Convex Nonlinear Battery Aging Model for Microgrid Sizing Optimization

The sizing of microgrids with energy storage systems can be a complex optimization problem, so accurate models of battery degradation are often discarded to avoid intractable computational times. However, aging can downgrade battery ratings over time, perturb the system operation and eventually depreciate the microgrid design objectives. To better account for battery degradation in microgrid sizing, a C-rate dependent nonlinear cycling aging model from the literature is analyzed. The computational tractability is shown by proving the convexity of the resulting aging-aware optimization problem. Two aspects of the battery degradation model are investigated: 1) nonlinear component cost due to the degradation-dependent lifetime and 2) capacity fade along time. A simple microgrid design problem, expanded with this nonlinear C-rate dependent battery degradation model, is solved numerically. This shows the impact of the degradation model on the system sizing and cost, but also on the battery operation and computational time. Results are compared to those from the classical constant energy throughput model, which is not C-rate dependent.