Alternating direction method of multipliers for the optimal siting, sizing, and technology selection of Li-ion battery storage

The present paper addresses the problem of optimal siting, sizing, and technology selection of Li-ion battery storage, employing a mathematical programming approach. The methodology extends the state-of-the-art by considering a nonlinear degradation mechanism of Li-ion batteries from the state of charge, depth of discharge, and storage temperature. Particularly, Mixed-Integer Convex Programming (MICP) problem formulation has been proposed to consider a nonlinear degradation behaviour of Li-ion battery storage with a piecewise quadratic approximation to meet the convexity requirements. The main drawback of the piecewise approximation resides in the inclusion of integer variables what increases a computational burden significantly. For the particular problem, it may easily become intractable with the increase of network size and a number of storage technologies considered. To overcome the issue of tractability and scalability of the combinatorial problem, the MICP problem has been decomposed per energy storage unit and resolved using the Alternating Direction Method of Multipliers. Finally, a sensitivity analysis has been performed within the proposed framework to evaluate the performance value of second-life energy storage solutions.