## 3 Results  
The evaluation of the approach has been executed on the data from 2017 and it includes all NYISO zones. Table 1 compiles the name, the abbreviation, and the average load for each zone. The power consumption is varying because the zones differ concerning the size of the area, the number of residents, and the type of housing (cities, villages, rural areas). New York City is the zone with the highest number of residents. The power consumption for that area is accordingly high. Mohawk Valley on the other side, has a relatively large area, a small number of residents and therefore a significantly smaller load [28]. The results obtained from the sequential encoder-stacked decoder with attention (SESDA) are evaluated together with the results of three other methods. First of them is the Hidden Markov Model approach from [29]. The Hidden Markov Models used there were created online using the data directly without any training procedure. Additionally, the results of the NYISO are taken into account [28; 32]. The third benchmark is a linear regression method from [3] and is named Tao's Vanilla Benchmark. It already has served as a benchmark for the GEFCom2012 load forecast competition and was under the first 25% best results of that competition [33]. The prediction error is measured by the Mean Absolute Percentage Error (MAPE) which is specified by Equation (20), with \(M\) as measured value and \(P\) as the predicted value. \[MAPE=\frac{100\%}{n}\sum_{i=1}^{n}\left|\frac{M_{t}-P_{t}}{M_{t}}\right| \tag{20}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Zone Name** & **Zone ID** & **Average Load [MW]** \\ \hline Capital & CAPITL & 1450 \\ Central & CENTRL & 1900 \\ Dunwoodie & DUNWOOD & 780 \\ Genes & GENESE & 1200 \\ Hudson Valley & HUD VL & 1200 \\ Long Island & LONGIL & 2500 \\ Millwood & MILL VD & 770 \\ Mohawk Valley & MHK VL & 980 \\ New York City & NYC & 6000 \\ North & NORTH & 590 \\ West & WEST & 1800 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: NYISO load zones. Figure 8 compiles the forecast error for 2017 delivered by all considered methods for each NYISO load zone. The attended sequential encoder-stacked decoder (SESDA) achieves the best results for all zones. It is, however, closely followed by the Hidden Markov Model with no training. The NYISO approach which combines regression with the usage of neural networks outperforms [PERSON]'s Vanilla Benchmark but seems to have some problems with the low load zone MHK VL. For this zone, all approaches deliver relatively high error which may be related to quite a wide area (15,230 square kilometers) and a small population of that zone. Figure 9 compares the daily MAPE for 2017 in New York City calculated using the two best approaches: SESDA and HMM. The SESDA approach returns a smaller error. The largest MAPE value for HMM is around 20% around 139 th day of the year. Generally, the highest HMM errors are concentrated between May and September. The highest attended sequential encoder-stacked decoder error is around 10%. It occurs on holidays, on 4 July 2017 and 25 December 2017. Moreover, the higher forecast error on average, the HMM approach delivers also more and higher error peaks on problematic days. Figure 10 compiles the results of SESDA and HMM evaluated for each day of 2017 in the load zone Mohawk Valley (MHK VL). The highest error delivered by the SESDA approach is around 10% and occurs on around the 165 and the 275 th day of the year. The HMM produces the highest error of around 20% also around 165. day of the year. On several days of the year, the MAPE returned by the HMM exceeds the 10% limit. The SESDA approach delivers therefore more stable results with significantly smaller error peaks. Figure 8: Evaluation of the 24 h ahead forecast error in 2017. Figure 9: Daily MAPE of a 24 h ahead forecast in NYC for 2017. Figure 11 shows forecast errors in New York City according to the hour of the day. For each hour the SESDA model outperforms the HMM reducing significantly the forecast errors.