The energy distance for ensemble and scenario reduction

Scenario reduction techniques are widely applied for solving sophisticated dynamic and stochastic programs, especially in energy and power systems, but are also used in probabilistic forecasting, clustering and estimating generative adversarial networks. We propose a new method for ensemble and scenario reduction based on the energy distance which is a special case of the maximum mean discrepancy. We discuss the choice of energy distance in detail, especially in comparison to the popular Wasserstein distance which is dominating the scenario reduction literature. The energy distance is a metric between probability measures that allows for powerful tests for equality of arbitrary multivariate distributions or independence. Thanks to the latter, it is a suitable candidate for ensemble and scenario reduction problems. The theoretical properties and considered examples indicate clearly that the reduced scenario sets tend to exhibit better statistical properties for the energy distance than a corresponding reduction with respect to the Wasserstein distance. We show applications to a Bernoulli random walk and two real data-based examples for electricity demand profiles and day-ahead electricity prices. This article is part of the theme issue ‘The mathematics of energy systems’.

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Scenario Reduction Network Based on Wasserstein Distance with Regularization

10.36227/techrxiv.17007967 ◽

2021 ◽

Author(s):

Yingyun Sun ◽

Xiaochong Dong ◽

Sarmad Majeed Malik

Keyword(s):

Power Systems ◽

Network Model ◽

Large Scale ◽

Optimization Problems ◽

Wasserstein Distance ◽

Structure Design ◽

Scenario Reduction ◽

High Penetration ◽

Neural Network Structure ◽

Unconstrained Problem

Power systems with high penetration of renewable energy contain various <a></a><a>uncertainties</a>. Scenario-based optimization problems need a large number of discrete scenarios to obtain a reliable approximation for the probabilistic model. It is important to choose typical scenarios and ease the computational burden. This paper presents a scenario reduction network model based on Wasserstein distance. Entropy regularization is used to transform the scenario reduction problem into an unconstrained problem. Through an explicit neural network structure design, the output of the scenario reduction network corresponds to Sinkhorn distance function. The scenario reduction network can generate the typical scenario set through unsupervised learning training. An efficient algorithm is proposed for continuous/discrete scenario reduction. The superiority of the scenario reduction network model is verified through case studies. The numerical results highlight high accuracy and computational efficiency of the proposed model over state-of-the-art model making it an ideal candidate for large-scale scenario reduction problems

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Scenario Reduction Network Based on Wasserstein Distance with Regularization

10.36227/techrxiv.17007967.v1 ◽

2021 ◽

Author(s):

Yingyun Sun ◽

Xiaochong Dong ◽

Sarmad Majeed Malik

Keyword(s):

Power Systems ◽

Network Model ◽

Large Scale ◽

Optimization Problems ◽

Wasserstein Distance ◽

Structure Design ◽

Scenario Reduction ◽

High Penetration ◽

Neural Network Structure ◽

Unconstrained Problem

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Data Augment Using Deep Convolutional Generative Adversarial Networks for Transient Stability Assessment of Power Systems

2020 39th Chinese Control Conference (CCC) ◽

10.23919/ccc50068.2020.9189289 ◽

2020 ◽

Author(s):

Jiamin Li ◽

Hongying Yang ◽

Liping Yan ◽

Zonghan Li ◽

Daowei Liu ◽

...

Keyword(s):

Power Systems ◽

Transient Stability ◽

Generative Adversarial Networks ◽

Stability Assessment ◽

Adversarial Networks

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Supervised dimensionality reduction for big data

Nature Communications ◽

10.1038/s41467-021-23102-2 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Joshua T. Vogelstein ◽

Eric W. Bridgeford ◽

Minh Tang ◽

Da Zheng ◽

Christopher Douville ◽

...

Keyword(s):

Dimensionality Reduction ◽

Data Science ◽

Real Data ◽

Low Rank ◽

Conditional Moment ◽

Desktop Computer ◽

Reduction Techniques ◽

Reduction Methods ◽

The Individual ◽

Low Dimensional

AbstractTo solve key biomedical problems, experimentalists now routinely measure millions or billions of features (dimensions) per sample, with the hope that data science techniques will be able to build accurate data-driven inferences. Because sample sizes are typically orders of magnitude smaller than the dimensionality of these data, valid inferences require finding a low-dimensional representation that preserves the discriminating information (e.g., whether the individual suffers from a particular disease). There is a lack of interpretable supervised dimensionality reduction methods that scale to millions of dimensions with strong statistical theoretical guarantees. We introduce an approach to extending principal components analysis by incorporating class-conditional moment estimates into the low-dimensional projection. The simplest version, Linear Optimal Low-rank projection, incorporates the class-conditional means. We prove, and substantiate with both synthetic and real data benchmarks, that Linear Optimal Low-Rank Projection and its generalizations lead to improved data representations for subsequent classification, while maintaining computational efficiency and scalability. Using multiple brain imaging datasets consisting of more than 150 million features, and several genomics datasets with more than 500,000 features, Linear Optimal Low-Rank Projection outperforms other scalable linear dimensionality reduction techniques in terms of accuracy, while only requiring a few minutes on a standard desktop computer.

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Day-ahead renewable scenario forecasts based on generative adversarial networks

10.36227/techrxiv.11839122.v2 ◽

2020 ◽

Author(s):

Congmei Jiang ◽

Yongfang Mao ◽

Yi Chai ◽

Mingbiao Yu

Keyword(s):

Power Systems ◽

Renewable Resources ◽

Large Scale ◽

Generative Adversarial Networks ◽

Power Sources ◽

Renewable Power ◽

Adversarial Networks ◽

Future Behavior ◽

Large Scale Integration ◽

Scale Integration

<p>With the increasing penetration of renewable resources such as wind and solar, the operation and planning of power systems, especially in terms of large-scale integration, are faced with great risks due to the inherent stochasticity of natural resources. Although this uncertainty can be anticipated, the timing, magnitude, and duration of fluctuations cannot be predicted accurately. In addition, the outputs of renewable power sources are correlated in space and time, and this brings further challenges for predicting the characteristics of their future behavior. To address these issues, this paper describes an unsupervised method for renewable scenario forecasts that considers spatiotemporal correlations based on generative adversarial networks (GANs), which have been shown to generate high-quality samples. We first utilized an improved GAN to learn unknown data distributions and model the dynamic processes of renewable resources. We then generated a large number of forecasted scenarios using stochastic constrained optimization. For validation, we used power-generation data from the National Renewable Energy Laboratory wind and solar integration datasets. The experimental results validated the effectiveness of our proposed method and indicated that it has significant potential in renewable scenario analysis.</p>

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Antinoise Learning and Coalitional Game GAN

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001422520012 ◽

2021 ◽

Author(s):

Hongyou Chen ◽

Hongjie He ◽

Fan Chen ◽

Yiming Zhu

Keyword(s):

Image Quality ◽

Real Data ◽

Training Dataset ◽

Generative Adversarial Networks ◽

Coalitional Game ◽

Generative Adversarial Network ◽

Adversarial Learning ◽

Network Convergence ◽

The Stability ◽

Zero Sum

Adversarial learning stability has an important influence on the generated image quality and convergence process in generative adversarial networks (GANs). Training dataset (real data) noise and the balance of game players have an impact on adversarial learning stability. In the gradient backpropagation of the discriminator, the noise samples increase the gradient variance. It can increase the uncertainty in the network convergence progress and affect stability. In the two-player zero-sum game, the game ability of the generator and discriminator is unbalanced. Generally, the game ability of the generator is weaker than that of the discriminator, which affects the stability. To improve the stability, an antinoise learning and coalitional game generative adversarial network (ANL-CG GAN) is proposed, which achieves this goal through the following two strategies. (i) In the real data loss function of the discriminator, an effective antinoise learning method is designed, which can improve the gradient variance and network convergence uncertainty. (ii) In the zero-sum game, a generator coalitional game module is designed to enhance its game ability, which can improve the balance between the generator and discriminator via a coalitional game strategy. To verify the performance of this model, the generated results of the designed GAN and other GAN models in CELEBA and CIFAR10 are compared and analyzed. Experimental results show that the novel GAN can improve adversarial learning stability, generate image quality, and reduce the number of training epochs.

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Outlier Detection Methods for Uncovering of Critical Events in Historical Phasor Measurement Records

E3S Web of Conferences ◽

10.1051/e3sconf/20186408006 ◽

2018 ◽

Vol 64 ◽

pp. 08006 ◽

Cited By ~ 1

Author(s):

Kummerow André ◽

Nicolai Steffen ◽

Bretschneider Peter

Keyword(s):

Power Systems ◽

Outlier Detection ◽

Training Data ◽

Detection Methods ◽

Data Sets ◽

Critical Events ◽

Failure Patterns ◽

Detection Algorithms ◽

Reduction Techniques ◽

Dimension Reduction Techniques

The scope of this survey is the uncovering of potential critical events from mixed PMU data sets. An unsupervised procedure is introduced with the use of different outlier detection methods. For that, different techniques for signal analysis are used to generate features in time and frequency domain as well as linear and non-linear dimension reduction techniques. That approach enables the exploration of critical grid dynamics in power systems without prior knowledge about existing failure patterns. Furthermore new failure patterns can be extracted for the creation of training data sets used for online detection algorithms.

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RoCGAN: Robust Conditional GAN

International Journal of Computer Vision ◽

10.1007/s11263-020-01348-5 ◽

2020 ◽

Vol 128 (10-11) ◽

pp. 2665-2683 ◽

Cited By ~ 1

Author(s):

Grigorios G. Chrysos ◽

Jean Kossaifi ◽

Stefanos Zafeiriou

Keyword(s):

Large Scale ◽

Real Data ◽

Superior Performance ◽

Target Space ◽

Generative Adversarial Networks ◽

Natural Scenes ◽

Adversarial Networks ◽

Target Manifold ◽

The Face ◽

Intense Noise

Abstract Conditional image generation lies at the heart of computer vision and conditional generative adversarial networks (cGAN) have recently become the method of choice for this task, owing to their superior performance. The focus so far has largely been on performance improvement, with little effort in making cGANs more robust to noise. However, the regression (of the generator) might lead to arbitrarily large errors in the output, which makes cGANs unreliable for real-world applications. In this work, we introduce a novel conditional GAN model, called RoCGAN, which leverages structure in the target space of the model to address the issue. Specifically, we augment the generator with an unsupervised pathway, which promotes the outputs of the generator to span the target manifold, even in the presence of intense noise. We prove that RoCGAN share similar theoretical properties as GAN and establish with both synthetic and real data the merits of our model. We perform a thorough experimental validation on large scale datasets for natural scenes and faces and observe that our model outperforms existing cGAN architectures by a large margin. We also empirically demonstrate the performance of our approach in the face of two types of noise (adversarial and Bernoulli).

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Simulation of Incidental Distributed Generation Curtailment to Maximize the Integration of Renewable Energy Generation in Power Systems

Energies ◽

10.3390/en13164173 ◽

2020 ◽

Vol 13 (16) ◽

pp. 4173 ◽

Cited By ~ 1

Author(s):

Ingo Liere-Netheler ◽

Frank Schuldt ◽

Karsten von Maydell ◽

Carsten Agert

Keyword(s):

Renewable Energy ◽

Power Systems ◽

Power System ◽

Distributed Generation ◽

System Integration ◽

Best Practice ◽

Flow Analysis ◽

Real Data ◽

Load Flow ◽

Practical Implementation

Power system security is increasingly endangered due to novel power flow situations caused by the growing integration of distributed generation. Consequently, grid operators are forced to request the curtailment of distributed generators to ensure the compliance with operational limits more often. This research proposes a framework to simulate the incidental amount of renewable energy curtailment based on load flow analysis of the network. Real data from a 110 kV distribution network located in Germany are used to validate the proposed framework by implementing best practice curtailment approaches. Furthermore, novel operational concepts are investigated to improve the practical implementation of distributed generation curtailment. Specifically, smaller curtailment level increments, coordinated selection methods, and an extension of the n-1 security criterion are analyzed. Moreover, combinations of these concepts are considered to depict interdependencies between several operational aspects. The results quantify the potential of the proposed concepts to improve established grid operation practices by minimizing distributed generation curtailment and, thus, maximizing power system integration of renewable energies. In particular, the extension of the n-1 criterion offers significant potential to reduce curtailment by up to 94.8% through a more efficient utilization of grid capacities.

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