# A Hybrid Model for Electricity Demand Forecast Using Improved Ensemble Empirical Mode Decomposition and Recurrent Neural Networks with ERA5 Climate Variables

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## Abstract

**:**

^{2}). The hybrid models perform exceptionally well in predicting electricity demand, and the ICEEMDAN-NARX hybrid model with correlated climate variables performs the best among the tested experiments as a useful prediction tool.

## 1. Introduction

_{2}emissions for the global power market as a whole. While many meteorological and socioeconomic aspects (demographic, GDP, economic activity, habitation, family composition, average earnings, etc.) could influence electricity usage, well-prepared electrical demand planning is vital for ensuring the reliability and sustainability of the energy supply [1,2].

_{2}mitigation from 2015 to 2050. Moreover, various scenarios were developed for the future injection of renewable energy and emission savings for future generation planning. San et al. [31] used a quantitative model to examine the impacts of rural household energy consumption on the economy and environment. The authors showed that economic and environmental costs for residents would be lower when biogas was introduced to replace nonconventional energy sources (fuelwood, plant waste, kerosene, and liquefied petroleum gas (LPG)). Hak et al. [32] designed qualitative and quantitative models using the Extended Snapshot (ExSS) tool for sustainable energy policy development in Cambodia and proposed five strategies for producing environmentally friendly plans for development towards 2050 that could reduce CO

_{2}emissions by approximately 55% and 57% by 2030 and 2050, respectively. Promsen et al. [33] studied wind energy potential using Wind Atlas Analysis and Application Program (WAsP) software to estimate the installed capacity of wind energy potential in southern Cambodia. All energy-related reviews in Cambodia focused on energy policy, emission mitigation, renewable energy, and economic and environmental impact assessments for household energy consumption.

## 2. Materials

#### 2.1. Study Area

#### 2.2. Data

#### 2.2.1. Electricity Demand

#### 2.2.2. ERA5 Climate Reanalysis

## 3. Methodology

#### 3.1. Data Preprocessing

#### 3.1.1. Imputation of Missing Values

#### 3.1.2. Normalization of the Input Data

#### 3.2. Decomposition Techniques

#### 3.2.1. Empirical Mode Decomposition (EMD)

_{0}= x.

_{k}to obtain the lower (upper) envelope e

_{min}(e

_{max}).

_{min}+ e

_{max})/2.

_{k+1}= r

_{k}− m.

_{k+1}an IMF?

_{k+1}, compute the residue ${r}_{k+1}=x-{\displaystyle \sum}_{i=1}^{k}{d}_{i}$, iterate k = k + 1, and treat r

_{k}as input data in step 2.

_{k+1}as input data in step 2.

_{k}satisfies some predefined stopping criterion.

#### 3.2.2. Ensemble Empirical Mode Decomposition (EEMD)

^{(i)}= x + $\beta $w

^{(i)}, where w

^{(i)}(i = 1,…,I) presents various realizations of white noise with zero mean and unit variance, and I is the value of realizations in the ensemble and the magnitude of added noise $\beta $ > 0.

^{(i)}(i = 1,…,I) entirely by EMD, acquiring the modes ${d}_{k}^{\left(i\right)}$, where k = 1, …, K presents the mode index.

^{(i)}can be decomposed independently of other realizations, and for every realization, a residue ${r}_{k}^{\left(i\right)}={r}_{k-1}^{\left(i\right)}-{d}_{k}^{\left(i\right)}$ is acquired at each stage, without any connections between the various realizations. Due to this situation, some EEMD downsides may occur, including (i) an incomplete decomposition and (ii) the possibility that different realizations of signals plus noise may produce varying amounts of modes, especially at low frequencies.

#### 3.2.3. Complete EEMD with Adaptive Noise (CEEMDAN)

^{(i)}is produced from x, and the initial mode ${\tilde{d}}_{1}={\overline{d}}_{1}$ is calculated precisely as in EEMD. Then, a unique first residue is acquired independent of the noise realization:

_{1}values plus various realizations of a particular noise. The second mode ${\tilde{d}}_{2}$ is defined as the average of these modes. The next residue is ${r}_{2}={r}_{1}-{\tilde{d}}_{2}$. This technique is repeated until a termination requirement is met.

_{k}(·) be the operator that generates the kth mode obtained by EMD, and let w

^{(i)}be a realization of white noise with zero average and unit variance. Then, the following method is employed:

_{k}(·), and let M(·) be the operator that produces the local mean of the signal to which it is applied. It can be noticed that E

_{1}(x) = x − M(x). Let w

^{(i)}be a realization of white Gaussian noise, x

^{(i)}= x + w

^{(i)}, and 〈·〉 be the action of mean throughout the realizations. For the first EEMD and original CEEMDAN modes, we have:

#### 3.2.4. Improved CEEMDAN

#### 3.3. RNN

#### 3.3.1. NAR Architecture

- (1)
- Feedback delay (FD): The autocorrelation of the training dataset was utilized to identify the FDs, and all significant values were employed as FDs in the model. $\left(FD=\left[1:397,475:527,660:1271,1304:1332\right]\right)$ (Figure 3).
- (2)
- Hidden layers: The number of hidden layer neurons was defined individually each time, for example, 10 neurons [48] and 15 neurons [12], ranging between 3 and 10 [49] and between 1 and 20 [50]. Therefore, the trial-and-error procedure was applied to investigate the number of hidden layer neurons by ranging it from 1 to 20.
- (3)
- Transfer function: Since FDs were utilized in a variety of values, the training time performance is technically the model’s constraint. Therefore, to lessen the need for both memory and time during training, Kumar and Murugan [51] proposed using scaled conjugate gradient-based back-propagation (trainscg) for this model.
- (4)
- Activation function: Sarkar et al. [52] and Vogl et al. [53] stated that the hyperbolic tangent-sigmoidal (tansig) transfer function Equation (18) could provide better results based on an error evaluation during the training process, and this function was accordingly considered as the activation function for the hidden layer and linear function (purelin) (Equation (19)) in the output layer in this study.
- (5)
- Weights and bias: The trial-and-error method employed a double loop for each number of hidden layer neurons, leading to 200 tests with randomly determined beginning weights and biases ranging from 1 to 10.

#### 3.3.2. NARX Architecture

- Step 1.
- Examine the input (climate variables) and target (power demand) from the extracted files, normalize or preprocess these raw data, and convert the data file from an hourly to daily dataset by extracting data at 10:00 a.m. (the peak hour) to represent the daily data.
- Step 2.
- Define the correlated climate variables using a cross-correlation function between the input (each climate variable) and the target (power demand). Set the bounds for eliminating the variables with low correlations and set the correlation coefficient of lag from 0 to 2 as the ID.
- Step 3.
- For random weight generation, use MAX_TRIAL and MAX_HIDDEN_NEURON to set the maximum number of trials and the maximum number of neurons, respectively, in the hidden layer.
- Step 4.
- Calculate the significant lags using the autocorrelation function and define the number of significant lags as the FD for the network.
- Step 5.
- For the first loop, starting from HIDDEN_NEURON = 1 to MAX_HIDDEN_NEURON = 20.
- Step 6.
- For the second loop, starting from TRIAL = 1 to MAX_TRIAL = 10.
- Step 7.
- Construct an NARX neural network algorithms; specify the input and target vectors, setting up number of hidden layers, training function (trainscg), and the transfer function used in the hidden (tansig) and output (purelin) layers.
- Step 8.
- Divide the dataset in half. First, there is a section for TRAINING, and then, there is a section for MULTISTEP TESTING. In the Section 1, the dataset is divided into training (75 percent), validation (15 percent), and testing (15 percent) datasets using the divideint function. The multistep testing period is utilized to validate the derived prediction in the Section 2.
- Step 9.
- Prepare the data using the preparet function with the input and target of the training period.
- Step 10.
- Train the open-loop neural network using the training function.
- Step 11.
- Simulate the closed-loop neural network using the closeloop function, then use the preparets function to prepare the closed-loop system with closed-loop parameters and execute it with the train function. By using the trained closed-loop network, multistep prediction is simulated with the second part of the dataset.
- Step 12.
- Denormalize or postprocess the simulated output data of the open-loop and closed-loop neural networks. Then, calculate the performance indices of the open-loop (normalized root mean square error (NMSE), ${R}_{o}^{2}$, mean absolute error (MAEo), mean absolute percentage error (MAPEo), and root mean square error (RMSEo)), closed-loop (NMSEc, ${R}_{c}^{2}$, MAEc, MAPEc, and RMSEc), and multistep prediction networks (NMSEp, ${R}_{p}^{2}$, MAEp, MAPEp, and RMSEp).
- Step 13.
- Record the results of the open-loop, closed-loop, and multistep prediction neural networks (the neuron size, number of trials, and performance indices in step 12) if the calculated performance indices are lower than those in the previous iteration. Skip this step otherwise.
- Step 14.
- END\\TRIAL
- Step 15.
- END\\HIDDEN_NEURON
- Step 16.
- From step 13, select the optimum NARX model.
- Step 17.
- Use the optimized NARX model for prediction.

#### 3.4. Hybrid Model

#### 3.4.1. Data Decomposition

#### 3.4.2. Experiments

^{®}2020a with Neural Network Toolbox™.

#### 3.5. Performance Evaluation

## 4. Results

#### 4.1. Climate Variables

#### 4.2. Decomposition Result

#### 4.3. Stand-Alone Models

#### 4.4. Hybrid Models

## 5. Discussion

#### 5.1. Sensitivity to the Number of Climate Variables

^{2}= 0.830, MAE = 3.814 MW, RMSE = 4.897 MW, and MAPE = 0.354) compared with the stand-alone NARX model with six high-correlation climate variables at the GS1 site (NMSE = 1.343, ${R}^{2}$ = 0.902, MAE = 2.228 MW, RMSE = 3.713 MW, and MAPE = 0.432), and the evaluation indices of thirty four climate variables of hybrid ICEEMDAN-NARX (NMSE = 0.062, ${R}^{2}$ = 0.937, MAE = 2.225 MW, RMSE = 2.967 MW, and MAPE = 0.302) underperformed compared to the six climate variables of hybrid ICEEMDAN-NARX (NMSE = 0.048, ${R}^{2}$ = 0.952, MAE = 1.923 MW, RMSE = 2.605 MW, and MAPE = 0.302), as shown in Table 5. Due to this experiment, the combination of low- and high-correlation climate variables probably prevented the improvement of the prediction models. Therefore, defining the bounds for highly correlated variable selection is the ideal solution that leads to outstanding prediction performance.

#### 5.2. Sensitivity to the Key Parameters in RNNs

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AC | All correlated |

ADB | Asian Development Bank |

AFD | Adaptive Fourier decomposition |

ANN | Artificial neural network |

ARIMA | Autoregressive integrated moving average |

BPNN | Back-propagation-based neural network |

CEEMDAN | Complete ensemble empirical mode decomposition with adaptive noise |

CNN | Convolution neural network |

CO_{2} | Carbon dioxide |

EAC | Electricity Authority of Cambodia |

ECMWF | European Center for Medium-Range Weather Forecast |

EDC | Electricité du Cambodge |

EEMD | Ensemble empirical mode decomposition |

EMD | Empirical mode decomposition |

ExSS | Extended snapshot |

FFNN | Feed-forward neural network |

GDP | Gross domestic production |

GS | Grid substation |

HC | Highly correlated |

HFO | Heavy fuel oil |

HFT | Hidden transfer function |

HHO | Harris hawks optimization |

ICEEMDAN | Improved complete ensemble empirical mode decomposition with adaptive noise |

IMF | Intrinsic mode function |

LEAP | Long-range alternatives energy planning |

LPG | Liquefied petroleum gas |

LRF | Linear recurrent formula |

LSSVM | Least-square-support vector machine |

LSTM | Long–short-term memory network |

MAE | Mean absolute error |

MAPE | Mean absolute percentage error |

MARS | Multivariate adaptive regression spline |

ML | Machine learning |

MLR | Multiple linear regression |

NAR | Nonlinear autoregressive neural network |

NARX | Nonlinear autoregressive neural network with exogenous inputs |

NMSE | Normalized mean square error |

OFT | Output transfer function |

PDP | Power development plan |

PSO | Particle swarm optimization |

RMSE | Root-mean square error |

RNN | Recurrent neural network |

SCADA | Supervisory control and data acquisition |

SDGs | Sustainable development goals |

SSA | Singular spectrum analysis |

SVR | Support vector regression |

SWPT | Stationary wavelet packet transform decomposition |

TCN | Temporal convolutional network |

VMD | Variational mode decomposition |

WAsP | Wind Atlas Analysis and Application Program |

WPP | West Phnom Penh grid substation |

## Appendix A. ERA5 Climate Variables

**Figure A1.**For the GS1 site, the outcomes of cross-correlation coefficient (daily) between electricity demand and climate variables from the ECMWF-ERA5 reanalysis dataset. The climate variables were selected based on their 95% confidence intervals and are demonstrated by the blue lines. The six chosen blue variables were based on the number of significant daily lags (from 0 to 2) and the number of decomposed power demand outputs. The details are described in Table A1.

Data Description | No. | Main Climate Variables | Acronym | Daily Dataset |
---|---|---|---|---|

Mean (1 January 2013) | ||||

ERA5 climatereanalysis | 1 | Boundary layer dissipation $({\mathrm{J}\mathrm{m}}^{-2})$ | BLD | 4303.75 |

2 | Boundary layer height $(\mathrm{m})$ | BLH | 563.93 | |

3 | Convective available potential energy $({\mathrm{J}\mathrm{kg}}^{-1})$ | CAPE | 0.04 | |

4 | $\mathrm{Charnock}(~)$ | CHNK | 0.02 | |

5 | Convective precipitation $(\mathrm{m})$ | CP | 0.00 | |

6 | 2-metre dewpoint temperature $(\mathrm{K})$ | D | 292.15 | |

7 | Evaporation $(\mathrm{m}\mathrm{of}\mathrm{water}\mathrm{equivalent})$ | E | 0.00 | |

8 | Eastward turbulent surface stress $({\mathrm{N}\mathrm{m}}^{-2}\mathrm{s})$ | EWSS | −109.38 | |

9 | Forecast albedo $(0-1)$ | FAL | 0.16 | |

10 | 10-metre wind gusts since previous postprocessing $({\mathrm{m}\mathrm{s}}^{-1})$ | FG10 | 6.12 | |

11 | Forecast logarithm of surface roughness for heat $(~)$ | FLSR | −3.84 | |

12 | Forecast surface roughness $(\mathrm{m})$ | FSR | 0.47 | |

13 | High cloud cover $(0-1)$ | HCC | 0.87 | |

14 | Instantaneous moisture flux $({\mathrm{kg}\mathrm{m}}^{-2}{\mathrm{s}}^{-1})$ | IE | 0.00 | |

15 | Instantaneous eastward turbulent surface stress $({\mathrm{N}\mathrm{m}}^{-2})$ | IEWS | −0.04 | |

16 | Instantaneous northward turbulent surface stress $({\mathrm{N}\mathrm{m}}^{-2})$ | INSS | −0.15 | |

17 | Instantaneous surface sensible heat flux $({\mathrm{W}\mathrm{m}}^{-2})$ | ISHF | −52.10 | |

18 | Low cloud cover $((0-1))$ | LCC | 0.17 | |

19 | Large-scale precipitation fraction $(\mathrm{s})$ | LSPF | 0.00 | |

20 | $\mathrm{Medium}\mathrm{cloud}\mathrm{cover}((0-1))$ | MCC | 0.06 | |

21 | Mean sea level pressure $(\mathrm{Pa})$ | MSL | 101,139.75 | |

22 | Northward turbulent surface stress $({\mathrm{N}\mathrm{m}}^{-2}\mathrm{s})$ | NSSS | −528.31 | |

23 | Vertical integral of potential, internal, and latent energy $({\mathrm{J}\mathrm{m}}^{-2})$ | P62.162 | 2,780,152,438.89 | |

24 | Vertical integral of total energy $({\mathrm{J}\mathrm{m}}^{-2})$ | P63.162 | 2,780,456,503.09 | |

25 | Vertical integral of eastward kinetic energy flux $({\mathrm{W}\mathrm{m}}^{-1})$ | P67.162 | −1,832,177.66 | |

26 | Vertical integral of eastward geopotential flux $({\mathrm{W}\mathrm{m}}^{-1})$ | P73.162 | −2,982,667,364.29 | |

27 | Vertical integral of northward geopotential flux$({\mathrm{W}\mathrm{m}}^{-1})$ | P74.162 | 2,069,308,190.16 | |

28 | Vertical integral of eastward total energy flux $({\mathrm{W}\mathrm{m}}^{-1})$ | P75.162 | −14,986,239,992.45 | |

29 | Vertical integral of eastward ozone flux $({\mathrm{kg}\mathrm{m}}^{-1}{\mathrm{s}}^{-1})$ | P77.162 | 0.02 | |

30 | $\mathrm{Runoff}(\mathrm{m})$ | RO | 0.00 | |

31 | Skin temperature $(\mathrm{K})$ | SKT | 300.50 | |

32 | Surface latent heat flux $({\mathrm{J}\mathrm{m}}^{-2})$ | SLHF | −286,915.24 | |

33 | $\mathrm{Surface}\mathrm{pressure}(\mathrm{Pa})$ | SP | 100,833.20 | |

34 | Skin reservoir content (m of water equivalent) | SRC | 0.00 | |

35 | Surface sensible heat flux $({\mathrm{J}\mathrm{m}}^{-2})$ | SSHF | −186,000.54 | |

36 | Surface net solar radiation $({\mathrm{J}\mathrm{m}}^{-2})$ | SSR | 692,607.54 | |

37 | Surface net solar radiation, clear sky $({\mathrm{J}\mathrm{m}}^{-2})$ | SSRC | 721,085.09 | |

38 | Surface net solar radiation, downwards $({\mathrm{J}\mathrm{m}}^{-2})$ | SSRD | 818,633.89 | |

39 | Soil temperature level 1$(\mathrm{K})$ | STL1 | 301.93 | |

40 | Soil temperature level 2$(\mathrm{K})$ | STL2 | 301.76 | |

41 | Soil temperature level 3$(\mathrm{K})$ | STL3 | 302.18 | |

42 | Soil temperature level 4$(\mathrm{K})$ | STL4 | 301.95 | |

43 | Surface net thermal radiation $({\mathrm{J}\mathrm{m}}^{-2})$ | STR | −222,398.82 | |

44 | Surface net thermal radiation, clear sky $({\mathrm{J}\mathrm{m}}^{-2})$ | STRC | −254,379.87 | |

45 | Surface thermal radiation, downwards $({\mathrm{J}\mathrm{m}}^{-2})$ | STRD | 1,435,890.80 | |

46 | Volumetric soil water layer 1$({\mathrm{m}}^{3}{\mathrm{m}}^{-3})$ | SWVL1 | 0.21 | |

47 | Volumetric soil water layer 2 $({\mathrm{m}}^{3}{\mathrm{m}}^{-3})$ | SWVL2 | 0.22 | |

48 | Volumetric soil water layer 3 $({\mathrm{m}}^{3}{\mathrm{m}}^{-3})$ | SWVL3 | 0.29 | |

49 | Volumetric soil water layer 4 $({\mathrm{m}}^{3}{\mathrm{m}}^{-3})$ | SWVL4 | 0.29 | |

50 | $2\text{-}\mathrm{metre}\mathrm{temperature}(\mathrm{K})$ | T2 M | 300.33 | |

51 | Total cloud cover $(0-1)$ | TCC | 0.88 | |

52 | Total column cloud liquid water $({\mathrm{kg}\mathrm{m}}^{-2})$ | TCLW | 0.02 | |

53 | $\mathrm{Total}\mathrm{column}\mathrm{ozone}({\mathrm{kg}\mathrm{m}}^{-2})$ | TCO3 | 0.00 | |

54 | Total column cloud ice water $({\mathrm{kg}\mathrm{m}}^{-2})$ | TCIW | 0.00 | |

55 | Total column water $({\mathrm{kg}\mathrm{m}}^{-2})$ | TCW | 37.75 | |

56 | $\mathrm{Total}\mathrm{column}\mathrm{water}\mathrm{vapor}({\mathrm{kg}\mathrm{m}}^{-2})$ | TCWV | 37.71 | |

57 | TOA incident solar radiation $({\mathrm{J}\mathrm{m}}^{-2})$ | TISR | 1,260,279.10 | |

58 | Total precipitation $(\mathrm{m})$ | TP | 0.00 | |

59 | Temperature of snow layer $(\mathrm{K})$ | TSN | 273.05 | |

60 | Top net solar radiation $({\mathrm{J}\mathrm{m}}^{-2})$ | TSR | 1,009,476.83 | |

61 | Top net solar radiation, clear sky $({\mathrm{J}\mathrm{m}}^{-2})$ | TSRC | 1,043,013.34 | |

62 | Top net thermal radiation $({\mathrm{J}\mathrm{m}}^{-2})$ | TTR | −863,546.10 | |

63 | Top net thermal radiation, clear sky $({\mathrm{J}\mathrm{m}}^{-2})$ | TTRC | −1,037,561.45 | |

64 | 10-metre U wind component $({\mathrm{m}\mathrm{s}}^{-1})$ | U10 | −0.48 | |

65 | Downward U.V. radiation at the surface $({\mathrm{J}\mathrm{m}}^{-2})$ | UVB | 95,201.23 | |

66 | 10-metre V wind component $({\mathrm{m}\mathrm{s}}^{-1})$ | V10 | −2.65 |

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**Figure 1.**Map of the study areas in Cambodia with the locations of grid substations (GSs) and the nearest grid points of the ECMWF-ERA5 reanalysis to the GSs in blue-shaded circles.

**Figure 2.**(

**a**) The original hourly power demand dataset at the GS1 site and (

**b**) the converted daily power demand dataset from the hourly demand.

**Figure 3.**Autocorrelation function result for the power demand. These significant points (red circles) were used as the FDs in the model development process.

**Figure 4.**Structures of the NARX and NAR models. The NAR and NARX models have basically the same structure, but the NAR model has no exogenous inputs.

**Figure 6.**Six climate variables from ERA5 reanalysis were selected by using the cross-correlation function. The upper and lower bounds (blue lines) of the confidence interval were set between −0.23 and 0.23. The chosen variables needed to have 3 (0:2) cross-correlation coefficients that were higher or lower than the bounds.

**Figure 7.**Decomposition results of the daily power demand using the ICEEMDAN method at the GS1 site with nine IMFs and the residue. The dark blue color, brown color, dark yellow color, dull violet color, green color, deep blue color, red color, navy color, tawny brown color, gold color, and purple color represent the characteristic of IMF1, IMF2, IMF3, IMF4, IMF5, IMF6, IMF7, IMF8, IMF9, residue, and actual data (daily power demand), respectively.

**Figure 8.**Prediction results over the model comparison period obtained using the stand-alone NAR and stand-alone NARX models for the GS1 site.

**Figure 9.**Prediction results of the power demand at GS1 using (

**a**) the hybrid ICEEMDAN−NAR and (

**b**) the hybrid ICEEMDAN−NARX models. The prediction results of each IMF are also presented, and the prediction results of the stand-alone models are shown for comparison.

**Figure 10.**Comparison of the predicted power demands among the stand−alone and hybrid models over the model comparison period with the power demand record at the GS1 site.

**Table 1.**Power demand information of the substations considered in this study and the nearest grid point information of ECMWF-ERA5 reanalysis with spatial and temporal resolutions.

Substation Name | Power Demand | ERA5 Reanalysis | ||||||
---|---|---|---|---|---|---|---|---|

Latitude | Longitude | Peak | Mean | Latitude | Longitude | Temporal Resolution | Horizontal Resolution | |

GS1 | 11.58989 | 104.91545 | 158.20 | 81.93 | 11.60 | 104.90 | Hourly | 0.1° × 0.1° Native resolution is 9 km |

GS2 | 11.52899 | 104.92944 | 167.10 | 91.13 | 11.60 | 104.90 | ||

GS3 | 11.55495 | 104.88438 | 145.20 | 76.25 | 11.60 | 104.90 | ||

WPP | 11.39941 | 104.77168 | 199.00 | 51.94 | 11.40 | 104.80 |

Rank | Description | Performance Ratting |
---|---|---|

1 | R^{2} ≥ 0.80 | Excellent |

2 | 0.70 < R^{2} < 0.60 | Good |

3 | 0.60 < R^{2} < 0.50 | Satisfactory |

4 | R^{2} ≤ 0.50 | Not satisfactory |

Model | NMSE | ${\mathbf{R}}^{2}$ | MAE (MW) | RMSE (MW) | MAPE (%) |
---|---|---|---|---|---|

Stand-alone NAR | 14.65 | 0.678 | 5.192 | 6.745 | 0.435 |

Stand-alone NARX | 1.343 | 0.902 | 2.288 | 3.713 | 0.432 |

Model | NAR | NARX | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

NMSE | ${\mathbf{R}}^{2}$ | MAE (MW) | RMSE (MW) | MAPE (%) | NMSE | ${\mathbf{R}}^{2}$ | MAE (MW) | RMSE (MW) | MAPE (%) | |

Stand-alone model | 14.65 | 0.678 | 5.192 | 6.745 | 0.435 | 1.343 | 0.902 | 2.288 | 3.713 | 0.432 |

IMF1 | 7.238 | 0.122 | 2.225 | 2.868 | 85.850 | 3.904 | 0.359 | 1.869 | 2.464 | 63.230 |

IMF2 | 0.173 | 0.838 | 0.787 | 1.030 | 15.330 | 0.007 | 0.969 | 0.184 | 0.466 | 0.158 |

IMF3 | 0.026 | 0.952 | 0.421 | 0.733 | 2.898 | 0.0003 | 0.995 | 0.044 | 0.251 | 0.074 |

IMF4 | 0.010 | 0.974 | 0.429 | 0.604 | 1.947 | 0.004 | 0.981 | 0.056 | 0.490 | 0.381 |

IMF5 | 0.003 | 0.978 | 0.281 | 0.387 | 8.677 | 3.95 × 10^{−}³ | 0.999 | 0.010 | 0.039 | 0.299 |

IMF6 | 0.016 | 0.952 | 0.421 | 0.583 | 15.785 | 6.23 × 10^{−9} | 0.999 | 0.003 | 0.016 | 0.105 |

IMF7 | 0.007 | 0.962 | 0.329 | 0.457 | 5.953 | 5.07 × 10^{−7} | 0.999 | 0.005 | 0.040 | 0.006 |

IMF8 | 0.004 | 0.961 | 0.360 | 0.411 | 11.361 | 3.06 × 10^{−11} | 0.999 | 0.001 | 0.004 | 0.004 |

IMF9 | 0.052 | 0.952 | 1.024 | 1.144 | 20.868 | 2.68 × 10^{−11} | 0.999 | 0.002 | 0.006 | 0.014 |

Residue | 0.096 | 0.898 | 0.980 | 1.089 | 0.402 | 1.65 × 10^{−13} | 0.999 | 0.001 | 0.001 | 5.62 × 10^{−5} |

Hybrid model | 0.074 | 0.926 | 2.519 | 3.240 | 0.214 | 0.048 | 0.952 | 1.923 | 2.605 | 0.032 |

**Table 5.**Statistical comparisons among highly correlated (HC) and all correlated (AC) variables using NARX for the GS1 site.

Model | $\mathbf{N}\mathbf{A}\mathbf{R}{\mathbf{X}}_{\mathbf{A}\mathbf{C}}$ | $\mathbf{N}\mathbf{A}\mathbf{R}{\mathbf{X}}_{\mathbf{H}\mathbf{C}}$ | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

NMSE | ${\mathbf{R}}^{2}$ | MAE (MW) | RMSE (MW) | MAPE (%) | NMSE | ${\mathbf{R}}^{2}$ | MAE (MW) | RMSE (MW) | MAPE (%) | |

Stand-alone model | 3.989 | 0.830 | 3.814 | 4.897 | 0.354 | 1.343 | 0.902 | 2.288 | 3.713 | 0.432 |

IMF1 | 6.396 | 0.1737 | 2.092 | 2.783 | 81.16 | 3.904 | 0.359 | 1.869 | 2.464 | 63.230 |

IMF2 | 0.020 | 0.944 | 0.390 | 0.5938 | 6.383 | 0.007 | 0.969 | 0.184 | 0.466 | 0.158 |

IMF3 | 0.003 | 0.983 | 0.193 | 0.431 | 0.674 | 0.0003 | 0.995 | 0.044 | 0.251 | 0.074 |

IMF4 | 9.58 × 10^{−7} | 0.999 | 0.039 | 0.061 | 0.011 | 0.004 | 0.981 | 0.056 | 0.490 | 0.381 |

IMF5 | 1.05 × 10^{−7} | 0.999 | 0.011 | 0.029 | 0.128 | 3.95 × 10^{−7} | 0.999 | 0.010 | 0.039 | 0.299 |

IMF6 | 1.27 × 10^{−10} | 0.999 | 0.002 | 0.005 | 0.026 | 6.23 × 10^{−9} | 0.999 | 0.003 | 0.016 | 0.105 |

IMF7 | 9.99 × 10^{−5} | 0.996 | 0.115 | 0.1624 | 0.470 | 5.07 × 10^{−7} | 0.999 | 0.005 | 0.040 | 0.006 |

IMF8 | 5.05 × 10^{−11} | 0.999 | 0.003 | 0.004 | 0.004 | 3.06 × 10^{−11} | 0.999 | 0.001 | 0.004 | 0.004 |

IMF9 | 1.76 × 10^{−7} | 0.999 | 0.038 | 0.045 | 0.042 | 2.68 × 10^{−11} | 0.999 | 0.002 | 0.006 | 0.014 |

Residue | 9.13 × 10^{−13} | 0.999 | 0.001 | 0.002 | 2.4 × 10^{−4} | 1.65 × 10^{−13} | 0.999 | 0.001 | 0.001 | 5.62 × 10^{−5} |

Hybrid model | 0.062 | 0.937 | 2.225 | 2.967 | 0.302 | 0.048 | 0.952 | 1.923 | 2.605 | 0.032 |

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## Share and Cite

**MDPI and ACS Style**

Chreng, K.; Lee, H.S.; Tuy, S. A Hybrid Model for Electricity Demand Forecast Using Improved Ensemble Empirical Mode Decomposition and Recurrent Neural Networks with ERA5 Climate Variables. *Energies* **2022**, *15*, 7434.
https://doi.org/10.3390/en15197434

**AMA Style**

Chreng K, Lee HS, Tuy S. A Hybrid Model for Electricity Demand Forecast Using Improved Ensemble Empirical Mode Decomposition and Recurrent Neural Networks with ERA5 Climate Variables. *Energies*. 2022; 15(19):7434.
https://doi.org/10.3390/en15197434

**Chicago/Turabian Style**

Chreng, Karodine, Han Soo Lee, and Soklin Tuy. 2022. "A Hybrid Model for Electricity Demand Forecast Using Improved Ensemble Empirical Mode Decomposition and Recurrent Neural Networks with ERA5 Climate Variables" *Energies* 15, no. 19: 7434.
https://doi.org/10.3390/en15197434