Optimization of the effective volume of urban sewage pumping station based on the fuzzy optimization method

The sewage pumping station plays a crucial role in water pollution treatment, serving as an indispensable component of municipal drainage systems responsible for collecting and discharging urban wastewater. The sewage pumping station has the characteristics of a single large discharge and long seasonal operation time (Gong & Zhu 2022). The operation of the system is almost entirely driven by electricity (Rinas et al. 2018), with pumps as the main power system, in constant operation, the load will gradually increase, and the corresponding energy consumption will increase. Although reducing the power output of the pump can reduce the loss rate, it will also increase the maintenance cost. According to statistics, the energy consumption of sewage pumping stations accounts for 20–30% of the sewage treatment system, which has brought heavy operating costs to enterprises (Badruzzaman et al. 2016).

At present, the optimization research of sewage pumping stations mainly focuses on the optimization of pump start-stop times (Ostojin et al. 2011) and energy consumption (Piri et al. 2021), which mainly involves algorithms and control strategies. Darsono & Labadie (2007) adopted the optimal control system based on a neural network to realize the optimal coordinated scheduling of discharge in the dynamic combined pumping station system and achieved good results in the local pumping station. Gorjian Jolfaei et al. (2019) proposed a new intelligent controller that generates pump switching commands through a series of rules, which is applied to Infoworks ICM and its built-in RTC editor, reducing daily power costs by 21% compared with traditional controllers. Improving conventional switching to achieve energy optimization and cost savings is a major challenge. Nonetheless, an effective pump scheduling program is a viable and economical way to save pumping costs. This is because there is no need to destroy existing infrastructure and existing pumps and piping can still contribute to our daily water supply.

Wang et al. (2021) took the time-varying electricity price as consideration, selected the number of units operating at each pumping station as a decision variable to establish a pumping station optimization model, and solved it with integer programming, which has significant economic benefits. Dadar et al. (2021) proposed a genetic algorithm optimization and used MATLAB software to verify the relationship between pump running time and flow rate under optimal energy consumption, which improved the power consumption efficiency of the pump and reduced the energy consumption by about 15 ∼ 20%. Yi & Wenhao (2023) set the research goal of minimizing the operation cost of a pumping station within the drainage cycle, combined with a genetic algorithm, and established a nonlinear mathematical model. Taking the Guazhou Pumping Station in Yangzhou, Jiangsu Province as an example, by optimizing the start-stop times of the pump, the electricity cost of the optimized scenario was respectively saved by 15.34 and 4.40% compared with the conventional scenario. Makaremi et al. (2017) proposed an adaptive NSGA-II algorithm for pump optimization with multi-objective constraint by using energy cost minimization and pump switching minimization as two objective functions. In the optimization process, a trade-off is made between the energy costs and the total number of pump switches, so that the total energy consumption is concentrated mainly in the medium load period and secondly in the low load period. They concluded that the total number of pump switches can be reduced by 69% while the energy cost increases by up to 10%. The above strategies have succeeded in increasing the computational efficiency of the applied optimization algorithms while providing computational tools for real-time applications, concurrently, the algorithms in question are becoming increasingly intricate. Currently, the research in multi-objective optimization is limited, particularly in terms of balancing competing objectives. The primary aim of the multi-objective model is to enhance the trade-offs between energy consumption and maintenance costs. The optimization process for pump scheduling seeks to equilibrate these two factors effectively, balancing energy costs against pump maintenance expenditures.

With increasing urban populations leading to rising sewage discharge volumes, the economical operation of sewage pumping stations becomes ever more critical in reducing enterprise costs. This study selected a residential area in Ningbo City as the study area, modeled the sewage network using Infoworks ICM software, and gathered data on the electric power consumption of the pump, electricity price standards, pump station drainage, pump start-stop times, and manhole flood depths. In order to minimize energy costs and maintenance costs associated with the pumping station, it is imperative to take into account the flood depth of the manhole, to ensure that the normal operation of the drainage system, and the emergence of overflow events. Consequently, the daily electricity cost, pump start-stop frequency, and flood depth are designated as preferred objectives. By integrating single-day electricity price fluctuations, study area sewage discharge patterns, and drainage network topologies, this study employed the fuzzy optimization method (Zadeh 1965) and multi-objective optimization methods (Bellman & Zadeh 1970) to analyze and optimize the effective volume of sewage pumping stations (Barán et al. 2005), aiming to decrease operational costs associated with sewage pumping stations.

Infoworks ICM software uses the one-dimensional hydrodynamic model to simulate the hydraulic conditions of domestic sewage, industrial wastewater, and other wastewater in sewage pipelines, which can output simulation data so that the hydraulic condition of existing or designed sewage networks can be evaluated, providing a data-driven effort for the optimization of sewage pumping station.

According to the physical exploration data, part of the as-built drawings and on-site research data, standardized data entry and topology correction are carried out to ensure the accuracy of the data and the connectivity of the system through repeated inspections and realize the establishment of the pipe network model. Based on the basic data of the drainage pipe network, sub-catchment division is carried out using the Tyson polygon method, and sewage events are set up based on the amount of sewage discharged by residents in the study area and the daily sewage change coefficient.

Optimizing sewage pumping stations involves various considerations, such as managing the daily electricity costs, minimizing pump start-stop times to prolong equipment lifespan and reduce maintenance expenses, and maximizing drainage system storage capacity while preventing overflow incidents. Consequently, sewage pumping station optimization presents a multi-objective challenge (Yagi & Shiba 1999) that necessitates multi-objective comparative analysis to transform it into a single-objective optimization task (Wang et al. 2023). In this research, utilizing the fuzzy optimization method (Shan et al. 2021), the daily electricity cost, pump start-stop frequency, and flood depth are designated as preferred objectives (Borges et al. 2016), and different effective volumes of the pumping station are assessed to categorize options and calculate the relative superiority of each (Zimmermann 2011). The scenario exhibiting the highest relative superiority (Woldt et al. 1996) is chosen as the optimal solution (Huo et al. 2023), leading to the identification of the most efficient and effective volume for the sewage pumping station.

The calculation of the relative superiority includes the following steps:

The data of the evaluation indicators are the target eigenvalues. K in the matrix X_mn represents the result data set of selected evaluation indicators obtained by simulation calculation for each scheme, that is ⁠. L in the matrix X_mn indicates that for each selected evaluation indicator, the resulting data set of the evaluation indicator obtained by the simulation calculation of all schemes, that is ⁠.

Table 1 lists all the simulation cases in this study, of which Case A1 is used to study the actual sewage flow in the area and the optimization of the effective volume of the pumping station reservoir. Cases Bs and Cs are used to study the effect of pump flow on the effective volume of the cistern; Cs to Es are used to study the effect of population size on the effective volume of the cistern of the sewage pumping station. For conditions As to Es, three different sewerage network volumes are set to study the effect of sewerage network volume on the effective volume of the sewage pumping station.

The Infoworks ICM software was utilized for simulating and analyzing the drainage system within the study area. This simulation aims to provide insights into the drainage conditions of the pumping station, including pump start-stop frequency and flooding depth under varying effective volumes of the sewage pumping station reservoir. Additionally, local time-based tariffs are integrated to calculate the daily electricity expenses associated with operating the sewage pumping station. The daily electricity cost comprises the total electricity consumption during a day of pump operation. This calculation considers the electricity price based on local time-based tariffs and charges, where the electricity consumed per pump operation cycle is computed as f = W × t × c, where W represents the electric power consumption of the pump and c denotes the unit electricity price during pump operation. Flood depth signifies the water level in manholes, a fixed manhole in the drainage network selected for this study; the maximum flood depth of this fixed manhole reached in the operating cycle was determined to calculate; any flood depth of manhole in the drainage network equal to or greater than zero triggers a bubbling event, which has been omitted from the data summary in this study. The wastewater pumping station functions on a seven-day cycle, necessitating all parameters to be evaluated and compared based on a single cycle.

In the study area, continuous sewage discharge leads to an increase in flood depth in manholes and water levels in the pumping station reservoir when the pumping station ceases operation. As sewage discharge rises, these levels escalate until they reach the start pumping level, prompting the pumping station to commence sewage discharge. Consequently, flood depths in manholes and reservoir levels drop significantly upon pump activation. On a particular day, the pumping station began operations four times correlating with substantial flood depths at the start pumping level. Pump start and stop times throughout the day exhibit non-uniform distributions, influenced by variations in daily sewage volume within the region. Notably, during the transition from the 1st to 2nd stoppage, the coefficient of variation for sewage exceeds 1, indicating higher variability compared to the subsequent transition. This implies that sewage flow in the former period surpasses that in the latter one. The sewage dynamics within the service area profoundly impact pumping station operations. During peak sewage periods, the drainage network experiences rapid elevation, necessitating more frequent pumping station operations.

Following consultations with pertinent practitioners and experts, as well as an analysis of relevant data, the prioritized ranking of the three assessment criteria is as follows: It is observed that the daily electricity cost carries greater importance compared to the number of pump start-stop frequencies, whereas flood depth serves as a metric for assessing overflow risks and holds lower significance than pump operations. After trial calculations, we concluded that the results are convergent with daily electricity cost of the pumping station (u₁₁ = 0.8), number of pump starts and stops (u₁₂ = 0.7), and flood depth (u₁₃ = 0.8). Substituting these values into Equation (6) results in W′ = (1, 0.42857, 0.25). Upon normalization, the weight values for each target become W = (0.5957, 0.2553, 0.1489). Equation (8) is then applied to compute the relative superiority degree for each scenario.

Utilizing data from the existing drainage system, pump flow characteristics, total service area population, and drainage network volume are examined as key factors for optimizing the sewage pumping station reservoir effective volume. Cases As–Es used in this section are shown in Table 3. Within this study, the drainage network volumes were determined to be 29.90, 39.12, and 43.94 m³ for sewage pumping station effective volume optimization scenarios. Ensuring that the effective volume exceeds the maximum 5-min water discharge of the largest pump, Case Bs with a pump flow rate of 0.094 m³/s falls within an effective volume range of (28.20, 47.45). Conversely, Cases Cs–Es with pump flow rates of 0.070 m³/s are associated with effective volume ranges of (21.00, 47.45). The electric power consumption of the pump varies based on different flow rates (0.118, 0.094, and 0.070 m³/s) and corresponding power ratings of 45, 41, and 36 kW, respectively. By applying the fuzzy optimization method to optimize the pumping station's effective volume across all operational conditions, the optimal scenario for each case can be identified.

During periods of pump inactivity at the sewage pumping station, the continuous discharge of sewage by residents causes both the drainage network and pumping station reservoir levels to rise. In the optimal scenario, when the pump flow diminishes, the effective volume of the pumping station decreases correspondingly. Under consistent sewage discharge conditions, faster pump activation leads to decreased reservoir levels at the pumping station and subsequently lower water levels within the drainage network. A smaller effective volume for the pumping station correlates with a reduction in the maximum flood depth of the drainage network.

This study leveraged the InfoWorks ICM software to simulate the sewage network within the study area, focusing on analyzing and optimizing the effective volume of the sewage pumping station reservoir. The optimization process integrated the fuzzy optimization method and a multi-objective optimization method, considering variables such as daily electricity price fluctuations, service area sewage discharge patterns, and drainage network topologies. By addressing pump flow, total population, and drainage pipe network volume, a sensitivity analysis was conducted for sewage pumping station reservoir effective volume optimization, leading to the following conclusions:

• 1. Applying the fuzzy optimization method involved weighing factors such as upstream drainage network topology, daily drainage variations, electric power consumption of the pump, electricity cost kurtosis, and sewage overflow risks. By assigning weights to each optimization objective and selecting the option with the highest relative superiority degree as the optimal scenario, the ideal effective volume for the sewage pumping station reservoir could be determined.

• 2. Under standard drainage system operations without overflow incidents, implementing the optimization scenario resulted in substantial cost savings for the pumping station, with up to a 15.89% reduction in daily electricity expenses and a 13.33% decrease in pump start-stop times. This optimized approach effectively lowered sewage pumping station operating costs while streamlining the effective volume optimization process.

• 3. The study revealed that the optimal effective volume of the pumping station correlates positively with increased pump flow rates, drainage network volumes, and total service area populations.

The authors gratefully appreciate the financial support from the National Key R&D Program of China (No. 2022YFC3203200), the Ningbo Key R&D Programs and ‘Listed and Commanded’ Projects (No. 2023Z216), and Project on Technical Study on Operation Assessment and Optimization of Stormwater and Sewerage Pumping Stations.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.