# A Two-Stage Household Electricity Demand Estimation Approach Based on Edge Deep Sparse Coding
## 4 Results
### Test Cases and Results
#### 4.2.3 Benchmarking of Load Demand Estimation Methods in Households  
To validate the effectiveness of the proposed two-stage estimation approach for household electricity demand, this study selected five other load demand forecasting methods for comparison under the preceding benchmarks. These methods are ARIMA, MLP, LSTM, LSTM with normal K-SVD, LSTM with 3-layer K-SVD and the forecasting algorithm proposed in [23]. The performance of the proposed two-stage LSTM with 3-layer appliance load based the K-SVD method and the five competitive techniques in terms of MAPE, MAE, and RMSE is provided in Table 2. For the testing sample, LSTM with 3-layer K-SVD outperformed ARIMA, MLP, normal LSTM, and LSTM with shallow K-SVD in all the metrics used. The novel electricity demand estimation method can further improve its performance with the introduction of appliance status into K-SVD coding. In particular, the proposed method resulted in 16.4%, 11.38%, and 18.16% reduction in MAE, MAPE, and RMSE, respectively, compared with LSTM with shallow K-SVD. Meanwhile, the improvement in MAE, MAPE, and RMSE using the proposed method reached 15.64%, 21.12%, and 25.37%, respectively, compared with algorithm proposed in [23]. Figure 9 presents the actual and forecasted load profiles using different methods on a random day. It was noted that currents estimated by the proposed method or other available forecasting methods were not completely consistent with the real currents, especially for higher values. It was mainly caused by the high randomness, volatility and uncertainty of load profiles at the household level and more sensitive to consumer behavior or environmental variables. Although the errors cannot be eliminated, the proposed algorithm made great progress and followed the trend of the actual load curve compared with the existing algorithms. The electricity consumption peak at approximately 08:00 and 11:30 was accurately captured, and overprediction of the peak at 09:15 and 13:00 due to inertia was avoided. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **MAPE (\%)** & **MAE (A)** & **RMSE (A)** \\ \hline ARIMA & 31.84\% & 109.63 & 192.80 \\ \hline MLP & 41.41\% & 143.49 & 233.54 \\ \hline LSTM & 27.62\% & 100.51 & 180.55 \\ \hline Ref. [23] & 23.92\% & 99.42 & 198.00 \\ \hline LSTM-KSVD (with normal K-SVD) & 24.14\% & 88.50 & 167.28 \\ \hline LSTM-3 Layer (with 3-layer K-SVD) & 22.67\% & 87.71 & 157.07 \\ \hline LSTM-3 LayerAL & & & \\ (with 3-layer appliance load based K-SVD) & 20.18\% & 78.42 & 147.76 \\ \hline Improvement from LSTM-KSVD to & & & \\ LSTM-3 LayerAL & & & \\ \hline Improvement from ARIMA to & & & \\ LSTM-3 LayerAL & & & \\ \hline Improvement from MLP to & & & \\ LSTM-3 LayerAL & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Forecasting performance comparison between proposed method and existing algorithms. This study selected five peak periods during a day (08:00, 10:00, 11:00, 17:30, and 18:00) to calculate the absolute error between the predicted and actual loads. Figure 10 illustrates that LSTM with shallow K-SVD inaccurately estimated the highest peak of electricity consumption throughout the day (08:00) with an error of 508 A, whereas the error of the proposed two-stage LSTM with 3-layer appliance load based on K-SVD remained below 90 A. Figure 10 shows that our novel estimation approach was more stable in nearly all peak periods, thereby establishing that the DUBPs acquired using edge deep K-SVD coding with appliance load improved the estimation accuracy of ultra-short term residential electricity demand. In order to verify the universality of the proposed method, this study selected five households with different load patterns and different consumption magnitude in REFIT to operate the experiment [34]. Sociodemographic information and other relevant information of each house is shown in Table 3. Experiment results are shown in Figure 11 and Table 3 and illustrated the proposed method can also achieve significant performance in all five houses.