1. Introduction
The term water–energy nexus (WEN) describes the interdependence of water and energy systems. Considering a smaller scale, the micro water–energy nexus integrates the electrical network and the water network to act as a single entity in a microgrid. This interdependence has become increasingly important as the world faces challenges such as population growth, urbanization, and climate change, which pressure water and energy systems. As the world’s population is projected to increase by 2 billion people by 2050, leading to an increased demand for water and electricity, approximately 40% of the world’s population is anticipated to suffer from the issue of water scarcity [
1]. Consequently, water and power operations and systems must be planned simultaneously, considering the water–energy nexus in decision-making and developing integrated water and energy management strategies to address these challenges. This entails investigating ways to optimize the use of water in energy production, enhancing the energy efficiency of water infrastructure, and creating integrated water and energy management techniques that can help ensure a sustainable and resilient water–energy system [
1,
2,
3,
4].
The integration of thermal desalination of seawater in combined-cycle power generation plants (CCPPs) has been indicated as a promised enhancement in power generation and water desalination. However, in order to minimize the operational cost of the WEN system and optimize the utilization of energy resources fed to the power plant, advanced resource management must be developed.
The UAE has limited natural water resources and uses desalination as the dominant technology to make seawater potable. Thermal desalination and reverse osmosis (RO) are the two leading desalination technologies [
5,
6,
7]. Thermal desalination has two primary types, namely, multi-effect distillation (MED) and multi-stage flash (MSF) distillation, which are conventionally a part of a combined-cycle or a cogeneration power plant [
8]. Cogeneration is a system that utilizes one primary energy source to produce two or more useful forms of energy at once. For example, in a combined-cycle gas turbine (CCGT), a gas turbine converts mechanical energy into electricity and exhausts waste heat, which a steam turbine uses to generate additional electricity [
9,
10,
11,
12]. The steam turbine produces electric energy and supplies a tremendous amount of low-pressure steam [
13]. As thermal energy is an essential energy input to produce freshwater, the MED and MSF desalination processes and electricity generation are integrated on the same site with the aim of satisfying demand from water and electric energy, respectively.
Thus, the thermal desalination of seawater supplies the majority of residential and industrial water needs in the UAE. Consequently, electricity generation is associated with water production from the combined-cycle cogeneration thermal plants. Currently, during winter, when the electric demand is severely reduced, the UAE has to operate its power plants at low efficiency to be able to meet the water demand that stays almost the same throughout the year, as shown in
Figure 1. The major target currently is to decouple electricity and water production by phasing out the cogeneration plants and shifting from thermal desalination to RO.
Several water–energy nexus concepts have been investigated in the literature to model the integration and co-optimization of electrical and water networks. The authors of [
14] use Bender’s decomposition method to model a robust two-stage operation that manages the water–energy nexus system at the distribution level to reduce the operational cost. However, the work assumes that the electrical, gas, and water networks are owned by a single entity. An optimization model is designed for integrated water and electricity systems for a remote island that does not have access to the utility networks to fulfill the electricity and water demands with three different desalination technologies, including MED, MSF, and RO [
15].
In [
16], a new optimization model is proposed to minimize the operational costs of an integrated water–energy nexus system where wind turbines generate power and RO desalinates water. This work simplifies the mixed-integer non-linear programming (MNLP) model and utilizes General Algebraic Mathematical Software (GAMS 42) to attain results with greater accuracy. Considering the uncertainty arising from wind generation outputs, the work in [
17] proposes a robust operation model for a multi-energy WEN in which the energy system involves natural gas transmission, district heating, a power transmission network, and a water distribution network (WDN).
Also, in [
18], Moazeni and Khazaei develop a co-optimization MNLP model by combining the wastewater treatment plant’s demand response and the residential loads in the smart grid’s economic dispatch. The proposed model minimizes the amount of energy consumed by the wastewater treatment plant and the cost of the generated power of the smart grid, resulting in high-quality treated wastewater. In [
19], the authors introduce the integration of water desalination within security-constrained unit commitment (SCUC), which significantly minimizes the system’s operational cost, especially with the enormous desalination size. As the water–energy nexus concept is mainly applied at the supply side, in [
20], the work considers the interconnections between water and energy demands in a reservoir to propose new supply-side management of optimal and smart hydro reservoirs and uses advanced neural networks to predict two different scenarios that simulate the annual operation and remote monitoring situations.
Several WEN approaches are investigated on the demand side. For instance, Fooladivanda et al. [
21] emphasize the importance of pump scheduling and energy and water flow optimization. They propose a mixed-integer second-order cone programming (MI-SOCP) relaxation to handle the non-convex terms produced by the hydraulic characteristics of the pumps and pipes. Similarly, Mkireb et al. use mixed-integer linear programming to model variable-speed pumps to enhance the demand response and manage the uncertainties of the water demand [
22]. However, it is noted that the authors of [
23,
24] discuss the water distribution system scheduling and operation without considering the coordination with the electrical systems. Atia and Fthenakis introduce active-salinity-control RO to enhance the integration of renewable energy and desalination loads, but they ignore the uncertainties of the demand response [
16].
To minimize the total operational cost and to serve the extra wind power systems, using MI-SOCP, the authors in [
25] develop a model that integrates electrical, heating, and water systems. Likewise, a model that optimally schedules water tanks and pumps was developed in [
26] to collect renewable energy from the electrical grid. The model proposed in [
27] optimizes the participation of RO desalination in the energy demand response and regulation markets, yet it ignores the constraints of the electrical system. A method that modifies the electric grid economic dispatch is proposed in [
28] to include a water system by focusing mainly on the cogeneration of electricity and water from fossil fuel plants; however, this work ignores the network structure and other cooperation aspects. The models proposed in [
25,
26,
27] investigate the potential demand response of the water network as an electric demand, yet the water production is not linked to the electrical system.
Furthermore, the work in [
29] uses a robust optimization technique (ROT) to model the uncertainties in the water and electrical demands of a WEN system that mainly consists of combined water power (CWP) and single water and power energy resources. In [
30], the multi-period optimization formulation includes optimal WEN in an integrated power generation and desalination systems’ design and operational strategies while considering seasonal variations in water and electrical demands and fuel availability and prices. Deploying renewable energy technologies, the authors of [
31] incorporated solar collectors and batteries into the same WEN’s model introduced in [
30] with the aim of reducing the carbon footprint. A novel optimization model is introduced for a water–energy nexus-based CHP operation to investigate the relationship between system operation optimization and water conservation [
32]. Similarly, a scheduling model is proposed for the optimal operation of a combined power and desalination (CPD) system, considering MSF, RO, thermal power plants, and water storage simultaneously [
33].
Based on the aforementioned discussion, it is clear that the developed WEN models lack the details needed for the design and operational variables of the integrated system. Moreover, the majority of the literature focuses heavily on the electric aspect of the system and includes minor details about the water network and the desalination processes. On the contrary, the literature that deeply tackles various desalination processes does not link water production to the electric system. Most importantly, it is clearly noted that the existing literature ignores the network structure and other integration aspects of the cogeneration of electricity and water from thermal power plants. Also, they did not respect the flow limitations and the effort variables, such as pressure and voltage at network nodes. This work builds explicitly upon previous related works to address these aspects and considerations.
To fill the research gap in the literature, a more detailed co-optimization mathematical model for a generation-level micro-WEN system is developed, considering more variables and more complex interactions between system components. Accordingly, the proposed co-optimization model quantifies the mass and energy streams of the cogeneration plant, considering several plant variations. The proposed system focuses on attaining optimum design values and operating conditions for the micro-WEN system while minimizing the total annual and operational costs, respectively, and satisfying the electrical and water demands. Several case studies are performed to validate and evaluate the effectiveness of co-operating and co-optimizing the two systems simultaneously.
The major contributions of this paper can be summarized as follows:
Proposing a new dynamic co-optimization framework for the design and operation of a micro-WEN system that meets the demands of the electrical and water networks at a minimum cost.
Decoupling electricity and water production and shifting to a more sustainable water desalination technique.
Optimizing the micro-WEN system over multiple timescales to provide solutions with a significantly smaller memory size and less computational time.
2. Problem Description
The schematic diagram of the proposed micro-WEN system is shown in
Figure 2. On the electricity side of the micro-WEN system, a generation network is established and seamlessly integrated with renewable energy sources. This integration enables the system to harness the power of various renewable resources, such as solar or wind, to generate electricity. The availability of renewable energy plays a crucial role in enhancing the system’s sustainability by alleviating the reliance on fossil fuels for desalination and reducing carbon emissions and environmental impact.
At the core of the micro-WEN system lies a CCPP, which serves as a key power generation unit. The CCPP efficiently converts fuel into electricity using both a gas turbine and a steam turbine, maximizing energy output from the available resources. Moreover, the waste heat produced during electricity generation is not wasted but instead redirected to the thermal desalination side of the system.
The water side of the micro-WEN system comprises a thermal desalination system, the MED, that utilizes the waste steam generated by the CCPP. In the MED process, seawater is heated in multiple evaporator stages, each operating at progressively lower pressure. The resulting vapor is condensed to produce freshwater, while the remaining brine is discharged. Additionally, to further enhance freshwater production and system flexibility, an RO desalination plant is also integrated into the water side of the micro-WEN system. The RO process involves pressurizing the feedwater against a semi-permeable membrane, separating salts and impurities from the freshwater production based on specific water source characteristics and demand patterns.
To facilitate the overall operation of the micro-WEN system, a reservoir is incorporated into the water side. Following the desalination processes, the produced freshwater is then stored in a strategically positioned reservoir. This reservoir plays a pivotal role in supplying a stable and continuous feed of freshwater to the water network, satisfying the water demand of consumers, and ensuring consistent water availability even during fluctuations in the desalination processes or water consumption patterns. While a typical water network includes pipe networks, pumps, and tanks, these elements are not explicitly considered in this work. The primary focus of the micro-WEN system is to examine the interaction and integration of the electricity generation and water desalination components, emphasizing the seamless collaboration between renewable energy utilization and sustainable freshwater production.
4. Results and Discussions
This section discusses the simulation results of the proposed approach, which was tested using the IEEE 24-bus generation system, as shown in
Figure 5. The system includes 24 nodes, 24 thermal units, and 38 transmission lines. The capacity of the IEEE 24-bus system is 2890 MW, with a maximum demand of 2850 MW, as shown in
Figure 6, illustrating the generated power at each bus.
Two possible approaches are introduced to optimize the design and operation of the proposed micro-WEN system based on the previously discussed mathematical models. First, for optimal design, we minimize the total annual cost of the developed micro-WEN system by co-optimizing the design of the CCPP and MED systems while meeting the daily electrical and water demands. Secondly, shifting to RO, the proposed micro-WEN system is co-optimized to achieve the minimum total operational cost, both with and without a PV system, for optimal system operation. The NLP optimization models and solving approaches are implemented in the GAMS modeling environment and solved using the CONOPT solver.
4.1. Performance Evaluation of Proposed Approach
Before optimization, model variables in the following model are initialized to values in recent related works to acquire feasible initial solutions that satisfy mass and energy balances in each component of the MED system and the CCPP. In the development of the simulation model, no objective function is initially considered. Instead, the feasible solution obtained for the model is used as an initialization point for minimizing the total annual cost of the micro-WEN system. The model variables for the CCPP and MED systems are bounded by lower and upper bounds from the recent related literature, as listed in
Table 1.
Applying the co-optimization approach,
Table 2 summarizes the optimal design values of the MED system and the CCPP that meet typical daily electrical and water load demands. The optimal operating conditions of all flows, such as mass flow rates, temperature, and pressure, are summarized in
Table 3. Most importantly, the results in
Table 2 and
Table 3 strongly align with findings in the existing literature and previous works, confirming the feasibility of the proposed approach.
The optimal distribution between the capital investment and operating costs, leading to the minimal total annual cost of the micro-WEN system, is presented in
Table 4, with ‘M’ denoting millions. The simultaneous co-optimization of both power and water aspects in the micro-WEN system offers a significant advantage. The observed reduction in computational time and cost, compared to independent optimization approaches typically used in the literature, showcases the efficiency and practicality of the proposed co-optimization approach.
To meet the demand in both the energy and water sectors, the cogeneration unit is designed with capacities of 145 m
3/h for water and 150 MW for electricity. Maintaining the same design specifications and operating conditions of the micro-WEN system, different case studies are investigated to estimate the number of cogeneration units needed to replace the generating units in the IEEE 24-bus system. These studies consider different percentages of the electricity consumed by the residential sector. According to [
45], UAE residents typically use approximately 0.55 m
3 of water and 25 kWh of electricity per day.
In the UAE, the consumption of the residential sector in Abu Dhabi constitutes 26.8% of the total consumption [
46]. Considering 26.8%, 50%, and 100% of the residential electricity consumption,
Table 5 summarizes the number of households that the electrical system can serve, their daily water consumption, and the corresponding number of cogeneration units meeting the water consumption needs. As shown in
Table 5, five cogeneration units totaling 750 MW capacity are needed to meet the water demand of 30,984 households. Consequently, as shown in
Figure 7, the generating units at buses 15, 22, and 23, with capacities of 82 MW, 300 MW, and 360 MW, respectively, are replaced by five cogeneration units located at buses 5, 15, 19, 22, and 23.
An increase in the number of households leads to a proportional increase in the required number of cogeneration units to meet the daily water demand. Thus, to meet the water demand of 57,806 households at 31,793.3 m
3/day, seventeen cogeneration units are required. Consequently, as shown in
Figure 8, seventeen cogeneration units are added, replacing all generating units of the IEEE 24-bus system except for the generator at bus 23.
To satisfy the electrical and water demands of an area comprising only the residential sector, twenty cogeneration units are installed, replacing all the generating units in the electrical network. Their locations are indicated in
Figure 9.
4.2. Effect of PV Integration
This subsection discusses the integration of a renewable energy resource into the generation network to assess its impact on meeting the electrical and water demands that the cogeneration unit should fulfill. Therefore, a 50 MW PV system is incorporated into the proposed micro-WEN system, located at bus 17.
To compare the 26.8% variation in the generated power at each bus before and after integrating the PV system into the proposed micro-WEN system serving households,
Figure 10 and
Figure 11 represent the hourly generated power at each bus and the hourly output power of the PV system, respectively.
As presumed, with the addition of the PV system, it can be inferred that the generated power at the buses hosting the cogeneration units decreases between 9:00 am and 5:00 pm when the PV system supplies power to the electrical network. If a PV system of sufficient size generates the same amount of electricity as a cogeneration unit, it can lead to the shutdown of the cogeneration unit. In such a scenario, the freshwater produced by the cogeneration units may not meet the water demand. To address this problem, we propose decoupling electricity and water production by gradually phasing out the cogeneration units and shifting to the reverse osmosis desalination technique.
4.3. Shifting to Reverse Osmosis (RO)
As previously discussed, if another source supplies the same amount of electricity that the cogeneration unit generates, it can result in its shutdown. In that case, the freshwater produced by the cogeneration units will not meet the water demand. Thus, this work proposes to shift to more sustainable water desalination and decouple electricity and water production. The best approach is to shift from thermal desalination, which consumes a significant amount of electricity, to RO. Nevertheless, any renewable energy resource, such as a PV system or a storage system like a battery, may provide this electricity to produce water. As a result, water desalination will not rely on thermal energy from the CCPP.
The optimization model defined in (60), incorporating a simple mathematical model of the RO desalination process reported in [
31,
41], is employed to obtain the optimal design values for an RO system that meets a typical daily water demand at a minimum cost. The corresponding values are reported in
Table 6. The reservoir has an initial capacity of 190.25 m
3 and is supplied hourly with a constant permeate of 145.48 m
3. Consequently, as shown in
Figure 12, the RO system satisfies the water demand regardless of whether it is integrated with a PV system or cogeneration units.
This work considers seasonal variations as the electricity demand varies depending on the season. It displays the year as four days, for a total of 96 h slots, where each day represents a season and constitutes 24 h slots. The normalized electrical demand of each season sample day is shown in
Figure 13. Also,
Figure 14 presents the hourly output power of the PV system across different seasons—winter, spring, summer, and autumn. It is evident that the output power of the PV system reflects the fluctuations in solar irradiance. The water pump consumes 887.144 kWh of electricity and pumps feed at a rate of 362.75 m
3/h to meet the water demand. On that account, considering a unity power factor, the reactive power is compensated in the water pumps of the RO system.
The addition of the water pump at bus 7 initially boosts power generation, but the subsequent inclusion of a PV system reduces it as the PV system contributes extra active power to the electrical network, as shown in
Figure 15.
4.4. Optimal Operation of a Micro-WEN System with RO
As summarized in
Table 7, the proposed co-optimization model in (60) yields the optimal operating conditions for the RO system using the mathematical model of the RO desalination process that is presented in [
31,
41].
Table 8 highlights the minimum operating cost of the proposed micro-WEN system, both without and with a PV system. Also, the total operating cost of the micro-WEN, with the RO system replacing the cogeneration units to satisfy the water demand, is defined. As a result, according to
Table 8, co-optimizing the overall system with PV saves approximately USD 0.01 M, and shifting from the cogeneration units to the RO system results in a 26.7% reduction in the total operational cost of the proposed micro-WEN system.