Stability Boundary

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Luis F C Alberto - One of the best experts on this subject based on the ideXlab platform.

Hsiao-dong Chiang - One of the best experts on this subject based on the ideXlab platform.

  • on the number of unstable equilibrium points on spatially periodic Stability Boundary
    IEEE Transactions on Automatic Control, 2016
    Co-Authors: Tao Wang, Hsiao-dong Chiang
    Abstract:

    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.

  • Characterization of Stability Region for General Autonomous Nonlinear Dynamical Systems
    IEEE Transactions on Automatic Control, 2012
    Co-Authors: Luis F C Alberto, Hsiao-dong Chiang
    Abstract:

    The existing characterization of Stability regions was developed under the assumption that limit sets on the Stability Boundary are exclusively composed of hyperbolic equilibrium points and closed orbits. The characterizations derived in this technical note are a generalization of existing results in the theory of Stability regions. A characterization of the Stability Boundary of general autonomous nonlinear dynamical systems is developed under the assumption that limit sets on the Stability Boundary are composed of a countable number of disjoint and indecomposable components, which can be equilibrium points, closed orbits, quasi-periodic solutions and even chaotic invariant sets.

  • direct methods for Stability analysis of electric power systems theoretical foundation bcu methodologies and applications
    2010
    Co-Authors: Hsiao-dong Chiang
    Abstract:

    Preface. Acknowledgments. 1. Introduction and Overview. 1.1 Introduction. 1.2 Trends of Operating Environment. 1.3 Online TSA. 1.4 Need for New Tools. 1.5 Direct Methods: Limitations and Challenges. 1.6 Purposes of This Book. 2. System Modeling and Stability Problems. 2.1 Introduction. 2.2 Power System Stability Problem. 2.3 Model Structures and Parameters. 2.4 Measurement-Based Modeling. 2.5 Power System Stability Problems. 2.6 Approaches for Stability Analysis. 2.7 Concluding Remarks. 3. Lyapunov Stability and Stability Regions of Nonlinear Dynamical Systems. 3.1 Introduction. 3.2 Equilibrium Points and Lyapunov Stability. 3.3 Lyapunov Function Theory. 3.4 Stable and Unstable Manifolds. 3.5 Stability Regions. 3.6 Local Characterizations of Stability Boundary. 3.7 Global Characterization of Stability Boundary. 3.8 Algorithm to Determine the Stability Boundary. 3.9 Conclusion. 4. Quasi-Stability Regions: Analysis and Characterization. 4.1 Introduction. 4.2 Quasi-Stability Region. 4.3 Characterization of Quasi-Stability Regions. 4.4 Conclusions. 5. Energy Function Theory and Direct Methods. 5.1 Introduction. 5.2 Energy Functions. 5.3 Energy Function Theory. 5.4 Estimating Stability Region Using Energy Functions. 5.5 Optimal Schemes for Estimating Stability Regions. 5.6 Quasi-Stability Region and Energy Function. 5.7 Conclusion. 6. Constructing Analytical Energy Functions for Transient Stability Models. 6.1 Introduction. 6.2 Energy Functions for Lossless Network-Reduction Models. 6.3 Energy Functions for Lossless Structure-Preserving Models. 6.4 Nonexistence of Energy Functions for Lossy Models. 6.5 Existence of Local Energy Functions. 6.6 Concluding Remarks. 7. Construction of Numerical Energy Functions for Lossy Transient Stability Models. 7.1 Introduction. 7.2 A Two-Step Procedure. 7.3 First Integral-Based Procedure. 7.4 Ill-Conditioned Numerical Problems. 7.5 Numerical Evaluations of Approximation Schemes. 7.6 Multistep Trapezoidal Scheme. 7.7 On the Corrected Numerical Energy Functions. 7.8 Concluding Remarks. 8. Direct Methods for Stability Analysis: An Introduction. 8.1 Introduction. 8.2 A Simple System. 8.3 Closest UEP Method. 8.4 Controlling UEP Method. 8.5 PEBS Method. 8.6 Concluding Remarks. 9. Foundation of the Closest UEP Method. 9.1 Introduction. 9.2 A Structure-Preserving Model. 9.3 Closest UEP. 9.4 Characterization of the Closest UEP. 9.5 Closest UEP Method. 9.6 Improved Closest UEP Method. 9.7 Robustness of the Closest UEP. 9.8 Numerical Studies. 9.9 Conclusions. 10. Foundations of the Potential Energy Boundary Surface Method. 10.1 Introduction. 10.2 Procedure of the PEBS Method. 10.3 Original Model and Artifi cial Model. 10.4 Generalized Gradient Systems. 10.5 A Class of Second-Order Dynamical Systems. 10.6 Relation between the Original Model and the Artifi cial Model. 10.7 Analysis of the PEBS Method. 10.8 Concluding Remarks. 11. Controlling UEP Method: Theory. 11.1 Introduction. 11.2 The Controlling UEP. 11.3 Existence and Uniqueness. 11.4 The Controlling UEP Method. 11.5 Analysis of the Controlling UEP Method. 11.6 Numerical Examples. 11.7 Dynamic and Geometric Characterizations. 11.8 Concluding Remarks. 12. Controlling UEP Method: Computations. 12.1 Introduction. 12.2 Computational Challenges. 12.3 Constrained Nonlinear Equations for Equilibrium Points. 12.4 Numerical Techniques for Computing Equilibrium Points. 12.5 Convergence Regions of Equilibrium Points. 12.6 Conceptual Methods for Computing the Controlling UEP. 12.7 Numerical Studies. 12.8 Concluding Remarks. 13. Foundations of Controlling UEP Methods for Network-Preserving Transient Stability Models. 13.1 Introduction. 13.2 System Models. 13.3 Stability Regions. 13.4 Singular Perturbation Approach. 13.5 Energy Functions for Network-Preserving Models. 13.6 Controlling UEP for DAE Systems. 13.7 Controlling UEP Method for DAE Systems. 13.8 Numerical Studies. 13.9 Concluding Remarks. 14. Network-Reduction BCU Method and Its Theoretical Foundation. 14.1 Introduction. 14.2 Reduced-State System. 14.3 Analytical Results. 14.4 Static and Dynamic Relationships. 14.5 Dynamic Property (D3). 14.6 A Conceptual Network-Reduction BCU Method. 14.7 Concluding Remarks. 15. Numerical Network-Reduction BCU Method. 15.1 Introduction. 15.2 Computing Exit Points. 15.3 Stability-Boundary-Following Procedure. 15.4 A Safeguard Scheme. 15.5 Illustrative Examples. 15.6 Numerical Illustrations. 15.7 IEEE Test System. 15.8 Concluding Remarks. 16. Network-Preserving BCU Method and Its Theoretical Foundation. 16.1 Introduction. 16.2 Reduced-State Model. 16.3 Static and Dynamic Properties. 16.4 Analytical Results. 16.5 Overall Static and Dynamic Relationships. 16.6 Dynamic Property (D3). 16.7 Conceptual Network-Preserving BCU Method. 16.8 Concluding Remarks. 17. Numerical Network-Preserving BCU Method. 17.1 Introduction. 17.2 Computational Considerations. 17.3 Numerical Scheme to Detect Exit Points. 17.4 Computing the MGP. 17.5 Computation of Equilibrium Points. 17.6 Numerical Examples. 17.7 Large Test Systems. 17.8 Concluding Remarks. 18. Numerical Studies of BCU Methods from Stability Boundary Perspectives. 18.1 Introduction. 18.2 Stability Boundary of Network-Reduction Models. 18.3 Network-Preserving Model. 18.4 One Dynamic Property of the Controlling UEP. 18.5 Concluding Remarks. 19. Study of the Transversality Conditions of the BCU Method. 19.1 Introduction. 19.2 A Parametric Study. 19.3 Analytical Investigation of the Boundary Property. 19.4 The Two-Machine Infi nite Bus (TMIB) System. 19.5 Numerical Studies. 19.6 Concluding Remarks. 20. The BCU-Exit Point Method. 20.1 Introduction. 20.2 Boundary Property. 20.3 Computation of the BCU-Exit Point. 20.4 BCU-Exit Point and Critical Energy. 20.5 BCU-Exit Point Method. 20.6 Concluding Remarks. 21. Group Properties of Contingencies in Power Systems. 21.1 Introduction. 21.2 Groups of Coherent Contingencies. 21.3 Identifi cation of a Group of Coherent Contingencies. 21.4 Static Group Properties. 21.5 Dynamic Group Properties. 21.6 Concluding Remarks. 22. Group-Based BCU-Exit Method. 22.1 Introduction. 22.2 Group-Based Verifi cation Scheme. 22.3 Linear and Nonlinear Relationships. 22.4 Group-Based BCU-Exit Point Method. 22.5 Numerical Studies. 22.6 Concluding Remarks. 23. Group-Based BCU-CUEP Methods. 23.1 Introduction. 23.2 Exact Method for Computing the Controlling UEP. 23.3 Group-Based BCU-CUEP Method. 23.4 Numerical Studies. 23.5 Concluding Remarks. 24. Group-Based BCU Method. 24.1 Introduction. 24.2 Group-Based BCU Method for Accurate Critical Energy. 24.3 Group-Based BCU Method for CUEPs. 24.4 Numerical Studies. 24.5 Concluding Remarks. 25. Perspectives and Future Directions. 25.1 Current Developments. 25.2 Online Dynamic Contingency Screening. 25.3 Further Improvements. 25.4 Phasor Measurement Unit (PMU)-Assisted Online ATC Determination. 25.5 Emerging Applications. 25.6 Concluding Remarks. Appendix. A1.1 Mathematical Preliminaries. A1.2 Proofs of Theorems in Chapter 9. A1.3 Proofs of Theorems in Chapter 10. Bibliography. Index.

  • a singular fixed point homotopy method to locate the closest unstable equilibrium point for transient Stability region estimate
    IEEE Transactions on Circuits and Systems Ii-express Briefs, 2004
    Co-Authors: Hsiao-dong Chiang
    Abstract:

    The closest unstable equilibrium point (UEP) method is a well-known direct method of the Lyapunov type for optimally estimating Stability regions of nonlinear dynamical systems. One key step involved in the closest UEP methodology is the computation of the closest unstable equilibrium point that has the lowest Lyapunov function value on the Stability Boundary. In this paper, a new computational algorithm to compute the closest UEP is presented. The proposed algorithm is based on a homotopy-continuation method combined with the singular fixed-point strategy. Numerical simulation results show that the algorithm outperforms previously reported existing techniques.

  • an investigation of invariant properties of unstable equilibrium points on the Stability Boundary for simple power system models
    International Symposium on Circuits and Systems, 1995
    Co-Authors: Hsiao-dong Chiang, James S Thorp
    Abstract:

    In recent developments of direct methods for power system transient Stability analysis, the task of finding the controlling unstable equilibrium point (u.e.p.) of the original system is performed on an artificial, dimension-reduction system for easily computing the controlling u.e.p. It has been shown that if the stable and unstable manifolds of a family of parametrized systems, which relates the original power system and an artificial, dimension-reduction system, satisfy the transversality condition as the parameter varies, then the artificial, dimension-reduction system contains the same set of u.e.p.'s on the Stability Boundary. In this paper, instead of direct verification of the transversality conditions, we show that under small mechanical power injections, the original power system model and the artificial, dimension-reduction system contain the same unstable equilibrium points on the Stability Boundary for one machine and two machine power system models.

Tadao Tsuboyama - One of the best experts on this subject based on the ideXlab platform.

  • effect of the muscle coactivation during quiet standing on dynamic postural control in older adults
    Archives of Gerontology and Geriatrics, 2013
    Co-Authors: Kazuki Uemura, Buichi Tanaka, Shuhei Mori, Koutatsu Nagai, Minoru Yamada, Noriaki Ichihashi, Tomoki Aoyama, Tadao Tsuboyama
    Abstract:

    Recently, several studies have reported that muscle coactivation during static postural control increases with aging. Although greater muscle coactivation during quiet standing enhances joint Stability, it may reduce dynamic postural control. The purpose of this study was to investigate the effect of muscle coactivation during quiet standing on dynamic postural control. Seventy older adults (81.1 ± 7.2 years) participated in this study. Static postural control was evaluated by postural sway during quiet standing, whereas dynamic postural control was evaluated by the functional reach and functional Stability Boundary tests. Electromyography of the soleus (SOL) and tibialis anterior (TA) was recorded during quiet standing, then coactivation was evaluated using the co-contraction index (CI). We used multiple regression analysis to identify the effect of muscle coactivation during standing on each dynamic postural control variable using age, body mass index (BMI), gender, timed up and go (TUG) tests, postural sway area and CI during quiet standing as independent variables. TUG tests were added to the model to evaluate the effect of functional mobility on dynamic postural control with a fixed base. The multiple regression analysis revealed that CI during standing was significantly related to all of the dynamic postural control tasks. The functional reach distance was significantly associated with CI during standing, age and TUG (p < 0.05). The functional Stability Boundary for forward and backward were associated only with CI during standing (p < 0.05). This study revealed that muscle coactivation during quiet standing is independently associated with dynamic postural control abilities.

  • effects of balance training on muscle coactivation during postural control in older adults a randomized controlled trial
    Journals of Gerontology Series A-biological Sciences and Medical Sciences, 2012
    Co-Authors: Koutatsu Nagai, Kazuki Uemura, Buichi Tanaka, Shuhei Mori, Minoru Yamada, Noriaki Ichihashi, Tomoki Aoyama, Tadao Tsuboyama
    Abstract:

    BACKGROUND: Recently, several studies have reported age-associated increases in muscle coactivation during postural control. A rigid posture induced by strong muscle coactivation reduces the degree of freedom to be organized by the postural control system. The purpose of this study was to clarify the effect of balance training on muscle coactivation during postural control in older adults. METHODS: Forty-eight subjects were randomized into an intervention (mean age: 81.0 ± 6.9 years) and a control group (mean age: 81.6 ± 6.4 years). The control group did not receive any intervention. Postural control ability (postural sway during quiet standing, functional reach, and functional Stability Boundary) was assessed before and after the intervention. A cocontraction index was measured during the postural control tasks to assess muscle coactivation. RESULTS: Cocontraction index values in the intervention group significantly decreased following the intervention phase for functional reach (p < .0125). Cocontraction index values had a tendency to decrease during functional Stability Boundary for forward and quiet standing tasks. Functional improvements were observed in some of the tasks after the intervention, that is, functional reach, functional Stability Boundary for forward, one-leg stance, and timed up and go (p < .05). CONCLUSIONS: Our study raised the possibility that balance training for older adults was associated with decreases in muscle coactivation during postural control. Postural control exercise could potentially lead older adults to develop more efficient postural control strategies without increasing muscle coactivation. Further research is needed to clarify in greater detail the effects of changes in muscle coactivation.

  • differences in muscle coactivation during postural control between healthy older and young adults
    Archives of Gerontology and Geriatrics, 2011
    Co-Authors: Koutatsu Nagai, Kazuki Uemura, Yosuke Yamada, Minoru Yamada, Noriaki Ichihashi, Tadao Tsuboyama
    Abstract:

    Abstract The purpose of this study was to clarify the difference in muscle coactivation during postural control between older and young adults and to identify the characteristics of postural control strategies in older adults by investigating the relationship between muscle coactivation and postural control ability. Forty-six healthy older adults (82.0 ± 7.5 years) and 34 healthy young adults (22.1 ± 2.3 years) participated. The postural tasks selected consisted of static standing, functional reach, functional Stability Boundary and gait. Coactivation of the ankle joint was recorded during each task via electromyography (EMG). The older adults showed significantly higher coactivation than the young adults during the tasks of standing, functional reach, functional Stability Boundary (forward), and gait (p

Miroslaw Pawlak - One of the best experts on this subject based on the ideXlab platform.

  • additive modeling and prediction of transient Stability Boundary in large scale power systems using the group lasso algorithm
    International Journal of Electrical Power & Energy Systems, 2019
    Co-Authors: Miroslaw Pawlak, Jiaqing Lv
    Abstract:

    Abstract In this paper, the problem of prediction of the transient Stability Boundary (TSB) of large-scale power systems is analyzed. For any given fault in a power system, whether a pre-contingency condition is considered as a stable operating point can be characterized by the critical clearing time (CCT). The mapping between the pre-contingency steady state and the CCT is in this paper modelled as additive multivariate regression of nonlinear functions of individual input features. Each individual univariate nonlinear function is approximated by an orthogonal polynomials representation, and then the Group Lasso as well as the adaptive Group Lasso algorithms are employed to estimate the original multivariate regression function. Although the original nonlinear structure is highly dimensional, it is shown in this paper that the final model exhibits a simple parsimonious form composed of only a few input features. This is due to the ability of the employed algorithms to recover the inherent sparsity in additive components of the proposed additive representation. This methodology is demonstrated by being applied to multiple fault cases in the context of a 470-bus power network. This approach is also compared with two competing methods recently applied in the dynamic security assessment literature: kernel ridge regression, as well as the Lasso method applicable to linear sparse models.

  • prediction of the transient Stability Boundary using the lasso
    IEEE Transactions on Power Systems, 2013
    Co-Authors: Miroslaw Pawlak, U D Annakkage
    Abstract:

    This paper utilizes a class of modern machine learning methods for estimating a transient Stability Boundary that is viewed as a function of power system variables. The simultaneous variable selection and estimation approach is employed yielding a substantially reduced complexity transient Stability Boundary model. The model is easily interpretable and yet possesses a stronger prediction power than techniques known in the power engineering literature so far. The accuracy of our methods is demonstrated using a 470-bus system.

Koutatsu Nagai - One of the best experts on this subject based on the ideXlab platform.

  • effect of the muscle coactivation during quiet standing on dynamic postural control in older adults
    Archives of Gerontology and Geriatrics, 2013
    Co-Authors: Kazuki Uemura, Buichi Tanaka, Shuhei Mori, Koutatsu Nagai, Minoru Yamada, Noriaki Ichihashi, Tomoki Aoyama, Tadao Tsuboyama
    Abstract:

    Recently, several studies have reported that muscle coactivation during static postural control increases with aging. Although greater muscle coactivation during quiet standing enhances joint Stability, it may reduce dynamic postural control. The purpose of this study was to investigate the effect of muscle coactivation during quiet standing on dynamic postural control. Seventy older adults (81.1 ± 7.2 years) participated in this study. Static postural control was evaluated by postural sway during quiet standing, whereas dynamic postural control was evaluated by the functional reach and functional Stability Boundary tests. Electromyography of the soleus (SOL) and tibialis anterior (TA) was recorded during quiet standing, then coactivation was evaluated using the co-contraction index (CI). We used multiple regression analysis to identify the effect of muscle coactivation during standing on each dynamic postural control variable using age, body mass index (BMI), gender, timed up and go (TUG) tests, postural sway area and CI during quiet standing as independent variables. TUG tests were added to the model to evaluate the effect of functional mobility on dynamic postural control with a fixed base. The multiple regression analysis revealed that CI during standing was significantly related to all of the dynamic postural control tasks. The functional reach distance was significantly associated with CI during standing, age and TUG (p < 0.05). The functional Stability Boundary for forward and backward were associated only with CI during standing (p < 0.05). This study revealed that muscle coactivation during quiet standing is independently associated with dynamic postural control abilities.

  • effects of balance training on muscle coactivation during postural control in older adults a randomized controlled trial
    Journals of Gerontology Series A-biological Sciences and Medical Sciences, 2012
    Co-Authors: Koutatsu Nagai, Kazuki Uemura, Buichi Tanaka, Shuhei Mori, Minoru Yamada, Noriaki Ichihashi, Tomoki Aoyama, Tadao Tsuboyama
    Abstract:

    BACKGROUND: Recently, several studies have reported age-associated increases in muscle coactivation during postural control. A rigid posture induced by strong muscle coactivation reduces the degree of freedom to be organized by the postural control system. The purpose of this study was to clarify the effect of balance training on muscle coactivation during postural control in older adults. METHODS: Forty-eight subjects were randomized into an intervention (mean age: 81.0 ± 6.9 years) and a control group (mean age: 81.6 ± 6.4 years). The control group did not receive any intervention. Postural control ability (postural sway during quiet standing, functional reach, and functional Stability Boundary) was assessed before and after the intervention. A cocontraction index was measured during the postural control tasks to assess muscle coactivation. RESULTS: Cocontraction index values in the intervention group significantly decreased following the intervention phase for functional reach (p < .0125). Cocontraction index values had a tendency to decrease during functional Stability Boundary for forward and quiet standing tasks. Functional improvements were observed in some of the tasks after the intervention, that is, functional reach, functional Stability Boundary for forward, one-leg stance, and timed up and go (p < .05). CONCLUSIONS: Our study raised the possibility that balance training for older adults was associated with decreases in muscle coactivation during postural control. Postural control exercise could potentially lead older adults to develop more efficient postural control strategies without increasing muscle coactivation. Further research is needed to clarify in greater detail the effects of changes in muscle coactivation.

  • differences in muscle coactivation during postural control between healthy older and young adults
    Archives of Gerontology and Geriatrics, 2011
    Co-Authors: Koutatsu Nagai, Kazuki Uemura, Yosuke Yamada, Minoru Yamada, Noriaki Ichihashi, Tadao Tsuboyama
    Abstract:

    Abstract The purpose of this study was to clarify the difference in muscle coactivation during postural control between older and young adults and to identify the characteristics of postural control strategies in older adults by investigating the relationship between muscle coactivation and postural control ability. Forty-six healthy older adults (82.0 ± 7.5 years) and 34 healthy young adults (22.1 ± 2.3 years) participated. The postural tasks selected consisted of static standing, functional reach, functional Stability Boundary and gait. Coactivation of the ankle joint was recorded during each task via electromyography (EMG). The older adults showed significantly higher coactivation than the young adults during the tasks of standing, functional reach, functional Stability Boundary (forward), and gait (p

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