Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input

2015 ◽  
Vol 3 (1) ◽  
pp. 873-896 ◽  
Author(s):  
P. Wang ◽  
D. A. Barajas-Solano ◽  
E. Constantinescu ◽  
S. Abhyankar ◽  
D. Ghosh ◽  
...  
Keyword(s):  
Power Systems ◽  
Density Function ◽  
Function Method ◽  
Power Input ◽  
Probabilistic Density Function ◽  
Stochastic Odes

scholarly journals Some Properties for Adjustable Entropy Function Method and Its Application to Power Systems Dynamic Economic Dispatch with Wind Integrated

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yaming Ren
Keyword(s):  
Power Systems ◽  
Function Method ◽  
Economic Dispatch ◽  
Entropy Function ◽  
Prediction Errors ◽  
Mathematical Methods ◽  
Spinning Reserve ◽  
Aggregate Function ◽  
Adjustable Entropy Function ◽  
Dynamic Economic Dispatch

With the continuous development of the world economy, the development and utilization of environmentally friendly and renewable energy have become the trend in many countries. In this paper, we study the dynamic economic dispatch with wind integrated. Firstly, we take advantage of the positive and negative spinning reserve to deal with wind power output prediction errors in order to establish a dynamic economic dispatch model of wind integrated. The existence of a min function makes the dynamic economic dispatch model nondifferentiable, which results in the inability to directly use the traditional mathematical methods based on gradient information to solve the model. Inspired by the aggregate function, we can easily transform the nondifferentiable model into a smooth model when parameter p tends to infinity. However, the aggregate function will cause data overflow when p tends to infinity. Then, for solving this problem, we take advantage of the adjustable entropy function method to replace of aggregate function method. In addition, we further discuss the adjustable entropy function method and point out that the solution generated by the adjustable entropy function method can effectively approximate the solution of the original problem without parameter p tending to infinity. Finally, simulation experiments are given, and the simulation results prove the effectiveness and correctness of the adjustable entropy function method.

scholarly journals Automated measurement of quasar redshift with a Gaussian process

2020 ◽  
Vol 498 (4) ◽  
pp. 5227-5239
Author(s):  
Leah Fauber ◽  
Ming-Feng Ho ◽  
Simeon Bird ◽  
Christian R Shelton ◽  
Roman Garnett ◽  
...  
Keyword(s):  
Gaussian Process ◽  
Density Function ◽  
Area Under Curve ◽  
Sloan Digital Sky Survey ◽  
Automated Measurement ◽  
Quasar Spectra ◽  
Sky Survey ◽  
Automated Technique ◽  
Probabilistic Density Function ◽  
Process Method

ABSTRACT We develop an automated technique to measure quasar redshifts in the Baryon Oscillation Spectroscopic Survey of the Sloan Digital Sky Survey (SDSS). Our technique is an extension of an earlier Gaussian process method for detecting damped Lyman α absorbers (DLAs) in quasar spectra with known redshifts. We apply this technique to a subsample of SDSS DR12 with BAL quasars removed and redshift larger than 2.15. We show that we are broadly competitive to existing quasar redshift estimators, disagreeing with the PCA redshift by more than 0.5 in only $0.38{{\ \rm per\ cent}}$ of spectra. Our method produces a probabilistic density function for the quasar redshift, allowing quasar redshift uncertainty to be propagated to downstream users. We apply this method to detecting DLAs, accounting in a Bayesian fashion for redshift uncertainty. Compared to our earlier method with a known quasar redshift, we have a moderate decrease in our ability to detect DLAs, predominantly in the noisiest spectra. The area under curve drops from 0.96 to 0.91. Our code is publicly available.

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