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For the popular second-order conic program (SOCP) formulation of AC optimal power flow (OPF) in a radial network, this paper first shows that it does not have the strong duality property in general. Then, through a series of restrictive reformulations, we derive a set of closed-form sufficient conditions on network parameters that ensure its strong duality. Numerical studies on IEEE 33-bus, 69-bus test networks and two real-world distribution systems confirm that non-negligible duality gaps do exist in this SOCP formulation, and also demonstrate the validity of the proposed sufficient conditions on closing the duality gap. Our results provide an analytical tool to ensure the strong duality of the SOCP power flow formulation and to support algorithm developments for its complex extensions. [ABSTRACT FROM AUTHOR]

This paper presents a chance constrained information gap decision model for multi-period microgrid expansion planning (MMEP) considering two categories of uncertainties, namely random and non-random uncertainties. The main task of MMEP is to determine the optimal sizing, type selection, and installation time of distributed energy resources (DER) in microgrid. In the proposed formulation, information gap decision theory (IGDT) is applied to hedge against the non-random uncertainties of long-term demand growth. Then, chance constraints are imposed in the operational stage to address the random uncertainties of hourly renewable energy generation and load variation. The objective of chance constrained information gap decision model is to maximize the robustness level of DER investment meanwhile satisfying a set of operational constraints with a high probability. The integration of IGDT and chance constrained program, however, makes it very challenging to compute. To address this challenge, we propose and implement a strengthened bilinear Benders decomposition method. Finally, the effectiveness of proposed planning model is verified through the numerical studies on both the simple and practical complex microgrid. Also, our new computational method demonstrates a superior solution capacity and scalability. Compared to directly using a professional mixed integer programming solver, it could reduce the computational time by orders of magnitude. [ABSTRACT FROM PUBLISHER]