# Short-Term Load Forecasting in Smart Grids: An Intelligent Modular Approach

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## 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

**Remark**

**1.**

**Remark**

**2.**

- (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 $p({h}_{1},{d}_{1})$.

**Remark**

**3.**

**Remark**

**4.**

- (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:$Accuracy(.)=100-\mathrm{MAPE}(.)$. We have measured this metric in %.
- Variance:$Var\left(i\right)=\frac{1}{m}{\sum}_{j=1}^{m}|{p}^{f}(i,j)-\overline{{p}^{a}(i,j)}|$. Where $\overline{{p}^{a}(i,j)}$ is the mean value of ${p}^{a}(i,j)$. 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 |

${T}_{DP}$ | Historical dew point temperature data matrix |

${T}_{DB}$ | Historical boiling point temperature data matrix |

${D}_{TYP}$ | Historical dew point temperature data matrix |

${p}_{{h}_{m},{d}_{n}}$ | Load value at mth hour of the nth day |

${p}_{max}^{{c}_{i}}$ | Local maxima for each column of P |

${P}_{nrm}$ | Locally normalized P |

${T}_{DP,nrm}$ | Locally normalized ${T}_{DP}$ |

${T}_{DB,nrm}$ | Locally normalized ${T}_{DB}$ |

$\mathrm{MI}(K,G)$ | Relative mutual information between input K and target G |

${p}_{r}(K,G)$ | Joint probability between K and G |

${p}_{r}\left(K\right)$ | Individual probability of K |

${S}_{f}$ | Selected features |

${S}_{T}$ | Training samples |

${S}_{V}$ | Validation samples |

$\mathrm{MAPE}$ | Mean absolute percentage error |

${p}^{a}$ | Actual load |

${p}^{f}$ | Forecasted load |

${I}_{th}$ | Irrelevancy threshold value |

${R}_{th}$ | Redundancy threshold value |

${y}_{i,j}^{{}^{\prime}t}$ | jth trial vector ${y}^{{}^{\prime}}$ for ith individual in generation t |

${x}_{i,j}^{t}$ | jth parent vector x for ith individual in generation t |

${u}_{i,j}^{t}$ | jth mutant vector u for ith individual in generation t |

${y}_{i,j}^{t}$ | jth offspring vector y for ith individual in generation t |

$rnd$ | Random number |

$F{F}_{N}(.)$ | Fitness function |

${E}_{F}$ | Forecast error |

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**Figure 6.**Relative performance of the proposed intelligent modular approach tested on historical data of DAYTOWN and EKPC grid: STLF results for 27 January 2015.

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 | $0.1$ |

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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## Share and Cite

**MDPI and ACS Style**

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

**AMA Style**

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 Style**

Ahmad, 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