The emergence of renewable energy sources (RES) introduces new gateways of uncertainty within power grid networks, necessitating robust and efficient probabilistic models to account for the inherent variability. This variability stems from renewable energy generation and various other factors, including load fluctuations and technical failures. Developing and applying such probabilistic methods is crucial for ensuring that policymakers can make informed decisions based on reliable information, thereby enhancing the stability and resilience of the energy sector.
In the first part of this work, we present the basic theory of Uncertainty Propagation and Monte Carlo sampling, followed by the theory of Polynomial Chaos Expansion (PCE) and Sensitivity Analysis (ANOVA, Saltelli, and Rank-based Estimation). Examples and allusions of how we can apply the theories to probabilistic power flow analysis (PPF) are given throughout the sessions using representations of the PF system. In the second part of this thesis, we present a case study using the European high-voltage transmission network 1354pegase, in which we analyze scenarios with different numbers of input random variables (RVs), ranging from 100 to 621 RVs. We then propose an efficient pipeline, in which PCE is combined with clustering techniques, and a new sensitivity analysis approach, with rank-based estimation, to reduce the size of the stochastic input space. Finally, we present the results and comparisons of the case analyses in the third and last part.