A convex–concave approach for energy scheduling of battery energy storage systems with degradation modeling

Battery energy storage systems (BESSs) are increasingly deployed in power system applications to enable an increased penetration of renewable energy sources. Incorporating battery degradation models into optimization schemes is vital for the economic scheduling of BESSs. However, battery degradation depends non-linearly
on its operating conditions, resulting in challenging optimization problems. Existing methods approximate non-convex degradation functions using piecewise-linear models with binary variables, resulting in mixed-integer linear programs (MILP) that scale poorly. Towards this direction, this work develops a convex–concave
approach (CCA) to yield fast and high-quality solutions. Specifically, the CCA approach represents the nonconvex degradation function as the difference of two convex functions. The first function is approximated using a convex piecewise linear function, while the second function is linearized around a solution point using a
first-order Taylor approximation. The resulting optimization problem with the convexified degradation model is used in an iterative algorithm that updates the solution point in each iteration. Moreover, the CCA approach is initialized with a good starting solution point to enhance its performance by approximating the original
degradation function using a convex function with two intersecting planes. The CCA approach is applied to both the original Unit Commitment (UC) problem and its relaxed version, which incorporate BESSs. Simulation results validate the efficacy of the proposed CCA approach to generate fast and high-quality solutions, achieving
speedups of more than 100x and 9600x for the original and relaxed UC problems, respectively, compared to the MILP approach and a state-of-the-art nonlinear solver.