Modeling, Simulation, and Analysis of Lithium-Ion Batteries for Grid-Scale Applications

Lithium-ion batteries have become universally present in daily life, being used across a wide range of portable consumer electronics. These batteries are advantageous compared to other forms of energy storage due to their high energy density and long cycle life. These characteristics make lithium-ion batteries advantageous for many new and developing applications that require large scale energy storage such as electric vehicles and the utility grid. Typical uses for lithium-ion batteries require consistent cycling patterns that are predictable and easy to approximate across all uses, but new large scale applications will have much more dynamic demands. The cycling patterns for electric vehicles will vary based on each individuals driving patterns and batteries used for energy storage in the grid must be flexible enough to account for continuous fluctuations in demand and generation with little advanced notice. Along with these requirements, large scale applications do not want to sacrifice on cycle life and need to know that adding batteries will make operational and economic sense in specific cases. It is not possible to experimentally validate every possible driving pattern or grid storage need because of the great expense of these large systems and the long timescale required for testing. Therefore modeling of these systems is advantageous to help study specific application constraints and understand how lithium-ion batteries operate under those constraints. A systems level model is developed to study lithium-ion battery systems for use with solar energy (in a solar-battery hybrid system) and electric vehicles. Electrochemical based battery models are used as a component within larger systems. To facilitate fast simulation a single step perturbation and switch method is outlined for increasing the speed and robustness of solving the systems of DAEs that result from the systems level model. Operational characteristics are studied for lithium-ion batteries used to store solar energy within the electric grid. Different grid demands are tested against the system model to better understand the best uses for the solar-battery hybrid system. Both generic site studies and site specific studies were conducted. Solar irradiance data from 2010-2014 was obtained from 10 US based sites and used as an input to the system model to understand how the same system will operate differently at various locations. Technological benefits such as system autonomy were simulated for each site as well as economic benefits based on a time-of-use pricing scenario. These models included the growth of the solid-electrolyte interface layer on the battery electrodes to measure capacity fade during operation. This capacity fade mechanism allowed tracking of the site specific effects on battery life. A systems level model for an electric vehicle was also developed to simulate the growth of the SEI layer caused from different types of driving cycles and charging patterns. Results from both system models are presented along with an optimization method for the solar-battery hybrid model. In addition to modeling, experimental tests of LiFePO4 lithium-ion battery cells were conducted to measure capacity fade associated with different types of cycling throughout a batterys life. Cycling protocols were tested to study traditional capacity fade and also to focus on increasing a cells lifetime benefit through application switching

Differential-Algebraic Equations

Differential-Algebraic Equations (DAE) are today an independent field of research, which is gaining in importance and becoming of increasing interest for applications and mathematics itself. This workshop has drawn the balance after about 25 years investigations of DAEs and the research aims of the future were intensively discussed

SciCADE 95: International conference on scientific computation and differential equations

This report consists of abstracts from the conference. Topics include algorithms, computer codes, and numerical solutions for differential equations. Linear and nonlinear as well as boundary-value and initial-value problems are covered. Various applications of these problems are also included

Coupled Electromagnetic Field/Circuit Simulation: Modeling and Numerical Analysis

Today's most common circuit models increasingly tend to loose their validity in circuit simulation due to the rapid technological developments, miniaturization and higher complexity of integrated circuits. This has motivated the idea of combining circuit simulation directly with distributed device models to refine critical circuit parts. In this thesis we consider a model, which couples partial differential equations for electromagnetic devices - modeled by Maxwell's equations -, to differential-algebraic equations, which describe basic circuit elements including memristors and the circuit's topology. We analyze the coupled system after spatial discretization of Maxwell's equations in a potential formulation using the finite integration technique, which is often used in practice. The resulting system is formulated as a differential-algebraic equation with a properly stated leading term. We present the topological and modeling conditions that guarantee the tractability index of these differential-algebraic equations to be no greater than two. It shows that the tractability index depends on the chosen gauge condition for Maxwell's equations. For successful numerical integration of differential-algebraic equations the index characterization plays a crucial role. The index can be seen as a measure of the equation's sensitivity to perturbations of the input functions and numerical difficulties such as the computation of consistent initial values for time integration. We generalize index reduction techniques for a general class of differential-algebraic equations by using the tractability index concept. Utilizing the index reduction we deduce local solvability and perturbation results for differential-algebraic equations having tractability index-2 and we derive an algorithm to calculate consistent initializations for the spatial discretized coupled system. Finally, we demonstrate our results by numerical experiments

Revisiting the Optimal PMU Placement Problem in Multi-Machine Power Networks

To provide real-time visibility of physics-based states, phasor measurement units (PMUs) are deployed throughout power networks. PMU data enable real-time grid monitoring and control -- and is essential in transitioning to smarter grids. Various considerations are taken into account when determining the geographic, optimal PMU placements (OPP). This paper focuses on the control-theoretic, observability aspect of OPP. A myriad of studies have investigated observability-based formulations to determine the OPP within a transmission network. However, they have mostly adopted a simplified representation of system dynamics, ignored basic algebraic equations that model power flows, disregarded including renewables such as solar and wind, and did not model their uncertainty. Consequently, this paper revisits the observability-based OPP problem by addressing the literature's limitations. A nonlinear differential algebraic representation (NDAE) of the power system is considered and implicitly discretized -- using various different discretization approaches -- while explicitly accounting for uncertainty. A moving horizon estimation approach is explored to reconstruct the joint differential and algebraic initial states of the system, as a gateway to the OPP problem which is then formulated as a computationally tractable integer program (IP). Comprehensive numerical simulations on standard power networks are conducted to validate various aspects of this approach and test its robustness to various dynamical conditions

AI Enhanced Control Engineering Methods

AI and machine learning based approaches are becoming ubiquitous in almost all engineering fields. Control engineering cannot escape this trend. In this paper, we explore how AI tools can be useful in control applications. The core tool we focus on is automatic differentiation. Two immediate applications are linearization of system dynamics for local stability analysis or for state estimation using Kalman filters. We also explore other usages such as conversion of differential algebraic equations to ordinary differential equations for control design. In addition, we explore the use of machine learning models for global parameterizations of state vectors and control inputs in model predictive control applications. For each considered use case, we give examples and results

Aproximación de ecuaciones diferenciales mediante una nueva técnica variacional y aplicaciones

[SPA] En esta Tesis presentamos el estudio teórico y numérico de sistemas de ecuaciones diferenciales basado en el análisis de un funcional asociado de forma natural al problema original. Probamos que cuando se utiliza métodos del descenso para minimizar dicho funcional, el algoritmo decrece el error hasta obtener la convergencia dada la no existencia de mínimos locales diferentes a la solución original. En cierto sentido el algoritmo puede considerarse un método tipo Newton globalmente convergente al estar basado en una linearización del problema. Se han estudiado la aproximación de ecuaciones diferenciales rígidas, de ecuaciones rígidas con retardo, de ecuaciones algebraico‐diferenciales y de problemas hamiltonianos. Esperamos que esta nueva técnica variacional pueda usarse en otro tipo de problemas diferenciales. [ENG] This thesis is devoted to the study and approximation of systems of differential equations based on an analysis of a certain error functional associated, in a natural way, with the original problem. We prove that in seeking to minimize the error by using standard descent schemes, the procedure can never get stuck in local minima, but will always and steadily decrease the error until getting to the original solution. One main step in the procedure relies on a very particular linearization of the problem, in some sense it is like a globally convergent Newton type method. We concentrate on the approximation of stiff systems of ODEs, DDEs, DAEs and Hamiltonian systems. In all these problems we need to use implicit schemes. We believe that this approach can be used in a systematic way to examine other situations and other types of equations.Universidad Politécnica de Cartagen