is paper presents a new mixed-integer second-order cone programming model for solving the restoration problem in active distribution systems considering the optimal control of distributed generators (DGs), voltage regulators (VRs), on-load tap changers (OLTCs), and capacitor banks (CBs). In contrast to most of the works found in the literature, temporary loops may be formed in the network during the restorative operation state. is operating condition allows restoring the service to more loads. In this way, the objective function of the problem minimizes (i) the total load not supplied, (ii) the number of switching operations, (iii) the changes in the statuses of the voltage control devices and in the dispatch of the DGs, and (iv) the number of basic loops formed in the system. Several tests are carried out using a 53-node system for single-fault and multiple-fault scenarios. e results obtained with the proposed approach outperform the solutions achieved when only radial configurations are allowed in the problem. Moreover, it is also verified that the voltage control allows for more efficient restoration schemes.
Artificial generation of the artificial substation at node 𝑖 used to ensure the connectivity of the network 𝑓 Artificial flow on line 𝑖𝑗 used to isolate the de-energized sections from the network 𝑔 Artificial generation of the artificial substation at node 𝑖 used to isolate the de-energized sections from the network 𝑓 Artificial flow on line 𝑖𝑗 that was generated at the real substation at node 𝑠used to avoid the interconnection of substations 𝑔 Artificial generation of the real substation 𝑠at node 𝑖 used to avoid the interconnection of substations Binary variables: 𝑦 Binary variable that indicates whether the demand at node 𝑖 is supplied, if 𝑦 = 0, or not, if 𝑦 = 1 𝑤 Binary variable that indicates if the switch of line 𝑖𝑗 is closed, 𝑤 = 1, or open, 𝑤 = 0 𝑤 Binary variable that indicates that the artificial flow on branch 𝑖𝑗 is from the real substation 𝑠, if 𝑤 = 1, or not, if 𝑤 = 0 𝑦 Binary variable that indicates that the real substation 𝑠is supplying the demand of node 𝑖, if 𝑦 = 1, or not, if 𝑦 = 0
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