Study of STATCOM and UPFC Controllers for Voltage Stability Evaluated by Saddle-Node Bifurcation Analysis

2006 ◽  
Author(s):  
A. Kazemi ◽  
V. Vahidinasab ◽  
A. Mosallanejad
Keyword(s):  
Bifurcation Analysis ◽  
Voltage Stability ◽  
Saddle Node Bifurcation ◽  
Saddle Node

A New Method for Static Voltage Stability Assessment based on The Local Loadability Boundary

2012 ◽  
Vol 13 (4) ◽  
Author(s):  
Thang Van Nguyen ◽  
Y. Minh Nguyen ◽  
Yong Tae Yoon
Keyword(s):  
Power System ◽  
Voltage Stability ◽  
Direct Method ◽  
Electric Power System ◽  
New Method ◽  
Stability Assessment ◽  
Saddle Node Bifurcation ◽  
Static Voltage Stability ◽  
Saddle Node ◽  
Thevenin Equivalent

Abstract This paper proposes a new method for assessing static voltage stability based on the local loadability boundary or P- Q curve in two dimensional power parameter space. The proposed method includes three main steps. The first step is to determine the critical buses and the second step is building the local loadability boundary or the saddle node bifurcation set for those critical buses. The final step is assessing the static voltage stability through the distance from current operating point to the boundary. The critical buses are defined through the right eigenvector by direct method. The boundary obtained by the proposed method that is combining a variation of standard direct method and Thevenin equivalent model of electric power system is a quadratic curve. And finally the distance is computed through the Euclid norm of normal vector of the boundary at the closest saddle node bifurcation point. The advantage of the proposed method is that it keeps the advantages of both efficient methods, the accuracy of the direct method and simple of Thevenin Equivalent based method. Thus, the proposed method holds some promise in terms of performing the real time voltage stability assessment of power system. Test results of New England 39 bus system are presented to show the effectiveness of the proposed method.

scholarly journals Complex Behaviors of Epidemic Model with Nonlinear Rewiring Rate

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Ding Fang ◽  
Yongxin Zhang ◽  
Wendi Wang
Keyword(s):  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Bifurcation Analysis ◽  
Epidemic Model ◽  
Multiple Equilibria ◽  
Homoclinic Bifurcation ◽  
Propagation Model ◽  
Bifurcation Curve ◽  
Saddle Node Bifurcation ◽  
Saddle Node

An SIS propagation model with the nonlinear rewiring rate on an adaptive network is considered. It is found by bifurcation analysis that the model has the complex behaviors which include the transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation, and Bogdanov–Takens bifurcation. Especially, a bifurcation curve with “S” shape emerges due to the nonlinear rewiring rate, which leads to multiple equilibria and twice saddle-node bifurcations. Numerical simulations show that the model admits a homoclinic bifurcation and a saddle-node bifurcation of the limit cycle.

Bifurcation analysis method of nonlinear traffic phenomena

2015 ◽  
Vol 26 (10) ◽  
pp. 1550111 ◽  
Author(s):  
Wenhuan Ai ◽  
Zhongke Shi ◽  
Dawei Liu
Keyword(s):  
Hopf Bifurcation ◽  
Traffic Flow ◽  
Bifurcation Analysis ◽  
Phase Plane ◽  
Flow Model ◽  
Analysis Method ◽  
Equilibrium Solutions ◽  
Saddle Node Bifurcation ◽  
Traffic Flow Model ◽  
Saddle Node

A new bifurcation analysis method for analyzing and predicting the complex nonlinear traffic phenomena based on the macroscopic traffic flow model is presented in this paper. This method makes use of variable substitution to transform a traditional traffic flow model into a new model which is suitable for the stability analysis. Although the substitution seems to be simple, it can extend the range of the variable to infinity and build a relationship between the traffic congestion and the unstable system in the phase plane. So the problem of traffic flow could be converted into that of system stability. The analysis identifies the types and stabilities of the equilibrium solutions of the new model and gives the overall distribution structure of the nearby equilibrium solutions in the phase plane. Then we deduce the existence conditions of the models Hopf bifurcation and saddle-node bifurcation and find some bifurcations such as Hopf bifurcation, saddle-node bifurcation, Limit Point bifurcation of cycles and Bogdanov–Takens bifurcation. Furthermore, the Hopf bifurcation and saddle-node bifurcation are selected as the starting point of density temporal evolution and it will be helpful for improving our understanding of stop-and-go wave and local cluster effects observed in the free-way traffic.

Bifurcation Analysis of the Wound Rotor Induction Motor

2015 ◽  
Vol 25 (12) ◽  
pp. 1550163 ◽  
Author(s):  
R. Salas-Cabrera ◽  
A. Hernandez-Colin ◽  
J. Roman-Flores ◽  
N. Salas-Cabrera
Keyword(s):  
Hopf Bifurcation ◽  
Induction Motor ◽  
Bifurcation Analysis ◽  
Open Loop ◽  
Experimental Results ◽  
Saddle Node Bifurcation ◽  
Saddle Node ◽  
Bifurcation Phenomena ◽  
Three Phase ◽  
The Individual

This work deals with the bifurcation phenomena that occur during the open-loop operation of a single-fed three-phase wound rotor induction motor. This paper demonstrates the occurrence of saddle-node bifurcation, hysteresis, supercritical saddle-node bifurcation, cusp and Hopf bifurcation during the individual operation of this electromechanical system. Some experimental results associated with the bifurcation phenomena are presented.

APPLICATION OF A TWO-DIMENSIONAL HINDMARSH–ROSE TYPE MODEL FOR BIFURCATION ANALYSIS

2013 ◽  
Vol 23 (03) ◽  
pp. 1350055 ◽  
Author(s):  
SHYAN-SHIOU CHEN ◽  
CHANG-YUAN CHENG ◽  
YI-RU LIN
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Sufficient Conditions ◽  
Type Model ◽  
Two Dimensional ◽  
Saddle Node Bifurcation ◽  
Trapping Region ◽  
Saddle Node ◽  
The Stability ◽  
Two Equilibria

In this study, we examine the bifurcation scenarios of a two-dimensional Hindmarsh–Rose type model [Tsuji et al., 2007] with four parameters and simulate some resemblances of neurophysiological features for this model using spike-and-reset conditions. We present possible classifications based on the results of the following assessments: (1) the number and stability of the equilibria are analyzed in detail using a table to demonstrate the matter in which the stability of the equilibrium changes and to determine which two equilibria collapse through the saddle-node bifurcation; (2) the sufficient conditions for an Andronov–Hopf bifurcation and a saddle-node bifurcation are mathematically confirmed; and (3) we elaborately evaluate the sufficient conditions for the Bogdanov–Takens (BT) and Bautin bifurcations. Several numerical simulations for these conditions are also presented. In particular, two types of bistable behaviors are numerically demonstrated: the BT and Bautin bifurcations. Notably, all of the bifurcation curves in the domain of the remaining parameters are similar when the time scale is large. Additionally, to show the potential for a limit cycle, the existence of a trapping region is demonstrated. These results present a variety of diverse behaviors for this model. The results of this study will be helpful in assessing suitable parameters for fitting the resemblances of experimental observations.

scholarly journals Bifurcation of an Orbit Homoclinic to a Hyperbolic Saddle of a Vector Field inR4

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Tiansi Zhang ◽  
Dianli Zhao
Keyword(s):  
Vector Field ◽  
Bifurcation Analysis ◽  
Transverse Section ◽  
Bifurcation Diagrams ◽  
Saddle Node Bifurcation ◽  
Saddle Node ◽  
Hyperbolic Saddle

We perform a bifurcation analysis of an orbit homoclinic to a hyperbolic saddle of a vector field inR4. We give an expression of the gap between returning points in a transverse section by renormalizing system, through which we find the existence of homoclinic-doubling bifurcation in the case1+α>β>ν. Meanwhile, after reparametrizing the parameter, a periodic-doubling bifurcation appears and may be close to a saddle-node bifurcation, if the parameter is varied. These scenarios correspond to the occurrence of chaos. Based on our analysis, bifurcation diagrams of these bifurcations are depicted.

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