This express brief proposes two new iterative approaches for solving the power flow problem in direct current (DC) networks as efficient alternatives to the classical Gauss–Seidel and Newton–Raphson methods. The first approach works with the set of nonlinear equations by rearranging them into a conventional fixed point form, generating a successive approximation methodology. The second approach is based on Taylors series expansion method by using a set of decoupling equations to linearize the problem around the desired operating point; these linearized equations are recursively solved until reach the solution of the power flow problem with minimum error. These two approaches are comparable to the classical Gauss–Seidel method and the classical Newton–Raphson method, respectively. Simulation results show that the proposed approaches have a better performance in terms of solution precision and computational requirements. All the simulations were conducted via MATLAB software by using its programming interface.

This research proposes an effective energy management dispatch (EMD) using a convex approximation for battery-based energy storage systems (ESS) and renewable sources in medium-voltage distribution networks. By means of the branch flow formulation, the exact nonlinear programming model representing the EMD is transformed into a convex model through a second-order cone programming relaxation. Two contributions are presented in this work. The first involves analyzing battery-based EES and renewable sources, specifically focusing on their operation with a variable power factor. This analysis considers the reactive power control capabilities of the power electronic converters that connect distributed energy resources to the grid. The second contribution involves evaluating a robust operation scenario by incorporating uncertainties in the availability of renewable generation and the expected daily demand profile. Numerical validations are conducted on two radial distribution networks composed of 27 and 33 nodes. These networks were chosen to represent the characteristics of rural and urban networks in the Colombian distribution system. The results are then compared against those obtained with a classical unitary power factor. The main goal of the proposed EMD is to minimize the expected annual grid energy losses and operating costs through a single-objective analysis. A comparison with metaheuristic optimization algorithms, such as the parallel version of the particle swarm optimizer, the vortex search algorithm, and a genetic algorithm, demonstrates the effectiveness of our convex EMD model for both objective functions under study. All numerical simulations, including the robust model, were run using MATLAB’s Yalmip tool.

This paper deals with the problem regarding the optimal siting and sizing of distribution static compensators (D-STATCOMs) in electrical distribution networks to minimize the expected total annual operating costs. These costs are associated with the investments made in D-STATCOMs and expected energy losses costs. To represent the electrical behavior of the distribution networks, a power flow formulation is used which includes voltages, currents, and power as variables via incidence matrix representation. This formulation generates a mixed-integer nonlinear programming (MINLP) model that accurately represents the studied problem. However, in light of the complexities involved in solving this MINLP model efficiently, this research proposes a mixed-integer convex reformulation. Numerical results regarding the final annual operating costs of the network demonstrate that the proposed mixed-integer convex model is efficient for selecting and locating D-STATCOMs in distribution networks, with the main advantage that it is applicable to radial and meshed distribution grid configurations. A comparative analysis with respect to metaheuristic optimizers and convex approximations confirms the robustness of the proposed formulation. All numerical validations were conducted in the MATLAB programming environment with our own scripts (in the case of metaheuristics) and the CVX convex disciplined tool via the Gurobi solver. In addition, the exact MINLP model is solved using the GAMS software.

This express brief addresses the voltage collapse problem in direct-current (DC) networks by using a recursive heuristic search algorithm based on the Newton–Raphson method. The determinant of the Jacobian matrix in the Newton–Raphson method is used as a sensitivity index to determine the maximum power consumption of the DC network. The recursive solution approach corresponds to a sequential power flow approach by incrementing all values of the power consumptions uniformly. Simulation results validate the efficiency of the proposed method in comparison to the large-scale nonlinear solvers available in the GAMS optimization package. The MATLAB programming environment was employed for implementing the proposed recursive Newton–Raphson method.

Photovoltaic (PV) systems are a clean energy source that allows for power generation integration into electrical networks without destructive environmental effects. PV systems are usually integrated into electrical networks only to provide active power during the day, without taking full advantage of power electronics devices, which can compensate for the reactive power at any moment during their operation. These systems can also generate dynamic reactive power by means of voltage source converters, which are called PV-STATCOM devices. This paper presents a convex formulation for the optimal integration (placement and sizing) of PV-STATCOM devices in electrical distribution systems. The proposed model considers reducing the costs of the annual energy losses and installing PV-STATCOM devices. A convex formulation was obtained to transform the hyperbolic relation between the products of the voltage into a second-order constraint via relaxation. Two simulation cases in the two IEEE test systems (33- and 69-node) with radial and meshed topologies were implemented to demonstrate the effectiveness of the proposed mixed-integer convex model. The results show that PV-STATCOM devices reduce the annual cost of energy losses of electrical networks in a more significant proportion than PV systems alone.