A storage degradation model of Li-ion batteries to integrate ageing effects in the optimal management and design of an isolated microgrid

Li-ion batteries are being increasingly used in stationary applications, allowing for greater autonomy and facilitating the integration of renewable energies. However, these devices lose their capacity over time, especially during their so-called second life. This degradation affects the operation of the system and its cost, and must be taken into consideration if an optimal management is to be found. In this work, we present a framework for the integration of the battery aging in a microgrid design and energy management problem. To do so, we first propose a method to simplify a reference model for cyclic degradation of batteries. The results show that the battery loss of capacity shall be compute on a weekly to monthly basis to accurately keep track of degradation effects. Also, at a first order, we show that ageing is dependent with the initial battery State of Health at every update and the energy exchanged normalized by the nominal capacity. This simplified model formulated with Mixed Integer Linear Programming is integrated in a management problem of an isolated energy system for cost minimization. Optimization results show the necessary trade-off between storage degradation and overall system performances. Finally, a tailored dynamic programming is proposed to simulate successive years for the optimal sizing of the considered system in terms of battery capacity and its replacements. Compared to the proposed pproach, not accounting for the storage degradation leads to inaccurate results and significant cost underestimations (>20 %).