Determination of economic loss levels in water distribution systems with different network conditions by a district stochastic optimization algorithm

Water losses, which consist of apparent losses and real losses, are one of the most fundamental problems faced by utilities (Farley & Trow 2003; Farley & Liemberger 2005). The service quality decreases, operating costs increase and network operating conditions deteriorate depending on the increase in water loss rate. Especially complex and old water distribution systems (WDSs) generally have high failure rates. Moreover, it is quite difficult and costly to detect, prevent and control unreported leaks in these systems (Lambert 2002; Farley & Liemberger 2005). The following works should be made for sustainable water loss management (WLM) in WDSs; recognizing and preventing the water losses, monitoring and controlling the system with information systems, analyzing and monitoring the system performance and defining the economic analysis standard (Firat et al. 2021; Bozkurt et al. 2022).

Globally, water loss rates in developing countries range from 24% to 45% (Kingdom et al. 2006). Water loss rate reports are published annually by the General Directorate of Water Management (SYGM) in Türkiye. Water loss rates in utilities (a total of 30 utilities) were around 34% in 2021 (SYGM 2022). In the reports prepared by the Turkish Water Institute (SUEN), the economic losses caused by water losses for utilities are approximately 7 billion TL (Turkish liras) (SUEN 2022). As can be seen, water losses do not only cause water resource inefficiency. They also create the costs of energy, apparent losses and real water losses. Therefore, reducing water losses is quite the important and critical issue.

Targets for water loss rates in all utilities are defined as 30% (in 2019) and 25% (in 2023) in the ‘Water loss prevention and control regulation’ published in Türkiye in 2014. However, since these defined targets could not be reached, the regulation was updated in 2019 and the targets were redefined as 30% in 2023 and 25% in 2028. Accordingly, it is understood that it is not realistic to set the same target for each utility. For this reason, the current conditions of the system, technical and personnel capacities should be considered in order to reduce the non-revenue water (NRW) to an acceptable level (Yilmaz et al. 2021).

The methods and processes used to manage the NRW involve direct economic costs. The main leakage detection and reduction methods (pressure management (PM), pipe material management (PMM), active leakage control (ALC) and failure management) require knowledge of the current network conditions and sufficient technological capacity (Lambert 2002; Frauendorfer & Liemberger 2010; Sechi & Zucca 2017). The basic equipment and devices (pressure reduction valves (PRV)) for PM and acoustic listening devices and regional noise loggers or correlators for ALC (Salguero et al. 2019), have been used for detection and reduction of water losses. However, the following question arises: ‘will the expenditures to reduce water loss be financially returned to the utility? (Firat et al. 2021; Yilmaz et al. 2022). Therefore, utilities should define the ideal water loss rate according to the current system status. The main issue in WLM is the definition of the economic leakage level (ELL) (Farley & Trow 2003; Pearson & Trow 2005; Islam & Babel 2013; Haider et al. 2019; Firat et al. 2021; Yilmaz et al. 2021, 2022).

The ELL can be defined as the NRW value at which the economically recoverable loss in a WDS equals the water production/sales cost. Reducing water losses in WDSs below the calculated ELL value will no longer be economical for utilities because the amount to be spent for loss reduction is more than the marginal benefit of the water to be obtained. Considering the current state of the network, economic conditions, costs and institution personnel, technical and financial capacity for the most appropriate loss level in WDSs will provide a more accurate approach (Deidda et al. 2014). The ideal loss level in systems where water production and network operating and energy costs are high will be lower than for gravity systems. Therefore, it is necessary to define the most appropriate water loss rate, i.e. the ELL value, according to the current network conditions (Wyatt & Alshafey 2012; Lim et al. 2015; Molinos-Senante et al. 2016; Haider et al. 2019). Various approaches based on mathematical and statistical methods are applied in ELL analysis (Choi et al.2015; Haider et al. 2019; Ahopelto & Vahala 2020; Moon 2020; Moslehi et al. 2020).

In the management of leakage in WDSs, the definition of the ELL is a real-time optimization problem based on the network characteristics (number of reported or unreported failures, number of leak detection and management teams, pressure limits and current situation), the requirements and constraints of prevention methods and their cost analysis (Firat et al. 2021). Utilities have applied methods that create high costs in order to reduce leaks, which is the most important problem in WDSs. A short-term ELL analysis model was developed for the ALC method, considering the cost components and field data. Model results showed that system operating pressure and infrastructure conditions directly affect the short-run ELL value (Moslehi et al. 2021).

Analyzing the operation pressure that can cause new failures or increase leakage volumes, defining the ideal operation pressure according to the network characteristic and defining the number of failure repair teams for failure management are the optimization variables. A model applying an optimization algorithm has been proposed in order to analyze the ELL, considering all the factors that cause failure and leakage, analyzing the effects, defining the costs and performing the cost–benefit analyses (Yilmaz et al. 2021). However, the budget allocated for the management of water losses in utilities is limited to a certain percentage of revenues. In other words, budget constraints should be considered for WLM practices (Yilmaz et al. 2022).

Considering the existing studies in the literature, network characteristics, water production and operating costs and the financial–technological–technological capacity of the utility should be considered in order to create a sustainable and long-term WLM plan. It is quite important that the ELL value should be analyzed for each system based on these parameters. For this reason, the aim of this study is to determine the ELL value with the optimization algorithm for the utilities with different network characteristics, water production and operating costs and institutional capacities. To achieve this aim, three pilot utilities with different system characteristics and water loss components were selected as application areas. The ELL values were analyzed and compared by considering real field data. Moreover, the leakage reduction methods (PM, PMM, ALC and failure management) that should be applied in these networks with different characteristics, depending on the calculated ELL values, were determined and the possible benefits for each method were calculated. Thus, in this study, the most appropriate water loss target (ELL) was defined depending on the characteristics of the network, the methods to be applied to achieve this target were defined and the potential benefits to be obtained from these methods (the amount of leakage saved to the system) were calculated.

Failures in WDSs occur due to various factors that cause operating conditions to deteriorate, increase costs, increase customer complaints and decrease service quality. In sustainable urban water management, it is quite important to reduce the failure rate and leakage amount, to ensure water and energy efficiency and to reduce investment and operating costs. Therefore, the most appropriate method should be applied to reduce the failure and leakage rates. The main methods applied in WLM are the district metered areas (DMAs) method (Alvisi et al. 2019; Creaco & Haidar 2019; Liu & Lansey 2020), minimum night flow (MNF) analysis (Hazelton 2019; Negharchi & Shafaghat 2020), leak localization and repair (Ociepa et al. 2019; Sophocleous et al. 2019) and material management (Salehi et al. 2017; Fridman-Bishop et al. 2019). The DMA approach is a method applied to manage water losses in distribution systems in a more effective and sustainable way. The main purpose of the DMA method is to obtain a controllable and manageable system that is isolated from other limited networks. In this method, system components are evaluated within themselves (Pearson 2019). The MNF analysis is a method applied to detect leaks in DMAs. In this method, the zone inlet flow is measured with a flow meter and potential preventable leaks are evaluated according to the inlet flow rates at the hour of the lowest consumption.

Although it is possible to monitor, detect, control and manage leaks by applying these methods, the requirements, limitations, investment and operation costs of the methods reach significant levels. Therefore, considering the operational components of the system, performing economic analyses for water loss components and defining the benefit and cost analysis model is quite important for effective and sustainable WLM (Mutikanga et al. 2013; Ezbakhe & Pérez-Foguet 2019; Jensen & Nair 2019; López et al. 2019). However, inefficient and costly investments are required to achieve the water loss rate targets defined for the utilities in WLM. For this reason, it is recommended that analysts determine the current conditions of the system and define the ELL by performing economic analyses in choosing the most appropriate prevention strategy (Lim et al. 2015; Molinos-Senante et al. 2016; Haider et al. 2019). Various approaches based on mathematical and statistical methods have been applied for ELL analysis (Choi et al. 2015; Haider et al. 2019; Ahopelto & Vahala 2020; Moon 2020; Moslehi et al. 2020).

It is a real-time optimization problem to determine the ELL value based on the network components and constraints (operating variables, leakage management team characteristics and minimum and maximum limits of pressure), the requirements and constraints of prevention methods and their cost analysis. The optimization parameters in the ELL model are the definition of the optimum values of the system operating pressure and the number of the failure management teams. Therefore, there is a need for an optimization-based model that considers all factors, defines cost components and is based on cost–benefit analysis in order to define the ELL.

It will not be possible to talk about water loss reduction methods and the ELL value for a system where the system's useful life was completed. Therefore, firstly, the useful life of the network should be calculated with the ELL model. The methods of PM and ALC are critical for the reduction of the water losses. However, the DMAs should be planned and implemented in the field in order to apply the PM and ALC methods. Therefore, the DMA implementation cost is considered a cost parameter in the ELL model.

In this study, the performance of the DSO method was also tested (as explained in Wang (2013)). The analysis steps of this algorithm can be given as follows (Firat et al. 2021):

• Step 1: Set an initial value to the current point and apply to objective function (Equation (5)) ⁠.

• Step 2: Generate a candidate solution (⁠⁠) randomly and calculate ⁠.

• Step 3: If then update solution ⁠.

• Step 4: If ⁠, where ε (epsilon) is a tolerance, stop search process, else increment iteration (n = n + 1) and go to Step 2.

In this model, an initial value for the OV vector is given. Then, the vector value is obtained by applying the objective function and the candidate solutions are tuned with the algorithm. This analysis can be continued up to a certain value or the maximum number of iterations (Ates et al. 2020).

In this study, three utilities are considered as application areas. In the selection of the regions, attention was paid to the differences in the basic characteristics of the network (main length, water production cost, number of customers, water loss amounts, etc.) and operating characteristics (pressure, failure densities, meter failure rates, etc.) (Table 1). Thus, it is intended to reveal that the ELL can be different depending on the network and system characteristics. The data for ELL in utilities were obtained from SCADA, geographical information systems (GIS), customer information systems and failure management systems.

The economic levels of NRW rates are 29% for System I, 16% for System II and 23% for System III. The economic level of NRW values varies between 16% and 30% in utilities, depending on the basic network and operating characteristics of the regions. Similarly, economic water loss rates were determined as 22% for System I, 16% for System II and 8% for System III.

The main reason for the differences in the economic levels of NRW rates determined in the pilot utilities is that the costs and benefits of the loss reduction methods and the current status of the networks differ, especially in System I, where water production costs are lower than in other systems. The fact that the economic level of NRW value is 29% reveals the effect of water production cost. It is seen that the investments made to reduce water losses in this utility will not provide economic efficiency after a certain point.

In System I, the operating pressure should be reduced from 55 to 46.36 m according to the results of the optimization model. In addition, this model suggests to increase the number of failure repair teams to 13 for effective leak management in this system. Similarly, operating pressure should be reduced from 45 to 31.5 m for leak management in System II. It is determined that the number of teams in this system is sufficient and should be kept constant. On the other hand, it is suggested by the model to reduce the operating pressure from 60 to 29.6 m in System III. It was also suggested that the number of leakage management teams should be increased to 29 for leak repair and management in this region.

The necessity of PM in all systems was revealed as a result of the analysis. It is understood that the average pressure of the regions should be reduced between 20% and 50%. It was observed that significant water losses can be reduced just by controlling the pressure in these systems, because the reduction in pressure not only reduces the losses due to existing failures but also has the ability to prevent possible losses by reducing the frequency of failure. Another water loss reduction method is the ALC method (covering the leak monitoring and detection). The results show that the ALC method will provide significant advantages in every system. This method, which gives more successful results in regions where the subscriber density per km is high and the pressure is above average, gives successful results in all three regions. The total benefits (reductions in seepage) obtained for all three utilities with the ALC method were calculated (Table 3 and Figure 2).

Management of failure repair teams is also an important issue for utilities. Although the establishment and operation of each team create a constant cost, it provides a serious advantage by shortening the failure resolution times in the failure management strategy. Shortening fault resolution times both reduces water losses and increases customer satisfaction level and service quality. For this reason, determining the ideal number of teams is necessary due to the influence of the economic and social effects in water management. The results showed that the number of teams in Systems I and III was insufficient and should be increased. In System II, the number of existing teams is optimum.

The application of the most basic methods in the field was foreseen in order to reach the economic levels of NRW volume and rate calculated by the optimization algorithm. The potential benefits (reduction in the amount of loss) that can be obtained depending on the implementation of basic water loss prevention methods are calculated (Table 4).

In System II, it is understood that no benefit can be obtained with team management since the number of failure repair teams remains constant as a result of optimization. Moreover, no benefit will be gained by replacing meters in this system due to the low rate of meters (0.28%) older than ten years in the current situation in this utility. In this system, the amount of leakage that can be saved by ALC is close to the value obtained from PM.

It is estimated that 296,000 m³/day leakage will be prevented by reducing the operating pressure from the current 60 to 29.6 m in System III. The most appropriate pressure level was determined in this system by considering the characteristics of the region, customer consumption behaviors, number of critical points and pressure requirements, regulation limit values, ALC and leakage management requirements. It is also understood that significant leaks can be prevented in this region depending on the application of the ALC method.

The method in which the most benefit is obtained in System I has been determined as ALC. Leakages can be reduced significantly depending on the implementation of PM in this system. The results show that the benefits to be obtained from water loss prevention methods may differ depending on the characteristics of the network. According to these results, before applying water loss prevention methods in distribution systems, current network conditions should be analyzed and potential benefits should be estimated. Moreover, the current network conditions should be considered to define the target for the water loss level in the system.

In this study, benefit and costs were calculated separately for the basic methods (Table 5). In this context, water production cost was used when calculating the benefits obtained with real losses and water sales prices were used when calculating the benefits and costs obtained with apparent losses. It is obvious that the utilities can gain significant benefits and increase water service quality and satisfaction with the application of water loss reduction methods. The results play a significant guiding role for utilities in calculating the economic levels of NRW.

In this study, ELL values were determined by the optimization algorithm for utilities with different network characteristics, water production and operating costs and institutional capacities. The NRW rates in these utilities are currently calculated as 57%, 50% and 37%, respectively. ELL values were analyzed by the optimization model to define the most appropriate water loss prevention strategy in regions with very high loss rates. The economic levels of the NRW in the pilot utilities were calculated as 29%, 16% and 23% by the optimization algorithm. Moreover, the most appropriate reduction methods to be applied according to the conditions of the utilities were determined in order to reach these defined ELL values. The potential benefits (reductions in the amount of losses) to be obtained in each utility condition were calculated with the application of these methods. In general, it has been seen that serious benefits can be obtained by applying the basic water loss reduction methods (PM, ALC, team management and water meter management). In the study, it was determined by the optimization algorithm that the PM and ALC methods are the most effective water loss reduction methods depending on different network characteristics. On the other hand, it was seen that methods of failure repair team management and water meter management will not always be economically beneficial for utilities. Therefore, the necessity of calculating the benefit costs according to the current conditions of the network was put forward before applying such methods. At the same time, ideal pressure levels were calculated for each region and it should not be forgotten that these pressures give the most useful results in the use of both ALC and PM methods.

Utilities are making quite a serious effort to reduce NRW volumes and rates. In general, the target values of NRW rates in utilities are defined with the regulations. Such targets cause many uneconomical and serious problems encountered in practice for utilities. It is possible to develop the most appropriate WLM strategy for utilities by the optimization model, which can be applied to any network where the data given in the table are measured. The main important issue in the implementation of this model is reliable and accurate data. The basic data of the system should be determined correctly for an accurate analysis. In addition, regular monitoring of operation and hydraulic data with information management systems such as SCADA and GIS is quite important. Especially, the cost of water production is a factor that directly affects the definition of the reduction method and ELL value. The definition of the reduction methods to reach the defined ELL is significant information for technical staff in utilities. It is thought that utilities can continue their loss reduction strategies by applying this model that will provide the most economical efficiency. The scope of the study can be expanded by considering new optimization parameters in the future for the algorithm. Four methods (PM, PMM, ALC and failure management) were considered as water loss reduction methods. In future studies, different water loss reduction methods can be integrated into the algorithm.

This research was supported by TUBITAK (Turkish National Science Foundation) under the Project Number 122M577.

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

The authors declare there is no conflict.