Identifying and Applying State-Space Models Derived from High-Fidelity Physical Models of Li-Ion Batteries
Authors: Weddle Peter , Vincent Tyrone , Kee Robert J. 
Published: February 2020

Linear state-space models play a variety of important roles in battery development and real-time control. The objective of the present paper is to derive state-space models from large-scale models that represent details of the battery physics, chemistry, and electrochemistry. The state-space models typically represent the battery behavior with tens of states, compared to full battery models that can involve many thousands of states. The present paper uses Siemens PLM (CD-Adapco) battery models, particularly the Battery Design Studio (BDS) software, as the basis for the physical models. These models have been extensively validated for a particular commercially available 18650-format Li-ion battery. The state-space models are derived computationally using pseudo-random binary sequences (PRBS). The low-dimensional state-space models are validated using direct comparisons with the large-scale physical models for a variety of charge-discharge profiles. The results show excellent agreement.
Transient, small-amplitude, step-change profiles from pseudo-random binary sequences (PRBS) are used for identifying battery dynamics over wide frequency ranges. For example, battery physics have frequency responses that range from relatively fast charge-transfer chemistry to relatively slow intercalation diffusion. The perturbed system outputs (e.g., voltage and cell temperature) are used to obtain a dynamic model using system-identification techniques that capture the input-output behavior. Although the state-space models need to represent battery dynamics over very large frequency ranges, the PRBS-derived models are most accurate within limited frequency ranges. Thus, the full state-space models are represented as smooth combinations of several models that are most accurate within limited frequency ranges. The single state-space model single is the result of a two-step algorithm. First, the large-scale physical model is exercised with PRBS actuation over a particular frequency range, identifying the frequency response and system poles. This information is then used to identify a single model that covers the frequency response over the entire frequency range of interest. With the poles identified in the first step, the second step is linear in the parameters, and thus numerically well characterized.
The Figure shows direct comparison between a 12-state gain-scheduled state-space model and a large-scale physical model. The imposed demand profile considers multiple charge and discharge intervals, with the battery beginning from a fully charged state and finally achieving a fully discharged state. The transient voltage-current and temperature profiles agree very well. Thus, the state-space model is seen to be accurate over greatly different battery states.
Validated state-space models can be used for a variety of purposes. The state-space models can be used very efficiently to simulate measurable electrochemical impedance spectra (EIS). Thus, the approach provides a means for physics-based interpretation of laboratory-scale EIS measurements. Additionally, because state-space models can be run in real time on microprocessors, they form the basis for implementing model-predictive control (MPC) strategies. The MPC controllers play important roles in the interpretation of sensors and using physical knowledge to guide control actuation. Finally, the state-space models provide a physics-based means evaluate battery state-of-health, influencing optimal control decisions and mitigating potentially hazardous operating conditions.

Figure 1