• Energy Research

Abstract Reduced-order physics-based models of lithium-ion cells provide the opportunity for a battery-management system to define battery-pack operational limits in terms of cell internal electrochemical processes in order to mitigate degradation and to avoid failure modes. For these physics-based models to be relevant over the lifetime of the battery pack, they must somehow adjust to describe the internal processes accurately at every stage of battery life. Two possible approaches to do so suggest themselves. First, an algorithm might somehow adapt the parameter values of the model during operation to match presently observed current–voltage behaviors; but, this must be done very carefully to avoid making the model unstable or physically nonmeaningful. Alternately, a set of models could be pre-computed at different feasible aging points and the model from this set that most closely predicts presently observed current–voltage dynamics could be selected from the set. This second approach guarantees stable and physically meaningful models since all models in the pre-computed set meet these criteria. We propose such an approach here. To do so, we first present a method for calculating a priori the changes to cell parameter values that will be produced by aging due to side reactions and/or material loss. These aged parameter values are utilized to produce reduced-order physics-based models at different stages of cell life. The reduced-order models are then used within a nonlinear interacting multiple-model Kalman filter to select the pre-computed model whose voltage predictions most resembles present measured voltage, so providing an estimate of the aged parameter values of a cell via the parameter values of this model. The selected model may then be used for state-of-charge estimation, state-of-power estimation, state-of-energy estimation, and other model-based battery-management tasks.

Abstract Reduced-order physics-based models of lithium-ion cells provide the opportunity for a battery-management system to define battery-pack operational limits in terms of cell internal electrochemical processes in order to mitigate degradation and to avoid failure modes. For these physics-based models to be relevant over the lifetime of the battery pack, they must somehow adjust to describe the internal processes accurately at every stage of battery life. Two possible approaches to do so suggest themselves. First, an algorithm might somehow adapt the parameter values of the model during operation to match presently observed current–voltage behaviors; but, this must be done very carefully to avoid making the model unstable or physically nonmeaningful. Alternately, a set of models could be pre-computed at different feasible aging points and the model from this set that most closely predicts presently observed current–voltage dynamics could be selected from the set. This second approach guarantees stable and physically meaningful models since all models in the pre-computed set meet these criteria. We propose such an approach here. To do so, we first present a method for calculating a priori the changes to cell parameter values that will be produced by aging due to side reactions and/or material loss. These aged parameter values are utilized to produce reduced-order physics-based models at different stages of cell life. The reduced-order models are then used within a nonlinear interacting multiple-model Kalman filter to select the pre-computed model whose voltage predictions most resembles present measured voltage, so providing an estimate of the aged parameter values of a cell via the parameter values of this model. The selected model may then be used for state-of-charge estimation, state-of-power estimation, state-of-energy estimation, and other model-based battery-management tasks.

Battery-management systems (BMS) seek to maximize battery-pack performance while extending life by optimizing dynamic operational power limits. To do so in a meaningful way, the BMS must have computationally simple yet accurate models of degradation to use in the optimization. As the growth of a solid-electrolyte interphase (SEI) layer on negative-electrode particles in lithium-ion cells is the dominant aging mechanism leading to capacity loss and resistance rise, we propose a reduced-order model of diffusion-or kinetics-limited SEI growth that could be used in an embedded optimization framework. This model approximates a full-order partial-differential-equation (PDE) model in the literature with less than 1 % relative error, at a speedup of more than 19 000 : 1.

Battery-management systems (BMS) seek to maximize battery-pack performance while extending life by optimizing dynamic operational power limits. To do so in a meaningful way, the BMS must have computationally simple yet accurate models of degradation to use in the optimization. As the growth of a solid-electrolyte interphase (SEI) layer on negative-electrode particles in lithium-ion cells is the dominant aging mechanism leading to capacity loss and resistance rise, we propose a reduced-order model of diffusion-or kinetics-limited SEI growth that could be used in an embedded optimization framework. This model approximates a full-order partial-differential-equation (PDE) model in the literature with less than 1 % relative error, at a speedup of more than 19 000 : 1.

Building a complete cell impedance model and quickly calculating its frequency response are essential for battery design, optimization, and online management. Based on the widely accepted pseudo-two-dimensional (P2D) model, we build a complete full-order partial-dierential-equation (PDE) model for porous-electrode lithium-ion cells that includes a configurable electrical double-layer model at the solid-electrolyte interface (SEI). With the help of a numeric method, cell impedance and frequency responses of the cell’s electrochemical variables at different locations inside the cell are obtained and analyzed. Moreover, in order to achieve the fast calculation of impedance and frequency responses, we derive transfer functions of the internal electrochemical variables, which give a set of exact closed-form equations for cell impedance and internal-variable frequency responses. The Nyquist plot results calculated by the closed-form equations are exactly consistent with the results of numeric simulations using the full-order model, which verifies the accuracy of the transfer functions and the effectiveness of the simplified method.

Building a complete cell impedance model and quickly calculating its frequency response are essential for battery design, optimization, and online management. Based on the widely accepted pseudo-two-dimensional (P2D) model, we build a complete full-order partial-dierential-equation (PDE) model for porous-electrode lithium-ion cells that includes a configurable electrical double-layer model at the solid-electrolyte interface (SEI). With the help of a numeric method, cell impedance and frequency responses of the cell’s electrochemical variables at different locations inside the cell are obtained and analyzed. Moreover, in order to achieve the fast calculation of impedance and frequency responses, we derive transfer functions of the internal electrochemical variables, which give a set of exact closed-form equations for cell impedance and internal-variable frequency responses. The Nyquist plot results calculated by the closed-form equations are exactly consistent with the results of numeric simulations using the full-order model, which verifies the accuracy of the transfer functions and the effectiveness of the simplified method.

Abstract This paper introduces the “discrete-time realization algorithm” (DRA) as a method to find a reduced-order, discrete-time realization of an infinite-order distributed-parameter system such as a transcendental impedance function. In contrast to other methods, the DRA is a bounded-time deterministic method that produces globally optimal reduced-order models. In the DRA we use the sample and hold framework along with the inverse discrete Fourier transform to closely approximate the discrete-time impulse response. Next, the Ho–Kalman algorithm is used to produce a state-space realization from this discrete-time impulse response. Two examples are presented to demonstrate the DRA using low-order rational-polynomial transfer functions, where the DRA solution can be compared to known solutions. A third example demonstrates the DRA with a transcendental impedance function model of lithium diffusion in the solid phase of a lithium-ion battery, showing that a third-order discrete-time model can closely approximate this infinite-order model behavior.