Skip to main content

Advertisement

Table 1 RMSD between the forecast and the target time series of the MAXBEX of each pair of countries, normalized by the average MAXBEX

From: Forecasting cross-border power transmission capacities in Central Western Europe using artificial neural networks

  DE/AT →NL NL →DE/AT DE/AT →BE BE →DE/AT
Average MAXBEX [MW] 3 020 2 340 3 182 3 026
norm. RMSD random [%] 53.8 44.8 44.4 44.8
norm. RMSD shuffle [%] 50.0 48.1 36.9 44.8
Forecast method CF NARX CF NARX CF NARX CF NARX
norm. RMSD 1 hour lag [%] 16.6 15.6 14.1 13.5 9.9 9.5 11.8 11.9
norm. RMSD 2 hour lag [%] 22.1 19.4 20.5 18.9 15.0 12.9 17.9 17.4
norm. RMSD 3 hour lag [%] 25.6 21.1 24.9 22.1 18.9 14.9 22.6 21.3
norm. RMSD 10 hour lag [%] 38.0 24.7 39.8 29.9 28.1 18.9 32.9 28.8
norm. RMSD 11 hour lag [%] 38.5 24.7 40.8 30.2 28.3 18.9 33.0 29.1
norm. RMSD 12 hour lag [%] 39.1 24.7 41.8 30.5 28.7 18.9 33.6 29.6
  DE/AT →FR FR →DE/AT NL →BE BE →NL
Average MAXBEX [MW] 3 733 4 102 2 130 3 219
norm. RMSD random [%] 62.4 42.0 40.6 39.6
norm. RMSD shuffle [%] 62.6 31.9 30.5 34.5
Forecast method CF NARX CF NARX CF NARX CF NARX
norm. RMSD 1 hour lag [%] 17.2 16.8 11.5 11.5 7.5 7.6 11.3 11.0
norm. RMSD 2 hour lag [%] 26.3 23.4 15.7 15.4 11.5 10.9 16.0 15.2
norm. RMSD 3 hour lag [%] 32.9 27.2 18.2 17.5 14.8 13.2 19.1 17.8
norm. RMSD 10 hour lag [%] 50.0 34.4 24.0 20.9 22.6 17.5 26.7 23.5
norm. RMSD 11 hour lag [%] 49.9 34.3 24.3 21.2 22.9 17.6 27.2 23.9
norm. RMSD 12 hour lag [%] 50.1 34.2 25.0 21.5 23.3 17.8 27.7 24.3
  NL →FR FR →NL BE →FR FR →BE
Average MAXBEX [MW] 2 006 3 536 2 475 4 010
norm. RMSD random [%] 69.6 40.7 49.4 28.6
norm. RMSD shuffle [%] 50.8 43.0 44.7 22.7
Forecast method CF NARX CF NARX CF NARX CF NARX
norm. RMSD 1 hour lag [%] 13.1 12.5 15.0 14.1 11.7 10.9 8.2 8.0
norm. RMSD 2 hour lag [%] 20.0 18.0 18.7 16.6 18.4 15.6 11.8 11.0
norm. RMSD 3 hour lag [%] 25.8 21.9 21.4 18.2 23.8 19.0 14.2 12.7
norm. RMSD 10 hour lag [%] 41.9 28.6 29.1 21.6 35.9 25.7 18.2 14.6
norm. RMSD 11 hour lag [%] 42.5 28.7 29.6 21.7 36.0 25.8 18.3 14.6
norm. RMSD 12 hour lag [%] 43.2 28.8 30.3 21.8 36.4 26.1 18.7 14.7
  1. Two forecast methods have been applied: A simple carry forward (CF), and a forecast based on the closed-loop application of the described ANN with 20 neurons in the hidden layer and two delays (NARX). Average MAXBEX values for all links are given, which allows retransforming the normalized RMSD values to absolute values. As a comparison, for all links the normalized RMSD between the forecast and both a random time series in the range of the minimum/maximum MAXBEX and the randomized time series itself is displayed