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Context: The use of capacitor banks is the most common and preferred solution for reducing power loss in electrical distribution networks, given their cost-effectiveness and low maintenance requirements. However, achieving their optimal integration in terms of location and size is a challenging problem. Method: This paper proposes a stochastic mixed-integer convex model based on a branch flow optimization model, which incorporates three different load-generation conditions, in order to address the stochastic nature of distribution systems. Results: The simulation results indicated that the proposed stochastic mixed-integer branch flow (SMIBF) model provides the best solution for all test feeders analyzed, reducing the objective function value by 39.81%, 35.29%, and 56.31% for the modified 33-, 69-, and 85-node test feeders, respectively. Conclusions: An SMIBF model was developed to optimally integrate fixed-step capacitor banks into electrical distribution grids. This model considered the stochastic nature of distribution systems under multiple operating conditions and ensured that the global optimum could be found.

The problem regarding the reconfiguration of electrical distribution grids is addressed in this research through the implementation of a practical solution using a constructive heuristic algorithm. The most important characteristic of the proposed heuristic approach is its low-computation effort, given that few power flow solutions are required in order to solve the reconfiguration problem. The constructive algorithm starts its exploration of the solution space by closing all the tie lines form a fully meshed distribution network. The distribution line with the minimum current is permanently opened. A new power flow evaluation is made for the new distribution system, and the distribution line with the minimum current is opened if and only if this action does not generate isolated nodes. This procedure is repeated until the number of closed lines is equal to the number of nodes minus one, which is a condition required to maintain a radial configuration. Numerical validations in test feeders composed of 16, 33, 69, 84, 136, and 415 nodes demonstrate that the proposed constructive algorithm finds adequate solutions with minimum processing times. The proposed approach is practical for distribution companies since its implementation only requires a power flow tool for distribution networks that can deal with radial and meshed configurations.

Abstract Objective: This work involves a convex-based mathematical reformulation for the optimal power flow problem in DC networks. The objective of the proposed optimization model corresponds to the minimization of the power losses through all the network branches considering a convex conic model that warranties finding the global optimal. Methodology: This is split into three stages: The first stage presents the mathematical model of optimal power flow for DC networks and all its geometric features that make it non-convex; the second stage presents the convex reformulation from a second order conic relaxation; the third stage shows the main characteristics of the DC system under study; and the fourth stage presents the optimal solution of the power flow problem and its comparisons with some methods reported in the specialized literature. Results: The numerical validations demonstrate that the model of proposed convex optimal power flow obtains the same solution as the exact model of the problem with an efficiency of 100%, which is in contrast with the variability of the results that are presented by the metaheuristic techniques reported as comparison methodologies. Conclusions: The proposed second-order conic relaxation warrantied the convexity of the solution space and therefore, the finding of the optimal solution at each execution; besides of this, demonstrated that for optimal power flow problems in DC networks, the numerical performance is better than most of the comparative metaheuristic methods; and the provided solution by the proposed relaxation is equivalent to that provided by the exact model. Keywords: Direct current networks, second-order conic relaxation, non-linear programming model, convex optimization.

The power flow solution is a classical problem in electrical engineering that has been studied for more than 60 years [1]. One of the most widely used methods corresponds to the Newton-Raphson approach, which is currently employed for analyzing power systems with meshed configurations and multiple generation sources, i.e., it is typically employed for power systems in high-voltage levels [2].

This paper deals with the problem of the optimal placement and sizing of distribution static compensators (D-STATCOM) in electrical distribution networks to reduce the total annual operative costs associated with the total costs of energy losses added with the investment costs in D-STATCOM. The metaheuristic sine-cosine optimization algorithm determines nodes with the location and optimal sizes of the D-STATCOM. A discrete-continuous codification represents the decision variables, where the discrete part is entrusted with the best candidate nodes selection. The continuous part deals with the optimal sizes assigned to the D-STATCOM. Numerical results in the IEEE 33- and IEEE 69-bus systems demonstrate the effectiveness of this approach since it helps to minimize the total grid operation costs compared with the solution of the mixed-integer nonlinear programming model in GAMS. All the numerical validations are carried out in the MATLAB programming environment.

This paper proposes a mixed-integer convex model for optimal load-balancing in bipolar DC networks while considering multiple constant power terminals. The proposed convex model combines the Branch and Cut method with interior point optimization to solve the problem of optimal load balancing in bipolar DC networks. Additionally, the proposed convex model guarantees that global optimum of the problem is found, which ensures minimal power losses in the bipolar DC distribution grid branches, as the total monopolar load consumption has been balanced at the substation's terminals. In addition, an optimal load balancing improves the voltage profiles due to current redistribution between the positive and negative poles. Numerical results in the 21- and 85-bus test feeders and a comparison with three metaheuristic techniques show the effectiveness of the proposed convex model in reducing the total grid imbalance while minimizing the power losses and improving the voltage profiles.

A Possible Classification for Metaheuristic Optimization Algorithms in Engineering and Science

In case of an error in the power system, it is the duty of the protection relays to isolate the faulty part from the rest of the system as soon as possible. Overcurrent and distance relays are usually used to protect the transmission and super distribution systems. The optimum coordination of these relays is very important. In this article, communication links are used to improve the optimal coordination of overcurrent and distance relays. In the proposed plan, the overcurrent relays on both sides of the line are equipped with a communication link for immediate action in the event of an error. Using this communication link, the complete coverage of the line is also provided by distance relays. The number and place of installation of the communication link greatly affect the operation time of overcurrent relays and the distance and coordination between them. The coordination problem is formulated by considering the location and number of communication links, and to solve it, the combined optimization algorithm of genetics and linear programming will be used. With the help of the genetic algorithm, the location and setting of the second zone of the distance relay, and by using the linear programming algorithm, the setting of the overcurrent relays is determined. The proposed method has been tested on the IEEE 14-bus (the simulation in MATLAB software) network and its results examined, and it will be seen how much the existence of a communication link can improve the performance time of the protection system.

El brote actual de la enfermedad por coronavirus (COVID-19), que se informó por primera vez en Wuhan, China, el 31 de diciembre de 2019, ha dejado un saldo al 19 de abril de 2020 de más de 3500000 infectados y 160000 muertes en 185 países. En este trabajo utilizamos un modelo basado en el Método de Cadena Microscópica de Markov (MCMM, Markov Microscopic Chain Approach) para estimar la propagación del COVID-19 en la ciudad de Pereira (Risaralda-Colombia). Este modelo incorpora importantes aspectos de la población, relacionados con: ubicación espacial dentro de la ciudad discretizada por comunas, movilidad entre comunas, estratificación por grupos de edad y separación de individuos en siete compartimientos epidemiológicos. Este modelo se utiliza para predecir, en una línea de tiempo, la incidencia de epidemias en poblaciones geolocalizadas, lo que se traduce en una herramienta indicadora para tomar medidas de control. Así, el resultado de la metodología caracteriza la evolución en el tiempo y el espacio de la proporción de los individuos en cada uno de los compartimientos epidemiológicos y en cada grupo etario. Los datos que se refieren a COVID-19, desde la municipalidad de Pereira, hasta el 20 de abril de 2020, se utilizan para alimentar el modelo y obtener las proyecciones espacio-temporales. Los resultados presentados consideran múltiples escenarios de movilidad, de forma que el aplanamiento de las curvas de los diferentes compartimientos epidemiológicos pueda ser visualizados de acuerdo a diferentes estrategias de confinamiento. Por tratarse de un modelo espacio-temporal, los resultados del modelo pueden ser presentados fácilmente como mapas de calor sobre cada uno de los compartimientos epidemiológicos, a fin de facilitar los procesos de toma de decisiones.

This paper illustrates the design and building of a planar transformer prototype with a 1:1 transformation ratio for high-frequency applications in power electronics. By using reference literature and considering the ferrite core dimensions, the windings were conceived and exported to Gerber format using PCB design software. The transformer prototype was then assembled and tested under laboratory conditions for frequencies from 800 Hz to 5 MHz, which showed a sinusoidal wave at the transformer output from 1.3 kHz onwards and a better performance starting at 10 kHz, where the loses were significantly reduced and the transformation ratio was closer to the originally designed. As a final step, a finite element method (FEM) analysis was carried out to understand the electromagnetic flux behavior using a 3D Multiphysics simulation software. The 3d building process and details are explained step by step and the resulting magnetic flux density is graphically shown for the core and the windings.

This paper deals with the problem of the optimal reconfiguration of medium voltage distribution networks by proposing a mixed-integer nonlinear programming (MINLP) model. This optimization model has as objective function the minimization of the total power losses in all the branches of the network constrained by active and reactive power balance equations, voltage regulation bounds and device capabilities, among others. The proposed MINLP formulation works with branch-to-node incidence that allows representing the active and reactive power flow in branches as a function of the real and imaginary parts of the voltages and currents. The solution of the MINLP model is reached through the general algebraic modeling system widely know as GAMS package by presenting it in a tutorial form. This software allows implementing in compact form the proposed model and solve it via branch and bound methods. Two test feeders composed by 5 and 14 nodes permits demonstrating the fidelity of the proposed MINLP model regarding power losses minimization when compared with literature reports.

En este artículo se presenta una metodología para la estimación de parámetros en transformadores de distribución considerando medidas de tensión y corriente mediante un modelo matemático de programación no lineal (PNL). Este modelo de programación es desarrollado a través de la aplicación de las leyes de Kirchhoff al modelo del circuito equivalente del transformador. Para resolver el modelo de PNL resultante se emplea el sistema de modelado algebraico general conocido como GAMS. La metodología de optimización propuesta se desarrolla a manera de tutorial con un ejemplo de implementación el cual corresponde a un transformador monofásico de 20 kVA y una relación de transformación de 8000/240 V. Los resultados numéricos muestran que la estimación paramétrica en transformadores mediante el modelo de PNL propuesto representa adecuadamente el comportamiento eléctrico de estos dispositivos en relación con su funcionamiento para diferentes escenarios de carga a los que se encuentren sometidos. Todas las simulaciones fueron realizadas con la versión 25.1.3 de GAMS licenciado por la Universidad Tecnológica de Bolívar.

This paper addresses the problem of the optimal stabilization of DC microgrids using a hierarchical control design. A recursive optimal power flow formulation is proposed in the tertiary stage that ensures the global optimum finding due to the convexity of the proposed quadratic optimization model in determining the equilibrium operative point of the DC microgrid as a function of the demand and generation inputs. An exact feedback controller with integral action is applied in the primary and secondary controller layers, which ensures asymptotic stability in the sense of Lyapunov for the voltage variables. The dynamical model of the network is obtained in a set of reduced nodes that only includes constant power terminals interfaced through power electronic converters. This reduced model is obtained by applying Kron’s reduction to the linear loads and step nodes in the DC grid. Numerical simulations in a DC microgrid with radial structure demonstrate the effectiveness and robustness of the proposed hierarchical controller in maintaining the stability of all the voltage profiles in the DC microgrid, independent of the load and generation variations.

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.

This paper deals with a classical problem in power system analysis regarding the optimal location and sizing of distributed generators (DGs) in direct current (DC) distribution networks using the mathematical optimization. This optimization problem is divided into two sub-problems as follows: the optimal location of DGs is a problem, with those with a binary structure being the first sub-problem; and the optimal sizing of DGs with a nonlinear programming (NLP) structure is the second sub-problem. These problems originate from a general mixed-integer nonlinear programming model (MINLP), which corresponds to an NP-hard optimization problem. It is not possible to provide the global optimum with conventional programming methods. A mixed-integer semidefinite programming (MI-SDP) model is proposed to address this problem, where the binary part is solved via the branch and bound (B&B) methods and the NLP part is solved via convex optimization (i.e., SDP). The main advantage of the proposed MI-SDP model is the possibility of guaranteeing a global optimum solution if each of the nodes in the B&B search is convex, as is ensured by the SDP method. Numerical validations in two test feeders composed of 21 and 69 nodes demonstrate that in all of these problems, the optimal global solution is reached by the MI-SDP approach, compared to the classical metaheuristic and hybrid programming models reported in the literature. All the simulations have been carried out using the MATLAB software with the CVX tool and the Mosek solver.

This paper deals with the global stabilization of the reaction wheel pendulum (RWP) in the discrete-time domain. The discrete-inverse optimal control approach via a control Lyapunov function (CLF) is employed to make the stabilization task. The main advantages of using this control methodology can be summarized as follows: (i) it guarantees exponential stability in closed-loop operation, and (ii) the inverse control law is optimal since it minimizes the cost functional of the system. Numerical simulations demonstrate that the RWP is stabilized with the discrete-inverse optimal control approach via a CLF with different settling times as a function of the control gains. Furthermore, parametric uncertainties and comparisons with nonlinear controllers such as passivity-based and Lyapunov-based approaches developed in the continuous-time domain have demonstrated the superiority of the proposed discrete control approach. All of these simulations have been implemented in the MATLAB software.

In this study, the voltage stability margin for direct current (DC) networks in the presence of constant power loads is analyzed using a proposed convex mathematical reformulation. This convex model is developed by employing a second-order cone programming (SOCP) optimization that transforms the non-linear non-convex original formulation by reformulating the power balance constraint. The main advantage of the SOCP model is that the optimal global solution of a problem can be obtained by transforming hyperbolic constraints into norm constraints. Two test systems are considered to validate the proposed SOCP model. Both systems have been reported in specialized literature with 6 and 69 nodes. Three comparative methods are considered: (a) the Newton-Raphson approximation based on the determinants of the Jacobian matrices, (b) semidefinite programming models, and (c) the exact non-linear formulation. All the numerical simulations are conducted using the MATLAB and GAMS software. The effectiveness of the proposed SOCP model in addressing the voltage stability problem in DC grids is verified by comparing the objective function values and processing time.

Objective: In this paper, is present a hybrid optimization methodology for the optimal location and sizing of distributed generators (DGs) in electrical distribution networks. We propose a mixed-integer nonlinear problem (MINLP) model for the mathematical formulation, whose objective function is the minimization of power losses due to the Joule effect in conductors. The constraints we considered include active and reactive power balance, voltage regulation, percentage of penetration of DGs into the distribution network, and total DGs allowed in such network. Methodology: To solve the MINLP model, we employed a master–slave strategy that uses the Chu-Beasley genetic algorithm (CBGA) and the optimal power flow (OPF) model as the master and slave algorithms, respectively. This hybrid technique helps to reduce the complexity of the MINLP model by eliminating binary variables through the master algorithm and then solving the resulting Nonlinear problem (NLP), which corresponds to the OPF model, using a classical interior-point method available in MATLAB’s fmincon toolbox. Results: We tested the efficiency and robustness of the proposed methodology in 33- and 69-node radial distribution networks. The results show its high performance in terms of power loss reduction and final sizing of DGs Conclusions: The results obtained in the test systems under analysis reveal that there is a direct and proportional relationship between technical losses, the percentage of distributed generation penetration, and the number of generators available.

Power systems have become more sensitive to voltage stability problems due to load growth and the increasing utilization of alternative energy. Voltage stability appears not to be properly evaluated by methods of static analysis, such as load flux, because these methods use simple models to describe the system’s components. Moreover, dynamic models for voltage stability analysis require high computational cost. Considering this, there is a need of developing more efficient and accurate methodologies. This article shows a model based on Artificial Neural Networks (ANN). ANN is a technique of artificial intelligence inspired in the biological neural networks of the human brain. An ANN is capable of learning through experience and takes the main characteristics of a dataset. Additionally, such networks may offer correct answers for inputs that present variations due to noise effects or distortions in the environment. ANNs provide a switching behavior as a function of the environment, that is, they get an input dataset and transform it into a consistent output set. This represents the rationale behind using ANNs for the development of this work; in other words, ANNs allow the prediction of a voltage-stability margin in power systems using information about their state variables. The training datasets are obtained from the load flux method, which delivers the initial conditions (i.e. the network input variables). Results are obtained through an estimating NN based methodology and compared to the results obtained when using estimating margin deterministic methods in a 4-node tests system.

Este documento presenta una metodología basada en algoritmos genéticos que permite adelantar el reordenamiento del parque de transformadores existente en el nivel de tensión I de los sistemas de distribución de Bogotá D.C., Colombia, con el fin de maximizar el reconocimiento de activos que el ente regulador CREG (Comisión Reguladora de Energía y Gas) realiza a los distintos operadores de red, según lo establecido en la resolución 097 de 2008. Para la aplicación del algoritmo se obtuvieron mediciones de potencia activa máxima para cada hora del año 2009 en un conjunto de 94 transformadores de diferentes capacidades, escogidos de forma aleatoria, instalados en el sistema de distribución de CODENSA S.A. ESP, empresa encargada de prestar el servicio de energía eléctrica en la ciudad de Bogotá D.C. Con esta información se construyeron curvas de carga diarias representativas y se elaboró una base de datos que contiene los costos operativos del movimiento de los equipos y de las tarifas, a partir de los cuales fue posible modelar la función objetivo y las restricciones del problema, obteniéndose un elevado número de combinaciones posibles (alrededor de 1*10(134)) debido al gran número de nodos y de transformadores presentes en el sistema de distribución. La búsqueda convencional de una solución en la anterior situación implicaría el empleo de tiempos prohibitivos, por lo cual se implementó un algoritmo genético clásico, obteniéndose de esta manera una solución óptima que ofrece una ganancia económica en el primer año, asociada al incremento en el cargo por uso, de $ 253.446.362,47 (COP), ganancias que podrían verse incrementadas considerablemente al ejecutar el algoritmo en parques de transformadores más grandes.This paper presents a methodology based on genetic algorithms that allows the reordering of the existing park transformers voltage level I of the distribution systems of Bogotá city, Colombia, in order to maximize the recognition of assets that the regulator CREG (Comisión Reguladora de Energía y Gas) made to the various network operators, as set out in resolution 097 of 2008. For the application of the algorithm, we obtained maximum active power measurements for each hour of the year 2009 in a number of transformers of different capacities, chosen at random, installed in the distribution system CODENSA SA ESP, the company that provides electric service in the Bogotá city. With this information we built representative daily load curves and developed a database that contains the operating costs of moving equipment and tariffs, from which it was possible to model the objective function and constraints of the problem, obtaining a high number of possible combinations (about 1*10(134)) due to the large number of nodes and processors present in the distribution system. Conventional search of a solution in the above situation implies the use of prohibitive times. For this reason we implemented a classical genetic algorithm, thus obtaining an optimal solution that offers a financial gain in the first year, associated with the increase in the usage charge, of $ 253.446.362,47 (COP), profits that could be increased considerably when running the algorithm on larger transformers parks.