# Optimal Design of Grid-Connected Hybrid Renewable Energy System Considering Electric Vehicle Station Using Improved Multi-Objective Optimization: Techno-Economic Perspectives

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## Abstract

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## 1. Introduction

_{2}emissions in the context of home microgrids. However, to increase reliability, optimize renewable energy sources, and lower overall costs, appropriate energy management and operation are necessary, along with an appropriate optimization technique based on techno-economic viewpoints.

_{2}emissions and operational costs. The framework considers renewable generation, load usage, and the charging/discharging time of PEVs as ambiguous variables. The work in [5] offered hybrid renewable energy systems combined with mobile hydrogen vehicle storage and stationary batteries for a zero-energy community comprising office, residential, and academic buildings based on real-world energy consumption data and simulations. A time-of-use grid penalty cost model was presented to achieve electricity grid economy and flexibility, which evaluates grid export and import during on-peak and off-peak times. In the coupled platform of TRNSYS and jEplus + EA, multi-objective optimizations are carried out to size zero-energy buildings and the community while considering the self-consumption of renewable energy, on-site load coverage, and grid penalty cost. Methods for incorporating hydrogen energy technology into hybrid energy systems, focusing on hydrogen fuel cell power generation, were examined in [6]. Energy storage integration, sizing techniques, energy flow control, and the software implementation and optimization methods that go along with them were covered. Published case studies seldom address issues beyond technical ones. The authors talked about this fact in the context of accessible software packages. To meet the design objectives for the energy system, a four-dimensional multi-objective metaheuristic function was suggested, with weights assigned to environmental, economic, socio-political, and technical aspects.

_{2}emissions, as indices. As a case study, the authors used an imagined average Japanese detached house to assess the environmental and economic effects of solar electricity self-consumption utilizing SB or V2H. The findings indicated that, by 2030, non-commuting EV owners should consider investing in V2H if the cost of a bidirectional charger is one-third that of an affordable SB. In [16], for regional integrated energy systems (RIESs), a multi-objective optimization that takes electric cars (EVs) and renewable energy uncertainty into account was suggested. The RIES can balance the system’s environmental friendliness and economy. First, an orderly model for charging and discharging EVs with the following driving rules is built. It considers the impact of elements like disorderly access and EV charging/discharging on system functioning. Then, to address the uncertainty of renewable energy generation, a robust optimization model with a polyhedral uncertainty set was built. Additionally, a multi-objective function is constructed to minimize both operation costs and carbon emissions. A carbon emission penalty component is implemented to reduce the multi-objective solution to a single-objective solution. Ultimately, an actual RISE performs the validation.

## 2. Mathematical Modeling of the Grid-Connected PV/WT/Battery System Combined with EVCS Using Vehicle-to-Grid (V2G) Technique

#### 2.1. Photovoltaic Panel Mathematical Modeling

_{t}is the temperature coefficient ($-$3.7 × ${10}^{-3}$) 1/C, ${T}_{{C}_{STC}}$ is the cell temperature (in °C) under standard test condition (STC), and ${T}_{amb}$ is the ambient temperature (in °C), respectively. ${G}_{\left(t\right)}$ refers to solar irradiance (in W/${\mathrm{m}}^{2}$), 1000 W/${\mathrm{m}}^{2}$ is the reference irradiance, and ${P}_{p{v}_{out}}\left(t\right)$ is the PV output power (in watts). Equation (2) can be used to obtain the ${T}_{C\left(STC\right)}$ [40]. NOCT is the nominal operating cell temperature in °C that the manufacturer can model.

#### 2.2. Wind Turbine Mathematical Modeling

#### 2.3. Battery Mathematical Modeling

#### 2.4. Converter Mathematical Modeling

#### 2.5. The Grid Mathematical Modeling

#### 2.6. Mathematical Modeling of Electric Vehicle Charging Station

## 3. Date Collection and Renewability–Economic–Technical Assessments

#### 3.1. The Study Site and Load Profile

#### 3.1.1. Al-Najaf Governorate in Iraq

#### 3.1.2. Load Profile

#### 3.2. Objective Function Formulation

#### 3.2.1. Levelized Cost of Electricity (LCOE)

#### 3.2.2. Grid Contribution Factor (GCF)

#### 3.2.3. Energy Sold to the Grid (${\mathrm{E}}_{\mathrm{S}\mathrm{O}\mathrm{L}\mathrm{D}})$

## 4. The Proposed Methodology for Sizing of the Grid-Connected PV/WT/Battery/EVCS System

#### 4.1. Energy Management Strategy and Its Scenarios in the Proposed System

- Operating Mode 1: Renewable energy sources (photovoltaic and wind power) supply power for running the system and charging the battery and the electric vehicle.
- Operating Mode 2: The battery supplies power for load and electric vehicle charging if there is no grid and insufficient RESs.
- Operating Mode 3: The main grid supplying power for electric vehicle charging (Buying–Charging–G2V) when batteries and RESs are not available and grid demand is required. The power flow will be unidirectional.
- Operating Mode 4: The electric vehicle supplying power for the grid (V2G–Sell–Discharging) when grid demand is high and batteries and RESs are unavailable. The flow of power will be bidirectional. The proposed operation modes of RB-EMS for the proposed system are listed in Table 2.

#### 4.2. Arithmetic Optimization Algorithm (AOA)

#### 4.2.1. Inspiration

#### 4.2.2. Initialization Phase

#### 4.2.3. Exploration Phase

#### 4.2.4. Exploitation Phase

#### 4.3. The Proposed Improved Arithmetic Optimization Algorithm (IAOA)

- FDB Strategy

- Chaotic map tactic

- Handling upper and lower boundaries

#### 4.4. The Proposed MOIAOA Method

## 5. Results and Discussion

#### 5.1. Performance Comparison between the Proposed IAOA and AOA, PSO, ALO

#### 5.2. Results of the MIAOA

## 6. Conclusions and Future Direction

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

${\mathrm{E}}_{\mathrm{S}\mathrm{O}\mathrm{L}\mathrm{D}}$ | The annual energy sold to the grid |

WT | Wind turbine |

EV | Electric Vehicle |

EVCS | electric vehicle charging station |

NS | Non-Scale |

PSO | Particle swarm optimization |

ALO | Ant Lion Optimizer |

EMS | Energy Management Strategy |

AOA | Arithmetic optimization algorithm |

HRES | Hybrid renewable energy system |

MOO | Multi-objective optimization |

STC | Standard Test Condition |

${\mathrm{P}}_{{\mathrm{p}\mathrm{v}}_{\mathrm{o}\mathrm{u}\mathrm{t}}}\left(\mathrm{t}\right)$ | The output power generated from PV |

${\mathrm{G}}_{\left(\mathrm{t}\right)}$ | Solar irradiance |

${\mathrm{P}}_{{(\mathrm{P}\mathrm{V}}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}})}$ | Rated power for PV |

NOCT | The nominal operating cell temperature |

${\mathrm{v}}_{\mathrm{c}\mathrm{u}\mathrm{t}-\mathrm{i}\mathrm{n}}$ | cut-in speed of the WT |

${\mathrm{v}}_{\mathrm{c}\mathrm{u}\mathrm{t}-\mathrm{o}\mathrm{u}\mathrm{t}}$ | cut-out speed of the WT |

${\mathrm{P}}_{\mathrm{r}}$ | Rated power of the WT |

${\mathrm{v}}_{\mathrm{r}}$ | Rated wind speed of the WT |

${\mathrm{P}}_{\mathrm{W}\mathrm{T}}$ | The generated output power of the WT |

BSS | Battery Storage System |

DOD | The depth of discharge |

${\mathrm{S}}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}}$ | The station rated capacity |

$\mathrm{cos}\mathrm{\varnothing}$ | The power factor |

${\mathrm{N}}_{\mathrm{s}\mathrm{l}\mathrm{o}\mathrm{t}}$ | The amount of charging slots for each EV |

${\mathrm{k}}_{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}$ | The overload factor for cover overloading in transients |

${\mathrm{P}}_{\mathrm{E}\mathrm{V}}$ | The maximum power rate of each EV |

${\mathrm{P}}_{\mathrm{i}\mathrm{n}\mathrm{v}}\left(\mathrm{t}\right)$ | The inverter rating |

${\mathrm{P}}_{\mathrm{L}}^{\mathrm{m}}\left(\mathrm{t}\right)$ | The peak load demand |

BT | Battery |

X | a collection of initialized solutions |

Rand | a random variable in the range [0, 1] |

${X}_{UB}$ and ${X}_{LB}$ | the upper and lower limits of the problem |

MOA (${\mathrm{C}}_{\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}})$ | the value at the t th iteration |

${\mathrm{M}}_{\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}}$ | the maximum number of iterations |

${\mathrm{r}}_{2}$ | randomly generated number that is conditioned between the D and M operations |

${\mathrm{U}\mathrm{B}}_{\mathrm{j}}$ and ${\mathrm{L}\mathrm{B}}_{\mathrm{j}}$ | the upper and lower limits |

ε$\epsilon $ | a tiny integer value |

${\mathrm{r}}_{3}$ | a randomly generated number that serves as a denotation for the A and S operators |

FF | Fitness Function |

PV | photovoltaic |

RESs | Renewable energy sources |

LCOE | Levelized Cost of Energy |

V2G | Vehicle-to-grid |

STC | Standard Test Conditions |

RB-EMS | Rule-Based Energy Management Strategy |

GCF | Grid Contribution Factor |

REF | Renewable Energy Fraction |

NPC | Economic criterion of net present cost |

IAOA | Improved arithmetic optimization algorithm |

MOIAOA | Multi-objective improved arithmetic optimization algorithm |

${\mathsf{\alpha}}_{\mathrm{t}}$ | Temperature coefficient |

${\mathrm{T}}_{{\mathrm{C}}_{\mathrm{S}\mathrm{T}\mathrm{C}}}$ | The cell temperature as reference temperature |

${\mathrm{T}}_{\mathrm{a}\mathrm{m}\mathrm{b}}$ | The ambient temperature |

${\mathrm{C}}_{\mathrm{B}}$ | Capacity of the battery |

${\mathrm{E}}_{\mathrm{L}}$ | The daily average load demand |

AD | the autonomy days |

v1, v2 | The wind speed |

h | hub height |

${\mathrm{h}}_{\mathrm{r}\mathrm{e}\mathrm{f}}$ | The reference height anemometer |

$\alpha $ | The power-law exponential known as wind gradient, Hellmann exponent, or friction coefficient |

SOC | State of Charge |

${\mathrm{P}}_{\mathrm{b}}\left(\mathrm{t}\right)$ | The battery’s output of electricity |

${\mathrm{P}}_{\mathrm{p}\mathrm{v}}\left(\mathrm{t}\right)$ | The total power generated by PV |

${\mathrm{P}}_{\mathrm{W}\mathrm{T}}\left(\mathrm{t}\right)$ | The total power generated by WT |

${\mathrm{P}}_{\mathrm{l}}\left(\mathrm{t}\right)$ | The total energy demand |

${\mathsf{\eta}}_{\mathrm{i}\mathrm{n}\mathrm{v}}$ | The inverter efficiency |

$\mathsf{\sigma}$ | The self-discharge rate of the battery |

${\mathsf{\eta}}_{\mathrm{b}}$ | Battery efficiency |

${\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}}_{\mathrm{f}\mathrm{e}\mathrm{e}\mathrm{d}-\mathrm{i}\mathrm{n}}$ | The feed-in tariff rate |

${\mathrm{E}}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}\left(\mathrm{s}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g}\right)}$ | The cost of selling energy |

${\mathrm{C}}_{\mathrm{p}}$ | The cost of buying electricity from the grid |

${\sum}_{t=1}^{8760}}{\mathrm{E}}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}\left(\mathrm{p}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{e}\mathrm{d}\right)$ | The per hour summation of annually buying electricity from the grid for one year |

MOA | Math Optimizer Accelerated |

${\mathrm{C}}_{\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}}$ | the current iteration |

Max & Min | The accelerated function’s maximum and lowest values are denoted by Max and Min (Maximum and minimum values of the MOA function) |

$\mu $ | a control variable set |

MOP | Math Optimizer Probability |

$\propto $ | a sensitive control parameter set |

FDB | Fitness–distance balance |

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**Figure 14.**Parameter space and convergence curve of the IAOA, ALO, AOA, and PSO on the first test function.

**Figure 15.**Parameter space and convergence curve of the IAOA, ALO, AOA, and PSO on the second test function.

**Figure 16.**Parameter space and convergence curve of the IAOA, ALO, AOA, and PSO on the third test function.

**Figure 17.**Parameter space and convergence curve of the IAOA, ALO, AOA, and PSO on the fourth test function.

**Figure 18.**Development of the aggregation function based on the NS multiple-run Pareto Front method.

**Figure 19.**Evaluation of fitness function based on optimal solutions using MOIAOA based on Non-Scale multiple-run Pareto Front concept.

**Figure 20.**Evaluation of ${\mathrm{E}}_{\mathrm{S}\mathrm{O}\mathrm{L}\mathrm{D}}$ (kWh), GCF (kWh), and LCOE (USD) values with different weight sets using MOIAOA based on Non-Scale Pareto Front concept.

Components | Parameter | Value | Unit |
---|---|---|---|

Wind Turbine (WT) | Rated Power of Wind Turbine $({\mathrm{P}}_{\mathrm{r}}$) | 1 | kW |

Cut-in speed (Vcin) | 3 | m/s | |

Cut-out speed (Vco) | 20 | m/s | |

Rated wind speed (Vrat) | 11 | m/s | |

Capital cost (per kW) | 2300 | USD | |

Replacement cost (per kW) | 1500 | USD | |

O & M cost (per kW) [operation + maintenance] | 2 | USD/vr | |

Hub height | 50 | M | |

Overall efficiency | 26 | % | |

Lifetime | 20 | years | |

Solar (PV) | Rated power (Ps r) | 325 | W |

Derating factor (f loss) | 88 | % | |

Capital cost (per kW) | 1200 | USD | |

Replacement cost (per kW) | 1200 | USD | |

O & M cost (per kW) | 4 | USD/yr | |

Lifetime | 20 | years | |

Battery | kVAh or kWh capacity | 6 | kWh |

Minimum state of charge (SOCmin) | 30 | % | |

Maximum state of charge (SOCmax) | 100 | % | |

Round trip efficiency (gbatt) | 92 | % | |

Capital cost (per unit battery) | 167 | USD | |

Replacement cost (per unit) | 67 | % | |

M & O cost (per unit) | 1.67 | USD/yr | |

Lifetime | 5 | years | |

Nominal battery capacity | 41 | Ah | |

Battery capacity | 75 | Ah | |

Rectifier (grec) and inverter (ginv) | Efficiency | 97% | |

Installation and capital cost (per kW) | 127 | USD/yr | |

O & M cost (per kW) | 1 | USD/yr | |

Lifetime | 20 | years | |

General Requirement | Interest rate | 6% | |

Project life (N) | 20 | years | |

EVs Capacity in kWh | 20 | kWh | |

Utility prices: | |||

Power export price to utility (selling) | 0.015 | USD/kWh | |

Power import price from utility (purchasing) | 0.013 | USD/kWh | |

Optimization of lower and upper bounds | Solar | 1200 | 1 |

Wind | 1000 | 15 | |

Battery | 1000 | 1 |

Rule No. | Modes | IF | THEN |
---|---|---|---|

1 | RESs | $\left({P}_{pv}\left(t\right)+{P}_{WT}\left(t\right)\right)>{P}_{l}\left(t\right)$ | $\left({P}_{pv}\left(t\right)+{P}_{WT}\left(t\right)\right)to{P}_{l}\left(t\right)andEV\left(t\right)$ |

2 | BT | ${P}_{b}\left(t\right)>\left[{P}_{l}\left(t\right)-{P}_{WT}\left(t\right)\right]-{P}_{PV}\left(t\right)\ast {\eta}_{inv}$ | ${P}_{b}\left(t\right)>\left[{P}_{l}\left(t\right)-{P}_{WT}\left(t\right)\right]-{P}_{PV}\left(t\right)\ast {\eta}_{inv}to{P}_{l}\left(t\right)andEV\left(t\right)$ |

3 | Charge (G2V) | ${E}_{grid}<{EV}_{demand}$ | ${E}_{grid}<{EV}_{demand}toEV\left(G2V\right)$ |

4 | Discharge (V2G) | ${E}_{grid}>{EV}_{demand}$ | ${E}_{grid}>{EV}_{demand}toEV\left(G2V\right)$ |

Benchmark Function | Dim | Range | Optimal Value |
---|---|---|---|

${\mathrm{f}}_{1}\left(\mathrm{x}\right)={\displaystyle {\sum}_{\mathrm{i}=1}^{\mathrm{d}}}{\mathrm{x}}_{\mathrm{i}}^{2}$ | 10 | [−100, 100] | 0 |

${\mathrm{f}}_{2}\left(\mathrm{x}\right)={\displaystyle {\sum}_{\mathrm{i}=1}^{\mathrm{d}}}\left|{\mathrm{x}}_{\mathrm{i}}\right|+{\displaystyle \prod _{\mathrm{i}=1}^{\mathrm{d}}}\left|{\mathrm{x}}_{\mathrm{i}}\right|$ | 10 | [−100, 100] | 0 |

${\mathrm{f}}_{3}\left(\mathrm{x}\right)={\mathrm{m}\mathrm{a}\mathrm{x}}_{\mathrm{i}}\left\{\left|{\mathrm{x}}_{\mathrm{i}}\right|,1\le \mathrm{i}\le \mathrm{t}\right\}$ | 10 | [−10, 10] | 0 |

${\mathrm{f}}_{4}\left(\mathrm{x}\right)={\displaystyle {\sum}_{\mathrm{i}=1}^{\mathrm{d}}}\left({\mathrm{x}}_{\mathrm{i}}^{2}-10\ast \mathrm{cos}\left({2\mathsf{\pi}\mathrm{x}}_{\mathrm{i}}\right)+10\mathrm{d}\right)$ | 10 | [−5.12, 5.12] | 0 |

Function | Algorithm | Best Value | Worst Value | Average Value | STD |
---|---|---|---|---|---|

${\mathrm{f}}_{1}\left(\mathrm{x}\right)$ | ALO | 1.6291$\times {10}^{-9}$ | 8.8636$\times {10}^{-9}$ | 4.0018$\times {10}^{-9}$ | 1.9334$\times {10}^{-9}$ |

PSO | 8.2671$\times {10}^{-121}$ | 2.5752$\times {10}^{-48}$ | 1.2876$\times {10}^{-49}$ | 5.7582$\times {10}^{-49}$ | |

AOA | 0 | 0 | 0 | 0 | |

IAOA | 0 | 0 | 0 | 0 | |

${\mathrm{f}}_{2}\left(\mathrm{x}\right)$ | ALO | 1.1730$\times {10}^{-5}$ | 0.4850 | 0.0254 | 0.1082 |

PSO | $1.2952\times {10}^{-14}$ | $9.0712\times {10}^{-6}$ | $1.0976\times {10}^{-6}$ | $2.5864\times {10}^{-6}$ | |

AOA | 0 | 0 | 0 | 0 | |

IAOA | 0 | 0 | 0 | 0 | |

${\mathrm{f}}_{3}\left(\mathrm{x}\right)$ | ALO | 1.1878$\times {10}^{-6}$ | 0.0025 | 1.8484$\times {10}^{-4}$ | 5.4351 $\times {10}^{-4}$ |

PSO | 1.4774$\times {10}^{-25}$ | 4.0204$\times {10}^{-13}$ | 2.0227$\times {10}^{-14}$ | 8.9870 $\times {10}^{-14}$ | |

AOA | 0 | 0 | 0 | 0 | |

IAOA | 0 | 0 | 0 | 0 | |

${\mathrm{f}}_{4}\left(\mathrm{x}\right)$ | ALO | 5.1427$\times {10}^{-5}$ | 0.0027 | 4.3189$\times {10}^{-4}$ | 5.8547 $\times {10}^{-4}$ |

PSO | $2.0618\times {10}^{-19}$ | $2.5902\times {10}^{-13}$ | $2.3924\times {10}^{-14}$ | $6.2083\times {10}^{-14}$ | |

AOA | 0 | 1.1591 × 10^{−186} | 5.7954 × 10^{−188} | 0 | |

IAOA | 0 | 1.7994 × 10^{−250} | 8.9970 × 10^{−252} | 0 |

**Table 5.**Optimal weight sets and configurations of the proposed system using MOIAOA based on Non-Scale multiple-run Pareto Front concept.

W1 | W2 | W3 | WT | PV | Bat | f | LCOE | GCF | ${\mathbf{E}}_{\mathbf{S}\mathbf{O}\mathbf{L}\mathbf{D}}$ | Elapsed Time (Seconds) |
---|---|---|---|---|---|---|---|---|---|---|

0.1 | 0.8 | 0.1 | 1 | 31 | 138 | 0.0762 | 2.37 × 10^{−2} | 0.0171 | 0.8596 | 4956.680489 |

0.1 | 0.7 | 0.2 | 1 | 32 | 108 | 0.1149 | 2.37 × 10^{−2} | 0.0171 | 0.8596 | 5536.762598 |

0.1 | 0.6 | 0.3 | 4 | 18 | 100 | 0.1344 | 2.33 × 10^{−2} | 0.0274 | 0.8337 | 4827.420494 |

0.1 | 0.5 | 0.4 | 1 | 18 | 93 | 0.145 | 0.022 | 0.8377 | 0 | 3438.61148 |

0.1 | 0.4 | 0.5 | 1 | 14 | 73 | 0.1343 | 0.0261 | 0.8376 | 0 | 2909.015921 |

0.1 | 0.3 | 0.6 | 1 | 13 | 63 | 0.1144 | 0.0304 | 0.8375 | 0 | 2731.221521 |

0.1 | 0.2 | 0.7 | 1 | 11 | 49 | 0.0942 | 0.0531 | 0.8371 | 0 | 2678.625856 |

0.1 | 0.1 | 0.8 | 1 | 12 | 106 | 0.0611 | 0.022 | 0.8377 | 0 | 5521.751529 |

0.2 | 0.7 | 0.1 | 6 | 27 | 70 | 0.0943 | 0.022 | 0.8377 | 0 | 2740.512867 |

0.2 | 0.6 | 0.2 | 4 | 22 | 147 | 0.1306 | 0.0237 | 0.0171 | 0.8596 | 4810.072815 |

0.2 | 0.5 | 0.3 | 1 | 20 | 91 | 0.1522 | 0.0237 | 0.0171 | 0.8596 | 3293.332732 |

0.2 | 0.4 | 0.4 | 2 | 15 | 63 | 0.1487 | 0.0253 | 0.0012 | 0.8475 | 3465.500523 |

0.2 | 0.3 | 0.5 | 1 | 15 | 83 | 0.1359 | 0.0531 | 0.8371 | 0 | 2780.494461 |

0.2 | 0.2 | 0.6 | 1 | 14 | 63 | 0.1095 | 0.022 | 0.8377 | 0 | 2766.968238 |

0.2 | 0.1 | 0.7 | 1 | 12 | 56 | 0.0779 | 0.0261 | 0.8376 | 0 | 3786.031941 |

0.3 | 0.6 | 0.1 | 5 | 31 | 59 | 0.1154 | 0.0216 | 0.1136 | 0.7579 | 3414.903356 |

0.3 | 0.5 | 0.2 | 3 | 24 | 68 | 0.1419 | 0.0233 | 0.0274 | 0.8337 | 2633.810036 |

0.3 | 0.4 | 0.3 | 1 | 19 | 103 | 0.1646 | 0.0237 | 0.0171 | 0.8596 | 5378.376291 |

0.3 | 0.3 | 0.4 | 1 | 15 | 56 | 0.1481 | 0.0246 | 0.0035 | 0.8554 | 2637.907928 |

0.3 | 0.2 | 0.5 | 1 | 12 | 63 | 0.13 | 0.0304 | 0.8375 | 0 | 2654.862484 |

0.3 | 0.1 | 0.6 | 1 | 12 | 56 | 0.0975 | 0.0261 | 0.8376 | 0 | 5068.761916 |

0.4 | 0.5 | 0.1 | 5 | 31 | 59 | 0.132 | 0.0243 | 0.0069 | 0.8475 | 3235.824878 |

0.4 | 0.4 | 0.2 | 4 | 12 | 56 | 0.1573 | 0.0239 | 0.0738 | 0.7026 | 4983.926465 |

0.4 | 0.3 | 0.3 | 1 | 16 | 63 | 0.161 | 0.0253 | 0.0012 | 0.8475 | 2682.447224 |

0.4 | 0.2 | 0.4 | 2 | 8 | 33 | 0.1522 | 2.66 × 10^{−2} | 7.34 × 10^{−5} | 0.8409 | 3272.623188 |

0.4 | 0.1 | 0.5 | 3 | 1 | 2 | 0.1156 | 0.0261 | 0.8376 | 0 | 2731.882521 |

0.5 | 0.4 | 0.1 | 3 | 24 | 68 | 0.1425 | 0.0262 | 0.0119 | 0.7838 | 2762.613745 |

0.5 | 0.3 | 0.2 | 1 | 19 | 68 | 0.1649 | 0.0239 | 0.0738 | 0.7026 | 5103.018621 |

0.5 | 0.2 | 0.3 | 1 | 15 | 52 | 0.1595 | 0.0246 | 0.0035 | 0.8554 | 5587.216803 |

0.5 | 0.1 | 0.4 | 3 | 1 | 1 | 0.1284 | 0.0246 | 0.0035 | 0.8554 | 2951.953591 |

0.6 | 0.3 | 0.1 | 5 | 17 | 42 | 0.1534 | 0.0262 | 0.0119 | 0.7838 | 2522.240268 |

0.6 | 0.2 | 0.2 | 5 | 7 | 25 | 0.1668 | 0.0266 | 7.34 × 10^{−5} | 0.8409 | 2629.085911 |

0.6 | 0.1 | 0.3 | 3 | 1 | 2 | 0.1418 | 2.46 × 10^{−2} | 3.50 × 10^{−3} | 0.8554 | 2904.915789 |

0.7 | 0.2 | 0.1 | 8 | 6 | 17 | 0.1542 | 0.0262 | 0.0119 | 0.7838 | 2771.440828 |

0.7 | 0.1 | 0.2 | 4 | 3 | 11 | 0.1518 | 0.0266 | 7.34 × 10^{−5} | 0.8409 | 5176.083577 |

0.8 | 0.1 | 0.1 | 5 | 10 | 4 | 0.1387 | 0.0246 | 3.50 × 10^{−3} | 0.8554 | 5424.871393 |

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Al-Sahlawi, A.A.K.; Ayob, S.M.; Tan, C.W.; Ridha, H.M.; Hachim, D.M.
Optimal Design of Grid-Connected Hybrid Renewable Energy System Considering Electric Vehicle Station Using Improved Multi-Objective Optimization: Techno-Economic Perspectives. *Sustainability* **2024**, *16*, 2491.
https://doi.org/10.3390/su16062491

**AMA Style**

Al-Sahlawi AAK, Ayob SM, Tan CW, Ridha HM, Hachim DM.
Optimal Design of Grid-Connected Hybrid Renewable Energy System Considering Electric Vehicle Station Using Improved Multi-Objective Optimization: Techno-Economic Perspectives. *Sustainability*. 2024; 16(6):2491.
https://doi.org/10.3390/su16062491

**Chicago/Turabian Style**

Al-Sahlawi, Ameer A. Kareim, Shahrin Md. Ayob, Chee Wei Tan, Hussein Mohammed Ridha, and Dhafer Manea Hachim.
2024. "Optimal Design of Grid-Connected Hybrid Renewable Energy System Considering Electric Vehicle Station Using Improved Multi-Objective Optimization: Techno-Economic Perspectives" *Sustainability* 16, no. 6: 2491.
https://doi.org/10.3390/su16062491