Stochastic Co-design of Storage and Control for Water Distribution Systems

TL;DR

This paper presents a stochastic co-design method for water distribution systems that optimizes infrastructure size and control parameters simultaneously, reducing costs and improving efficiency under uncertain demand and prices.

Contribution

It introduces a tractable stochastic co-design approach using Markov chain theory to optimize tank size and control parameters, applicable to both new and existing water systems.

Findings

Method reduces operational costs in water systems.

Validated with real-world case study and examples.

Converges to optimal long-term operating costs.

Abstract

Water distribution systems (WDSs) are typically designed with a conservative estimate of the ability of a control system to utilize the available infrastructure. The controller is designed and tuned after a WDS has been laid out, a methodology that may introduce unnecessary conservativeness in both system design and control, adversely impacting operational efficiency and increasing economic costs. To address these limitations, we introduce a method to simultaneously design infrastructure and develop control parameters, the co-design problem, with the aim of improving the overall efficiency of the system. Nevertheless, the co-design of a WDS is a challenging task given the presence of stochastic variables (e.g. water demands and electricity prices). In this paper, we propose a tractable stochastic co-design method to design the best tank size and optimal control parameters for WDS, where the expected operating costs are established based on Markov chain theory. We also give a theoretical result showing that the average long-run operating cost converges to the expected operating cost with probability~1. Furthermore, this method is not only applicable to greenfield projects for the co-design of WDSs but can also be utilized to improve the operations of existing WDSs in brownfield projects. The effectiveness and applicability of the co-design method are validated through three illustrative examples and a real-world case study in South Australia.