## 4 Analysis of Prediction Results
### Prediction Results of the Deep Neural Network  
Since the embedding dimension is \(m\) = 5 as determined by the C-C method, there were five input neurons in the DNN. The cross-validation shows that when the number of layers in the hidden layer was 5, the predicted value showed a significant over-fitting. Therefore, the number of layers of the hidden layer was taken as 4, and the neurons of each hidden layer were taken as 5, 4, 3, and 2. The DNN used the single-step prediction and only predicted the next 5 min load value at a time. The predicted result is shown in Figure 5. The black solid line is the actual net load, the red solid line is the ultrashort-term prediction value based on the phase space reconstruction and DNN, and the blue dotted line is the ultrashort-term prediction value based on the traditional BP neural network.  
In Figure 5, at approximately 12:00 noon on a clear day (12 th), a negative power was present in the payload due to an increase in the amount of PV power generation. The prediction results based on the phase space reconstruction and DNN were closer to the actual net load value, which was obviously better than the prediction results using the traditional BP neural network.  
On cloudy days (13-15 May), when the net load sharply fluctuated due to the fluctuation of the PV output, although the actual net load value was stable, the predicted value of the traditional BP neural network still had large fluctuations, which resulted in a large deviation. However, the prediction results based on the phase space and DNN did not strongly deviate and basically conformed to the actual trend of the net load.  
To accurately evaluate the accuracy of the model prediction and the accuracy of prediction, the mean absolute percentage error (MAPE) and root mean square error (RMSE) were used as evaluation indicators. In Formulas (17) and (18), \(n\) is the number of predicted samples, \(p_{i}\) is the actual value of the net load at time \(i\), and \(\hat{p}_{i}\) is the predicted value of the net load at time \(i\).  
\[\text{MAPE}= \frac{1}{n}\sum_{i=1}^{n}\left|\frac{p_{i}-\hat{p}_{i}}{p_{i}} \right|\times 100\% \tag{17}\] \[\text{RMSE}= \sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(p_{i}-\hat{p}_{i}\right)^{2}} \tag{18}\]  
The prediction accuracy is shown in Table 1. Compared with the prediction model based on the traditional BP neural network, the forecasting scheme proposed in this paper improved the accuracy  
Figure 5: Load forecasting results based on different models: (**a**) 12 May; (**b**) 13 May; (**c**) 14 May; (**d**) 15 May.  
of net load forecasting under different weather conditions. On a cloudy day (15 May), the power of PV power generation was very small. The accuracy of the prediction model based on the phase space reconstruction and the deep neural network was basically identical to that based on the traditional BP neural network. However, on a sunny day (12 May), the PV power was relatively high, and the difference of MAPE between the two models was nearly 10%. The predictive models based on the phase space reconstruction and DNN still had higher prediction accuracy even in the case of large distributed PV power access and large power fluctuation.