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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. [ABSTRACT FROM AUTHOR]

This research addresses the efficient integration and sizing of flexible alternating current transmission systems (FACTS) in electrical distribution networks via a convex optimization approach. The exact mixed-integer nonlinear programming (MINLP) model associated with FACTS siting and sizing aims for the minimization of the expected annual operating costs of the network (i.e., energy losses and FACTS purchasing costs). The constraints of this problem include power equilibrium equalities, voltage regulation bounds, and device capacities, among others. Due to the power equilibrium constraints per node and period, the MINLP model is a non-convex optimization problem. To transform the exact MINLP model into a mixed-integer convex one, the approximation of the product between two variables in the complex domain is relaxed through its hyperbolic equivalent, which generates a set of convex cones. The main advantage of the proposed mixed-integer convex model is that it ensures the global optimum of the problem, even when considering objective multiplexes. Numerical simulations in the IEEE 33-, 69-, and 85-bus grids demonstrate the effectiveness and robustness of FACTS integration via the proposed convex approach in comparison with the exact solution of the MINLP model in the GAMS software as well as with combinatorial optimization algorithms (i.e., the black widow optimizer and the vortex search algorithm). All simulations were carried out in MATLAB with Yalmip optimization and the Gurobi and Mosek solvers. The simulation results show that, for a fixed operation of the FACTS devices (i.e., a VAR compensator) during the day, the annual operating costs are reduced by 12.63%, 13.97%, and 26.53% for the IEEE 33-, 69-, and 85-bus test systems, respectively, while for the operation variable, the reductions are by 14.24%, 15.79%, and 30.31%, respectively. [ABSTRACT FROM AUTHOR]

The problem regarding the optimal placement and sizing of different FACTS (flexible alternating current transmission systems) in electrical distribution networks is addressed in this research by applying a master–slave optimization approach. The FACTS analyzed correspond to the unified power flow controller (UPFC), the thyristor-controlled shunt compensator (TCSC, also known as the thyristor switched capacitor, or TSC), and the static var compensator (SVC). The master stage is entrusted with defining the location and size of each FACTS device using hybrid discrete-continuous codification through the application of the black widow optimization (BWO) approach. The slave stage corresponds to the successive approximations power flow method based on the admittance grid formulation, which allows determining the expected costs of the energy losses for a one-year operation period. The numerical results in the IEEE 33-, 69-, and 85-bus grids demonstrate that the best FACTS device for locating in distribution networks is the SVC, given that, when compared to the UPFC and the TCSC, it allows for the best possible reduction in the equivalent annual investment and operating cost. A comparative analysis with the General Algebraic Modeling System software, with the aim to solve the exact mixed-integer nonlinear programming model, demonstrated the proposed BWO approach's effectiveness in determining the best location and size for the FACTS in radial distribution networks. Reductions of about 12.63 % and 13.97 % concerning the benchmark cases confirmed that the SVC is the best option for reactive power compensation in distribution grids. [ABSTRACT FROM AUTHOR]

This paper addresses the problem concerning the efficient minimization of power losses in asymmetric distribution grids from the perspective of convex optimization. This research's main objective is to propose an approximation optimization model to reduce the total power losses in a three-phase network using the concept of electrical momentum. To obtain a mixed-integer convex formulation, the voltage variables at each node are relaxed by assuming them to be equal to those at the substation bus. With this assumption, the power balance constraints are reduced to flow restrictions, allowing us to formulate a set of linear rules. The objective function is formulated as a strictly convex objective function by applying the concept of average electrical momentum, by representing the current flows in distribution lines as the active and reactive power variables. To solve the relaxed MIQC model, the GAMS software (Version 28.1.2) and its CPLEX, SBB, and XPRESS solvers are used. In order to validate the effectiveness of load redistribution in power loss minimization, the initial and final grid configurations are tested with the triangular-based power flow method for asymmetric distribution networks. Numerical results show that the proposed mixed-integer model allows for reductions of 24.34 % , 18.64 % , and 4.14 % for the 8-, 15-, and 25-node test feeders, respectively, in comparison with the benchmark case. The sine–cosine algorithm and the black hole optimization method are also used for comparison, demonstrating the efficiency of the MIQC approach in minimizing the expected grid power losses for three-phase unbalanced networks. [ABSTRACT FROM AUTHOR]

Due to the need to include renewable energy resources in electrical grids as well as the development and high implementation of PV generation and DC grids worldwide, it is necessary to propose effective optimization methodologies that guarantee that PV generators are located and sized on the DC electrical network. This will reduce the operation costs and cover the investment and maintenance cost related to the new technologies (PV distributed generators), thus satisfying all technical and operative constraints of the distribution grid. It is important to propose solution methodologies that require short processing times, with the aim of exploring a large number of scenarios while planning energy projects that are to be presented in public and private contracts, as well as offering solutions to technical problems of electrical distribution companies within short periods of time. Based on these needs, this paper proposes the implementation of a Discrete–Continuous Parallel version of the Particle Swarm Optimization algorithm (DCPPSO) to solve the problem regarding the integration of photovoltaic (PV) distributed generators (DGs) in Direct Current (DC) grids, with the purpose of reducing the annual costs related to energy purchasing as well as the investment and maintenance cost associated with PV sources in a scenario of variable power demand and generation. In order to evaluate the effectiveness, repeatability, and robustness of the proposed methodology, four comparison methods were employed, i.e., a commercial software and three discrete–continuous methodologies, as well as two test systems of 33 and 69 buses. In analyzing the results obtained in terms of solution quality, it was possible to identify that the DCPPSO proposed obtained the best performance in relation to the comparison methods used, with excellent results in relation to the processing times and standard deviation. The main contribution of the proposed methodology is the implementation of a discrete–continuous codification with a parallel processing tool for the evaluation of the fitness function. The results obtained and the reports in the literature for alternating current networks demonstrate that the DCPPSO is the optimization methodology with the best performance in solving the problem of the optimal integration of PV sources in economic terms and for any kind of electrical system and size. [ABSTRACT FROM AUTHOR]

Currently, with the quick increase in global population, the energetic crisis, the environmental problematic, and the development of the power electronic devices generated the need to include new technologies for supporting and potentiating electrical distributions systems; Distribution Static Compensators (D-STATCOMs) are highly used for this task due to the advantages that this technology presents: reduction in power loss, operation costs, and chargeability of branches, among others. The possibility to include this kind of technology within the electrical system has shown the need to develop efficient methodologies from the point of view of quality solution, repeatability and processing times by considering operation and investment costs as well as the technical conditions of the electrical grids under a scenario of variable power demand and then representing the real operation of the electrical grid. With the aim to propose a solution for this requirement, this paper presents a new Discrete-Continuous Particle Swarm Optimization (DCPSO) algorithm to solve the problem of the optimal integration of D-STATCOMs into Electrical Distribution Systems (EDSs). In this case, the objective function is the minimization of annual operating costs by using a weighted mono-objective function composed of the annual power loss and the investment cost and by including all constraints associated with the operation of an EDS in a distributed reactive compensation environmentinside the mathematical formulation. In order to evaluate the effectiveness and robustness of the proposed solution method, this study implemented two tests systems (i.e., 33- and 69-bus), as well as four comparison methods, and different considerations related to the inclusion of D-STATCOMs in the EDSs. Furthermore, for evaluating the repeatability of the solution obtained by each solution methods used, each algorithm was executed 100 times in Matlab software. The results obtained demonstrated that the proposed DCPSO/HSA methodology achieved the best trade-off between solution quality and processing time, with low standard deviation values for EDSs of any size. [ABSTRACT FROM AUTHOR]

Bipolar direct current (DC) networks are emerging electrical systems used to improve the distribution capabilities of monopolar DC networks. These grids work with positive, negative, and neutral poles, and they can transport two times the power when compared to monopolar DC grids. The distinctive features of bipolar DC grids include the ability to deal with bipolar loads (loads connected between the positive and negative poles) and with unbalanced load conditions, given that the loads connected to the positive and neutral poles are not necessarily equal to the negative and neutral ones. This load imbalance deteriorates voltages when compared to positive and negative poles, and it causes additional power losses in comparison with balanced operation scenarios. This research addresses the problem of pole-swapping in bipolar DC networks using combinatorial optimization methods in order to reduce the total grid power losses and improve the voltage profiles. Bipolar DC networks with a non-solidly grounded neutral wire composed of 21 and 85 nodes are considered in the numerical validations. The implemented combinatorial methods are the Chu and Beasley genetic algorithm, the sine-cosine algorithm, and the black-hole optimization algorithm. Numerical results in both test feeders demonstrate the positive effect of optimal pole-swapping in the total final power losses and the grid voltage profiles. All simulations were run in the MATLAB programming environment using the triangular-based power flow method, which is intended for radial distribution system configurations. [ABSTRACT FROM AUTHOR]

This paper analyzes the power flow solution in bipolar direct current networks with radial structures considering multiple monopolar and bipolar constant power loads. The electrical configuration of the bipolar DC grid considers that the reference pole is non-grounded along the feeder, which produces important neutral currents and voltage imbalances along the DC grid. The power flow problem is formulated through the triangular-based representation of the grid topology, which generates a recursive formulation that allows determining the voltage values in the demand nodes through an iterative procedure. The linear convergence of the triangular-based power flow method is tested through multiple load variations with respect to the nominal grid operative condition. Numerical results in the 21- and the 85-bus grids reveal the relevant variations in the voltage profiles and total grid power losses when the neutral cable is solidly grounded or not. [ABSTRACT FROM AUTHOR]

This paper proposes a new hybrid master–slave optimization approach to address the problem of the optimal placement and sizing of distribution static compensators (D-STATCOMs) in electrical distribution grids. The optimal location of the D-STATCOMs is identified by implementing the classical and well-known Chu and Beasley genetic algorithm, which employs an integer codification to select the nodes where these will be installed. To determine the optimal sizes of the D-STATCOMs, a second-order cone programming reformulation of the optimal power flow problem is employed with the aim of minimizing the total costs of the daily energy losses. The objective function considered in this study is the minimization of the annual operative costs associated with energy losses and installation investments in D-STATCOMs. This objective function is subject to classical power balance constraints and device capabilities, which generates a mixed-integer nonlinear programming model that is solved with the proposed genetic-convex strategy. Numerical validations in the 33-node test feeder with radial configuration show the proposed genetic-convex model's effectiveness to minimize the annual operative costs of the grid when compared with the optimization solvers available in GAMS software. [ABSTRACT FROM AUTHOR]

Phase balancing is a classical optimization problem in power distribution grids that involve phase swapping of the loads and generators to reduce power loss. The problem is a non-linear integer and, hence, it is usually solved using heuristic algorithms. This paper proposes a mathematical reformulation that transforms the phase-balancing problem in low-voltage distribution networks into a mixed-integer convex quadratic optimization model. To consider both conventional secondary feeders and microgrids, renewable energies and their subsequent stochastic nature are included in the model. The power flow equations are linearized, and the combinatorial part is represented using a Birkhoff polytope B 3 that allows the selection of phase swapping in each node. The numerical experiments on the CIGRE low-voltage test system demonstrate the use of the proposed formulation. [ABSTRACT FROM AUTHOR]

This paper addresses the Optimal Power Flow (OPF) problem in DC power microgrids via a combinatorial optimization technique known as Black Hole Optimization (BHO). Such optimization method allows to solve OPF problems via algorithmic strategies trough a master-slave formulation. In the master stage, the total power generated by each Distributed Generator (DG) is determined by the BHO, while the slave strategy is entrusted with solving the resulting conventional power flow problem via a classical Gauss-Seidel (GS) numerical method. For comparison purposes, this work uses nonlinear optimization methods available in General Algebraic Modeling System (GAMS) as well as continuous metaheuristic optimization techniques. Two test feeders with 21 and 69 nodes were considered for validating the proposed hybrid BHO-GS optimization method, which enables to demonstrate its applicability, robustness and efficiency compared to conventional approaches. The results of all the simulations were obtained via MATLAB 2017a. [ABSTRACT FROM AUTHOR]

This paper deals with the optimal pole-swapping problem in bipolar asymmetric distribution networks by proposing a mixed-integer conic approximation (MICA) model to minimize the total grid power losses for a particular load condition. The non-convex relation between voltage and power in the constant power loads is relaxed through equivalent cones. The effect of the neutral wire's connection is considered in the proposed MICA model via an auxiliary variable associated with the total current drained to the earth in the case of a solidly grounded connection. Numerical comparisons with three combinatorial optimization methods (black-hole optimization, sine-cosine algorithm, and the Chu & Beasley genetic algorithm) and a mixed-integer quadratic approximation in two test feeders composed of 21 and 85 buses demonstrate the effectiveness of the proposed MICA model. Reductions of about 3.9411 and 10.1706% were obtained after applying the MICA model to the optimal pole-swapping problem. All numerical validations were carried out in the MATLAB programming environment, using the convex disciplined tool known as CVX with the Gurobi solver. • Optimal load balancing in bipolar asymmetric DC networks minimizes its power losses. • The mixed-integer nonlinear model of the pole-swapping is transformed as a convex one. • The neutral floating connection presents the worst scenario for power losses. • Combinatorial methods find local solutions as the number of network nodes increases. [ABSTRACT FROM AUTHOR]

This paper proposes a new power flow (PF) formulation for electrical distribution systems using the current injection method and applying the Laurent series expansion. Two solution algorithms are proposed: a Newton-like iterative procedure and a fixed-point iteration based on the successive approximation method (SAM). The convergence analysis of the SAM is proven via the Banach fixed-point theorem, ensuring numerical stability, the uniqueness of the solution, and independence on the initializing point. Numerical results are obtained for both proposed algorithms and compared to well-known PF formulations considering their rate of convergence, computational time, and numerical stability. Tests are performed for different branch R / X ratios, loading conditions, and initialization points in balanced and unbalanced networks with radial and weakly-meshed topologies. Results show that the SAM is computationally more efficient than the compared PFs, being more than ten times faster than the backward–forward sweep algorithm. • Two novel efficient power flow algorithms for distribution systems. • Linearization using Laurent series expansion. • Convergence and stability analysis using Banach fixed-point theorem. • Proposed algorithms are at least three times faster than the backward–forward sweep. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new discrete-continuous codification of the Chu–Beasley genetic algorithm to address the optimal placement and sizing problem of the distribution static compensators (D-STATCOM) in electrical distribution grids. The discrete part of the codification determines the nodes where D-STATCOM will be installed. The continuous part of the codification regulates their sizes. The objective function considered in this study is the minimization of the annual operative costs regarding energy losses and installation investments in D-STATCOM. This objective function is subject to the classical power balance constraints and devices' capabilities. The proposed discrete-continuous version of the genetic algorithm solves the mixed-integer non-linear programming model that the classical power balance generates. Numerical validations in the 33 test feeder with radial and meshed configurations show that the proposed approach effectively minimizes the annual operating costs of the grid. In addition, the GAMS software compares the results of the proposed optimization method, which allows demonstrating its efficiency and robustness. [ABSTRACT FROM AUTHOR]

This study analyzes the numerical convergence and processing time required by several classical and new solution methods proposed in the literature to solve the power-flow problem (PF) in direct-current (DC) networks considering radial and mesh topologies. Three classical numerical methods were studied: Gauss–Jacobi, Gauss–Seidel, and Newton–Raphson. In addition, two unconventional methods were selected. They are iterative and allow solving the DC PF in radial and mesh configurations. The first method uses a Taylor series expansion and a set of decoupling equations to linearize around the desired operating point. The second method manipulates the set of non-linear equations of the DC PF to transform it into a conventional fixed-point form. Moreover, this method is used to develop a successive approximation methodology. For the particular case of radial topology, three methods based on triangular matrix formulation, graph theory, and scanning algorithms were analyzed. The main objective of this study was to identify the methods with the best performance in terms of quality of solution (i.e., numerical convergence) and processing time to solve the DC power flow in mesh and radial distribution networks. We aimed at offering to the reader a set of PF methodologies to analyze electrical DC grids. The PF performance of the analyzed solution methods was evaluated through six test feeders; all of them were employed in prior studies for the same application. The simulation results show the adequate performance of the power-flow methods reviewed in this study, and they permit the selection of the best solution method for radial and mesh structures. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]