Robustness of Discrete Decisions to the Worst Case Distribution

1978 ◽  
Vol 29 (2) ◽  
pp. 159
Author(s):  
Stanley Schenkerman
Keyword(s):  
Energies ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 2317
Author(s):  
Heng Yang ◽  
Ziliang Jin ◽  
Jianhua Wang ◽  
Yong Zhao ◽  
Hejia Wang ◽  
...  

As the penetration of intermittent renewable energy increases and unexpected market behaviors continue to occur, new challenges arise for system operators to ensure cost effectiveness while maintaining system reliability under uncertainties. To systematically address these uncertainties and challenges, innovative advanced methods and approaches are needed. Motivated by these, in this paper, we consider an energy integrated system with renewable energy and pumped-storage units involved. In addition, we propose a data-driven risk-averse two-stage stochastic model that considers the features of forbidden zones and dynamic ramping rate limits. This model minimizes the total cost against the worst-case distribution in the confidence set built for an unknown distribution and constructed based on data. Our numerical experiments show how pumped-storage units contribute to the system, how inclusions of the aforementioned two features improve the reliability of the system, and how our proposed data-driven model converges to a risk-neutral model with historical data.


Author(s):  
J.D. Geller ◽  
C.R. Herrington

The minimum magnification for which an image can be acquired is determined by the design and implementation of the electron optical column and the scanning and display electronics. It is also a function of the working distance and, possibly, the accelerating voltage. For secondary and backscattered electron images there are usually no other limiting factors. However, for x-ray maps there are further considerations. The energy-dispersive x-ray spectrometers (EDS) have a much larger solid angle of detection that for WDS. They also do not suffer from Bragg’s Law focusing effects which limit the angular range and focusing distance from the diffracting crystal. In practical terms EDS maps can be acquired at the lowest magnification of the SEM, assuming the collimator does not cutoff the x-ray signal. For WDS the focusing properties of the crystal limits the angular range of acceptance of the incident x-radiation. The range is dependent upon the 2d spacing of the crystal, with the acceptance angle increasing with 2d spacing. The natural line width of the x-ray also plays a role. For the metal layered crystals used to diffract soft x-rays, such as Be - O, the minimum magnification is approximately 100X. In the worst case, for the LEF crystal which diffracts Ti - Zn, ˜1000X is the minimum.


2008 ◽  
Author(s):  
Sonia Savelli ◽  
Susan Joslyn ◽  
Limor Nadav-Greenberg ◽  
Queena Chen

Author(s):  
Akira YAMAWAKI ◽  
Hiroshi KAMABE ◽  
Shan LU
Keyword(s):  

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