scholarly journals A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors

Electronics ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 2062
Author(s):  
Luis Fernando Grisales-Noreña ◽  
Oscar Danilo Montoya ◽  
Walter Julian Gil-González ◽  
Alberto-Jesus Perea-Moreno ◽  
Miguel-Angel Perea-Moreno
Keyword(s):  
Direct Current ◽  
Power Flow ◽  
Processing Time ◽  
Linear Equations ◽  
Triangular Matrix ◽  
Taylor Series Expansion ◽  
Distribution Networks ◽  
Matrix Formulation ◽  
Numerical Convergence ◽  
Solution Methods

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.

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 Metaheuristic Optimization Methods for Optimal Power Flow Analysis in DC Distribution Networks

2020 ◽  
Vol 1 (1) ◽  
pp. 13-31
Author(s):  
Luis Fernando Grisales Noreña ◽  
Oscar Daniel Garzón Rivera ◽  
Jauder Alexander Ocampo Toro ◽  
Carlos Andres Ramos Paja ◽  
Miguel Angel Rodriguez Cabal
Keyword(s):  
Objective Function ◽  
Direct Current ◽  
Power Loss ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Flow Problem ◽  
Electrical Grid ◽  
Optimal Power ◽  
Solution Methods ◽  
Power Flow Problem

In this paper is addressed the optimal power flow problem in direct current grids, by using solution methods based on metaheuristics techniques and numerical methods. For which was proposed a mixed integer nonlinear programming problem, that describes the optimal power flow problem in direct current grids. As solution methodology was proposed a master–slave strategy, which used in master stage three continuous solution methods for solving the optimal power flow problem: a particle swarm optimization algorithm, a continuous version of the genetic algorithm and the black hole optimization method. In the slave stages was used a methods based on successive approximations for solving the power flow problem, entrusted for calculates the objective function associated to each solution proposed by the master stage. As objective function was used the reduction of power loss on the electrical grid, associated to the energy transport. To validate the solution methodologies proposed were used the test systems of 21 and 69 buses, by implementing three levels of maximum distributed power penetration: 20%, 40% and 60% of the power supplied by the slack bus, without considering distributed generators installed on the electrical grid. The simulations were carried out in the software Matlab, by demonstrating that the methods with the best performance was the BH/SA, due to that show the best trade-off between the reduction of the power loss and processing time, for solving the optimal power flow problem in direct current networks.

scholarly journals Optimal Integration of Photovoltaic Sources in Distribution Networks for Daily Energy Losses Minimization Using the Vortex Search Algorithm

2021 ◽  
Vol 11 (10) ◽  
pp. 4418
Author(s):  
Alejandra Paz-Rodríguez ◽  
Juan Felipe Castro-Ordoñez ◽  
Oscar Danilo Montoya ◽  
Diego Armando Giral-Ramírez
Keyword(s):  
Objective Function ◽  
Power Flow ◽  
Search Algorithm ◽  
Peak Load ◽  
Distribution Networks ◽  
Energy Losses ◽  
Continuous Version ◽  
Continuous Section ◽  
Daily Energy ◽  
Discrete Part

This paper deals with the optimal siting and sizing problem of photovoltaic (PV) generators in electrical distribution networks considering daily load and generation profiles. It proposes the discrete-continuous version of the vortex search algorithm (DCVSA) to locate and size the PV sources where the discrete part of the codification defines the nodes. Renewable generators are installed in these nodes, and the continuous section determines their optimal sizes. In addition, through the successive approximation power flow method, the objective function of the optimization model is obtained. This objective function is related to the minimization of the daily energy losses. This method allows determining the power losses in each period for each renewable generation input provided by the DCVSA (i.e., location and sizing of the PV sources). Numerical validations in the IEEE 33- and IEEE 69-bus systems demonstrate that: (i) the proposed DCVSA finds the optimal global solution for both test feeders when the location and size of the PV generators are explored, considering the peak load scenario. (ii) In the case of the daily operative scenario, the total reduction of energy losses for both test feeders are 23.3643% and 24.3863%, respectively; and (iii) the DCVSA presents a better numerical performance regarding the objective function value when compared with the BONMIN solver in the GAMS software, which demonstrates the effectiveness and robustness of the proposed master-slave optimization algorithm.

scholarly journals Stochastic Expansion Planning of Various Energy Storage Technologies in Active Power Distribution Networks

2021 ◽  
Vol 13 (10) ◽  
pp. 5752
Author(s):  
Reza Sabzehgar ◽  
Diba Zia Amirhosseini ◽  
Saeed D. Manshadi ◽  
Poria Fajri
Keyword(s):  
Energy Storage ◽  
Power Distribution ◽  
Power Flow ◽  
Lithium Ion ◽  
Distribution Networks ◽  
Renewable Energy Resources ◽  
Flow Equations ◽  
Second Order Cone ◽  
Li Ion ◽  
The Cost

This work aims to minimize the cost of installing renewable energy resources (photovoltaic systems) as well as energy storage systems (batteries), in addition to the cost of operation over a period of 20 years, which will include the cost of operating the power grid and the charging and discharging of the batteries. To this end, we propose a long-term planning optimization and expansion framework for a smart distribution network. A second order cone programming (SOCP) algorithm is utilized in this work to model the power flow equations. The minimization is computed in accordance to the years (y), seasons (s), days of the week (d), time of the day (t), and different scenarios based on the usage of energy and its production (c). An IEEE 33-bus balanced distribution test bench is utilized to evaluate the performance, effectiveness, and reliability of the proposed optimization and forecasting model. The numerical studies are conducted on two of the highest performing batteries in the current market, i.e., Lithium-ion (Li-ion) and redox flow batteries (RFBs). In addition, the pros and cons of distributed Li-ion batteries are compared with centralized RFBs. The results are presented to showcase the economic profits of utilizing these battery technologies.

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.

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