scholarly journals Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks

Computers ◽  
2021 ◽  
Vol 10 (9) ◽  
pp. 109
Author(s):  
Oscar Danilo Montoya ◽  
Luis Fernando Grisales-Noreña ◽  
Edwin Rivas-Trujillo
Keyword(s):  
Power Flow ◽  
Reactive Power ◽  
Search Algorithm ◽  
Triangular Matrix ◽  
Mixed Integer ◽  
Decision Variable ◽  
Convex Model ◽  
Electric Networks ◽  
Three Phase ◽  
Final Steady State

With this study, we address the optimal phase balancing problem in three-phase networks with asymmetric loads in reference to a mixed-integer quadratic convex (MIQC) model. The objective function considers the minimization of the sum of the square currents through the distribution lines multiplied by the average resistance value of the line. As constraints are considered for the active and reactive power redistribution in all the nodes considering a 3×3 binary decision variable having six possible combinations, the branch and nodal current relations are related to an extended upper-triangular matrix. The solution offered by the proposed MIQC model is evaluated using the triangular-based three-phase power flow method in order to determine the final steady state of the network with respect to the number of power loss upon the application of the phase balancing approach. The numerical results in three radial test feeders composed of 8, 15, and 25 nodes demonstrated the effectiveness of the proposed MIQC model as compared to metaheuristic optimizers such as the genetic algorithm, black hole optimizer, sine–cosine algorithm, and vortex search algorithm. All simulations were carried out in MATLAB 2020a using the CVX tool and the Gurobi solver.

scholarly journals Optimal Demand Reconfiguration in Three-Phase Distribution Grids Using an MI-Convex Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1124
Author(s):  
Oscar Danilo Montoya ◽  
Andres Arias-Londoño ◽  
Luis Fernando Grisales-Noreña ◽  
José Ángel Barrios ◽  
Harold R. Chamorro
Keyword(s):  
Objective Function ◽  
Reactive Power ◽  
Phase Distribution ◽  
Mathematical Formulation ◽  
Mixed Integer ◽  
Decision Variable ◽  
Convex Model ◽  
Load Redistribution ◽  
Three Phase ◽  
The Ideal

The problem of the optimal load redistribution in electrical three-phase medium-voltage grids is addressed in this research from the point of view of mixed-integer convex optimization. The mathematical formulation of the load redistribution problem is developed in terminals of the distribution node by accumulating all active and reactive power loads per phase. These loads are used to propose an objective function in terms of minimization of the average unbalanced (asymmetry) grade of the network with respect to the ideal mean consumption per-phase. The objective function is defined as the l1-norm which is a convex function. As the constraints consider the binary nature of the decision variable, each node is conformed by a 3×3 matrix where each row and column have to sum 1, and two equations associated with the load redistribution at each phase for each of the network nodes. Numerical results demonstrate the efficiency of the proposed mixed-integer convex model to equilibrate the power consumption per phase in regards with the ideal value in three different test feeders, which are composed of 4, 15, and 37 buses, respectively.

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

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1282 ◽  
Author(s):  
Brandon Cortés-Caicedo ◽  
Laura Sofía Avellaneda-Gómez ◽  
Oscar Danilo Montoya ◽  
Lazaro Alvarado-Barrios ◽  
Harold R. Chamorro
Keyword(s):  
Power Loss ◽  
Power Flow ◽  
Distribution Systems ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Programming Environment ◽  
Efficient Tool ◽  
Three Phase ◽  
Integer Nonlinear Programming

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.

scholarly journals An Approximate Mixed-Integer Convex Model to Reduce Annual Operating Costs in Radial Distribution Networks Using STATCOMs

Electronics ◽  
2021 ◽  
Vol 10 (24) ◽  
pp. 3102
Author(s):  
Oscar Danilo Montoya ◽  
Lázaro Alvarado-Barrios ◽  
Jesus C. Hernández
Keyword(s):  
Optimal Power Flow ◽  
Large Scale ◽  
Location Problem ◽  
Reactive Power ◽  
Programming Model ◽  
Search Algorithm ◽  
Distribution Networks ◽  
Mixed Integer ◽  
Convex Model ◽  
Integer Quadratic Programming

The problem of optimal siting and sizing of distribution static compensators (STATCOMs) is addressed in this research from the point of view of exact mathematical optimization. The exact mixed-integer nonlinear programming model (MINLP) is decoupled into two convex optimization sub-problems, named the location problem and the sizing problem. The location problem is addressed by relaxing the exact MINLP model, assuming that all the voltages are equal to 1∠0∘, which allows obtaining a mixed-integer quadratic programming model as a function of the active and reactive power flows. The solution of this model provides the best set of nodes to locate all the STATCOMs. When all the nodes are selected, it solves the optimal reactive power problem through a second-order cone programming relaxation of the exact optimal power flow problem; the solution of the SOCP model provides the optimal sizes of the STATCOMs. Finally, it refines the exact objective function value due to the intrinsic non-convexities associated with the costs of the STATCOMs that were relaxed through the application of Taylor’s series expansion in the location and sizing stages. The numerical results in the IEEE 33- and 69-bus systems demonstrate the effectiveness and robustness of the proposed optimization problem when compared with large-scale MINLP solvers in GAMS and the discrete-continuous version of the vortex search algorithm (DCVSA) recently reported in the current literature. With respect to the benchmark cases of the test feeders, the proposed approach reaches the best reductions with 14.17% and 15.79% in the annual operative costs, which improves the solutions of the DCVSA, which are 13.71% and 15.30%, respectively.

scholarly journals Optimal Selection of Conductors in Three-Phase Distribution Networks Using a Discrete Version of the Vortex Search Algorithm

Computation ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 80
Author(s):  
John Fernando Martínez-Gil ◽  
Nicolas Alejandro Moyano-García ◽  
Oscar Danilo Montoya ◽  
Jorge Alexander Alarcon-Villamil
Keyword(s):  
Objective Function ◽  
Power Flow ◽  
Phase Distribution ◽  
Search Algorithm ◽  
Distribution Networks ◽  
Discrete Version ◽  
Optimal Selection ◽  
Flow Method ◽  
Three Phase ◽  
Selection Of

In this study, a new methodology is proposed to perform optimal selection of conductors in three-phase distribution networks through a discrete version of the metaheuristic method of vortex search. To represent the problem, a single-objective mathematical model with a mixed-integer nonlinear programming (MINLP) structure is used. As an objective function, minimization of the investment costs in conductors together with the technical losses of the network for a study period of one year is considered. Additionally, the model will be implemented in balanced and unbalanced test systems and with variations in the connection of their loads, i.e., Δ− and Y−connections. To evaluate the costs of the energy losses, a classical backward/forward three-phase power-flow method is implemented. Two test systems used in the specialized literature were employed, which comprise 8 and 27 nodes with radial structures in medium voltage levels. All computational implementations were developed in the MATLAB programming environment, and all results were evaluated in DigSILENT software to verify the effectiveness and the proposed three-phase unbalanced power-flow method. Comparative analyses with classical and Chu & Beasley genetic algorithms, tabu search algorithm, and exact MINLP approaches demonstrate the efficiency of the proposed optimization approach regarding the final value of the objective function.

scholarly journals Accurate and Efficient Derivative-Free Three-Phase Power Flow Method for Unbalanced Distribution Networks

Computation ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 61
Author(s):  
Oscar Danilo Montoya ◽  
Juan S. Giraldo ◽  
Luis Fernando Grisales-Noreña ◽  
Harold R. Chamorro ◽  
Lazaro Alvarado-Barrios
Keyword(s):  
Power Flow ◽  
Triangular Matrix ◽  
Distribution Networks ◽  
Flow Method ◽  
Processing Times ◽  
Three Phase ◽  
Derivative Free ◽  
Upper Triangular Matrix ◽  
Power Flow Problem ◽  
Power Flow Method

The power flow problem in three-phase unbalanced distribution networks is addressed in this research using a derivative-free numerical method based on the upper-triangular matrix. The upper-triangular matrix is obtained from the topological connection among nodes of the network (i.e., through a graph-based method). The main advantage of the proposed three-phase power flow method is the possibility of working with single-, two-, and three-phase loads, including Δ- and Y-connections. The Banach fixed-point theorem for loads with Y-connection helps ensure the convergence of the upper-triangular power flow method based an impedance-like equivalent matrix. Numerical results in three-phase systems with 8, 25, and 37 nodes demonstrate the effectiveness and computational efficiency of the proposed three-phase power flow formulation compared to the classical three-phase backward/forward method and the implementation of the power flow problem in the DigSILENT software. Comparisons with the backward/forward method demonstrate that the proposed approach is 47.01%, 47.98%, and 36.96% faster in terms of processing times by employing the same number of iterations as when evaluated in the 8-, 25-, and 37-bus systems, respectively. An application of the Chu-Beasley genetic algorithm using a leader–follower optimization approach is applied to the phase-balancing problem utilizing the proposed power flow in the follower stage. Numerical results present optimal solutions with processing times lower than 5 s, which confirms its applicability in large-scale optimization problems employing embedding master–slave optimization structures.

scholarly journals Efficient Operative Cost Reduction in Distribution Grids Considering the Optimal Placement and Sizing of D-STATCOMs Using a Discrete-Continuous VSA

2021 ◽  
Vol 11 (5) ◽  
pp. 2175
Author(s):  
Oscar Danilo Montoya ◽  
Walter Gil-González ◽  
Jesus C. Hernández
Keyword(s):  
Objective Function ◽  
Reactive Power ◽  
Programming Model ◽  
Search Algorithm ◽  
Solution Space ◽  
Distribution Networks ◽  
Optimal Placement ◽  
Mixed Integer ◽  
Solution Vector ◽  
The Impact

The problem of reactive power compensation in electric distribution networks is addressed in this research paper from the point of view of the combinatorial optimization using a new discrete-continuous version of the vortex search algorithm (DCVSA). To explore and exploit the solution space, a discrete-continuous codification of the solution vector is proposed, where the discrete part determines the nodes where the distribution static compensator (D-STATCOM) will be installed, and the continuous part of the codification determines the optimal sizes of the D-STATCOMs. The main advantage of such codification is that the mixed-integer nonlinear programming model (MINLP) that represents the problem of optimal placement and sizing of the D-STATCOMs in distribution networks only requires a classical power flow method to evaluate the objective function, which implies that it can be implemented in any programming language. The objective function is the total costs of the grid power losses and the annualized investment costs in D-STATCOMs. In addition, to include the impact of the daily load variations, the active and reactive power demand curves are included in the optimization model. Numerical results in two radial test feeders with 33 and 69 buses demonstrate that the proposed DCVSA can solve the MINLP model with best results when compared with the MINLP solvers available in the GAMS software. All the simulations are implemented in MATLAB software using its programming environment.

scholarly journals Optimal Reactive Power Scheduling Using Cuckoo Search Algorithm

2017 ◽  
Vol 7 (5) ◽  
pp. 2349 ◽  
Author(s):  
Surender Reddy Salkuti
Keyword(s):  
Power System ◽  
Reactive Power ◽  
Search Algorithm ◽  
Cuckoo Search ◽  
Cuckoo Search Algorithm ◽  
Optimization Techniques ◽  
Mixed Integer ◽  
Integer Programming Problem ◽  
Scheduling Problem ◽  
Power Scheduling

<p>This paper solves an optimal reactive power scheduling problem in the deregulated power system using the evolutionary based Cuckoo Search Algorithm (CSA). Reactive power scheduling is a very important problem in the power system operation, which is a nonlinear and mixed integer programming problem. It optimizes a specific objective function while satisfying all the equality and inequality constraints. In this paper, CSA is used to determine the optimal settings of control variables such as generator voltages, transformer tap positions and the amount of reactive compensation required to optimize the certain objective functions. The CSA algorithm has been developed from the inspiration that the obligate brood parasitism of some Cuckoo species lay their eggs in nests of other host birds which are of other species. The performance of CSA for solving the proposed optimal reactive power scheduling problem is examined on standard Ward Hale 6 bus, IEEE 30 bus, 57 bus, 118 bus and 300 bus test systems. The simulation results show that the proposed approach is more suitable, effective and efficient compared to other optimization techniques presented in the literature.</p>

scholarly journals Grid-tie Three-phase Inverter With Active And Reactive Power Flow Control Capability

2014 ◽  
Vol 19 (4) ◽  
pp. 397-405
Author(s):  
Leonardo Poltronieri Sampaio ◽  
Moacyr Aureliano Gomes de Brito ◽  
Guilherme de Azevedo e Melo ◽  
Carlos Alberto Canesin
Keyword(s):  
Flow Control ◽  
Power Flow ◽  
Reactive Power ◽  
Power Flow Control ◽  
Phase Inverter ◽  
Active And Reactive Power ◽  
Reactive Power Flow ◽  
Three Phase ◽  
Control Capability ◽  
Three Phase Inverter

scholarly journals Heuristic Methodology for Planning AC Rural Medium-Voltage Distribution Grids

Energies ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 5141
Author(s):  
Oscar Danilo Montoya ◽  
Federico Martin Serra ◽  
Cristian Hernan De Angelo ◽  
Harold R. Chamorro ◽  
Lazaro Alvarado-Barrios
Keyword(s):  
Power Flow ◽  
Minimum Spanning Tree ◽  
Search Algorithm ◽  
Flow Simulation ◽  
Mixed Integer ◽  
Voltage Distribution ◽  
Medium Voltage ◽  
Planning Project ◽  
Distribution Grids ◽  
Selection Of

The optimal expansion of AC medium-voltage distribution grids for rural applications is addressed in this study from a heuristic perspective. The optimal routes of a distribution feeder are selected by applying the concept of a minimum spanning tree by limiting the number of branches that are connected to a substation (mixed-integer linear programming formulation). In order to choose the caliber of the conductors for the selected feeder routes, the maximum expected current that is absorbed by the loads is calculated, thereby defining the minimum thermal bound of the conductor caliber. With the topology and the initial selection of the conductors, a tabu search algorithm (TSA) is implemented to refine the solution with the help of a three-phase power flow simulation in MATLAB for three different load conditions, i.e., maximum, medium, and minimum consumption with values of 100%, 60%, and 30%, respectively. This helps in calculating the annual costs of the energy losses that will be summed with the investment cost in conductors for determining the final costs of the planning project. Numerical simulations in two test feeders comprising 9 and 25 nodes with one substation show the effectiveness of the proposed methodology regarding the final grid planning cost; in addition, the heuristic selection of the calibers using the minimum expected current absorbed by the loads provides at least 70% of the calibers that are contained in the final solution of the problem. This demonstrates the importance of using adequate starting points to potentiate metaheuristic optimizers such as the TSA.

scholarly journals Analysis of Three Phase 3-Level NPC Voltage Source Converter for AC-DC Conversion

2020 ◽  
Vol 06 (09) ◽  
pp. 144-148
Author(s):  
A Divya Teja and Dr. N Sambasiva Rao
Keyword(s):  
Power Quality ◽  
Power Flow ◽  
Reactive Power ◽  
Neutral Point ◽  
Voltage Source ◽  
Voltage Source Converter ◽  
Phase 3 ◽  
Control Techniques ◽  
Point Potential ◽  
Three Phase

The use of power electronic converters influences the generation of harmonics and reactive power flow in power system. Therefore, three-phase multilevel improved power quality AC-DC converters are gaining lot of popularity in power conversion applications. This work deals with critical problem of multilevel structure i.e neutral point potential (NPP) variation. In this paper, a simplified current controlled scheme is presented to ensure unity power factor operation. Neutral point potential (NPP) of three-phase, 3-level NPC AC-DC converter is controlled by modifying control signal in the controller using NPP regulator. An auxiliary circuit is being presented in this paper as an alternative option for controlling the neutral point potential of the converter. Comparison has been carried out between these control techniques in terms of power quality. A complete mathematical model is presented for better understanding of both techniques used for NPP control. The presented control techniques has been verified through simulation investigations and validated

Sign in / Sign up

Export Citation Format

Share Document