Profit maximizing storage allocation in power grids

This work investigates the interaction between nodal price signals and the optimal allocation and operation of distributed energy storage systems (ESS) in alternating current (AC) power networks. We model a multi-period optimal power flow (OPF) problem with charge and discharge dynamics for energy storage collocated with load and/or generation. We then apply a convex relaxation based on semidefinite programming (SDP) and derive the storage subproblem from the Lagrangian dual. We use the storage subproblem to investigate the relationship between the storage variables and the locational marginal prices (LMPs), which are market-based price signals defined by the dual variables associated with the nodal active power flow balance. Our theoretical results prove that LMPs drive charging and discharging dynamics, and that storage is allocated and operated to maximize the storage operator's profits, i.e. minimize the system costs in a purely competitive market. We then use this framework to illustrate LMP-based storage dynamics.