• Journal of Electrical Engineering and Technology
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• v.8 no.2
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• pp.206-214
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• 2013

This paper proposes a new method for monitoring local voltage stability using the saddle node bifurcation set or loadability boundary in two dimensional power parameter space. The method includes three main steps. First step is to determine the critical buses and the second step is building the static voltage stability boundary or the saddle node bifurcation set. Final step is monitoring the voltage stability through the distance from current operating point to the boundary. Critical buses are defined through the right eigenvector by direct method. The boundary of the static voltage stability region is a quadratic curve that can be obtained by the proposed method that is combining a variation of standard direct method and Thevenin equivalent model of electric power system. 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 gets the advantages of both methods, the accuracy of the direct method and simple of Thevenin Equivalent model. Thus, the proposed method holds some promises in terms of performing the real-time voltage stability monitoring of power system. Test results of New England 39 bus system are presented to show the effectiveness of the proposed method.

• The Transactions of the Korean Institute of Power Electronics
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• v.5 no.4
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• pp.394-402
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• 2000

This paper proposes a bifurcation theory method applied for voltage stability analysis and shows the improvement of voltage stability by attaching the FACTS devices in the power system. A power system is generally expressed by a set of equations of highly nonlinear dynamical system which includes system parameters(real or reactive power). Sometimes variation of parameters in the system may result in complication behaviors which give rise to system instability. The addition of FACTS increases the range of voltage stability in the power system. The effect of FACTS which improves voltage stability are illustrated in the case studies by delaying of Unstable Hopf Bifurcation and Saddle Node Bifurcation.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.52 no.10
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• pp.557-562
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• 2003

This paper presents a power transfer capability calculation algorithm considering the closest saddle node bifurcation for voltage stability margin. In this method, voltage stability margin constraints considering the closest saddle node bifurcation are incorporated into a power transfer capability formulation to guarantee adequate voltage security levels in an interconnected power system. The proposed method is applied to IEEE-24 reliability test system and the results show the effectiveness of the method.

• Proceedings of the KIEE Conference
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• 2002.11b
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• pp.88-90
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• 2002

This paper presents a power transfer capability calculation algorithm Considering A Closest Saddle Node Bifurcation For Voltage Stability Margin. In this method, voltage stability margin constraints considering a closest saddle node bifurcation are incorporated into a power transfer capability formulation to guarantee adequate voltage security levels in an interconnected Power System. The proposed method is applied to IEEE-24 Reliability Test System and the results shows the effectiveness of the method.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.8
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• pp.958-964
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• 1999

The distance in load parameter space to the closest saddle node bifurcation (CSNB) point provides the worst case power margin to voltage instability and the left eigenvector at CSNB identifies the most effective direction to steer the system to maximize voltage stability under contingency. This paper presents an improved direct method for computing CSNB: the order of nonlinear systems equations is reduced to about twice of the size of load flow equations in contrast to about three-times in Dobson's direct method; the initial guess for the direct method is computed efficiently and robustly by combined use of continuation power flow, a pair of multiple load flow solution with Lagrange interpolation. It is also shown that voltage stability may be enhanced significantly with shift of generations in the direction of the left eigenvector at CSNB.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.695-713
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• 2013

We formulate and study a predator-prey model with non-monotonic functional response type and weak Allee effects on the prey, which extends the system studied by Ruan and Xiao in [Global analysis in a predator-prey system with nonmonotonic functional response, SIAM J. Appl. Math. 61 (2001), no. 4, 1445-1472] but containing an extra term describing weak Allee effects on the prey. We obtain the global dynamics of the model by combining the global qualitative and bifurcation analysis. Our bifurcation analysis of the model indicates that it exhibits numerous kinds of bifurcation phenomena, including the saddle-node bifurcation, the supercritical and the subcritical Hopf bifurcations, and the homoclinic bifurcation, as the values of parameters vary. In the generic case, the model has the bifurcation of cusp type of codimension 2 (i.e., Bogdanov-Takens bifurcation).

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.1-16
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• 2017

In this paper we study a four dimensional tourism-based social-ecological dynamical system. In fact we analyse tourism profitability, compatibility and sustainability by using bifurcation theory in terms of structural properties of attractors of system. For this purpose first we transformed it into a three dimensional system such that the reduced system is the extended and modified model of the previous three dimensional models suggested for tourism with the same dimension. Then we investigate transcritical, pitchfork and saddle-node bifurcation points of system. And numerically by finding some branches of stable equilibria for system show the profitability of tourism industry. Then by determining the Hopf bifurcation points of system we find a family of stable attractors for that by numerical techniques. Finally we conclude the existence of these stable limit cycles implies profitability and compatibility and then the sustainability of tourism.

• Journal of Electrical Engineering and Technology
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• v.8 no.4
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• pp.719-728
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• 2013

Probabilistic assessment of voltage stability margin (VSM) with existence of correlated wind speeds is investigated. Nataf transformation is adopted to establish wind speed correlation (WSC) model. Based on the saddle-node bifurcation transversality condition equations and Monte Carlo simulation technique, probability distribution of VSM is determined. With correlation coefficients range low to high value, the effect of WSC on VSM is studied. In addition, two risk indexes are proposed and the possible threat caused by WSC is evaluated from the viewpoint of risk analysis. Experimental results show that the presence of correlated wind speeds is harmful to safe and stable operation of a power system as far as voltage stability is concerned. The achievement of this paper gives a detailed elaboration about the influence of WSC on voltage stability and provides a potentially effective analytical tool for modern power system with large-scale wind power sources integration.

• KIEE International Transactions on Power Engineering
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• v.4A no.1
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• pp.1-5
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• 2004

The model of a power system with load dynamics is studied by investigating qualitative changes in its behavior as the reactive power demand at a load bus is increased. The load is created using induction motors parallel with the constant power and constant impedance load. As the load increases, the system experiences various bifurcations such as sub critical and supercritical Hopf, period-doubling and saddle-node bifurcation. The latter may lead the system to voltage collapse. A nonlinear controller is used to control the subcritical Hopf bifurcation and hence mitigate voltage collapse. It is applied to the KEPCO (Korean Electric Power Company) system to demonstrate its validity.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.289-294
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• 2001

Three kinds of viscoelastic damper model, which has a non-linear spring as an element is studied analytically and numerically. The behavior of the damper model shows non-linear hysteresis curves which is qualitatively similar to those of real viscoelastic materials. The motion is governed by a non-linear constitutive equation and an additional equation of motion. Harmonic balance method is applied to get analytic solutions of the system. The frequency-response curves show that multiple solutions co-exist and that the jump phenomena can occur. In addition, it is shown that separate solution branch exists and that it can merge with the primary response curve. Saddle-node bifurcation sets explain the occurrences of such non-linear phenomena.