Economic zone data-enabled predictive control for connected open water systems

TL;DR

This work addresses real-time water level regulation in a connected open water system by introducing a data-enabled predictive control framework that enforces zone tracking and reduces pump energy. The method combines a mixed-integer, lexicographic DeePC formulation with a Bayesian-optimized control target zone, enabling robust operation under disturbances without explicit first-principles models. Key findings show that the approach keeps water levels within the target zone for 97.04% of operating time and achieves substantial energy savings compared with baseline controllers, while outperforming alternatives in zone tracking and reliability. The approach offers a practical, data-driven route to safer, more energy-efficient operation of large-scale hydraulic networks and can adapt to nonlinearities and disturbances via offline data and online optimization.

Abstract

Real-time regulation of water distribution in connected open water systems is critical for ensuring system safety and meeting operational requirements. In this work, we consider a connected open water system that includes linkage hydraulic structures such as weirs, pumps and sluice gates. We propose a mixed-integer economic zone data-enabled predictive control (DeePC) approach, which is used to maintain the water levels of the branches within desired zones to avoid floods and reduce the energy consumption of the pumps in the considered water system. The proposed DeePC-based approach predicts the future dynamics of the system water levels, and generates optimal control actions based on system input and output data, thereby eliminating the need for both first-principles modeling and explicit data-driven modeling. To achieve multiple control objectives in order of priority, we utilize lexicographic optimization and adapt traditional DeePC cost function for zone tracking and energy consumption minimization. Additionally, Bayesian optimization is utilized to determine the control target zone, which effectively balances zone tracking and energy consumption in the presence of external disturbances. Comprehensive simulations and comparative analyses demonstrate the effectiveness of the proposed method. The proposed method maintains water levels within the desired zone for 97.04% of the operating time, with an average energy consumption of 33.5 kWh per 0.5 h. Compared to baseline methods, the proposed approach reduces the zone-tracking mean square error by 98.82% relative to economic zone DeePC without Bayesian optimization, and lowers energy consumption by 44.08% relative to economic set-point tracking DeePC. As compared to passive pump/gate control, the proposed method lowers the frequency of zone violations by 86.94% and the average energy consumption by 4.69%.

Figures (13)

• Figure 1: A schematic diagram of the connected open water system, adapted from horvath2022Potential. The dark blue areas represent the controlled branches, and the light blue areas indicate the external rivers. The number of black arrows at each station correspond to the number of pumps, with the direction of each arrow indicating the flow direction for the corresponding pump. The blue arrow indicates the permitted flow direction through the sluice gate.
• Figure 2: Schematic diagrams of weir and gate flows.
• Figure 3: Characteristic curves, system demand curve, and feasible operating region of each pump potter2011mechanics.
• Figure 4: An illustrative diagram of Bayesian optimization applied to control target zone determination.
• Figure 5: A representative set of disturbance trajectories including the water levels of external rivers and the disturbance inflow to branches 1, 7, 10, and 14.

Theorems & Definitions (4)

• Definition 1
• Lemma 1
• Remark 1
• Remark 2