Energy-efficient and reliable coordinated scheduling for water distribution systems: enhancing hydraulic conditions and water quality

Urban water distribution systems (WDSs) play a critical role in ensuring safe and reliable water supply to cities (Singh & Kekatos 2020; Tsegaye et al. 2020). As urbanization continues to expand and climate change introduces new challenges, the need for robust and efficient WDS scheduling becomes increasingly urgent (Pereira et al. 2020; Vieira et al. 2020).

In the realm of urban water management, the optimal scheduling of WDSs stands as a critical component, ensuring the efficient delivery of water resources while maintaining the integrity and sustainability of urban water infrastructure (Shamir & Salomons 2008; Pu et al. 2023; Sukri et al. 2023). Effective scheduling not only safeguards against potential disruptions in the water supply but also plays a pivotal role in minimizing energy consumption and improving the reliability of the water supply, which are of paramount importance given the growing demands and complexities of urban water networks (Mala-Jetmarova et al. 2017). Optimal scheduling of WDSs will improve customer satisfaction while reducing operating costs and promoting sustainable urban development under the increasing water demand of cities (Wu et al. 2015; Bachtiar et al. 2023; Parvaze et al. 2023).

The optimal scheduling of WDSs involves the strategic management of various system components to achieve specific objectives (Thomas & Sela 2024). These components include the operation of drinking water treatment plants (DWTPs) and pump scheduling, which are the primary decision variables in the scheduling process (Bonvin et al. 2021; Xu et al. 2022). The scheduling objectives are multifaceted, often focusing on minimizing operational costs, ensuring water quality, and maintaining system reliability. However, these objectives are subject to a range of constraints that reflect the physical and operational limitations of a specific WDS, such as water demand satisfaction, pressure and flow requirements, and equipment capacity limits (Broad et al. 2010; Hu et al. 2023).

One of the primary directions in optimal scheduling is the minimization of energy consumption, which is closely associated with the operation of pumps within the system (Fooladivanda & Taylor 2018; Bonthuys et al. 2019). Pump scheduling optimization, in particular, has been a focal point for researchers, as it involves determining the optimal timing and sequencing of pump activations to meet water demand while minimizing energy use (Barán et al. 2005; Stokes et al. 2015; Nogmov et al. 2023).

Another direction in optimal scheduling is water quality optimization with several aspects considered in the literature (Mala-Jetmarova et al. 2018). These include the optimization of disinfectant dosages to maintain a residual concentration throughout the network, the scheduling of booster disinfection stations to improve water quality (Moeini et al. 2023), and the real-time control of WDSs to minimize water age and associated disinfectant byproducts (Price & Ostfeld 2016; Xin et al. 2016; Boindala et al. 2023). Other studies have focused on the optimal location and operation of water treatment facilities within WDSs to improve water quality while considering operational costs (Smith et al. 2018; Gullotta et al. 2021).

The development of an optimal scheduling method that integrates energy efficiency, hydraulic security, and water quality enhancement requires a comprehensive understanding of the interplay among these factors. It also necessitates the use of advanced modeling techniques, robust optimization algorithms, and real-time monitoring systems (Shamir & Salomons 2008; Hu et al. 2023). The integration of water quality objectives into the optimization model could lead to tradeoffs between energy consumption and hydraulic performance, which must be carefully managed to achieve a balanced solution (Price & Ostfeld 2016).

The coupling of energy consumption, hydraulic performance, and water quality within large-scale urban WDS presents a formidable challenge that necessitates sophisticated optimization techniques but has not been extensively addressed in the literature (Matsumoto & Miyaoka 1981; Sakarya & Mays 2000; Li et al. 2022). Although the development and application of advanced algorithms, such as genetic algorithm (GA) (Parvaze et al. 2023), ant colony optimization (López-Ibáñez et al. 2008), and particle swarm optimization (Dini et al. 2022), have been instrumental in addressing scheduling problems (Deb 2000; Qiu et al. 2020), the multiple objectives scheduling is time-consuming and inefficient for real-time control of water utilities (Xu et al. 2019).

In conclusion, the optimal scheduling of WDSs is a multifaceted problem that requires an integrated approach to balance the often-competing objectives of energy conservation, hydraulic reliability, and water quality enhancement. With the growing body of research in this area, it is crucial to develop innovative optimization methods that can effectively address these challenges and provide sustainable solutions for WDS operations. By integrating prior expert knowledge, this study develops an efficient and robust optimization method combining GA and multiple criteria analysis (MCA) which coordinates energy conservation, hydraulic condition improvement, and water age optimization in WDS.

The study was designed with a comprehensive methodology encompassing four key phases: data processing, where historical operational data from DWTPs was collected and preprocessed to form a solution dataset; model optimization, utilizing a GA to develop an optimal scheduling method that minimized energy consumption while ensuring water supply and pressure requirements were met; results evaluation, applying MCA to assess the performance of the optimized models based on energy savings, water supply with unsatisfied pressure, and water age; and extend period optimization of results analysis, interpreting the outcomes to provide strategic recommendations for 24 h operation of WDSs, demonstrating the method's effectiveness in real-world scenarios.

The WDS of City A, China, was used to apply the proposed methodology and analyze results. The City A municipal surface area covers over 775 km² and serves around 4,800 customer units, inclusive of residential and nonresidential customers. The daily water supply capacity of the WDS in City A is over 3 million cubic meters, with power consumption of about 700,000 kWh. Around 200 facilities, such as DWTPs and valves, are involved in the WDS.

This study used the hourly historical operational data of each DWTP from January, April, July, and October 2021, which includes four seasons of DWTPs' operational data. The dataset has a total of 141,696 entries, containing data points on energy consumption, water supply quantity, pressure, and pump efficiency of the corresponding DWTP.

Table 2 demonstrates the data related to energy consumption, water supply quantity, pressure, and pump efficiency of some DWTPs, which contribute more than 75% of the water supply quantity and 80% of the energy consumption of the WDS, ordered by their mean energy consumption. The coefficient of variation (CV) of pump efficiency, energy consumption, water supply quantity, and pressure are important indicators, displaying the fluctuations in the operation of DWTPs. The larger the CV, the greater the optimization potential of a DWTP. Notably, the pump efficiency of the DWTPs ranges from 10.46 to 98.99% with CV ranging from 0.022 to 0.168, which shows the great potential of choosing proper operational conditions to improve energy efficiency.

This study focused on the efficiency and feasibility of the optimization scheduling method of large-scale WDSs, and developed an optimal scheduling method for WDSs based on historical operational information to optimize the water supply quantity and water pressure of each DWTP in City A. As mentioned in Section 2.1.2, the pump efficiency of DWTPs varies greatly, so it is significant for water utilities to select appropriate operational solutions.

This study defined a discrete solution space, which linked each DWTP's water supply quantity, pressure, and energy consumption as a single feasible solution, and combined the solution space of all DWTPs for optimal scheduling decisions. This will significantly reduce the solution space of the commonly used GA-based optimal scheduling methods.

As shown in Figure 2, based on the historical operational data of the DWTPs, the top 50% of pump efficiency operational solutions were refined, and a solution-searching space was constructed. The corresponding energy consumption for each water supply quantity and pressure was obtained as a schema for optimization.

The objective was to save energy through hydraulic condition improvement and water age optimization. The method comprised two steps: (1) optimizing the DWTP operation with GA, and (2) evaluating the scheduling solution with MCA. The system boundary of this method was constrained by the DWTPs' water supply quantity and pressure.

The search for the optimal operation solution was based on GA. As an adaptive optimization algorithm based on ‘survival of the fittest’, GA begins to optimize the problem with an initial population consisting of N chromosomes or individuals. Through the evolution of the chromosome group from generation to generation, including reproduction, crossover and mutation, the algorithm converges to the individual with the best performance for the model, as shown in Figure 3.

The optimization steps were repeated until the fitness of the best individual remained unchanged for a certain number of consecutive generations, or until the predefined maximum number of generations was reached. The population size and maximum iteration number in GA were 300 and 100, respectively.

In the operation of WDS, pressure and water quality are major factors affecting the user experience, and guaranteeing a certain water supply pressure and quality is crucial for the reliability of the WDS. The scheduling solution must meet these pressure and quality requirements, which are vital evaluation criteria for the optimization algorithm. Therefore, in addition to the energy consumption explicitly expressed in the objective function, we also considered the volume of water supplied at unsatisfactory pressure and the water age as critical assessment indicators.

The continuity of the optimal scheduling scheme is essential for guiding the operation of the DWTPs. By generating a 24-h continuous optimization solution, we could demonstrate the optimization of the daily scheduling situation, and analyze energy consumption, water supply volume with unsatisfied pressure, and water age, respectively. To achieve this, we established the extended period solution generation workflow for the GA-MCA method.

In this study, we first established a baseline for water demand and system conditions by selecting a reference date: 31 October 2021. Next, we implemented the extended period solution generation method. The GA-MCA method generated n solutions per hour to identify the optimal scheduling solution. Each solution encompassed the searching space index for each DWTP. The hourly optimization process has been detailed above in Section 2.2. Concurrently, we calculated the benchmark values for energy consumption, water supply volume with unsatisfied pressure, and water age to facilitate solution assessment.

Subsequently, we conducted hydraulic and quality assessments to ensure the reliability of the WDS. This process eliminated solutions with higher water supply volumes with unsatisfied pressure and water age compared to the benchmark. Utilizing the ESR, UWDR, and WAR, we calculated the FS for each solution. The GA-MCA method then selected the solution with the highest FS.

Finally, based on the optimal 24-h solution, we created visualizations of the WDS optimization for energy consumption, water supply volume with unsatisfied pressure, and water age. These graphs were used to present the final outcomes of our study.

The method was implemented and tested on a laptop with an AMD Ryzen 7 7735H with a Radeon Graphics processor (3.20 GHz), 32 GB of RAM, 512 GB of SSD, and Windows 11 operating system. The algorithm ran in Python 3.9, which uses Scikit-learn, NumPy, Matplotlib, and Pandas among other related packages. In this study, EPANET provides the calculation engine for the scheduling method, while WaterDesk is used for depicting the hydraulic model map. During the GA-MCA method optimization, the hydraulic model was called Python Epanet-Toolkit.

Following the introduction of Section 2.3, we selected 31 October 2021 as the benchmark day, and input the benchmark water demand ⁠, the benchmark water supply volume with unsatisfied pressure and the average water age into the method for optimization and MCA. Subsequently, we used the 24-h extended period solution generation method described in Section 2.3 to obtain the optimal scheduling scheme for WDS.

In the case of the highest water supply quantity hour, plants 8 and 10 have relatively fixed optimization indices, while plants 3 and 7 have a more dispersed optimization region, indicating that in this optimization state, plants 8 and 10 obtain relatively stable water supply optimization, while plants 3 and 7 mainly cooperate with the optimization of the other plants. In the instance of the lowest energy consumption, the optimized index of plant 8 is highly concentrated, indicating that plant 8 achieves the lowest overall energy consumption by fixing the water supply at that point, which is also dependent on the total water supply quantity of the WDS. As for the water supply pressure, plants 2, 3, 6, 7, 10, and 15 present various pressure ranges during the optimization which reflects the scheduling potential of fine control. The pressure of plants 4, 5, 8, and 9 remains stable which demonstrates its priority of supply pressure.

In addition, Tables S2 and S3 in the Supplementary Material show the water supply quantity and pressure changes at the water plant before and after optimization at 10:00 a.m. and 2:00 a.m. According to the results, in order to improve the performance of WDS, plant 7 should raise its water supply quantity and pressure, whereas plant 14 should reduce its water supply quantity and pressure. This analysis could provide valuable advice for the operation and improvement of DWTPs.

The above analysis shows that in the 24-h extended period simulation, the decline in energy consumption, water supply volume with unsatisfied pressure, and water age are highly correlated with the water supply quantity and pressure of each DWTP. For different water supplies, we can evaluate the optimal performance of certain DWTPs by using a relatively fixed amount of water supply in combination with other DWTPs. This approach can guide the operation of the WDS and provide recommendations for different DWTPs, facilitating the scheduling of variable-speed pumps.

To validate the effectiveness of the method under different scenarios and demonstrate its ability to handle real-world, complex water supply network scheduling tasks, we conducted scenario analysis to determine how to optimize the WDS for scheduling under a surge in water use and a partial shutdown of the DWTPs.

In the summer of 2023, City A's water demand surged, posing a great challenge to the water demand of the WDS which achieved 4,184,880 m³ with a 29.6% increase compared to average demand. Accordingly, it is necessary to consider the water demand surge scenario. Therefore, we conducted this day's water demand as a scenario, reflecting the scenario of a water demand surge case, and the water demand of the WDS in each hour is shown in the Supplementary Material Table S3.

In this scenario, we obtained the 24-h extended period energy consumption, water supply volume with unsatisfied pressure, and average water age of WDS optimization results, which are shown in Table 3. Due to the water demand surge, the energy consumption rises and the flow rate increases, resulting in more head loss and less water age. As shown in Table 3, the energy consumption, water supply volume with unsatisfied pressure and average water age of the water demand surge reduces by 13.1, 5.7, and 2.9%, respectively, relative to the surge demand condition, and the energy consumption, and water supply volume with unsatisfied pressure increase by 15.4 and 0.5%, respectively, relative to the original condition. The results show the significant effect of GA-MCA optimization during the water demand surge scenario.

In this study, we presented an optimization method that integrates prior expert knowledge to reduce the solution search space. Additionally, because the prior knowledge includes pump station efficiency, the constructed solution space ensures that the optimized solutions exhibit high pump station efficiency. Nevertheless, this method must be considered in light of certain limitations. In the operational searching space, we obtained the historical schema as a solution, and the energy consumption is recorded corresponding to the water supply quantity and pressure. However, the operation of pump groups is also an essential factor affecting energy consumption due to the multiple combinations of fixed-speed pumps and variable-speed pumps. For example, the same water supply quantity and pressure with different pump groups could result in utterly different energy consumption which directly affects the pump efficiency. Limited by the database, the system boundary of the method was constrained by DWTPs' water supply quantity and pressure; hence, the operational state of the pump groups was not taken into consideration by the optimal scheduling method.

Moreover, the coordinating effect of energy conservation, hydraulic condition improvement, and water age optimization requires further research, which could take NSGA-III into consideration. Based on the location of DWTPs, each plant's contribution to reliability and robustness should be well identified, and specific optimal scheduling should be more appropriately introduced for the DWTPs.

In this study, the GA-MCA method was introduced, leveraging the high-pump efficiency operational solutions to enhance the efficiency and reliability of the WDS's optimal scheduling scheme, which coordinated energy conservation, hydraulic condition improvement and water age optimization in the WDS.

The effectiveness of the GA-MCA method is evident in large-scale WDSs, showcasing significant improvements in energy consumption, water supply volume with unsatisfied pressure, and average water age. In this study, we optimized the operation of 16 DWTPs in City A. As a result, the energy consumption of the WDS decreased by 23.0%, the volume of water supply with unsatisfied pressure reduced by 16.7%, and the water age decreased by 2.5% over a 24-h extended optimization period. According to the plant operation analysis under the optimal solution for the water supply quantity and pressure of each DWTP, we identified high-efficiency operation conditions. Specifically, plant 7 should increase its water supply quantity and pressure, while plant 14 should decrease both.

Furthermore, the GA-MCA method demonstrates its capability to excavate the energy conservation, hydraulic condition improvement, and water age optimization potential of WDSs. In scenarios involving water demand surges during summer, the GA-MCA method ensures that water supply volume with unsatisfied pressure and average water age remain lower than the standard condition. The water surge scenario would place a high-water supply burden on plant 8, necessitating further safeguards to ensure the reliability of the WDS in City A. In future research, pump groups should be considered essential scheduling elements and optimization constraints for practical application.

This work was financially supported by the National Key R&D Program of China (Grant No. 2023YFC3208100).

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.