Convexity of the annualized cost of energy systems with usage-dependent component lifetimes

An energy system optimization (joint sizing & dispatch) which accounts for the effect of component aging on the annualized cost of the system is proposed. Despite being nonlinear, the model is proved to be convex under a generalized "lifetime = size/usage" hypothesis. This assumption is shown to cover the classical energy counting model for battery cycling aging, while a linear approximation is needed to account for the operating hours of dispatchable generators. The convexity of the model allows for a piecewise linear approximation which is solved efficiently with linear programming solvers. On an illustrative open-source microgrid sizing test case, the proposed model significantly reduces the levelized cost of energy compared to the classical fixed-lifetime approaches. Solving time is kept within the same order of magnitude, thanks to the model convexity. The proposed model also compares favorably with the more advanced "usage penalty" approaches, even though an improved variant of these is formulated and used.