In this paper, a risk-based security assessment methodology is presented, which allows the assessment of operational security of a power system’s future state under uncertainty deriving from varying topology scenarios (contingencies) and forecast errors (loads and renewable infeeds). The methodology models input uncertaintywith a copula function-based Monte–Carlo (MC) framework. Furthermore, it provides the highest level of accuracy on initiating causes of failures through an AC power flow (AC PF) framework. Finally, it achieves speed in solution by the combination of twomeasures of risk. A fast screening tool, based on severity functions, allows us to quickly screen the system for the most severe states. A detailed analysis tool, based on an AC optimal power flow (AC OPF) framework and the notion of lost load, provides additional valuable information, including remedial actions to steer away from severe system states. This paper presents results from the application of the methodology proving the necessity of such a framework. It is shown that not taking into account stochastic
dependence through a proper MC setup seriously underestimates system risk and that an AC framework is needed, as voltage deviations are shown to often be initiators of system collapse.

Preconditioners based on incomplete factorization are very popular for a fast convergence of the PCG-algorithm. However, these preconditioners are hard to parallelize since most operations are inherently sequential. In this paper we present the RRB-solver, which is a PCG-type solver using an incomplete Cholesky factorization based on the Repeated Red-Black (RRB) method. The RRB-solver scales nearly as well as Multigrid, and in this paper we show that this method can be parallelized very efficiently on modern computing architectures including GPUs. For an efficient parallel implementation a clever storage scheme turns out to be the key. The storage scheme is called r1=r2=b1=b2 and it ensures that memory transfers are coalesced throughout the algorithm, yielding near-optimal performance of the RRB-solver. The r1=r2=b1=b2-storage scheme in combination with a CUDA implementation on the GPU gives speedup factors of more than 30 compared to a sequential implementation on one CPU core for 5-/9-point stencils problems. A comparison with algebraic Multigrid further shows that the RRB-solver can be implemented very efficiently on the GPU.