Water-Energy Nexus

Optimization, Control, &  Machine Learning Applications to Water-Energy Systems

The water and energy sectors are the two interlinked, critical infrastructures, which are essential to to be operated in an efficient environment leading to economic savings. Realizing this need, CONCISE lab introduced the following efficient methods to deal with the sustainable operations of the water-energy nexus:

1. Mixed-Integer Programming for the Joint Optimization of the Integrated Water Energy Systems

2. Machine Learning Models for the Economic Dispatch of the Integrated Water Energy Systems

3. Model-Based and Data-Driven Co-control of the Water-Energy Nexus

1. Mixed-Integer Programming for the Joint Optimization of the Integrated Water Energy Systems

The focus in on optimization of 1) demand response using water management, 2) combined water and energy systems, and 3) building's energy management system integrated with water-energy systems to develop a smart and sustainable city in the future. We developed mathematical optimization models that minimize the energy consumption of water-energy systems by developing single-objective, multi-level, and co-optimization models using mixed integer nonlinear programming (MINLP) formulation. Via co-optimization models, we minimized the energy consumption of the pumps in water distribution systems (WDS) considering the uncertain behavior of renewable sources including solar or wind energy generation units. We contemplated an integer variable for the status of each pump which takes in 0 and 1 depending on the amount of water supplied to the network, the amount available in the tank, and the demand at every hour. Additionally, to obtain a global optimum solution for the proposed non-linear programming formulations, we develop convex optimization models using bivariate and univariate piecewise linear approximation to linearize the nonlinear constraints.

2. Machine Learning Models for the Economic Dispatch of the Integrated Water Energy System

Efficiently managing interconnected water and energy infrastructure is crucial for meeting the needs of a growing population and ensuring both operational and economic stability. Addressing this challenge in real-time is difficult due to the complexity of numerous decision variables and constraints, making it a nonlinear and non-convex issue. Traditional numerical methods are often resource-intensive, especially for large-scale systems. Our recent works introduces a novel approaches using machine learning (ML) to tackle the combined economic dispatch problem within an isolated water-energy microgrid. These studies introduces the applications of ML models including multilayer perceptron (MLP), random forest (RF),  support vector machines (SVM), and Gradient Boosting methods. These models are trained on datasets derived from solving the mixed-integer nonlinear programming (MINLP) framework for integrated water-energy systems. The investigations revealed that the optimal power dispatch obtained from ML models are highly accurate with significant improvement in the runtime efficiency compared with the traditional numerical solutions.  These findings demonstrated that ML models are highly effective for real-time, minute-based economic dispatch, marking a significant step forward in the management of integrated water-energy systems.

3. Model-Based and Data-Driven Co-control of the Water-Energy Nexus

The interdependence of water energy is inevitable. As indicated by the IEEE standard association, the largest category of water consumption is electric power generation while the largest electricity demand is water extraction and distribution. Hence, this strong independence motivates the development of closed-loop control to provide 1) optimal demand management, 2) cost and energy-efficient operation, and 3) stable operation with feedback control. Based on these objectives, we implemented an optimal control for the integrated water energy specified to islanded microgrids and water distribution systems (WDSs) via model predictive control (MPC).  The control involves 1) feedback control to consider the error from the system’s output, 2) feed-forward control to consider disturbances, and 3) optimal control formulation to account for different operational objectives. The studied WDS involves interconnected water tanks with pumps and valves, while the microgrid includes wind turbines, diesel generators, battery energy storage systems, and solar photovoltaic (PV) generation. The findings demonstrated that control of the integrated system allows 1) higher energy savings which led to greater cost savings of up to $360 k/year at the expense of lower security levels for storage tanks, 2) pumps' energy consumption and the diesel generator's power dispatch decreased up to 30% and 60%, respectively, while still maintaining demand compliance, and 3) smoothness of the system operation and longer lifespan of batteries are obtained during high penetration of wind power. 

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