• Energy Research

Abstract Physics-based models of lithium-ion battery dynamics are developed from fundamental electrochemical principles and describe cell internal electrochemical variables in addition to terminal voltage. Real-time estimates of the values taken on by internal cell variables provided by such models might be leveraged by future battery-management systems to control fast-charging and routine use of a battery pack to maximize performance but minimize aging. These models are most naturally described as sets of coupled partial-differential equations (PDEs), and so the greatest obstacle to their adoption stems from the computational complexity involved in finding solutions to the model equations. To make a feasible physics-based model for battery management, we must construct reduced-order approximations to these PDE models. In this paper, we present four methods to find high-fidelity discrete-time state-space reduced-order models (ROMs) that approximate infinite-order transcendental transfer functions that model the PDE relationships of all electrochemical variables of interest. These four methods are compared for a single cell based on speed, memory usage, robustness, and accuracy of the predictions of the resulting reduced-order models with respect to precise numerical simulations of the PDEs. We find that all four methods produce ROMs that match the linearized PDEs closely in the frequency domain and that yield time-domain simulations that match those from the nonlinear PDEs as well, but that each xRA method has distinct features so that different applications might prefer one method versus another.

Abstract One approach to creating physics-based reduced-order models (ROMs) of battery-cell dynamics requires first generating linearized Laplace-domain transfer functions of all cell internal electrochemical variables of interest. Then, the resulting infinite-dimensional transfer functions can be reduced by various means in order to find an approximate low-dimensional model. These methods include Pade approximation or the Discrete-Time Realization algorithm. In a previous article, Lee and colleagues developed a transfer function of the electrolyte concentration for a porous-electrode pseudo-two-dimensional lithium-ion cell model. Their approach used separation of variables and Sturm–Liouville theory to compute an infinite-series solution to the transfer function, which they then truncated to a finite number of terms for reasons of practicality. Here, we instead use a variation-of-parameters approach to arrive at a different representation of the identical solution that does not require a series expansion. The primary benefits of the new approach are speed of computation of the transfer function and the removal of the requirement to approximate the transfer function by truncating the number of terms evaluated. Results show that the speedup of the new method can be more than 3800.

Abstract Battery management systems (BMS) require computationally simple but highly accurate models of the battery cells they are monitoring and controlling. Historically, empirical equivalent-circuit models have been used, but increasingly researchers are focusing their attention on physics-based models due to their greater predictive capabilities. These models are of high intrinsic computational complexity and so must undergo some kind of order-reduction process to make their use by a BMS feasible: we favor methods based on a transfer-function approximation to battery-cell dynamics. In prior works, transfer functions have been found from full-order PDE models via two assumptions: (1) a linearization assumption—which is a fundamental necessity in order to make transfer functions—and (2) an assumption made out of expedience that decouples the electrolyte-potential and electrolyte-concentration PDEs in order to render an approach to solve for the transfer functions from the PDEs. This paper shows how to eliminate the need for the second assumption, thus retaining the coupling between these two PDEs and improving overall model accuracy. Time-domain models created from these transfer functions are especially improved when simulating constant-current profiles since the electrolyte concentration gradient increases the coupling between the electrolyte-potential and electrolyte-concentration PDEs.

Abstract Although electrochemical models have superior capabilities of internal states estimation to equivalent-circuit models, they have larger numbers of parameter values to be determined while predicting the behaviors of a real cell. Parameter identification of electrochemical models is essential but present methods are time-consuming and complex. In the “Part1” paper in this series, a lumped-parameter electrochemical model was built with the redundant/unobservable parameters removed. Using the this model, this paper proposes a novel stepwise method that can identify the whole set of parameter values for a physical cell using simple tests. The lumped-parameter model is specifically reformulated mostly based on frequency decomposition, and a reference electrode is included in the model to achieve electrode decoupling. The method is decomposed into four tests and eight steps, where the number of parameters to be identified in each step is significantly reduced, enhancing the computational efficiency and improving the identification accuracy. The identified values are first directly compared to the true values, and then the time-domain predictions of the lumped-parameter model using the identified values are compared to those of the full-order model using the true parameter values in terms of the terminal voltage and electrochemical states under different operation conditions.

Abstract Battery-management systems rely on mathematical sets of equations known as models when implementing battery controls procedures. Models are used in state-of-charge, state-of-health, available-energy, and available-power estimation tasks. These models should be high fidelity for good estimates but also computationally lightweight for inexpensive implementation. This paper and its Part-2 companion concern themselves with simple but accurate models of lithium-ion cells having composite electrodes, which are composed of a blend of multiple active materials. In this paper, we develop two forms of equivalent-circuit model (ECM): the series ECM and the parallel ECM—and show how to find values for the model parameters using current–voltage input–output data. We compare simulations of the ECMs to truth data from simulations of a full-order model and show that an ECM designed with knowledge of the material blend can outperform a standard ECM of similar complexity. In the companion paper, we show that it is further possible to create physics-based reduced-order models that have greater predictive power.

Abstract Physics-based battery models can predict not only voltage behaviors of a cell but also internal electrochemical variables such as lithium concentrations and electrical potentials. Knowledge of these variables will be critical in future battery management systems to be able to devise controls that extract the maximum performance from a cell while also slowing down its degradation, since available performance and degradation are both direct functions of the values of these internal electrochemical variables. This paper and its Part-1 companion concern themselves with simple but accurate models of lithium-ion cells having electrodes that are composed of a blend of multiple active materials. In this paper, we show how to create a physics-based reduced-order model (ROM). This ROM not only gives better voltage predictions than the equivalent-circuit models proposed in the Part-1 paper, but is also able to predict all cell internal electrochemical variables. Additionally, its computational complexity is similar to that of the circuit model.