Experimental Analysis of the Input Variables’ Relevance to Forecast Next Day’s Aggregated Electric Demand Using Neural Networks
Abstract
:1. Introduction
2. Data, Tools and Methodologies to Be Used in the Study
2.1. Dataset Employed
2.2. Methodology
2.2.1. Analysis of the Variables of Interest
- Past aggregated load: an autocorrelation analysis will be carried out to detect the influence of the previous days’ aggregated load on the next day’s demand.
- Climate variables: those variables that have a most significant influence on the aggregated load will be detected.
- r = +1: perfect positive linear correlation.
- 0.0 < |r| < 0.09: no correlation.
- 0.1 < |r| < 0.25: small linear correlation.
- 0.26 < |r| < 0.55: medium linear correlation.
- 0.56 < |r| < 1: strong linear correlation.
- r = 0: both variables are not linearly related.
- −1 < r < 0: negative linear correlation.
- r = −1: perfect negative linear correlation.
2.2.2. Forecasting Models Based on ANNs
- Mean Absolute Percentage Error (MAPE): this is the most widely used measure by the industry, and thus allows comparing the results with previous studies. MAPE error is defined as:
- Root Mean Square Error (RMSE): MAPE error lacks sensitivity for errors which are more than two standard deviations away from the mean. However, this kind of error, though uncommon, is of great importance for utilities. Obviously, the weight of big deviations is greater for a squared function than for the absolute value function, and therefore the former has been selected. RMSE error is defined as:
- Maximum Error (ME): this measure complements the previous two and evaluates the maximum difference between the forecasts and the real values. A single but very big deviation could have dramatic consequences for a production system. ME error is defined as:
3. Analysis of the Relevant Variables to Forecast the Aggregated Load
3.1. Autocorrelation of Aggregated Load
- Working days correlate with the day coming immediately before them and with the same day of the week for the previous three weeks.
- Similarly, non-working days correlate with the day coming immediately before them and with the same day of the week for the previous two weeks.
3.2. Climate Variables
All days | AL | MT | MRH | ASR | MWD | MWS | MP |
---|---|---|---|---|---|---|---|
AL | 1.00000 | −0.4508 | 0.3226 | −0.4239 | 0.25437 | 0.20064 | 0.02355 |
MT | −0.4508 | 1.00000 | −0.61656 | −0.09186 | −0.19514 | −0.23928 | 0.05872 |
MRH | 0.32157 | −0.61656 | 1.00000 | 0.27902 | 0.08449 | 0.24059 | −0.06951 |
ASR | −0.4239 | −0.09186 | 0.27902 | 1.00000 | 0.16316 | 0.01912 | 0.00309 |
MWD | 0.25437 | −0.19514 | 0.08449 | 0.16316 | 1.00000 | 0.32152 | −0.07974 |
MWS | 0.20064 | −0.23928 | 0.24059 | 0.01912 | 0.32152 | 1.00000 | −0.08816 |
MP | 0.02355 | 0.05872 | −0.06951 | 0.00309 | −0.07974 | −0.08816 | 1.00000 |
4. Models Proposed to Forecast the Aggregated Load
- Forecast with Aggregated Load (F_AL): as shown in Section 3.1, aggregated load is closely related to the previous day’s aggregated load, as well as to aggregated loads corresponding to the same day of the week for the previous three weeks, regardless of whether this is a working day or not, and this holds for all days of the week. With this in mind, in the F_AL model the chosen inputs are the aggregated load of the previous day, and the same days of the week, of the previous three weeks. This makes 4 inputs and 1 target.
- Forecast with Aggregated Load and Type of Day [working/non-working](F_AL_W): five new variables are added to the F_AL, indicating whether each of the days is a working day or not. They refer to the past days and the day for which the forecast is made. This makes nine inputs and one target.
- Forecast with Aggregated Load, Type of Day (working/non-working) and Day of the Week (F_AL_WD): 10 new variables are added to the F_AL_W, indicating the day of the week (Sunday = 0; Monday = 1; Friday = 5; Saturday = 6) in the sine and cosine forms. These refer to the past days and the day to be forecast. This makes 19 inputs and one target. As mentioned, for circular variables (days of the week, etc.), the use of two inputs for each variable (in its sine and cosine forms) has been shown to improve performance, since values are uniformly distributed between 0 and 2π, allowing the network to perceive periodic behavior more efficiently and reducing training time, as shown in Ramezani et al. [34] and in Razavi and Tolson [35].
- Forecast with Aggregated Load, Type of Day (working/non-working), Day of the Week and Mean Temperature (F_AL_W_DW_MT): In this model, five new variables are added to the F_AL_W_DW, representing the mean temperature of the past days and the day for which the forecast is made. This makes 24 inputs and one target.
- Forecast with Aggregated Load, Type of Day (working/non-working), Day of the Week and Relative Humidity (F_AL_W_DW_RH): In this model, five new variables are added to the F_AL_W_DW, representing the relative humidity of the past days and the day for which the forecast is made. This makes 24 inputs and one target.
- Forecast with Aggregated Load, Type of Day (working/non-working), Day of the Week and Solar Radiation (F_AL_W_DW_SR): In this model, five new variables are added to the F_AL_W_DW, representing the solar radiation of the past days and the day for which the forecast is made. This makes 24 inputs and one target.
- Forecast with Aggregated Load, Type of Day (working/non-working), Day of the Week (F_AL_W) and all Weather (F_AL_W_DW_allW): In this model, 15 new variables are added to the F_AL_W_DW, representing the mean temperature, relative humidity and solar radiation of the past days and the day for which the forecast is made. This makes 34 inputs and one target.
5. Results
traingd | traingdm | traingda | traingdx | trainrp | traincgf | traincgp | |||||||||||||||
(1) | (2) | (3) | (1) | (2) | (3) | (1) | (2) | (3) | (1) | (2) | (3) | (1) | (2) | (3) | (1) | (2) | (3) | (1) | (2) | (3) | |
F_AL | 1 | 27.84 | 9.13 | 1 | 27.99 | 8.70 | 13 | 8.39 | 0.96 | 1 | 27.07 | 8.67 | 7 | 6.90 | 0.46 | 11 | 6.81 | 0.37 | 13 | 6.98 | 0.53 |
F_AL_W | 5 | 40.87 | 18.85 | 5 | 39.26 | 18.59 | 6 | 7.09 | 1.64 | 5 | 42.20 | 19.12 | 7 | 5.34 | 0.42 | 15 | 5.26 | 0.42 | 12 | 5.37 | 0.51 |
F_AL_W_DW | 1 | 30.92 | 9.04 | 1 | 28.47 | 8.67 | 8 | 5.31 | 1.09 | 1 | 29.70 | 10.38 | 7 | 3.90 | 0.44 | 13 | 3.61 | 0.36 | 13 | 3.67 | 0.51 |
F_AL_W_DW_MT | 1 | 29.90 | 8.99 | 1 | 28.93 | 10.08 | 10 | 5.89 | 1.05 | 1 | 30.39 | 8.82 | 8 | 4.21 | 0.47 | 12 | 3.83 | 0.39 | 11 | 3.99 | 0.51 |
F_AL_W_DW_RH | 1 | 27.67 | 8.01 | 1 | 29.52 | 9.64 | 9 | 5.98 | 1.15 | 1 | 29.35 | 9.19 | 8 | 4.16 | 0.54 | 15 | 3.68 | 0.42 | 16 | 3.82 | 0.41 |
F_AL_W_DW_SR | 1 | 28.96 | 9.89 | 1 | 29.01 | 9.24 | 12 | 5.89 | 1.21 | 1 | 29.80 | 8.44 | 8 | 4.13 | 0.60 | 17 | 3.66 | 0.48 | 15 | 3.77 | 0.40 |
F_AL_W_DW_allW | 1 | 28.14 | 9.43 | 1 | 29.01 | 9.31 | 5 | 6.54 | 1.68 | 1 | 28.42 | 9.00 | 7 | 4.44 | 0.56 | 16 | 3.93 | 0.49 | 18 | 3.99 | 0.46 |
traincgb | trainscg | trainbfg | trainoss | trainlm | trainbr | ||||||||||||||||
(1) | (2) | (3) | (1) | (2) | (3) | (1) | (2) | (3) | (1) | (2) | (3) | (1) | (2) | (3) | (1) | (2) | (3) | ||||
F_AL | 13 | 6.85 | 0.36 | 13 | 6.96 | 0.43 | 10 | 6.98 | 0.37 | 15 | 7.04 | 0.45 | 13 | 7.06 | 1.36 | 11 | 6.37 | 0.22 | |||
F_AL_W | 18 | 5.31 | 0.51 | 15 | 5.43 | 0.52 | 8 | 5.49 | 0.35 | 15 | 5.54 | 0.51 | 19 | 5.33 | 0.84 | 7 | 4.44 | 0.15 | |||
F_AL_W_DW | 16 | 3.66 | 0.43 | 13 | 3.72 | 0.57 | 10 | 4.06 | 0.34 | 12 | 3.79 | 0.46 | 18 | 3.96 | 0.85 | 4 | 3.13 | 0.17 | |||
F_AL_W_DW_MT | 14 | 3.95 | 0.48 | 14 | 3.96 | 0.56 | 8 | 4.42 | 0.49 | 11 | 4.21 | 0.68 | 15 | 4.53 | 0.79 | 3 | 3.26 | 0.18 | |||
F_AL_W_DW_RH | 15 | 3.85 | 0.41 | 15 | 3.84 | 0.51 | 8 | 4.35 | 0.45 | 8 | 4.01 | 0.64 | 14 | 4.52 | 1.45 | 3 | 3.12 | 0.17 | |||
F_AL_W_DW_SR | 16 | 3.73 | 0.47 | 18 | 3.79 | 0.58 | 9 | 4.43 | 0.64 | 8 | 4.05 | 0.62 | 15 | 4.46 | 1.64 | 4 | 2.98 | 0.15 | |||
F_AL_W_DW_allW | 15 | 4.02 | 0.40 | 14 | 4.05 | 0.48 | 10 | 4.64 | 0.51 | 9 | 4.29 | 0.64 | 17 | 4.94 | 1.29 | 3 | 3.18 | 0.19 |
- Non-working days that fall on weekdays, as well as some days that immediately follow them. Since no additional information is available for the different patterns, the network did not take into account whether the day was a working day. The period between 23 June and 28 June, which corresponds to the local festivals. Except for Thursday 24, and Sunday 27, which are non-working days, the rest of the days within the period are working days, but in practice they are similar to non-working days. As previously, this information is not available for the network.
- A high number of Saturdays show an error between 15% and 25%. This can be explained considering that Saturdays are working days (the network forecasts a high aggregated load value), but in fact aggregated load is lower than on the Monday-Friday period. From the previous analysis, the need for the model to know whether the days are working days becomes clear. Therefore, the F_AL_W model uses this variable as an input, for the past days and the forecast day. As it can be observed in Figure 6, the model still fails during the local festivals’ week, as well as on Saturdays. However, the error for non-working days is lower than the mean in all cases, i.e., adding the new variable (working/non-working) as an input improves the forecast.
6. Conclusions and Future Work
Acknowledgements
Conflict of Interest
References
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Hernández, L.; Baladrón, C.; Aguiar, J.M.; Calavia, L.; Carro, B.; Sánchez-Esguevillas, A.; García, P.; Lloret, J. Experimental Analysis of the Input Variables’ Relevance to Forecast Next Day’s Aggregated Electric Demand Using Neural Networks. Energies 2013, 6, 2927-2948. https://doi.org/10.3390/en6062927
Hernández L, Baladrón C, Aguiar JM, Calavia L, Carro B, Sánchez-Esguevillas A, García P, Lloret J. Experimental Analysis of the Input Variables’ Relevance to Forecast Next Day’s Aggregated Electric Demand Using Neural Networks. Energies. 2013; 6(6):2927-2948. https://doi.org/10.3390/en6062927
Chicago/Turabian StyleHernández, Luis, Carlos Baladrón, Javier M. Aguiar, Lorena Calavia, Belén Carro, Antonio Sánchez-Esguevillas, Pablo García, and Jaime Lloret. 2013. "Experimental Analysis of the Input Variables’ Relevance to Forecast Next Day’s Aggregated Electric Demand Using Neural Networks" Energies 6, no. 6: 2927-2948. https://doi.org/10.3390/en6062927