A mixed integer SDP approach for the optimal placement of energy storage devices in power grids with renewable penetration

In power networks, Energy Storage Systems (ESS) can help to cope with intermittent availability of renewable sources. However, fixed, maintenance, and operating costs are a critical aspect that must be considered in the positioning and sizing of these devices. This paper addresses the problem of placing storage devices in order to achieve an Optimal Power Flow (OPF) in presence of renewable sources. The problem is addressed formulating a Mixed Integer Semidefinite Program (MI-SDP) that takes into account energy production and ESS costs. While this approach provides a solution that does not guarantee a physical meaning, this latter is recoverable from the dual solution of the MI-SDP with fixed storage devices locations. The approach is demonstrated on the IEEE 14 and 30 bus benchmark systems where power demand, renewable generation profiles and costs have been taken from real data.