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This paper provides a methodology to assist a strategic producer in making informed decisions on generation investment. A single target year is considered with demand variations modeled through blocks. The strategic behavior of the producer is represented through a bilevel model: the upper-level considers both investment decisions and strategic production actions and the lower-level corresponds to market clearing. Prices are obtained as dual variables of power balance equations. Rival uncertainties (on offering and investment) are characterized through scenarios. The resulting model is a large-scale mixed-integer LP problem solvable using currently available branch-and-cut techniques. Results pertaining to an illustrative example and a case study are reported and discussed. [ABSTRACT FROM PUBLISHER]

Solution approaches to chance constrained programming (CCP) have been recently developed and applied in many areas for optimization under uncertainty. Due to the nonlinear model with multiple uncertain variables as well as multiple output constraints, CCP has not been directly applied to optimal power flow (OPF) under uncertainty. The objective of this paper is twofold. First, we introduce the CCP approach to OPF under uncertainty and analyze the computational complexity of the chance constrained OPF. Second, the effectiveness of implementing a back-mapping approach and a linear approximation of the nonlinear model equations to solve the formulated CCP problem is investigated. Load power uncertainties are considered as multivariate random variables with correlated normal distribution. Based on both the nonlinear and the linearized model, results of a five-bus system and the IEEE 30-bus test system are presented to demonstrate the scope of chance constrained OPF. [ABSTRACT FROM PUBLISHER]

To resolve one of uncertainty features, randomness, in ontologies, this paper shows how to characterize uncertainty of concepts from a statistical viewpoint. In addition, with a focus on indirect entities, which are computed from direct entities through mathematical models, the uncertainties propagated from those direct entities are important and should be quantified. Thus, a novel algorithm, named Stochastic Reduced Order Model (SROM), is presented to be applied to quantify the ontological uncertainty propagation in presence of multiple input entities. This SROM-based method could approximate the statistics of indirect entities accurately and efficiently by using a very small amount of samples of input entities. The computational cost is considerably reduced while guaranteeing a reasonable degree of accuracy. Furthermore, the predicted statistics of output entities could be regarded as high-level information and be beneficial for other ontological operations, such as ontology filtering and ontology reasoning. The implementation of the SROM algorithm is non-intrusive to the mathematical model; therefore, this algorithm could be applicable to quantify uncertainty in ontologies with any mathematical relationships. [ABSTRACT FROM AUTHOR]