scholarly journals Convergence analysis of the triangular-based power flow method for AC distribution grids

2022 ◽  
Vol 12 (1) ◽  
pp. 41
Author(s):  
Maria Camila Herrera ◽  
Oscar Danilo Montoya ◽  
Alexander Molina-Cabrera ◽  
Luis Fernando Grisales-Noreña ◽  
Diego Armando Giral-Ramirez
Keyword(s):  
Convergence Analysis ◽  
Power Flow ◽  
Distribution Networks ◽  
Banach Fixed Point Theorem ◽  
Voltage Profile ◽  
Triangular Matrices ◽  
Admittance Matrix ◽  
Radial Distribution Networks ◽  
Newton Raphson ◽  
Distribution Grids

<p>This paper addresses the convergence analysis of the triangular-based power flow (PF) method in alternating current radial distribution networks. The PF formulation is made via upper-triangular matrices, which enables finding a general iterative PF formula that does not require admittance matrix calculations. The convergence analysis of this iterative formula is carried out by applying the Banach fixed-point theorem (BFPT), which allows demonstrating that under an adequate voltage profile the triangular-based PF always converges. Numerical validations are made, on the well-known 33 and 69 distribution networks test systems. Gauss-seidel, newton-raphson, and backward/forward PF methods are considered for the sake of comparison. All the simulations are carried out in MATLAB software.</p>

scholarly journals On the Matricial Formulation of Iterative Sweep Power Flow for Radial and Meshed Distribution Networks with Guarantee of Convergence

2020 ◽  
Vol 10 (17) ◽  
pp. 5802 ◽  
Author(s):  
Oscar Danilo Montoya ◽  
Walter Gil-González ◽  
Diego Armando Giral
Keyword(s):  
Distribution System ◽  
Power Flow ◽  
Incidence Matrix ◽  
System Analysis ◽  
Distribution Networks ◽  
Banach Fixed Point Theorem ◽  
Convergence Test ◽  
Admittance Matrix ◽  
Newton Raphson ◽  
Basic Concepts

This paper presents a general formulation of the classical iterative-sweep power flow, which is widely known as the backward–forward method. This formulation is performed by a branch-to-node incidence matrix with the main advantage that this approach can be used with radial and meshed configurations. The convergence test is performed using the Banach fixed-point theorem while considering the dominant diagonal structure of the demand-to-demand admittance matrix. A numerical example is presented in tutorial form using the MATLAB interface, which aids beginners in understanding the basic concepts of power-flow programming in distribution system analysis. Two classical test feeders comprising 33 and 69 nodes are used to validate the proposed formulation in comparison with conventional methods such as the Gauss–Seidel and Newton–Raphson power-flow formulations.

scholarly journals Laplacian Matrix-Based Power Flow Formulation for LVDC Grids with Radial and Meshed Configurations

Energies ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1866
Author(s):  
Zahid Javid ◽  
Ulas Karaagac ◽  
Ilhan Kocar ◽  
Ka Wing Chan
Keyword(s):  
Fixed Point ◽  
Power Flow ◽  
Low Voltage ◽  
Mathematical Formulation ◽  
Distribution Networks ◽  
Load Flow ◽  
Banach Fixed Point Theorem ◽  
Loading Conditions ◽  
Flow Equations ◽  
Uniqueness Of The Solution

There is an increasing interest in low voltage direct current (LVDC) distribution grids due to advancements in power electronics enabling efficient and economical electrical networks in the DC paradigm. Power flow equations in LVDC grids are non-linear and non-convex due to the presence of constant power nodes. Depending on the implementation, power flow equations may lead to more than one solution and unrealistic solutions; therefore, the uniqueness of the solution should not be taken for granted. This paper proposes a new power flow solver based on a graph theory for LVDC grids having radial or meshed configurations. The solver provides a unique solution. Two test feeders composed of 33 nodes and 69 nodes are considered to validate the effectiveness of the proposed method. The proposed method is compared with a fixed-point methodology called direct load flow (DLF) having a mathematical formulation equivalent to a backward forward sweep (BFS) class of solvers in the case of radial distribution networks but that can handle meshed networks more easily thanks to the use of connectivity matrices. In addition, the convergence and uniqueness of the solution is demonstrated using a Banach fixed-point theorem. The performance of the proposed method is tested for different loading conditions. The results show that the proposed method is robust and has fast convergence characteristics even with high loading conditions. All simulations are carried out in MATLAB 2020b software.

scholarly journals Protection Coordination of Properly Sized and Placed Distributed Generations–Methods, Applications and Future Scope

2018 ◽  
Author(s):  
Sunny Katyara ◽  
Lukasz Staszewski ◽  
Zbigniew Leonowicz
Keyword(s):  
Distributed Generation ◽  
Distribution System ◽  
Power Flow ◽  
Distribution Networks ◽  
System Stability ◽  
Distributed Generations ◽  
High Penetration ◽  
Multi Agent ◽  
Utility Network ◽  
Radial Distribution Networks

The radial distribution networks are designed for unidirectional power flows and are passive in nature. However, with the penetration of Distributed Generation (DG), the power flow becomes bidirectional and the network becomes active. The integration of DGs into distribution network creates many issues with: system stability, protection coordination, power quality, islanding, proper placement and sizing etc. Among these issues, the two most significant are optimal sizing and placement of DGs and their protection coordination in utility network. The proper coordination of relays with high penetration of DGs placed at optimal location increases the availability and reliability of the network during abnormal operating conditions.This research addresses most of the available methods for efficient sizing and placement of DGs in distribution system (numerical, analytical and heuristic) as well as the developed protection coordination techniques for utility networks in the presence of DGs (Artificial Intelligence (AI), adaptive and non-adaptive, multi-agent, hybrid). This paper indicates the possible research gaps and highlights the applications possibilities and methods&rsquo; limitations in the area of DGs.

scholarly journals A Novel Three-Phase Harmonic Power Flow Algorithm for Unbalanced Radial Distribution Networks with the Presence of D-STATCOM Devices

Electronics ◽  
2021 ◽  
Vol 10 (21) ◽  
pp. 2663
Author(s):  
Raavi Satish ◽  
Kanchapogu Vaisakh ◽  
Almoataz Y. Abdelaziz ◽  
Adel El-Shahat
Keyword(s):  
Radial Distribution ◽  
Power Flow ◽  
Distribution Networks ◽  
Flow Solution ◽  
Three Phase ◽  
Harmonic Pollution ◽  
Flow Algorithm ◽  
Non Linear ◽  
Radial Distribution Networks ◽  
Harmonic Power

Due to the rapid advancement in power electronic devices in recent years, there is a fast growth of non-linear loads in distribution networks (DNs). These non-linear loads can cause harmonic pollution in the networks. The harmonic pollution is low, and the resonance problem is absent in distribution static synchronous compensators (D-STATCOM), which is the not case in traditional compensating devices such as capacitors. The power quality issue can be enhanced in DNs with the interfacing of D-STATCOM devices. A novel three-phase harmonic power flow algorithm (HPFA) for unbalanced radial distribution networks (URDN) with the existence of linear and non-linear loads and the integration of a D-STATCOM device is presented in this paper. The bus number matrix (BNM) and branch number matrix (BRNM) are developed in this paper by exploiting the radial topology in DNs. These matrices make the development of HPFA simple. Without D-STATCOM integration, the accuracy of the fundamental power flow solution and harmonic power flow solution are tested on IEEE−13 bus URDN, and the results are found to be precise with the existing work. Test studies are conducted on the IEEE−13 bus and the IEEE−34 bus URDN with interfacing D-STATCOM devices, and the results show that the fundamental r.m.s voltage profile is improved and the fundamental harmonic power loss and total harmonic distortion (THD) are reduced.

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