Biblio

Following substantial advancements in stochastic classes of decision-making optimization problems, scenario-based stochastic optimization, robust\textbackslashtextbackslash distributionally robust optimization, and chance-constrained optimization have recently gained an increasing attention. Despite the remarkable developments in probabilistic forecast of uncertainties (e.g., in renewable energies), most approaches are still being employed in a univariate framework which fails to unlock a full understanding on the underlying interdependence among uncertain variables of interest. In order to yield cost-optimal solutions with predefined probabilistic guarantees, conditional and dynamic interdependence in uncertainty forecasts should be accommodated in power systems decision-making. This becomes even more important during the emergencies where high-impact low-probability (HILP) disasters result in remarkable fluctuations in the uncertain variables. In order to model the interdependence correlation structure between different sources of uncertainty in power systems during both normal and emergency operating conditions, this paper aims to bridge the gap between the probabilistic forecasting methods and advanced optimization paradigms; in particular, perdition regions are generated in the form of ellipsoids with probabilistic guarantees. We employ a modified Khachiyan's algorithm to compute the minimum volume enclosing ellipsoids (MVEE). Application results based on two datasets on wind and photovoltaic power are used to verify the efficiency of the proposed framework.

Control algorithms, like model predictive control, can be computationally expensive and may benefit from being executed over the cloud. This is especially the case for nodes at the edge of a network since they tend to have reduced computational capabilities. However, control over the cloud requires transmission of sensitive data (e.g., system dynamics, measurements) which undermines privacy of these nodes. When choosing a method to protect the privacy of these data, efficiency must be considered to the same extent as privacy guarantees to ensure adequate control performance. In this paper, we review a transformation-based method for protecting privacy, previously introduced by the authors, and quantify the level of privacy it provides. Moreover, we also consider the case of adversaries with side knowledge and quantify how much privacy is lost as a function of the side knowledge of the adversary.