Distributed Nonconvex Optimization for Control of Water Networks with Time-coupling Constraints

Area of Science:

• Water resource management
• Optimization theory
• Network control systems

Background:

• Optimizing water distribution networks for pressure and water quality is complex.
• Existing nonlinear solvers struggle with time-varying constraints and large-scale networks.
• Temporal variations between pressure and water quality controls exacerbate optimization challenges.

Purpose of the Study:

• To develop and evaluate a novel control model for optimizing pressure and water quality in water distribution networks.
• To address the computational challenges posed by nonconvex, nonlinear optimization problems in real-time control.
• To investigate the efficacy of distributed optimization techniques, specifically the alternating direction method of multipliers (ADMM).

Main Methods:

• Formulation of a time-coupling constraint model for managing temporal pressure variations.
• Implementation and evaluation of a standard ADMM scheme and a two-level ADMM variant.
• Numerical experiments on a benchmarking water network and a large-scale UK operational network.

Main Results:

• The two-level ADMM algorithm demonstrated robust convergence across all tested water network instances.
• Standard ADMM exhibited convergence issues in certain scenarios.
• Both distributed ADMM algorithms, with appropriate parameter tuning, achieved solutions suitable for near real-time control.

Conclusions:

• Distributed optimization, particularly the two-level ADMM, offers a viable solution for computationally intensive water network control problems.
• The proposed methods enable near real-time (hourly) optimization for large-scale water distribution systems.
• Effective parameter tuning is crucial for achieving optimal performance with distributed ADMM algorithms.