  With the introduction of massive renewable energy sources and storage
devices, the traditional process of grid operation must be improved in order to
be safe, reliable, fast responsive and cost efficient, and in this regard power
flow solvers are indispensable. In this paper, we introduce an Interior
Point-based (IP) Multi-Period AC Optimal Power Flow (MPOPF) solver for the
integration of Stationary Energy Storage Systems (SESS) and Electric Vehicles
(EV). The primary methodology is based on: 1) analytic and exact calculation of
partial differential equations of the Lagrangian sub-problem, and 2) exploiting
the sparse structure and pattern of the coefficient matrix of Newton-Raphson
approach in the IP algorithm. Extensive results of the application of proposed
methods on several benchmark test systems are presented and elaborated, where
the advantages and disadvantages of different existing algorithms for the
solution of MPOPF, from the standpoint of computational efficiency, are brought
forward. We compare the computational performance of the proposed
Schur-Complement algorithm with a direct sparse LU solver. The comparison is
performed for two different applicational purposes: SESS and EV. The results
suggest the substantial computational performance of Schur-Complement algorithm
in comparison with that of a direct LU solver when the number of storage
devices and optimisation horizon increase for both cases of SESS and EV. Also,
some situations where computational performance is inferior are discussed.
