Development and analysis of a battery degradation model for use in mixed-integer linear programming

The transition towards electromobility in conjunction with increasing bidirectional charging is also placing greater focus on battery aging. Given the popularity of mixed-integer linear programming (MILP) in analyzing energy systems, there is a significant need for suitable battery degradation models. However, the complicated battery aging processes are often highly simplified in the literature. Therefore, we develop and evaluate a more suitable and accurate model. For this purpose, an existing non-linear continuous battery degradation model is discretized and piecewise linearized. The discretization error is kept below 0 . 1 % , while the additional linearization causes a maximum deviation of 2 . 3 % for calendar and 1 % for cyclic degradation. To further evaluate the model and its variants, it is implemented in an optimization problem representing a residential bidirectional charging use case. Distinct State-of-Charge (SOC) modeling for calendar degradation results in solving times that vary significantly (minutes to days), while this variation is less severe for different cyclic temperature variants. Although the effect on the optimal operating strategy is only limited, the general neglect leads to considerable differences, especially regarding the dominating calendar degradation. The concluding comparison with a frequently used energy throughput method shows an increase in solving time (seconds vs. minutes), but also significant differences in operating strategy. The developed model leads to lower SOCs due to calendar degradation, and provides a more accurate cyclic degradation and economic evaluation of bidirectional charging, offering the possibility of a more adequate integration of battery degradation and its effects into MILP models. • Development of a BEV battery degradation model for mixed-integer linear programming. • Discretization and linearization error is less than 2.3% (calendar) and 1% (cyclic). • Model offers comparatively quick and accurate consideration of battery degradation. • Optimal operating strategy is primarily influenced by calendar degradation. • Simplified energy throughput method is only suitable to a very limited extent.