Author: Wander Wadman Affiliation: CWI Amsterdam, Netherlands Email: [email protected] URL: http://homepages.cwi.nl/~wadman/ Title: A splitting technique to estimate power grid reliability indices Abstract: The reliability of modern electrical power grids is vulnerable to uncertain nodal power injections, due to increasing penetration of wind and solar power generators as well as varying consumption patterns. Violations of voltage or current constraints caused by extreme power injections are rare but highly undesirable as then power must be curtailed. Therefore, grid operators want to estimate various grid reliability indices that measure the extent --- e.g. the probability, expected duration or expected frequency --- of these rare occurrences during a time interval given the distribution of the nodal power injections. We extend a Crude Monte Carlo method with a splitting technique to compute unbiased estimators for several indices. The relative variance of index estimators can be controlled and we show that for a small power grid orders of magnitude less workload is required than when using an equivalent Crude Monte Carlo method. Finding a suitable importance function for large power grids is challenging as multiple separated subsets of the power injection space may contribute significantly to the rare event probability. Using the normalized distance to the nearest subset is intuitive but may reward the wrong behavior since the most likely path to the rare event set may be very different from the most likely path to an intermediate level. Therefore, in a general splitting setting we propose to mitigate this problem of path deviation by estimating the subset probabilities separately using a modified splitting technique. In an example on the real line the relative variance of the estimator is shown to be significantly higher when using standard splitting than when using separated splitting simulations. This suggests that one should address different typical sample paths to the rare event of a constraint violation separately.
© Copyright 2024 ExpyDoc
