Power system small signal stability analysis

Power system small signal stability analysis aims to explore diierent small signal stability conditions and controls, namely, 1) exploring the power system security domains and boundaries in the space of power system parameters of interest, including load ow feasibility, saddle node and Hopf bifurcation ones, 2) nding the maximum and minimum damping conditions, and 3) determining control actions to provide and increase small signal stability. These problems are presented in the paper as diierent modiications of a general optimization problem, and each of them has multiple minima and maxima. The usual optimization procedures converge to a minimum/maximum depending on the initial guesses of variables and numerical methods used. In the considered problems, all the extreme points are of interest. Additionally, there are diiculties with nding the derivatives of the objective functions with respect to parameters. Numerical computations of derivatives in traditional optimization procedures are time consuming. In the paper, we propose a new black box genetic optimization technique for comprehensive small signal stability analysis, which can eeectively cope with highly nonlinear objective functions with multiple minima and maxima and derivatives which can not be expressed analytically. The optimization result then can be used to provide such important informations as system optimal control decision making, assessment of the maximum network's transmission capacity, etc.