accommodated by the existing infrastructure without requiring significant upgrades or causing reliability issues.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{P}_{\\text{m}\\text{a}\\text{x}\\_zone}^{RDG}=HF\\times\\:{P}_{Demand}^{Zone}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eLikewise, the varying effective ratings of RDGs (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{P}_{zone}^{RDG}\\)\u003c/span\u003e\u003c/span\u003e) should fall between the minimum (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{P}_{\\text{m}\\text{i}\\text{n}\\_zone}^{RDG}\\)\u003c/span\u003e\u003c/span\u003e) and maximum (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{P}_{\\text{m}\\text{a}\\text{x}\\_zone}^{RDG}\\)\u003c/span\u003e\u003c/span\u003e) ratings. Additionally, the reactive power (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Q}^{DSTATCOM}\\)\u003c/span\u003e\u003c/span\u003e) should be kept within the working range of DSTATCOMs, where (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Q}_{min}^{DSTATCOM}\\)\u003c/span\u003e\u003c/span\u003e) and (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Q}_{max}^{DSTATCOM}\\)\u003c/span\u003e\u003c/span\u003e) are the upper and lower working ranges of DSTACOMs, respectively. Equations\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) and (\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) illustrate the working ranges of RDGs and DSTATCOMs [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e], [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e], [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e].\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{P}_{\\text{m}\\text{i}\\text{n}\\_zone}^{RDG}\\le\\:{P}_{zone}^{RDG}\\le\\:\\:{P}_{\\text{m}\\text{a}\\text{x}\\_zone}^{RDG}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{Q}_{min}^{DSTATCOM}\\le\\:{Q}^{DSTATCOM}\\le\\:\\:{Q}_{max}^{DSTATCOM}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Cost analysis\u003c/h2\u003e \u003cp\u003e \u003cem\u003eA- DSTATCOM Cost\u003c/em\u003e \u003c/p\u003e \u003cp\u003eThe annual investment cost (\u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e \\(\\:{AC}_{DSTATCOM}\\) \u003c/span\u003e \u003c/span\u003e) of the DSTATCOM can be calculated using the formula provided in Eq.\u0026nbsp;(\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e), where \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e \\(\\:{C}_{DSTATCOM}\\) \u003c/span\u003e \u003c/span\u003e​ represents the cost of the DSTATCOM, \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e \\(\\:{B}_{D}\\) \u003c/span\u003e \u003c/span\u003e is the rate of return, and \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e \\(\\:{n}_{D}\\) \u003c/span\u003e \u003c/span\u003e is the operational lifetime of the DSTATCOM in years. For this analysis, we assume \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e \\(\\:{C}_{DSTATCOM}\\) \u003c/span\u003e \u003c/span\u003e​=50 \u003cspan\u003e$\u003c/span\u003e/kVAr, \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e \\(\\:{n}_{D}\\) \u003c/span\u003e \u003c/span\u003e=1 year, and \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e \\(\\:{B}_{D}\\) \u003c/span\u003e \u003c/span\u003e=0.1 [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e].\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e \n$$\\:{AC}_{DSTATCOM}={C}_{DSTATCOM}\\frac{{\\left(1+{B}_{D}\\right)}^{{n}_{D}}\\:\\times\\:\\:{B}_{D}}{{\\left(1+{B}_{D}\\right)}^{{n}_{D}}-1}$$ \u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn this context, the total annual cost savings (\u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e \\(\\:TACS\\) \u003c/span\u003e \u003c/span\u003e) are determined by considering the overall energy loss costs before and after the installation of the DSTATCOM. This can be calculated using Eq.\u0026nbsp;(\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e), where \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e \\(\\:{K}_{{P}_{loss}}\\) \u003c/span\u003e \u003c/span\u003e is the energy cost of losses (given as 0.06 \u003cspan\u003e$\u003c/span\u003e/kWh), \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e \\(\\:T\\) \u003c/span\u003e \u003c/span\u003e represents the total annual hours (8760 hours), and \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e \\(\\:{P}_{loss}^{Before}\\) \u003c/span\u003e \u003c/span\u003e​ and \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e \\(\\:{P}_{loss}^{After}\\) \u003c/span\u003e \u003c/span\u003e​ are the total active power losses before and after the installation of the DSTATCOM, respectively [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e].\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e \n$$\\:TACS={K}_{{P}_{loss}}\\left(T\\times\\:{P}_{loss}^{Before}\\right)-{K}_{{P}_{loss}}\\left(T\\times\\:{P}_{loss}^{After}\\right)-{AC}_{DSTATCOM}$$ \u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe total annual cost savings in the per-unit system can then be expressed through Eq.\u0026nbsp;(\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e), incorporating the specifics of the power losses and energy costs into a comprehensive financial analysis [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e].\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:{TACS}_{p.u}=\\frac{TACS}{{K}_{{P}_{loss}}\\left(T\\times\\:{P}_{loss}^{Before}\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThese equations provide a structured method for evaluating the financial benefits of DSTATCOM implementation, allowing for an accurate assessment of both the initial investment and the potential cost savings over time. This methodology is crucial for ensuring the economic feasibility and justification of deploying DSTATCOMs in power systems.\u003c/p\u003e \u003cp\u003e \u003cem\u003eB- PV Cost\u003c/em\u003e \u003c/p\u003e \u003cp\u003eThe total cost of PV (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{PV}_{Total\\_Cost}\\)\u003c/span\u003e\u003c/span\u003e) can be broken down into many costs, such as solar modules, solar inverters, structural balance of system (BOS), electrical balance of system (BOS), installation of labor and equipment, contractor overhead, sales tax, permitting, inspection and interconnection (PII), transmission line costs, developer overhead, contingency budget, and contractor and developer profit [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. Therefore, the total cost of the PV distributed generator is calculated via Eq.\u0026nbsp;(\u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e7\u003c/span\u003e).\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:{PV}_{Total\\_Cost}={C}_{PV/W}\\times\\:{PV}_{size}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003e \u003cem\u003ewhere\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{PV/W}\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003eis the total cost of PV per watt and\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{PV}_{size}\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003eis the size of the PV.\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Technical modeling of the system\u003c/h2\u003e \u003cp\u003eThe technical modeling sector can be divided into power balance, voltage limits, reactive power limitations of DSTATCOM, and real power limitations of RDG. The locations of the RDG and DSTATCOM are essential parameters in the power equations of the RDS.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003e1- Power balance\u003c/h3\u003e\n\u003cp\u003eThe power balance constraints are expressed as follows:\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\:{P\\:}_{Total\\_Loss}+\\:\\sum\\:{P}_{m}^{Demand}\\:+\\:\\sum\\:{P}_{m}^{EVCS}\\:=\\:\\sum\\:(\\:{P}_{m}^{DSTATCOM}\\:+\\:{P}_{m}^{RDGs})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe variables \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{P\\:}_{Total\\_Loss},\\:{P}_{m}^{Demand},\\:{{P}_{m}^{EVCS},\\:P}_{m}^{DSTATCOM}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{P}_{m}^{RDGs}\\)\u003c/span\u003e\u003c/span\u003e indicate the total power loss in the RDS, the total demand of the RDS, the total demand of the EVCSs, the power of the DSTATCOM, and the power injected by the RDGs, respectively.\u003c/p\u003e\n\u003ch3\u003e2- Voltage limit\u003c/h3\u003e\n\u003cp\u003eThe voltage limits at the m-th bus in the RDS are given by:\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{m}^{min}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:{V}_{m}^{max}\\)\u003c/span\u003e\u003c/span\u003e are the lower and upper limits of the bus voltage, respectively.\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{m}.\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003ch3\u003e3- Reactive power compensation\u003c/h3\u003e\n\u003cp\u003eThe limit of reactive power compensation DSTATCOM is denoted in Eq.\u0026nbsp;(\u003cspan refid=\"Equ10\" class=\"InternalRef\"\u003e10\u003c/span\u003e), where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Q}_{DSTATCOM\\left(m\\right)}^{min}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Q}_{DSTATCOM\\left(m\\right)}^{MAX}\\)\u003c/span\u003e\u003c/span\u003e are the lower and upper limits of the DSTATCOM reactive power, respectively.\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$$\\:{Q}_{DSTATCOM\\left(m\\right)}^{min}\\le\\:{Q}_{DSTATCOM\\left(m\\right)}\\le\\:\\:{Q}_{DSTATCOM\\left(m\\right)}^{MAX}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\n\u003ch3\u003e4- Real power compensation by RDG\u003c/h3\u003e\n\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eRDGs exhibit limits dictated by the RDS characteristics and the geographic region within each country. HF-RDGs vary across nations. For instance, in Egypt, the HF-RDG is established at 1.5% of the maximum demand load of the RDS. Conversely, in Portugal, the upper threshold for HF-RDG stands at 25%, while in South Africa, it is specified not to surpass 15% [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe RDG must ensure that the power injected at each optimized bus falls within the specified minimum and maximum limitations. The maximum RDG power of each zone is indicated in Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) specifies the specific quantity of real power adjustment that RDG \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{P}_{RDG\\left(zone\\right)}\\)\u003c/span\u003e\u003c/span\u003e provides for the system in each zone.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e\n\u003ch3\u003e5- Voltage Deviation Index (VDI)\u003c/h3\u003e\n\u003cp\u003eOne of the objectives is to minimize the voltage deviation index. Voltage deviation refers to the difference between the nominal voltage and the measured value. The closer the bus voltage is to the nominal voltage, the better the voltage condition of the system. The calculation of the VDI is displayed in Eq.\u0026nbsp;(\u003cspan refid=\"Equ11\" class=\"InternalRef\"\u003e11\u003c/span\u003e) [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e], where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{i}\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{Ni}\\)\u003c/span\u003e\u003c/span\u003eare the voltage and nominal voltage at the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{i}^{th}\\)\u003c/span\u003e\u003c/span\u003e node, respectively.\u003cdiv id=\"Equ11\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ11\" name=\"EquationSource\"\u003e\n$$\\:VDI=\\sum\\:_{i}^{Ni}\\left|{V}_{n}-{V}_{i}\\right|$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\n\u003ch3\u003e6- Voltage Stability Index (VSI)\u003c/h3\u003e\n\u003cp\u003eVarious criteria are applied to evaluate the safety level of power systems. This research offers a Voltage Stability Index (VSI) designed for steady-state settings aimed at detecting nodes with heightened sensitivity to voltage collapse. Derived from power flow analysis, the index, abbreviated as VSI and expressed by Eq.\u0026nbsp;(\u003cspan refid=\"Equ12\" class=\"InternalRef\"\u003e12\u003c/span\u003e) [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e], serves to determine the stability of the voltage at each node. For stable operation of an RDS, the VSI should be equal to or greater than zero (m\u0026thinsp;\u0026ge;\u0026thinsp;0). Nodes with lower VSI values imply a greater need for compensators to provide voltage stability.\u003cdiv id=\"Equ12\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ12\" name=\"EquationSource\"\u003e\n$$\\:VSI\\left(m+1\\right)={\\left|{V}_{m+1}\\right|}^{4}-4\\:{\\left[{P}_{m,m+1}\\:{X}_{m,m+1}-{Q}_{m,m+1}\\:{R}_{m,m+1}\\right]}^{2}-4\\left[{P}_{m,m+1}\\:{R}_{m,m+1}+{Q}_{m,m+1}\\:{X}_{m,m+1}\\right]\\:{\\left|{V}_{m,m+1}\\right|}^{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{m+1}\\:\\)\u003c/span\u003e \u003c/span\u003e denotes the voltage magnitude at the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{(m+1)}^{th}\\)\u003c/span\u003e\u003c/span\u003e bus, while \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{m,m+1},\\:\\:{R}_{m,m+1},{Q}_{m,m+1}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:{P}_{m,m+1}\\)\u003c/span\u003e\u003c/span\u003e refer to the resistance, reactance, reactive power flow, and real power flow, respectively, of the line connecting the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{m}^{th}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{(m+1)}^{th}\\)\u003c/span\u003e\u003c/span\u003e buses.\u003c/p\u003e\n\u003ch3\u003e7- The objective function\u003c/h3\u003e\n\u003cp\u003eThe aim of this study is to determine the optimal locations of EVCSs, DSTATCOMs, and RDGs. The optimal locations are the locations that achieve the minimum active power loss (P\u003csub\u003eloss\u003c/sub\u003e), reactive power loss (Q\u003csub\u003eloss\u003c/sub\u003e), voltage deviation index (VDI), installation cost of PVs or DSTATCOMs (C\u003csub\u003einstal\u003c/sub\u003e), and total annual savings (TAS) while improving the VSI. The following equation presents the weighted fitness function to determine the optimal solution. where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{1}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{2}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{3}\\)\u003c/span\u003e\u003c/span\u003e,\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:{w}_{4}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{5}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{6}\\)\u003c/span\u003e\u003c/span\u003e are the weight factors used to equilibrate the fitness function.\u003cdiv id=\"Equ13\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ13\" name=\"EquationSource\"\u003e\n$$\\:Fit\\:fun={w}_{1}\\:{P}_{loss}+{w}_{2}\\:{Q}_{loss}+{w}_{3}\\:\\text{V}\\text{D}-{w}_{4}\\:{VSI}_{min}+{w}_{5}\\:{C}_{install}+{w}_{6}\\:TAS$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e13\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"4. Hippopotamus optimization algorithm","content":"\u003cp\u003eThe Hippopotamus Optimization (HO) algorithm has been among the most frequently used and well-developed bioinspired metaheuristic optimization techniques used to solve complex optimization problems. This process is inspired by the social behavior and defense mechanisms of their herds. The HO algorithm consists of three phases:\u003c/p\u003e \u003cp\u003e \u003cb\u003ePhase 1: Hippopotamuses Position Update in the River or Pond (Exploration)\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThis phase aims at exploring the search space similarly to how hippos go about their environment, the water. Therefore, the movement and location of individual males (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{x}_{ij}}^{M\\:hippo}\\)\u003c/span\u003e\u003c/span\u003e), females, and the dominant hippo (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{D}^{hippo}\\)\u003c/span\u003e\u003c/span\u003e) control the exploration process. From Eq.\u0026nbsp;(\u003cspan refid=\"Equ14\" class=\"InternalRef\"\u003e14\u003c/span\u003e), the dominant hippo (representing the current best solution) moves other individuals in relation to its distance from it. This distance is, in turn, a function of not only the dominance of the hippo but also of a random vector (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{ij}\\)\u003c/span\u003e\u003c/span\u003e). (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\chi\\:}_{i}\\)\u003c/span\u003e\u003c/span\u003e), and (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{1}\\)\u003c/span\u003e\u003c/span\u003e) and an integer (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{I}_{1}\\)\u003c/span\u003e\u003c/span\u003e) representing inherent variability observed in exploration [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e].\u003cdiv id=\"Equ14\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ14\" name=\"EquationSource\"\u003e\n$$\\:{{\\chi\\:}}_{i}^{M\\:hippo}:{{x}_{ij}}^{M\\:hippo}={x}_{ij}+{y}_{1}\\cdot\\:\\left({D}^{hippo}-I1{x}_{ij}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e14\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIf a male or female hippopotamus's position results in a superior objective function value compared to the current dominant hippopotamus, the dominant's position is then replaced with that individual's position. This mechanism ensures that the exploration process continuously seeks better solutions.\u003c/p\u003e \u003cp\u003e \u003cb\u003ePhase 2: The defense action of Hippopotamus against predators (exploration)\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe defense mode comes into play when something to defend against (e.g., crocodiles of the Nile) is detected by the herd. Immediate defense from the predator is undertaken, accompanied by loud vocalization. Eq.\u0026nbsp;(\u003cspan refid=\"Equ15\" class=\"InternalRef\"\u003e15\u003c/span\u003e) can be used to model the rapid turn toward the threat. where the random movement of predators (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\mathcal{P}\\text{\\:redator}}_{j}\\)\u003c/span\u003e\u003c/span\u003e) is denoted by a random vector (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\overrightarrow{r}}_{8}\\)\u003c/span\u003e\u003c/span\u003e) ranging from zero to one within the upper (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{ub}_{j}\\)\u003c/span\u003e\u003c/span\u003e) and lower (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{ll}_{j}\\)\u003c/span\u003e\u003c/span\u003e) limits of the decision variables at (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{j}^{th}\\)\u003c/span\u003e\u003c/span\u003e). Additionally, Eq.\u0026nbsp;(\u003cspan refid=\"Equ16\" class=\"InternalRef\"\u003e16\u003c/span\u003e) models the change in distance between predator and hippo after the defense response [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e].\u003cdiv id=\"Equ15\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ15\" name=\"EquationSource\"\u003e\n$$\\:\\text{Predator\\::\\:}{\\mathcal{P}\\text{\\:redator}}_{j}\\text{\\:}={ll}_{j}+{\\overrightarrow{r}}_{8}\\cdot\\:\\left({ub}_{j}-{ll}_{j}\\right),\\:j=\\text{1,2},\\dots\\:,m$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e15\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ16\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ16\" name=\"EquationSource\"\u003e\n$$\\:\\overrightarrow{\\mathcal{D}}=\\left|{\\mathcal{P}\\text{\\:redator}}_{j}\\text{\\:}-{x}_{i\\varvec{j}}\\right|$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e16\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cb\u003ePhase 3: Hippopotamus Escaping from the Predator (Exploitation)\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe hippos may escape overwhelming predator attacks or situations in which they cannot mount a sufficient defense to more protected areas. Mathematically, these stochastic refugia are modeled to simulate the unpredictability of escape routes. Since a new location provides a better objective function value (indicating a better solution), this would characterize how a hippo escapes, symbolizing a successful escape.\u003c/p\u003e \u003cp\u003eThe HO algorithm is a sophisticated method that considers the complexities of optimization problems and devises an efficient search strategy by mimicking the behavior of hippos. Throughout successive iterative phases simulating herd dynamics and defensive mechanisms, the algorithm proves to be robust and efficient for most optimization problems. The following is the pseudocode and flowchart describing the HO algorithm in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eStart\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDefine the optimization problem at hand.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEstablish the maximum number of iterations (denoted as \"it\") and determine the quantity of hippopotamuses (referred to as \"N\").\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGenerate the initial population of hippopotamuses and evaluate the objective function for this initial set.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFor i\u0026thinsp;=\u0026thinsp;1: it\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUpdate the position of the dominant hippopotamus on the criterion of objective function value criterion\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePhase 1: Updating the hippopotamus's position in the river or pond\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFor i\u0026thinsp;=\u0026thinsp;1 : N/2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCalculate new position for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{i}^{th}\\)\u003c/span\u003e\u003c/span\u003e hippopotamus\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUpdate position for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{i}^{th}\\)\u003c/span\u003e\u003c/span\u003e hippopotamus\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEnd for\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePhase 2: Hippopotamus defense against predators\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFor i\u0026thinsp;=\u0026thinsp;1\u0026thinsp;+\u0026thinsp;N/2:N\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGenerate random position for predator\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCalculate new position for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{i}^{th}\\)\u003c/span\u003e\u003c/span\u003e hippopotamus\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUpdate position for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{i}^{th}\\)\u003c/span\u003e\u003c/span\u003e hippopotamus\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEnd for\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePhase 3: Hippopotamus escaping from the predator\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCalculate new bounds of variables decision\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFor i\u0026thinsp;=\u0026thinsp;1:N\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCalculate the new position for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{i}^{th}\\)\u003c/span\u003e\u003c/span\u003e hippopotamus\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUpdate position for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{i}^{th}\\)\u003c/span\u003e\u003c/span\u003e hippopotamus\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEnd for\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSave the best candidate solution found thus far.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEnd for\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOutput the best solution of the objective function\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eEND\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"5. Results and Discussion","content":"\u003cp\u003eThis study investigates the impact of increasing electric vehicle (EV) adoption and renewable energy sources on the performance of a local power grid, specifically a Radial Distribution Network (RDN). The Renewable Distributed Generation Hosting Factor (RDG-HF) and the EV Hosting Factor (EV-HF) are used to represent these variables.\u003c/p\u003e \u003cp\u003eThe analysis is conducted using the IEEE 69-bus system, which represents a scenario with 3.80 MW of active power and 2.69 MVAR of reactive power, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea. Five distinct scenarios are explored to understand the effects of varying EV-HF and RDG-HF values, simulating the integration of the latest EV and renewable energy technologies into the RDN.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe RDN is divided into four zones, each with a specific number of buses. The EV-HF in each zone is a ratio of the total demand within that zone, as detailed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and Fig.\u0026nbsp;3.\u003c/p\u003e \u003cp\u003e \u003cem\u003eFigure 3: The clustering of the RDN.\u003c/em\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe number of buses included in each zone and the sizes of EVCSs in each zone at different EV-HFs.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eBuses at each zone\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTotal demand load\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c7\" namest=\"c4\"\u003e \u003cp\u003eEVCS demand load due to EV-HF\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e40%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e50%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e60%\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZone 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2-3-4-5-6-7-8-9-10-11-12-51-52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e510.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e153.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e204.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e255.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e306.06\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZone 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e28-29-30-31-32-33-34-35-53-54-55-56-57-58-59-60-61-62-63-64-65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1808.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e542.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e723.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e904.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1084.95\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZone 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e36-37-38-39-40-41-42-43-44-45-46-47-48-49-50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1034\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e310.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e413.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e517.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e620.42\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZone 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e13-14-15-16-17-18-19-20-21-23-24-25-26-27-66-67-68-69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e393.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e118.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e157.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e196.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e236.28\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eScenario 1: Integrating EVCSs with the RDN\u003c/b\u003e \u003c/p\u003e \u003cp\u003eIn this scenario, the optimal placement of Electric Vehicle Charging Stations (EVCSs) in each zone is determined using the HO algorithm. The EV-HF values considered are 0.3, 0.4, 0.5, and 0.6. The size of each EVCS is calculated based on the EV-HF and the total demand load of each zone, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The optimal locations for the EVCSs are at buses 2, 28, 36, and 66, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs EV-HF increases, both the total active and reactive power increase, while the VSI, voltage deviation, and minimum voltage decrease compared to those in the base case, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. The voltage profile and power losses across buses for different EV-HF values are illustrated in Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cb\u003eScenario 2: Integration of EVCS and DSTATCOM\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe HO algorithm is utilized to ascertain the optimal sizing and placement of DSTATCOMs in various zones, as well as the ideal locations for EVCSs. The integration of DSTATCOMs is intended to counteract the negative impacts of elevated EV-HF on power loss and voltage stability. The findings reveal significant reductions in active power losses (between 27% and 30%) and reactive power losses of 28% in comparison to the baseline scenario. Relative to the initial scenario, the reductions are approximately 31% for both active and reactive power losses. Additionally, there is a decrease in the voltage deviation index, while improvements are observed in the minimum voltage levels and the Voltage Stability Index (VSI) at all EV-HF levels. These effects are detailed in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, which highlights the impact of DSTATCOMs on these metrics. Figures\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e illustrate the voltage and power loss profiles of scenario 2, providing a comparison with the baseline case.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe impact of EV-HF on the objectives in scenario 2.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBase\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e \u003cp\u003eScenario 2\u003c/p\u003e \u003cp\u003eEVCSs \u0026amp; DSTATCOMs\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEV-HF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e30%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e40%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e50%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e60%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{P}_{loss}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e225\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e155.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e156.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e158.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e162.97\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Q}_{loss}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e102.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e72.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e72.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e73.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e75.63\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{VSI}_{min}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.6868\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.7449\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.7451\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7443\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.7389\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVDI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0993\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0594\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0593\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0609\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.0652\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{min}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9092\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9279\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9280\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9277\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9260\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e outlines the results obtained through the HO algorithm, which identifies the optimal sizes and placements of DSTATCOMs across different zones. The sizes and locations of the DSTATCOMs vary due to the differing HFs in each zone. The average installation cost of DSTATCOMs across various EV-HF levels is estimated at \u003cspan\u003e$\u003c/span\u003e94,000, with annual savings fluctuating based on the EV-HF, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDSTATCOMs\u0026rsquo; specifications in Scenario 2.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003ezone\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e \u003cp\u003eScenario 2 (EVCSs \u0026amp; DSTATCOM)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e \u003cp\u003eEV-HF\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eDSTATCOM Size (KVAR)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ezone 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e303\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e549\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e433\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ezone 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ezone 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ezone 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e597\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e428\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e541\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e550\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eDSTATCOM\u003c/p\u003e \u003cp\u003eLocation (Bus)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ezone 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ezone 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e61\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ezone 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ezone 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eTotal DSTATCOMs cost (\u003cspan\u003e$\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e95050\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e99200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e100450\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e80750\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eAnnual Savings Costs (\u003cspan\u003e$\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e36560.6121\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e35983.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e34973.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e32600.68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eScenario 3: The Integration of EVCSs and RDGs\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThis scenario maintains the same EVCS size and location as in Scenario 1. The HO algorithm is used to determine the optimal locations and sizes of Renewable Distributed Generators (RDGs) in the IEEE 69-bus RDN, considering the RDG-HF restricted limitations (not exceeding 25%) [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe optimal locations for RDGs in zone two are determined to be at bus number 64. The recommended sizes for this location are 349 kW, 369 kW, 380 kW, and 392 kW for EV-HF levels of 0.3, 0.4, 0.5, and 0.6, respectively, with no additional RDGs needed in other zones, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e. This integration reduces active and reactive power losses by approximately 29% for all EV-HF values compared to the base case, resulting in an enhanced voltage profile, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The voltage deviation index is reduced to approximately 0.075 in all cases, while the VSI and minimum voltage improve to approximately 0.74 and 0.928, respectively, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e. The PV calculation parameters are based on the location of Cairo, Egypt, which is situated at 30.033\u0026deg; latitude and 31.562\u0026deg; longitude.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eScenario 4: The Integration of EVCSs, DSTATCOMs, and RDGs\u003c/b\u003e \u003c/p\u003e \u003cp\u003eBy optimizing the locations of the EVCSs, DSTATCOMs, and RDGs, this scenario achieves the best performance outcomes. The active and reactive power losses decreased by approximately 30.4% and 27%, respectively, across all EV-HF values compared to those of the base case, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. The voltage deviation index decreases to approximately 0.073 for different EV-HF scenarios, while the VSI and minimum voltage increase to 0.7724 and 0.93, respectively. The best voltage and power loss profiles across all scenarios are achieved in this scenario, as illustrated in Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe optimal placement for the DSTATCOM and RDG was determined to be at bus 64. The sizing for the DSTATCOM is specified as 264 kVAR, 272 kVAR, 273 kVAR, and 278 kVAR for EV-HF values of 0.3, 0.4, 0.5, and 0.6, respectively. Correspondingly, the size of the RDG is equal to that of the DSTATCOM but measured in kW.\u003c/p\u003e \u003cp\u003eIn summary, the integration of EVCSs, DSTATCOMs, and RDGs significantly enhances the performance of the RDN by reducing power losses and improving voltage stability. These results underscore the importance of the optimal placement and sizing of these components in addressing the challenges posed by increasing EV and renewable energy integration in distribution networks.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe impact of EV-HF on the objectives in various scenarios.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eScenario\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBase\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eP\u003c/b\u003e\u003csub\u003e\u003cb\u003eloss\u003c/b\u003e\u003c/sub\u003e \u003cb\u003e(kW)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e225\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e230.88\u0026ndash;237.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e155.45\u0026ndash;162.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e159.85\u0026ndash;159.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e154.11\u0026ndash;156.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eQ\u003c/b\u003e\u003csub\u003e\u003cb\u003eloss\u003c/b\u003e\u003c/sub\u003e \u003cb\u003e(kVAR)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e102.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e105.14\u0026ndash;108.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e72.18\u0026ndash;75.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e74.84\u0026ndash;75.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e72.37\u0026ndash;73.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eVSI\u003c/b\u003e\u003csub\u003e\u003cb\u003emin\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.6868\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.6845\u0026thinsp;\u0026minus;\u0026thinsp;0.6821\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.745\u0026thinsp;\u0026minus;\u0026thinsp;0.739\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7363\u0026ndash;0.7445\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.742\u0026ndash;0.7421\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eVDI\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0993\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.1034\u0026ndash;0.1076\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0594\u0026ndash;0.0653\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0723\u0026ndash;0.0754\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.0738\u0026ndash;0.0761\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eV\u003c/b\u003e\u003csub\u003e\u003cb\u003emin\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9092\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9085\u0026thinsp;\u0026minus;\u0026thinsp;0.9077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.928\u0026thinsp;\u0026minus;\u0026thinsp;0.9261\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9296\u0026thinsp;\u0026minus;\u0026thinsp;0.9286\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9289\u0026thinsp;\u0026minus;\u0026thinsp;0.9287\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eCosts ($)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan\u003e$\u003c/span\u003e80,750 - \u003cspan\u003e$\u003c/span\u003e100,450\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan\u003e$\u003c/span\u003e365,310 - \u003cspan\u003e$\u003c/span\u003e388,080\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan\u003e$\u003c/span\u003e275,880 - \u003cspan\u003e$\u003c/span\u003e290,510\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eAnnual saving Costs ($)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan\u003e$\u003c/span\u003e32,600.7 - \u003cspan\u003e$\u003c/span\u003e36,560.6121\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan\u003e$\u003c/span\u003e44915.1 - \u003cspan\u003e$\u003c/span\u003e39988.2204\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan\u003e$\u003c/span\u003e52,568-\u003c/p\u003e \u003cp\u003e\u003cspan\u003e$\u003c/span\u003e53,495\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePayback Period (Years)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.7\u0026ndash;3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.7\u0026ndash;9.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e9.8\u0026ndash;10.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eTotal Profit ($)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan\u003e$\u003c/span\u003e714,267.5 - \u003cspan\u003e$\u003c/span\u003e816,515\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan\u003e$\u003c/span\u003e747,877.5 - \u003cspan\u003e$\u003c/span\u003e999,705\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan\u003e$\u003c/span\u003e1,039,320 - \u003cspan\u003e$\u003c/span\u003e1,052,365\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFrom a technical perspective, integrating EVCSs alone in Scenario 1 resulted in an increase in power loss from 225 kW to between 230.88 kW and 237.28 kW (2.6\u0026ndash;5.4%) and an increase in reactive power loss from 102.2 kVAR to between 105.14 kVAR and 108.39 kVAR (2.9\u0026ndash;6%). However, Scenario 2, which combines EVCSs with DSTATCOM, significantly reduces these losses, with the power loss decreasing to between 155.45 kW and 162.98 kW (31\u0026ndash;27.6%) and the reactive power loss decreasing to between 72.18 kVAR and 75.63 kVAR (29.4\u0026ndash;26%).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003ePV integration alone in Scenario 3 maintains a stable reduction in power loss of approximately 159.85 kW to 159.89 kW (29%) and a decrease in reactive power loss of approximately 74.84 kVAR to 75.25 kVAR (26.8\u0026ndash;26.1%). The combined integration of EVCSs, PVs, and DSTATCOMs in Scenario 4 shows the most significant improvements, with the power loss reduced to between 154.11 kW and 156.5 kW (31.5\u0026ndash;30.5%) and the reactive power loss reduced to between 72.37 kVAR and 73.85 kVAR (29.2\u0026ndash;27.8%).\u003c/p\u003e \u003cp\u003eThe voltage stability also improved across the scenarios. VSI\u003csub\u003emin\u003c/sub\u003e increases from 0.6868 to between 0.745 and 0.739 (8.5\u0026ndash;7.6%) in Scenario 2. V\u003csub\u003emin\u003c/sub\u003e increases from 0.9092 p.u. to between 0.928 p.u. and 0.9261 p.u. (2.1\u0026ndash;1.9%) in Scenario 2, indicating enhanced voltage stability. Furthermore, the VDI improved from 0.0993 to between 0.0594 and 0.0653 (40.2\u0026ndash;34.2%) in Scenario 2.\u003c/p\u003e \u003cp\u003eEconomically, Scenario 2, which integrates EVCS and DSTATCOM, presents significant benefits, with total DSTATCOM costs ranging from \u003cspan\u003e$\u003c/span\u003e80,750 to \u003cspan\u003e$\u003c/span\u003e100,450 and annual savings between \u003cspan\u003e$\u003c/span\u003e32,600.7 and \u003cspan\u003e$\u003c/span\u003e36,560.6, resulting in a payback period of 2.7 to 3 years. Scenario 3, which focuses on PV integration, has installation costs ranging from \u003cspan\u003e$\u003c/span\u003e365,310 to \u003cspan\u003e$\u003c/span\u003e388,080, with a payback period of 8.7 to 9.4 years and a total profit over 25 years ranging from \u003cspan\u003e$\u003c/span\u003e747,877.5 to \u003cspan\u003e$\u003c/span\u003e999,705. Scenario 4, which combines EVCS, PV, and DSTATCOM, has total costs ranging from \u003cspan\u003e$\u003c/span\u003e275,880 to \u003cspan\u003e$\u003c/span\u003e290,510, with annual savings of \u003cspan\u003e$\u003c/span\u003e52,568 to \u003cspan\u003e$\u003c/span\u003e53,495, a payback period of 9.8 to 10.4 years, and a total profit over 25 years ranging from \u003cspan\u003e$\u003c/span\u003e1,039,320 to \u003cspan\u003e$\u003c/span\u003e1,052,365.\u003c/p\u003e"},{"header":"6. Conclusion","content":"\u003cp\u003eThe integration of EVCSs, PV systems, and DSTATCOMs significantly enhances power grid performance by reducing power and reactive power losses and improving voltage stability. The combined scenario (EVCS, PV, and DSTATCOM) demonstrated the most substantial improvements, with reductions in power loss of 31.5% and reactive power loss of 29.2%, alongside significant economic benefits, including a total profit of up to \u003cspan\u003e$\u003c/span\u003e1,052,365 over 25 years and a payback period of 9.8 to 10.4 years. The strategic deployment and optimization of these components using the Hippopotamus Optimization algorithm (HO) is essential for achieving an efficient, stable, and cost-effective power distribution network. The findings underscore the importance of optimizing the integration of EVCSs, PVs, and DSTATCOMs to maximize both technical performance and economic benefits.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting interests:\u003c/h2\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding:\u003c/h2\u003e \u003cp\u003eOpen access funding was provided by The Science, Technology \u0026amp; Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAll the authors share this paper\u0026rsquo;s activities equally\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eData availability: The datasets generated during the current study are available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eH. 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Khodadadi, \u0026ldquo;Hippopotamus optimization algorithm: a novel nature-inspired optimization algorithm,\u0026rdquo; Sci Rep, vol. 14, no. 1, Dec. 2024, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1038/s41598-024-54910-3\u003c/span\u003e\u003cspan address=\"10.1038/s41598-024-54910-3\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Electric Vehicles Charging Stations, Photovoltaic Integration, DSTATCOM, Voltage Stability, Power Losses, Economic analysis","lastPublishedDoi":"10.21203/rs.3.rs-4752135/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4752135/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study explores the intricate relationships among renewable energy integration, electric vehicle (EV) adoption, and their effects on power grid performance. The need for optimized integration of EV charging stations (EVCSs), Distribution Static Compensators (DSTATCOMs), and photovoltaic (PV) systems to enhance network efficiency and stability is addressed. Using the IEEE 69-bus system, this study evaluates four scenarios, each incorporating different combinations of EVCSs, PVs, and DSTATCOMs. Introducing the Renewable Distributed Generation Hosting Factor (RDG-HF) and Electric Vehicle Hosting Factor (EV-HF) as pivotal metrics, this research aims to optimize the placement and sizing of these components using the Hippopotamus Optimization Algorithm (HO). The integration of EVCSs, PVs, and DSTATCOMs significantly reduced the power loss (up to 31.5%) and reactive power loss (up to 29.2%), highlighting the technical benefits of optimized integration. Economically, the scenarios demonstrate varying payback periods (2.7 to 10.4 years) and substantial long-term profits (up to \u003cspan\u003e$\u003c/span\u003e1,052,365 over 25 years), emphasizing the importance of strategic integration for maximizing economic benefits alongside technical performance improvements.\u003c/p\u003e","manuscriptTitle":"Optimizing Energy-Efficient Grid Performance: Integrating Electric Vehicles, DSTATCOM, and Renewable Sources using the Hippopotamus Optimization Algorithm","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-08-12 09:59:37","doi":"10.21203/rs.3.rs-4752135/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-09-23T11:36:55+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-09-17T09:17:38+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-09-12T03:31:43+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-09-07T15:06:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"8518063886654669237035558009166907556","date":"2024-09-06T09:34:18+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"101700853886994560923686837160498969444","date":"2024-09-06T04:55:33+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"35235746375484621026677985162779517401","date":"2024-09-05T23:46:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"100202214275065026950913821565135352968","date":"2024-09-05T20:07:03+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"62519687766253243958215980464346906092","date":"2024-09-05T18:46:23+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"68810184552333857704903073609921949709","date":"2024-09-05T17:43:05+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-09-05T16:37:08+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-09-05T02:16:44+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-07-23T13:06:35+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-07-18T03:27:32+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-07-16T19:42:18+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"222d8d62-1d4d-4063-9a1f-e66adc64435e","owner":[],"postedDate":"August 12th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":35859126,"name":"Physical sciences/Engineering/Energy infrastructure/Energy grids and networks"},{"id":35859127,"name":"Physical sciences/Engineering/Energy infrastructure/Power distribution"}],"tags":[],"updatedAt":"2024-11-25T16:06:48+00:00","versionOfRecord":{"articleIdentity":"rs-4752135","link":"https://doi.org/10.1038/s41598-024-79381-4","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2024-11-22 15:57:39","publishedOnDateReadable":"November 22nd, 2024"},"versionCreatedAt":"2024-08-12 09:59:37","video":"","vorDoi":"10.1038/s41598-024-79381-4","vorDoiUrl":"https://doi.org/10.1038/s41598-024-79381-4","workflowStages":[]},"version":"v1","identity":"rs-4752135","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4752135","identity":"rs-4752135","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}