Distributed energy storage devices are commonly employed as an effective approach for addressing operational challenges introduced by the large scale integration of renewables. However, the modeling of storage devices results in intertemporal coupling of the individual optimal power flow (OPF) problems defined at each subdivision of the time period of interest. The resulting multiperiod optimal power flow (MPOPF) problem becomes intractable prohibiting, forecasting, and planning over long time periods. Interior point (IP) methods have been extensively employed for the solution of OPF and MPOPF problems. This work proposes an efficient IP algorithm, BELTISTOS, particularly designed for MPOPF problems. The structure of the linear system associated with the Karush-Kuhn-Tucker conditions is revisited, and a Schur-complement-based approach tailored to its structure is proposed. Through benchmark cases involving power-grid models of increasing complexity, the BELTISTOS algorithm is demonstrated to provide several orders of magnitude faster solution times than standard optimization methods, such as IPOPT, MIPS, and KNITRO, using significantly less memory.