# Recurrent Neural Network Based Short-Term Load Forecast with Spline Bases and Real-Time Adaptation
## 3 Test Results
### Comparison of ANN, MIX, SPM and RNN Model Performance  
In this sub-section, performance of different STLF methods are compared, including a two-stage Artificial Neural Network (ANN) model and an STLF model developed previously by TPC with special attention being given to the adjustments of the peak and nadir load forecasts [26], and a mixed model (MIX) with a weighted average of the ANN and against our basic RNN without Lasso variable selection or temperature calibration, where the weights are inversely proportional to the MAPEs of the previous day. The performances of the next (\(D+1\))-day monthly MAPEs for these four forecasting models are presented in Table 5, for the year 2018. As the table shows, each model has its own advantages and disadvantages in daily load profile and max/min load forecasts. For example, the RNN model has the best overall yearly average performance for monthly MAPEs: 2.34 for the daily loads and 2.23 for daily peak loads. The SPM model, however, performs the best for nadir loads, with an average monthly MAPE of 2.18. The RNN performance is the best in the spring seasons and fairly good in the winter, when daily load patterns are stable. The SPM performance is the best in the summer season when the weather varies more. The MIX model has its best accuracy in the winter season. The ANN does very well in February and August, when there is the most uncertainty in the load pattern. Both the ANN and MIX models have large biases in June, however, especially for days adjacent to special days. In more closely examining the daily MAPEs of the four models, we find that there are only 2 days for which all four models have MAPEs greater than 4, thus failing to catch the real load patterns: the day before Chinese New Year's Eve in February and the \"nine in one\" election day in November. Figure 7 shows the actual and (\(D+1\))-day forecasts for the four models made on the previous \(D\)-day of these two days. All four models have similar forecasts with large biases to the real load on these two days. This indicates that these two days should be considered as special days in the future, so as to avoid large biases being included in the training samples for future forecasts, thereby helping improving the biases, particularly in February, for the SPM and RNN models. Figure 8 presents the boxplots of daily MAPEs in 2018, after deleting the two days mentioned above. The performances of SPM and RNN are shown to be generally more robust, with fewer extremely large MAPEs. Figure 9 provides two subfigures with the actual and forecasted loads in two of the days where both ANN and MIX have large biased forecasts. \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**ANN**} & \multicolumn{3}{c}{**MIX**} & \multicolumn{3}{c}{**SPM**} & \multicolumn{3}{c}{**RNN**} \\ \cline{2-13}
**Month** & **Daily** & **Peak** & **Nadir** & **Daily** & **Peak** & **Nadir** & **Daily** & **Peak** & **Nadir** & **Daily** & **Peak** & **Nadir** \\ \hline
201801 & 1.77 & 1.33 & 2.30 & 1.95 & 1.61 & 2.78 & 2.60 & 3.18 & 2.48 & 1.41 & 1.21 & 0.96 \\
201802 & 2.19 & 2.63 & 2.21 & 2.38 & 2.82 & 2.43 & 4.09 & 4.51 & 3.18 & 3.64 & 3.81 & 2.94 \\
201803 & 2.40 & 2.18 Figure 8: Performance Comparisons of the Daily MAPEs for \((D+1)\)-day Forecasts with the ANN, Mixed, Semi-Parametric and RNN Models. Figure 7: Actual Load and \((D+1)\)-day Forecasts for 14 February and 24 November 2018 by the ANN (Artificial Neural Network), Mixed, SPM and RNN Models Made on the Previous \(D\)-Day. Figure 9: Actual Load and \((D+1)\)-day Forecasts for 13 June and 16 November 2018 by the ANN, Mixed, SPM and RNN Models Made on the Previous \(D\)-day. One of those days is 13 June 2018, where the MIX and ANN have similar daily forecasts, while the SPM and RNN perform reasonably well. The other day is 11 June 2018, where the MIX model is slightly better than the ANN, with smaller biases.