A new hybrid model combining EMD and neural network for multi-step ahead load forecasting

Abstract

The electric load forecasting (ELF) is a key area of the modern power system (MPS) applications and also for the virtual power plant (VPP) analysis. The ELF is most prominent for the distinct applications of MPS and VPP such as real-time analysis of energy storage system, distributed energy resources, demand side management and electric vehicles etc. To manage the real-time challenges and map the stable power demand, in different time steps, the ELF is evaluated in yearly, monthly, weekly, daily, and hourly, etc. basis. In this study, an intelligent load predictor which is able to forecast the electric load for next month or day or hour is proposed. The proposed approach is a hybrid model combining empirical mode decomposition (EMD) and neural network (NN) for multi-step ahead load forecasting. The model performance is demonstrated by suing historical dataset collected form GEFCom2012 and GEFCom2014. For the demonstration of the performance, three case studies are analyzed into two categories. The demonstrated results represents the higher acceptability of the proposed approach with respect to the standard value of MAPE (mean absolute percent error).

Keywords

Feature extraction decomposition intelligent data analytics short-term forecasting power system planning

1 Introduction

Generally, in the MPS, there are mainly five type of forecasting mechanisms in different time-horizon (TH), which are used in the power system’s distinct applications such as [1 –9]: 1) time horizon 1-year to 10-years, 2) time horizon 1-week to 1-year, 3) time horizon 1-minute to 1-week, 4) time horizon millisecond to seconds and 5) time horizon Nano-seconds to micro-seconds. There are different application area with respect to (w.r.t.) the time horizon such as: forecasting between 1-year to 10-years is utilized for the power system planning; forecasting between 1-week to 1year is used maintenance scheduling; forecasting between 1-minute to 1-week is used for UCA (unit commitment analysis), ELD (economic load dispatch), OPF (optimal power flow) and automatic generation control; forecasting between milliseconds to seconds is utilized for MPS dynamic analysis; and finally forecasting between nanoseconds to microseconds is use for MPS transient analysis [3].

The ELF is an emergent requirement for the MPS planning, which is required for the following applications such as: 1) capacity planning, 2) network planning, 3) generation & transmission capital investment planning, 4) financial forecast, 5) efficient power procurement, 6) selling of excess power, 7) fuel ordering planning, 8) optimal supply and scheduling, 9) renewable planning, and 10) fuel mix selection planning etc. in the MPS. Moreover, there are numerous benefits for the ELF such as: ELF ensures the availability of electricity supply; ELF provides the means of avoiding over & underutilization of generating capacity; ELF supports to make use of best possible use of capacity; ELF save unnecessary capital expenditure; and ELF prevent economic growth of OPF etc. Therefore, apart of these benefits, there are some uncertainties for ELF such as: forecasting the future needs of electricity; electricity production & distribution are highly capital intensive; projects lead times are very long due to large size of project; forecasting is not isolated activity; electrical energy role should be highlighted in the society; national policy & strategy are very key-points; it may effect due to policies, public perception; additional needs for ELF in DSM & conservation policies; to make highly preciseness; single ELF may not be reliable; higher uncertainties. Therefore, ELF is highly rely on numerous key-factors such as: land, city/ industrial/ community development plans, alternative energy resources, load density, population growth, historical data and geographical factors etc.

In the present scenario, different type of forecasting models have been developed by the researchers, such as: 1) statistical models (SMs), 2) artificial intelligent (AI)/ machine learning models (AIM-MLMs), and 3) hybrid models (HMs) [1 –9].

The SMs are known as mathematical model which are based on a set of statistical assumption and hypothesis. The SMs represent the mathematical relationship between variables. The few SMs are AR (autoregressive), MA (moving average), ARMA (Autoregressive Moving Average), ARIMA (Autoregressive Integrated Moving Average), ARFIMA (Autoregressive Fractionally Integrated Moving Average), SARIMA (Seasonal Autoregressive Integrated Moving Average), ARMAX, ARIMAX, NAR (Non-linear Autoregressive), NMA (Nonlinear Moving Average), TAR (Threshold Autoregressive), ARCH (Autoregressive Conditional Heteroskedasticity), GARCH (Generalized ARCH), EARCH (Exponential Generalized ARCH), Kalman filter model, ES (exponential smoothing), and GM (Grey model). These SMs are used to forecast the electric load according to linear time series and non-linear time series analysis. Apart of SMs, the AIM-MLMs are used for the ELF due to its superiority over the conventional method. These methods are NN, SVM (support vector machine), ELM (extreme learning machine), Fuzzy-logic, wavelet, GA (genetic algorithm), expert system, GEP (gene expression programming) and its associated hybrid models etc.

The organization of this paper comprises into five sections, including introduction in section-1, study area and data collection in secion-2, proposed hybrid approach in section-3, results and discussion in section-4 and finally conclusion in section-5.

2 Study area and data collection

Hourly basis electrical load pattern dataset is collected from GEFCom2012 [10], which includes historical dataset of twenty zones from 2004 to 2008. Based on these dataset, three case studies have been performed in this paper: 1) Month-ahead forecast, 2) Day-ahead forecast and 3) Hour-ahead forecast. According to these proposed case studies, historical data set is rearranged and preprocessed. Moreover, few statistical characteristics are analyze to show the internal property of the recorded dataset. These statistical characteristics are represented in Figs. 1 to 4 for min (minimum), max (maximum), mean and STD (standard deviation) respectively. Moreover, per hour recorded data set is represented in Figs. 5 to 8 for the time interval of “1 to 6 hour”, “7 to 12 hour”, “13 to 18 hour” and “19 to 24 hour” respectively

Fig.1

Monthly minimum value of the historical recorded dataset.

Fig.2

Monthly maximum value of the historical recorded dataset.

Fig.3

Monthly mean value of the historical recorded dataset.

Fig.4

Monthly STD of the historical recorded dataset.

Fig.5

Per day hourly-value of the historical recorded dataset.

Fig.6

Per day hourly-value of the historical recorded dataset.

Fig.7

Per day hourly-value of the historical recorded dataset.

Fig.8

Per day hourly-value of the historical recorded dataset.

3 Proposed hybrid model

The proposed hybrid model for multi-step ahead electric load forecasting is presented in Fig. 9. The proposed hybrid model is the combination of EMD and NNs. The proposed approach is comprises into five sub-parts such as: 1) Historical dataset collection, 2) Data pre-processing and decomposition, 3) different NNs model development and training performance, 4) unification of the trained models output and 5) testing and model adoptability checking.

Fig.9

Flowchart of the proposed hybrid model.

In part-1, historical records of the EL dataset are collected then it is pre-processed to extract the features by using EMD method in sub-part-2. Then obtained IMFs are used as predicting variable to the NNs model. In sub-part-3, different NNs models are developed according the step of forecasting. Here in this paper, forecasting is performed upto level of 3 which is performed for all three different types of case studies (i.e., moth, day and hour – ahead forecasting). After the proper training of the NN models, testing phase is performed, where its adoptability is checked whether trained model is acceptable or retrained to enhance its performance and accuracy. Thereafter, unification of the output of all developed model is performed, which gives the final output of the ELF. The main key-feature of the proposed approach are:

Real-time analysis

Data pre-processing without high memory capacity

Multi-step testing and forecasting in a continuous manner

Self-adoptability check with respect to the step-ahead forecasting

Forecasting with and/or without feature extraction to maintain the processing time limit

Each step of forecasting are correlated to each other, so no global trapping problem with NNs

3.1 Empirical Mode Decomposition (EMD) [11 –17]

There are several data pre-processing methods in the research domain, which are utilized to decompose the linear and/or non-linear data samples. EMD is the one of them. The EMD method has several key features such as: 1) it process the multi-frequency signals into a series of IMFs, 2) any complicated dataset can be decomposed into a finite components, 3) it is adaptive, 4) highly efficient, 5) the number of IMFs are controllable in nature via user etc.

The implementation procedure of EMD to generate the IMF is represented in Fig. 10. A generated IMF is defined as a function if it satisfies following two main conditions: 1) In collected all historical records, the number of extrema and the number of zero-crossings must either be equal or differ at most by one, and 2) At any point, the mean value of the envelope is zero.

Fig.10

EMD method implementation procedure.

After the implementation of the EMD on the historical dataset, generated IMFs are represented in Fig. 11 for the electric load pattern of year 2004. Although, the IMFs for all recorded data set have been generated, but due to constraint of the page limit, the IMFs for 2004 have been presented for the better visualization and understanding point of view in this section. Moreover, the generated IMFs for other dataset have been used for the forecasting purpose as mentioned in the proposed approach. In this study, the following different type of IMFs are generated for all recorded historical dataset: 1) IMFs generation for monthly forecast, 2) IMFs generation for daily forecast, and 3) IMFs generation for hourly forecast.

Fig.11

IMFs representation for hour#1 of 2004 dataset.

The Fig. 11 shows the generated IMFs for hourly forecast only for the time duration of first hour out of 24 hours of a day. For the visualization of the generated IMFs of remaining hours, the evaluated energy magnitude is represented in Fig. 12 for all hourly datasets of the year 2004.

Fig.12

Energy magnitude representation for genrted IMFs of hour#1 to hour#24 of 2004 dataset.

3.2 Neural Network (NN) [3–7 , 15–20]

In this study, used NN architecture of a single hidden layer MLP is represented in Fig. 13. Let’s assume i1, i2 are input1 and input2 respectively of the training dataset I (i.e., I = [x₁, x₂, . . . . . x_n]).

Fig.13

Flowchart of the NNs model’s implementation.

The mathematical modeling for NN architecture is as follow:

Step1) evaluation at input layer: $S (x_{i}) = x_{i}, i = 1, 2, . . . ., n;$ (1) $S (x_{0}) = 1$ (2)

Step2) evaluation at hidden layer: $z_{h} = \sum_{i = 0}^{n} w_{ih}^{I} S (x_{i}), h = 1, 2, . . . ., q$ (3) $S (z_{h}) = \frac{1}{1 + e^{- z_{h}}}, h = 1, 2, . . . ., q$ (4) $S (z_{0}) = 1$ (5)

Step3) evaluation at output layer: $y_{j} = \sum_{h = 0}^{q} w_{hj}^{H} S (z_{h}), j = 1, 2, . . . ., p$ (6) $S (y_{j}) = \frac{1}{1 + e^{- y_{j}}}, j = 1, 2, . . . ., p$ (7)

Where, $W^{I} = [w_{ih}^{I}]_{(n + 1) \times q}$ =weight vector between input and hidden layer and $W^{H} = [w_{hj}^{H}]_{(q + 1) \times p}$ =weight vector between hidden and output layer.

$W^{I} = [\begin{matrix} w_{i 1 H 1} \\ w_{i 1 H 2} \\ w_{i 1 H 3} \end{matrix} \begin{matrix} w_{i 2 H 1} \\ w_{i 2 H 2} \\ w_{i 2 H 3} \end{matrix}]$ , $W^{H} = [\begin{matrix} w_{H 1 O_{1}} \\ w_{H 2 O_{1}} \\ w_{H 3 O_{1}} \end{matrix}]$ , , and B2 = [b₄].

The number of hidden layer neuron are evaluated as: $Neurons = (\frac{I_{N} + O_{N}}{2} + \sqrt{N_{train}}) \pm 10$ (8) Where, I_N=number of inputs, O_N=number of outputs and N_train=number of training samples

3.3 Accuracy evaluation indices

In the research domain of the forecasting and prediction, several standard indices are implemented to analyze the performance of the proposed forecasting approach/models. Some of them are: MAE, MAPE and RMSE. In this study, MAPE is used to evaluate the performance of the proposed forecasting models.

Mean absolute error (MAE): ${MAE}_{NNs} = \frac{1}{N} \sum_{t = 1}^{N} | F (t) - O (t) |$ (9) Mean absolute percentage error (MAPE): ${MAPE}_{mod el} = (\frac{1}{N} \sum_{t = 1}^{N} | \frac{F (t) - O (t)}{O (t)} |) \times 100$ (10) Root mean square error (RMSE). ${RMSE}_{mod el} = \sqrt{\frac{1}{N} \sum_{t = 1}^{N} {[F (t) - O (t)]}^{2}}$ (11) Where, F (t)=forecasted value, O (t)=observed value, and t = time interval.

4 Results demonstration

The results demonstration are represented into two categories: 1) One-Step Ahead forecasting and 2) Multi-Step Ahead forecasting. Both categories of forecasting are further analyzed into three sub-micro levels. These demonstration of micro-levels are as follows: a) Monthly basis, b) daily basis and c) hourly basis. The information of the used dataset for forecasting models is represented in Table 1 and obtained best optimal results from each case study have been demonstrated in Table 3. Table 2 represents the total number of developed NN models in this study.

Table 1
Dataset used for NNs model formation for ELF

Years Monthly ELF Daily ELF Hourly ELF

2004 Data sample 12 366 8784

2005 Data sample 12 365 8760

2006 Data sample 12 365 8760

2007 Data sample 12 365 8760

Years	Monthly ELF	Daily ELF	Hourly ELF
2004 Data sample	12	366	8784
2005 Data sample	12	365	8760
2006 Data sample	12	365	8760
2007 Data sample	12	365	8760

Table 2

Developed NNs models for multi-step forecasting

Used dataset type for NN model	One-Step Ahead	Two-Step Ahead	Three-Step Ahead
Raw Dataset	1	1	1
IMF1	1	1	1
IMF2	1	1	1
IMF3	1	1	1
IMF4	1	1	1
IMF5	1	1	1
IMF6	1	1	1
IMF7	1	1	1
Total	8	8	8

Table 3

NNs performance for ELF: MAPE value

Performance phase	Monthly ELF	Daily ELF	Hourly ELF
2004-05 Data (Training phase)	3.14	4.57	6.50
2006 Data (Testing phase#1)	5.05	6.83	9.15
2007 Data (Testing phase#2)	4.88	7.85	9.92

These three case studies (i.e., monthly, daily and hourly forecasting) are formulated with consideration of it distinct and valuable application in the power system such as system planning, maintenance scheduling, unit commandment, economic load dispatch management, OPF (optimal power flow) analysis, automatic generation control etc.

4.1 One-step ahead forecasting

4.1.1 Month-ahead forecasting

The month-ahead forecasting is very useful for maintenance scheduling of the system in the power system network. In this section, one-step ahead forecasting results for monthly forecasting has been presented, which are represented in Table 4 for the training and testing phase. According to the [21], the value of MAPE of a forecasting model is less than 10% then model is highly acceptable condition. In this case study, the maximum and minimum MAPE for training phase is 3.66 and 5.93 respective and the average MAPE for all month in a year is 4.42. In the testing phase, the evaluated minimum and maximum MAPE is 4.7 and 7.6 respectively. Therefore, after analyzing Table 4, it is clear that developed NN model for one-step ahead forecasting is more acceptable and it can be used for further analysis in multi-step ahead forecasting. Fig. 14 represents the obtained results of one-step ahead forecasting for monthly basis.

Table 4
ANN model performance for case study#1: MAPE for Month-ahead LF

Month 2004–05 2006 2007

Jan. 3.66 5.6 5.77

Feb. 4.24 4.76 6.95

March 4.13 5.78 6.27

April 5.93 5.7 5.37

May 4.68 6.46 5.76

June 4.49 6.51 6.8

July 4.33 5.57 6.69

Aug. 4.37 7.56 5.63

Sep. 3.95 6.28 6.39

Oct. 3.76 7.48 4.7

Nov. 4.66 7.6 7.24

Dec. 4.8 7.03 6.69

Average 4.42 6.36 6.19

Month	2004–05	2006	2007
Jan.	3.66	5.6	5.77
Feb.	4.24	4.76	6.95
March	4.13	5.78	6.27
April	5.93	5.7	5.37
May	4.68	6.46	5.76
June	4.49	6.51	6.8
July	4.33	5.57	6.69
Aug.	4.37	7.56	5.63
Sep.	3.95	6.28	6.39
Oct.	3.76	7.48	4.7
Nov.	4.66	7.6	7.24
Dec.	4.8	7.03	6.69
Average	4.42	6.36	6.19

Fig.14

Performance measures for single step ahead monthly forecasting.

4.1.2 Day-ahead forecasting

In this section, the day-ahead forecasting results for testing phase have been represented in Figs. 15 and 16 for the tested dataset of year 2006 and 2007 respectively. From the test result analysis, it is shown that the average value of MAPE for Monday to Sunday are 5.63, 6.26, 5.98, 7.42, 9.23, 5.95, and 7.32 respectively for the year of 2006. And for the year 2007, the testing results are 6.41, 6.84, 9.5, 8.5, 2.99, 10.9, and 9.78 for the day of Monday to Sunday respectively. In the both cases (2006 and 2007), the weekly average value of MAPE are 6.83 and 7.85 respectively, which are highly acceptable for the forecasting problems.

Fig.15

Performance measures for single-step ahead daily forecasting (Test#1 : 2006 dataset).

Fig.16

Performance measures for single-step ahead daily forecasting (Test#2 : 2007 dataset).

4.1.3 Hour-ahead forecasting

In this section, the hour-ahead forecasting results for testing phase have been represented in Fig. 17 (in four continuous Fig) for the tested dataset of year 2007 respectively for visualization point of view. From the test result analysis, it is shown that the average value of MAPE for hour#1 to hour#24 (for each day) for Monday to Sunday are 9.72, 9.78, 9.64, 10.38, 9.82, 10.42, and 9.68 respectively for the year of 2007. And the average value for all 24 hours in a week is 9.92, which is lesser that 10. Hence, developed NN models for hour-ahead forecasting is highly acceptable.

Fig.17

Performance measures for single-step ahead hourly forecasting (Test#2 : 2007 dataset).

4.2 Multi-step ahead forecasting

Based on the performance analysis of the developed NN models for one-step ahead forecasting, multi-step ahead forecasting is performed in the step of two-step and three-step for the all three cases (i.e., monthly, daily and hourly forecasting of the laod) as explained in sub-sequence sections.

4.2.1 Month-ahead forecasting

In this section, two-step ahead and three-step ahead forecasting results for monthly load forecast have been presented, which are tabulated in Tables 5 and 6 respectively for the training and testing phase of the models.

Table 5
Two-step ahead MAPE for monthly forecasting

Month Train: 2004–05 Test#1 : 2006 Test#2 : 2007

Jan. 3.03 4.95 5.13

Feb. 3.61 4.11 6.31

March 3.5 5.13 5.63

April 5.3 5.05 4.73

May 4.05 5.81 5.12

June 3.86 5.86 6.16

July 3.7 4.92 6.05

Aug. 3.74 6.91 4.99

Sep. 3.32 5.63 5.75

Oct. 3.13 6.83 4.06

Nov. 4.03 6.95 6.6

Dec. 4.17 6.38 6.05

Average 3.79 5.71 5.55

Month	Train: 2004–05	Test#1 : 2006	Test#2 : 2007
Jan.	3.03	4.95	5.13
Feb.	3.61	4.11	6.31
March	3.5	5.13	5.63
April	5.3	5.05	4.73
May	4.05	5.81	5.12
June	3.86	5.86	6.16
July	3.7	4.92	6.05
Aug.	3.74	6.91	4.99
Sep.	3.32	5.63	5.75
Oct.	3.13	6.83	4.06
Nov.	4.03	6.95	6.6
Dec.	4.17	6.38	6.05
Average	3.79	5.71	5.55

Table 6

Three-step ahead MAPE for monthly forecasting

Month	Train: 2004–05	Test#1 : 2006	Test#2 : 2007
Jan.	3.66	5.6	5.77
Feb.	4.24	4.76	6.95
March	4.13	5.78	6.27
April	5.93	5.7	5.37
May	4.68	6.46	5.76
June	4.49	6.51	6.8
July	4.33	5.57	6.69
Aug.	4.37	7.56	5.63
Sep.	3.95	6.28	6.39
Oct.	3.76	7.48	4.7
Nov.	4.66	7.6	7.24
Dec.	4.8	7.03	6.69
Average	4.42	6.36	6.19

In the two-step ahead load forecasting case study, the maximum and minimum MAPE for training phase is 3.03 and 5.3 respective and the average MAPE for all month in a year is 3.79. Whereas, in the testing phase, the evaluated minimum and maximum MAPE is varied from 4.11 and 6.95 and its average values of MAPE for the year 2006 and 2007 are 5.71 and 5.55 respectively.

Similarly, in the three-step ahead forecasting case study, the maximum and minimum MAPE for training phase is 3.66 and 5.93 respective and the average MAPE for all month in a year is 4.42. Whereas, in the testing phase, the evaluated minimum and maximum MAPE is varied from 4.7 and 7.6 and its average values of MAPE for the year 2006 and 2007 are 6.36 and 6.19 respectively.

Therefore, after analyzing Tables 5 and 6, it is clear that developed NN models for two-step ahead and three-step ahead forecasting are more acceptable and it can be utilized for further implementation on real-side.

4.2.2 Day-ahead forecasting

This section presents the results of daily-ahead load forecasting for two-step ahead and three-step ahead forecasting, which are listed in the Tables 7 to 10 for the testing phase. Tables 7 and 9 represents the testing phase results for the historical dataset of the year 2006 for two-step and three-step ahead forecasting respectively. Similarly, Tables 8 and 10 represents the testing phase results for the historical dataset of the year 2007 for two-step and three-step ahead forecasting respectively.

Table 7
Two-step ahead MAPE for daily EL forecasting (Test#1 : 2006 Dataset)

Monday Tuesday Wednesday Thursday Friday Saturday Sunday Weekly Average

Jan. 4.78 10.5 6.57 8.16 5.71 8.06 6.71 7.21

Feb. 5.45 4.96 5.96 13.7 6.36 7.45 10.2 7.73

March 5.14 3.12 5.83 9.11 5.28 5.12 7.78 5.91

April 6.15 6.59 4.28 7.46 5.58 7.45 5.97 6.21

May 9.05 5.54 6.97 6.34 9.58 8.12 10.5 8.02

June 2.93 4.91 6.2 7.47 4.59 7.02 8.75 5.98

July 3.88 8.11 4.75 5.88 8.49 8.05 4.86 6.29

Aug. 4.97 8.27 6.41 6.07 10.2 6.16 9.13 7.32

Sep. 5.75 7.76 5.75 6.53 9.55 7.08 4.64 6.72

Oct. 8.37 4.02 5.26 5.75 10.1 6.67 3.64 6.26

Nov. 9.98 7.91 8.68 8.07 10.2 8.68 10.7 9.18

Dec. 3.78 6.11 7.71 7.22 4.8 5.9 8.3 6.26

Monthly Average 5.85 6.48 6.2 7.65 7.54 7.15 7.6 6.92

	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday	Weekly Average
Jan.	4.78	10.5	6.57	8.16	5.71	8.06	6.71	7.21
Feb.	5.45	4.96	5.96	13.7	6.36	7.45	10.2	7.73
March	5.14	3.12	5.83	9.11	5.28	5.12	7.78	5.91
April	6.15	6.59	4.28	7.46	5.58	7.45	5.97	6.21
May	9.05	5.54	6.97	6.34	9.58	8.12	10.5	8.02
June	2.93	4.91	6.2	7.47	4.59	7.02	8.75	5.98
July	3.88	8.11	4.75	5.88	8.49	8.05	4.86	6.29
Aug.	4.97	8.27	6.41	6.07	10.2	6.16	9.13	7.32
Sep.	5.75	7.76	5.75	6.53	9.55	7.08	4.64	6.72
Oct.	8.37	4.02	5.26	5.75	10.1	6.67	3.64	6.26
Nov.	9.98	7.91	8.68	8.07	10.2	8.68	10.7	9.18
Dec.	3.78	6.11	7.71	7.22	4.8	5.9	8.3	6.26
Monthly Average	5.85	6.48	6.2	7.65	7.54	7.15	7.6	6.92

Table 8

Two-step ahead MAPE for daily EL forecasting (Test#2 : 2007 Dataset)

	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday	Weekly Average
Jan.	11.5	5.41	11.7	10.3	11.3	4.45	12.8	9.65
Feb.	7.75	6.11	8.02	7.22	5.8	8.49	8.08	7.35
March	6.34	5.17	9.34	7.08	7.22	6.12	7.54	6.97
April	5.11	6.26	12.1	8.28	9.12	4.22	10.6	7.96
May	3.5	6.11	9.35	6.32	4.12	4.8	7.74	5.99
June	6.07	7.11	9.63	9.5	6.23	8.73	11.6	8.4
July	4.25	6.3	7.56	8.46	8.22	6.02	9.2	7.14
Aug.	7.05	7.57	8.44	11.9	11.1	6.22	4.19	8.07
Sep.	8.86	9.6	9.26	10.7	9.22	10.1	7.32	9.3
Oct.	7.71	6.23	8.96	6.92	5.48	7.36	5.74	6.91
Nov.	6.26	8.76	11.8	8.18	8.23	6.25	8.52	8.28
Dec.	5.1	10.1	10.5	9.9	7.01	10.2	6.08	8.42
Monthly Average	6.63	7.06	9.72	8.73	7.76	6.92	8.29	7.87

Table 9

Three-step ahead MAPE for daily EL forecasting (Test#1 : 2006 Dataset)

	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday	Weekly Average
Jan.	4.96	10.6	6.75	8.35	5.9	8.25	6.86	7.39
Feb.	5.63	5.14	6.14	13.9	6.55	7.64	10.4	7.91
March	5.32	3.3	6.01	9.3	5.47	5.31	7.93	6.09
April	6.33	6.77	4.46	7.65	5.77	7.64	6.12	6.39
May	9.23	5.72	7.15	6.53	9.77	8.31	10.7	8.2
June	3.11	5.09	6.38	7.66	4.78	7.21	8.9	6.16
July	4.06	8.29	4.93	6.07	8.68	8.24	5.01	6.47
Aug.	5.15	8.45	6.59	6.26	10.4	6.35	9.28	7.5
Sep.	5.93	7.94	5.93	6.72	9.74	7.27	4.79	6.9
Oct.	8.55	4.2	5.44	5.94	10.3	6.86	3.79	6.44
Nov.	10.2	8.09	8.86	8.26	10.4	8.87	10.8	9.36
Dec.	3.96	6.29	7.89	7.41	4.99	6.09	8.45	6.44
Monthly Average	6.03	6.66	6.38	7.84	7.73	7.34	7.75	7.1

Table 10

Three-step ahead MAPE for daily EL forecasting (Test#2 : 2007 Dataset)

	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday	Weekly Average
Jan.	11.7	5.59	11.9	10.4	11.5	4.64	13	9.83
Feb.	7.93	6.29	8.2	7.41	5.99	8.68	8.23	7.53
March	6.52	5.35	9.52	7.27	7.41	6.31	7.69	7.15
April	5.29	6.44	12.3	8.47	9.31	4.41	10.8	8.14
May	3.68	6.29	9.53	6.51	4.31	4.99	7.89	6.17
June	6.25	7.29	9.81	9.69	6.42	8.92	11.7	8.58
July	4.43	6.48	7.74	8.65	8.41	6.21	9.35	7.32
Aug.	7.23	7.75	8.62	12.1	11.3	6.41	4.34	8.25
Sep.	9.04	9.78	9.44	10.9	9.41	10.3	7.47	9.48
Oct.	7.89	6.41	9.14	7.11	5.67	7.55	5.89	7.09
Nov.	6.44	8.94	12	8.37	8.42	6.44	8.67	8.46
Dec.	5.28	10.3	10.7	10.1	7.2	10.4	6.23	8.6
Monthly Average	6.81	7.24	9.9	8.92	7.95	7.11	8.44	8.05

In the two-step ahead daily-load forecasting case study, the average maximum and minimum MAPE for testing phase is 5.85–7.65 (for 2006 test dataset) and 6.63–9.72 (for 2007 test dataset), and the overall-average MAPE for all days of the months is 6.92 (for 2006 test dataset) and 7.87 (for 2007 test dataset).

Similarly, in the three-step ahead daily-load forecasting case study, the average maximum and minimum MAPE for testing phase is 6.03–7.84 (for 2006 test dataset) and 6.81–9.9 (for 2007 test dataset), and the overall-average MAPE for all days of the months is 7.1 (for 2006 test dataset) and 8.05 (for 2007 test dataset).

Therefore, after analyzing Tables 7 to 10, it is concluded that developed NN models for two-step ahead and three-step ahead forecasting for daily load forecast are more acceptable and it can be implemented for further uses on real-side.

4.2.3 Hour-ahead forecasting

In this section, the obtained results of an hour-ahead load forecasting for two-step ahead and three-step ahead forecasting are demonstrated, which are listed in the Tables 11 to 12 for the testing phase. Table 11 represents the testing phase results for the historical dataset of the year 2007 for two-step forecasting. Similarly, Table 12 represents the testing phase results for the historical dataset of the year 2007 for three-step ahead forecasting.

Table 11
Two-step ahead MAPE for hourly EL forecasting (Test#2 : 2007 Dataset)

Monday Tuesday Wednesday Thursday Friday Saturday Sunday Weekly Average

Hour1 9.79 9.07 8.9 11.2 8.77 9.85 8.52 9.45

Hour2 9.13 8.79 7.28 7.39 6.56 9.18 9.58 8.28

Hour3 9.68 6.66 11.3 10.4 10 10.7 8.77 9.64

Hour4 7.69 10.2 11.3 9.85 10.7 10.7 10.2 10.1

Hour5 10.7 6.74 8.13 15.1 10.6 10.4 8.24 9.99

Hour6 8.61 14.7 13.5 13.7 14.7 13 12.5 13

Hour7 5.52 9.17 14.8 10.5 9.21 11.2 6.16 9.51

Hour8 9.64 12.9 10.9 6.89 7.39 14.8 13.1 10.8

Hour9 9.68 7.18 6.49 9.88 8.87 11.9 7.09 8.73

Hour10 9.72 7.88 7.45 12 7.18 11.2 8.43 9.12

Hour11 13.2 10.9 12.3 9.6 12.5 12 5.93 10.9

Hour12 7.04 8.55 11.6 8.59 12 10.9 10.3 9.85

Hour13 13.3 8.32 6.49 14.3 11.3 11.6 6.55 10.3

Hour14 11.8 8.42 8.79 10.6 7.9 8.28 10.6 9.5

Hour15 7.77 15.3 13.9 14.5 12.1 13.2 14.5 13.1

Hour16 9.58 12.3 8.58 10.1 11.7 9.58 7.14 9.87

Hour17 7.38 12.6 7.52 12.5 12.8 9.83 14 11

Hour18 13.1 7.35 9.68 6.19 7.17 11.2 8.66 9.06

Hour19 11.3 9.06 8.96 7.3 7.77 8.65 10.2 9.03

Hour20 10.6 8.49 10.7 7.73 10.1 9.23 8.44 9.32

Hour21 13.7 12.8 5.47 13.1 7.03 11.2 15.2 11.2

Hour22 10.9 10.4 9.73 10.8 12.1 7.96 7.53 9.91

Hour23 5.5 9.71 9.88 6.15 10.3 6.25 12.7 8.65

Hour24 8.02 7.3 7.38 11.2 7.8 6.78 7.59 8.02

Hourly Average 9.72 9.79 9.63 10.4 9.86 10.4 9.67 9.93

	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday	Weekly Average
Hour1	9.79	9.07	8.9	11.2	8.77	9.85	8.52	9.45
Hour2	9.13	8.79	7.28	7.39	6.56	9.18	9.58	8.28
Hour3	9.68	6.66	11.3	10.4	10	10.7	8.77	9.64
Hour4	7.69	10.2	11.3	9.85	10.7	10.7	10.2	10.1
Hour5	10.7	6.74	8.13	15.1	10.6	10.4	8.24	9.99
Hour6	8.61	14.7	13.5	13.7	14.7	13	12.5	13
Hour7	5.52	9.17	14.8	10.5	9.21	11.2	6.16	9.51
Hour8	9.64	12.9	10.9	6.89	7.39	14.8	13.1	10.8
Hour9	9.68	7.18	6.49	9.88	8.87	11.9	7.09	8.73
Hour10	9.72	7.88	7.45	12	7.18	11.2	8.43	9.12
Hour11	13.2	10.9	12.3	9.6	12.5	12	5.93	10.9
Hour12	7.04	8.55	11.6	8.59	12	10.9	10.3	9.85
Hour13	13.3	8.32	6.49	14.3	11.3	11.6	6.55	10.3
Hour14	11.8	8.42	8.79	10.6	7.9	8.28	10.6	9.5
Hour15	7.77	15.3	13.9	14.5	12.1	13.2	14.5	13.1
Hour16	9.58	12.3	8.58	10.1	11.7	9.58	7.14	9.87
Hour17	7.38	12.6	7.52	12.5	12.8	9.83	14	11
Hour18	13.1	7.35	9.68	6.19	7.17	11.2	8.66	9.06
Hour19	11.3	9.06	8.96	7.3	7.77	8.65	10.2	9.03
Hour20	10.6	8.49	10.7	7.73	10.1	9.23	8.44	9.32
Hour21	13.7	12.8	5.47	13.1	7.03	11.2	15.2	11.2
Hour22	10.9	10.4	9.73	10.8	12.1	7.96	7.53	9.91
Hour23	5.5	9.71	9.88	6.15	10.3	6.25	12.7	8.65
Hour24	8.02	7.3	7.38	11.2	7.8	6.78	7.59	8.02
Hourly Average	9.72	9.79	9.63	10.4	9.86	10.4	9.67	9.93

Table 12

Three-step ahead MAPE for hourly EL forecasting (Test#2 : 2007 Dataset)

	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday	Weekly Average
Hour1	10.2	9.488	9.27	11.64	9.196	10.21	8.82	9.832
Hour2	9.543	9.211	7.648	7.805	6.994	9.538	9.88	8.659
Hour3	10.09	7.083	11.63	10.77	10.43	11.06	9.07	10.02
Hour4	8.1	10.59	11.68	10.27	11.1	11.08	10.5	10.48
Hour5	11.12	7.161	8.496	15.52	11.05	10.72	8.54	10.37
Hour6	9.018	15.1	13.92	14.16	15.14	13.37	12.8	13.36
Hour7	5.927	9.588	15.14	10.97	9.638	11.56	6.46	9.897
Hour8	10.05	13.36	11.32	7.312	7.816	15.2	13.4	11.21
Hour9	10.09	7.595	6.861	10.3	9.298	12.25	7.39	9.11
Hour10	10.13	8.301	7.816	12.42	7.611	11.55	8.73	9.507
Hour11	13.6	11.32	12.67	10.02	12.95	12.37	6.23	11.31
Hour12	7.448	8.967	11.95	9.011	12.46	11.26	10.6	10.23
Hour13	13.71	8.737	6.861	14.7	11.69	11.99	6.85	10.65
Hour14	12.26	8.836	9.156	11.03	8.335	8.637	10.9	9.884
Hour15	8.179	15.76	14.3	14.95	12.56	13.56	14.8	13.45
Hour16	9.986	12.71	8.953	10.57	12.15	9.938	7.44	10.25
Hour17	7.789	13	7.894	12.95	13.18	10.19	14.3	11.34
Hour18	13.53	7.773	10.05	6.613	7.595	11.58	8.96	9.444
Hour19	11.67	9.484	9.334	7.723	8.198	9.012	10.5	9.412
Hour20	10.97	8.912	11.03	8.146	10.56	9.593	8.74	9.706
Hour21	14.06	13.26	5.835	13.54	7.462	11.58	15.5	11.61
Hour22	11.28	10.85	10.1	11.22	12.48	8.321	7.83	10.3
Hour23	5.908	10.13	10.25	6.568	10.76	6.61	13	9.031
Hour24	8.432	7.72	7.746	11.65	8.228	7.141	7.89	8.401
Hourly Average	10.13	10.21	9.997	10.83	10.29	10.76	9.97	10.31

In the two-step ahead hourly-load forecasting case study, the 24-hour’s average maximum and minimum MAPE for testing phase is 9.63–10.4 (for 2007 test dataset), and the overall-average MAPE for all hours of the all 7-days is 9.93.

Similarly, in the three-step ahead hourly-load forecasting case study, the 24-hour’s average maximum and minimum MAPE for testing phase is 9.97–10.83 (for 2007 test dataset), and the overall-average MAPE for all 24-hours of the all 7-days is 10.31.

Hence, after analyzing Tables 11 and 12, it is finalized that the developed NN models for 2-step-ahead and 3-step-ahead forecasting for hourly load forecast are acceptable and its performance is highly reliable and the proposed approach can be implemented for future prospective on real-side applications.

5 Conclusion

In this study, an intelligent load predictor which is able to forecast the electric load for next-month or next-day or next-hour has been proposed. The developed proposed approach is a hybrid model which has been combined with EMD and NN for multi-step ahead ELF. The proposed model performance is experimentally demonstrated by suing historical dataset collected form GEFCom2012 and GEFCom2014. For the demonstration of the performance, three case studies (monthly, daily and hourly) have been analyzed into two categories (One-Step Ahead and Multi-Step Ahead). The total twenty four NN models have been developed and demonstrated in different sections, which have been represented in the section-4. The overall average performance of the proposed models is in term of MAPE during training phase of 3.14 (for MAF), 4.57 (for DAF) and 6.5 (for HAF). Whereas, the overall average performance of the proposed models is in term of MAPE during testing phase for test dataset#1 of year 2006 is 5.05 (for MAF), 6.83 (for DAF), and 9.15 (for HAF); and for test dataset#2 of year 2007 is 4.88 (for MAF), 7.85 (for DAF) and 9.92 (for HAF). The demonstrated results represents the higher acceptability of the proposed approach with respect to the standard value of MAPE, which is always lesser than 10 for all cases.

Hence, the proposed approach may be utilized for online ELF for the different MPS applications.

Footnotes

Acknowledgment

“The authors extend their appreciation to the Researchers Supporting Project at King Saud University, Riyadh, Saudi Arabia, for funding this research work through the project number RSP-2020/278”.

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A new hybrid model combining EMD and neural network for multi-step ahead load forecasting

Abstract

Keywords

1 Introduction

2 Study area and data collection

Table 1 Dataset used for NNs model formation for ELF Years Monthly ELF Daily ELF Hourly ELF 2004 Data sample 12 366 8784 2005 Data sample 12 365 8760 2006 Data sample 12 365 8760 2007 Data sample 12 365 8760

4.1.1 Month-ahead forecasting

4.2.1 Month-ahead forecasting

Footnotes

Acknowledgment

References

Table 1
Dataset used for NNs model formation for ELF

Years Monthly ELF Daily ELF Hourly ELF

2004 Data sample 12 366 8784

2005 Data sample 12 365 8760

2006 Data sample 12 365 8760

2007 Data sample 12 365 8760