A Leja-Interpolation Based Indirect Exponential Operator for the Small-Signal Stability Assessment

The small-signal stability problem is one of the most significant stability issues of power systems. In this paper, a Leja-interpolation based indirect exponential operator (IEO) is proposed for evaluating the small-signal stability. Firstly, all unstable eigenvalues can be obtained without omission, benefiting from the well spectral performance of the IEO. Compared with the direct exponential operator (DEO), the IEO method avoids the direct calculations of exponential matrix and vector product (EMVP), as well as the high complexity and inaccuracy caused by EMVP. Therefore, the accuracy is significantly enhanced while the computational burden is reduced. Finally, the effectiveness is demonstrated through tests on the Brazilian power grid, where the accuracy is enhanced by about 3 orders of magnitude and the calculation burden is reduced by more than 80%.