Look-ahead Scheduling of Energy-Water Nexus Integrated with Power2X Conversion Technologies under Multiple Uncertainties

Co-optimizing energy and water resources in a microgrid can increase efficiency and improve economic performance. Energy-water storage (EWS) devices are crucial components of a high-efficient energy-water microgrid (EWMG). The state of charge (SoC) at the end of the first day of operation is one of the most significant variables in EWS devices since it is used as a parameter to indicate the starting SoC for the second day, which influences the operating cost for the second day. Hence, this paper examines the benefits and applicability of a look-ahead optimization strategy for an EWMG integrated with multi-type energy conversion technologies and multi-energy demand response to supply various energy-water demands related to electric/hydrogen vehicles and commercial/residential buildings with the lowest cost for two consecutive days. In addition, a hybrid info-gap/robust optimization technique is applied to cover uncertainties in photovoltaic power and electricity prices as a tri-level optimization framework without generating scenarios and using the probability distribution functions. Duality theory is also used to convert the problem into a single-level MILP so that it can be solved by CPLEX. According to the findings, the implemented energy-water storage systems and look-ahead strategy accounted for, respectively, 4.03% and 0.43% reduction in the total cost.


Overview
Globally, energy consumption, climate change, and the escalation of environmental degradation have emerged as critical issues [1]. These challenges have given rise to a vast research field focused on how to develop and operate energy systems efficiently. A multi-energy microgrid (MMG) is a multi-energy system with several primary energy sources and diverse energy demands [2]. Multiple energy sources can be stored and converted cost-effectively in an MMG to meet diverse energy needs. MMGs were first introduced as part of the "Vision of Future Energy Networks" project in an attempt to boost their efficiency and flexibility in terms of supplying varied energy needs [3]. On the basis of developed energy conversion and storage technologies, various energy carriers may serve as inputs to an MMG and be turned into one another to achieve multiple energy demands such as power, heating, cooling, and hydrogen. Developing and optimizing the usage of electric cars (EVs) and hydrogen vehicles (HVs) in MMGs is another strategy for addressing the issues posed by climate change and the rise in environmental pollutants [4], [5] EVs and HVs could improve air quality and human health while producing less CO 2 than fossil fuel cars [6]. To speed the transition to a future with reduced carbon emissions, it is essential to encourage the use of alternative vehicles to fossil fuel cars, such as EVs and HVs. So, in order to develop and promote EVs and HVs, providing a highly efficient energy management structure is necessary.
Moreover, increasing demand, expanding scales, climate change, and natural catastrophes will make the energy and water dilemma one of the most pressing issues of the future. According to data, the demand for energy and water will increase by around 40% and 30%, respectively, by 2035 [7]. Water treatment facilities use 8% of the world's energy, making energy and water systems intricately linked [8]. At various stages, water can be employed to provide and consume electricity, whereas electricity can be used to extract, transport, distribute, and purify water.
Consequently, integrated methodologies may be utilized to schedule and run water and energy systems through socalled energy-water microgrids (EWMGs) to fulfill demands cost-effectively. To achieve a highly efficient EWMG, the optimal management and operation of energy-water storage (EWS) devices are so important since they are essential elements of such networks [9]. On the other hand, the state of charge (SoC) at the end of the first day of operation is one of the most critical characteristics of EWS devices. Typically in most studies, it is assumed that the final SoC value for energy storage devices should be equal to its initial value at the end of the scheduling horizon, and it is utilized as a parameter to determine the beginning SoC for the second day, which determines the second day's operating cost. The final SoC value can be described as a variable in the optimization models, and its optimal value can be determined using an objective function that considers the future [10]. For this purpose, this paper proposes a look-ahead scheduling approach for the optimal operation of an EWMG equipped with multi-type conversion facilities to meet different energy demands with the lowest total operating cost.

Literature review
Many papers have focused on the optimal day-ahead scheduling and operation of MMGs equipped with multienergy conversion facilities to meet various energy demands at a minimum cost. The authors of [11] studied a distributionally robust optimum dispatch technique to address the joint operation of MMGs, as well as energy sharing and coordinated demand response across MGs, in which Kullback-Leibler divergence is applied to simulate the ambiguous set of PV output probability distribution. The authors of [12] proposed an optimal multi-energy dispatch model to meet the demands related to power and heat in the presence of EV parking lots (EVPLs), where a robust optimization model is adopted to deal with fluctuations in electricity prices. A conditional value-at-risk (CVaR) stochastic model is employed in [13] to minimize the operation cost of an MMG equipped with photovoltaic (PV) and power-to-hydrogen (P2H 2 ) units while supplying the demands of EVs and HVs simultaneously. The authors of [14] designed a decentralized optimization approach to meet various energy demands such as electricity, heat, and hydrogen in the presence of hybrid refuelling stations in an MMG, where the uncertainty of electricity price is handled by the robust optimization approach. An info-gap optimization model for risk management of an MMG integrated with renewable energy resources, and hybrid refuelling stations is also suggested in [15], where the main objective of the model is to supply power, hydrogen, and heat at a minimum cost. A risk-averse optimization model is also proposed in [16] to minimize the energy cost of a power-and hydrogen-based MG integrated with hydrogen refuelling stations (HRSs), in which a data-driven robust optimization technique controls the uncertainties associated with renewable energy resources and demands. In [17], a fully decentralized operation model based on gradient projection for multi-carrier energy systems, where the uncertainty of energy demand has been modelled using stochastic programming. A study in [18] has developed a robust decentralized peer-to-peer (P2P) energy trading framework based on the alternating direction method of multipliers (ADMM) for a community of microgrids, where the impact of various flexible technologies on P2P trading has been analysed. Another piece of research in [19], has introduced a local energy market for power-and hydrogen-based microgrids earmarked with a hybrid uncertainty management approach that enables them to share power and hydrogen with each other to decline their daily operation costs.
Several studies have been carried out to minimize the operation cost of EWMGs in the presence of renewable energy sources by considering different energy needs. A mixed-integer linear programming (MILP) problem is presented in [20] to solve an energy-water dispatch model for MGs integrated with water and energy systems, where intelligent control of the indoor temperature during occupied and unoccupied hours is considered for energy control of multiple building applications. A stochastic optimization framework is also formulated in [21] to assess the uncertainties related to renewable energy resources and multi-energy demands in an EWMG, where the results show the effect of multi-energy demand response on decreasing the total operation cost. The authors of [22] provided a unique planning technique to design an integrated system for an EWMG to support the realization of decentralized energy supply strategies for boosting community resilience and environmental sustainability. An effective energy management approach for an EWMG integrated with a water supply system is presented in [23], which offers a twostage algorithm to solve the scheduling problem efficiently. Based on the analytical hierarchy process and the energy, water, and food nexus, an integrative assessment tool is employed in [24] to model a decision-making strategy that helps guide policymakers in creating national priorities and sectorial methods. The authors of [25] presented a MILP problem to solve a multi-objective optimization model for an EWMG to simultaneously minimize energy and carbon emissions in the studied EWMG. Another study in [26] has developed an optimal multi-objective model for a cement factory to meet power, heat and water demand considering exergy and total annual cost as objectives. Study [27] takes the water and energy nexus into account in a real-time framework to minimize the expected operation cost, where a stochastic/info-gap approach has been proposed for uncertainty management. In [28], a centralized stochastic scheduling model has been proposed for networked EWMGs in order to enable them to cooperate with each other under the concept of transactive energy.
A few studies have been conducted on the application of the look-ahead optimization model in power and energy systems. A look-ahead operation strategy for a power system integrated with compressed air energy storage (CAES) is proposed in [29], where the uncertainties associated with wind power, electric demand, and electricity prices are handled by the conditional value-at-risk-based stochastic model. The numerical results show the look-ahead optimization model can improve the operation cost and the optimal performance of CAES in the studied power system. In [30], a look-ahead bi-level optimization technique is proposed to improve an energy storage's bidding strategy by taking into account both the day ahead and the next day. The model provides the opportunity to optimize the SoC at the end of the first day to maximize the profit of the storage operator on both days. The authors of [31] investigated a look ahead optimization strategy to minimize the operation cost of an MMG, including a combined heat and power (CHP) unit, PV unit, electric and gas boilers, and electrical storage to cover different energy demands, where a stochastic approach is applied to focus on handling fluctuations of demands and PV power in the optimal MMG scheduling.
Some recent studies have focused on how to manage uncertainties based on hybrid approaches, taking into account the distinction between the nature of uncertain parameters in a more efficient manner. In [32], a hybrid stochastic/info-gap optimization model is proposed to overcome uncertainties of renewable energy sources and energy demands in the optimal scheduling of off-grid integrated refueling stations, including power, hydrogen, and gas vehicles. An integrated CVaR-stochastic/info-gap optimization is also considered in [33] to address the uncertainties in wind power and energy demands in the day-ahead scheduling of a coupled power and gas distribution system. A two-stage stochastic-robust optimization formwork for the optimal planning of battery energy storage systems planning in a power distribution system is introduced in [34], considering various uncertainties such as electricity price, wind power, and electric vehicle behavior in parking lots. In [35], a hybrid stochastic/info-gap optimization model is described in which common uncertainties are treated using scenarios, and component failures are modeled using info-gap optimization in a robust way. A bi-level hybrid stochastic/robust optimization technique is also proposed in [36] to minimize the operation cost of a mixed power plant in the wholesale market.

Gaps and contributions
The following gaps are identified based on the reviewed studies:

RG1:
In most studies, the authors did not consider the application of the look-ahead optimization method to improve the performance of EWS devices in minimizing MMG operation costs, despite the fact that the SoC of EWS devices at the end of the first day can influence the optimal scheduling of MMGs on the second day. In studies [29][30][31], the authors have only calculated the initial SoC of electrical storage for the second day, and the effect of other energy storage systems has been neglected.

RG2:
The interconnection of energy and water resources in MMGs has not been considered in some studies, even though that desalination units and water storage systems play an important role in the optimal scheduling of MMGs.
In studies [21][22][23][24][25], the authors have mainly focused on the power-water microgrids, and the role of new energy resources and technologies such as P2H 2 and EVPLs has been ignored.

RG3:
There has been no research into using a hybrid uncertainty management approach to cover uncertainties without using scenario generation and probability distribution functions. In fact, the authors in previous works combined stochastic programming with info-gap or robust optimization approaches to achieve a hybrid uncertainty control approach.
According to the defined gaps and Table 1, this study proposes a look-ahead info-gap/robust optimization technique to minimize the total operation cost of an EWMG for two consecutive days under uncertainties. The introduced EWMG is integrated with multi-type energy conversion equipment, EWD devices, and multi-energy demand response to meet a variety of energy-water needs, such as electric/hydrogen vehicles and commercial/residential buildings for two consecutive days in a cost-effective manner. The proposed hybrid info-gap-robust optimization approach is formulated as a tri-level optimization model that enables the EWMG operator to overcome various uncertainties with minimal access to information on uncertain parameters such as probability distribution functions. The main contributions of this paper are defined as follows: 1. A look-ahead optimization framework is introduced to improve the flexibility of energy and water storage devices such as power, heat, cooling, hydrogen, and water storage to minimize the total operation cost of EWMG for two consecutive days. In doing so, the SoC of the storage systems is optimally determined for the next day which causes less operating costs. Despite the traditional day-ahead scheduling models, this framework paves the way for running operating models with a longer time horizon that can significantly reduce the operating costs in the long term. (Address RG1) 2. An integrated energy-water structure is proposed to meet various energy-water demands such as power, heating, cooling, hydrogen, and water at a minimum cost in the presence of vehicle-to-grid (V2G)-capable EVPLs, HRSs, multi-energy demand response (DR) and multi-type energy conversion devices. In light of such a framework, water and energy nexus in modern energy systems is considered and integration of emerged technologies is facilitated. (Address RG2) 3. A hybrid info-gap/robust optimization approach is proposed to cover the uncertainty of PV power and electricity price for two consecutive days without making assumptions about scenario generation or probability distribution. The model is formulated as a tri-level optimization framework and turned into a single-level MILP model using the duality theory to be solved by common solvers and guarantee solution optimality. (Address RG3)

Paper organization
The remainder of this paper is organized as follows: Section 2 is devoted to describing the suggested model and formulating the problem, respectively. Section 3 reports on the numerical and simulation results. Furthermore, section 4 contains the paper's conclusion.

The EWMG Description and Formulation
EWMG is made up of several energy-water resources to efficiently meet a range of energy-water demands, as shown in Fig. 1. The EWMG operator can satisfy electrical demands by using a variety of technologies, including CHP units, PV units, EVPLs with V2G capabilities, and electrical storage (ES), in addition to purchasing electricity from the market. The operator can deploy CHP units, gas boilers (GB), electric boilers (EB), and thermal storage (TS) to meet the heating demands. The gas fuel needed by CHP and GB to produce electricity and heat is provided by purchasing the gas fuel from the gas market. Electric chillers (EC) and cooling storage (CS) are also employed to address cooling requirements. P2H 2 and hydrogen storage (HS) also help to fulfill the HFS's need for hydrogen.
Also, the operator employs a water desalination unit (WDU) and water storage (WS) to satisfy the potable water demand. In addition, multi-energy demand response is considered to shift the electricity and heat demands from high price hours to low price hours to reduce the operation cost of EWMG.

Deterministic optimization model
This section outlines the look-ahead optimization mathematical model for the proposed EWMG without taking into account the PV power and electricity price uncertainties, which comprise the objective function and other constraints.

 Objective function
The main aim of this study is to minimize the overall operating cost of the EWMG for two consecutive days. The objective function in (1) shows the operational costs for two days, which are divided into two sections. The first section displays the operation cost for the first day, while the second section indicates the operation cost for the second day. The operation costs for the first and second days are presented in (2) and (3), respectively, which include the power purchase cost from the market, the operation and maintenance costs of the CHP unit and the operation cost of the GB, respectively. The parameter s  represents the operator's strategy and willingness to balance the first and second-day costs. It is noted that since the deployed storage systems are small-scale in distribution level, the degradation cost is ignored in the objective function [37].

 Heating system constraints
The constraints for the heating system, including the energy balance, DR, and heat generating units, are shown in (4)- (21). The feasible operation region for the co-generation of electricity and heat by a CHP unit is shown in Fig.   2, which is modeled by the constraints (4)-(7) [38]. The heat generation restrictions for GB and EB are shown in constraints (8) and (9), respectively. The power used by EB is calculated by (10). TS's charge and discharge are limited by constraints (11) and (12) for the whole scheduling horizon. The TS is not designed to operate simultaneously in charge and discharge modes, as defined in (13). The SoC of TS is calculated as (14) at each hour and should be restricted by (15). The first day's initial SoC and the second day's final SoC should be the same, as described by (16). According to the model, the SoC at the end of the first day should be equal to the SoC at the beginning of the second day (17). Heat demand must be equal before and after the implementation of DR within the whole scheduling horizon, according to constraint (18). The amount of shiftable demand that can be changed each hour is limited by (19). The heat balance at each time is also defined as (20).

 Water system constraints
This section presents the water system's formulation, which has multiple parts, including WDU and WST. The amount of energy used by WDU to desalinate saltwater and provide the demand for potable water is represented as (21), and the volume of water that can be obtained through WDU is constrained by (22).

2.15
from the water source such as WDU. The WST's charge and discharge restrictions are indicated in (23) and (24).
Constraint (25) prohibits the WST from being charged and discharged simultaneously. Constraint (26) indicates the WST water level at time t, which is restricted by (27). The initial SoC for the first day and the final SoC for the second day should be the same in WST, as stated by (28). The SoC of the WS system at the first day's finish should match the SoC of the WS system at the start of the second day, based on the constraint (29). The water balance constraint is found in (30 , ,

 Cooling system constraints
In this study, cooling demand is assumed to be met at all times by both EC and CS. EC's capacity to produce cooling is limited by (31). The electricity used by EC is determined via (32). Constraints (33) and (34) limit CS's charge and discharge throughout the scheduling horizon. The CS cannot operate concurrently in the charge and discharge modes, as described in (35). The SoC of CS is calculated as (36) every hour and should be limited by (37). As expressed in (38), the initial SoC for the first day and the final SoC for the second day should be the same in CS.
According to constraint (39), the SoC of CS at the end of the first day should coincide with the SoC of CS at the beginning of the second day. The cooling demand must be met by EC and CS as defined in (40

 Hydrogen fueling station constraints
This section provides constraints related to HRS to meet its demand via P2H 2 technology and the HS system. In this paper, P2H 2 technology and the HS system supply demand are associated with HRS. The demand for HRS is forecasted hourly by the EWMG operator for two days. The hydrogen produced by P2H2 is restricted by (41). The amount of power consumed by P2H2 is calculated as (42). Constraints (43) and (44) The linearized DistFlow model is used in this paper to include power microgrid constraints [39]. Constraints (72) , , , , , , , , , 1 1

Risk-based optimization model
The suggested framework enables the EWMG operator to use an appropriate uncertainty management strategy. In contrast with previous hybrid approaches, the suggested hybrid technique does not require the creation of scenarios or probability distribution functions. In reality, the authors have previously integrated stochastic programming with a robust or information-gap optimization strategy to cope with uncertainties in less computational time. To tackle uncertainties without the use of probability distribution functions, this work employs a hybrid info-gap/robust optimization technique. Furthermore, the EWMG operator can employ a risk-averse strategy by distinguishing between accessible information about unknown parameters and that which is not. The robust optimization method involves optimizing the objective function based on the worst-case variation range for the unknown parameter. The term "info-gap optimization" refers to a non-scenario-based technique in which the operator encounters an information gap while dealing with uncertain parameters. In this approach, decision-makers do not have access to the variation interval of uncertain parameters.

 Robust optimization
This part considers the electricity price u, which is addressed by the robust optimization approach. In general, the mathematical model of optimization problems can be expressed as (82) and (83).
In these equations, x i and x j are defined as the continuous and binary variables of i th and j th . j  is a known parameter with available forecasted ( exp j  ) and maximum ( max j  ) amounts. The robust optimization model can be formulated as [36]: In (84), the exterior term denotes the minimization of the objective function, whereas the interior term corresponds to the maximum of the worst case of the unknown parameter. To build a reliable decision-making model, Γ must be specified as an integer parameter with values between [0, Nj] that controls how conservative the optimal answer should be. Nj stands for the total number of unknown parameters. To disregard the impact of unknown parameter changes on the goal function, Γ is set to zero. The most cautious scenario is when Γ = Nj, which means that uncertainty at all time frames will be taken into account for changes in the objective function. Using the auxiliary variables x and y, (84) is transformed into a more solvable optimization problem as (85).
Additionally, the objective function (85) can be changed into (86)-(90) using the duality theory. So, the min-max model is converted into a minimization problem, considerably reducing the complexity of the objective function, which can be solved as common commercial solvers.
Therefore, the proposed model can be formulated under robust optimization considering the worst case of electricity price for two consecutive days as follows: .

 Hybrid info-gap/robust optimization
The PV power uncertainty is also addressed in this section, using an info-gap optimization strategy. The info-gap optimization finds the best solution to fulfill pre-specified expectations. This strategy is used when the EWMG operator has a sizable knowledge gap about unknown parameters [40].   2  2  2  2  2  22   ,  ,  ,  ,  , ,

Test system
To verify the effectiveness of the proposed methodology, the well-known IEEE 33-bus system is put forward as a real case study. Then this test system is modified and considered as an energy-water microgrid as follows. It is assumed that water devices including a water desalination unit with a capacity of 470 (m 3 ) and water storage are connected to the electrical network at bus #2; electrical devices including electrical storage, electric vehicle parking lot, and PV panels are connected to the test system through bus #4; heating equipment comprised a CHP unit, electrical and gas boilers both with the capacity of 2 (MWt), and thermal storage is integrated with the electrical network via bus #10; hydrogen technologies including hydrogen storage, power-to-hydrogen facility, and hydrogen refueling station are placed at bus #21; and finally electric chiller with the capacity of 4 (MWt) and cooling storage are cited at bus #30. All the considered technologies form an EWMG, shown schematically in Fig. 4, to work together to supply multi-energy and water loads. The load and PV power profiles are demonstrated in Fig. 5 for two consecutive days. It is noteworthy that the hydrogen demand was originally stated in kg. However, to keep all energy units uniform in the paper, it has been converted to MW (1kg hydrogen=0.0336MWh). Electrical and heating loads are assumed to be flexible by up to 10% to participate in the DR program. PV power profiles have been extracted from [41], and multi-energy loads have been obtained from [29,42]. Moreover, Fig. 6 depicts electricity prices for both days of the look-ahead scheduling [43]. Technical details of the CHP unit and the storage systems are given in Fig. 2 and Table 2, respectively. Furthermore, the data associated with electric vehicles is available in [44]. All the simulations are carried out on a standard PC system with Intel ® Core TM i7-1195G7 @ 2.90 GHz and 16 GB RAM using GAMS software and CPLEX solver. It is also noted that the results are given in a deterministic manner with details for subsections 4.2-4.4, then the impact of the uncertainty is analyzed comprehensively in the last subsection.  Table 3 shows the impact of the look-ahead scheduling on daily and total operational costs. According to this table, the total operational cost in the case of ignoring the look-ahead strategy, similar to studies conducted in [12], [14], [16], [20], [21], is $28402.12. This value, however, declined by about $106.7 (0.37%) by considering the look-ahead strategy with = 0.75. Further, the full consideration of the second-day costs in the scheduling by setting = 1 leads the total cost to reduce to $28278.97, which in comparison with the no look-ahead strategy, $123.15 (0.43%) could be saved. According to these statistics, the positive impact of the considering look-ahead strategy in scheduling is concluded. It is noted that the rest of the results are presented for = 1. Table 3. Impact of the look-ahead on the operation costs Cost ($)
Since after = 19, electricity prices have reduced, EVs are applied in charging mode to satisfy their final SoC requirement. Despite the ignorance of EVPL in some of the works like [16], [20], [21], [31], the findings of this work Finally, Fig. 10 illustrates the electrical network's voltage profiles for on-peak and off-peak load hours. As is seen, the voltage deviation of none of the buses violates 0.1 p.u, which shows the proposed methodology has not compromised the technical constraints of the electrical network.  Fig. 11 depicts the hourly dispatch of heating devices. As can be seen, from the initial hour of both days till = 11, gas fuel-based devices, i.e., the GB and CHP, have lower commitment rather than the EB. The reason is back to the low electricity price during the first half of both days which cause the operation of the EB to be more affordable.

Heating/cooling dispatch analysis of EWMG under look-ahead optimization
However, after = 11, when the electricity prices go up, the GB and CHP are operated to supply the load. The TS also assisted the EWMG by charging before the electricity prices start to rise and discharging afterward to prevent EB operation during on-peak hours. Fig. 12 illustrates the impact of the demand response on the heating load profiles. It is obviously viewed that the load is shifted from a period of = 12 − 22 to the other hours. In light of this load shifting, the requirement for the EB commitment during on-peak electricity price hours is reduced.
Although the multi-energy demand response has not been considered in [16], [20], [32], [36], its implementation in this work for electrical and heating loads results in a $518.65 (1.83%) reduction in the total cost for two days.
Further, Fig.13 is supplied to show the cooling dispatch between the EC and CS. The main equipment to supply the cooling load is the EC; however, the CS compensates for the EC's low commitment during high electricity price periods like = 12 − 14,17 − 19. The operation of TS and CS together causes to $222.30 (0.78%) decrease in the total cost for two days.  Regarding the hydrogen dispatch, according to Fig. 14 Fig. 15. The whole water load must be supplied with the cooperation of the WDS and WS. Since the WDS uses electricity to work, the WS is applied in charging mode during hours = 1 − 10, when the electricity prices are low, and applied to discharging mode during hours = 11,14 − 23, when electricity prices are high.

WDU WS
This subsection investigates the performance of the proposed hybrid info-gap/robust uncertainty management approach. To do so, firstly, the robust optimization is applied and the obtained results are reported through Figs. [16][17]. As the robust optimization is based on a budget uncertainty set, it is sensitive to the value of Γ. Hence, the results are provided for different values of this parameter including Γ ∈ {4, 8,12,16,20,24}. It is noted that Γ = 0 implies the uncertainty is ignored and the problem, in this case, is the same as the deterministic one. As can be seen in Fig.   16, the daily and total operating costs have experienced an increase by raising the value of Γ. This is because the more value is assigned to Γ, the more hours are selected to be considered as the worst-case scenario in the optimization. In other words, according to the robust behavior of the methodology, the optimization assumes the electricity price of those hours included in the worst-case scenario will be increased up to the considered price deviation rate (10%) in real-time and schedules the energy system in a way the incurred cost is minimized. The most affected variable by applying the robust optimization is the purchased power from the grid, which is demonstrated in 14.3% at each hour in real-time, the imposed operation costs will be less than the guaranteed values.
To evaluate the proposed model, it is compared with two different scenario-based models. The first model is hybrid info-gap/stochastic, in which the electricity market uncertainty is modeled via the stochastic approach, and the PV power uncertainty is still handled via the info-gap method. To do so, 1000 scenarios using Monte Carlo simulation with Normal distribution ( = 10%) are generated. Then, the SCENRED toolbox in GAMS software is used to reduce the number of scenarios to 10 via the backward selection method. The same procedure with = 20% is used in the second approach, i.e., hybrid stochastic/robust, where the stochastic is used to consider the PV power uncertainty and the robust optimization is applied to handle the electricity market uncertainty. After then, it is assumed that the electricity prices have increased by 10% and the PV power has reduced by 20% at each time slot after the fact, meaning after the uncertainty realization. The imposed actual costs for all three methods are reported in Table 4. As enumerated, the proposed approach could reach $28.4 and $41.28 lower total operation cost for two days in comparison with, respectively, the hybrid info-gap/stochastic and hybrid stochastic-robust approaches.
Moreover, according to the supplied execution statistics, the proposed model could be performed in a lesser period with a lower number of decision variables in comparison with the other two methods. Hence, the proposed hybrid info-gap/robust approach outperforms both of the scenario-based methods in all aspects.    Fig. 18. Impact of the robustness parameter on the uncertainty region

Conclusion
The world's population is now growing to a stage where drinkable water and energy supply have become catch-all challenges. The work presented in this paper introduced an integrated platform that incorporates the energy and water nexus under the concept of an energy-water microgrid (EWMG) to deal with these challenges. Then, a lookahead optimization was proposed to not only optimally schedule the EWMG but also figure out the optimal energy level of storage systems at the end of the first day. Lastly, a hybrid info-gap/robust uncertainty management approach was proposed to tackle the PV power and electricity market intermittencies. The presented methodology was successfully carried out on a real test system. According to the obtained results, the implemented energy-water storage systems accounted for a 4.03% total cost reduction. Moreover, the multi-energy demand response (DR) and vehicle-to-grid (V2G) capable electric vehicle parking lots (EVPL) declined the total cost by about 1.83% and 0.69%, respectively. In addition, the look-ahead scheduling comprised about 0.43% of the total cost reduction.
Finally, an after-the-fact analysis of the proposed hybrid info-gap/robust technique and comparison with scenario- This work can be further extended by modeling other energy networks, such as district heat and cooling, incorporating more and accurate limitations. In addition, there is space for extension in terms of uncertainty management to model other uncertain parameters and introduce a linear optimization problem.