Multicriteria Decision-Making to Determine the Optimal Energy Management Strategy of Hybrid PV–Diesel Battery-Based Desalination System

This paper identifies the best energy management strategy of hybrid photovoltaic–diesel battery-based water desalination systems in isolated regions using technical, economic and techno–economic criteria. The employed procedures include Criteria Importance Through Intercriteria Correlation (CRITIC) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) as tools for the solution. Twelve alternatives, containing three–four energy management strategies; four energy management strategies, load following (LF), cycle charging (CC), combined LF–CC, and predictive strategy; and three different sizes of brackish water reverse osmosis (BWRO) water desalination units, BWRO-150, BWRO-250, and BWRO-500, are investigated with capacity of 150, 250, and 500 m3/day, respectively. Eight attributes comprising different technical and economic metrics are considered during the evaluation procedure. HOMER Pro® software is utilized to perform the simulation and optimization. The main findings confirmed that the best energy management strategies are predictive strategies and the reverse osmosis (RO) unit’s optimal size is RO-250. For such an option, the annual operating cost and initial costs are $4590 and $78,435, respectively, whereas the cost of energy is $0.156/kWh. The excess energy and unmet loads are 27,532 kWh and 20.3 kWh, respectively. The breakeven grid extension distance and the amount of CO2 are 6.02 km and 14,289 kg per year, respectively. Compared with CC–RO-150, the amount of CO2 has been sharply decreased by 61.2%.


Introduction
The exponential growth in fossil fuels resulted in plenty of health and environmental problems [1,2]. A massive work has been done to raise the efficiency of the current processes [3] and use new devices that are environmentally friendly and have high efficiency. validity; step 3: calculation procedure; and step 4: selecting the optimal RES based on using optimal MCDM methods [31].
Among the different MCDM methods, TOPSIS is an effective method that shows a real solution for several issues [56]. TOPSIS helps decision-makers (DMs) to understand, complete examination and correlations quickly, and rank the other options. According to the needs, the determination of a reasonable alternative(s) will be made. Notwithstanding, numerous dynamic issues inside associations will be a synergistic exertion. Thus, this examination will stretch out TOPSIS to oblige the choice condition to fit honest work. A comprehensive and effective strategy for decision-making will then be obtained. The main idea of TOPSIS is relatively direct. It starts with the concept of a dislodged ideal point from which the tradeoff arrangement has the briefest separation [57,58]. Hwang and Yoon [56] further suggest that the positioning of choices will be founded on the shortest good ways from the positive ideal solution (PIS) and so-far negative ideal solution (NIS) or base. TOPSIS thinks about the separations between the two PIS and NIS, and an inclination request is positioned by their relative closeness and a mix of these two separation measures. As per Kim et al. [59], four TOPSIS preferences are tended to: (i) a sound rationale that speaks to the reason of human decision; (ii) a scalar worth that represents both the best and most noticeably awful options at the same time; (iii) a basic calculation measure that can be handily modified into a spreadsheet; and (iv) the presentation proportions of all choices, based on characteristics, can be pictured on a polyhedron, in any event for any two measurements. These focal points make TOPSIS a significant MCDM strategy as contrasted to other related procedures, for example, hierarchical analytical process (AHP) and ELECTRE [56]. Truth be told, TOPSIS is a utility-based strategy that analyzes every option legitimately, relying upon the information in the assessment frameworks and loads [60]. Moreover, as per the recreation correlation from Zanakis et al. [61], TOPSIS has the least position inversions among the classification's techniques. Hence, TOPSIS is picked as the principal group of advancement. The high adaptability of this idea can oblige further expansion to settle on better decisions in different circumstances. This is the inspiration of our examination.
It is not phenomenal for specific gatherings to continually settle on complex selections inside relatives. Notwithstanding, for using any MCDM approach, e.g., TOPSIS, it is generally approved that the selected data is provided ahead of time by grouping the assignment. Hence, Shih et al. [62] propose to upgrade TOPSIS as a critical thinking apparatus. However, this remuneration needs a cooperative choice emotionally supportive network to satisfy its destinations. To rearrange the dynamic exercises, we will recommend an incorporated gathering TOPSIS strategy for considering the genuine issues to settle on successful choices. This paper's main objective is to identify the best energy management strategy of hybrid photovoltaic-diesel battery-based water desalination systems in isolated regions considering technical, economic, and techno-economic criteria. The selection procedure combines CRITIC and TOPSIS as a solution method. Twelve alternatives, containing threefour energy management strategies; four energy management strategies, load following (LF), cycle charging (CC), combined LF-CC, and predictive strategy; and three different sizes of brackish water reverse osmosis (BWRO) water desalination units, BWRO-150, BWRO-250, and BWRO-500, are investigated with capacity of 150, 250, and 500 m 3 /day, respectively. Different attributes comprising economic and technical metrics are used during the evaluation procedure.

Information about the Analyzed Location and Load Demand
A water desalination plant in Wadi-Addwaser (Saudi Arabia) is selected as a case study. It is situated at 20.4493 • N, 44.8501 • E, as displayed in Figure 1. The location of Wadi-Addwaser City has a high average solar irradiance level. The mean solar radiation and clearance index for one year are shown in Figure 2. The average horizontal solar radiation per day is 6.16 kWh/m 2 . The maximum value of irradiance per day is 7.64 kWh/m 2 , occurred in June, while the minimum one is 4.31 kWh/m 2 in December. The electrical energy required is 210 kWh/day, and the maximum power needed is 10.5 kW for BWRO-150 unit. The electrical and technical specifications of different sizes of BWRO units are presented in Table 1. It is worth mentioning that the variation of the different operating conditions mentioned in Table 1 would affect the overall performance of the RO. For instance, the temperature of the feed water would affect the performance of the RO process, where the increase in the feed temperature will result in increasing the water permeability, increasing salt permeability, and decreasing the energy consumption [63]; additionally, the water recover rates in the RO units depend on the inorganic contents and its varied from 60 to 85% [64,65]. However, as long as the RO unit is operated within the condition mentioned in Table 1, "that is very close of the commercial conditions," the mentioned energy demand would be accepted. The proposed hybrid system's techno-economic parameters are listed in Table 2 [66,67]. These parameters are employed to determine the proposed system's optimal sizes using HOMER Pro ® software [68,69].     The proposed hybrid system's techno-economic parameters are listed in Table 2 [66,67]. These parameters are employed to determine the proposed system's optimal sizes using HOMER Pro ® software [68,69].

HOMER Software
In this work, HOMER software is applied to identify the best size for different alternatives. The photovoltaic/diesel generator/batter (PV/DG/B) optimal size is determined such that the cost of energy (COE) and total net present cost (NPC) are minimized. The formula of the NPC can be written as follows [66,67]: C ann,tot is the total cost per year, i is the real interest rate per year, N is the project's lifetime, and CRF is the capital recovery factor. The formula of CRF can be written as follows: The total cost C ann,tot comprises capital cost, operational and maintenance (O&M) cost, and replacement cost. The value salvage can be computed as follows: C rep is the replacement cost, R rem is the remaining life; R comp is the project's life span. The COE can be determined as follows:

TOPSIS Method
To incorporate the numerous inclinations of more than one DM, which will consider the detachment measures by taking the mathematical mean or number juggling mean of the people for TOPSIS. The standardization strategies and separation measures are also mulled over. Contrasted with the original TOPSIS technique, the proposed model offers an overall perspective on TOPSIS with a bunch of inclination collections. The nitty-gritty system, with a couple of choices inside each progression, is shown in the accompanying [43][44][45][46]. Stage 1. Create the decision matrix for every DM as following: where x k ij denotes the alternative performance rating; x k ij denotes the element of D k . Stage 2. Create the normalized decision matrix (R k , k = 1, . . . , K) for every DM as following.
where x k * j = max i x k ij and x k∼ j = min i x k ij for i = 1, . . . , m; j = 1, . . . , n; and k = 1, . . . , K. For normalization, Equation (6) for benefit criterion j will be as follows: Equation (7) for cost criterion j will be as follows: Moreover, the standardized value of r k ij is considered as the value of the corresponding element x k ij divided by the operation of its column elements, i.e., vector standardized; then: where i = 1, . . . , m; j = 1, . . . , n; and k = 1, . . . , K.
Note that while utilizing Equation (10) for standardization, a distinction will be made as one of the cost criteria for further manipulation.

Stage 4.
Determine the weight vector (W) to the attribute set for the group.
Each DM will provoke weights for attributes as w k j , where j = 1, . . . , n, and ∑ n j=1 w k j = 1, and for each DM, k = 1, . . . , K. Each element of the weight vector (W) represents the operation of the attributes' weights per DM elements.

Stage 5.
Estimate the distance between the best solution (S + i ) and a negative one (S − i ) for the group as following: Stage 5a. Calculate the measures from PIS and NIS and for DM k. In this phase, Minkowski's L p metric is applied to estimate the distance between PIS and NIS, as following: where p ≥ 1 and integer, w k j is the attribute weight for j and DM k, and ∑ n j=1 w k j = 1 and k = 1, ...., k. If p = 2, the metric is a Euclidean distance. Equations (13) and (14) will be: Stage 5b. Estimate the PIS and NIS for the group. Additionally, the measure of the group separation for every option will be joint via an operation for all DMs, as following.
Several selections are presented in operation, like geometric mean, arithmetic mean, or their modifications. Therefore, the above equation will be: where i = 1, . . . , m and k = 1, . . . , K.
Stage 6. Calculate the group relative closeness (C * i ) to the ideal solution, as following: where 0 ≤ S * i ≤ 1 The final step is ranking the alternatives based on the descending order of S * i .

Results of HOMER
This section introduces the details of the feasibility and techno-economic evaluation for the PV/DG/B system to power the BWRO desalination plant. To identify the most cost-effective and best size of this system, three different sizes of BWRO plants, BWRO-150, BWRO-250, and BWRO-500; and four energy management control strategies, LF, CC, combined, and predictive, were considered in the current research work. Eight main criteria, the COE, operating cost, renewable fraction (RF), initial cost (IC), excess energy, unmet load, environmental impact (size of CO 2 ), and breakeven grid extension distance (BED), are used to determine the best alternatives for the case study. Using Homer software, the values of the eight parameters for all options are shown in Table 3.
Considering the above table, the following remarks can be outlined: The annual operating cost varies from $3010/kWh to $10,139/kWh. The minimum operating cost can be achieved using BWRO-500 unit and the predictive control strategy. The renewable fraction valued varies from 46.1% to 96.8%. The maximum RF values are also achieved using the BWRO-500 unit and the predictive control strategy. The minimum initial cost of $50,223 is assigned to the BWRO-150 unit and the combined control strategy. Simultaneously, the energy cost values are changed from $0.156/kWh to $0.203/kWh. The minimum and maximum COE are achieved by the BWRO-250 unit and the predictive control strategy and BWRO-500 unit and the combined control strategy, respectively. The minimum excess energy and unmet load are 14,654 kWh and 0.1 kWh, respectively, for BWRO-150 unit with the load following (LF) strategy and BWRO-150 unit with the cycle charging (CC) control strategy. Compared to the grid extension, the break-even distance values are varied from 6.02 km to 9.63 km. The minimum BED is achieved by BWRO-250 unit with the predictive control strategy.
Regarding the annual amount of CO 2 emissions, the values are changed from 2076 kg to 36,873 kg, respectively, for BWRO-500 unit with the predictive strategy and BWRO-150 unit with CC strategy. Based on this discussion, it can be concluded that it is very difficult to identify the optimal alternative, directly. To solve this dilemma, multicriteria decision-making must be applied to identify the most suitable size of the hybrid system for the case study. The results of MCDM analysis will present in the next section. The optimal size and related costs of various elements of hybrid system with varying the rating of BWRO unit and control strategy are presented in Tables 4-6. The photovoltaic (PV) array size varies from 27.5 kW to 65.7 kW, respectively, for BWRO-150 unit with combined approach and BWRO-500 unit with LF strategy. The required number of batteries storage is varied from 13 units to 98 units. The minimum number of batteries storage (BS) is achieved by BWRO-150 unit with combined strategy, whereas the largest number is assigned to BWRO-500 unit with predictive strategy.  Table 5. The optimal size and the corresponding costs of various elements of the hybrid system using BWRO-250 plant.  Table 6. Optimal size and related costs of various elements of a hybrid system using BWRO-500 plant. For BWRO-150 plant, the minimum total NPC of $175,362.91 is achieved using a combined strategy. In this case, the fuel cost is $89,291.91 (50.92%), which represents the largest part of the total NPC flowed by the initial cost of 50,223.20$ (28.65%). The full replacement cost is $20,522.11, which represents around 11.7% of the total NPC. The replacement cost of diesel generator (DG) is $15,448.59, which represents 75.3% of the total replacement cost.

LF-EMS
For BWRO-250 plant, the minimum total NPC of $137,772.51 is achieved using a predictive control strategy. For this case, the capital cost of $78,434.54 (56.93%) represents the largest part of the total NPC flowed by the fuel cost of $35,353.29 (25.66%). The PV array cost is $53,505.76, which represents around 68.17% of the total system capital cost.
For BWRO-500 plant, the minimum total NPC of $171,373.32 is achieved using a predictive control strategy. In this case, the capital cost of $132,465.88 (77.3%) represents the largest part of the total NPC flowed by the replacement cost of $27,540.96 (16.07%). The replacement cost of batteries is $23,210.01, which represents 84.3% of the total replacement cost. The replacement cost is high, as that the batteries need to be changed many times during the project lifetime. Table 7 shows the details of the annual produced energy, annually consumed energy, annual excess energy, annual unmet load, annual capacity shortage, and the renewable fraction under different sizes of the BWRO-plant and various control strategies. Increasing the size of the BWRO-plant increases the renewable fraction. This is because increasing the size of the BWRO-plant decreases the required number of operating hours. However, this also increases the size of the PV array and, accordingly, the generated PV energy. The maximum annual generated PV energy of 127,037 kWh is achieved by BWRO-500 unit with the LF control strategy, whereas the yearly minimum generated PV energy of 52,336 kWh is achieved by BWRO-150 unit with the combined control strategy. On the contrary, increasing the size of the BWRO-plant decreases the dependency on the diesel generation system. The minimum annual generated DG energy of 2255 kWh is achieved by BWRO-500 unit with a predictive control strategy, whereas the maximum annual generated DG energy of 41,740 kWh is achieved by BWRO-150 unit with the CC control strategy.

LF-EMS CC-EMS CS-EMS P-EMS
Yearly produced energy (kWh) From the environmental impact, using BRWO-150 plant increases the annual production of produced CO 2 . The maximum amount of CO 2 is 36,873 kg, which is produced using BWRO-150 unit with the CC control strategy. This result is compatible with most dependency on the DG under this condition. On the contrary, the amount of CO 2 can be significantly reduced, thanks to increasing the size of BWRO-plant. The lowest annual amount of CO 2 is 2076 kg. It is achieved by BWRO-500 plant with a predictive control strategy. Moreover, the other pollutants are reduced, compared to BWRO-150 plant. Table 8 shows the detailed amount of different pollutant emissions by different sizes of BWRO-plant and various control strategies.

Results of MCDM
As discussed in Section 4.1, it is challenging to determine the optimal alternative directly, because no option has the best parameters. To solve this problem, multicriteria decision-making must be applied to identify the hybrid system's most suitable size for the case study. Based on Table 3, the normalized technical criteria values for the case study are presented in Table 9. The CRITIC method is employed to determine the importance of technical criteria. The results confirmed that the most and least important technical criteria were C3 (initial cost) and C7 (BED), respectively, as presented in Table 10. The weighted normalized decision matrix for the technical criteria presented in Table 11 was constructed using Tables 9 and 10. Regarding to Table 11, the technical criteria for ideal and nonideal solutions for the alternatives are determined and presented in Table 12. These results were used to evaluate the alternatives for ideal and nonideal distances for the case study, as illustrated in Table 13. As illustrated in Table 13, the final rank for all alternatives has been determined. Alternative A8, which represents BWRO-250 plant with a predictive control strategy, is the best option for the case study, followed by A6 (BWRO-250 plant with CC strategy) and A11 (BWRO-500 plant with combined strategy), whereas the worst option is alternative A7, which represents BWRO-250 plant with a combined control strategy. The optimal components' sizes corresponding to the best alternative are 44.6 kW PV array, 10 kW DG, 24 units of batteries storge, and a 17.8 kW converter. Under this situation, the technical, economic, and environmental parameters are the annual operating cost ($4590), a renewable fraction (77.5%), initial cost ($78,435), the cost of energy ($0.156/kWh), the excess energy (27,532 kWh), unmet load (6.84 kWh), BED (6.02 km), and the annual amount of CO 2 (14,289 kg). The total present cost is $137,772.5. The capital cost of $78,434.54 (56.93%) represents the largest part of the total NPC flowed by the fuel cost of $35,353.29 (25.66%). The cost of PV array cost is $53,505.76, which represents around 68.17% of the total system capital cost. The total annual produced energy is 99,602 kWh. A total of 84.5 % (84,179 kWh) of the produced energy is generated by the PV array, whereas the remainder amount (15.5%) is generated by DG.

Conclusions
Determination of the best energy management strategy and the optimal size of the water desalination unit was the main objective of this research work. Three-four energy management strategies; four energy management strategies, load following (LF), cycle charging (CC), combined LF-CC, and predictive strategy; and three different sizes of BWRO desalination units, BWRO-150, BWRO-250, and BWRO-500 were considered. Various parameters, such as operating cost, renewable fraction, initial cost, the cost of energy, excess energy, unmet load, breakeven grid extension distance, and the amount of CO 2 , were considered during the identification process. Based on HOMER software, by combining Criteria Importance Through Intercriteria Correlation (CRITIC) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), the best alternative for the case study has been determined. The main finding can be outlined as follows: • Increasing the size of the BWRO-plant increases the renewable fraction and decreases the dependency on the diesel generation system. • Using the BRWO-150 plant increases the annual production of CO 2 . The maximum amount of CO 2 is 36,873 kg, which was produced using BWRO-150 unit with the CC control strategy.

•
The lowest annual amount of CO 2 is 2076 kg. It is achieved by BWRO-500 plant with a predictive control strategy. • BWRO-250 plant with the predictive control strategy is the best option for the case study, followed by A6 (BWRO-250 plant with CC strategy) and A11 (BWRO-500 plant with combined strategy).

•
The worst alternative is the BWRO-250 plant with the combined control strategy.