Water Network Partitioning Algorithm for District Metered Areas
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Solution Overview
Problem
Current network partitioning algorithms, such as multi-level graph partitioning and k-means, fail to ensure the presence of at least one source in each district for water distribution networks and do not support load balancing, leading to unfeasible partitions due to over-loaded parts with unsatisfied water demands.
Innovation Solution
A computer-implemented method using a generation algorithm that defines distances between nodes based on pre-defined metrics, assigns nodes to district metered areas with multiple poles, and moves poles to central positions to achieve hydraulic separation and load balancing, allowing for feasible partitions with varying sizes and shapes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If k-means algorithm is used to partition the network into predefined number of parts, then the partitioning converges quickly, but the obtained partition only provides a local optimum depending on initial selection of centroids with no guarantee that it is a global optimum
Solution Approach 1:
The patent applies preliminary action by performing multiple initializations of the k-means algorithm with different random centroids before selecting the final partition. This preliminary exploration of multiple starting points increases the likelihood of finding a global optimum while maintaining the fast convergence characteristic of k-means.
2Ease of operation
If multi-level graph partitioning algorithm is used to partition the network, then load balancing constraints are fulfilled, but it is not possible to ensure the fulfillment of other critical constraints such as the presence of at least one source in each district
Solution Approach 1:
The patent uses an intermediary approach by introducing a post-processing step that verifies and enforces additional constraints (such as source presence in each district) after the multi-level graph partitioning algorithm produces its initial partition. This mediator step ensures both load balancing and critical constraint fulfillment without compromising either.
3Loss of energy
If network is partitioned into smaller components to limit elevation range of users, then energy for pumping is saved and leakages are reduced, but the partitioning algorithms do not support load balancing leading to over-loaded parts
Solution Approach 1:
The patent applies segmentation by dividing the network into smaller district components (DMAs) with controlled elevation ranges to reduce pumping energy and leakages. Simultaneously, it integrates load balancing considerations into the partitioning process to ensure that each segmented district does not become over-loaded, thus maintaining productivity while achieving energy savings.
4Reliability
If k-means algorithm is run several times with different initial centroids to find optimal partition, then better partition quality is achieved, but the computational time increases significantly
Solution Approach 1:
The patent applies partial action by running the k-means algorithm a limited number of times with different initial centroids rather than exhaustively searching all possible initializations. This partial exploration achieves satisfactory partition quality while avoiding excessive computational time, finding a practical balance between solution quality and computational resources.
Data Source
AI summary
Partitioning a water distribution network comprising a set of nodes, a distance between each pair of nodes is defined based on a pre-defined metric, is provided. At least one candidate partition of the water distribution network is determined. For each candidate partition, a plurality of centrally positioned nodes for each district metered area is identified. Repeating: assigning the set of nodes to a particular district metered area and moving the plurality of centrally positioned nodes according to a local objective function based on distances of other nodes of the particular district metered area from the plurality of centrally positioned nodes, until at least one convergence condition is satisfied. A candidate partition of the water distribution network is selected according to at least one selection criterion. The selected candidate partition is configured to decrease water pressure in each district metered area of the selected candidate partition.