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Data is missing again -- Reconstruction of power generation data using $k$-Nearest Neighbors and spectral graph theory

Amandine Pierrot, Pierre Pinson

Abstract

The risk of missing data and subsequent incomplete data records at wind farms increases with the number of turbines and sensors. We propose here an imputation method that blends data-driven concepts with expert knowledge, by using the geometry of the wind farm in order to provide better estimates when performing Nearest Neighbor imputation. Our method relies on learning Laplacian eigenmaps out of the graph of the wind farm through spectral graph theory. These learned representations can be based on the wind farm layout only, or additionally account for information provided by collected data. The related weighted graph is allowed to change with time and can be tracked in an online fashion. Application to the Westermost Rough offshore wind farm shows significant improvement over approaches that do not account for the wind farm layout information.

Data is missing again -- Reconstruction of power generation data using $k$-Nearest Neighbors and spectral graph theory

Abstract

The risk of missing data and subsequent incomplete data records at wind farms increases with the number of turbines and sensors. We propose here an imputation method that blends data-driven concepts with expert knowledge, by using the geometry of the wind farm in order to provide better estimates when performing Nearest Neighbor imputation. Our method relies on learning Laplacian eigenmaps out of the graph of the wind farm through spectral graph theory. These learned representations can be based on the wind farm layout only, or additionally account for information provided by collected data. The related weighted graph is allowed to change with time and can be tracked in an online fashion. Application to the Westermost Rough offshore wind farm shows significant improvement over approaches that do not account for the wind farm layout information.
Paper Structure (18 sections, 13 equations, 5 figures, 7 tables, 1 algorithm)

This paper contains 18 sections, 13 equations, 5 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Imputation using Nearest Neighbors and graphs
  3. Weighted Nearest Neighbor imputation
  4. Wind farms as unweighted graphs
  5. Graphs
  6. Laplacian eigenmaps
  7. Wind farms as weighted graphs
  8. Weighting the original graph
  9. Online, changing graphs
  10. Computational complexity of the estimators
  11. Application and case-study: Westermost Rough
  12. The Westermost Rough graph representations
  13. Imputation of power generation values
  14. Evaluation setup
  15. Hyperparameter selection
  16. ...and 3 more sections

Figures (5)

  • Figure 1: Position and name of the 35 wind turbines in Westermost Rough offshore wind farm (UK).
  • Figure 2: Graph of the Westermost Rough offshore wind farm with color code.
  • Figure 3: Representation of the wind turbines according to dimensions 1 and 2 (left) and dimensions 2 and 3 (right).
  • Figure 4: Improvements over the naive estimator by wind turbine in the complete setup.
  • Figure 5: Improvements over the naive estimator by wind turbine in the incomplete setup.