Alexander Molina-Cabrera

Bio: Alexander Molina-Cabrera is an academic researcher from Technological University of Pereira. The author has contributed to research in topics: Electric power system & Nonlinear programming. The author has an hindex of 5, co-authored 18 publications receiving 57 citations. Previous affiliations of Alexander Molina-Cabrera include University of Los Andes.

A Hybrid Approach Based on SOCP and the Discrete Version of the SCA for Optimal Placement and Sizing DGs in AC Distribution Networks

Abstract: 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.

A second-order cone programming reformulation of the economic dispatch problem of bess for apparent power compensation in ac distribution networks

Abstract: The problem associated with economic dispatch of battery energy storage systems (BESSs) in alternating current (AC) distribution networks is addressed in this paper through convex optimization. The exact nonlinear programming model that represents the economic dispatch problem is transformed into a second-order cone programming (SOCP) model, thereby guaranteeing the global optimal solution-finding due to the conic (i.e., convex) structure of the solution space. The proposed economic dispatch model of the BESS considers the possibility of injecting/absorbing active and reactive power, in turn, enabling the dynamical apparent power compensation in the distribution network. A basic control design based on passivity-based control theory is introduced in order to show the possibility of independently controlling both powers (i.e., active and reactive). The computational validation of the proposed SOCP model in a medium-voltage test feeder composed of 33 nodes demonstrates the efficiency of convex optimization for solving nonlinear programming models via conic approximations. All numerical validations have been carried out in the general algebraic modeling system.

Improved Genetic Algorithm for Phase-Balancing in Three-Phase Distribution Networks: A Master-Slave Optimization Approach

Abstract: This paper addresses the phase-balancing problem in three-phase power grids with the radial configuration from the perspective of master–slave optimization. The master stage corresponds to an improved version of the Chu and Beasley genetic algorithm, which is based on the multi-point mutation operator and the generation of solutions using a Gaussian normal distribution based on the exploration and exploitation schemes of the vortex search algorithm. The master stage is entrusted with determining the configuration of the phases by using an integer codification. In the slave stage, a power flow for imbalanced distribution grids based on the three-phase version of the successive approximation method was used to determine the costs of daily energy losses. The objective of the optimization model is to minimize the annual operative costs of the network by considering the daily active and reactive power curves. Numerical results from a modified version of the IEEE 37-node test feeder demonstrate that it is possible to reduce the annual operative costs of the network by approximately 20% by using optimal load balancing. In addition, numerical results demonstrated that the improved version of the CBGA is at least three times faster than the classical CBGA, this was obtained in the peak load case for a test feeder composed of 15 nodes; also, the improved version of the CBGA was nineteen times faster than the vortex search algorithm. Other comparisons with the sine–cosine algorithm and the black hole optimizer confirmed the efficiency of the proposed optimization method regarding running time and objective function values.

Phase Balancing in Power Distribution Systems: A heuristic approach based on group-theory

Abstract: Phase balancing is a highly complex problem that consists of minimizing power losses by swapping generation and loads along a distribution feeder. Being a discrete and nonlinear problem, its solution is usually subject to the use of heuristic methods such as Genetic Algorithms or Particle Swarm Optimization. However, the representation of the feasible space is challenging for conventional approaches. This paper proposes a heuristic algorithm which is based on group-theory, an algebraic modeling that allows a compact and efficient representation of the feasible space. The proposed representation not only allows to develop an algorithm that guarantees feasibility along the generations, but also permits its implementation in the crossover and the mutation steps. Formal definitions of groups are presented and complemented with a matrix homomorphisms that allows the implementation of the algorithm. Numerical calculations on the IEEE 13, IEEE 37 and IEEE 123 nodes test feeders complement the proposed analysis and confirm the efficiency of what is proposed.

PV and battery energy storage integration in distribution networks using equilibrium algorithm

Abstract: Summary Taking advantage of the favorable operating efficiencies, photovoltaic (PV) with Battery Energy Storage (BES) technology becomes a viable option for improving the reliability of distribution networks; however, achieving substantial economic benefits involves an optimization of allocation in terms of location and capacity for the incorporation of PV units and BES into distribution networks. This article suggests a methodology based on the Equilibrium Optimization (EO) algorithm for optimal integration of PV with BES in radial distribution networks. Multifarious objectives are comprised to minimize the cost of energy not supplied (CENS), the investment cost of PV and BES installations, their operational costs, the power losses through the distribution lines, the produced CO2 emissions relative to the grid and PV systems. Added to that, the power losses through the voltage source converter (VSC) interface between integrated PV and BES with the grid are assessed. The proposed methodology is applied on two radial distribution systems of 30-bus and 69-bus. The optimal integration of PV systems with BES have been obtained by considering various case studies by imposing several limits on the number of PV-BES and the state of charge (SoC) for BES. Subsequently, comparative performance analysis is performed using genetic algorithm (GA), EO algorithm, particle swarm optimization (PSO), differential evolution (DE), and grey wolf optimization (GWO).

A mixed-integer convex model for the optimal placement and sizing of distributed generators in power distribution networks

Abstract: The optimal placement and sizing of distributed generators is a classical problem in power distribution networks that is usually solved using heuristic algorithms due to its high complexity. This paper proposes a different approach based on a mixed-integer second-order cone programming (MI-SOCP) model that ensures the global optimum of the relaxed optimization model. Second-order cone programming (SOCP) has demonstrated to be an efficient alternative to cope with the non-convexity of the power flow equations in power distribution networks. Of relatively new interest to the power systems community is the extension to MI-SOCP models. The proposed model is an approximation. However, numerical validations in the IEEE 33-bus and IEEE 69-bus test systems for unity and variable power factor confirm that the proposed MI-SOCP finds the best solutions reported in the literature. Being an exact technique, the proposed model allows minimum processing times and zero standard deviation, i.e., the same optimum is guaranteed at each time that the MI-SOCP model is solved (a significant advantage in comparison to metaheuristics). Additionally, load and photovoltaic generation curves for the IEEE 69-node test system are included to demonstrate the applicability of the proposed MI-SOCP to solve the problem of the optimal location and sizing of renewable generators using the multi-period optimal power flow formulation. Therefore, the proposed MI-SOCP also guarantees the global optimum finding, in contrast to local solutions achieved with mixed-integer nonlinear programming solvers available in the GAMS optimization software. All the simulations were carried out via MATLAB software with the CVX package and Gurobi solver.

Application of the Vortex Search Algorithm to the Phase-Balancing Problem in Distribution Systems

Abstract: This article discusses the problem of minimizing power loss in unbalanced distribution systems through phase-balancing. This problem is represented by a mixed-integer nonlinear-programming mathematical model, which is solved by applying a discretely encoded Vortex Search Algorithm (DVSA). The numerical results of simulations performed in IEEE 8-, 25-, and 37-node test systems demonstrate the applicability of the proposed methodology when compared with the classical Cuh & Beasley genetic algorithm. In addition, the computation times required by the algorithm to find the optimal solution are in the order of seconds, which makes the proposed DVSA a robust, reliable, and efficient tool. All computational implementations have been developed in the MATLAB® programming environment, and all the results have been evaluated in DigSILENT© software to verify the effectiveness and the proposed three-phase unbalanced power-flow method.