Distributionally Robust Stochastic Optimal Water Flow and Risk Management

Abstract

We present a computationally efficient framework to solve a multi-stage optimal water flow (OWF) problem with stochastic water demands. The proposed framework explicitly considers the feedback control policies and adjustable water flow with forecast errors over a planning horizon. The objective is to find an optimal operation schedule of controllable devices (e.g., pumps and valves) to trade off operational performance, such as economic efficiency, safety, and smoothness, and risk of constraint violations. We compute feedback policies that are robust to forecast errors in order to accommodate the fluctuating water demands. Given a probabilistic description of forecast errors, our formulations provide two broad approaches based on Conditional Value-at-Risk (CVaR) and distributionally robust optimization (DRO) that offer alternatives to the existing stochastic OWF formulations based on chance-constrained and robust optimization. Numerical case studies on a three-tank water network demonstrate that the proposed framework achieves effective and explicitly adjustable trade offs between operational efficiency and constraint violation risk.