water Article Appraising the Impact of Pressure Control on Leakage Flow in Water Distribution Networks Thapelo C. Mosetlhe 1,2, * ,† , Yskandar Hamam 2,3,† , Shengzhi Du 2,† and Eric Monacelli 4,†   Citation: Mosetlhe, T.C; Hamam, Y.; Du, S.; Monacelli, E. Appraising the Impact of Pressure Control on Leakage Flow in Water Distribution Networks. Water 2021, 13, 2617. https://doi.org/10.3390/w13192617 Academic Editor: Gabriele Freni Received: 1 July 2021 Accepted: 14 September 2021 Published: 23 September 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Department of Electrical Engineering, University of South Africa, Florida 1709, South Africa 2 Department of Electrical Engineering, Tshwane University of Technology, Pretoria 0183, South Africa; hamama@tut.ac.za (Y.H.); dus@tut.ac.za (S.D) 3 École Supérieure d’Ingénieurs en Électrotechnique et Électronique, 2 Boulevard Blaise Pascal, 93160 Noisy-Le-Grand, France 4 Laboratoire d’Ingénierie des Systémes de Versailles, Université de Versailles Saint-Quentin-en-Yvelines UVSQ, Université Paris-Saclay, 10-12 Avenue de l’Europe, 78140 Vélizy, France; eric.monacelli@uvsq.fr * Correspondence: mosettc@unisa.ac.za † These authors contributed equally to this work. Abstract: Water losses in Water Distribution Networks (WDNs) are inevitable. This is due to joints interconnections, ageing infrastructure and excessive pressure at lower demand. Pressure control has been showing promising results as a means of minimising water loss. Furthermore, it has been shown that pressure information at critical nodes is often adequate to ensure effective control in the system. In this work, a greedy algorithm for the identification of critical nodes is presented. An emulator for the WDN solution is put forward and used to simulate the dynamics of the WDN. A model-free control scheme based on reinforcement learning is used to interact with the proposed emulator to determine optimal pressure reducing valve settings based on the pressure information from the critical node. Results show that flows through the pipes and nodal pressure heads can be reduced using this scheme. The reduction in flows and nodal pressure leads to reduced leakage flows from the system. Moreover, the control scheme used in this work relies on the current operation of the system, unlike traditional machine learning methods that require prior knowledge about the system. Keywords: water distribution networks; pressure control; leakage minimisation; reinforcement learning 1. Introduction The existence of leakages in water supply systems is inevitable. The nature of their interconnection renders them susceptible to wear and tear and therefore resulting in water losses. Management of these leakages now becomes a critical task considering the scarcity of the resource, mostly in sub-Saharan Africa. For water distribution networks (WDNs), leakage minimisation has been the subject of research dating from the early 80s [1]. With the ageing water supply infrastructures, water utilities and municipalities are faced with more frequent occurrences of pipe breaks and increased leakages. In South Africa, it is estimated that annually, 7 billion ZAR is lost as a result of leakages on the nodes, pipes or valves [2,3]. Furthermore, the United State of America experiences almost 20% of water loss due to leakages [4]. Globally, the demand for water supply has increased due to steady population growth [5]. However, a significant portion of water is lost as a result of leakages in WDNs [6]. However, it is asserted in [7] that reducing the leakage component to zero is neither technically nor economically feasible. Water loss may pose a great threat to the availability of this important scarce resource [8]. The quantity of water lost due to leakages varies from different networks. The operation, state of the network and the location of the network determine the quantity of water lost. To date, pressure management is a strategy under research for effective leakage minimisation [9–12]. Installation of pressure reduction valves (PRVs) and their appropriate Water 2021, 13, 2617. https://doi.org/10.3390/w13192617 https://www.mdpi.com/journal/water