Stochastics based methods enabling testing of grid related algorithms through simulation

This dissertation presents stochastics-based methods enabling testing related to three different aspects of the transition towards Smart Grids: the overall increase in sources of uncertainty, the need for studying the effects of higher shares of distributed generation on distribution grids, and the focus on single consumers through concepts such as demand side management. A nonintrusive Polynomial Chaos approach is developed for fast uncertainty analysis. It is shown that by combining Polynomial Chaos and numerical integration, black box use of Polynomial Chaos can be achieved. Additionally, by using a single polynomial basis, the procedure is automated for parameters with arbitrary probability distributions, avoiding adjustments traditionally performed in Polynomial Chaos. It is shown that the results of 10000 Monte Carlo simulations can be achieved by post-processing as little as 6 simulations per random parameter, using deterministic integration points as inputs.In order to allow for robust testing of distribution grid-related methods with several different topologies, an algorithm based on concepts from Graph Theory is designed for generating random distribution grid models. The algorithm separately generates medium voltage grid and low voltage grid models. A geographical reference is used in order to facilitate the assignment of distances and electrical properties, and through these the construction of admittance matrices for further use. The algorithm is validated by comparing the statistics of real grids with those of generated grids.Finally, a framework is developed for the random generation of single load profiles for arbitrary types of consumers, based on standard load profiles as a reference for user activity. The generated profiles represent realistic challenges for simulation and testing thanks to the abrupt consumption behaviour, contrary to the smooth standard load profiles which can only be considered realistic for large numbers of consumers. It is shown through an implementation for households that a large number of generated load profiles behave similarly as the original standard load profile, thereby demonstrating their statistical correctness