Donald J. Docimo

Joseph M. Pisani, Christopher T. Aksland, Philip M. Renkert et al.

Modern energy systems in vehicles and built infrastructure are governed by high-dimensional dynamics spanning multiple physical domains (e.g., electrical, thermal, mechanical) and timescales. This tutorial paper presents a graph-based modeling approach created to facilitate the modeling, analysis, control, estimation, optimization, and design of these systems. Matured and validated through more than a decade of research spanning multiple academic institutions and companies, the graph-based approach combines transient energy conservation with an explicit mathematical representation of the network by which energy is stored and transferred within a system. Following a mathematical overview of graph-based models, examples of multi-domain component and system models from the recent literature are presented, including single-phase thermal systems, two-phase thermal systems, and electro-mechanical systems. This is followed by a survey of recent applications for decentralized and hierarchical model predictive control, design optimization, and control co-design. Lastly, the paper describes an open-source toolbox created to facilitate the generation and analysis of graph-based models.

Preston T. Abadie, Donald J. Docimo

This work explores controllability and the control effort required for lithium-ion batteries. Battery packs have become a critical technology in both personal and professional applications as a means to store large amounts of energy. Management of cells in a pack becomes increasingly difficult though, with charging and discharging operations requiring more complex strategies due to parameter variations between the cells. There are numerous studies which develop effective estimation and control schemes to reduce the impact of the imbalances present in battery packs, but the receptiveness of the individual cells to these schemes is much less explored. This paper performs a nonlinear controllability analysis for experimentally parameterized cells. A connection is shown between the condition number of a battery's controllability matrix and the amount of control effort that battery will require. This reveals that if a cell's dynamics are poorly mathematically conditioned, it will require more time or higher power to control than one that is not. The controllability condition number of each cell's model is then determined both with new and aged parameters, and a sensitivity analysis shows that the cells' conditioning is equally impacted by all parameters. This offers insight into the increased control effort required for a battery as it ages and the culprit of said increase. The results of this analysis are then used to determine the best conditioned assemblies for a batch of cells with a mix of new and second-life parameters.

Leeroy Makusha, Preston Abadie, Donald J. Docimo

Design, control, and estimation for dynamic systems require accurate and analytically tractable models. However, modern engineered systems contain components that are described with heterogeneous modeling paradigms, as well as subsystems that are challenging to model from physics alone. There have been significant efforts to address this through heterogeneous coupling frameworks and data-driven modeling. However, these two paths have been pursued in parallel. This work bridges this gap by introducing a control-oriented framework to couple physics-based and data-driven models. A physics-based microgrid with a data-driven data center load model is used to demonstrate the proposed four step methodology. Application of the framework yields a coupled system that allows for rigorous assessment of control properties. Equilibrium and stability tests are conducted, and they both reveal that the coupling structure and functions play a critical role in determining physically meaningful equilibrium points and stability of the integrated system. This information could only be accessed through the proposed framework, highlighting its importance.

Asmaou S. Ouedraogo, Donald J. Docimo

This paper presents a unified optimization framework for phase change material (PCM) based cooling systems. Thermal management is critical in applications such as photovoltaic (PV) modules, battery packs, and power electronics, where excessive heat reduces performance and lifespan. Designing such systems is challenging because energy dynamics, capacity, heat rejection, and structural constraints must all be considered. Although prior studies have investigated PCM applications and heat transfer enhancement, there are limited efforts that unify such diverse performance objectives through formalized design methods. This paper develops a framework that formulates the PCM design problem using critical energy-based terms, with static and dynamic objectives capturing the PCM physical design and control aspects. Two case studies are used to validate the approach: the first explores passive cooling, and the second implements an active cooling configuration. The results compare the design and control of these systems, showing improvement in individual performance metrics between the two options.

Tania Rifat Jahan, Donald J. Docimo

This work explores methods to identify energy system designs for infeasible control co-design optimization problems. Control co-design, or CCD, has been recognized as a powerful tool to maximize energy system capabilities through simultaneous determination of plant and controller parameters. However, due to the inherent nonlinearities, complexity, and conflicting criteria of energy systems, CCD optimization problems are susceptible to infeasibility and can lack potential solutions. While transforming the optimization problem by relaxing constraints has been developed for optimal control infeasibility challenges, solution feasibility for CCD is relatively unexplored. This paper proposes a framework to convert infeasible optimization problems into solvable forms for a class of CCD problems. The framework introduces a procedure to rank metric bounds from least likely to most likely to cause infeasibility. This provides guidance to algorithmically relax a limited number of constraints, leaving others intact. The proposed framework is applied to a CCD problem for designing a battery within a microgrid. Comparison against a baseline approach for relaxing optimization problems shows the framework requires only a reduced number of iterations to determine a solution.