© 2024 The authors. This article is published by IIETA and is licensed under the CC BY 4.0 license (http://creativecommons.org/licenses/by/4.0/).
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Addressing the challenge of meeting power demand with high reliability at low cost in Renewable energy (RE) generation is vital issue. The Autonomous Hybrid Energy Storage System (AHESS) to cover electrical deficit in Zigen clinic in southern Libya is introduced. It designed to produce 4 kW. The system comprises of photovoltaic (PV), Battery Energy Storage System (BESS) Flywheel Storage System (FESS) and Supercapacitance Storage System (SCSS). Six PVBESS combinations, six criteria and three scenarios are studied. The research aim is to find the optimal PVBESS combination based on low cost and high reliability. MultiCriteria Decision Methods (MCDM) is implemented to select the optimal combination. The study utilizes Net Present Costs (NPC), Loss Power Supply Probability (LPSP), and Levelized Cost of Energy (LCOE) to assess each criterion. Six combinations of AHESS are implemented in MATLAB. Three MCDM methods are used to determine the optimal sizing of PVBESS. Simulation results show that 30 PV panels and BESS 60 Ah are the optimal choices based on these results NPC = 19801 \$/kWh, LPSP = 0.104 \$/kWh, and LCOE = 0.032 \$/kWh.
TOPSIS, ARAS, SVNS, reliability, MCDM, renewable energy, flywheel, intelligent selection
The cost of installation and the reliability of an AHESS system are the main factors in its implementation. To determine the correct number of AHESS components, that might help to decrease the net present cost and increase the reliability of the system. A control system is implemented to reduce costs and increase reliability [1]. An autonomous system, PV, Wind Turbine (WT), SCSS, BESS, and hydrogen tank are presented to minimize costs and increase reliability. BESS is reduced to 56%, and the level of hydrogen is increased to 98% [2]. Selecting a suitable battery for a renewable hybrid energy storage system by using MCDM based on different criteria is implemented [3]. Based on the MCDM analysis, selecting the BESS according to customer opinion is implemented [4]. MCDM is used to select the RE system projects based on four main criteria and 30 subcriteria, The MCDM selects social acceptance, net presented cost, and noise which have a high impact [5]. Nine configurations of Energy Storage System (ESS) are implemented with MCMD based on ten economicreliabilityenvironmental criteria to select the optimal configuration [6]. The selection of RE source for the RE power plant is conducted with five RE sources, and six criteria (efficiency, emission, production, cost, land, and maintenance) are analyzed with MCDM to select the proper Renewable Energy Sources (RES) for the plant [7]. AHESS for remote villages in India is selected by MCDM based on the three criteria of cost, investment, and environmental impact. The selected cost is \$0.21/kWh [8]. Six barriers criteria and nineteen subcriteria prevent the RE system installation in Malawi; the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is implemented to select the highimpact barrier. The economic and investment costs are determined [9]. A study in Ghan for five different types of RE sources with thirteen criteria was implemented with MCDM, and the result was that the hydro source was the optimal one [10]. To reduce the carbon emissions caused by transportation, a suitable batteryelectric vehicle is studied based on its economic and technical specifications. MCDM is applied to select the suitable batteryelectric vehicle [11]. Offgrid generates 5.75 kW with a PV, and a hydrogen Fuel Cell (FC) system is applied based on the LCOE and lowest NPC [12]. To develop the battery’s aging, hybrid PV/BESS with FESS and without FESS are presented. The BESS lifetime has improved by 1.72% and increased by two years with a low cost of 22,128.54 and 1.82% of LPSP [13]. An AHESS of PV/WT/BESS/FESS is introduced to minimize the total cost, and an operation cost is introduced [14]. Two system configurations to cover ruler healthcare in Northern Nigeria, PV/Deasil Generator (DG)/BESS and WT/DG/BESS, are presented to select the economic configuration based on the total cost [15]. Three different types of BESS are used with the offgrid system: PV, FC, and BESS to determine the appropriate type, it is conducted based on reliability and economic factors. The results showed the lithium iron phosphate battery with fuel cell and retired electric vehicle battery are more economical with LPSP < 1%. The LPSP from 10% to 0.98% is very high at 12745$ [16]. To minimize the LCOE of an AHESS, the power pinch analysis is applied in literature [17]. Two loops of optimization are implemented. Energy management strategy, economic model predictive control, and Genetic Algorithm Optimization (GAO) are used to find the optimum numbers of components [18]. Three different loads are applied to PV/BESS with GAO to find the optimal sizing based on economic, residential, and industrial loads [19]. Nine configurations of PV / WT / BESS / SCSS are implemented in Hybrid Optimization of Multiple Energy Resources (HOMER) based on technical and economic concepts [20]. PV/BESS configuration is implemented based on technical and economical concepts to satisfy village demand [21]. As a critic, most of the previous papers on AHESS systems used the PSPL, LCOE based on various BESS, configurations, cost to select the optimal solution. To select the number of PV panels with BESS capacity based on six related parameters such as NPC, LPSP and LCOE is not supported therefore PV/BESS with MCDM methods for six criteria and 10 subcriteria are introduced.
The research presented in this paper focuses on the implementation of MCDM techniques, specifically F Single Value Neutrosophic Logic Linear Scale Transformation, Max Method (FSVNS), Additive Ratio Assessment (ARAS), and TOPSIS, to determine the optimal number PV and BESS capacity configuration for AHESS. The study aims to address the energy needs of the Zegin village clinic in south Libya by proposing a system design with 4 kW. The proposed system includes different numbers of PV panel ranging from 20 to 36 panels, and BESS capacities from 40 to 75 Ah. In this proposed system, fixed FESS and SCSS are maintained constant.
This study aims to select the most suitable PV number and BESS capacity based on six main criteria and 10 subcriteria. These criteria include LCOE, NPC, LPSP, Current consumption (I), Charging Energy (Q), and Discharging Time (DT). By evaluating these criteria, the optimal system configuration AHESS should meet the energy demand of the Zegin village clinic.
The main motivations behind this research lie in addressing the pressing need for sustainable and reliable energy solutions in remote locations. The motivations and contribution of this study can be summarized as following.
Three intelligent methods for decisionmaking MCDM have been implemented to ensure selection accuracy: FSVNS, TOPSIS, and ARAS. These methods have been applied to six combinations, labelled PV1 to PV6 based on six factors: NPC, LCOE, LPSP, I, DT, and Q.
The criteria weights selection is a critical undertaking for decisionmakers. The MCDM has been used for different purposes, such as determining the optimal RE reign, RE economic, political, and social aspects. Study on reliability and economics for BESS, Hydrogen Storage System (HSS), and DG without considering the number of PV and WT [6]. The most costeffective renewable energy sources (PV, WT, biomass, solar thermal, and hydropower) have been implemented [10]. All literature studies do not take the PV panel numbers and the battery capacity based on NPC, LCOE, LPSP, I, DT, and Q into consideration therefore, this study is unique because it fills the gap of knowledge in AHESS.
The applicability methodology's effectiveness is demonstrated, through its application in a case study, specifically focusing on the PVBESS selection for the Zigen clinic's AHESS. This case study involves handling uncertain, indeterminate, and inconsistent information.
The article is organized into nine sections. The introduction and literature review are presented in the first section. The system description is located in the second part. The third section covers AHESS system modelling. The fourth section describes the system cost. The data set for the system is organized in the fifth section. MCDM methodology and applications are covered in sections six and seven, respectively. Finally, the eighth and ninth sections summarize the results and conclusions.
The AHESS comprises variable component PV, BESS, and constant component FESS, and SCSS. This proposed system integrates three distinct ESS technologies to capitalize on their unique strengths and advantages in charging and discharging capabilities. The FESS, known for its high efficiency of approximately 95%, minimal maintenance requirements, and extended lifespan. The BESS and SCSS complement each other in the system, each offering unique characteristics to enhance overall performance. The BESS mainly functions as a backup generator during periods of solar energy unavailability. On the other hand, the SCSS characterizes attributes such as low energy density, high power density, and rapid responsiveness, it is quickly adapting the changes in power demand. One of the key advantages of the proposed AHESS system is its environmentally friendly, as it operates without the need for fossil fuels, thereby promoting environmental sustainability. To ensure optimal system performance, the control system is implemented to manage the charging and discharging of the ESS.
Table 1. Clinic power consumption
Item 
NO 
Power Consump./W 
Working Hours 
Item Total Power/Wh 
Computer 
1 
500 
3 
1500 
Printer 
1 
450 
1 
450 
Bulb 
6 
10 
8 
480 
Abdominal Ultrasound 
1 
400 
1 
400 
Air condition 
1 
1000 
2 
2000 
Slit Lab. 
1 
1650 
0.5 
820 
Figure 1. Average daily Ampere consumption of the clinic
Table 1 illustrates the load profile of electrical equipment and the clinic's electricity consumption. With a designed capacity to produce 4 kW to meet the clinic's demand load, the average ampere consumption throughout the year is shown in Figure 1, fluctuating around 8.5 A at 380 V AC, with an average power consumption of approximately 3230 W. Notably, the peak load during the year reaches up to 3914 W, with a maximum current draw of 10.3 A, while the system generates around 4180 W at 11 A and 380 V AC. Figure 2 presents a schematic diagram of the AHESS, depicting the schematic layout of the six PV and BESS criteria under consideration.
Figure 2. Schematic diagram of the proposed system
3.1 Photovoltaic component
PV is widely used, especially in sunny regions like Africa. There are two types of PV methods: The Singlediode Method (SDM) and the Doublediode Method (DDM) [22]. the solar cells temperature has a significant impact on the currentvoltage and powervoltage curves, which is why PV energy generation is relatively expensive. The PV current can be obtained by Eq. (1) [23].
$I=I_LI_o\left[e^{\frac{I R_S}{a}}1\right]\frac{I R_S}{R_{s h}}$ (1)
where the $I_L$ is the diode current, $I_o$ is the reverse saturation current, $R_s$ is the series resistance, $a$ is the modified ideality current, $R_{s h}$ is the shunt resistance [23]. PV power output can be obtained by Eq. (2) [24].
$P_{P V}=Y_{P V\text { rated }} f_{P V} \frac{H_T}{H_S}\left[1+K_{P V}\left(T cT_{r e f}\right)\right]$ (2)
where $Y_{P V {rated }}$ is the rated power of PV based on Standard Test Conditions (STC), $f_{P V}$ is the derating factor of $\mathrm{PV}, H_T$ is incident solar radiation on the surface, $H s$ is constant $\left(1\mathrm{kW} / \mathrm{m}^2\right.$ STC), $K_{P V}$ is the temperature coefficient. $T c$ is the PV cell temperature and $T_{{ref }}$ is constant STC (25℃) [24]. Table 2 illustrates PV profile.
Table 2. PV array profile
V_{mp}/V 
I_{mp}/A 
P _{PV} /W 
Price/ One 
Rsh/ Ω 
Rs/ Ω 
Life Time 
50.3 
8.15 
410 
82$ 
202.2 
0.378 
25 
3.2 Battery energy storage system component
Energy storage system technologies are used in a variety of ways to reduce costs and increasing reliability. BESS is divided into two types: primary BESS and secondary BESS (rechargeable BESS) [25]. The BESS can maximize returns by storing surplus energy and using it when needed or selling it when it is pricey [26]. The design and development of BESS began 140 years ago. The technology evolved from leadacid BESS to NaS and LiFePO4 BESS [27]. The BESS lifecycle is 1200–1800 cycles, with an efficiency of 75–80% and a lifespane of 5–15 years [28]. Table 3 shows the technical data for BESS. State of Charge (SoC) can be obtained from Eq. (3) [28].
$\operatorname{SOC}(t)=\frac{Q(t)}{Qn}$ (3)
where $Q(t)$ is the current capacity of $\mathrm{BESS}, Qn$ is the nominal capacity of BESS. The initial $S o C$ and final $S o C$ have a strong relationship with charging time replacement, the BESS charging time $T_{B\ Chr}$ can be calculated by Eq. (4) [29].
$T_{B\ Chr}=\frac{\left(S O C_{end }S O C_{inti}\right) W_B}{P_{Ch\ a}}$ (4)
where $S o C_{end}$ and $S o C_{inti}$ represent the finished $S o C$ and initial $S o C$ respectively, $W_B$ represent batteryrated capacity, and $P_{Ch\ a}$ constant charging power. Table 3 illustrates the BESS which technical data of proposed system.
Table 3. Technical data of BESS
BESS Type 
BESS Energy/Ah 
Price/$ 
Lifecycle 
Parallel 
Series 
Total Cost/$ 
Lifetime/Year 
NiCd 48 V 2 kW 
40 
100 
3000 
1 
8 
800 
10 
50 
120 
960 

60 
140 
1120 

75 
160 
1280 
3.3 Flywheel energy storage system component
The flywheel is a mechanical storage mechanism used in a variety of applications. FESS characteristics include large life cycles, a long lifespan, rapid response, and environmental [30]. FESS has a high efficiency of 90–95% [31]. The cycle lifetime of FESS is more than 1,000,000 cycles [32]. FESS energy storage depends on angular velocity and moment of inertia [13]. FESS applications are increasing; they can be utilized in aerospace, renewable energy systems, power smoothing, military vehicles, and uninterruptible power supplies (USP) [33]. FESS is made from many materials. Table 4 shows various different types of FESS [34]. FESS's negative aspects include a high capital cost for high rotation, a high selfdischarge rate, and a low energy density [35].
A FESS based on the maximum and minimum speeds can be calculated in Eq. (5) [36].
Table 4. Different type of FESS [28]
Material 
Density (kg/m^{3}) 
Tensile Strength (MPa) Max 
Max. Energy Density (for 1 kg) (MJ/kg) 
Cost ($/kg) 
Composites Eglass 
2000 
100 
0.05 
11.0 
S2glass 
1920 
1470 
0.76 
24.6 
Carbon T1000 
1520 
1950 
1.28 
101.8 
Carbon AS4C 
1510 
1650 
1.1 
31.3 
$E=\frac{1}{2} I \omega_{{\max }^2}\left(1\frac{\left(\omega_{\min }\right)^2}{\left(\omega_{\max }\right)^2}\right)$ （5）
where $\omega_{\min }$ and $\omega_{\max }$ represent minimum and maximum velocity respectively. $I$, represents the moment of inertia. The main parameters of FESS parameters are maximum stress $\sigma_{max}$ and energy density [36]. Table 5 shows FESS technical data which is used in this paper.
Table 5. FESS technical data
FESS 
Parameters 
Material of FESS 
Carbon AS4C 
Density 
$1510 \mathrm{ Kg} / \mathrm{m}^3$ 
Tensile strength 
$1650 * 10^6 \ Pascal$ 
The energy density of the material 
$0.30 kWh / kg$ 
Mass of FESS 
10 kg 
The energy density of FESS 
$0.31 * 10=3.1 Kwh$ 
Speed 
1500 rpm 
Diameter 
25.4 cm 
Width 
2 cm 
FESS efficiency 
90%  95% 
Lifetime 
25 years 
Life cycle 
Handers thousands 
FESS cost 
31.3*10 = 313 $ 
Backup time 
10s – 2 m 
3.4 Supercapacitor storage system component
Electric doublelayer capacitors (EDLC) are a type of SCSS [37]. EDLC stores the energy in the physical process [38] The combination of the supercapacitor and battery provides a complementary strength [39]. The supercapacitor's energy capacitance can be obtained using Eq. (6) [40]. Table 6 shows SCSS technical data which is used in the proposed system.
$C_{s c}=\frac{2 E_{s c}}{V_a^2V_b^2}$ (6)
where E_{sc} is the energy requirement of the SCSS, V_{a} and V_{b} represent the maximum and minimum operating voltage of the SCSS, respectively.
The selection of ESSs in this study is based on detailed evaluations of technical parameters, characteristics, and advantages. For example, the nickelcadmium BESS is favored for its longer lifecycle and extended lifespan compared to lithiumion and leadacid, making it suitable for applications like Uninterruptible Power Supply (UPS) and renewable energy (RE) systems. FESS is preferred for its long lifespan, high efficiency of 90% to 95%, quick response time, low maintenance needs, and environmental friendliness. The Carbon AS4C type of FESS was selected for this study due to its outstanding features, including a high tensile strength of 1650*10^{6} Pascal and an energy density of approximately 3.1 kWh. Additionally, the SCSS distinguishes itself with rapid charging and discharging cycles that can potentially reach up to a million cycles, highlighting its reliability and durability. The SCSS and BESS properties complement each other, with the SCSS offering a balance of low energy density and highpower density. SCSS rated at 3 V and 3400 F is employed in the system design. By strategically selecting these diverse ESS types based on their technical attributes and performance capabilities to enhance overall efficiency and reliability.
Table 6. Technical data of SCSS
Supercapacitor 
Parameters 
Cell Capacity 
3 V/3400 F 
Number of series 
65 pcs 
Number of parallel 
3 pcs 
Delivered power 
300 W 
Discharged time 
2 min 
Price for Cell 
35 $ 
Price for the system 
2240 $ 
Lifetime / Lifecycle 
>15 y/500000 
In the proposed system, the main factor is the total cost of all equipment. Three cost elements are considered: NPC, Replacement Cost (RC), and Operating and Maintenance Cost (O&M). Table 7 shows the costs, quantities, and lifetimes of each system component. It is important to note that the quantities of PV panels and BESS are still being evaluated. The cost analysis for each criterion is computed. Additionally, the LPSP serves as a metric for system reliability, ranging from 0, which represents low reliability, to 1, which represents high reliability. The reliability factor is positively correlated with the number of PV panels and BESS capacity, thereby increasing system reliability. The LPSP for each criterion, denoted from PV1 to PV6, is calculated using a specified Eq. (7). Table 8 illustrates the data set for the six combinations.
MCDM methods play a crucial role in ranking criteria based on specific constraints. Within the context of the AHESS, the combination of PV panels and BESS is evaluated using various combinations (PV1 to PV6) through implementation in MATLAB. Six combinations are implemented in MATLAB to generate data for each criterion, which is subsequently utilized in the MCDM method. Key parameters considered for each criterion include Q, I, DT, BESS capacity, NPC, LCOE, and LPSP. Notably, LCOE and LPSP are of significant importance as they reflect the economic viability and reliability of the system, respectively. Table 8 presents the dataset obtained for the six combinations, with varying numbers of PV panels ranging from 20 to 36 and BESS capacities ranging from 45 Ah to 75 Ah. By utilizing this data and employing MCDM methods, the study aims to derive optimal solutions for PV and BESS capacity for AHESS.
Table 7. System’s components cost
Items 
Number of Items 
P_{T} / kW 
Total Price / $ 
Lifetime / Years 
PV Array 
202428303236 
4 
 
25 
Boost Converter 
1 
1 
395 
15 
FESS 
1 
3 
313 
> 20 
BESS 
40506075 Ah (8) 
3 
 
10 
SCSS 
64 
0.3 
2000 
>15 
DC/AC Inverter 
1 
10 
2100 
10 
Bidirectional converters 
1 
4 
350 
10 
Bidirectional converters 
1 
4 
350 
10 
Bidirectional converters 
1 
0.3 
100 
10 
DC motor 
1 
2 
400 
15 
Table 8. Data set of six combinations of the proposed system
PV / Panels 
BESS / Ah 
LCOE / $ / kWh 
NPC / $ 
LPSP / % 
I / A 
Q / Ah 
DT / Min 
(PV1)20 
40 
0.028 
17,587 
0.188 
4.2 
33.8 
150 
(PV2)24 
40 
0.029 
17,948 
0.175 
4.48 
35.8 
228 
(PV3)28 
50 
0.03 
18,965 
0.145 
5.6 
45 
324 
(PV4)30 
60 
0.032 
19,801 
0.104 
6.4 
51 
390 
(PV5)32 
60 
0.033 
19,982 
0.041 
6.8 
55 
426 
(PV6)36 
75 
0.034 
20,999 
0.0 
8.8 
70 
588 
Average charging current (I) of the system for 20 panels = 134/380 +50/380+... +707/380 = 4.2 A
Energy charged capacity Q = 4.2 A* 8 h = 33.8 Ah. (BESS capacity = 40 Ah)
14 h with 1A = 14 Ah (clinic is closed)
Battery energy at 8 clock = 33.8 14 = 19.8 Ah
Average current of Clinic = 8 A
Discharging Time (DT) from 8 clock = 19.8Ah/8A = .2.5 h (clinic is open)
The LPSP is defined as the ratio between the sum of the lost power supply and the sum of the demand load. NPC, LCOE, and LPSP can be obtained using Eq. (7) [41], Eqs. (8) and (9) [42].
$L P S P=\frac{\sum_{t=1}^T{loss\ power\ supply}\ (h)}{\sum_{t=1}^T {demand\ load}}$ (7)
$N P C=\frac{C}{C R F\left(i,\ P_{(lifetime)}\right.}$ (8)
where C is total annualized cost, i is real interest rate per annual, P_{lifetime} is the project lifetime. The LCOE can be calculated by the Eq. (9).
$L C O E=\frac{{Total\ annual\ cost}(\$)}{{Electrical\ load\ served }({kWh})}$ (9)
The MCDM is a multifaceted method and complexity reaches heightened levels [43]. Various methods to decisionmaking have been employed in several fields [44]. MCDM is regarded as the finest method for criteria ranking [45]. MCDM is used for RE ranking based on energy production [46]. In recent years the MCDM has been implemented for the optimal selection of energy sources based on various criteria [47]. The toolkit of MCDM includes methodologies like the Analytic Hierarchy Process (AHP), Analytic Network Process (ANP), TOPSIS, ARSA, DecisionMaking Trial and Evaluation Laboratory (DEMATEL), Elimination and Choice Translating Reality (ELECTRE), along with various hybrid approaches [48]. MCDM is widely used, and based on the “ScienceDirect” database (between 2012–2022), 7619 articles from 10,116 are conducted by MCDM [49]. They have steps to rank their objectives [50]. Experts have turned to MCDM methods because of the multiplicity of aspects that must be taken into consideration [51]. Three types of MCDM are illustrated below: FSVNS, TOPSIS, and ARAS, all of which have benefits that motivate researchers to employ them. They are generally simple to learn, apply, and adapt to a wide range of research applications, and they can deal with ambiguity and partial information. Weight each criterion depending on its relative value. They can estimate the relative closeness of each possibility by taking into account both its positive and negative qualities.
6.1 Fuzzy single valued neutrosophic with linear scale transformation, max method
Sometimes, due to a lack of knowledge, the decisionmaker cannot make an optimal decision. Also, the limitations of the classical and intelligent algorithms could affect the final decision to overcome these drawbacks [52]. All membership functions independently in the range of [0, 1]. To define the Single Valued Neutrosophic Set (FSVNS), the SVNS is represented by the Eq. (10).
$\begin{gathered}\left\{x,\left(T_s(x), I_s(x), F_s(x)\right) x \in U\right\} \\ T_s(x), I_s(x), F_s(x): U \rightarrow[0,1], 0<T_s(x)+ \\ I_s(x)+F_s(x) \geq 3, \text { for each ploint of } \mathrm{x} \in \mathrm{U}\end{gathered}$ (10)
where x is the object, T_{s }is the truth membership function, I_{s}indeterminacy membership function and F_{s} falsity membership function.
The methodology of the intelligent decisionmaking method can be implemented by following steps [53].
Step 1. Identify the objective of MCDM for selection, ranking, sorting, and evaluation for decisionmaking.
Step 2. Collection of various alternatives and attributes involved in the selection procedure.
Step 3. Preparation of the Decision Matrix.
Step 4. Conversion of qualitative data into quantitative data.
Step 5. Generalization/ Normalization of matrix for beneficial criteria and non beneficial criteria normalization are carried out with Eqs. (11) and (12) respectively:
$R_{i j}=\frac{X_{i j}}{\sqrt{\sum_{i=1}^m X_{i j}^2}} \forall i, j$ (11)
$R_{i j}^*=1\frac{X_{i j}}{\sqrt{\sum_{i=1}^m X_{i j}^2}} \forall i, j$ (12)
where the x_{ij} performance of the alternative value i concerning criterion j.
Step 6. The positive ideal solution and the negative ideal solution are given by the Eqs. (13) and (14) respectively:
$\begin{gathered}\left(T_{i j}(x), I_{i j}(x), F_{i j}(x)\right) =\left(R_{i j}(x), 1R_{i j}(x), 1R_{i j}(x)\right)\end{gathered}$ (13)
$\begin{gathered}\left(T_{i j}(x), I_{i j}(x), F_{i j}(x)\right) =\left(1R_{i j}(x), R_{i j}(x), R_{i j}(x)\right)\end{gathered}$ (14)
where $T_{i j}(x), I_{i j}(x)$ and $F_{i j}(x)$ represent truth value, indeterminacy and falsity considering criterion $j$ respectively.
Step 7. Find the ideal solution for beneficial and nonbeneficial attributes that can be obtained by the Eqs. (15) and (16) respectively:
BAIS $=\left(T_{\max }^*(x), I_{\min }^*(x), F_{\text {min }}^*(x)\right)=(1,0,0)$ (15)
$B A I S=\left(T_{\min }^*(x), I_{\max }^*(x), F_{\text {maz }}^*(x)\right)$ (16)
where T*_{max}is truth max value, I*_{min}is indeterminacy min value and F*_{min} is falsity min value.
Step 8. and Step 9. Calculation then ranking, the calculation of the alternative weight can be calculated by the Eq. (17):
$\begin{gathered}A w=\sum_{j=1}^m\left(\left(\left(T_{i j}(\mathrm{x}) \times T_{i j}^*(x)\right)+\left(I_{i j}(x) \times I_{i j}^*(x)\right.\right.\right. \left.+\left(F_{i j}(x) \times F(x)\right)\right)\end{gathered}$ (17)
6.2 Additive Ratio Assessment (ARAS)
Chatterjee and Chakraborty [54] adopted the ARAS technique to solve a problem related to gear selection. Likewise, Nguyen et al. [55] harnessed this method to tackle the issue of selecting conveyor equipment in scenarios characterized by uncertainty. The ARAS methods offer a structured approach to dealing with intricate decision scenarios by offering a quantitative framework to evaluate and compare options. The fundamental idea is that a higher value of the weighted sum indicates a more favorable alternative. The ARAS method is a MCDM techniques. In summary, the entire ARAS procedure can be distilled into a series of six steps.
Step 1. and Step 2. Creating the decision matrix and standardize matrix, that can be obtained by Eqs. (18) and (19).
$\overline{x_{i j}}=\frac{x_{i j}}{\sum_{i=1}^m x_{i j}}$ (18)
$x_{i j}=\frac{1}{x_{i j}^*}$ (19)
where x_{ij} is the performance value of the alternative i concerning criterion j; x*_{ij} represent the normalized values of the normalized decisionmaking matrix X and x_{ij}* stands for the original value of minimized criteria.
Step 3. Creating the weightednormalized matrix X using the following Eq. (20):
$\hat{x}_{i j}=\bar{x}_{i j} w_j ; \forall i=1, \ldots, m$ and $j=1, \ldots n$ (20)
where, $\bar{x}_{i j}$ is the normalized value of the criterion $j ; w_j$ is the weight of the criterion $j$.
Step 4. and Step 5. Establishing the values of the optimality function S_{i} and the relative efficiency K_{i} of a viable alternative, that can be find by Eqs. (21) and (22) respectively:
$S_i=\sum_{j=1}^n \hat{x}_{i j} \ \forall i=1, \ldots, m$ (21)
$K_i=\frac{S_i}{S_o} \forall i=1, \ldots, m$ (22)
where, S_{0} is the optimal value (i.e., the maximum value of S_{i}) and the calculated values K_{i} are in the interval [0,1].
Step 6. Arranging the utility degree values Ki in ascending order for the ranking the alternatives.
6.3 Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)
The operational concept of the TOPSIS is rooted in the assessment of alternatives within the context of MCDM. This approach involves gauging the relative closeness of these alternatives to both the optimal and suboptimal benchmarks [56]. It encompasses the evaluation of a set of alternatives in alignment with preestablished criteria. This methodology finds practical utilization across a spectrum of business sectors, emerging as a valuable instrument for instances demanding judicious, dataoriented analytical choices. Generally, the TOPSIS can be distilled into a sequence of seven steps [57, 58].
Step 1. Formulate a matrix comprising M alternatives and N criteria, commonly referred to as an "evaluation matrix."
Step 2. and Step 3. Normalize evaluation matrix and compute the weighted normalized decision matrix, that can be calculated by the Eqs. (23), (24) and (25).
$\alpha_{i j}=\frac{x_{i j}}{\sqrt{\sum_{i=1}^M\left(x_{i j}\right)^2}}$ (23)
where $\alpha_{i j}$ is normalized value and $x_{i j}$ represents the performance of the ith alternative with respect to the j th criterion. The metric performance can be improved by Eq. (24).
$x_{i j}=\alpha_{i j \times} w_j$ (24)
$w_j=\frac{w_j}{\sum_{j=1}^M w_j} ; \sum_{j=1}^M w_j=1$ (25)
where w_{j} represents the criteria weights.
Step 4. Identify the best and worst alternatives for each criterion. That can be calculated by Eqs. (26) and (27).
$x_j^b=max _{i=1}^m x_{i j}$ (26)
$x_j^w=min _{i=1}^m x_{i j}$ (27)
where $x_j^b$ represents the best alternative and $x_j^w$ represents the worst alternative.
Step 5. and Step 6. Compute the Euclidean distance separating the target alternative and compute the likeness to the least favourable alternative for each option. That can be calculated by Eqs. (28), (29) and (30).
$d_i^b=\sqrt{\sum_{j=1}^N\left(x_{i j}x_j^b\right)^2}$ (28)
$d_i^w=\sqrt{\sum_{j=1}^N\left(x_{i j}x_j^w\right)^2}$ (29)
$S_i=\frac{d_i^w}{d_i^w+d_i^d}$ (30)
where $d_i^b$ is separating dstance of best alternative, $d_i^w$ is separating distance of worst alternative and $S_i$ is optimal solution.
Step 7. Rank the alternatives in descending order based on their TOPSIS scores.
SVNS, TOPSIS, and ARAS methods have been implemented based on six criteria and ten subcriteria in this study. These criteria can be categorized into two different groups: benefits criteria and nonbenefits criteria. The benefits criteria pertain to positive attributes that should be maximized or increased, while the nonbenefits criteria encompass negative attributes that should be minimized or decreased. fundamentally, the ideal alternatives are those that optimize benefit attributes and minimize cost attributes, whereas the negative ideal alternatives strive to minimize benefit attributes and maximize cost attributes. Table 9 provides a comprehensive overview of the classification of criteria and subcriteria within the proposed system, delineating the specific attributes that fall under each category. This structured approach enables the identification of solutions that strike a balance between maximizing positive attributes and minimizing negative attributes, ultimately leading to decisionmaking in the system design and implementation process.
NPC, LPSP, and LCOE are assigned greater importance among the variables due to their immediate significance to cost and reliability. To conduct MCDM based on these important criteria, it is necessary to classify the significant criteria. Table 10 illustrates the criteria classification; they assigned positive and negative criteria. The MCDM selection will be conducted based on their importance. For example, BESS is assigned a value of 1 as a positive criterion, while I is assigned a value of 0 as a negative criterion, which indicates that BESS is considered more important than I. that means four criteria are more significant than others.
Table 9. Criteria and subcriteria
Criteria 
Benefits 
Sub Criteria 
NPC 
Minimize 
Increase of the business investment of RES Decrease of environment pollution 
LCOE 
Minimize 
Decrease the electrical payment of residential Sealing of the surplus power 
LPSP 
Maximize 
System stability Cover the load demand 
Current 
Maximize 
A guarantee of an equipment operation 
Energy Charging 
Maximize 
A guarantee of the ESS supports the RESS Increase of the load supporting of all equipment on the same time 
Discharging Time 
Maximize 
Decrease the number of ESS 
Table 10. The positive and negative criteria

BESS 
LCOE 
NPC 
LPSP 
I 
Q 
DT 
FSVNS 
(+) 
(+) 
(+) 
(+) 
() 
() 
() 
1 
1 
1 
1 
0 
1 
1 

TOPSIS 
(+) 
(+) 
(+) 
(+) 
() 
() 
() 
1 
1 
1 
1 
0 
1 
1 

ARAS 
(+) 
(+) 
(+) 
(+) 
() 
() 
() 
1 
1 
1 
1 
0 
1 
1 
Criteria dataset of the AHESS is used for MCDM, FSVNS with, TOPSIS, and ARSA. The objective is to determine the PV panel number and BESS capacity based on the dataset in Table 8 and the classified criteria, positive and negative in Table 10.
8.1 The simulation results of three methods MCDM, FSVNS, TOPSIS and ARAS
Results using F SVNS N LSTMM
% 06 Attributes BESS (+) LCOE (+) NPC (+) I () LPSP (+) Q () DT ()
PV1=1, PV2=2, PV3=3, PV4=4, PV5=5, PV6=6
PV = 4 1 6 2 3 5
Rnk = 1 2 3 4 5 6
Results using TOPSIS
Enter 1 for benefit and 0 for cost criterion
identn = PV = 6 4 5 1 2 3
Rnk = 1 2 3 4 5 3
Results using ARAS
identn = PV = 5 4 6 1 3 2
Rnk = 1 2 3 4 5 6
The optimal number of PV panels and BESS capacity are determined using MCDM methods, FSVNS, ARAS, and TOPSIS. The simulation results of MCDM methods based on positive and negative criteria are presented in Table 11. According to the results, FSVNS selects PV4 (30 panels and BESS 60 Ah) as the optimal solution, ranking it in the first position. TOPSIS also selects PV4 (30 panels and BESS 60 Ah), ranking it in the second position. Similarly, ARAS selects PV4 (30 panels and BESS 60 Ah) and ranks it in second place. Based on these simulation results, it is evident that PV4 emerges as the optimal solution since it achieves three favourable positions (first, second, and second) compared to other alternatives.
Table 11. Simulation results by MCDM methods
FSVNS 
TOPSIS 
ARAS 

Six Configuration 
Ranking 
Six Configuration 
Ranking 
Six Configuration 
Ranking 
PV4 
4 
PV6 
6 
PV5 
5 
PV1 
1 
PV4 
4 
PV4 
4 
PV6 
6 
PV5 
5 
PV6 
6 
PV2 
2 
PV1 
1 
PV1 
1 
PV3 
3 
PV3 
3 
PV3 
3 
PV5 
5 
PV2 
2 
PV2 
2 
Figure 3. Selected configuration diagram of AHESS
8.2 Optimal system operating
The proposed AHESS features two fixed energy storage systems, FESS and SCSS, and one variable energy storage system integrated with PV. The optimal configuration of PV panels and BESS capacity is determined through the application of intelligent MCDM methods. The selected system comprises 30 PV panels and a BESS capacity of 60 Ah, SCSS, and FESS. This configuration is chosen based on their criteria, including the minimization of NPC, LCOE, and the maximization of LPSP. Figure 3 shows an optimal configuration diagram of AHESS. Table 12 shows the system component values, which are used for AHESS. The chosen system is capable of generating approximately 4 kW, thereby satisfying the demand load of the clinic while ensuring low costs and high reliability, as validated by three intelligent methods.
Table 12. System components values
Component 
Symbol 
Value 
Boost converter 
L_{PV} 
15e3 H 
C_{1} 
900e5 F 

C_{2} 
10e3 F 

BESS 
L_{B} 
50e3 H 
R_{B1} 
0.1 Ω 

R_{B2} 
0.1 Ω 

C_{B1} 
1 µF 

C_{B2} 
30 mF 

SCSS 
L_{SC} 
1.3e2 H 
R_{SC1} 
0.1 Ω 

R_{SC2} 
400 Ω 

C_{SC1} 
0.03 F 

C_{SC2} 
900e5 F 

FESS 
L_{FL} 
50e3 H 
R_{FL1} 
0.1 Ω 

R_{FL2} 
0.1 Ω 

C_{FL1} 
1 µF 

C_{FL2} 
30 mF 

Controller 1 
PI(z)1 
P = 0.85 I = 10 
Controller 2 
PI(z)2 
P = 0.01 I= 10 
Pulse generator 
PWM 
Freq. =5000 Hz 
8.2.1 Boost converter
The DCDC boost converter is a key component in RE systems. It works by converting input power to a higher output based on the duty cycle. When the transistor switch activates, the inductor current rises until fully charged. Conversely, when the transistor switch is off, the inductor current flows to the capacitor and the load [59]. The DCDC boost converter is crucial in renewable energy systems (RES), with practical efficiencies ranging from 70% to 95% [60]. Table 13 provides the parameters of the boost converter. The input of the boost converter, supplied by the PV system, is approximately 271 VDC and 16 A, through the converter, it is regulated to achieve 380 VDC and 11 A. The gain of the boost converter's output voltage (V_{out}) and the peaktopeak ripple current (ΔI_{L}) can be calculated using Eqs. (31) and (32) [61].
$V_{\text {out }}=\frac{V_{P V}}{(1k)}$ (31)
$\Delta I_L=\frac{V_{P V} k}{f L}$ (32)
where $V_{P V}$ is voltage output of PV system, and $k$ is duty cycle, $f$ is Switching Frequency, L is inductor value.
Table 13. Boost converter parameters
Parameters 
Values 
Voltage Input V_{in} 
271 V DC 
Current Input I_{n} 
16 A 
Voltage output V_{out} 
380 V DC 
Current output I_{out} 
11 A 
Power output Pout 
4.180→ 
8.2.2 Bidirectional buck boost converter
Continuous advancements in power electronics sciences contribute to improved electrical power conversion in renewable energy systems [62]. These converters feature a bidirectional structure that combines elements of both buck and boost converters. In buck mode, Q_{1} is in the ON state while Q_{2} is in the OFF state. Conversely, in the boost mode, Q_{1} is in the OFF state and Q_{2} is in the ON state. The duty cycle of the converter determines the sequence of these modes [63] The primary function of the bidirectional converter is to facilitate charging and discharging processes, which are controlled by the system's control.
8.2.3 DC/AC inverter
DC/AC inverter is technically classified into two types: Pulse Width Modulation (PWM) and multilevel modulation [64]. The switching losses in PWM are a significant issue in DC/AC inverters; 1/3 PWM has more features than 2/3 PMW and 3/3 PMW [65]. A threephase inverter with three legs is used in this model. DC/AC inverter of threephase fullbridge inverter at 180° is used. The input of the DC/AC inverter is 380 VDC and 11 A. The output of the inverter is 380 VAC, and the maximum power of the inverter is 7 kW.
8.2.4 Control system
The control system is implemented to manage the charging and discharging BESS, SCSS, and FESS. The role of the control is to enhance the energy storage system to increase the power reliability of the proposed system. The system has three scenarios: the first scenario is the power load less than the power bus (P_{L} < P_{bus}), the second scenario is the power load equal to the power bus (P_{L} = P_{bus}), and the third scenario is the power load more than the power bus (P_{L} > P_{bus}). The V_{BUS} represents the power generated by the AHESS. V_{ref} represents the set point value, which is set at 380 V.
The first summing comparator takes the difference between the V_{ref} and the V_{BUS} to obtain the error e(t)V of the BESS. That error passes through the first desecrate Proportional Integral (PI) controller of BESS to generate two values (8 or 0); these values represent the I_{ref}. The second comparator will take the difference between the BESS current I_{B} and the I_{ref} to obtain the e(t)I_{B} of BESS for the second PI; the role of the second desecrate PI is to generate 1 or 0 for PMW; the output control is complementing values (1 or 0); and finally, the complement values are connected to the S_{1}  Sʹ_{1} of the BESS bidirectional converter to determine the power direction form or to the DC bus.
The same procedure is applied for S_{2} Sʹ_{2} of the FESS bidirectional converter and S_{3} Sʹ_{3} of the SCSS directional converter. At night, the PV system is not available, so the controller will compare the V_{BUS}, which is zero at this moment, with the set point V_{ref} (380 V). At this time, the controller will set the BESS bidirectional converter to discharge the power from BESS to the DC bus. This situation is contentious until the PV generates more power than the set point, then the controller sets BESS to be charging, and the PV system becomes a supplier to the DC bus. This procedure is applied to SCSS and FESS as well.
8.2.5 System output
Figures 46 illustrate the system output of the AHESS to meet the demand load requirements of a clinic. The control system plays a crucial role in managing the priority of ESS for charging and discharging operations. In scenarios where the PV is not available, BESS/SCSS/FESS serves as the primary energy source to support the demand load based on control system sequences, which are reflected in the system output curves.
Figure 4. PV/BESS/SCSS/FESS output
Figure 4 shows the PV/BESS/SCSS/FESS output, it is presented with distinct curves representing each ESS: a red line for PV, a black line for BESS, a green line for SCSS, and a yellow line for FESS. The power source exchange among these components is visible during specific time intervals, such as 11:35 to 11:49, 12:68 to 12:87, and 14:66 to 14:84, showing the power charging and discharging of the AHESS.
Figure 5. PV/BESS/SCSS output
Figure 6. PV/BESS output
Figure 5 shows the PV/BESS/SCSS, illustrating the power sources exchange between these components during different time intervals, such as from (0:12 to 0:30) minutes, (8:11 to 8:30) as the SCSS response based on BESS drops, and (11:17 to 11:26), showing the relationship between the energy sources as the behavior of PV and BESS fluctuates.
Figure 6 shows the power sources exchange between PV and BESS in time intervals from 11:00 h to 17:00 h. The Figures 46 show the response of energy storage systems based on the decrease and increase in PV, as well as on the energy stored in the ESS. All of these sequences are based on the control system.
The implementation of an AHESS system integrating components PV/BESS/SCSS/ FESS has been proposed to address the energy requirements of the Zigen clinic in southern Libya. The primary focus of this system is to ensure costeffectiveness and reliability, as measured by the metrics NPC, LCOE, LPSP, DT, Q, I, and BESS capacity. To determine the optimal number of PV panels and BESS capacity, MCDM methods were employed based on six criteria and six combinations. Specifically, three intelligent decisionmaking methods, FSVNS with LSTMM, TOPSIS, and ARAS, were utilized in MATLAB to assess the various criteria and identify the most efficient solution based on the criteria. The MCDM analysis revealed that the combination of (P4) 30 PV panels and a 60 Ah BESS capacity was considered optimal solution based on the determined criteria. In particular, the results highlighted the PV4 over others, with rankings placing it in the first and second positions across different MCDM methods. Consequently, selecting PV4 with specific conditions was identified as the most suitable choice for the proposed AHESS, offering a favorable LCOE of 0.032 and NPC of 19801$.
Future work is to find the optimal configurations for AHESS, potentially integrating an air compressor storage system with PV, including more criteria, such as technical as well as costs and reliability criteria to determine the optimal configuration of components.
Acronyms 

LPSP 
loss power supply probability 
NPC 
net present cost 
LCOE 
levelized cost of energy 
MCDM 
multi criteria decision maker 
FSVNS 
F single value neutrosophic logic 
LSTMM 
linear scale transformation, max method 
TOPSIS 
technique for order preference by similarity to ideal solution 
ARAS 
additive ratio assessment 
SCSS 
suppercondenser storage system 
BESS 
battery energy storage system 
FESS 
flywheel energy storage system 
EDLC 
electric doublelayer capacitor 
RC 
replacement cost 
PWM 
pulse width modulation 
AHESS 
autonomous hybrid energy storage system 
GAO 
genetic algorithm optimization 
AHP 
analytic hierarchy process 
ANP 
analytic network process 
RE 
renewable energy 
RES 
renewable energy source 
PV 
photovoltaic 
PWM 
pulse width modulation 
ANP 
analytic network process 
DEMATEL 
decisionmaking trial and evaluation laboratory 
WT 
wind turbine 
HSS 
hydrogen storage system 
I 
current 
DT 
discharging time 
Q 
energy capacity 
ESS 
energy storage system 
DG 
deasil generator 
FC 
fuel cell 
SDM 
single diode method 
DDM 
double diode methods 
UPS 
uninterruptible power supplies 
EDLC 
electric doublelayer capacitor 
O&M 
operation and maintance 
ELECTRE 
elimination and choice translating reality 
STC 
standard test condition 
SoC 
state of charge 
HOMER 
hybrid optimization of multiple energy resources 
STC 
standard test condition 
AC 
alternative current 
DC 
direct current 
Symbols 

I_{L} 
Diode current 
Io 
Reverse saturation current 
a 
Modified ideality current 
R_{s} 
Series resistance 
R_{sh} 
Shunt resistance 
C 
Total annualized cost 
P_{lifetime} 
Project lifetime 
C_{SC} 
Supercapacitor energy capacitance 
$W_B$ 
Batteryrated capacity 
$P_{ch\ a}$ 
Constant charging power 
$Y_{P Vr a t e d}$ 
Rated power 
$H_T$ 
Incident solar radiation 
$H_S$ 
Constant (1kW/m^{2 }STC) 
$K_{PV}$ 
Temperature coefficient 
$T_C$ 
PV cell temperature 
$T_{ref}$ 
Constant STC (25℃) 
$Q(t)$ 
BESS current capacity 
$Q_n$ 
BESS nominal capacity 
$T_{B_{C h r}}$ 
BESS charging time 
$SoC_{i n t i}$ 
Initial SoC 
$SoC_{end}$ 
Finished SoC 
$P_{Ch\ a }$ 
Constant charging power 
$E_{s c}$ 
Energy requirement 
$V_{a}$ 
SCSS max. operating voltage 
V_{b} 
SCSS min. operating voltage 
C 
Total annualized cost 
i 
Real interest rate per annual 
P_{lifetime} 
Project lifetime 
$V_{P V}$ 
Voltage output 
k 
Duty cycle 
f 
Switching frequency 
L 
Inductance 
$x_{i j}$ 
Performance of the Alternative value 
$R_{i j}$ 
Beneficial criteria 
$R_{i j}^*$ 
Non beneficial criteria 
$A w$ 
Alternative weight 
T*_{max} 
Truth max value 
I* _{min } 
Indeterminacy min value 
F* _{min } 
Falsity min value 
$\overline{x_{i j}}$ 
Decision matrix 
$\hat{x}_{i j}$ 
Weight of normalized matrix 
$S_0$ 
Optimal value 
$K_i$ 
Relative efficiency 
$w_j$ 
Weight 
$x_j^b$ 
Best alternatives of criterion. 
$x_j^w$ 
Worst alternatives of criterion. 
$d_i^b$ 
Separating distance of $x_j^b$ 
$d_i^w$ 
Separating distance of $x_j^w$ 
$S_i$ 
Optimal solution 
BAIS 
Benefit attribute ideal solution 
T_{S} 
Truthmembership function 
I_{S} 
Indeterminacymembership function 
F_{S} 
Falsitymembership function 
Q_{1} and Q_{2} 
Transistor Switches 
P_{L} 
Power Load 
P_{bus } 
Power Bus 
V_{ref } 
Reference voltage 
V_{BUS} 
Bus Voltage 
I_{B} 
BESS current 
I_{ref} 
Reference current 
PI 
Proportional Integration 
S_{1}  Sʹ_{1} 
BESS bidirectional converter switches 
S_{2}  Sʹ_{2} 
FESS bidirectional converter switches 
S_{3}  Sʹ_{3} 
SCSS bidirectional converter switches 
Greek symbols 

Ω 
Ohm 
$\omega_{min}$ 
Minimum velocity 
$\omega_{max}$ 
Maximum velocity 
$\Delta I_L$ 
Ripple current 
Ʃ 
Summing 
$\alpha_{i j}$ 
Normalize evaluation matrix 
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