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This paper presents a stochastic scenario-based approach to finding an efficient plan for the electrical power distribution systems. In this paper the stochasticity for the distribution system expansion planning (DSEP) problem refers to the loads and wind speed behavior. The proposed DSEP model consist the expansion and/or construction of new substations, installation of new primary feeders and/or reinforcement the existing, installation of wind-distributed generation based, reconfiguration of existing network, and the proposed DSEP is solved considering uncertainty in electric demand and distributed generation. In this regard, a two-stage stochastic programming model is used, wherein the first stage the investment decision is made and the second stage calculates the expected operating value which depends on the stochastic scenarios. The mathematical approach is based on a mixed integer conic programming (MICP) model. By using this MICP model and a commercial optimization solver, finding the optimal global solution is guaranteed. Moreover, in this paper by using the B Juan Manuel Home Ortiz

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.

This paper presents a mixed-integer conic programming model (MICP) and a hybrid solution approach based on classical and heuristic optimization techniques, namely matheuristic, to handle long-term distribution systems expansion planning (DSEP) problems. The model considers conventional planning actions as well as sizing and allocation of dispatchable/renewable distributed generation (DG) and energy storage devices (ESD). The existing uncertainties in the behavior of renewable sources and demands are characterized by grouping the historical data via the k-means. Since the resulting stochastic MICP is a convex-based formulation, finding the global solution of the problem using a commercial solver is guaranteed while the computational efficiency in simulating the planning problem of medium-or large-scale systems might not be satisfactory. To tackle this issue, the subproblems of the proposed mathematical model are solved iteratively via a specialized optimization technique based on variable neighborhood descent (VND) algorithm. To show the effectiveness of the proposed model and solution technique, the 24-node distribution system is profoundly analyzed, while the applicability of the model is tested on a 182node distribution system. The results reveal the essential requirement of developing specialized solution techniques for large-scale systems where classical optimization techniques are no longer an alternative to solve such planning problems.Index Terms-Distribution systems expansion planning, energy storage devices, VND-based matheuristic algorithm, mixed-integer conic programming, stochastic programming.

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 𝑠 used to avoid the interconnection of substations 𝑔 Artificial generation of the real substation 𝑠 at 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 𝑠 is supplying the demand of node 𝑖, if 𝑦 = 1, or not, if 𝑦 = 0

The optimal power flow (OPF) problem is a widely studied subject in the literature that has been solved through classical and metaheuristic optimization techniques. Nowadays, significant advances in computational resources and commercial optimization solvers allow solving complex optimization problems by combining the best of both worlds in approaches that are known as matheuristics, however, in order to solve the OPF problem, matheuristic approaches have been little explored. In this regard, this paper presents a novel Variable Neighborhood Descent (VND) matheuristic approach to solve the OPF problem for large-scale systems. The proposed algorithm combines the classic OPF model and the VND heuristic algorithm. The OPF problem is formulated as a mixed-integer nonlinear programming (MINLP) model, in which the objective function aims to minimize the fuel generation costs, subject to the physical and operational constraints of the power system. The integer variables of this MINLP model represent the control of taps positions of the on-load tap changers and the reactive shunt compensation equipment. To validate the proposed methodology, 17 power systems of specialized literature were tested with sizes from 14 to 4661 buses, and the obtained solutions are compared with the solutions provided by the commercial optimization solver Knitro. Results show the superiority of the proposed matheuristic algorithm compared with Knitro to solve the MINLP-OPF model for large-scale systems.