Short Term Electric Power Load Forecasting Using Principal Component Analysis and Recurrent Neural Networks
Abstract
:1. Introduction
2. Methodology
2.1. Dimensionality Reduction Using Principal Component Analysis (PCA)
2.2. Recurrent Neural Network (RNN)
3. Result Analysis
3.1. Load Forecasting for HAM-(RHM-1)
3.2. Load Forecasting for HAM-(RHM-2)
3.3. Load Forecasting for DAM-(RDM-1)
3.4. Load Forecasting for DAM-(RDM-2)
3.5. Comparative Result Analysis
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
Load at hour | |
Load at one hour before from the time of prediction | |
Load at two hours before from the time of prediction | |
Load at three hours before from time of prediction | |
Load at one day before from the time of prediction | |
Load at two days before from the time of prediction | |
Load at three days before from time of prediction | |
Load at one week before from the time of prediction | |
Load at two weeks before from the time of prediction | |
Load at three weeks before from time of prediction | |
MSE | Mean Square Error |
MAE | Mean Absolute Error |
RMSE | Root Mean Square Error |
a | Hidden neuron current activation state |
a | Hidden neuron previous activation state |
Bias parameter for hidden layer | |
Bias parameter for output layer | |
Weight matrix between input and hidden layer | |
Weight matrix between output and hidden layer | |
DAM | Day ahead market |
HAM | Hourly ahead market |
RHM-1 | Recurrent Neural Network Model for Hourly Ahead Market |
RHM-2 | Light weight recurrent neural network Model for Hourly Ahead Market |
RDM-1 | Recurrent Neural Network Model for day ahead market |
RDM-2 | Light weight recurrent neural network Model for day ahead market |
Actual load from sample | |
Predicted load with sample |
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Reference | Year | Contribution | Disadvantage |
---|---|---|---|
[12] | 2021 | novel stacking ensemble-based algorithm | Model complexity |
[13] | 2021 | multi-temporal-spatial-scale technique | Missing Weekly impact |
[14] | 2021 | k-Medoid based algorithm | Model complexity |
[15] | 2021 | Markov-chain mixture distribution model | Accuracy |
[16] | 2021 | Fusion forecasting approach | Accuracy |
[17] | 2021 | Bi-directional GRU and LSTM | Model complexity |
[18] | 2021 | Deep Residual Network with convolution layer | Model complexity |
[19] | 2021 | Regression Models | Accuracy |
[20] | 2021 | LSTM and Factor Analysis | Accuracy |
[22] | 2020 | ANN | Accuracy |
Parameters | RHM-1 | RHM-2 | RDM-1 | RDM-2 |
---|---|---|---|---|
Input neurons () | 9 | 6 | 6 | 4 |
Output Neurons () | 1 | 1 | 1 | 1 |
Hidden Neurons () | 13 | 11 | 13 | 7 |
Hidden Layers | 1 | 1 | 1 | 1 |
Hidden Layer activation | Tanh | Tanh | Tanh | Tanh |
Output Layer activation | Sigmoid | Sigmoid | Sigmoid | Sigmoid |
Weights & bias | 313 | 210 | 274 | 92 |
Statistical Parameters | Output |
---|---|
Count | 1680.00 |
Mean | 5904.52 |
Std. | 1077.75 |
Min | 3377.92 |
25% | 5138.90 |
50% | 5795.62 |
75% | 6618.66 |
Max | 8841.67 |
Number of training samples | 1512 |
Number of testing samples | 168 |
Nodes | Training | Testing | Trainable | |
---|---|---|---|---|
MSE | RMSE | MAE | Param | |
21 | 0.0104 | 0.124 | 0.093 | 673 |
18 | 0.0103 | 0.120 | 0.088 | 523 |
15 | 0.0102 | 0.115 | 0.081 | 391 |
13 | 0.0101 | 0.115 | 0.08 | 313 |
11 | 0.0102 | 0.117 | 0.083 | 243 |
10 | 0.0104 | 0.117 | 0.083 | 211 |
No. of Hidden | Training | Testing | Trainable | ||
---|---|---|---|---|---|
Layers | Nodes | MSE | RMSE | MAE | Parameters |
1 | 13 | 0.01 | 0.115 | 0.08 | 313 |
2 | 13 | 0.01 | 0.124 | 0.094 | 664 |
3 | 13 | 0.01 | 0.131 | 0.1 | 1015 |
Statistical Parameters | Training | Testing | |
---|---|---|---|
MSE | RMSE | MAE | |
count | 10 | 10 | 10 |
mean | 0.0103 | 0.1168 | 0.0831 |
std | 0.000125 | 0.001751 | 0.003725 |
min | 0.0101 | 0.115 | 0.079 |
25% | 0.0103 | 0.11525 | 0.08 |
50% | 0.0103 | 0.1165 | 0.082 |
75% | 0.010375 | 0.11775 | 0.08575 |
max | 0.0105 | 0.12 | 0.09 |
PC-1 | PC-2 | PC-3 | PC-4 | PC-5 | PC-6 |
---|---|---|---|---|---|
1.15773 | −0.03658 | −0.15948 | 0.080498 | −0.03406 | −0.09375 |
1.206716 | 0.022011 | −0.06865 | 0.10224 | 0.020807 | −0.02302 |
1.317927 | 0.087764 | −0.15442 | 0.286619 | 0.173571 | 0.137578 |
1.474023 | 0.247519 | −0.14054 | 0.327771 | 0.017663 | 0.282082 |
1.585102 | 0.250539 | −0.10991 | 0.301018 | 0.04917 | 0.098137 |
1.528944 | 0.003412 | −0.09801 | 0.148669 | −0.02632 | 0.071544 |
1.675344 | −0.22242 | −0.34602 | 0.148969 | −0.08434 | 0.103249 |
1.571563 | −0.28011 | −0.51846 | 0.037141 | −0.23163 | 0.15251 |
1.335613 | −0.03608 | −0.48765 | 0.030066 | −0.05095 | 0.214678 |
1.035098 | 0.156347 | −0.3284 | 0.417524 | −0.17399 | 0.139219 |
Hidden Nodes | Training | Testing | Trainable Parameters | |
---|---|---|---|---|
MSE | RMSE | MAE | ||
9 | 0.0111 | 0.122 | 0.089 | 154 |
10 | 0.0114 | 0.119 | 0.086 | 181 |
11 | 0.0110 | 0.117 | 0.084 | 210 |
12 | 0.0111 | 0.121 | 0.088 | 241 |
13 | 0.0110 | 0.121 | 0.089 | 274 |
No. of Hidden | Training | Testing | Trainable Parameters | ||
---|---|---|---|---|---|
Layers | Nodes | MSE | RMSE | MAE | |
1 | 11 | 0.0110 | 0.117 | 0.084 | 210 |
2 | 11 | 0.0112 | 0.119 | 0.086 | 463 |
3 | 11 | 0.0113 | 0.12 | 0.088 | 716 |
4 | 11 | 0.0113 | 0.2 | 0.087 | 969 |
Statistical Parameters | Training | Testing | |
---|---|---|---|
MSE | RMSE | MAE | |
Count | 10 | 10 | 10 |
mean | 0.0112 | 0.1194 | 0.0861 |
std | 0.0001 | 0.0014 | 0.0018 |
min | 0.0110 | 0.1170 | 0.0840 |
25% | 0.0112 | 0.1190 | 0.0850 |
50% | 0.0112 | 0.1190 | 0.0860 |
75% | 0.0113 | 0.1208 | 0.0868 |
max | 0.0115 | 0.1210 | 0.0890 |
Model | Trainable Parameters | Testing | |
---|---|---|---|
RMSE | MAE | ||
RHM-1 | 313 | 0.115 | 0.080 |
RHM-2 | 210 | 0.117 | 0.084 |
% of absolute change | 32.91 | 1.7 | 5 |
Hidden Nodes | Training | Testing | Trainable Parameters | |
---|---|---|---|---|
MSE | RMSE | MAE | ||
18 | 0.0155 | 0.1510 | 0.1140 | 469 |
15 | 0.0155 | 0.1500 | 0.1100 | 346 |
13 | 0.0155 | 0.1420 | 0.1030 | 274 |
12 | 0.0155 | 0.1460 | 0.1090 | 241 |
11 | 0.0155 | 0.1480 | 0.1100 | 210 |
No. of Hidden | Training | Testing | Trainable Parameters | ||
---|---|---|---|---|---|
Layers | Nodes | MSE | RMSE | MAE | |
1 | 13 | 0.0155 | 0.142 | 0.103 | 274 |
2 | 13 | 0.0154 | 0.148 | 0.108 | 625 |
3 | 13 | 0.0156 | 0.148 | 0.109 | 976 |
Statistical Parameter | Training | Testing | |
---|---|---|---|
MSE | RMSE | MAE | |
Count | 10 | 10 | 10 |
mean | 0.0155 | 0.1475 | 0.1089 |
std | 0.0001 | 0.0040 | 0.0041 |
min | 0.0154 | 0.1420 | 0.1030 |
25% | 0.0154 | 0.1440 | 0.1065 |
50% | 0.0155 | 0.1475 | 0.1090 |
75% | 0.0156 | 0.1498 | 0.1100 |
max | 0.0157 | 0.1540 | 0.1160 |
Hidden Nodes | Training | Testing | Trainable Param | |
---|---|---|---|---|
MSE | RMSE | MAE | ||
5 | 0.0165 | 0.145 | 0.107 | 56 |
6 | 0.0164 | 0.144 | 0.107 | 73 |
7 | 0.0165 | 0.143 | 0.106 | 92 |
9 | 0.0167 | 0.145 | 0.107 | 136 |
11 | 0.0164 | 0.146 | 0.109 | 188 |
No. of Hidden | Training | Testing | Trainable Parameters | ||
---|---|---|---|---|---|
Layers | Nodes | MSE | RMSE | MAE | |
1 | 7 | 0.0165 | 0.143 | 0.106 | 92 |
2 | 7 | 0.0165 | 0.144 | 0.108 | 197 |
3 | 7 | 0.0166 | 0.150 | 0.114 | 302 |
Statistical Parameters | Training | Testing | |
---|---|---|---|
MSE | RMSE | MAE | |
count | 10 | 10 | 10 |
mean | 0.0165 | 0.1465 | 0.1092 |
std | 0.0002 | 0.0021 | 0.0029 |
min | 0.0163 | 0.1430 | 0.1050 |
25% | 0.0164 | 0.1448 | 0.1065 |
50% | 0.0165 | 0.1470 | 0.1095 |
75% | 0.0166 | 0.1480 | 0.1115 |
max | 0.0168 | 0.1490 | 0.1130 |
Model | Trainable Parameters | Testing | |
---|---|---|---|
RMSE | MAE | ||
RDM-1 | 274 | 0.142 | 0.103 |
RDM-2 | 92 5 | 0.143 | 0.105 |
% of absolute change | 66.42 | 0.7 | 1.9 |
Model | MSE | RMSE | ||
---|---|---|---|---|
Training | Testing | Training | Testing | |
ANN Model [29] | 0.29 | 1.59 | 0.54 | 1.26 |
ANN Model [30] | 0.23 | 0.44 | 0.48 | 0.66 |
ANN Model [22] | 0.2 | 0.32 | 0.45 | 0.57 |
SLR Model [19] | 0.0973 | 0.0163 | 0.312 | 0.128 |
PR Model [19] | 0.0171 | 0.0158 | 0.131 | 0.126 |
MLR Model [19] | 0.0723 | 0.0119 | 0.269 | 0.109 |
LSTM-HAM-Model1 [20] | 0.0109 | 0.013 | 0.104 | 0.114 |
LSTM-HAM-Model2 [20] | 0.0125 | 0.0146 | 0.112 | 0.121 |
LSTM-DAM-Model1 [20] | 0.0156 | 0.02 | 0.125 | 0.141 |
LSTM-DAM-Model2 [20] | 0.0166 | 0.02 | 0.129 | 0.1414 |
RHM-1 | 0.0101 | 0.0132 | 0.1 | 0.115 |
RHM-2 | 0.011 | 0.0138 | 0.105 | 0.117 |
RDM-1 | 0.0154 | 0.02 | 0.124 | 0.141 |
RDM-2 | 0.0163 | 0.0205 | 0.128 | 0.143 |
Parameter | [29] | [30] | [22] | RHM-1 | RHM-2 | RDM-1 | RDM-2 |
---|---|---|---|---|---|---|---|
Mean | 0.2975 | 0.2500 | 0.2250 | 0.0135 | 0.0143 | 0.0215 | 0.0215 |
SD | 0.0200 | 0.0100 | 0.0100 | 0.0002 | 0.0003 | 0.0010 | 0.0006 |
Min | 0.2800 | 0.2400 | 0.2000 | 0.0132 | 0.0138 | 0.0200 | 0.0205 |
25% | 0.2800 | 0.2475 | 0.2175 | 0.0133 | 0.0141 | 0.0208 | 0.0209 |
50% | 0.2950 | 0.2500 | 0.2200 | 0.0135 | 0.0143 | 0.0217 | 0.0216 |
75% | 0.3050 | 0.2525 | 0.2350 | 0.0136 | 0.0145 | 0.0221 | 0.0218 |
Max | 0.3300 | 0.2600 | 0.2500 | 0.0139 | 0.0147 | 0.0232 | 0.0223 |
Batch Size | RHM-1 | RHM-2 | RDM-1 | RDM-2 | No. of Back Propagations |
---|---|---|---|---|---|
1 | 624 | 1167 | 820 | 1182 | 151,200 |
8 | 131 | 148 | 106 | 153 | 18,900 |
16 | 74 | 82 | 50 | 85 | 9500 |
32 | 24 | 24 | 33 | 47 | 4800 |
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Veeramsetty, V.; Chandra, D.R.; Grimaccia, F.; Mussetta, M. Short Term Electric Power Load Forecasting Using Principal Component Analysis and Recurrent Neural Networks. Forecasting 2022, 4, 149-164. https://doi.org/10.3390/forecast4010008
Veeramsetty V, Chandra DR, Grimaccia F, Mussetta M. Short Term Electric Power Load Forecasting Using Principal Component Analysis and Recurrent Neural Networks. Forecasting. 2022; 4(1):149-164. https://doi.org/10.3390/forecast4010008
Chicago/Turabian StyleVeeramsetty, Venkataramana, Dongari Rakesh Chandra, Francesco Grimaccia, and Marco Mussetta. 2022. "Short Term Electric Power Load Forecasting Using Principal Component Analysis and Recurrent Neural Networks" Forecasting 4, no. 1: 149-164. https://doi.org/10.3390/forecast4010008