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Thus, in this thesis, we also develop a simple online algorithm where the knowledge of the future demand information is not necessary.Leveraging the zero duality gap property in the OPF problem, we first characterize the optimal solution of the OPF problem and decomposed problems which are decoupled over time.Energy management is of prime importance for power system operators to enhance the use of the existing and new facilities, while maintaining a high level of reliability.
Therefore, in this thesis, we study the optimal power flow problem with energy storage dynamics in purely resistive power networks.
We first formulate it as a dynamic nonconvex OPF problem.
First, we study the optimal power flow (OPF) in ac-dc grids, which is a non-convex optimization problem.
We use convex relaxation techniques and transform the problem into a semidefinite program (SDP).
Then we propose an efficient second order cone programming (SOCP) relaxation for this nonconvex problem.