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This paper deals with the problem regarding the optimal operation of photovoltaic (PV) generation sources in AC distribution networks with a single-phase structure, taking into consideration different objective functions. The problem is formulated as a multi-period optimal power flow applied to AC distribution grids, which generates a nonlinear programming (NLP) model with a non-convex structure. Three different objective functions are considered in the optimization model, each optimized using a single-objective function approach. These objective functions are (i) an operating costs function composed of the energy purchasing costs at the substation bus, added with the PV maintenance costs; (ii) the costs of energy losses; and (iii) the total CO2 emissions at the substation bus. All these functions are minimized while considering a frame of operation of 24 h, i.e., in a day-ahead operation environment. To solve the NLP model representing the studied problem, the General Algebraic Modeling System (GAMS) and its SNOPT solver are used. Two different test feeders are used for all the numerical validations, one of them adapted to the urban operation characteristics in the Metropolitan Area of Medellín, which is composed of 33 nodes, and the other one adapted to isolated rural operating conditions, which has 27 nodes and is located in the department of Chocó, Colombia (municipality of Capurganá). Numerical comparisons with multiple combinatorial optimization methods (particle swarm optimization, the continuous genetic algorithm, the Vortex Search algorithm, and the Ant Lion Optimizer) demonstrate the effectiveness of the GAMS software to reach the optimal day-ahead dispatch of all the PV sources in both distribution grids. [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]

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. [ABSTRACT FROM AUTHOR]

This paper proposes a new solution methodology based on a mixed-integer conic formulation to locate and size photovoltaic (PV) generation units in AC distribution networks with a radial structure. The objective function comprises the annual expected energy costs of the conventional substation in addition to the investment and operating costs of PV sources. The original optimization model that represents this problem belongs to the family of mixed-integer nonlinear programming (MINLP); however, the complexity of the power balance constraints make it difficult to find the global optimum. In order to improve the quality of the optimization model, a mixed-integer conic (MIC) formulation is proposed in this research in order to represent the studied problem. Numerical results in two test feeders composed of 33 and 69 nodes demonstrate the effectiveness of the proposed MIC model when compared to multiple metaheuristic optimizers such as the Chu and Beasley Genetic Algorithm, the Newton Metaheuristic Algorithm, the Vortex Search Algorithm, the Gradient-Based Metaheuristic Optimization Algorithm, and the Arithmetic Optimization Algorithm, among others. The final results obtained with the MIC model show improvements greater than USD 100,000 per year of operation. All simulations were run in the MATLAB programming environment, using its own scripts for all the metaheuristic algorithms and the disciplined convex tool known as CVX with the Gurobi solver in order to solve the proposed MIC model. [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]

The minimization of annual operating costs in radial distribution networks with the optimal selection and siting of fixed-step capacitor banks is addressed in this research by means of a two-stage optimization approach. The first stage proposes an approximated mixed-integer quadratic model to select the nodes where the capacitor banks must be installed. In the second stage, a recursive power flow method is employed to make an exhaustive evaluation of the solution space. The main contribution of this research is the use of the expected load curve to estimate the equivalent annual grid operating costs. Numerical simulations in the IEEE 33- and IEEE 69-bus systems demonstrate the effectiveness of the proposed methodology in comparison with the solution of the exact optimization model in the General Algebraic Modeling System software. Reductions of 33.04 % and 34.29 % with respect to the benchmark case are obtained with the proposed two-stage approach, with minimum investments in capacitor banks. All numerical implementations are performed in the MATLAB software using the convex tool known as CVX and the Gurobi solver. The main advantage of the proposed hybrid optimization method lies in the possibility of dealing with radial and meshed distribution system topologies without any modification on the MIQC model and the recursive power flow approach. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of determining the optimal location and operation of distribution static synchronous compensators (D-STATCOMs) in power distribution networks. Metaheuristic algorithms have been conventionally used to solve this mixed-integer nonlinear programming problem. In contrast, we propose a mixed-integer second-order cone programming (MI-SOCP) model that guarantees global optimum and fast convergence of the algorithms in optimization solvers. The model seeks to minimize the annual installation cost and the operating cost, subject to active and reactive power balance constraints, voltage regulation bounds, devices capabilities, and the number of D-STATCOMs available to be connected. The multiobjective nature of the problem is also analyzed and solved using the proposed MI-SOCP model. An extensive set of simulations on the IEEE-33 nodes test system demonstrate the advantages of this approach compared to conventional heuristic algorithms and with solutions given by algebraic modeling software. • D-STACOMs permit annual operative costs reduction in distribution grids. • MI-SOCP formulation allows finding the global optimal solution of the exact MINLP model through solution space convexification. • The proposed optimization model does not require statistical evaluation to validate its efficiency since it is mixed-integer convex in nature. [ABSTRACT FROM AUTHOR]

This paper proposes an interconnection of the MATLAB and GAMS software interfaces, which were designed based on a master-slave methodology, to solve the mixed-integer nonlinear programming (MINLP) model problem associated with the problem regarding the optimal location and sizing of static distribution compensators (D-STATCOMs) in meshed and radial distribution networks, considering the problem of optimal reactive power flow compensation and the fact that the networks have commercial, industrial, and residential loads for a daily operation scenario. The objective of this study is to reduce the annual investment and operating costs associated with energy losses and the installation costs of D-STATCOMs. This objective function is based on the classical energy budget and the capacity constraints of the device. In the master stage, MATLAB software is used to program a discrete version of the sine-cosine algorithm (DSCA), which determines the locations where the D-STATCOMs will be installed. In the slave stage, using the BONMIN solver of the GAMS software and the known locations of the D-STATCOMs, the MINLP model representing the problem under study is solved to find the value of the objective function and the nominal power of the D-STATCOMs. To validate the effectiveness of the proposed master-slave optimizer, the 33-node IEEE test system with both radial and meshed topologies is used. With this test system, numerical comparisons were made with the exact solution of the MINLP model, using different solvers in the GAMS software, the genetic-convex strategy, and the discrete-continuous versions of the Chu and Beasley genetic algorithm and the salp swarm optimization algorithm. The numerical results show that DSCA-BONMIN achieves a global solution to the problem under study, making the proposed method an effective tool for decision-making in distribution companies. [ABSTRACT FROM AUTHOR]

The problem of optimal phase-balancing in three-phase asymmetric distribution networks is addressed in this research from the point of view of combinatorial optimization using a master–slave optimization approach. The master stage employs an improved sine cosine algorithm (ISCA), which is entrusted with determining the load reconfiguration at each node. The slave stage evaluates the energy losses for each set of load connections provided by the master stage by implementing the triangular-based power flow method. The mathematical model that was solved using the ISCA is designed to minimize the annual operating costs of the three-phase network. These costs include the annual costs of the energy losses, considering daily active and reactive power curves, as well as the costs of the working groups tasked with the implementation of the phase-balancing plan at each node. The peak load scenario was evaluated for a 15-bus test system to demonstrate the effectiveness of the proposed ISCA in reducing the power loss (18.66%) compared with optimization methods such as genetic algorithm (18.64%), the classical sine cosine algorithm (18.42%), black-hole optimizer (18.38%), and vortex search algorithm (18.59%). The IEEE 37-bus system was employed to determine the annual total costs of the network before and after implementing the phase-balancing plan provided by the proposed ISCA. The annual operative costs were reduced by about 13% with respect to the benchmark case, with investments between USD 2100 and USD 2200 in phase-balancing activities developed by the working groups. In addition, the positive effects of implementing the phase-balancing plan were evidenced in the voltage performance of the IEEE 37-bus system by improving the voltage regulation with a maximum of 4% in the whole network from an initial regulation of 6.30 % . All numerical validations were performed in the MATLAB programming environment. [ABSTRACT FROM AUTHOR]

This study presents a master–slave methodology to solve the problem of optimally locating and sizing photovoltaic (PV) generation units in electrical networks. This problem is represented by means of a Mixed-Integer Nonlinear Programming (MINLP) model, whose objective function is to reduce the total annual operating costs of a network for a 20-year planning period. Such costs include (i) the costs of purchasing energy at the conventional generators (the main supply node in this particular case), (ii) the investment in the PV generation units, and (iii) their corresponding operation and maintenance costs. In the proposed master–slave method, the master stage uses the Discrete–Continuous version of the Crow Search Algorithm (DCCSA) to define the set of nodes where the PV generation units will be installed (location), as well as their nominal power (sizing), and the slave stage employs the successive approximation power flow technique to find the value of the objective function of each individual provided by the master stage. The numerical results obtained in the 33- and 69-node test systems demonstrated its applicability, efficiency, and robustness when compared to other methods reported in the specialized literature, such as the vortex search algorithm, the generalized normal distribution optimizer, and the particle swarm optimization algorithm. All simulations were performed in MATLAB using our own scripts. [ABSTRACT FROM AUTHOR]