On the Network Topology Dependent Solution Count of the Algebraic Load Flow Equations

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.

Download Full-text

A Novel Approach to Model a Gas Network

Applied Sciences ◽

10.3390/app9061047 ◽

2019 ◽

Vol 9 (6) ◽

pp. 1047 ◽

Cited By ~ 7

Author(s):

Ali Ekhtiari ◽

Ioannis Dassios ◽

Muyang Liu ◽

Eoin Syron

Keyword(s):

Linear System ◽

End Users ◽

Load Flow ◽

Electrical Network ◽

Flow Equations ◽

Gas Network ◽

Wide Range ◽

Non Linear ◽

Novel Method ◽

Non Linear System

The continuous uninterrupted supply of Natural Gas (NG) is crucial to today’s economy, with issues in key infrastructure, e.g., Baumgarten hub in Austria in 2017, highlighting the importance of the NG infrastructure for the supply of primary energy. The balancing of gas supply from a wide range of sources with various end users can be challenging due to the unique and different behaviours of the end users, which in some cases span across a continent. Further complicating the management of the NG network is its role in supporting the electrical network. The fast response times of NG power plants and the potential to store energy in the network play a key role in adding flexibility across other energy systems. Traditionally, modelling the NG network relies on nonlinear pipe flow equations that incorporate the demand (load), flow rate, and physical network parameters including topography and NG properties. It is crucial that the simulations produce accurate results quickly. This paper seeks to provide a novel method to solve gas flow equations through a network under steady-state conditions. Firstly, the model is reformulated into non-linear matrix equations, then the equations separated into their linear and nonlinear components, and thirdly, the non-linear system is solved approximately by providing a linear system with similar solutions to the non-linear one. The non-linear equations of the NG transport system include the main variables and characteristics of a gas network, focusing on pressure drop in the gas network. Two simplified models, both of the Irish gas network (1. A gas network with 13 nodes, 2. A gas network with 109 nodes) are used as a case study for comparison of the solutions. Results are generated by using the novel method, and they are compared to the outputs of two numerical methods, the Newton–Raphson solution using MATLAB and SAINT, a commercial software that is used for the simulation of the gas network and electrical grids.

Download Full-text

An algebraic-geometric and topological analysis of the solution to the load-flow equations for a power system

10.1109/cdc.1981.269431 ◽

1981 ◽

Cited By ~ 1

Author(s):

John Baillieul ◽

Christopher I. Byrnes ◽

Robert B. Washburn

Keyword(s):

Power System ◽

Topological Analysis ◽

Load Flow ◽

Flow Equations

Download Full-text

Bifurcation analysis of the load flow equations

10.1109/cdc.1980.271876 ◽

1980 ◽

Cited By ~ 2

Author(s):

A. Arapostathis ◽

S. Sastry ◽

P. Varaiya

Keyword(s):

Bifurcation Analysis ◽

Load Flow ◽

Flow Equations

Download Full-text

A Probability Method for Very Short-Term Steady State Analysis of a Distribution System with Wind Farms

International Journal of Emerging Electric Power Systems ◽

10.2202/1553-779x.1883 ◽

2008 ◽

Vol 9 (5) ◽

Cited By ~ 3

Author(s):

Antonio Bracale ◽

Pierluigi Caramia ◽

Guido Carpinelli ◽

Pietro Varilone

Keyword(s):

Steady State ◽

Distribution System ◽

Wind Farm ◽

Probabilistic Method ◽

Wind Farms ◽

Load Flow ◽

Probability Method ◽

Short Term ◽

Flow Equations ◽

Three Phase

In this paper, a probabilistic method is proposed to analyze the very short-term steady-state performance of an unbalanced distribution electrical system characterized by the presence of wind farms. This method, which can take into account the uncertainties of loads and wind productions, is based on a Monte Carlo simulation procedure applied to the non-linear three-phase load flow equations, including wind farm models. Bayesian time series models are used to predict the next hour's wind speed probability density functions, making possible a predictive evaluation of the very short-term system steady-state behavior. Numerical applications are presented and discussed with reference to the three-phase unbalanced IEEE 34-bus test distribution system in the presence of wind farms connected at different busbars.

Download Full-text

Optimal Power Management of a DISCO with Integrations of Reliability Considerations and Wind Farm Based on Benders Decomposition

Mathematical Problems in Engineering ◽

10.1155/2011/812364 ◽

2011 ◽

Vol 2011 ◽

pp. 1-24

Author(s):

M. Baghdadi ◽

S. S. Mortazavi ◽

A. Saidian

Keyword(s):

Wind Farm ◽

Benders Decomposition ◽

Unit Commitment ◽

Energy Resource ◽

Load Flow ◽

Spinning Reserve ◽

Flow Equations ◽

Reliability Indices ◽

Distribution Company ◽

Comprehensive Framework

This paper presents a comprehensive framework model of a distribution company with security and reliability considerations. A probabilistic wind farm, which is a renewable energy resource, is modeled in this work. The requirement energy of distribution company can be either provided by distribution company's own distributed generations or purchased from power market. Two reliability indices as well as DC load flow equations are also considered in order to satisfy reliability and security constraints, respectively. Since allocating proper spinning reserve improves reliability level, the amount of spinning reserve will be calculated iteratively. In this work, all equations are expressed in a linear fashion in which unit commitment formulation depends on binary variables associated with only on/off of units. The benders decomposition method is used to solve security-based unit commitment.

Download Full-text

Power Flow Regulation by UPFC in Networks with Voltage Dependent Loads

International Journal of Recent Technology and Engineering - 2 ◽

10.35940/ijrte.f7517.038620 ◽

2020 ◽

Vol 8 (6) ◽

pp. 925-932

Keyword(s):

Power Flow ◽

Flow Analysis ◽

Flow Regulation ◽

Load Flow ◽

Constant Current ◽

Voltage Source ◽

Unified Power Flow Controller ◽

Flow Equations ◽

Load Flow Analysis ◽

Voltage Dependent

In this paper calculations are made to find out the power flow regulation capabilities of Unified Power Flow Controller (UPFC) in load flow analysis with loads which are voltage dependent. New equations for load flow analysis are developed that includes the models of voltage sensitive loads and voltage sources model of UPFC. Newton Raphson algorithm is used to solve the power flow equations of the network. UPFC voltage source model when included in the power equations has unique advantages over other modeling approaches. Analysis is done for two types of Loads. In the first analysis Constant current, Constant Power and Constant Impedance type of loads are examined. In the second analysis Composite loads are analyzed. The results of analysis on standard 5 bus system is presented here as a case study.

Download Full-text