# Water Network Partitioning into District Metered Areas: A State-Of-The-Art Review

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## Abstract

**:**

## 1. Introduction

## 2. Principles of District Metered Areas

- Maximum percentage of leakage allowed by the water utility;
- Topography and number of properties per DMA;
- Characteristics and topological taxonomy of WDNs;
- Variations in nodal elevation, water demand, and pressure;
- The number of flow meters and gate valves; and
- Water quality considerations.

## 3. Clustering to Create Feasible DMAs

#### 3.1. Graph Theory

#### 3.2. Community Structure Algorithm

#### 3.3. Modularity-Based Algorithm

#### 3.4. Multilevel Graph Partitioning

#### 3.5. Spectral Graph Algorithms

- $L$ is symmetric and positive-semidefinite with eigenvalues ${\lambda}_{i}\ge 0$ for all $i$.
- Every row sum and column sum of $L$ equals zero.
- The smallest eigenvalue ${\lambda}_{1}$ of $L$ equals zero.
- $L$ has $n$ non-negative and the number of connected components in the graph equals the algebraic multiplicity of ${\lambda}_{1}=0\le {\lambda}_{2}\le \cdots \le {\lambda}_{n}$.

- intracluster edges:${E}_{1}{\displaystyle \cup}{E}_{1}{\displaystyle \cup}\cdots {\displaystyle \cup}{E}_{p}$, and
- intercluster edges:$\partial \left({V}_{1}\right){\displaystyle \cup}\partial \left({V}_{2}\right){\displaystyle \cup}\cdots {\displaystyle \cup}\left({V}_{p}\right)$.

#### 3.6. Multi-Agent Approach

- Each agent has an imperfect standard or may lack the capacity for problem solving, and therefore has a somewhat limited and unbalanced perspective;
- There is no global information;
- Data is decentralized; and
- Computation is asynchronous.

## 4. Sectorization to Locate Flow Meters and Valves

#### 4.1. Single-Objective Optimization Approach

#### 4.2. Multiple-Objective Optimization Approach

#### 4.3. Iterative Approach

#### 4.4. Adaptive Sectorization for Dynamic DMAs

## 5. Performance Assessment of Water Network Partitioning

## 6. Discussion and Future Work

- Clustering is the crucial phase for WNP. Several algorithms and software tools were developed to deal with the large-scale networks that are burdensome to tackle manually. Various engineering aspects were embedded as weights to modulate WDN characteristics. More extensions of the existing graph clustering algorithms to weighted networks would be of great interest, as well as novel methods for clustering directed graphs.
- While there were many different approaches for the identification of DMAs in water networks, few studies tackled to determine the optimal number of DMAs for a given network. It is an open question and requires a decision-making procedure utilizing various network performance quantification metrics.
- In the sectorization phase, it still lacks how to assess the pump and tank operations in the partitioned network. Moreover, an approach to consider the consequences of device placements to the leakage, energy use, and post-damage restoration should be studied quantitatively in this phase.
- A demand-driven analysis (DDA) is generally used for WNP under the normal working condition at peak hour demand. In DDA, the supplied demand is assumed to be independent of pressure and this approach is valid when the pressure is above the minimum pressure requirement. In reality, a WDN works more likely as a pressure-driven analysis (PDA), in which the nodal consumption depends on the nodal pressure. Therefore, in pressure-deficient conditions (e.g., pipe failures, fire-fighting, unexpected water demand increase), a PDA should be applied for the novel dynamic WNP that adapts flexibly under the abnormal operating conditions.
- Last but not least, a WDN is supplied by single or multiple sources, with different elevations, divergent intended pressure in each zone. It also can be expanded or replaced according to urban planning needs. Further research should address the change of network’s topology, controlling hydraulic uniformity in each zone as well as improving system resilience. Future research needs to be conducted to improve the abovementioned limits and eventually to provide optimal DMA layouts for efficient network operation and management.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**Steps of water network partitioning: (

**a**) Overall main procedures, (

**b**) steps for clustering, and (

**c**) steps for sectorization.

**Figure 5.**Different phases of a multi-level recursive bisection algorithm [72].

Advantages | Disadvantages |
---|---|

Improved burst detection and leakage identification | Reduced resilience to failures |

Advantaged subarea management and reduced NRW | Reduced operational flexibility |

Improved subarea pressure control | Potential negative impact on water quality |

Improved protection against contamination | Security issues in peripheral areas and emergency cases |

Reduced maintenance and repair costs | High initial investment cost |

Characterized demand curve, especially at night | Reduced hydraulic redundancy |

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**MDPI and ACS Style**

Khoa Bui, X.; S. Marlim, M.; Kang, D.
Water Network Partitioning into District Metered Areas: A State-Of-The-Art Review. *Water* **2020**, *12*, 1002.
https://doi.org/10.3390/w12041002

**AMA Style**

Khoa Bui X, S. Marlim M, Kang D.
Water Network Partitioning into District Metered Areas: A State-Of-The-Art Review. *Water*. 2020; 12(4):1002.
https://doi.org/10.3390/w12041002

**Chicago/Turabian Style**

Khoa Bui, Xuan, Malvin S. Marlim, and Doosun Kang.
2020. "Water Network Partitioning into District Metered Areas: A State-Of-The-Art Review" *Water* 12, no. 4: 1002.
https://doi.org/10.3390/w12041002