The globally installed capacity of battery energy storage systems (BESS) has been increasing steadily over the last years. Even with the cost reductions of lithium-ion cells that are fuelling this trend, the cell costs themselves remain one of the main cost factors for modern BESSs, making it beneficial to extend their lifetime and optimize the value generated. Due to a multitude of cell-internal aging effects, lithium-ion cells are subject to degradation, which manifests itself foremost in the form of reduced system capacity, but also in the form of increasing cell resistance as well as safety implications, in particular toward the end of life.
As it has been shown in various existing aging studies, the rate of degradation depends on stress factors, that can be directly influenced through the chosen operating strategy. The primary stress factors that can be influenced during operation are Charge/Discharge Throughput, Start of Charge, Depth of Discharge, cell temperature and current. Degradation models quantify this dependency of stress factors on system capacity and therefore enable aging aware operation of battery energy storage systems. Existing model types can be loosely categorized into empirical models, semi-empirical models and physiochemical models. While empirical models consists of data fits with no direct consideration of the underlying physics (e.g. through reduced order models or machine learning approaches), semi-empirical models incorporate physically informed equations such as the Tafel or Arrhenius equation. Lastly, physiochemical models aim to model the underlying cell-internal electrochemical processes, usually through a set of differential equations.
Reviewing existing literature shows, that most studies in the field of battery energy storage system degradation and operation focus on using empirical and semi-empirical modelling approaches with only few publications using physiochemical models. Furthermore, energy arbitrage sticks out as the stationary storage application that has been most frequently examined with regards to battery degradation.
Through a simulative case study with the in-house developed simulation framework SimSES, we highlight the importance of considering model discretization and path dependency when applying the above models types for techno-economical studies or operation of BESSs. Two approaches investigated here are the direct derivative approach and the approach of using virtual time / virtual full equivalent cycles. The underlying assumption with virtual time is that the future degradation rate correlates more with the extend of degradation that has already happened, than the total time that has passed. This leads to differences in degradation behaviour especially for varying external stress factors. In addition to model discretization, the fit quality itself also plays a significant role, especially when extrapolating over long-time horizons, which is shown by evaluating the respective confidence intervals.
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