Multi-Criteria Decision-Making Approach to the Intelligent Selection of PV-BESS Based on Cost and Reliability

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

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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.

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Figure 2. Schematic diagram of the proposed system

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.

The MCDM is a multifaceted method and complexity reaches heightened levels [43]. Various methods to decision-making 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, Decision-Making 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: F-SVNS, 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 decision-maker 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 (F-SVNS), 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_sindeterminacy membership function and F_s falsity membership function.

The methodology of the intelligent decision-making method can be implemented by following steps [53].

Step 1. Identify the objective of MCDM for selection, ranking, sorting, and evaluation for decision-making.

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:

$\begin{gathered}\left(T_{i j}(x), I_{i j}(x), F_{i j}(x)\right) =\left(R_{i j}(x), 1-R_{i j}(x), 1-R_{i j}(x)\right)\end{gathered}$     (13)

$\begin{gathered}\left(T_{i j}(x), I_{i j}(x), F_{i j}(x)\right) =\left(1-R_{i j}(x), R_{i j}(x), R_{i j}(x)\right)\end{gathered}$     (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 non-beneficial 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*_maxis truth max value, I*_minis 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 decision-making matrix X and x_ij* stands for the original value of minimized criteria.

Step 3. Creating the weighted-normalized 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, S₀ 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 pre-established criteria. This methodology finds practical utilization across a spectrum of business sectors, emerging as a valuable instrument for instances demanding judicious, data-oriented 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 i-th 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.

Table 11. Simulation results by MCDM methods

F-SVNS		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

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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

8.2.1 Boost converter

The DC-DC 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 DC-DC 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 peak-to-peak ripple current (ΔI_L) can be calculated using Eqs. (31) and (32) [61].

$V_{\text {out }}=\frac{V_{P V}}{(1-k)}$     (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

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, Q₁ is in the ON state while Q₂ is in the OFF state. Conversely, in the boost mode, Q₁ is in the OFF state and Q₂ 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 three-phase inverter with three legs is used in this model. DC/AC inverter of three-phase full-bridge 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 S₁ - Sʹ₁ of the BESS bidirectional converter to determine the power direction form or to the DC bus.

The same procedure is applied for S₂ Sʹ₂ of the FESS bidirectional converter and S₃ Sʹ₃ 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 4-6 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.

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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.

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Figure 5. PV/BESS/SCSS output

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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 4-6 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.