Statistical Uncertainty Quantification for Robustness Stability Analysis using Appropriate Sampling in Power Systems

A statistical framework is presented to perform uncertainty quantification (UQ) of electric power system subjected to randomness. A statistical relationship between just the input source of randomness and output measurements needs to be built up by sampling the data at an appropriate rate. Appropriate sampling is achieved by concentrating on the dynamics caused by the uncertainty alone on the desired output measurements. The correlation amongst the multiple randomness in the power system has been considered using Gaussian Copulas. The effectiveness of performing statistical characterization of randomness using Gaussian mixture models (GMM), Statistical distance, Quantile-Quantile plots and Regression analysis has been examined by performing Robustness stability analysis of an electrical power system. Such statistical UQ can be used to test the performance and robust stability of the power system under different range of uncertainties, thereby putting a permissible limit on the range and magnitude of randomness in the power system. The above framework is tested on IEEE-9 Bus and IEEE-68 Bus systems.