The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform
Y Takemura - One of the best experts on this subject based on the ideXlab platform.
-
Unstable Equilibrium point in chaotic domain wall motion and ott grebogi yorke control
Journal of Applied Physics, 2001Co-Authors: H Okuno, Y TakemuraAbstract:A method for finding the Unstable Equilibrium points in Bloch wall motion is proposed, which is important for controlling the chaotic domain-wall motion by using the Ott–Grebogi–Yorke (OGY) method. The dynamics of Bloch wall motion are expressed by a nonlinear differential equation with the terms of inertia, damping, restoring, and an external magnetic drive force. An equation is transformed into the difference equations by following the OGY method, approximating linearly around an Unstable Equilibrium point (a saddle point), and adding a controlling input. The Unstable Equilibrium points are obtained by using the return map and the condition of hyperbolic fixed point. The time series of domain-wall motion successfully controlled on the Unstable Equilibrium points by the OGY method is shown.
-
Unstable Equilibrium point in chaotic domain-wall motion and Ott–Grebogi–Yorke control
Journal of Applied Physics, 2001Co-Authors: H Okuno, Y TakemuraAbstract:A method for finding the Unstable Equilibrium points in Bloch wall motion is proposed, which is important for controlling the chaotic domain-wall motion by using the Ott–Grebogi–Yorke (OGY) method. The dynamics of Bloch wall motion are expressed by a nonlinear differential equation with the terms of inertia, damping, restoring, and an external magnetic drive force. An equation is transformed into the difference equations by following the OGY method, approximating linearly around an Unstable Equilibrium point (a saddle point), and adding a controlling input. The Unstable Equilibrium points are obtained by using the return map and the condition of hyperbolic fixed point. The time series of domain-wall motion successfully controlled on the Unstable Equilibrium points by the OGY method is shown.
Hsiaodong Chiang - One of the best experts on this subject based on the ideXlab platform.
-
robustness of the closest Unstable Equilibrium point along a p v curve
Power and Energy Society General Meeting, 2019Co-Authors: Robert Owusumireku, Hsiaodong ChiangAbstract:In this paper, we study numerically the behavior of the closest Unstable Equilibrium point (UEP) on the stability boundary of a stable Equilibrium point (SEP) of a post-switching power system along a P-V curve. Using the structure-preserving model of the WSCC 9-bus 3-machine system, we show that along the load curve, the closest UEP can switch to a new UEP. We also show that the stability region of the post-switching SEP can expand and contract as the load moves towards the nose point of the P-V curve. Our numerical results also show the impact of the direction of movement of the closest UEP on the size and shape of the stability region of a SEP.
-
a dynamic theory based method for the computation of an Unstable Equilibrium point
arXiv: Dynamical Systems, 2018Co-Authors: Robert Owusumireku, Hsiaodong ChiangAbstract:In this paper, a new combination of a dynamic transformation method and a trajectory-based integration technique is proposed for the model independent computation of Unstable Equilibrium points (UEPs). The transformation method converts a UEP into a stable Equilibrium point (SEP) to expand the convergence region by creating a quotient gradient system. The resulting SEP is then calculated using a quasi-Newton form of the pseudo-transient continuation method that exploits the structure of the quotient gradient system to speed up computation. The proposed method's conditions for convergence are presented, and the method is tested on the WSCC 9-bus 3-machine system and the IEEE 145-bus 50-machine system. The results show that the proposed method gives accurate results, it is sufficiently fast, numerically stable, and enlarges the convergence region of the UEP.
-
on the number of Unstable Equilibrium points on spatially periodic stability boundary
IEEE Transactions on Automatic Control, 2016Co-Authors: Tao Wang, Hsiaodong ChiangAbstract:Unstable Equilibrium points are fundamental in the study of dynamical systems, and can have various implications for nonlinear physical and engineering systems. In the present technical note, we derive lower bound as well as upper bound on the number of Unstable Equilibrium points on the stability boundary. For a class of nonlinear dynamical systems, by taking advantage of the spatial-periodicity, it is shown that there are at least (k + 1)C n k typek Equilibrium points on a stability boundary, where C n k = n!/k!(n - k)!. Meanwhile, an upper bound is obtained by applying the Bezout's Theorem, when the system can be converted to polynomials by variable substitution.
-
On the Number and Types of Unstable Equilibria in Nonlinear Dynamical Systems With Uniformly-Bounded Stability Regions
IEEE Transactions on Automatic Control, 2016Co-Authors: Hsiaodong Chiang, Tao WangAbstract:Classical theorems on the complete characterization of stability boundaries provided little information about the existence and types of Unstable Equilibrium points on a stability boundary. In this technical note, we derive analytical results and sufficient conditions about the existence of all types of Unstable Equilibrium points in a dynamical system whose stability regions are uniformly bounded. Some applications of these analytical results are illustrated using electric power systems.
-
controlling Unstable Equilibrium point theory for stability assessment of two time scale power system models
Power and Energy Society General Meeting, 2008Co-Authors: Luis F C Alberto, Hsiaodong ChiangAbstract:This paper presents the foundations of the controlling Unstable Equilibrium point (CUEP) theory for stability assessment of two-time-scale power system models. A conceptual two-time-scale algorithm to calculate the CUEP is provided. Taking into account the time scale features of power systems in the CUEP theory has several advantages from both a numerical and analytical point of view. Numerically, the two-time scale algorithm to calculate the CUEP is faster and more robust when compared to the traditional BCU algorithm. Analytically, we gain more insight into power system dynamics and obtain less conservative estimates of stability region and critical clearing time.
Mohammed Benidris - One of the best experts on this subject based on the ideXlab platform.
-
a homotopy based method for robust computation of controlling Unstable Equilibrium points
IEEE Transactions on Power Systems, 2020Co-Authors: Joydeep Mitra, Mohammed BenidrisAbstract:This paper proposes a homotopy-based method for efficiently computing and precisely determining controlling Unstable Equilibrium points (CUEPs) in transient stability analysis and screening using direct methods. The proposed method is intended to overcome potential numerical convergence problems associated with computing CUEPs. These convergence problems are mostly due to irregularities in the region of convergence of CUEPs which make it difficult to determine suitable initial points. The most commonly used initial points in computing CUEPs are minimum gradient points (MGPs) on the stability boundary which in turn rely on the determination of exit points (Eps—points at which sustained-fault trajectories exit system stability boundaries). However, determination of MGPs and EPs are computationally involved and sophisticated numerical methods have been introduced such as stability-boundary-following procedure and shadowing method to correct the solution trajectory. The proposed method does not depend on MGPs and also does not require accurate EPs. The proposed method maps the solution from EPs to the CUEPs. The proposed method is applied on several known systems including the NE 39 bus system and the reduced WECC system and the results are provided. The results are compared with the traditional methods such as Boundary of stability region based CUEP method (BCU method).
-
use of homotopy based approaches in finding controlling Unstable Equilibrium points in transient stability analysis
Power Systems Computation Conference, 2016Co-Authors: Joydeep Mitra, Mohammed BenidrisAbstract:This paper introduces the use of homotopy-based approaches in computing the Controlling Unstable Equilibrium Points (controlling UEPs) in transient stability analysis using direct methods. It is well known that the regions of convergence of the controlling UEPs are very sensitive to the initial guesses, and traditional iterative methods fail to find the correct controlling UEPs if the initial guesses lie outside their regions of convergence. On the other hand, homotopy-based approaches are very reliable in finding solutions because they are globally convergent. However, homotopy-based approaches are intrinsically slow if the initial point is far from the desired solution because these methods map the trajectory of the solution from an easy and known solution to the desired solution. This paper proposes an algorithm that uses a homotopy-based approach with the exit point as an initial point to reliably find the correct controlling UEP. To reduce computational effort, the proposed method uses an approximate exit point rather than computing an accurate exit point as is common practice in finding controlling UEPs. Further, this method eliminates the necessity of computing the Minimum Gradient Point (MGP), which makes the homotopy-based approaches comparable with the other iterative methods in terms of the speed of computation. An explicit characterization of the region of convergence of a controlling UEP and its boundary starting from an exit point for a typical power system is derived. The method is applied on the WECC and the NE 39 test systems to demonstrate its effectiveness in finding the controlling UEPs.
-
PSCC - Use of homotopy-based approaches in finding Controlling Unstable Equilibrium Points in transient stability analysis
2016 Power Systems Computation Conference (PSCC), 2016Co-Authors: Joydeep Mitra, Mohammed BenidrisAbstract:This paper introduces the use of homotopy-based approaches in computing the Controlling Unstable Equilibrium Points (controlling UEPs) in transient stability analysis using direct methods. It is well known that the regions of convergence of the controlling UEPs are very sensitive to the initial guesses, and traditional iterative methods fail to find the correct controlling UEPs if the initial guesses lie outside their regions of convergence. On the other hand, homotopy-based approaches are very reliable in finding solutions because they are globally convergent. However, homotopy-based approaches are intrinsically slow if the initial point is far from the desired solution because these methods map the trajectory of the solution from an easy and known solution to the desired solution. This paper proposes an algorithm that uses a homotopy-based approach with the exit point as an initial point to reliably find the correct controlling UEP. To reduce computational effort, the proposed method uses an approximate exit point rather than computing an accurate exit point as is common practice in finding controlling UEPs. Further, this method eliminates the necessity of computing the Minimum Gradient Point (MGP), which makes the homotopy-based approaches comparable with the other iterative methods in terms of the speed of computation. An explicit characterization of the region of convergence of a controlling UEP and its boundary starting from an exit point for a typical power system is derived. The method is applied on the WECC and the NE 39 test systems to demonstrate its effectiveness in finding the controlling UEPs.
H Okuno - One of the best experts on this subject based on the ideXlab platform.
-
Unstable Equilibrium point in chaotic domain wall motion and ott grebogi yorke control
Journal of Applied Physics, 2001Co-Authors: H Okuno, Y TakemuraAbstract:A method for finding the Unstable Equilibrium points in Bloch wall motion is proposed, which is important for controlling the chaotic domain-wall motion by using the Ott–Grebogi–Yorke (OGY) method. The dynamics of Bloch wall motion are expressed by a nonlinear differential equation with the terms of inertia, damping, restoring, and an external magnetic drive force. An equation is transformed into the difference equations by following the OGY method, approximating linearly around an Unstable Equilibrium point (a saddle point), and adding a controlling input. The Unstable Equilibrium points are obtained by using the return map and the condition of hyperbolic fixed point. The time series of domain-wall motion successfully controlled on the Unstable Equilibrium points by the OGY method is shown.
-
Unstable Equilibrium point in chaotic domain-wall motion and Ott–Grebogi–Yorke control
Journal of Applied Physics, 2001Co-Authors: H Okuno, Y TakemuraAbstract:A method for finding the Unstable Equilibrium points in Bloch wall motion is proposed, which is important for controlling the chaotic domain-wall motion by using the Ott–Grebogi–Yorke (OGY) method. The dynamics of Bloch wall motion are expressed by a nonlinear differential equation with the terms of inertia, damping, restoring, and an external magnetic drive force. An equation is transformed into the difference equations by following the OGY method, approximating linearly around an Unstable Equilibrium point (a saddle point), and adding a controlling input. The Unstable Equilibrium points are obtained by using the return map and the condition of hyperbolic fixed point. The time series of domain-wall motion successfully controlled on the Unstable Equilibrium points by the OGY method is shown.
John C Hannon - One of the best experts on this subject based on the ideXlab platform.
-
the physics of feldenkrais part 5 Unstable Equilibrium and its application to movement therapy
Journal of Bodywork and Movement Therapies, 2001Co-Authors: John C HannonAbstract:Abstract This article, fifth in a series, explores the concept of Unstable Equilibrium as a form of dynamic repose. This presumes that movement best complies with the Principle of Least Effort when the initial posture incorporates maximal potential energy with minimal inertia. Such action, properly controlled, incorporates strength, dexterity and a quickened reaction time. Also introduced is the idea of reversibility; an attribute, described by Feldenkrais, indicating excellence in motor control. Different forms of gait provide a vehicle for discussion. Exercises and a sitting treatment featuring Unstable Equilibrium are presented.
-
The physics of Feldenkrais®Part 5: Unstable Equilibrium and its application to movement therapy
Journal of Bodywork and Movement Therapies, 2001Co-Authors: John C HannonAbstract:Abstract This article, fifth in a series, explores the concept of Unstable Equilibrium as a form of dynamic repose. This presumes that movement best complies with the Principle of Least Effort when the initial posture incorporates maximal potential energy with minimal inertia. Such action, properly controlled, incorporates strength, dexterity and a quickened reaction time. Also introduced is the idea of reversibility; an attribute, described by Feldenkrais, indicating excellence in motor control. Different forms of gait provide a vehicle for discussion. Exercises and a sitting treatment featuring Unstable Equilibrium are presented.
