Sparse methods for wind energy prediction

© 2012 IEEE.  Personal use of this material is permitted.  Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.International Joint Conference on Neural Networks (IJCNN), celebrado en 2012 en Brisbane, QLD, AustraliaIn this work we will analyze and apply to the prediction of wind energy some of the best known regularized linear regression algorithms, such as Ordinary Least Squares, Ridge Regression and, particularly, Lasso, Group Lasso and Elastic-Net that also seek to impose a certain degree of sparseness on the final models. To achieve this goal, some of them introduce a non-differentiable regularization term that requires special techniques to solve the corresponding optimization problem that will yield the final model. Proximal Algorithms have been recently introduced precisely to handle this kind of optimization problems, and so we will briefly review how to apply them in regularized linear regression. Moreover, the proximal method FISTA will be used when applying the non-differentiable models to the problem of predicting the global wind energy production in Spain, using as inputs numerical weather forecasts for the entire Iberian peninsula. Our results show how some of the studied sparsity-inducing models are able to produce a coherent selection of features, attaining similar performance to a baseline model using expert information, while making use of less data features.The authors of the paper acknowledge partial support from grant TIN2010-21575-C02-01 of the TIN Subprogram from Spain’s MICINN and of the C´atedra UAM-IIC en Modelado y Predicci´on. The first author is also supported by the FPU– MEC grant AP2008-00167. We also thank Red E´ectrica de Espa˜na, Spain’s TSO, for providing historic wind energy dat

Sparse Linear Wind Farm Energy Forecast

In this work we will apply sparse linear regression methods to forecast wind farm energy production using numerical weather prediction (NWP) features over several pressure levels, a problem where pattern dimension can become very large. We shall place sparse regression in the context of proximal optimization, which we shall briefly review, and we shall show how sparse methods outperform other models while at the same time shedding light on the most relevant NWP features and on their predictive structure.With partial support from grant TIN2010-21575-C02-01 of Spain's Ministerio de Econom a y Competitividad and the UAM{ADIC Chair for Machine Learning in Modelling and Prediction. The rst author is supported by the FPU{MEC grant AP2008-00167. We thank our colleague Alvaro Barbero for the software used in this work

Intra-hour cloud index forecasting with data assimilation

We introduce a computational framework to forecast cloud index (CI)fields for up to one hour on a spatial domain that covers a city. Such intra-hour CI forecasts are important to produce solar power forecasts of utility scale solar power and distributed rooftop solar. Our method combines a 2D advection model with cloud motion vectors (CMVs)derived from a mesoscale numerical weather prediction (NWP)model and sparse optical flow acting on successive, geostationary satellite images. We use ensemble data assimilation to combine these sources of cloud motion information based on the uncertainty of each data source. Our technique produces forecasts that have similar or lower root mean square error than reference techniques that use only optical flow, NWP CMV fields, or persistence. We describe how the method operates on three representative case studies and present results from 39 cloudy days

Enhancing Energy Production with Exascale HPC Methods

High Performance Computing (HPC) resources have become the key actor for achieving more ambitious challenges in many disciplines. In this step beyond, an explosion on the available parallelism and the use of special purpose processors are crucial. With such a goal, the HPC4E project applies new exascale HPC techniques to energy industry simulations, customizing them if necessary, and going beyond the state-of-the-art in the required HPC exascale simulations for different energy sources. In this paper, a general overview of these methods is presented as well as some specific preliminary results.The research leading to these results has received funding from the European Union's Horizon 2020 Programme (2014-2020) under the HPC4E Project (www.hpc4e.eu), grant agreement n° 689772, the Spanish Ministry of Economy and Competitiveness under the CODEC2 project (TIN2015-63562-R), and from the Brazilian Ministry of Science, Technology and Innovation through Rede Nacional de Pesquisa (RNP). Computer time on Endeavour cluster is provided by the Intel Corporation, which enabled us to obtain the presented experimental results in uncertainty quantification in seismic imagingPostprint (author's final draft

Covariance Estimation in High Dimensions via Kronecker Product Expansions

This paper presents a new method for estimating high dimensional covariance matrices. The method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product series expansion of the true covariance matrix. Assuming an i.i.d. Gaussian random sample, we establish high dimensional rates of convergence to the true covariance as both the number of samples and the number of variables go to infinity. For covariance matrices of low separation rank, our results establish that PRLS has significantly faster convergence than the standard sample covariance matrix (SCM) estimator. The convergence rate captures a fundamental tradeoff between estimation error and approximation error, thus providing a scalable covariance estimation framework in terms of separation rank, similar to low rank approximation of covariance matrices. The MSE convergence rates generalize the high dimensional rates recently obtained for the ML Flip-flop algorithm for Kronecker product covariance estimation. We show that a class of block Toeplitz covariance matrices is approximatable by low separation rank and give bounds on the minimal separation rank $r$ that ensures a given level of bias. Simulations are presented to validate the theoretical bounds. As a real world application, we illustrate the utility of the proposed Kronecker covariance estimator for spatio-temporal linear least squares prediction of multivariate wind speed measurements.Comment: 47 pages, accepted to IEEE Transactions on Signal Processin

A Holistic Approach to Forecasting Wholesale Energy Market Prices

Electricity market price predictions enable energy market participants to shape their consumption or supply while meeting their economic and environmental objectives. By utilizing the basic properties of the supply-demand matching process performed by grid operators, known as Optimal Power Flow (OPF), we develop a methodology to recover energy market's structure and predict the resulting nodal prices by using only publicly available data, specifically grid-wide generation type mix, system load, and historical prices. Our methodology uses the latest advancements in statistical learning to cope with high dimensional and sparse real power grid topologies, as well as scarce, public market data, while exploiting structural characteristics of the underlying OPF mechanism. Rigorous validations using the Southwest Power Pool (SPP) market data reveal a strong correlation between the grid level mix and corresponding market prices, resulting in accurate day-ahead predictions of real time prices. The proposed approach demonstrates remarkable proximity to the state-of-the-art industry benchmark while assuming a fully decentralized, market-participant perspective. Finally, we recognize the limitations of the proposed and other evaluated methodologies in predicting large price spike values.Comment: 14 pages, 14 figures. Accepted for publication in IEEE Transactions on Power System