Correlated Failures of Power Systems: Analysis of the Nordic Grid

Sammanfattning: The emphasis of this master's thesis is modeling and simulation of failures in large-scale power grids. The linear DC-model governing the active power 　ows is derived and discussed, and the optimal load shedding problem is introduced. Using Monte Carlo simulations, we have analyzed the eects of correlations between failures of power lines on the total system load shed. Correlations are introduced by a Bernoulli failure model with its rst two ordinary moments given explicitly. The total system load shed is determined by solving the optimal load shedding problem in a MATLAB environment using YALMIP and the GLPK solver. We have introduced a Monte Carlo simulation framework for sampling the statistics of the system load shed as a function of stochastic network parameters, and provide explicit guarantees on the sampling accuracy. This framework has been applied to a 470 bus model of the Nordic power grid. It has been found that increased correlations between Bernoulli failures of power lines can dramatically increase the expected value as well as the variance of the system load shed.