This paper deals with the problem of the optimal placement and sizing of distributed generators (DGs) in alternating current (AC) distribution networks by proposing a hybrid master–slave optimization procedure. In the master stage, the discrete version of the sine–cosine algorithm (SCA) determines the optimal location of the DGs, i.e., the nodes where these must be located, by using an integer codification. In the slave stage, the problem of the optimal sizing of the DGs is solved through the implementation of the second-order cone programming (SOCP) equivalent model to obtain solutions for the resulting optimal power flow problem. As the main advantage, the proposed approach allows converting the original mixed-integer nonlinear programming formulation into a mixed-integer SOCP equivalent. That is, each combination of nodes provided by the master level SCA algorithm to locate distributed generators brings an optimal solution in terms of its sizing; since SOCP is a convex optimization model that ensures the global optimum finding. Numerical validations of the proposed hybrid SCA-SOCP to optimal placement and sizing of DGs in AC distribution networks show its capacity to find global optimal solutions. Some classical distribution networks (33 and 69 nodes) were tested, and some comparisons were made using reported results from literature. In addition, simulation cases with unity and variable power factor are made, including the possibility of locating photovoltaic sources considering daily load and generation curves. All the simulations were carried out in the MATLAB software using the CVX optimization tool.

This paper deals with the problem of optimal location and reallocation of battery energy storage systems (BESS) in direct current (dc) microgrids with constant power loads. The optimization model that represents this problem is formulated with two objective functions. The first model corresponds to the minimization of the total daily cost of buying energy in the spot market by conventional generators and the second to the minimization of the costs of the daily energy losses in all branches of the network. Both the models are constrained by classical nonlinear power flow equations, distributed generation capabilities, and voltage regulation, among others. These formulations generate a nonlinear mixed-integer programming (MINLP) model that requires special methods to be solved. A dc microgrid composed of 21-nodes with existing BESS is used for validating the proposed mathematical formula. This system allows to identify the optimal location or reallocation points for these batteries by improving the daily operative costs regarding the base cases. All the simulations are conducted via the general algebraic modeling system, widely known as the General Algebraic Modeling System (GAMS).

This article addresses a comprehensive analysis of power electrical systems, employing a combined approach of genetic algorithms and mathematical optimization through nonlinear programming with discontinuous derivatives (DNLP) in GAMS. The primary objective is to minimize economic losses and associated costs faced by the network operator following disruptive events. The analysis is divided into two fundamental aspects. Firstly, it addresses the topological reconfiguration of the network, involving the addition of lines and distributed energy resources such as distributed generation. To determine the optimal topological reconfiguration, a genetic algorithm was developed and implemented. This approach aims to restore electrical service to the maximum load within the system. Secondly, an optimal energy dispatch was performed for each generator, considering the variation in load throughout the day. The system’s load curve is taken into account to determine the optimal energy distribution. Thus, the problem of economic losses is approached from two perspectives: the minimization of costs due to nonsupplied electrical energy and the determination of efficient energy dispatch for each generator after network reconfiguration. For the analysis and case studies, simulations were conducted on the IEEE 9- and 30-node test systems. The results demonstrate the effectiveness of the proposed solution, evaluated in terms of reduced load shedding and economic losses.

This article assesses the costs and benefits of incorporating battery energy storage systems (BESS) in transmission network expansion planning (TEP) over multiple time periods. We propose a mixed-integer programming model (MIP) for joint planning of the installation of battery energy storage systems (BESS) and construction of new transmission lines in multiple periods of time. The mathematical formulation of the presented model is based on the strategies of the agents of a transmission network to maximize their benefit, and on the operational restrictions of the power flows in transmission networks. This analysis is performed for the Garver 6 node test system takes into account the power losses in the lines and the restrictions for the energy stored in BESS. The power flows obtained with the MIP model are compared with AC power flows generated with specialized software for flows in power systems. This allows us to demonstrate the potential of models based on DC power flows to achieve approximate results applicable to the behavior and characteristics of real transmission networks. The results show that the BESS increase the net profit in the transmission networks and reduce their power losses.