A Novel Exponential Transform Method for Evaluating the Small Signal Stability with Enhanced Efficiency and Accuracy

The judgment of the small signal stability is very important for the operation and control of power systems. An improved exponential transform method is put forward in the paper for calculating the unstable eigenvalues with enhanced accuracy and efficiency. Firstly, the unstable eigenvalues are made to be dominant by the exponential transform. Next, the Krylov-Schur method is implemented to compute the dominant ones. During the process, the implicit trapezoidal method is utilized to compute the exponential matrix and vector multiplications so that the calculation efficiency is significantly improved. Benefiting from the good spectral performance of exponential spectral transform, all dominant eigenvalues are obtained easily. Finally, all unstable eigenvalues can be inverted from the dominant eigenvalues. Based on the proposed novel inverse exponential transform, the calculation accuracy is also significantly improved. Numerical tests are carried out on two systems from the Brazilian power system to verify the effectiveness of the improved exponential transform method.