In this paper we present a procedure for the optimal siting and sizing of Energy Storage Systems (ESSs) owned, and directly controlled by network operators of Active Distribution Networks (ADNs). The peculiarity of the proposed planning procedure consists in embedding the grid reconfiguration. We use a recently proposed conditionally exact convex Optimal Power Flow (OPF) as the core of the optimization model. We appropriately model the objective function to include both technical and economic aspects, while keeping the exactness of the relaxed convex OPF. In particular, the proposed procedure accounts for the minimization of: voltage-magnitude deviations, feeders'/lines' congestion, cost of supplying loads, and investment costs related to the ESSs. In addition, the seasonal configurations of the grid are determined based on (1) network security constraints, and (2) the minimum resistive losses. The stochasticity of loads and renewable productions also are taken into account. We suitably modeled the ESSs to consider their ability to support the network by both active and reactive powers. Two test cases are used to demonstrate, and quantify, the capabilities of the proposed procedure for providing optimal and feasible solutions.

The recent literature discusses the use of the relaxed Second Order Cone Programming for formulating Optimal Power Flow (OPF) for radial grids. However, if the shunt parameters of the lines are considered, the methods do not provide sufficient conditions that can be verified ex ante for the exactness of the optimal solutions. The same formulations also have not correctly accounted for the lines' ampacity constraint. Similar to the inclusion of upper voltage-magnitude limit, the SOCP relaxation faces difficulties when the ampacity constraints of the lines are binding. To overcome these limitations, we propose a convex formulation for the OPF in radial grids, for which the AC-OPF equations, including the transverse parameters, are considered. To limit the lines' current together with the nodal voltage-magnitudes, we augment the formulation with a new set of more conservative constraints. Sufficient conditions are provided to ensure the feasibility and optimality of the proposed OPF solution. The proofs of the exactness of the SOCP relaxation are provided. Using standard grids, we show that these conditions are mild and hold for real distribution networks.

The ever-increasing penetration of Distributed Generators (DGs) in distribution networks suggests to enable their potentials in better fulfilling the restoration objective. The objective of the restoration problem is to resupply the maximum energy of loads considering their priorities using minimum switching operations. Basically, it is desired to provide a unique configuration that is valid regarding the load and generation profiles along the entire restorative period. However, this unique configuration may not satisfy at the same time: I) the DG start-up requirements at the beginning of the restoration plan and II) the topological conditions that would allow the DG to provide later on the most efficient support for the supply of loads. Therefore, it is proposed in this paper to allow a limited number of reconfiguration steps according to the DG start-up requirements. In addition, this paper presents a novel formulation for the reconfiguration problem that accounts for partial restoration scenarios where the whole unsupplied area cannot be restored. The overall model is formulated as a mixed-integer second-order cone programming. Two simulation scenarios are studied in order to illustrate different features of the proposed strategy and to demonstrate its effectiveness particularly in the case of large-scale outages in distribution networks.

The ever-increasing utilization of sensitive loads in the industrial, commercial and residential areas in distribution networks requires enhanced reliability and quality of supply. This can be achieved thanks to self-healing features of smart grids that already include the control technologies necessary for the restoration strategy in case of a fault. In this paper, an analytical and global optimization model is proposed for the restoration problem. A novel mathematical formulation is presented for the reconfiguration problem reducing the number of required binary variables while covering more practical scenarios compared to the existing models. The considered self-healing actions besides the network reconfiguration are the nodal load-rejection, the tap setting modification of voltage regulation devices (incl. OLTCs, SVR, and CBs), and the active/reactive power dispatch of DGs. The voltage dependency of loads is also considered. Thus, the proposed optimization problem determines the most efficient restoration plan minimizing the number of de-energized nodes with the minimum number of self-healing actions. The problem is formulated as a Mixed-Integer Second Order Cone Programming (MISOCP) and solved using the Gurobi solver via the MATLAB interface YALMIP. A real 83-node distribution network is used to test and verify the presented methodology.