Stability boundary approximation of a power system using the real normal form of vector fields

Saha, Swapan Kumar; Fouad, A. A.; Kliemann, Wolfgang; Vittal, Vijay

doi:10.1109/59.589689

Cited by 56 publications

(22 citation statements)

References 11 publications

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“…With the real normal form, ref. [19] obtained the second order approximation for the stability region boundary, but this method requires the computation for all the eigenvectors and eigenvalues of the Jacobian matrix, which results in burdensome computation. To improve the normal form computation, ref.…”

Section: Introductionmentioning

confidence: 99%

Power system transient stability assessment based on quadratic approximation of stability region

Xue

et al. 2006

Electric Power Systems Research

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IssuedAbstract--This paper presents an approach to estimate the Critical Clearing Time (CCT) of the multi-machine power systems based on the quadratic surface which approximates the boundary of stability region relating to the controlling unstable equilibrium point. A decomposition method is developed to obtain the coefficients of the quadratic approximation surface. The CCT is determined by the crossing point of the quadratic surface and the continuous faulted trajectory. Simulations in IEEE 9-bus and New England system show the effectiveness of the proposed approach.

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Section: Introductionmentioning

confidence: 99%

Power system transient stability assessment based on quadratic approximation of stability region

Xue

et al. 2006

Electric Power Systems Research

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“…This transformation yields (4) The elements of the diagonal matrix are the eigenvalues of , , and is the matrix of left eigenvectors of . The state equation for the th Jordan form variable is of the form (5) is the th element of the matrix (6) The term in the brackets is an matrix; is the th element of the matrix . Notice that the terms of the summation in (5) constitute a homogeneous polynomial of second order, i.e., all the terms of the polynomial are of second order.…”

Section: Methods Of Normal Formsmentioning

confidence: 99%

“…In a manner similar to small-signal stability analysis, the method of Normal Forms begins by performing a Taylor series expansion of the nonlinear system of interest, , in the neighborhood of a stable operating point (This expansion can also be done in the neighborhood of an unstable equilibrium point [6]). However, unlike small-signal stability analysis the expansion is carried out beyond the first-order (linear) term.…”

Section: Methods Of Normal Formsmentioning

confidence: 99%

“…The results shown in this table indicate that none of the combination modes have a settling time that is close to one half of the settling time of the dominant Mode (5, 6) (i.e., 1 /2 20.4 s). The combination modes (5,5) and (6,6) have half the settling time but their interaction coefficients given in Table IV are relatively small. This indicates that there is no significant nonlinear interaction.…”

Section: B Normal Form Analysis Of Casementioning

confidence: 99%

“…In this case, a stable post disturbance equilibrium will not be available. However, the Normal Forms analysis can be conducted at the appropriate unstable equilibrium point using the real Normal Forms approach as demonstrated in [6] and critical qualitative results regarding the trajectory and dynamic performance can be obtained.…”

Section: A Initial Condition Formentioning

confidence: 99%

See 2 more Smart Citations

Analysis of higher order terms for small signal stability analysis

Sanchez-Gasca

Vittal

Gibbard

et al.

IEEE Power Engineering Society General Meeting, 2005

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Abstract-This paper summarizes the work done by the Task Force on Assessing the Need to Include Higher Order Terms for Small-Signal (Modal) Analysis. This Task Force was created by the Power System Dynamic Performance Committee to investigate the need to include higher order terms for small signal (modal) analysis. The focus of the work reported here is on establishing and documenting the practical significance of these terms in stability analysis using the method of Normal Forms. Special emphasis was placed on determining and describing conditions when higher order terms need to be included to accurately describe modal interactions. Test cases were developed on a standard test system to demonstrate the application of appropriate indices to detect the occurrence of nonlinear interaction and hence the need for higher order terms in stability analyzes. The use of the higher order terms in the site selection for a damping controller is also documented.Index Terms-Method of normal forms, modal analysis, modal damping, modal frequency, nonlinear modal interaction.

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Models for Transmission Expansion Planning Based on Reconfigurable Capacitor Switching

Momoh

Mili

2009

Economic Market Design and Planning for Electric Power Systems

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Stability boundary approximation of a power system using the real normal form of vector fields

Cited by 56 publications

References 11 publications

Power system transient stability assessment based on quadratic approximation of stability region

Power system transient stability assessment based on quadratic approximation of stability region

Analysis of higher order terms for small signal stability analysis

Models for Transmission Expansion Planning Based on Reconfigurable Capacitor Switching

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