Optimal Battery Energy Storage Control for Multi-Service Provision Using a Semidefinite Programming-Based Battery Model

Battery energy storage systems (BESS) capable of simultaneously providing multiple grid services can assist a distribution grid operator in overcoming various challenges due to the high penetration of distributed solar photovoltaics and accelerated electrification. The seamless provision of multiple services can be ensured with BESS control decisions based on an accurate model reflecting the battery characteristics. Thus, this paper presents a novel Li-ion battery model based on linear matrix inequalities along with a semidefinite programming (SDP)-based model to determine the optimal BESS control decisions for the provision of multiple services in distribution systems. Peak shaving, power factor improvement, and electricity cost savings are considered for the services. Moreover, the mathematical analysis reveals that the original nonconvex problem can be equivalently transformed into the SDP model. The effectiveness of using BESS in the distribution system is verified through simulations using real-world data. Ultimately, a comparative analysis with a conventional linear model demonstrates that the proposed battery model reduces the energy losses in the batteries, in the simulation condition, and help maintain the battery states within normal operating limits.