Chance-constrained optimization (CCO) has been widely used for uncertainty management in power system operation. With the prevalence of wind energy, it becomes necessary to consider curtailment as a dispatch variable CCO. However, will cause an impulse distribution, yielding challenges explicit modeling chance constraint. In this paper, novel data-driven framework is developed handle issue. By ...

This paper presents a chance constrained information gap decision model for multi-period microgrid expansion planning (MMEP) considering two categories of uncertainties, namely random and non-random uncertainties. The main task of MMEP is to determine the optimal sizing, type selection, and installation time of distributed energy resources (DER) in microgrid. In the proposed formulation, inform...

We hypothesise that all electroweak symmetry breaking terms such as fermion masses and the W and Z gauge boson masses arise radiatively from just one explicit symmetry breaking term in the Lagrangian. Our hypothesis is motivated by the lack of experimental support and the lack of predictivity of the standard symmetry breaking scenario. We construct a simple model which illustrates our ideas. We...

For obstacle avoidance against randomly moving traffic participants, stochastic model predictive control is promising. In crowded environments, however, feasible trajectories satisfying chance constraints do not necessarily exist; crowding induces a relaxation of that causes deterioration safety. To address this issue, we developed velocity method decelerates the ego vehicle to speed satisfies ...

In this paper, convexity of chance constrained problems have been investigated. A new generalization of convexity concept, named h-concavity, has been introduced and it has been shown that this new concept is the generalization of the α-concavity. Then, using the new concept, some of the previous results obtained by Shapiro et al. [in Lecture Notes on Stochastic Programming Modeling and Theory,...

Various applications in reliability and risk management give rise to optimization problems with constraints involving random parameters, which are required to be satisfied with a pre-specified probability threshold. There are two main difficulties with such chance-constrained problems. First, checking feasibility of a given candidate solution exactly is, in general, impossible since this requir...

Many control design problems subject to uncertainty can be cast as chance constrained optimization programs. The Scenario Approach provides an intuitive way to address these problems by replacing the chance constraint with a finite number of sampled constraints (scenarios). The sample size critically depends on the so-called Helly’s dimension, which is always upper bounded by the number of deci...

In his ‘Objective Bayesian calibration and the problem of non-convex evidence’, Gregory Wheeler criticises the principle I invoke in Williamson (2010) for calibrating degrees of belief with chances. Bayesian epistemologists commonly appeal to some sort of Calibration norm that says that degrees of belief should be calibrated to known chances. Typically they invoke a principle variously known as...

Ambiguous Chance Constrained Programs: Algorithms and Applications Emre Erdoğan Chance constrained problems are optimization problems where one or more constraints ensure that the probability of one or more events occurring is less than a prescribed threshold. Although it is typically assumed that the distribution defining the chance constraints are known perfectly; in practice this assumption ...