## 3 Results and Discussion
The future power load predictions have higher variance from the diagonal which shows the future power load prediction error. The point's color intensity represents how far into the future the prediction is made; the current predictions are the darkest but as the predictions are made farther out in time the point's color gets lighter. The power load predictions made further out into the future have higher error from the reported power load. Interestingly enough, the overall slope of the ANN predictions that use the LSTM future weather predictions is closer to the diagonal (right) then the ANN predictions of the current power load predictions (left) that used the actual weather measurements. This observation is an evidence that the ensemble of a temporal and an associative model together produce power load predictions with less error that are closer to the measured trends. The reported results in Figure 7 used all weather features available without performing Principal Component Analysis to determine which weather variable captures the variance in the measured power load. The forecasting accuracy was measured using the normalized mean squared error \(MSE=\frac{1}{N}\sum_{i=1}^{N}(\hat{g}(i)-y(i))^{2}\) for the number of validation samples \(N\), where \(\hat{g}(i)\) is the LSTM's output on the data point \(i\) given the past weather window and the \(y(i)\) is the expected (measured) value on the data point \(i\). The verification set size was 20% (7731 possible measurements) of the entire data set. The validation results for the ANN trained to associate the weather conditions and the power load showed in Figure 7 had the MSE = 3.61 \(\times\) 10\({}^{-3}\) to predict the current power load (left) and the MSE = 3.65 \(\times\) 10\({}^{-3}\) to predict the future power load for 40 min into the future (right). How much power load prediction depends solely on the temperature is showed in the results Figure 8. Instead of using all available weather features, we trained the ANN to only use the temperature to predict the current power load (left) and used the LSTM's predictions for the next 40 min to forecast the power load. The results indicate that the power load is dependent on other weather factors than just the temperature. The results in Figure 8 show this by an order of magnitude higher MSE than the power predictions using all available weather features (Figure 7). The MSE in Figure 8 had the MSE = 1.20 \(\times\) 10\({}^{-2}\) for the current power load predictions and MSE = 1.66 \(\times\) 10\({}^{-2}\) to predict the future power load conditions. Figure 7: The results of the forecast power load. The x-axis has the predicted power load, while the y-axis has the measured power load. **(Left)** Predicted power load for the current weather conditions with the MSE = 3.61 \(\times\) 10\({}^{-3}\). **(Right)** Predicted power load using the future LSTM weather predictions with the MSE = 3.65 \(\times\) 10\({}^{-3}\). Furthermore, Figure 8 shows that using only the temperature had disproportionally lower quality of the power load predictions for the reported power load values less than 0.5 for both the current and future predictions. The results in Figure 7 used the full weather feature vector had high generalization across the range of possible power load values. In summary, the presented results show that including additional weather conditions to the feature set will result in more accurate forecasts. The final results set in Figure 9 show the ability of the individual LSTM models to generalize the weather condition trends to predict the current and the future weather conditions. The sample results in the left column had overall lower generalization error loss, while the weather conditions in the right column were predicted more accurately with higher error loss (see Figure 4 for details).