• Title, Summary, Keyword: normal forms of vector fields

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Power System Nonlinearity Modal Interaction by the Normal Forms of Vector Fields

  • Zhang, Jing;Wen, J.Y.;Cheng, S.J.
    • Journal of Electrical Engineering and Technology
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    • v.3 no.1
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    • pp.8-13
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    • 2008
  • Because of the robust nonlinear characteristics appearing in today's modern power system, a strong interaction exists between the angle stability and the voltage stability, which were conventionally studied insularly. However, as the power system is a complex unified system, angle instability always happens in conjunction with voltage instability. The authors propose a novel method to analyze this type of stability problem. In the proposed method, the theory of normal forms of vector fields is utilized to treat the auxiliary dynamic system. By use of this method, the interaction between response modes caused by the nonlinearity of the power system can be analyzed. Consequently, the eigenvalue analysis method is extended to cope with performance analysis of the power system with heavy nonlinearity. The effectiveness of the proposed methodology is verified on a 3-bus power system.

Identification of Optimum Sites for Power System Controller using Normal Forms of Vector Field (벡터계 정규 형식을 이용한 전력시스템 제어기 설치 위치 선정)

  • 장길수;이인수;권세혁
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.53 no.4
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    • pp.227-233
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    • 2004
  • In stressed power system due to the presence of increased nonlinearity and the existence of nonlinear modal interactions. there exist some limitations to the use of conventional linear system theory to identify the optimum sites for a controller. This paper suggests an approach based on the method of normal forms to identify the optimum sites for controllers with incorporating the nonlinear interaction . In this paper, nonlinear participation factors and coupling factors are proposed as measures of the nonlinear interactions, and identification procedure of optimum sites for a controller is also proposed. The proposed procedure is applied to the 10-generator New England System and the KEPCO System in the year of 2010, and the results illustrate its capabilities.


  • Kim, Dong-Soo;Kim, Seon-Bu;Kim, Young-Ho;Park, Seong-Hee
    • Bulletin of the Korean Mathematical Society
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    • v.39 no.4
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    • pp.671-680
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    • 2002
  • In this article, we show that if a semi-Riemannian space form carries a conformal vector field V of which the tangential part $V^T$ on a connected hypersurface $M^N$ ecomes a conformal vector field and the normal part $V^N on $M^N$ does not vanish identically, then $M^N$ is totally umbilic. Furthermore, we give a complete description of conformal vector fields on semi-Riemannian space forms.

Closed-form Green's functions for transversely isotropic bi-solids with a slipping interface

  • Yue, Zhong Qi
    • Structural Engineering and Mechanics
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    • v.4 no.5
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    • pp.469-484
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    • 1996
  • Green's functions are obtained in exact closed-forms for the elastic fields in bi-material elastic solids with slipping interface and differing transversely isotropic properties induced by concentrated point and ring force vectors. For the concentrated point force vector, the Green functions are expressed in terms of elementary harmonic functions. For the concentrated ring force vector, the Green functions are expressed in terms of the complete elliptic integral. Numerical results are presented to illustrate the effect of anisotropic bi-material properties on the transmission of normal contact stress and the discontinuity of lateral displacements at the slipping interface. The closed-form Green's functions are systematically presented in matrix forms which can be easily implemented in numerical schemes such as boundary element methods to solve elastic problems in computational mechanics.


    • East Asian mathematical journal
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    • v.36 no.3
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    • pp.389-415
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    • 2020
  • Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (𝜙, ξ, η, g) in a complex space form Mn+1(c), c ≠ 0. We denote by Rξ and R'X be the structure Jacobi operator with respect to the structure vector ξ and be R'X = (∇XR)(·, X)X for any unit vector field X on M, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a scalar 𝜃(≠ 2c) and any vector fields X and Y on M. In this paper, we prove that if it satisfies Rξ𝜙 = 𝜙Rξ and at the same time R'ξ = 0, then M is a Hopf real hypersurfaces of type (A), provided that the scalar curvature ${\bar{r}}$ of M holds ${\bar{r}}-2(n-1)c{\leq}0$.