Dynamics of large constrained nonlinear systems-a taxonomy theory [power system stability]

Venkatasubramanian, V.; Schättler, Heinz; Zaborsky, J.

doi:10.1109/5.481633

Cited by 166 publications

(128 citation statements)

References 62 publications

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“…The bifurcation set B can be obtained by combing Equations (12) and (13) to eliminate the state variable vector X. Appendix A shows a typical catastrophe mechanism explaining the principle of catastrophe theory.…”

Section: Catastrophe Theorymentioning

confidence: 99%

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Research on a Small Signal Stability Region Boundary Model of the Interconnected Power System with Large-Scale Wind Power

Liu¹,

Ge²,

Lv³

et al. 2015

Energies

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Abstract:For the interconnected power system with large-scale wind power, the problem of the small signal stability has become the bottleneck of restricting the sending-out of wind power as well as the security and stability of the whole power system. Around this issue, this paper establishes a small signal stability region boundary model of the interconnected power system with large-scale wind power based on catastrophe theory, providing a new method for analyzing the small signal stability. Firstly, we analyzed the typical characteristics and the mathematic model of the interconnected power system with wind power and pointed out that conventional methods can't directly identify the topological properties of small signal stability region boundaries. For this problem, adopting catastrophe theory, we established a small signal stability region boundary model of the interconnected power system with large-scale wind power in two-dimensional power injection space and extended it to multiple dimensions to obtain the boundary model in multidimensional power injection space. Thirdly, we analyzed qualitatively the topological property's changes of the small signal stability region boundary caused by large-scale wind power integration. Finally, we built simulation models by DIgSILENT/PowerFactory software and the final simulation results verified the correctness and effectiveness of the proposed model.

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Section: Catastrophe Theorymentioning

confidence: 99%

“…In theory, the small signal stability region boundary [11,12] consists of saddle node bifurcation (SNB), Hopf bifurcation (HB) and singularity induced bifurcation (SIB). Among them, HB [13,14], which physically represents a pair of conjugate eigenvalues crossing the imaginary axis, is related to the system oscillatory instability.…”

Section: Introductionmentioning

confidence: 99%

Research on a Small Signal Stability Region Boundary Model of the Interconnected Power System with Large-Scale Wind Power

Liu¹,

Ge²,

Lv³

et al. 2015

Energies

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show abstract

“…they result in fast collapse type of instability [14]. The load flow feasibility boundary corresponds to a surface where the load flow Jacobian matrix Jif is singular, and it restricts a region in the space of power system parameters where load flow solutions exist.…”

Section: Introductionmentioning

confidence: 99%

A general method for small signal stability analysis

Makarov

Zhang²,

Hill³

1998

IEEE Trans. Power Syst.

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A b s t r a c t -This paper presents a new general method for computing the different specific power system small signal stability conditions. The conditions include the points of minimum and maximum damping of oscillations, saddle node and Hopf bifurcations, and load flow feasibility boundaries. All these characteristic points are located by optimizing an eigenvalue objective function along the rays specified in the space of system parameters. The set of constraints consists of the load flow (equations, and requirements applied to the dynamic state matrix eigenvalues and eigenvectors. Solutions of the optimization problem correspond to specific points of interest mentioned above. So, the proposed general method gives a Comprehensive characterization of the power system small signal stability properties. The specific point obtained depends upon the initial guess of variables and numerical methods used to solve the constrained optimization problem. The technique is tested by analyzing the small signal stability properties for well-known example systems. I. I N T R O D U C T I O NModern power grid:; are becoming more and more stressed with the load demands increasing rapidly. The voltage collapses which occurred recently have again drawn much attention to the issue of stability security margins in power systems [I]. The small signal stability margins are highly dependent upon such system factors as load flow feasibility boundaries, minimum and maximum damping conditions, saddle node and Hopf bifurcations, etc. Unfortunately, it is very difficult to say in advance which of these factors will make a decisive contribution to instability. Despite the progress achieved recently, the existing approaches deal with these factors independently -see [a], [3] for example, and additional attempts are needed to get a more comprehensive view on small-signal stability problem.To study the power system small signal stability problem, an appropriate model for the machine and load dy- (differential) variables, x~ is the vector of algebraic variables, y is the vector of specified system parameters, and T is a parameter chosen for bifurcation analysis. In many cases y is a function of T.In the small signal stability analysis, the set (1) is then linearized at an equilibrium point to get the system Jacobian and state matrix. The structure of the system Jacobian J is shown in Fig. 1 The problem addressed here is that these different small signal stability conditions correspond to different physical phenomena and mathematical descriptions [13]. Saddle node bifurcations happen where the state matrix J" = J 1 1 -JlzJ,-,lJzl becomes singular and, for example, a static (aperiodic) type of voltage collapse or angle instability may be observed as a result. Hopf bifurcations occur when the system state iiiatrix J has a pair of conjugate eigenvalues passing the imaginary axis while the other eigenvalues have negative real parts, and the unstable oscillatory behavior may be seen. Singularity induced bifurcations are caused by singularity of t...

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“…For example, minimization of switching events does not fit a normal optimization framework [30]. Also, assessment of stability limits is technically difficult [31].…”

Section: Challenges In Dynamic Performance Enhancementmentioning

confidence: 99%

Dynamic Embedded Optimization and Shooting Methods for Power System Performance Assessment

Hiskens

Park

Donde

Power Electronics and Power Systems

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Power system dynamic performance enhancement can often be formulated as a dynamic embedded optimization problem. The associated cost function quantifies performance and involves dynamically evolving state variables. The dynamic model is embedded within the constraints. Power systems form an important example of hybrid systems, with interactions between continuous dynamics and discrete events playing a fundamental role in behavior. However, it is shown that for a large class of problems, the cost function is smooth even though the underlying dynamic response is non-smooth. Complementing this design-oriented optimization framework, techniques for assessing power system performance and vulnerability can often be expressed as boundary value problems, and solved using shooting methods. It is shown that performance limitations are closely related to grazing phenomena. Techniques are presented for determining parameter values that induce limit cycles and grazing.179 I.A. Hiskens, J-W. Park and V. Donde, "Dynamic embedded optimization and shooting methods for power system performance assessment", in Applied Mathematics for Deregulated

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Dynamics of large constrained nonlinear systems-a taxonomy theory [power system stability]

Cited by 166 publications

References 62 publications

Research on a Small Signal Stability Region Boundary Model of the Interconnected Power System with Large-Scale Wind Power

Research on a Small Signal Stability Region Boundary Model of the Interconnected Power System with Large-Scale Wind Power

A general method for small signal stability analysis

Dynamic Embedded Optimization and Shooting Methods for Power System Performance Assessment

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