An Uncertain Optimal Energy Flow Model for CCHP Campus Microgrid Using Parameterized Probability Boxes

Due to the uncertain fluctuations of renewable energy and load power, the state variables such as bus voltages and pipeline mass flows in the combined cooling, heating, and power campus microgrid(CCHP-CMG) may exceed the secure operation limits. In this paper, an optimal energy flow(OEF) model for a CCHP-CMG using parameterized probability boxes(p-boxes) is proposed to describe the higher-order uncertainty of renewables and loads. In the model, chance constraints are used to describe the secure operation limits of the state variable p-boxes, and variance constraints are introduced to reduce their random fluctuation ranges. To solve this model, the chance and variance constraints are transformed into the constraints of interval cumulants(ICs) of state variables based on the p-efficient point theory and interval Cornish-Fisher expansion. With the relationship between the ICs of state variables and node power, and using the affine interval arithmetic method, the original optimization model is finally transformed into a deterministic nonlinear programming model. It can be solved by the CONOPT solver in GAMS software to obtain the optimal operation point of a CCHP-CMG that satisfies the secure operation requirements considering the higher-order uncertainty of renewables and loads. Case study on a CCHP-CMG demonstrates the correctness and effectiveness of the proposed OEF model.

Reliability analysis of a composite laminate using estimation theory

Composite laminates are made up of composite single-plies sequence. The plies generally have the same fiber and resin and their difference in fiber orientation results in a difference in various laminates' strength. Tsai-Hill failure criterion as a limiting state function to analyze structural reliability of a composite laminate and estimation theory in order to estimate statistical parameters of effective stress were utilized to construct probability box. Finally, we used the Monte Carlo simulation and FERUM software to calculate the upper and lower bounds of probability of failure.

Measuring reliability under epistemic uncertainty:Review on non-probabilistic reliability metrics

In this paper, a systematic review of non-probabilistic reliability metrics is conducted to assist the selection of appropriate reliability metrics to model the influence of epistemic uncertainty. Five frequently used non-probabilistic reliability metrics are critically reviewed, i.e., evidence- theory-based reliability metrics, interval-analysis-based reliability metrics, fuzzy-interval-analysis- based reliability metrics, possibility-theory-based reliability metrics （posbist reliability） and uncertainty-theory-based reliability metrics （belief reliability）. It is pointed out that a qualified reli- ability metric that is able to consider the effect of epistemic uncertainty needs to （ 1 ） compensate the conservatism in the estimations of the component-level reliability metrics caused by epistemic uncertainty, and （2） satisfy the duality axiom, otherwise it might lead to paradoxical and confusing results in engineering applications. The five commonly used non-probabilistic reliability metrics are compared in terms of these two properties, and the comparison can serve as a basis for the selection of the appropriate reliability metrics.