Reinhardt Klein

Electrochemical Model Based Observer Design for a Lithium-Ion Battery

Batteries are the key technology for enabling further mobile electrification and energy storage. Accurate prediction of the state of the battery is needed not only for safety reasons, but also for better utilization of the battery. In this work we present a state estimation strategy for a detailed electrochemical model of a lithium-ion battery. The benefit of using a detailed model is the additional information obtained about the battery, such as accurate estimates of the internal temperature, the state of charge within the individual electrodes, overpotential, concentration and current distribution across the electrodes, which can be utilized for safety and optimal operation. Based on physical insight, we propose an output error injection observer based on a reduced set of partial differential-algebraic equations. This reduced model has a less complex structure, while it still captures the main dynamics. The observer is extensively studied in simulations and validated in experiments for actual electric-vehicle drive cycles. Experimental results show the observer to be robust with respect to unmodeled dynamics as well as to noisy and biased voltage and current measurements. The available state estimates can be used for monitoring purposes or incorporated into a model based controller to improve the performance of the battery while guaranteeing safe operation.

Optimal charging strategies in lithium-ion battery

There is a strong need for advanced control methods in battery management systems, especially in the plug-in hybrid and electric vehicles sector, due to cost and safety issues of new high-power battery packs and high-energy cell design. Limitations in computational speed and available memory require the use of very simple battery models and basic control algorithms, which in turn result in suboptimal utilization of the battery. This work investigates the possible use of optimal control strategies for charging. We focus on the minimum time charging problem, where different constraints on internal battery states are considered. Based on features of the open-loop optimal charging solution, we propose a simple one-step predictive controller, which is shown to recover the time-optimal solution, while being feasible for real-time computations. We present simulation results suggesting a decrease in charging time by 50% compared to the conventional constant-current / constant-voltage method for lithium-ion batteries.

Modeling, estimation, and control challenges for lithium-ion batteries

Increasing demand for hybrid electric vehicles (HEV), plug-in hybrid electric vehicles (PHEV) and electric vehicles (EV) has forced battery manufacturers to consider energy storage systems that are better than contemporary lead-acid batteries. Currently, lithium-ion (Li-ion) batteries are believed to be the most promising battery system for HEV, PHEV and EV applications. However, designing a battery management system for Li-ion batteries that can guarantee safe and reliable operation is a challenge, since aging and other performance degrading mechanisms are not sufficiently well understood. As a first step to address these problems, we analyze an existing electrochemical model from the literature. Our aim is to present this model from a systems & controls perspective, and to bring forth the research challenges involved in modeling, estimation and control of Li-ion batteries. Additionally, we present a novel compact form of this model that can be used to study the Li-ion battery. We use this reformulated model to derive a simple approximated model, commonly known as the single particle model, and also identify the limitations of this approximation.

State estimation of a reduced electrochemical model of a lithium-ion battery

Batteries are the key technology for enabling further mobile electrification and energy storage. Accurate prediction of the state of the battery is needed not only for safety reasons, but also for better utilization of the battery. In this work we present a state estimation strategy for a detailed electrochemical model of a lithium-ion battery. The benefit of using a detailed model is the additional information obtained about the battery, such as accurate estimates of the state of charge within the individual electrodes, overpotential, concentration and current distribution across the electrodes, which can be utilized for safety and optimal operation. We propose an observer based on a reduced set of partial differential-algebraic equations, which are solved on a coarse spatial grid. The reduced model has a less complex structure, while still capturing the main dynamics. The observer is tested in experiments for actual electric-vehicle drive cycles. Experimental results show the observer to be robust with respect to unmodeled dynamics, as well as to noisy and biased voltage and current measurements. The available state estimates can be used for monitoring purposes, or incorporated into a model based controller to improve the performance of the battery while guaranteeing safe operation.

Advanced control of a reactive distillation column

Abstract The paper presents a detailed analysis of the dynamic behavior of a reactive distillation column. A control relevant dynamic model is derived using firstprinciples modeling and it is used to study the dynamic behavior of the process at high and low purity operating regimes. The results are used to analyze the performance of linear and nonlinear model predictive control in comparison to coupled PID control.

Battery State Estimation for a Single Particle Model With Electrolyte Dynamics

This paper studies a state estimation scheme for a reduced electrochemical battery model, using voltage and current measurements. Real-time electrochemical state information enables high-fidelity monitoring and high-performance operation in advanced battery management systems, for applications such as consumer electronics, electrified vehicles, and grid energy storage. This paper derives a single particle model (SPM) with electrolyte that achieves higher predictive accuracy than the SPM. Next, we propose an estimation scheme and prove estimation error system stability, assuming that the total amount of lithium in the cell is known. The state estimation scheme exploits the dynamical properties, such as marginal stability, local invertibility, and conservation of lithium. Simulations demonstrate the algorithm’s performance and limitations.

Investigation of projection-based model-reduction techniques for solid-phase diffusion in Li-ion batteries

In this work, we apply the projection-based model-reduction framework for PDEs of [1] to the diffusion process governing the intercalation of lithium ions into spherical particles that appears in electrochemical models of Li-ion batteries. We first invoke the projection framework with different projections (the so-called natural-i.e. Galerkin-and volume-averaging projections-NP and VAP, respectively) and different basis sets (even monomials and eigenfunctions of the PDE) to arrive at different reduced models, which we then benchmark in a dimensionless frequency-domain setting. Surprisingly, we find that VAP of an even monomial basis yields an unstable reduced model for anything but the lowest order; however, NP yields suitable results for the basis sets and orders considered. Furthermore, we find that the NP-eigenfunction combination makes for a slow convergence when compared to NP with even monomials; however, room for further improvement is seen when compared with a balanced truncation, which is not applicable in the nonlinear setting of concentration-dependent diffusivity.

Approximations for Partial Differential Equations Appearing in Li-Ion Battery Models

Li-ion based batteries are believed to be the most promising battery system for HEV/PHEV/EV applications due to their high energy density, lack of hysteresis and low self-discharge currents. However, designing a battery, along with its Battery Management System (BMS), that can guarantee safe and reliable operation, is a challenge since aging and other mechanisms involving optimal charge and discharge of the battery are not sufficiently well understood. In a previous article [1], we presented a model that has been studied in [2]–[5] to understand the operation of a Li-ion battery. In this article, we continue our work and present an approximation technique that can be applied to a generic battery model. These approximation method is based on projecting solutions to a Hilbert subspace formed by taking the span of an countably infinite set of basis functions. In this article, we apply this method to the key diffusion equation in the battery model, thus providing a fast approximation for the single particle model (SPM) for both variable and constant diffusion case.Copyright

State Estimation for an Electrochemical Model of Multiple-Material Lithium-Ion Batteries

This paper presents state estimation for a system of diffusion equations coupled in the boundary appearing in reduced electrochemical models of lithium-ion batteries with multiple active materials in single electrodes. The observer is synthesized from a single particle model and is based on the backstepping method for partial differential equations. The observer is suitable for state of charge estimation in battery management systems and is an extension of existing backstepping observers which were derived only for cells with electrodes of single active materials. Observer gains still can be computed analytically in terms of Bessel and modified Bessel functions. This extension is motivated by the trend in cell manufacturing to use multiple active materials to combine power and energy characteristics or reduce degradation.

Towards adaptive health-aware charging of Li-ion batteries: A real-time predictive control approach using first-principles models

Todays charging strategies of Li-ion batteries are often designed off-line and do not balance optimal fast charging and battery lifetime. By a lack of adaptation during operation, the off-line charging strategies do not allow aging-related changes of the battery properties to be taken into account. As such, to achieve safe operation, batteries and cells are typically operated in a range that is far away from the achievable operational limits. This article presents a nonlinear predictive control strategy that allows real-time optimal health-aware charging based on detailed first-principles models. The approach balances fast charging while improving battery lifetime. By considering the on-line adjustment of battery model parameters, the approach is able to directly take aging- and environment-related changes into account.