Carnegie Mellon University
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Modeling and Control of New and Existing Energy Systems

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posted on 2023-06-26, 17:34 authored by Vibhav DabadghaoVibhav Dabadghao


Tightly-coupled integrated energy systems of the future represent a class of technologies that promise to play a crucial role in improving modern power systems across a wide range of criteria towards our shared goal of decarbonization. Differential-algebraic equation (DAE) models represent a large class of process models resulting from phenomenological description of dynamic processes in energy systems. Model predictive control (MPC) is an optimization-based form of control that is capable of naturally handling multi-input multi-output systems and inequality constraints. It exploits fully nonlinear process models, usually DAEs, to provide high accuracy and reliability. The performance of MPC is contingent on the accuracy and reliability of the embedded DAE model itself. This thesis proposes DAE modeling and reformulationtechniques and improves performance of optimization and MPC for large-scale energy systems via fundamental developments in tools and frameworks for modeling and optimization. First, we develop an index reduction reformulation for ill-posed, high-index DAEs and apply it to a multiscale dynamic model for a flue gas desulfurization process. This reformulation enables tractable numerical solution as well as using various advanced control strategies. An economic MPC framework is developed to demonstrate optimal operational strategies compared to ad-hoc operating policies. Next, we consider a reversible solid-oxide fuel cell system (rSOFC) that can flexibly operate between fuel production and power generation modes. We present a comprehensive analysis of careful control of such systems using Nonlinear MPC (NMPC) and compare it to sophisticated classical control strategies. Reversible SOFCs are highly complex systems and can play a crucial role in decarbonization and grid stabilization, especially in the context of increasing complexity of modern power systems due to increasing integration of renewable energy sources. We develop a control framework that enables the system to quickly switch between setpoints while ensuring safe operation by avoiding large thermal gradients that are detrimental to the physical health of the fuel cell stack. Finally, we consider the phenomenon of vapor-liquid equilibrium (VLE) that has wide-ranging applications including, and especially, in energy systems in which power generation processes or supporting equipment involve phase changes. We propose an improved formulation for VLE that enables application of VLE in large-scale flowsheet optimization for virtually any operating conditions via complementarity formulations that deal seamlessly with phase transitions and even supercritical excursions. Moreover, the proposed approach is efficient, non-intrusive and can be extended to incorporate a wider range of thermodynamic models. The approach is demonstrated on the optimization of an air separation column with non-ideal flash calculations and disappearing phases.




Degree Type

  • Dissertation


  • Mechanical Engineering

Degree Name

  • Doctor of Philosophy (PhD)


Lorenz Biegler