# Optimization of Water Pressure of a Distribution Network within the Water-Energy Nexus
## 1 Introduction  
The supply of energy and drinking water is a fundamental aspect of the sustainable development of cities and societies, but it is limited by various factors with complicated relationships. Climate change has restricted the ability to supply drinking water, and concerns about greenhouse gas emissions have catalyzed a worldwide interest in improving energy efficiency [1, 2]. In addition, population growth increases water and energy demands in various sectors, including the household sector [3]. Due to water-energy interactions, there is potential for synergy between the two sectors. Therefore, the nexus between them and the importance of integrated water and energy planning are important research topics [4, 5]. Water distribution networks (WDNs), which transmit water to consumers after physical and chemical treatment, are vital parts of water supply systems. The role of WDNsis amplified when there is a demand for higher water pressure, as this leads to the implementation of domestic pumps that consume a significant amount of energy. Various studies have examined the design of WDNs through different approaches, such as cost minimizing [6], contamination control [7], energy recovery [8], and flexible designs using multi-objective optimization [9; 10]. Several cost-related factors (e.g., leaks, pipe breaks, water network repair, and the energy required to pump water into the network) are generally considered by all water companies. Analyses of such factors have revealed the significant role of network pressure on the operation of WDNs [11; 12]. Pressure is an adjustable parameter that, if manipulated correctly, can reduce the maintenance costs of water companies. Using local field data, [PERSON] et al. [13] proposed a probabilistic approach that considers uncertain demands and pipe roughness to determine the effects of pressure on burst frequency. The Monte Carlo method was used to implement this probabilistic approach in the water network of Hamilton, Ontario, Canada. Due to the significant effect of pressure reduction on burst frequency, they proposed to re-evaluate pressure standards for WDNs. [PERSON] et al. [14; 15] proposed a head out flow relationship (HOR) modeling approach which takes into account the residential environment of consumers and various water-supply methods. The robustness of this method is assessed by selecting two demonstration blocks and evaluating the available flow rate supplies under abnormal conditions. This method provides a reliable pressure-driven analysis by applying a rational and objective HOR selection procedure. Water leakage in WDNs, the relationship between water leakage and pressure, and the methods for detecting leaks have been widely researched [16]. Because leakage plays a vital role in water loss and non-revenue water, water companies have tried to reduce leakage by replacing pipes, implementing leakage detection strategies, and reducing pressure in WDNs [17]. Pressure reducing valves (PRVs) automatically reduce high inlet pressure to a steady and low level of downstream pressure [18]. The utilization of PRVs has become a common method for pressure management in the WDNs. There are two major categories of applying management commands and adjusting these valves: mechanical control and electronic control [17]. In mechanical control, adjustment of PRV is generally manual. These valves work even in changing flow rate or varying inlet pressure and for many years, have been used to reduce service pressure to an appropriate level. The setting of these valves can be adjusted to meet the demand alterations of the system, but they cannot be adjusted continuously in real time. Therefore, pressure management in this mechanical control method is on a daily or monthly basis [19]. In recent years, because of the advancements of electronic technologies and control algorithms, mechanical control and conventional PRVs have become obsolete [20].