A new eigen-analysis method of steady-state stability studies for large power systems: S matrix method
TL;DR: In this paper, an advanced version of the S matrix method, an eigenvalue technique for the analysis of the steady-state stability (or the stability against small signals) of large power systems is discussed.
Abstract: The authors discuss an advanced version of the S matrix method, an eigenvalue technique for the analysis of the steady-state stability (or the stability against small signals) of large power systems. The dynamic characteristics of power systems can be linearly approximated with a set of differential equations. The technique transforms the matrix A into the matrix S and then determines several eigenvalues with the largest absolute values from matrix S that correspond to the dominant eigenvalues of matrix A. In the process of identifying the appropriate eigenvalues, the method uses the refined Lanczos process, which makes high-speed calculation possible through the use of the sparsity and the structural uniformity of matrices. >
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TL;DR: In this paper, an efficient algorithm for the damping control of electromechanical oscillations in large-scale power systems is presented, which involves the calculation of transfer function residues and represents an important extension of the powerful methodology described by V. Arcidiaconos et al. (see IEEE Trans. Power Apparatus and Systems, vol.PAS-99, p.769-78, 1980), whose use was up to now restricted to power systems of limited size.
Abstract: Efficient algorithms are presented for the solution of two important problems in the area of damping control of electromechanical oscillations in large-scale systems. The proposed algorithms allow the determination of: the most suitable generators for installing power system stabilizers; the most suitable buses in the system for placing static VAr compensators in order to damp the critical modes of oscillation. These algorithms involve the calculation of transfer function residues and represent an important extension of the powerful methodology described by V. Arcidiaconos et al. (see IEEE Trans. Power Apparatus and Systems, vol.PAS-99, p.769-78, 1980), whose use was up to now restricted to power systems of limited size. A major advantage of this methodology is that there is no limitation on the degree of modeling of the power system being studied. >
363 citations
Book•
08 Oct 2008
TL;DR: Stochastic Security Analysis of Electrical Power Systems and Power System Transient Stability Analysis and Small-Signal Stability Analysis of Power Systems.
Abstract: Mathematical Model and Solution of Electric Network.- Load Flow Analysis.- Stochastic Security Analysis of Electrical Power Systems.- Power Flow Analysis in Market Environment.- HVDC and FACTS.- Mathematical Model of Synchronous Generator and Load.- Power System Transient Stability Analysis.- Small-Signal Stability Analysis of Power Systems.
248 citations
TL;DR: A package of integrated programs for small-signal stability analysis of large interconnected power systems is described, which has extensive modeling capability and uses alternative eigenvalue calculation techniques, making it suitable for the analysis of a wide range of stability and control problems.
Abstract: A package of integrated programs for small-signal stability analysis of large interconnected power systems is described. The package has extensive modeling capability and uses alternative eigenvalue calculation techniques, making it suitable for the analysis of a wide range of stability and control problems. Results of eigenvalue calculations for three power systems of differing size and complexity are presented and the accuracy, consistency and convergence of the alternative calculation methods are discussed. >
189 citations
TL;DR: In this paper, two sparsity-based eigenvalue simultaneous iterations and the modified Arnoldi method are presented and their application to the small signal stability analysis of large power systems is discussed.
Abstract: Two sparsity-based eigenvalue simultaneous iterations and the modified Arnoldi method are presented and their application to the small signal stability analysis of large power systems is discussed. An algorithm utilizing these two methods is proposed for calculating the eigenvalues around a fixed point which can be placed at will in various parts of the complex plane. The sparsity is fully preserved in the algorithm by using the augmented system state equations as the linearized power system small signal model and performing the corresponding sparsity-oriented calculations. Several applications of the algorithm are discussed and illustrated by numerical examples. Comparisons are made for the two eigenvalue methods with other techniques. >
150 citations
Cites methods from "A new eigen-analysis method of stea..."
...PEALS [2] is mainly aimed at the computation of slow inter-area oscillatory modes; the S-Method [3] is most efficient for finding the unstable modes; STEPS [4] can be used for computing the eigenvalues belonging to a small study zone; [5] gives an implementation of the inverse iterations....
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TL;DR: In this article, the location index for effective damping (LIED) is proposed for large scale power systems with more than two hundred generators without conducting a number of digital simulations and eigenvalue analyses.
Abstract: Variable impedance apparatus such as a static VAr compensator (SVC) and a variable series capacitor (VSC) can improve the steady-state stability of a power system if they are located appropriately. The present paper proposes an index for identifying the location of SVC and VSC in large scale power systems for effective damping. The index is called LIED (location index for effective damping) by the authors. Since LIED can be computed quickly for large scale power systems which have more than two hundred generators without conducting a number of digital simulations and eigenvalue analyses, it is valuable for the system planner who needs to identify the effective location of SVC and VSC. The proposed index is applied to the New England test system and its validity is demonstrated through digital simulations. >
106 citations
References
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TL;DR: In this article, two efficient algorithms for frequency response and eigenvalue estimation are presented. But they are not suitable for the analysis of small signal stability of multimachine power systems.
Abstract: Frequency response and eigenvalue techniques are fundamental tools in the analysis of small signal stability of multimachine power systems. This paper describes two highly efficient algorithms which are expected to enhance the practical application of these techniques. One algorithm calculates exact eigenvalues and eigenvectors for a large power system, while the other produces the frequency response of the transfer functions between any two variables in the system. This paper also presents alternative computing procedures for the AESOPS eigenvalue estimation algorithm which are simpler and at least as efficient as those described in [1].
195 citations
TL;DR: In this paper, the authors describe the small signal performance of a multi-machine synchronous power system by a set of differential equations of the form [x] = [A] [x], allowing standard multivariable control theory to be used in dynamic stability studies.
Abstract: Describing the small signal performance of a multi- machine synchronous power system by a set of differential equations of the form [x] = [A] [x] allows standard multivariable control theory to be used in dynamic stability studies. The construction of the [A] matrix for a multimachine power system involves the application of Kron's rotational transformation to the transmission network admittance matrix, and a matrix analysis of the synchronous machines using internal flux linkages as state variables.
140 citations
TL;DR: In this article, a method of analyzing the small signal stability of very large power systems is described based on a frequency-domain approach which concentrates on the electromechanical modes of the power system under study.
Abstract: A method of analyzing the small signal stability of very large power systems is described. The method is based on a frequency-domain approach which concentrates on the electromechanical modes of the power system under study. By using a modular modeling concept and an efficient sparsity network solution routine, systems having up to 12000 buses and 1000 detailed generator models can be studied. A comparison is made between eigenvalues calculated by this method and by other existing programs. >
103 citations
TL;DR: In this article, a digital computer program for the analysis of small signal dynamic stability of power systems is described, which uses the state space approach and determines the stability by computing the eigenvalues of the coefficient matrix of the linearized systems.
Abstract: A digital computer program for the analysis of small signal dynamic stability of power systems is described. The program uses the state space approach and determines the stability by computing the eigenvalues of the coefficient matrix of the linearized systems. Results of some of the investigations carried out using the program are presented. The examples considered demonstrate how the program has been used as a useful analytical tool by an electric utility for solving a variety of stability problems.
64 citations
TL;DR: In this article, the eigenvalues of an arbitrary matrix with complex elements were found in two steps: first, the matrix A was reduced to a tri-diagonal (i.e., Jacobi) matrix J; and second, the coefficients of J were computed.
Abstract: The eigenvalues of an arbitrary matrix with complex elements were found in two steps. First, the matrix A was reduced to a tri-diagonal (i.e., Jacobi) matrix J; and second, the eigenvalues of J were computed. In step one the biorthogonal method of Lanezos [1] was used and in step two a method of determinant evaluation (see Frank [2]) was employed. Lanczos' method involves the construction of two biorthogonal sets of vectors xi , x2, * x*,n and yi, Y2, * * * Yn y using the recursion formulas
6 citations