# Improved methodologies for the calculation of critical eigenvalues in small signal stability analysis

@article{Angelidis1996ImprovedMF, title={Improved methodologies for the calculation of critical eigenvalues in small signal stability analysis}, author={George Angelidis and Adam Semlyen}, journal={IEEE Transactions on Power Systems}, year={1996}, volume={11}, pages={1209-1217} }

This paper presents improved and new methodologies for the calculation of critical eigenvalues in the small-signal stability analysis of large electric power systems. They augment the robustness and efficiency of existing methods and provide new alternatives. The procedures are implementations of Newton's method, inverse power and Rayleigh quotient iterations, equipped with implicit deflation, and restarted Arnoldi with a locking mechanism and either shift-invert or semi-complex Cayley…

## 89 Citations

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An algorithm, based on subspace accelerated Rayleigh quotient iteration (SARQI), for the automatic computation of the rightmost eigenvalues of large-scale (descriptor) system matrices and can be used for stability analysis in any other field of engineering.

## References

SHOWING 1-10 OF 30 REFERENCES

### Efficient calculation of critical eigenvalue clusters in the small signal stability analysis of large power systems

- Computer Science
- 1995

The paper presents a methodology for the calculation of a selected set of eigenvalues, considered critical in the small signal stability analysis of power systems, and analyzes several alternatives, ranging from constant-matrix iterative refinement to Newton's method, which is much faster than existing approaches.

### New methods for fast small-signal stability assessment of large scale power systems

- Mathematics
- 1995

This paper describes new matrix transformations suited to the efficient calculation of critical eigenvalues of large scale power system dynamic models. The key advantage of these methods is their…

### An efficient and robust eigenvalue method for small-signal stability assessment in parallel computers

- Computer Science, Engineering
- 1995

A parallel version of the bi-iteration method and of a new hybrid method specially developed for parallel processing are introduced and their performance compared with the results obtained with the parallel lop-sided simultaneous iterations algorithm are compared.

### Application of sparse eigenvalue techniques to the small signal stability analysis of large power systems

- EngineeringConference Papers Power Industry Computer Application Conference
- 1989

The authors present two sparsity-based eigenvalue techniques: simultaneous iterations and the modified Arnoldi method. It is shown that these two methods can be applied successfully to the matrices…

### Refactored bi-iteration: a high performance eigensolution method for large power system matrices

- Engineering, Mathematics
- 1996

Small-signal stability analysis of interconnected power systems involves the computation of many eigenvalues/eigenvectors of very large unsymmetric matrices. A new numerical linear algebra method for…

### A new eigen-analysis method of steady-state stability studies for large power systems: S matrix method

- Engineering
- 1988

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.…

### Eigenvalue analysis of very large power systems

- Engineering
- 1988

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…

### Eigenvalue analysis of very large power systems

- Engineering
- 1988

A method of analysing 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…

### Efficient Eigenvalue and Frequency Response Methods Applied to Power System Small-Signal Stability Studies

- EngineeringIEEE Transactions on Power Systems
- 1986

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…

### Selective modal analysis of power system oscillatory instability

- Computer Science
- 1988

An extension to the original selective modal analysis (SMA) approach that has been inspired by the oscillatory stability problem is presented and shows significant reductions in storage and computation requirements as compared to straight eigenanalysis.