scholarly journals Convergence Region of Newton Iterative Power Flow Method: Numerical Studies

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Jiao-Jiao Deng ◽  
Hsiao-Dong Chiang
Keyword(s):  
Power Flow ◽  
Test System ◽  
Initial Guess ◽  
Fractal Boundary ◽  
Convergence Region ◽  
Nonlinear Load ◽  
Flow Equations ◽  
Flow Method ◽  
Numerical Studies ◽  
Power Flow Method

Power flow study plays a fundamental role in the process of power system operation and planning. Of the several methods in commercial power flow package, the Newton-Raphson (NR) method is the most popular one. In this paper, we numerically study the convergence region of each power flow solution under the NR method. This study of convergence region provides insights of the complexity of the NR method in finding power flow solutions. Our numerical studies confirm that the convergence region of NR method has a fractal boundary and find that this fractal boundary of convergence regions persists under different loading conditions. In addition, the convergence regions of NR method for power flow equations with different nonlinear load models are also fractal. This fractal property highlights the importance of choosing initial guesses since a small variation of an initial guess near the convergence boundary leads to two different power flow solutions. One vital variation of Newton method popular in power industry is the fast decoupled power flow method whose convergence region is also numerically studied on an IEEE 14-bus test system which is of 22-dimensional in state space.

Two three-phase linear power flow models for distribution power system under polar coordinates

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Wenjin Mao ◽  
Hongwei Li
Keyword(s):  
Power System ◽  
Power Flow ◽  
Polar Coordinates ◽  
Constant Current ◽  
Content Type ◽  
Flow Equations ◽  
Flow Method ◽  
Three Phase ◽  
Zip Load ◽  
Power Flow Method

Purpose The purpose of this study is to provide a non-iterative linear method to solve the power flow equations of alternating current (AC) power grid. Traditional iterative power flow calculation is limited in speed and reliability, and it is unsuitable for the real-time and online applications of the modern distribution power system (DPS). Thus, it would be of great significance if a fast and flexible linear power flow (LPF) solution could be introduced particularly necessary for the robust and fast control of DPS, especially when the system consists of star and delta connections ZIP load (a constant impedance, Z, load, a constant current, I, load and a constant power, P, load) and the high penetration of distributed solar and wind power generators. Design/methodology/approach Based on the features of DPS and considering the approximate balance of three-phase DPS, several approximations corresponding to the three-phase power flow equations have been discussed and analyzed. Then, based on those approximations, two three-phase LPF models have been developed under the polar coordinates. One model has been formulated with the voltage magnitudes [referred to the voltage magniudes based linear power flow method (VMLPF)], and another model has been formulated with the logarithmic transform of voltage magnitudes [referred to the logarithmic transform of voltage based linear power flow method LGLPF)]. Findings The institute of electrical and electronic engineers (IEEE) 13-bus, 37-bus, 123-bus and an improved 615-bus unbalanced DPSs are used to test the performances of the methods considering star and delta connections ZIP load and PV buses (voltage-controlled buses). The test results validate the effectiveness and accuracy of the proposed two models. Especially when considering the PV buses and delta connection ZIP load, the proposed two models perform much well. Moreover, the results show that VMLPF performs a bit better than LGLPF. Research limitations/implications Except for the transformer with Yg–Yg connection winding can be dealt with directly, the transformers with other connections are not discussed in this proposed paper and need to be further studied. Originality/value These proposed two models can deal with ZIP load with star and delta connections as well as multi slack buses and PV buses. The single-phase, two-phase and three-phase hybrid networks can be directly included too. The proposed two models are capable of offering enough accuracy level, and they are therefore suitable for online applications that require a large number of repeated power flow calculations.

scholarly journals Analysis of Tire Acoustic Cavity Resonance Energy Transmission Characteristics in Wheels Based on Power Flow Method

2021 ◽  
Vol 11 (9) ◽  
pp. 3979
Author(s):  
Wei Zhao ◽  
Yuting Liu ◽  
Xiandong Liu ◽  
Yingchun Shan ◽  
Xiaojun Hu
Keyword(s):  
Power Flow ◽  
Resonance Energy ◽  
Cavity Resonance ◽  
Propagation Path ◽  
Material Structure ◽  
Transmission Characteristics ◽  
Energy Transmission ◽  
Flow Method ◽  
Acoustic Cavity ◽  
Power Flow Method

As a kind of low-frequency vehicle interior noise, tire acoustic cavity resonance noise plays an important role, since the other noise (e.g., engine noise, wind noise and friction noise) has been largely suppressed. For the suspension system, wheels stand first in the propagation path of this energy. Therefore, it is of great significance to study the influence of wheel design on the transmission characteristics of this vibration energy. However, currently the related research has not received enough attention. In this paper, two sizes of aluminum alloy wheel finite element models are constructed, and their modal characteristics are analyzed and verified by experimental tests simultaneously. A mathematically fitting sound pressure load model arising from the tire acoustic cavity resonance acting on the rim is first put forward. Then, the power flow method is applied to investigate the resonance energy distribution and transmission characteristics in the wheels. The structure intensity distribution and energy transmission efficiency can be described and analyzed clearly. Furthermore, the effects of material structure damping and the wheel spoke number on the energy transmission are also discussed.

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.

Decoupled AC/DC Power Flow Strategy for Multiterminal HVDC Systems

2018 ◽  
Vol 19 (1) ◽  
Author(s):  
Yixiang Gao ◽  
Shuhui Li ◽  
Weizhen Dong ◽  
Bing Lu
Keyword(s):  
Power Flow ◽  
Control Mode ◽  
Power Flow Calculation ◽  
Flow Calculation ◽  
Power System Control ◽  
Flow Method ◽  
Hvdc System ◽  
Dc Power ◽  
Bus System ◽  
Power Flow Method

AbstractThis paper proposes a decoupled AC/DC power flow approach for multi-terminal HVDC systems. The proposed method simplifies the power flow computation of multi-terminal HVDC systems while accurately reflecting the operation and control characteristics of VSC (voltage source converter) stations in a HVDC network. In the DC network, the power flow calculation is conducted based on a slack DC bus VSC station and power commends issued to other VSC stations from the power system control center. Then, in the AC power flow calculation, VSC stations are treated as special AC generators that can generate and absorb power from the AC grid in active and reactive power or active power and bus voltage control mode. For validation purpose, the conventional unified power flow method for multi-terminal HVDC systems is built. The paper compares the proposed method with the unified power flow method for an 8-bus multi-terminal HVDC system based on MATPOWER. Then, more case studies for different VSC control modes are conducted and evaluated for the 8-bus system. Afterwards, the proposed method is applied to the power flow study of a more practical and complicated multi-terminal HVDC system based on the IEEE 118-bus system.

Efficient Reduction in the Annual Investment Costs in AC Distribution Networks via Optimal Integration of Solar PV Sources Using the Newton Metaheuristic Algorithm

2021 ◽  
Vol 11 (23) ◽  
pp. 11525
Author(s):  
Oscar Danilo Montoya ◽  
Luis Fernando Grisales-Noreña ◽  
Lázaro Alvarado-Barrios ◽  
Andres Arias-Londoño ◽  
Cesar Álvarez-Arroyo
Keyword(s):  
Power Flow ◽  
Fitness Function ◽  
Solution Space ◽  
Distribution Networks ◽  
Optimal Placement ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Solar Pv ◽  
Flow Method ◽  
Power Flow Method

This research addresses the problem of the optimal placement and sizing of (PV) sources in medium voltage distribution grids through the application of the recently developed Newton metaheuristic optimization algorithm (NMA). The studied problem is formulated through a mixed-integer nonlinear programming model where the binary variables regard the installation of a PV source in a particular node, and the continuous variables are associated with power generations as well as the voltage magnitudes and angles, among others. To improve the performance of the NMA, we propose the implementation of a discrete–continuous codification where the discrete component deals with the location problem and the continuous component works with the sizing problem of the PV sources. The main advantage of the NMA is that it works based on the first and second derivatives of the fitness function considering an evolution formula that contains its current solution (xit) and the best current solution (xbest), where the former one allows location exploitation and the latter allows the global exploration of the solution space. To evaluate the fitness function and its derivatives, the successive approximation power flow method was implemented, which became the proposed solution strategy in a master–slave optimizer, where the master stage is governed by the NMA and the slave stage corresponds to the power flow method. Numerical results in the IEEE 34- and IEEE 85-bus systems show the effectiveness of the proposed optimization approach to minimize the total annual operative costs of the network when compared to the classical Chu and Beasley genetic algorithm and the MINLP solvers available in the general algebraic modeling system with reductions of 26.89% and 27.60% for each test feeder with respect to the benchmark cases.

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