Excessive pressure in water distribution networks (WDNs) may lead to undesirable effects, such as increased pipe failure rate and leakages. Pressure management (PM) techniques are indeed attractive to address these issues, reducing energy and water losses. Among the most recent PM techniques, pumps working as turbines (PATs) can be employed to both control pressure and recover energy. However, finding the best location, setting, and number of PATs to maximize both leakage reduction and energy production within a WDN is particularly challenging due to the severe nonlinearity of the problem and the large number of decision variables. To address the setting problem, a promising derivative-free nonlinear programming method is herein presented. The proposed method, modified to account for bound-type constraints, is capable of finding the optimal setting of a chosen number of PATs, given their position, direction, and machine type (characteristic curve), accounting for both energy and saved water volumes costs. In addition, this method is also able to establish whether the installed PATs must be bypassed or not. The proposed method capabilities are tested on a hypothetical complex WDN taken from the literature.

供水网络（WDN）中的压力过大可能会导致不良后果，例如管道故障率增加和泄漏。压力管理（PM）技术确实很有吸引力，可以解决这些问题，从而减少能源和水的损失。在最新的PM技术中，可用作涡轮（PAT）的泵可用于控制压力和回收能量。然而，由于问题的严重非线性和大量决策变量，找到最佳位置，设置和PAT数量以最大化WDN内的泄漏减少和能量产生特别具有挑战性。为了解决设置问题，本文提出了一种有前途的无导数非线性编程方法。提出的方法经过修改以解决绑定类型约束，能够根据位置，方向和机器类型（特性曲线）找到选定数量的PAT的最佳设置，同时考虑到能源和节省的水量成本。此外，此方法还可以确定是否必须绕过已安装的PAT。拟议的方法功能在取自文献的假设复杂WDN上进行了测试。