Evaluation of the Forward-Backward Sweep Load Flow Method using the Contraction Mapping Principle

2016 ◽  
Vol 6 (6) ◽  
pp. 3229
Author(s):  
Diego Issicaba ◽  
Jorge Coelho
Keyword(s):  
Distribution System ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
System Analysis ◽  
Feasible Solution ◽  
Contraction Mapping Principle ◽  
Load Flow ◽  
Contraction Mapping Theorem ◽  
Flow Method ◽  
Theoretical Results

<p>This paper presents an assessment of the forward-backward sweep load flow method to distribution system analysis. The method is formally assessed using fixed-point concepts and the contraction mapping theorem. The existence and uniqueness of the load flow feasible solution is supported by an alternative argument from those obtained in the literature. Also, the closed-form of the convergence rate of the method is deduced and the convergence dependence of loading is assessed. Finally, boundaries for error values per iteration between iterates and feasible solution are obtained. Theoretical results have been tested in several numerical simulations, some of them presented in this paper, thus fostering discussions about applications and future works.</p>

scholarly journals Evaluation of the Forward-Backward Sweep Load Flow Method using the Contraction Mapping Principle

2016 ◽  
Vol 6 (6) ◽  
pp. 3229
Author(s):  
Diego Issicaba ◽  
Jorge Coelho
Keyword(s):  
Distribution System ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
System Analysis ◽  
Feasible Solution ◽  
Contraction Mapping Principle ◽  
Load Flow ◽  
Contraction Mapping Theorem ◽  
Flow Method ◽  
Theoretical Results

<p>This paper presents an assessment of the forward-backward sweep load flow method to distribution system analysis. The method is formally assessed using fixed-point concepts and the contraction mapping theorem. The existence and uniqueness of the load flow feasible solution is supported by an alternative argument from those obtained in the literature. Also, the closed-form of the convergence rate of the method is deduced and the convergence dependence of loading is assessed. Finally, boundaries for error values per iteration between iterates and feasible solution are obtained. Theoretical results have been tested in several numerical simulations, some of them presented in this paper, thus fostering discussions about applications and future works.</p>

scholarly journals Rotational Load Flow Method for Radial Distribution Systems

2016 ◽  
Vol 6 (3) ◽  
pp. 1344
Author(s):  
Diego Issicaba ◽  
Jorge Coelho
Keyword(s):  
Radial Distribution ◽  
Distribution System ◽  
Distribution Systems ◽  
System Analysis ◽  
Distribution Networks ◽  
Load Flow ◽  
Active Power ◽  
Actual Distribution ◽  
Flow Method ◽  
Node Voltage

This paper introduces a modified edition of classical Cespedes' load flow method to radial distribution system analysis. In the developed approach, a distribution network is modeled in different complex reference systems and reduced to a set of connected equivalent subnetworks, each without resistance, while graph topology and node voltage solution are preserved. Active power losses are then not dissipated in the modeled subnetworks and active power flows can be obtained as a consequence of radiality. Thus, the proposed method preprocesses a series of variable transformations concomitant to an iterative algorithm using a forward-backward sweep to arrive at the load flow solution. The proposed approach has been tested using literature and actual distribution networks, and efficiency improvements are verified in comparison to Cespedes' load flow method.

Rotational Load Flow Method for Radial Distribution Systems

2016 ◽  
Vol 6 (3) ◽  
pp. 1344
Author(s):  
Diego Issicaba ◽  
Jorge Coelho
Keyword(s):  
Radial Distribution ◽  
Distribution System ◽  
Distribution Systems ◽  
System Analysis ◽  
Distribution Networks ◽  
Load Flow ◽  
Active Power ◽  
Actual Distribution ◽  
Flow Method ◽  
Node Voltage

This paper introduces a modified edition of classical Cespedes' load flow method to radial distribution system analysis. In the developed approach, a distribution network is modeled in different complex reference systems and reduced to a set of connected equivalent subnetworks, each without resistance, while graph topology and node voltage solution are preserved. Active power losses are then not dissipated in the modeled subnetworks and active power flows can be obtained as a consequence of radiality. Thus, the proposed method preprocesses a series of variable transformations concomitant to an iterative algorithm using a forward-backward sweep to arrive at the load flow solution. The proposed approach has been tested using literature and actual distribution networks, and efficiency improvements are verified in comparison to Cespedes' load flow method.

scholarly journals Convergence Evaluation of a Load Flow Method based on Cespedes' Approach to Distribution System Analysis

2016 ◽  
Vol 6 (6) ◽  
pp. 3276
Author(s):  
Diego Issicaba ◽  
Jorge Coelho
Keyword(s):  
Steady State ◽  
Convergence Rate ◽  
Numerical Simulations ◽  
Closed Form ◽  
Distribution System ◽  
System Analysis ◽  
Load Flow ◽  
Steady State Analysis ◽  
Flow Method ◽  
State Analysis

<p>This paper evaluates the convergence of a load flow method based on Cespedes' formulation to distribution system steady-state analysis. The method is described and the closed-form of its convergence rate is deduced. Furthermore, convergence dependence of loading and the consequences of choosing particular initial estimates are verified mathematically. All mathematical results have been tested in numerical simulations, some of them presented in the paper.</p>

scholarly journals Stochastic periodic solutions of stochastic periodic differential equations

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1353-1362 ◽  
Author(s):  
Xinhong Zhang ◽  
Guixin Hu ◽  
Ke Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Theoretical Results

In this paper, the periodic stochastic differential equations are studied. By applying the theory of Lyapunov?s second method, contraction mapping principle and establishing new lemmas, the existence and uniqueness of stochastic periodic solutions to stochastic periodic differential equations are obtained. Moreover, several examples are introduced to illustrate our theoretical results.

Convergence Evaluation of a Load Flow Method based on Cespedes' Approach to Distribution System Analysis

2016 ◽  
Vol 6 (6) ◽  
pp. 3276
Author(s):  
Diego Issicaba ◽  
Jorge Coelho
Keyword(s):  
Steady State ◽  
Convergence Rate ◽  
Numerical Simulations ◽  
Closed Form ◽  
Distribution System ◽  
System Analysis ◽  
Load Flow ◽  
Steady State Analysis ◽  
Flow Method ◽  
State Analysis

<p>This paper evaluates the convergence of a load flow method based on Cespedes' formulation to distribution system steady-state analysis. The method is described and the closed-form of its convergence rate is deduced. Furthermore, convergence dependence of loading and the consequences of choosing particular initial estimates are verified mathematically. All mathematical results have been tested in numerical simulations, some of them presented in the paper.</p>

scholarly journals On singular systems of nonlinear equations involving 3n-Caputo derivatives

2020 ◽  
Vol 23 (2) ◽  
pp. 179-192
Author(s):  
Amele Taïeb
Keyword(s):  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Singular Systems ◽  
Nonlinear Differential Equations ◽  
Contraction Mapping Principle ◽  
Systems Of Nonlinear Equations ◽  
Fractional Systems ◽  
Caputo Derivatives ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

We study singular fractional systems of nonlinear differential equations involving 3n-Caputo derivatives. We investigate existence and uniqueness results using the contraction mapping principle. We also discuss the existence of at least one solution by means of Schauder fixed point theorem. Moreover, we define and discuss the Ulam–Hyers stability and the generalized Ulam–Hyers stability of solutions for such systems. To illustrate the main results, we present some examples.

scholarly journals A New Existence and Uniqueness Theorem for Continuous Games

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Seamus D Hogan
Keyword(s):  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Jacobian Matrix ◽  
Iterative Sequence ◽  
Response Functions ◽  
Unique Equilibrium ◽  
Contraction Mapping Theorem ◽  
Best Response ◽  
General Sufficient Condition ◽  
General Game

This paper derives a general sufficient condition for existence and uniqueness in continuous games using a variant of the contraction mapping theorem applied to mappings from a subset of the real line on to itself. We first prove this contraction mapping variant, and then show how the existence of a unique equilibrium in the general game can be shown by proving the existence of a unique equilibrium in an iterative sequence of games involving such mappings. Finally, we show how a general condition for this to occur is that a matrix derived from the Jacobian matrix of best-response functions has positive leading principal minors, and how this condition generalises some existing uniqueness theorems for particular games. In particular, we show how the same conditions used in those theorems to show uniqueness, also guarantee existence in games with unbounded strategy spaces.

scholarly journals Periodic solutions of Volterra integral equations

1988 ◽  
Vol 11 (4) ◽  
pp. 781-792 ◽  
Author(s):  
M. N. Islam
Keyword(s):  
Periodic Solutions ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Volterra Integral Equations ◽  
System Of Equations ◽  
Convolution Kernel ◽  
Basic Tool ◽  
Resolvent Function

Consider the system of equationsx(t)=f(t)+∫−∞tk(t,s)x(s)ds,           (1)andx(t)=f(t)+∫−∞tk(t,s)g(s,x(s))ds.       (2)Existence of continuous periodic solutions of (1) is shown using the resolvent function of the kernelk. Some important properties of the resolvent function including its uniqueness are obtained in the process. In obtaining periodic solutions of (1) it is necessary that the resolvent ofkis integrable in some sense. For a scalar convolution kernelksome explicit conditions are derived to determine whether or not the resolvent ofkis integrable. Finally, the existence and uniqueness of continuous periodic solutions of (1) and (2) are btained using the contraction mapping principle as the basic tool.

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