Data-driven modeling and optimization of flexible and efficient power and water systems management

The accelerating transition towards low‑carbon energy systems and increasing pressure on water resources are transforming how societies plan, operate, and coordinate their critical infrastructures. Power systems face rising challenges due to growing demand driven by the electrification of multiple sectors and increasing uncertainty from variable renewable energy generation, which together place new requirements on flexibility, reliability, and market design. Water systems simultaneously confront growing demand, reduced freshwater availability, and the need to manage energy-intensive treatment and distribution under increasingly volatile energy prices, making their operation more tightly coupled to the dynamics of the energy system. At the same time, the deep physical and economic interdependence between energy and water creates new opportunities for flexibility, efficiency, and resilience, provided that decision-making frameworks can jointly represent their coupled physics, market interactions, and key uncertainties, thereby facilitating the so-called water-energy nexus transition. This thesis advances such an integrated view by developing data-driven mathematical optimization frameworks that support flexible, technology-aware planning, market participation, and operation of coupled energy and water systems and their associated technologies under uncertainty. The central aim is to enable a system-level approach to investment and operational decisions that accounts for the physics of power and water infrastructures, their interdependence, and the techno-economic characteristics of the underlying technologies. The core contribution lies in employing novel mathematical techniques, such as reformulation and approximation techniques, as well as machine-learning-based surrogate modelling, to make otherwise intractable integrated water-energy problems computationally tractable while preserving physical accuracy and market realism. In particular, tailored approximation methods based on convex relaxations and input convex neural networks (ICNNs) are developed to represent complex nonlinear hydraulic relationships. These approximation methods are embedded within optimal water flow formulations, allowing accurate yet scalable representation of water network hydraulic behavior within large-scale optimization models. Additionally, the models are designed to capture the stochastic nature of renewable energy generation and the price volatility. Uncertainty is modelled through distributionally robust chance-constrained (DRCC) formulations based on data-driven moment information. These DRCC models support uncertainty-aware planning and operational decisions that remain feasible and economically robust under worst-case forecast errors, while avoiding computationally demanding scenario-based formulations and the need to assume a probability distribution. Throughout the thesis, this core contribution is embedded within a market-based integrated water-energy framework, in which the water system functions as a flexible resource for the power system, generating financial value and new revenue opportunities for power and water network operators. The proposed frameworks are applied to a series of case studies, including electricity price-driven pump scheduling, coordinated dispatch of flexible water and power assets across coupled markets, energy storage investment planning considering cross-temporal arbitrage across multiple market segments, and techno-economic optimization of hydrogen production from non-potable water that jointly selects electrolysis technologies, water treatment configurations, and multi-market strategies. The integration of tractable optimization, robust uncertainty modelling, and machine-learning-based surrogates demonstrates a coherent, data-driven toolbox for system-level, technology-aware decision-making. This toolbox supports policymakers and practitioners in enhancing flexibility, exploiting cross-sector synergies, and improving the efficiency and resilience of emerging renewable-based energy and water systems.