Short-Term Load Forecasting in Smart Grids: An Intelligent Modular Approach
Abstract
:1. Introduction
- The proposed model takes into account external DALF influencing factors such as meteorological and exogenous variables.
- Due to better accuracy and less execution time, we have used MARA for training which none of the existing forecast models has used for training.
- To improve the forecast accuracy and minimize the execution of the forecast model, we have performed local training which none of the existing forecast models has used.
- We have used our modified version of the EDE in the error minimization module. The existing Bi-level strategy [28] has used EDE algorithm in the error minimization module.
- We have tested our proposed model on the datasets of two USA grids: DAYTOWN and EKPC. For evaluation and validation purposes, we have compared our proposed model with two existing forecast models (bi-level forecast and MI+ANN forecast) and provided extensive simulation results.
2. Related Work
2.1. Linear Models
2.2. Non-Linear Models
3. The Proposed Forecast Strategy
3.1. Pre-Processing Module
- (a)
- The ANN is trained by all elements of the matrix P except the first row.
- (b)
- The ANN is trained only by the 1st column of the matrix P except .
- (i)
- If the data set size is small (≤1 month), feature selection has no significant impact on the computational complexity of the overall strategy.
- (ii)
- If the data set size is moderate (≥1 month and ≤3 months), feature selection somehow affects the computational complexity of the overall strategy.
- (iii)
- If the data set size is large (≥3 months), feature selection has a significant impact on the computational complexity of the overall strategy.
3.2. Forecast Module
3.3. Optimization Module
4. Simulation Results
- Accuracy:. We have measured this metric in %.
- Variance:. Where is the mean value of . Monthly variance is calculated by using the same formula while considering the calculated daily variances.
- Execution time: During simulations, the time taken by the system to completely execute a given forecast strategy. The strategy for which execution time is small converges more quickly and vice versa. In simulations, we have measured execution time in seconds.
5. Conclusions and Future Work
Author Contributions
Funding
Conflicts of Interest
Nomenclature
SG | Smart grid |
DAL | Day-ahead load |
DALF | Day-ahead load forecast(ing) |
AN | Artificial neuron |
ANN | Artificial neural network |
MARA | Multivariate auto regressive algorithm |
ARMA | Auto regressive and moving average |
EDE | Enhanced differential evolution algorithm |
mEDE | Modified version of EDE algorithm |
NIST | National institute of standards and technology |
MSE | Minimum square error |
P | Historical load data matrix |
Historical dew point temperature data matrix | |
Historical boiling point temperature data matrix | |
Historical dew point temperature data matrix | |
Load value at mth hour of the nth day | |
Local maxima for each column of P | |
Locally normalized P | |
Locally normalized | |
Locally normalized | |
Relative mutual information between input K and target G | |
Joint probability between K and G | |
Individual probability of K | |
Selected features | |
Training samples | |
Validation samples | |
Mean absolute percentage error | |
Actual load | |
Forecasted load | |
Irrelevancy threshold value | |
Redundancy threshold value | |
jth trial vector for ith individual in generation t | |
jth parent vector x for ith individual in generation t | |
jth mutant vector u for ith individual in generation t | |
jth offspring vector y for ith individual in generation t | |
Random number | |
Fitness function | |
Forecast error |
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Forecast Class | Accuracy | Execution Time | Convergence Rate | Remarks |
---|---|---|---|---|
Support vector machine-based models [11,12,13] | Moderate | High | Slow | These models achieve relatively moderate accuracy, however, at the cost of high execution time (slow convergence rate) due to high complexity. |
Markov chain-based models [14,15,16] | Low | Low | Fast | Forecast accuracy of these models needs improvement. |
ANN-based models [27,28,39,40] | Low to moderate | Low to high | Fast to slow | Hybrid ANN-based models improve the forecast accuracy of ANN-based models, but at the cost of high execution time (slow convergence rate). |
Fuzzy ANN-based models [21,22,23,24,25,26] | Low to moderate | High | Slow | Execution time (convergence rate) need improvement. |
Stochastic distribution-based models [17,18,19,20] | Low | High | Slow | Both forecast accuracy, and execution time (convergence rate) need improvement. |
Parameter | Value |
---|---|
Forecasters | 24 |
Hidden layers | 1 |
Maximum iterations | 100 |
Neurons (in the hidden layer) | 5 |
Bias | 0 |
Initial weights | |
Momentum | 0 |
Load data (historical) | 1 year |
Maximum generations | 100 |
Day | Forecast Model | |||||
---|---|---|---|---|---|---|
MI+ANN | Bi-Level | MI+ANN+mEDE | ||||
MAPE | Variance | MAPE | Variance | MAPE | Variance | |
1 | 3.99 | 1.89 | 2.40 | 1.50 | 1.04 | 1.12 |
2 | 3.42 | 1.78 | 1.97 | 1.46 | 1.32 | 0.97 |
3 | 4.10 | 2.08 | 2.61 | 1.26 | 1.15 | 1.09 |
4 | 3.67 | 1.91 | 2.13 | 1.41 | 1.44 | 0.96 |
5 | 3.79 | 1.70 | 1.97 | 1.37 | 1.16 | 1.05 |
6 | 3.62 | 1.88 | 2.43 | 1.48 | 1.29 | 0.97 |
7 | 3.93 | 1.73 | 2.62 | 1.39 | 1.40 | 1.11 |
8 | 3.97 | 1.94 | 1.92 | 1.28 | 1.19 | 1.03 |
9 | 3.54 | 2.04 | 2.18 | 1.42 | 1.39 | 0.90 |
10 | 3.46 | 1.79 | 2.21 | 1.36 | 1.10 | 1.03 |
11 | 4.05 | 1.72 | 1.85 | 1.39 | 1.25 | 1.05 |
12 | 4.21 | 1.84 | 1.97 | 1.29 | 1.29 | 0.90 |
13 | 3.89 | 2.00 | 1.94 | 1.33 | 1.07 | 1.03 |
14 | 3.62 | 1.75 | 1.84 | 1.46 | 1.36 | 1.10 |
15 | 3.79 | 1.99 | 2.11 | 1.26 | 1.14 | 0.93 |
16 | 3.47 | 1.81 | 2.44 | 1.38 | 1.36 | 1.07 |
17 | 4.24 | 2.10 | 2.26 | 1.26 | 1.20 | 1.04 |
18 | 4.20 | 1.74 | 2.61 | 1.41 | 1.23 | 1.08 |
19 | 3.86 | 1.97 | 2.44 | 1.46 | 1.07 | 0.96 |
20 | 3.61 | 1.80 | 2.52 | 1.42 | 1.18 | 0.98 |
21 | 3.82 | 1.95 | 2.29 | 1.48 | 1.36 | 1.12 |
22 | 3.77 | 2.03 | 2.62 | 1.45 | 1.42 | 0.99 |
23 | 4.23 | 1.86 | 2.53 | 1.51 | 1.34 | 1.01 |
24 | 3.94 | 1.77 | 2.38 | 1.29 | 1.11 | 0.92 |
25 | 3.44 | 1.73 | 2.20 | 1.47 | 1.32 | 1.14 |
26 | 3.56 | 1.94 | 2.23 | 1.34 | 1.10 | 0.97 |
27 | 3.81 | 1.78 | 2.29 | 1.40 | 1.24 | 1.11 |
28 | 3.39 | 1.82 | 1.94 | 1.29 | 1.39 | 1.03 |
29 | 4.19 | 2.05 | 2.43 | 1.32 | 1.08 | 0.98 |
30 | 3.52 | 1.77 | 1.98 | 1.42 | 1.12 | 1.06 |
31 | 4.01 | 1.99 | 1.82 | 1.42 | 1.33 | 0.99 |
Average | 3.81 | 1.84 | 2.23 | 1.38 | 1.24 | 1.03 |
Month | Forecast Model | |||||
---|---|---|---|---|---|---|
MI+ANN | Bi-Level | MI+ANN+mEDE | ||||
MAPE | Variance | MAPE | Variance | MAPE | Variance | |
January | 3.81 | 1.84 | 2.23 | 1.38 | 1.24 | 1.03 |
February | 3.85 | 1.75 | 2.15 | 1.44 | 1.20 | 0.99 |
March | 4.76 | 1.90 | 2.26 | 1.39 | 1.26 | 1.05 |
April | 3.84 | 1.76 | 2.19 | 1.41 | 1.29 | 1.00 |
May | 3.80 | 1.71 | 1.20 | 1.47 | 1.23 | 1.02 |
June | 3.73 | 1.73 | 2.16 | 1.35 | 1.21 | 1.01 |
July | 3.72 | 1.81 | 2.29 | 1.40 | 1.24 | 1.07 |
August | 3.84 | 1.70 | 1.28 | 1.40 | 1.25 | 1.03 |
September | 3.82 | 2.90 | 2.22 | 1.33 | 1.20 | 0.99 |
October | 3.82 | 1.88 | 2.15 | 1.36 | 1.30 | 1.01 |
November | 4.77 | 1.75 | 1.17 | 1.48 | 1.22 | 1.06 |
December | 4.80 | 1.82 | 1.27 | 1.32 | 1.27 | 1.02 |
Average | 3.79 | 1.80 | 2.13 | 1.39 | 1.24 | 1.01 |
Day | Forecast Model | |||||
---|---|---|---|---|---|---|
MI+ANN | Bi-Level | MI+ANN+mEDE | ||||
MAPE | Variance | MAPE | Variance | MAPE | Variance | |
1 | 3.72 | 1.70 | 2.59 | 1.36 | 1.20 | 1.02 |
2 | 3.60 | 1.86 | 2.38 | 1.30 | 1.31 | 1.10 |
3 | 3.54 | 1.90 | 2.20 | 1.51 | 1.35 | 0.97 |
4 | 3.81 | 1.88 | 1.77 | 1.27 | 1.25 | 0.95 |
5 | 3.78 | 1.92 | 2.57 | 1.41 | 1.32 | 1.07 |
6 | 4.07 | 1.83 | 2.65 | 1.33 | 1.21 | 0.96 |
7 | 3.88 | 1.79 | 2.58 | 1.43 | 1.35 | 1.11 |
8 | 3.62 | 1.81 | 2.25 | 1.28 | 1.22 | 1.01 |
9 | 4.30 | 1.88 | 2.25 | 1.50 | 1.15 | 0.90 |
10 | 3.71 | 1.93 | 2.43 | 1.44 | 1.27 | 1.03 |
11 | 3.59 | 1.77 | 2.27 | 1.30 | 1.34 | 1.12 |
12 | 3.82 | 1.74 | 2.34 | 1.37 | 1.24 | 0.95 |
13 | 3.77 | 1.84 | 2.50 | 1.25 | 1.29 | 1.06 |
14 | 4.15 | 1.83 | 2.64 | 1.31 | 1.16 | 1.13 |
15 | 3.69 | 1.91 | 1.88 | 1.40 | 1.28 | 0.93 |
16 | 3.87 | 1.89 | 2.47 | 1.52 | 1.30 | 1.12 |
17 | 4.27 | 2.76 | 2.60 | 1.33 | 1.29 | 1.10 |
18 | 3.64 | 1.78 | 2.15 | 1.42 | 1.31 | 1.00 |
19 | 4.18 | 1.84 | 1.86 | 1.40 | 1.21 | 1.12 |
20 | 3.75 | 1.99 | 2.31 | 1.28 | 1.19 | 0.99 |
21 | 3.58 | 1.97 | 2.05 | 1.39 | 1.18 | 1.05 |
22 | 3.83 | 2.72 | 2.70 | 1.30 | 1.32 | 0.98 |
23 | 4.88 | 1.99 | 2.60 | 1.38 | 1.37 | 1.09 |
24 | 3.73 | 1.88 | 2.44 | 1.29 | 1.18 | 1.12 |
25 | 4.21 | 2.01 | 1.91 | 1.47 | 1.33 | 0.92 |
26 | 3.59 | 1.76 | 1.79 | 1.32 | 1.21 | 1.04 |
27 | 3.80 | 1.96 | 2.20 | 1.37 | 1.24 | 1.10 |
28 | 3.66 | 1.89 | 1.97 | 1.27 | 1.22 | 1.03 |
29 | 4.25 | 1.81 | 2.33 | 1.49 | 1.15 | 0.98 |
30 | 3.51 | 1.92 | 1.90 | 1.24 | 1.36 | 1.03 |
31 | 4.03 | 1.95 | 1.88 | 1.43 | 1.20 | 1.06 |
Average | 3.86 | 1.92 | 2.27 | 1.36 | 1.25 | 1.03 |
Month | Forecast Model | |||||
---|---|---|---|---|---|---|
MI+ANN | Bi-Level | MI+ANN+mEDE | ||||
MAPE | Variance | MAPE | Variance | MAPE | Variance | |
January | 3.86 | 1.92 | 3.27 | 1.36 | 1.25 | 1.03 |
February | 3.85 | 1.71 | 2.30 | 1.47 | 1.20 | 0.99 |
March | 3.80 | 1.75 | 2.20 | 1.44 | 1.22 | 1.05 |
April | 3.71 | 1.79 | 2.24 | 1.38 | 1.27 | 1.06 |
May | 3.79 | 1.87 | 2.28 | 1.40 | 1.22 | 1.02 |
June | 3.72 | 1.85 | 2.13 | 1.30 | 1.24 | 1.07 |
July | 3.76 | 1.76 | 2.22 | 1.36 | 1.28 | 0.99 |
August | 3.87 | 1.76 | 2.18 | 1.43 | 1.26 | 1.08 |
September | 3.70 | 2.70 | 2.29 | 1.38 | 1.23 | 1.02 |
October | 3.77 | 1.88 | 2.17 | 1.36 | 1.21 | 1.09 |
November | 3.83 | 1.83 | 2.27 | 1.50 | 1.27 | 1.00 |
December | 3.80 | 1.81 | 2.25 | 1.33 | 1.21 | 1.01 |
Average | 3.78 | 1.88 | 2.31 | 1.39 | 1.23 | 1.03 |
Dataset | Forecast Model | Iterations | Training | Testing | Validation |
---|---|---|---|---|---|
DAYTOWN | MI+ANN | 20 | 0.9626 | 0.9619 | 0.9556 |
Bi-Level | 94 | 0.9787 | 0.9799 | 0.9776 | |
MI+ANN+mEDE | 95 | 0.9876 | 0.9890 | 0.9872 | |
EKPC | MI+ANN | 23 | 0.9622 | 0.9617 | 0.9551 |
Bi-Level | 95 | 0.9769 | 0.9783 | 0.9766 | |
MI+ANN+mEDE | 96 | 0.9877 | 0.9892 | 0.9878 |
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Ahmad, A.; Javaid, N.; Mateen, A.; Awais, M.; Khan, Z.A. Short-Term Load Forecasting in Smart Grids: An Intelligent Modular Approach. Energies 2019, 12, 164. https://doi.org/10.3390/en12010164
Ahmad A, Javaid N, Mateen A, Awais M, Khan ZA. Short-Term Load Forecasting in Smart Grids: An Intelligent Modular Approach. Energies. 2019; 12(1):164. https://doi.org/10.3390/en12010164
Chicago/Turabian StyleAhmad, Ashfaq, Nadeem Javaid, Abdul Mateen, Muhammad Awais, and Zahoor Ali Khan. 2019. "Short-Term Load Forecasting in Smart Grids: An Intelligent Modular Approach" Energies 12, no. 1: 164. https://doi.org/10.3390/en12010164