In this study, a probabilistic approach for the optimal charging of electric vehicles (EVs) in distribution systems is proposed. The costs of both demand and energy losses in the system are minimised, subjected to a set of constraints that consider EVs smart charging characteristics and operative aspects of the electric network. The stochastic driving patterns for EVs’ owners, battery capacity and active and reactive power demanded at load nodes are considered. The optimal charging of EVs connected to the system benefits the system's operation, as it does a strategy to minimise the cost of energy losses and evaluate the capability of the system to charge EVs’ batteries fully under certain penetration scenarios. Priority periods of EVs’ recharge and the variation of energy price contribute to an adequate demand response, assisting the network operator for complying with quality indices (decrement of power losses) set forward by regulatory entities and developing studies of risk analysis for decision making. On the other hand, there is a valuable participation of the EVs’ owners in improving the operation of the distribution system. Monte Carlo simulation (MCS) is used to assess the stochastic nature of the problem in a secondary (low voltage) distribution network.

In the last decade, the deployment of electric vehicles (EVs) has been largely promoted. This development has increased challenges in the power systems in the context of planning and operation due to the massive amount of recharge needed for EVs. Furthermore, EVs may also offer new opportunities and can be used to support the grid to provide auxiliary services. In this regard, and considering the research around EVs and power grids, this paper presents a chronological background review of EVs and their interactions with power systems, particularly electric distribution networks, considering publications from the IEEE Xplore database. The review is extended from 1973 to 2019 and is developed via systematic classification using key categories that describe the types of interactions between EVs and power grids. These interactions are in the framework of the power quality, study of scenarios, electricity markets, demand response, demand management, power system stability, Vehicle-to-Grid (V2G) concept, and optimal location of battery swap and charging stations.

Transportation electrification has demonstrated a significant position on power utilities and logistic companies, in terms of assets operation and management. Under this context, this paper presents the problem of seeking feasible and good quality routes for electric light commercial vehicles considering battery capacity and charging station siting on the power distribution system. Different transportation patterns for goods delivery are included, such as the capacitated vehicle routing problem and the shortest path problem for the last mile delivery. To solve the problem framed within a mixed integer linear mathematical model, the GAMS software is used and validated on a test instance conformed by a 19-customer transportation network, spatially combined with the IEEE 34 nodes power distribution system. The sensitivity analysis, performed during the computational experiments, show the behavior of the variables involved in the logistics operation, i.e., routing cost for each transport pattern. The trade-off between the battery capacity, the cost of the charging station installation, and energy losses on the power distribution system is also shown, including the energy consumption cost created by the charging operation.

This research addresses the problem of the optimal placement and sizing of (PV) sources in medium voltage distribution grids through the application of the recently developed Newton metaheuristic optimization algorithm (NMA). The studied problem is formulated through a mixed-integer nonlinear programming model where the binary variables regard the installation of a PV source in a particular node, and the continuous variables are associated with power generations as well as the voltage magnitudes and angles, among others. To improve the performance of the NMA, we propose the implementation of a discrete–continuous codification where the discrete component deals with the location problem and the continuous component works with the sizing problem of the PV sources. The main advantage of the NMA is that it works based on the first and second derivatives of the fitness function considering an evolution formula that contains its current solution $\left(x_i^t\right)$ and the best current solution $\left(x_{\mathrm{best}}\right)$, where the former one allows location exploitation and the latter allows the global exploration of the solution space. To evaluate the fitness function and its derivatives, the successive approximation power flow method was implemented, which became the proposed solution strategy in a master–slave optimizer, where the master stage is governed by the NMA and the slave stage corresponds to the power flow method. Numerical results in the IEEE 34- and IEEE 85-bus systems show the effectiveness of the proposed optimization approach to minimize the total annual operative costs of the network when compared to the classical Chu and Beasley genetic algorithm and the MINLP solvers available in the general algebraic modeling system with reductions of $26.89\%$ and $27.60\%$ for each test feeder with respect to the benchmark cases.

This paper addresses the voltage stability margin calculation in medium-voltage distribution networks in the context of exact mathematical modeling. This margin calculation is performed with a second-order cone (SOCP) reformulation of the classical nonlinear non-convex optimal power flow problems. The main idea around the SOCP approximation is to guarantee the global optimal solution via convex optimization, considering as the objective function the $\lambda$-coefficient associated with the maximum possible increment of the load consumption at all the nodes. Different simulation cases are considered in one test feeder, described as follows: (i) the distribution network without penetration of distributed generation; (ii) the distribution network with penetration of distributed generation; and (iii) the distribution grid with capacitive compensation. Numerical results in the test system demonstrated the effectiveness of the proposed SOCP approximation to determine the $\lambda$-coefficient. In addition, the proposed approximation is compared with nonlinear tools available in the literature. All the simulations are carried out in the MATLAB software with the CVX package and the Gurobi solver.

The problem of the optimal load redistribution in electrical three-phase medium-voltage grids is addressed in this research from the point of view of mixed-integer convex optimization. The mathematical formulation of the load redistribution problem is developed in terminals of the distribution node by accumulating all active and reactive power loads per phase. These loads are used to propose an objective function in terms of minimization of the average unbalanced (asymmetry) grade of the network with respect to the ideal mean consumption per-phase. The objective function is defined as the $l_1$-norm which is a convex function. As the constraints consider the binary nature of the decision variable, each node is conformed by a $3\times 3$ matrix where each row and column have to sum 1, and two equations associated with the load redistribution at each phase for each of the network nodes. Numerical results demonstrate the efficiency of the proposed mixed-integer convex model to equilibrate the power consumption per phase in regards with the ideal value in three different test feeders, which are composed of 4, 15, and 37 buses, respectively.