An innovative model for electrical load forecasting: A case study in Australia

Abstract

Short-term load prediction has always played an increasingly important part in power system administration, load dispatch, and energy transfer scheduling. However, how to build a novel model to improve the accuracy of load forecasts is not only an extremely challenging problem but also a concerning problem for the power market. Specifically, the individual model pays no attention to the significance of data selection, data preprocessing, and model optimization. So these models cannot always satisfy the time series forecasting’s requirements. With these above-mentioned ignored factors considered, to enhance prediction accuracy and reduce computation complexity, in this study, a novel and robust method were proposed for multi-step forecasting, which combines the power of data selection, data preprocessing, artificial neural network, rolling mechanism, and artificial intelligence optimization algorithm. Case studies of electricity power data from New South Wales, Australia, are regarded as exemplifications to estimate the performance of the developed novel model. The experimental results demonstrate that the proposed model has significantly increased the accuracy of load prediction in all quarters. As a result, the proposed method not only is simple, but also capable of achieving significant improvement as compared with the other forecasting models, and can be an effective tool for power load forecasting.

Keywords

Short-term load prediction data selection data preprocessing optimization forecasting

1 Introduction

Precise short-term load prediction plays an increasingly significant role in the electricity market operation. A highly precise prediction approach is one of the most crucial methods utilized in advancing electrical power system development [1]. Effective prediction is beneficial for formulating economic policies for relevant departments and reducing management risk [2]. And it is an essential role in electricity risk management [3]. On the contrary, inaccurate electrical load forecasts lead to a considerable loss for electric power systems [4]. A reduction in load prediction error in terms of the mean absolute percentage error (MAPE) of 1% reduces the variable generation cost by between $0.6 and $1.6 million annually for a 10,000 MW utility with a MAPE of approximately 4% [5]. As we know, the world has happened many times major blackouts, such as the 2003 U.S.-Canada Blackout [6], and the Indian power grid collapse [7], severely affecting the production of enterprises and life of millions of people. If these events can be given an early warning ahead of us, on the basis of an excellent forecasting algorithm, these accidents can be avoided.

As a result, various statistical models are universally implemented in load forecasting, including the autoregressive model [8], autoregressive moving average model [9, 10], autoregressive integrated moving average model [11, 12], regression model [13], multiple linear regression [14], general exponential smoothing [15], and the Kalman filtering method [16], and so on. Nevertheless, the related literature displays that the conventional statistical method has the inevitable drawbacks that it can not properly explain the complicated relationship between the electric power load and the random variables, as a result, the drawbacks can result in highly uncertain changes in electricity demand [17]. Furthermore, traditional statistical prediction models are poorly adapted to data series and have excellent prediction performance for time series with fixed variation patterns, which are not capable enough to handle the nonlinear characteristics of power load data series. Meanwhile, due to the simple structure of traditional prediction models, the accuracy of the prediction of power load data series is not high, especially when the volatility of data series is high. Hence, artificial intelligence algorithms, such as the Elman neural network [18, 19], and support vector machines [20, 21], are considered as one forceful prediction appliance with strong robustness and fault tolerance to settle the short term load prediction issue and related studies. Zhang et al. [22] implement a two-layer decomposition approach, extreme learning machine, and differential evolution algorithm to achieve short-term electricity load forecasting. Demonstrated by Australian and Spanish power data that the developed model has a good performance. Afrasiabi et al. [23] employ a deep learning strategy in power market forecasting, which is an available method. An advanced hybrid method, utilizing modified variational mode decomposition to decompose the power load data and employing a machine learning technique optimized by a sparrow search algorithm to predict power demand, is proposed in [24]. Yang et al. [25] combine adaptive parameter-based variational mode decomposition, optimal kernel-based extreme learning machine model, and chaotic sine cosine algorithm to predict electricity price. Iwabuchi et al. [26] conduct electricity price prediction based on switching mother wavelets, wavelet transform, and long short-term memory, and achieve good forecasting results. Meng et al. [27] employ empirical wavelet transform, long short-term memory network, as well as the crisscross optimization algorithm to predict power price. Khan et al. [28] introduce a convolutional neural network to solve the problem of power load prediction and achieve satisfactory results. Özen and Yıldırım [29] propose a Bootstrap aggregation approach to power price prediction. Du et al. [30] combine a grey model with fractional order accumulation, seasonal factors, sine cosine algorithm as well as an error correction strategy to predict power consumption, which has strong adaptability and usefulness. In general, machine learning technology has achieved very effective research results in power load prediction and related fields, and has become one of the main hot research directions in power load prediction.

As we know, the back propagation neural network (BPNN), as one of the typical machine learning technology, is capable of performing the nonlinear system. However, the performance of BPNN can be unstable on account of the random allocation of input weights and hidden biases. To cope with this question, in this paper, a novel prediction model was put forward, combined with data selection, wavelet de-noising (WD) algorithm, BPNN, rolling mechanism (RM), and modified artificial bee colony (MABC) algorithm, denoted by WDRMABCBP. Specifically, data selection is designed to select suitable training datasets to build the model, while WD data preprocessing algorithm is employed to reduce the interferences from the original data. Besides, the RM is developed to achieve multi-step forecasting and improve forecast accuracy, meanwhile, the global search technique MABC is established to detect the optimal initial parameters of weights and biases for the BPNN model. To measure the availability of the proposed model, electricity load data of New South Wales, Australia, is considered as the case study, and two experiments are conducted in this paper. The experimental results demonstrate that the proposed model has better performance than other algorithms.

The main contributions of this paper can be summarized as follows:

An innovative multi-step forecasting model is developed for electrical load forecasting, which combines the merits of data selection, data preprocessing, artificial neural network, modified artificial intelligence optimization algorithm, and rolling mechanism. Its forecasting ability is validated well in the Australia electricity market.

Different from some previous studies, data selection is considered in the modeling process, which can further improve the forecasting performance by providing training datasets with the same properties as testing datasets.

A modified artificial intelligence optimizer is employed to search the main parameters and develop the optimal forecasting model, while data preprocessing is designed to remove noise from the original electrical power load data. Experimental results prove that data preprocessing and intelligent optimization can enhance the forecasting model’s performance.

Rolling mechanism is designed for achieving multi-step forecasting, which can improve the overall forecasting accuracy of the developed model for multi-step forecasting. Experimental results reveal that the rolling mechanism can be considered an alternative for multi-step forecasting.

The rest of this paper is arranged as follows. A general depiction of the essential methods of the novel approach is displayed in Section 2. Section 3 provides the main establishment process of the proposed model. We present and discuss the experiments and evaluation results in Section 4. Finally, Section 5 summarizes the conclusions.

2 Methodology

In this part, a global depiction of the essential methods of the novel approach is shown detailedly.

2.1 Data preprocessing

The wavelet de-noising algorithm, as a data preprocessing tool, is employed to remove the interferences from the original data. The relevant literature suggests that several decomposed wavelet details are related to the mean value of noise, whereas others are connected with the ‘clean’ series [31]. Hence, if we remove the ‘unimportant’ noise information, the original signal can be reconstructed without losing any significant details of the original signal [32 –34]. The wavelet function ‘wden’ is the general form for denoising in practice [35]. Hence, the function is performed to denoise the original signal in this paper.

The determination of parameter settings plays a significant part in achieving satisfying results of de-noising. The relevant reference suggested that the best results were acquired by the Coif, Daubechies, and Symlet wavelets [33]. Therefore, only these wavelet basis functions are considered in this study. Besides, the choice of the level and thresholding (soft or hard) is also important for obtaining an ideal de-noising effect. Four threshold selection algorithms, as shown in Table 1, are available in this paper.

Table 1
Four threshold selection algorithms [33]

Name Description

Minimax Minimax thresholding principle

Rigrsure Adaptive threshold selection by the principle of SURE

Sqtwolog Threshold equals sqrt (2**log(length(X)))

Heursure Heuristic variant of Rigrsure* and Sqtwolog

Name	Description
Minimax	Minimax thresholding principle
Rigrsure	Adaptive threshold selection by the principle of SURE
Sqtwolog	Threshold equals sqrt (2*log(length(X)))
Heursure	Heuristic variant of Rigrsure and Sqtwolog

The noise removing algorithm is given as follows: $S (n) = f (n) + σ e (n)$ (1) where S and f denote the produced signal and the denoised signal, respectively, and e is the noise; σ is the strength, and a randomly distributed value is marked as n.

The algorithm is designed to achieve the suppression of the interference e permitting to gain of the raw signal. To achieve the best result, three threshold rescaling options (one, sln, and mln) can be employed in this process. The option ‘one’ is based on the white-noise model as shown in Equation (1), while the scheme ‘sln’ is related to the fundamental model and employs an unscaled white-noise method using an individual estimation of the noise level. The ‘mln’ corresponds to the noise algorithm with the non-white noise method. The choice of threshold rescaling algorithm depends upon the noise estimated level.

2.2 Basic forecasting model

The BPNN model, which is trained by the method called back-propagation learning algorithm, is one of the typical artificial neural network models. It is composed of three types of layers: the input layer, hidden layer, and output layer. The architecture of BPNN is determined by the number of nodes in each layer. And each node is a neuron that computed the inner product of the input vector and weight vector using a nonlinear transfer function to get a scalar result.

The BPNN algorithm can be depicted as Algorithm 1:

Algorithm 1: BPNN
1: /Initialization, include the ω _ij* and θ _j */
2: FOR EACH sample X , DO
3: WHILE not stopping, DO
4: /forwards propagation of the input/
5: FOR EACH unit j in the hidden and output layer, DO
6: Calculate the output O_j, $O_{j} = \frac{1}{1 + e^{- S_{j}}} = \frac{1}{1 + e^{- (\sum_{i} ω_{ij} a_{i} + θ_{j})}}$
7: END FOR
8: FOR EACH unit j in the output layer, DO
9: Calculate the error E _j , E_j = O_j (1 - O_j) ∑_k ω_jkE_k
10: END FOR
11: /Backpropagation of the error/
12: FOR EACH unit j in the hidden layer, DO
13: calculate the error E _j , E_j = O_j (1 - O_j) ∑_k ω_jkE_k
14: END FOR
15:/adjust the network parameters/
16: FOR EACH network weight ω _ij , DO
17: ω_ij = ω_ij + (l) E_jO_j
18: END FOR
19: FOR EACH biased θ _j , DO
20: θ_j = θ_j + (l) E_j
21: END FOR
22: END WHILE
23: END FOR

2.3 Artificial intelligence optimization algorithm

In this part, the principle of the original artificial bee colony algorithm is mentioned, and then the modified optimization algorithm is described in detail.

2.3.1 Original artificial bee colony algorithm

Karaboga established an artificial bee colony (ABC) algorithm to settle practical issues, which is an artificial intelligence method inspired by the performance of honeybees foraging for nectar [36]. The ABC algorithm is composed of three groups of honeybees: employed bees, onlookers, and scouts. As shown in Fig. 1, the honeybee foraging behavior can help us understand the ABC algorithm better [37].

Fig. 1

Behavior of honeybee foraging for nectar.

The population of the ABC algorithm is composed of SND-dimensional vectors of decision variables, and each solution X _i is represented as $X_{i} = {x_{i, 1}, x_{i, 2}, . . ., x_{i, D}}, i = 1, 2, . . ., SN$ (2) where D is the solution space, and the number of food sources equals half the population size, which is marked as SN.

In the beginning, each solution X _i can be created with the lower and upper bounds, and it is obtained by Equation (3): $x_{_{i, j}} = x_{\min, j} + r a n d (0, 1) (x_{\max, j} - x_{\min, j})$ (3) where i = 1,2, ...,SN, j = 1,2, ...,D, rand (0, 1) is a random number from 0 to 1.

Each employed bee is responsible for modifying the position of the food source by randomly selecting an around food source. A new food source V _i can be obtained as follows: $v_{i, j} = x_{i, j} + φ_{i, j} (x_{i, j} - x_{k, j})$ (4) where k &z.epsi;1,2, ...,SN, j &z.epsi;1,2, ...,D are randomly selected indexes; k must not be equal to i, and φ _ij is a random number in the range [–1, 1].

Each watching bee selects a better source from all the hired bees. The watching bee chooses a source by applying the roulette wheel selection method, which is represented as $p_{i} = {fit}_{i} / \sum_{j = 1}^{SN} {fit}_{i}$ (5) where fit denotes the fitness value of the solution. After this process, the watching bee will improve the solution of the hired bee using Equation (4).

If an individual cannot be further improved after a given number of trials (denoted by limit), then the individual is discarded. If X _i is abandoned, then the scout comes into being a novel solution to replace X _i calculated by Equation (3).

2.3.2 Modified artificial bee colony algorithm

The relevant literature suggests that the search equation determined by Equation (4) does excellently at exploration but weakly at exploitation [38, 39]. To overcome the weakness of the original ABC, a modified search equation is developed as: $v_{i, j} = w \cdot X_{best, j} + θ_{i, j} (X_{best, j} - X_{i, j})$ (6) where w denotes the inertia weight and X _best,j denotes the best solution in the current population. The modified search equation guides the movement of the population using the information of X _best,j . The new solution is driven by the previous cycle’s best solution. The weight w presents the impact from the best solution X _best,j . A small one accelerates the convergence to optima, while a large one promotes global exploration. Therefore, the modified equation can improve the development capability and speed up the convergence. If the stop criterion of the algorithm is reached, this process will end and output the best solution. Generally, the maximum cycle number (MCN) is widely applied in stopping the algorithm.

The MABC algorithm can be generalized as Algorithm 2:

Algorithm 2: MABC
1: /Initialization /
2: Randomly generate SN points in the search space as the initial population.
3: Calculate the objective function values of the population.
4: WHILE MCN < Max.MCN, DO
5: /The employed bee phase /
6: FORi = 1,2, ...,SN, DO
7: Generate a candidate solution V_i by Equation (6)
8: Evaluate f (V_i) and set MCN = MCN + 1
9: IFf (V_i) < f (X_i), THEN
10: Set X_i = V_i, trial_i = 1, otherwise, set trial_i = trial_i + 1
11: END IF
12: END FOR
13: /Calculate the probability values p_i by Equation (5), set t = 0, i = 1/
14: /The onlookers phase /
15: WHILEt≤SN, DO
16: IFrand (0, 1) < p_i, THEN
17: Generate a candidate solution V_i by Equation (6).
18: Evaluate f (V_i) and set MCN = MCN + 1
19: END IF
20: IFf (V_i) < f (X_i), THEN
21: Set X_i = V_i, trial_i = 1, otherwise, set trial_i = trial_i + 1
22: Set t = t + 1
23: End IF
24: Set i = i + 1
25: IFi = SN, THEN
26: Set i = 1
27: END IF
28: END WHILE
29: /The scouts phase /
30: IF max (trail_i)> limit, THEN
31: Replace X _i with a new random solution by Equation (3).
32: END IF
33: END WHILE
34: RETURN the best solution

2.4 Forecasting with rolling mechanism

As we know, recent data can be applied for improving prediction accuracy [40]. The rolling mechanism, as a metabolism method, updates the input by abandoning old data in each loop. Normally, it is employed to improve the forecast performance [41]. In each loop, the next step of forecasting always uses the most recent data. Of course, the ‘recent data’ not only refers to the true value but can also be understood as a predictive value. In this context, the rolling mechanism also can be combined with one forecasting model to achieve multi-step forecasting.

The BPNN model with rolling mechanism, denoted as RBP algorithm, can be depicted as Algorithm 3:

Algorithm 3: RBP
1: Build a BP model using the training data
2: Set k = 1, s = step
3: WHILEk ≤ s, DO
4: Input the data set, get the simulation result prediction
5: Reconstruct the input data using the latest simulation result prediction_k
6: Set k = k + 1
7: END WHILE
8: RETURN the prediction data set: (prediction_1, prediction_2,_…,prediction_s)

From Fig. 2, we can understand the forecasting process of the RBP algorithm well. The model is established to make multi-step predictions.

Fig. 2

An example of the forecasting procedure by RBP.

3 The proposed electrical power load forecasting model

The proposed model will be elaborated in this section, and the flowchart is displayed in Fig. 3. It is composed of four parts.

Fig. 3

The flowchart of the proposed model.

3.1 Part one: Data selection and data preprocessing

The neural network is very sensitive to historical data, bad data will make the training and prediction of neural network disturbance [42]. On the one hand, training data is crucial for one model’s forecasting performance. As a result, in this study, data selection (see Fig. 4 Part b). is designed to select suitable training datasets to build the model, which can further improve the forecasting performance by providing training datasets with the same properties as testing datasets. On the other hand, the power load signals are generally noisy, hence, in this study, the wavelet de-noising algorithm is employed to reduce the interferences from the original data to elevate the influence of noise information. Compared with the low-frequency component, the high-frequency component has more randomness and less influence on future electrical load data. As a result, the sequence with the highest frequency is eliminated, other sequences are reconstructed, and major fluctuations of load sequence are maintained, which are input into the load prediction model as independent variables.

Fig. 4

The overview of our experiments.

3.2 Part two: Input and output selection

Selecting suitable network inputs and outputs plays a vital role in establishing the network structure because the dynamic behavior of the network is highly dependent on the selected inputs and outputs. Many researchers choose the load data in the first few periods as inputs, and some recent load data as outputs. There will be more than one input and output, especially the number of outputs, it is possible to weaken the performance of forecast and the possibility of improving the accuracy due to the complex structure of the BPNN that is caused by large amounts of weight and biases. In this paper, we found that the first three periods of load, are the prevalent candidate inputs having an important influence on the characters of the load profile. Therefore, in this paper, taking one-step forecasting as an example, the input number is 3, meaning that the electrical power load forecasting value

$\hat{x} (t)$ (model output) is obtained according to the denoised historical data {x (t - 1) , x (t - 2) , x (t - 3)} (model input). Similarly, the optimal input set and corresponding output for multi-step forecasting can be determined in conjunction with the rolling mechanism.

3.3 Part three: Determine the optimization techniques

There are many studies of optimization techniques to optimize neural networks. Nevertheless, it is noted that directly optimizing the basic BPNN model is time-consuming due to the structure of the model becoming complicated with the increasing number of nodes. As we mentioned above, our BPNN model has a proper size, so we can get an excellent model by artificial intelligence optimization methods. In this study, the MABC algorithm is adopted as an optimization technique. This method improves the performance of the model and solves the problem that the model is easy to fall into the local minimum because it can achieve the goal without considering the error function that is differentiable or not. The algorithm shows great strength in assessing connection weights and improving performance. Therefore, the MABC is suitable for optimizing the BPNN model.

3.4 Part four: Building the model and evaluation

In this section, the optimal parameters adjusted by MABC are performed to train the BPNN model. And then, combined with the rolling mechanism, we build the proposed model. Eventually, the novel model is adopted to predict the 1-step and 6-step load data forecasting. After the predicted values of the models are acquired, the comparison between different models was conducted in this paper to evaluate and prove the superiority of the proposed model for multi-step power load forecasting.

4 Experiments and analysis

For the sake of assessing the performance of the proposed model in conducting load forecasting, two experiments are conducted in this part with the load data of the State of New South Wales, Australia. The schematic diagram of our experiments is displayed in Fig. 4 Part a.

4.1 Data selection

The selection of datasets is one of the vital steps in prediction. For the sake of improving forecasting performance and verifying the adaptability of the novel model applied in short term load prediction, in this paper, we also have to take the influence of the seasonal factors on the power load data into account. As can be seen from Fig. 4 Part b. in this paper, we first classify the data by the quarter, and then we identify the index of weekdays or weekends [43] in each quarter. Therefore, the original dataset is divided into totally eight types of electrical power data, and we will separately predict the electrical power of different types.

4.2 The performance metric

To better evaluate the predictive performance and learn the model features more comprehensively, three performance measurement rules are first adopted, as shown in Table 2. The smaller indices values represent better forecast performance.

Table 2
Three metric rules

Metric Definition Equation

MAE The mean absolute forecast error of T times forecast results $MAE = \frac{1}{T} \sum_{i = 1}^{T} | p_{i}^{true} - p_{i}^{forecast} |$

RMSE The square root of the average of the prediction error squares $RMSE = \sqrt{\frac{1}{T} \sum_{i = 1}^{T} {| p_{i}^{true} - p_{i}^{forecast} |}^{2}}$

MAPE The average absolute percentage error $MAPE = \frac{1}{T} \sum_{i = 1}^{T} \frac{| p_{i}^{true} - p_{i}^{forecast} |}{p_{i}^{true}} \times 100 %$

Metric	Definition	Equation
MAE	The mean absolute forecast error of T times forecast results	$MAE = \frac{1}{T} \sum_{i = 1}^{T} \| p_{i}^{true} - p_{i}^{forecast} \|$
RMSE	The square root of the average of the prediction error squares	$RMSE = \sqrt{\frac{1}{T} \sum_{i = 1}^{T} {\| p_{i}^{true} - p_{i}^{forecast} \|}^{2}}$
MAPE	The average absolute percentage error	$MAPE = \frac{1}{T} \sum_{i = 1}^{T} \frac{\| p_{i}^{true} - p_{i}^{forecast} \|}{p_{i}^{true}} \times 100 %$

Besides, to evaluate the improvement percentages of accuracy between the two algorithms, the decreased relative error (RE) is proposed in the study, as presented in Table 3.

Table 3

The decreased relative error (RE)

Metric	Definition	Equation
RE _MAE	The decreased relative error of MAE	${RE}_{{MAE}_{ij}} = \frac{{MAE}_{{model}_{i}} - {MAE}_{{model}_{j}}}{{MAE}_{{model}_{i}}} \times 100 %$
RE _RMSE	The decreased relative error of RMSE	${RE}_{{RMSE}_{ij}} = \frac{{RMSE}_{{model}_{i}} - {RMSE}_{{model}_{j}}}{{RMSE}_{{model}_{i}}} \times 100 %$
RE _MAPE	The decreased relative error of MAPE	${RE}_{{MAPE}_{ij}} = \frac{{MAPE}_{{model}_{i}} - {MAPE}_{{model}_{j}}}{{MAPE}_{{model}_{i}}} \times 100 %$

4.3 Experimental setup

To assess the performance of the proposed novel model, two experiments are conducted in this paper. As previously mentioned, the original dataset is divided into totally eight types of electrical power data, and respectively predict the different power series with the power load of New South Wales, and separately compare the performance of the different models. And the testing sample is composed of one and five day’s data for the case study of weekdays, and one day’s data for the case study of weekends. Although we separately choose one day and five days as the testing sample and showed all the metrics values for the testing sample that we choose in weekday’s study, instead of listing all the figures of testing results, we only list the figure of the testing result by five days sample for weekdays. The one-day testing sample is only adopted to verify the proposed model can effectively apply for load forecasting without retraining the network using the recent data. It means that the proposed model has a high generalization performance. Furthermore, it is believed that a retraining network can be applied for improving forecasting accuracy as long as the conditions permit. Retraining the network, however, is not the major concentration of this study. Therefore, we adopt a simple method that achieves the ideal accuracy without retraining the network using the new data.

Moreover, to determine the best experimental parameters of Wavelet de-noising, BPNN, and MABC, such as the number of decomposition levels, the number of nodes, the number of follower bees, and so on, the trial and error approach are employed to settle this question. Table 4 shows the selection result of the experimental parameters by the method.

Table 4
The experiment parameters in this study

Experimental parameters Default value

Wavelet de-noising

Mother wavelets sym

Decomposition levels 2

Threshold selection algorithm heursure

Soft or hard thresholding s

Threshold rescaling options mln

BPNN

Node number of the input layer 3

Node number of the hidden layer 7

Node number of the output layer 1

The learning velocity 0.1

The maximum number of training 500

Training requirements precision 0.00004

MABC

The number of follower bees 30

Total number of food sources 15

Maximum cycle number 500

Limit for abandonment 100

The lower and upper bounds [–1, 1]

Experimental parameters	Default value
Wavelet de-noising
Mother wavelets	sym
Decomposition levels	2
Threshold selection algorithm	heursure
Soft or hard thresholding	s
Threshold rescaling options	mln
BPNN
Node number of the input layer	3
Node number of the hidden layer	7
Node number of the output layer	1
The learning velocity	0.1
The maximum number of training	500
Training requirements precision	0.00004
MABC
The number of follower bees	30
Total number of food sources	15
Maximum cycle number	500
Limit for abandonment	100
The lower and upper bounds	[–1, 1]

4.4 Experiment I: Based on half-hourly load data

For the sake of estimating the effectiveness of the novel model, three models are established to make one-step predictions and six-step predictions. Table 5-6 displays the comparison of the four quarterly prediction results of each model. And MAE, MAPE, RMSE, TIME are adopted to measure the forecasting performance. Besides, the average value of the indexes of the four quarters is calculated to show the model’s average performance level in one year. Meanwhile, Fig. 5 shows the prediction results of one-step, six-step ahead achieved by the different models based on five day’s samples. Whether on weekdays or weekends, it is also clear that the proposed model performs better than any other.

Fig. 5

The forecasting results of the developed model and other models (Experiment I).

Table 5

The results of the proposed model and other models (Experiment I)

Metric	(1) Testing on weekdays sample (1 day)						(2) Testing on weekdays sample (5 days)						(3) Testing on weekends sample (5 days)
One step			Six step			One step			Six step			One step			Six step
RBP	RM	WDRM	RBP	RM	WDRM	RBP	RM	WDRM	RBP	RM	WDRM	RBP	RM	WDRM	RBP	RM	WDRM
ABCBP	ABCBP	ABCBP	ABCBP	ABCBP	ABCBP	ABCBP	ABCBP	ABCBP	ABCBP	ABCBP	ABCBP
First Quarter
MAE	85.7196	80.7152	51.3762	265.0867	228.5385	203.0402	90.4396	84.8808	48.0833	270.9624	238.9903	187.2943	79.7506	79.6086	52.1151	265.5847	252.6654	208.3759
MAPE	0.99%	0.91%	0.60%	3.03%	2.63%	2.24%	1.03%	0.95%	0.55%	3.13%	2.68%	2.16%	1.03%	0.95%	0.69%	3.15%	2.93%	2.51%
RMSE	85.7196	80.7152	51.3762	304.8073	262.2434	236.8856	90.4396	84.8808	48.0833	310.6628	274.0830	218.7465	79.7506	79.6086	52.1151	311.9090	292.1804	245.1831
TIME	17.8332	179.8898	291.0254	17.8332	179.8898	291.0254	17.8332	179.8897	291.0253	17.8332	179.8898	291.0254	5.3239	161.6442	176.9455	5.3239	161.6442	176.9455
Second Quarter
MAE	89.1883	71.7553	58.7048	270.9088	251.7841	230.0887	111.1125	95.3567	87.4009	359.3288	346.2365	342.4631	116.4519	116.5882	74.5603	381.1779	361.2086	311.6916
MAPE	0.96%	0.78%	0.65%	2.95%	2.77%	2.53%	1.19%	1.03%	0.94%	3.84%	3.77%	3.69%	1.30%	1.35%	0.80%	4.32%	3.95%	3.39%
RMSE	89.1883	71.7553	58.7048	318.5574	301.1997	275.1045	111.1125	95.3567	87.4009	417.9844	413.0928	403.1601	116.4519	116.5882	74.5603	444.7346	427.6981	367.0893
TIME	18.9979	182.2998	290.0561	18.9979	182.2998	290.0561	18.9979	182.2998	290.0560	18.9979	182.2998	290.0561	4.2605	180.4059	178.8546	4.2605	180.4058	178.8545
Third Quarter
MAE	98.8070	92.4772	72.7160	394.5758	362.4342	346.2530	107.9591	103.0581	81.3610	437.2439	395.4712	390.8002	82.3839	92.8976	49.9508	338.9031	242.5593	199.1061
MAPE	1.07%	1.01%	0.80%	4.13%	3.89%	3.58%	1.20%	1.15%	0.90%	4.95%	4.43%	4.39%	1.05%	1.17%	0.62%	4.47%	3.23%	2.52%
RMSE	98.8070	92.4772	72.7160	460.7456	426.4145	412.8572	107.9591	103.0581	81.3610	513.0927	466.4038	468.6007	82.3839	92.8975	49.9508	399.1477	271.2948	234.0266
TIME	17.5793	180.3888	294.5463	17.5793	180.3888	294.5463	17.5793	180.3888	294.5463	17.5793	180.3888	294.5463	4.2059	170.5569	170.8954	4.2059	170.5569	170.8954
Fourth Quarter
MAE	91.6738	87.9120	25.0847	310.8427	289.0915	246.0250	81.8187	82.9622	25.8862	251.8524	247.1590	193.2928	59.6657	53.1674	23.8008	253.4294	205.6471	171.8144
MAPE	0.97%	0.92%	0.27%	3.01%	2.82%	2.44%	0.97%	0.93%	0.30%	2.86%	2.75%	2.14%	0.84%	0.76%	0.33%	3.71%	3.00%	2.43%
RMSE	91.6738	87.9120	25.0847	363.5344	337.3087	308.3076	81.8187	82.9622	25.8862	291.9273	287.0334	237.8314	59.6657	53.1674	23.8008	302.2310	238.9702	210.1584
TIME	19.0580	184.3887	289.8896	19.0580	184.3887	289.8896	19.0580	184.3887	289.8896	19.0580	184.3887	289.8896	4.3973	170.1266	185.8674	4.3973	170.1267	185.8674
Average
MAE	91.3472	83.2150	51.9704	310.3535	282.9621	256.3517	97.8325	91.5645	60.6828	329.8469	306.9643	278.4626	84.5630	85.5655	50.1067	309.7738	265.5201	222.7470
MAPE	1.00%	0.91%	0.58%	3.28%	3.03%	2.70%	1.09%	1.02%	0.67%	3.70%	3.41%	3.10%	1.05%	1.06%	0.61%	3.91%	3.28%	2.71%
RMSE	91.3472	83.2150	51.9704	361.9112	331.7916	308.2887	97.8325	91.5645	60.6828	383.4168	360.1533	332.0847	84.5630	85.5654	50.1067	364.5056	307.5359	264.1144
TIME	18.3671	181.7418	291.3793	18.3671	181.7418	291.3793	18.3671	181.7417	291.3793	18.3671	181.7418	291.3793	4.5469	170.6834	178.1407	4.5469	170.6834	178.1407

(1) Table 5. Part (1) shows the comparison result of the different models using half-hourly data from weekdays, and the testing sample composed of one day’s data. By comparing the three prediction models, it can be seen that the proposed model is robust and can obtain better performance, as shown by the smaller MAPE value, MAE value, and RMSE value. For instance, in the first quarter, the one-step and six-step forecasting MAPE of the proposed model is 0.60% and 2.24% respectively, and the RBP model is 0.99% and 3.03% the RMABCBP model is 0.91% and 2.63%. For the weekday one-step forecasting in the first quarter, we can come to the conclusion that, compared with RBP and RMABCBP, the developed model leads to reductions of 39.3939% and 34.0659% in MAPE. For six-step forecasting, compared with RBP and RMABCBP, the developed model leads to reductions of 26.0726% and 14.8289% in MAPE, respectively. For the other three quarters, the RE values are represented in Table 6. Part (1).

Table 6

The decreased relative error (RE, %) between different models (Experiment I)

(1) Testing on weekdays sample (1 day)						(2) Testing on weekdays sample (5 days)						(3) Testing on weekends sample (5 days)
Metric	RMABCBP		WDRMABCBP		WDRMABCBP		RMABCBP		WDRMABCBP		WDRMABCBP		RMABCBP		WDRMABCBP		WDRMABCBP
	vs RBP		vs RMABCBP		vs RBP		vs RBP		vs RMABCBP		vs RBP		vs RBP		vs RMABCBP		vs RBP
	1-step	6-step	1-step	6-step	1-step	6-step	1-step	6-step	1-step	6-step	1-step	6-step	1-step	6-step	1-step	6-step	1-step	6-step
First Quarter
RE _MAE	5.8381	13.7873	36.3488	11.1571	40.0648	23.4061	6.1464	11.7995	43.3520	21.6310	46.8338	30.8781	0.1781	4.8645	34.5358	17.5289	34.6524	21.5407
RE _MAPE	8.0808	13.2013	34.0659	14.8289	39.3939	26.0726	7.7670	14.3770	42.1053	19.4030	46.6019	30.9904	7.7670	6.9841	27.3684	14.3345	33.0097	20.3175
RE _RMSE	5.8381	13.9642	36.3488	9.6696	40.0648	22.2835	6.1464	11.7748	43.3520	20.1897	46.8338	29.5872	0.1781	6.3251	34.5358	16.0850	34.6524	21.3927
Second Quarter
RE _MAE	19.5463	7.0595	18.1875	8.6167	34.1788	15.0678	14.1800	3.6435	8.3432	1.0898	21.3402	4.6937	–0.1170	5.2388	36.0482	13.7087	35.9733	18.2294
RE _MAPE	18.7500	6.1017	16.6667	8.6643	32.2917	14.2373	13.4454	1.8229	8.7379	2.1220	21.0084	3.9062	–3.8462	8.5648	40.7407	14.1772	38.4615	21.5278
RE _RMSE	19.5463	5.4488	18.1875	8.6638	34.1788	13.6405	14.1800	1.1703	8.3432	2.4045	21.3402	3.5466	–0.1170	3.8307	36.0482	14.1709	35.9733	17.4588
Third Quarter
RE _MAE	6.4062	8.1459	21.3687	4.4646	26.4060	12.2468	4.5397	9.5536	21.0533	1.1811	24.6372	10.6219	–12.7618	28.4281	46.2303	17.9145	39.3683	41.2498
RE _MAPE	5.6075	5.8111	20.7921	7.9692	25.2336	13.3172	4.1667	10.5051	21.7391	0.9029	25.0000	11.3131	–11.4286	27.7405	47.0085	21.9814	40.9524	43.6242
RE _RMSE	6.4062	7.4512	21.3687	3.1794	26.4060	10.3937	4.5397	9.0995	21.0533	–0.4710	24.6372	8.6713	–12.7617	32.0315	46.2302	13.7372	39.3683	41.3684
Fourth Quarter
RE _MAE	4.1035	6.9975	71.4661	14.8972	72.6370	20.8523	–1.3976	1.8636	68.7976	21.7941	68.3615	23.2516	10.8912	18.8543	55.2342	16.4518	60.1097	32.2042
RE _MAPE	5.1546	6.3123	70.6522	13.4752	72.1649	18.9369	4.1237	3.8462	67.7419	22.1818	69.0722	25.1748	9.5238	19.1375	56.5789	19.0000	60.7143	34.5013
RE _RMSE	4.1035	7.2141	71.4661	8.5978	72.6370	15.1916	–1.3976	1.6764	68.7976	17.1416	68.3615	18.5306	10.8912	20.9313	55.2342	12.0566	60.1097	30.4643
Average
RE _MAE	8.9025	8.8259	37.5468	9.4042	43.1067	17.4001	6.4069	6.9373	33.7267	9.2850	37.9728	15.5782	–1.1855	14.2858	41.4405	16.1092	40.7463	28.0937
RE _MAPE	9.0000	7.6220	36.2637	10.8911	42.0000	17.6829	6.4220	7.8378	34.3137	9.0909	38.5321	16.2162	–0.9524	16.1125	42.4528	17.3780	41.9048	30.6905
RE _RMSE	8.9025	8.3224	37.5468	7.0836	43.1067	14.8165	6.4069	6.0674	33.7267	7.7935	37.9728	13.3881	–1.1854	15.6293	41.4405	14.1192	40.7463	27.5417

(2) From Table 5. Part (2), it can also be concluded that the proposed model forecast the half-hourly load data effectively, and among all models, the proposed model has obtained the best prediction results. When comparing Table 5. Parts (1) and (2), we can conclude that: (a) With the increase in the number of test samples, if the test results change in a good direction, it can be said that the model has a strong ability to forecast the power load. For example, in the first quarter and fourth quarter, the latter evaluation index values are smaller than the former. These results state clearly that our proposed model can effectively apply to electricity load forecasting, at least in the first and fourth quarters; (b) In the second and third quarters, the latter result is worse than the former. But, we can’t assert that our proposed model is poor at forecasting. Because the former result shows that our developed model can realize high-precision forecasting. The accuracy shown by the latter result is also acceptable to some extent; (c) As for us, the reason why the latter becoming worse is that the load data has a weak regularity in these quarters. We assume that if we add new data into the training sample after the end of each day, and then retrain the model, the performance should be better.

(3) From Table 5. Part (3) and Table 6. Part (3), can be analyzed that: (a) The proposed model has the best performance among all models, indicating that the model can capture the characteristics of the load data series, and achieve good load forecasting performance. In addition to the second quarter, the MAPE value of our proposed model is less than 3% in the six-step forecasting experiment, and the MAPE value of one-step and six-step prediction are all within a reasonable range. The one-step and six-step average MAPE values of this year are 0.61% and 2.71% respectively; (b) When comparing the proposed model with the original model, the former has improved the performance of the latter. The average MAPE promoting percentages of the individual RBP model by the proposed model in one-step and six-step predictions are 41.9048% and 30.6905% respectively; (c) When comparing the proposed model with the RMABCBP model, the former has also improved the performance of the latter considerably. The MAPE promoting percentages of the RMABCBP model by the proposed model in one-step and six-step predictions are 42.4528% and 17.3780% respectively; (d) The cause of the phenomenon displayed in (a) - (c) is that: the combination of the WD algorithm and the MABC algorithms has promoted the forecasting capacity of the individual RBP model effectively. Because the WD algorithm reduces the jumping character of the original load data and the MABC algorithms select the best initial weights and biases for the built RBP model, the optimized BPNN model can obtain high accuracy prediction performance.

In summary, we can reach our conclusion that the proposed model can forecast the one-step and six-step half-hourly load data effectively on weekdays and weekends.

4.5 Experiment II: Based on hourly load data

In this section, we will compare the performance of the different models in the six-step forecasting based on hourly load data that is divided into weekdays data and weekend data. The weekday prediction precision measurements of the four quarters are calculated and compared in this experiment, and the results are displayed in Tables 7–8. Meanwhile, Fig. 6 shows the prediction results at five days’ samples of six-step ahead forecasting achieved by the different models. Whether on weekdays or weekends, it is also clear that the proposed method performs better than any other model.

Fig. 6

The forecasting results of the developed model and other models (Experiment II).

Table 7

The results of the proposed model and other models (Experiment II)

Metric	(1) Testing on weekdays sample (1 day)			(2) Testing on weekdays sample (5 days)			(3) Testing on weekends sample (5 days)
	RBP	RMABCBP	WDRMABCBP	RBP	RMABCBP	WDRMABCBP	RBP	RMABCBP	WDRMABCBP
First Quarter
MAE	451.0889	358.7513	276.0700	336.7305	297.5169	250.6921	319.0316	263.9950	197.9846
MAPE	5.10%	4.16%	3.12%	3.73%	3.34%	2.82%	4.12%	3.58%	2.72%
RMSE	529.2162	415.8172	318.5797	404.8212	344.3646	294.3878	360.4585	294.4515	232.7260
TIME	10.5950	164.9105	162.6505	10.5950	164.9105	162.6505	10.3968	202.0124	203.0905
Second Quarter
MAE	461.8105	339.7543	286.4142	698.9062	490.9293	488.0048	539.3617	529.2699	390.7298
MAPE	4.74%	3.69%	2.91%	7.59%	5.40%	4.98%	6.79%	6.45%	4.63%
RMSE	577.4967	409.2892	353.6900	847.3419	581.3913	580.8470	640.1419	607.9552	439.6245
TIME	11.5453	160.4535	158.5661	11.5453	160.4535	158.5661	11.8249	210.1285	205.9875
Third Quarter
MAE	519.1095	464.8408	262.0661	469.9496	429.3766	343.9463	377.2923	351.5416	262.4008
MAPE	6.51%	5.59%	2.98%	5.82%	5.11%	3.35%	4.80%	4.45%	3.28%
RMSE	620.6591	547.1462	304.8690	557.8416	505.5938	406.1993	443.9068	420.3026	312.5485
TIME	13.5459	163.8865	160.3553	13.5459	163.8865	160.3552	10.0257	205.8674	206.4576
Fourth Quarter
MAE	301.2628	275.9744	176.5807	483.7693	388.3008	252.8533	306.1548	286.9488	187.3172
MAPE	3.31%	3.04%	1.98%	5.08%	4.15%	2.72%	3.95%	3.67%	2.38%
RMSE	349.7239	315.5972	200.6702	567.2558	447.3525	298.1826	349.8921	325.0924	219.4091
TIME	10.0255	159.5690	166.5557	10.0255	159.5689	166.5557	12.6559	210.0456	211.9665
Average
MAE	433.3179	359.8302	250.2828	497.3389	401.5309	333.8741	385.4601	357.9388	259.6081
MAPE	4.92%	4.12%	2.75%	5.56%	4.50%	3.47%	4.92%	4.54%	3.25%
RMSE	519.2740	421.9625	294.4522	594.3151	469.6756	394.9042	448.5998	411.9504	301.0770
TIME	11.4279	162.2049	162.0319	11.4279	162.2049	162.0319	11.2258	207.0134	206.8755

(1) Table 7. Part (1) shows the comparison result of the different models using hourly data of weekdays, and the testing sample composed of one day’s data. By comparing the three prediction models, it can be seen that the proposed model has good robustness and can obtain better performance, as shown by the smaller MAPE value, MAE value, and RMSE value. For instance, in the fourth quarter, the six-step forecasting MAPE of the proposed model is 1.98% and the RBP model is 3.31% the RMABCBP model is 3.04%. And the proposed model’s average MAPE value of six-step prediction is 2.75%.

(2) When comparing the proposed model with the RBP model and the RMABCBP model, the performance of the proposed model is better than the others. For example, in the first quarter, the developed model leads to reductions of 38.8235% and 25.0000% in MAPE in six-step prediction. This demonstrates that the de-noising method is powerful in the field of data preprocessing.

(3) As shown in Table 7. Part (1), in addition to the first quarter, the MAPE value of our proposed model is less than 3% in the six-step forecasting experiment, and the MAPE value of the six-step prediction is all within a reasonable range. The six-step prediction MAPE values of four quarters are 3.12% 2.91% 2.98% and 1.98% respectively. The six-step average MAPE values of this year are 2.75% respectively.

(4) To further validate the model for weekday load forecasting capability, more data was selected as the testing sample. Table 7. Part (2) and Table 8. Part (2), shows the result of the different models using hourly data of weekdays (5 days as test sample) and the corresponding RE values. According to the comparisons of the results, the proposed algorithm is superior to other algorithms and has a satisfactory forecasting performance in six-step forecasting. Therefore, we can conclude that our data preprocessing methods and optimization algorithm is effective. Furthermore, the developed model can predict the load data effectively on weekdays.

Table 8

The decreased relative error (RE, %) between different models (Experiment II)

Metric	(1) Testing on weekdays sample (1 day)			(2) Testing on weekdays sample (5 days)			(3) Testing on weekends sample (5 days)
	RMABCBP	WDRMABCBP	WDRMABCBP	RMABCBP	WDRMABCBP	WDRMABCBP	RMABCBP	WDRMABCBP	WDRMABCBP
	vs RBP	vs RMABCBP	vs RBP	vs RBP	vs RMABCBP	vs RBP	vs RBP	vs RMABCBP	vs RBP
First Quarter
RE_MAE	20.4699	23.0470	38.7992	11.6454	15.7385	25.5511	17.2511	25.0044	37.9420
RE_MAPE	18.4314	25.0000	38.8235	10.4558	15.5689	24.3968	13.1068	24.0223	33.9806
RE_RMSE	21.4277	23.3847	39.8016	14.9341	14.5128	27.2795	18.3120	20.9629	35.4361
Second Quarter
RE_MAE	26.4299	15.6996	37.9801	29.7575	0.5957	30.1759	1.8711	26.1757	27.5570
RE_MAPE	22.1519	21.1382	38.6076	28.8538	7.7778	34.3874	5.0074	28.2171	31.8115
RE_RMSE	29.1270	13.5843	38.7546	31.3865	0.0936	31.4507	5.0281	27.6880	31.3239
Third Quarter
RE_MAE	10.4542	43.6224	49.5162	8.6335	19.8964	26.8121	6.8251	25.3571	30.4516
RE_MAPE	14.1321	46.6905	54.2243	12.1993	34.4423	42.4399	7.2917	26.2921	31.6667
RE_RMSE	11.8443	44.2802	50.8798	9.3661	19.6590	27.1838	5.3174	25.6373	29.5914
Fourth Quarter
RE_MAE	8.3941	36.0156	41.3865	19.7343	34.8821	47.7327	6.2733	34.7210	38.8162
RE_MAPE	8.1571	34.8684	40.1813	18.3071	34.4578	46.4567	7.0886	35.1499	39.7468
RE_RMSE	9.7582	36.4157	42.6204	21.1374	33.3450	47.4342	7.0878	32.5087	37.2924
Average
RE_MAE	16.9593	30.4442	42.2404	19.2641	16.8497	32.8679	7.1399	27.4714	32.6498
RE_MAPE	16.1750	33.3131	44.0997	18.9919	22.9444	37.5788	7.6806	28.3196	33.8250
RE_RMSE	18.7399	30.2184	43.2954	20.9720	15.9198	33.5531	8.1697	26.9143	32.8852

(5) The weekends’ prediction precision measurements of the four quarters are also calculated and compared in this experiment, and the results are displayed in Table 7. Part (3) and Table 8. Part (3). As can be seen from Table 7. Part (3) and Table 8. Part (3), the proposed model achieves the highest precision compared with the RBP model and RMABCBP model. More precisely, in the six-step forecasting, in the first quarter, the developed model achieves reductions of 33.9806% and 24.0223% in the MAPE in comparison with the RBP and RMABCBP models. In the meantime, the decreases in MAE are 37.9420% and 25.0044% and the decreases in RMSE are 35.4361% and 20.9629% severally. For the other three quarters, the decreases in MAPE and MAE are distinctly presented in Table 8 Part (3),. the result of the different models using hourly data of weekends is also clearly listed in Table 7 Part (3).

In summary, combining the result shown in Tables 7-8 and Fig. 6, a conclusion can be drawn that the developed model can forecast the six-step hourly load data effectively on weekdays and weekends.

5 Conclusions

In this study, an innovative model based on data selection, data preprocessing, artificial neural network, modified artificial intelligence optimization algorithm, and rolling mechanism is developed for electrical load multi-step forecasting. Based on the case study in the Australia electricity market, the following findings and contributions can be summarized: (1) the developed model improves the electrical power load forecasting performance when compared with the benchmark models; (2) the data selection ensures that the developed model can be trained using datasets with the same properties as testing datasets; (3) the modified optimization algorithm can improve the model from perspectives of parameters optimization, while data preprocessing can reduce the difficulty of modeling from the perspective of data characteristics; (4) the rolling mechanism can be combined with forecasting technique to achieve multi-step forecasting, which can be considered as a promising method in the future study.

In addition, the main focus of this study is developing an innovative multi-step forecasting model based on historical electrical power load data, while leaving some research directions for future study. On the one hand, some variables like weather conditions can be considered to take full advantage of influencing factors from the perspectives of experimental data; on the other hand, a more powerful time series forecasting model can be established based on deep learning methods and other techniques from the perspectives of modeling technique. Furthermore, in the future study, the modeling framework and idea can be extended to other forecasting fields, such as wind speed forecasting [44], grey forecasting model [45], tourism demand forecasting [46], oil price forecasting [47], bending force forecasting in the hot strip rolling process [48], air quality prediction [49], and building energy consumption prediction [50].

Footnotes

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No. 72101138), Humanities and Social Science Fund of Ministry of Education of the People’s Republic of China (Grant No. 21YJCZH198); Shandong Provincial Natural Science Foundation, China (Grant No. ZR2021QG034, ZR2022QG036); Social Science Planning Project of Shandong Province (Grant No. 22DJJJ24); and Special Support for Post-doc Creative Funding in Shandong, China (Grant No. 202103018).

References

, Huang

, Hu

et al. Ultra-short term power load forecasting based on CEEMDAN-SE and LSTM neural network, Energy and Buildings 279 (2023), 112666.

Önkal

, Sayım

K.Z.

and Lawrence

, Wisdom of groupforecasts: Does role-playing play a role? Omega 40(6) (2012), 693–702.

Yang

, Guo

, Sun

et al. An interval decomposition-ensemble approach with data-characteristic-driven reconstruction for short-term load forecasting, Applied Energy 306 (2022), 117992.

Yang

, Wang

and Wang

, Research and application of a novel hybrid model based on data selection and artificial intelligence algorithm for short term load forecasting, Entropy 19(2) (2017), 52.

Xiao

, Shao

, Yu

et al. Research and application of a hybrid wavelet neural network model with the improved cuckoo search algorithm for electrical power system forecasting, Applied Energy 198 (2017), 203–222.

Grid security: the common responsibility of the whole society. http://finance.people.com.cn/GB/8215/77189/77192/5290158.html.

Indian power grid collapse-the most serious power outage in the universal history of electric power http://www.indiancn.com/news/shehui/608.html.

Fischer

and Wilfert

H.H.

, Updating of daily load prediction in power systems using AR-modles//Stochastic control: proceedings of the 2nd IFAC symposium, Vilnius, Lithuanian SSR, USSR, 19-23 May, Pergamon 2 (1987), 243.

Pappas

S.S.

, Ekonomou

, Karampelas

et al. Electricity demand load forecasting of the Hellenic power system using an ARMA model, Electric Power Systems Research 80(3) (2010), 256–264.

10.

Ling

, Shantz

, Mahadevan

et al. Stochastic prediction of fatigue loading using real-time monitoring data, International Journal of Fatigue 33(7) (2011), 868–879.

11.

Lee

C.M.

and Ko

C.N.

, Short-term load forecasting using lifting scheme and ARIMA models, Expert Systems with Applications 38(5) (2011), 5902–5911.

12.

Wang

, Wang

, Zhao

et al. Application of residual modification approach in seasonal ARIMA for electricity demand forecasting: a case study of China, Energy Policy 48 (2012), 284–294.

13.

Al-Hamadi

H.M.

and Soliman

S.A.

, Long-term/mid-term electric load forecasting based on short-term correlation and annual growth, Electric Power Systems Research 74(3) (2005), 353–361.

14.

Mohamed

and Bodger

, Forecasting electricity consumption in New Zealand using economic and demographic variables, Energy 30(10) (2005), 1833–1843.

15.

Christiaanse

W.R.

, Short-term load forecasting using general exponential smoothing. Power Apparatus and Systems, IEEE Transactions On (1971), 900–911.

16.

Zhang

, Bao

, Yan

, Cao

and Du

, Research on processing of short-term historical data of daily load based on Kalman filter, Power System Technol 10 (2003), 9.

17.

Kelo

and Dudul

, A wavelet Elman neural network for short-term electrical load prediction under the influence of temperature, International Journal of Electrical Power & Energy Systems 43(1) (2012), 1063–1071.

18.

Xie

, Yi

, Hu

et al. Short-term power load forecasting based on Elman neural network with particle swarm optimization, Neurocomputing 416 (2020), 136–142.

19.

Wang

, Yu

, Chen

et al. Short-term load forecasting considering improved cumulative effect of hourly temperature, Electric Power Systems Research 205 (2022), 107746.

20.

, Kong

, Yue

et alShort-term electrical load forecasting using hybrid model of manta ray foraging optimization and support vector regression, Journal of Cleaner Production (2023), 135856.

21.

Dai

, Yang

and Leng

, Forecasting power load: A hybrid forecasting method with intelligent data processing and optimized artificial intelligence, Technological Forecasting and Social Change 182 (2022), 121858.

22.

Zhang

, Tang

, Wu

et al. Short term electricity price forecasting using a new hybrid model based on two-layer decomposition technique and ensemble learning, Electric Power Systems Research 205 (2022), 107762.

23.

Mousa

, Aghaei

, Afrasiabi

et al. Probability density function forecasting of electricity price: Deep Gabor convolutional mixture network, Electric Power Systems Research 213 (2022), 108325.

24.

Gao

, Niu

, Ji

et al. Mid-term electricity demand forecasting using improved variational mode decomposition and extreme learning machine optimized by sparrow search algorithm, Energy 261 (2022), 125328.

25.

Yang

, Sun

, Hao

et al. A novel machine learning-based electricity price forecasting model based on optimal model selection strategy, Energy 238 (2022), 121989.

26.

Iwabuchi

, Kato

, Watari

et al. Flexible electricity price forecasting by switching mother wavelets based on wavelet transform and Long Short-Term Memory, Energy and AI 10 (2022), 100192.

27.

Meng

, Wang

, Zhai

et al. Electricity price forecasting with high penetration of renewable energy using attention-based LSTM network trained by crisscross optimization, Energy 254 (2022), 124212.

28.

Khan

Z.A.

, Ullah

, Haq

I.U.

et al. Efficient short-term electricity load forecasting for effective energy management, Sustainable Energy Technologies and Assessments 53 (2022), 102337.

29.

Özen

and Yıldırım

, Application of bagging in day-ahead electricity price forecasting and factor augmentation, Energy Economics 103 (2021), 105573.

30.

, Sun

, Wang

et al. A novel two-stage seasonal grey model for residential electricity consumption forecasting, Energy 258 (2022), 124664.

31.

Gradolewski

and Redlarski

, Wavelet-based de-noising method for real phonocardiography signal recorded by mobile devices in noisy environment, Computers in Biology and Medicine 52 (2014), 119–129.

32.

Hubbard

B.B.

The World According to Wavelets The Story of a Mathematical Technique in the Making, Universities Press 1998.

33.

Messer

S.R.

, Agzarian

and Abbott

, Optimal wavelet de-noising for phonocardiograms, Microelectronics Journal 32(12) (2001), 931–941.

34.

Kaiser

A friendly guide to wavelets, Springer Science & Business Media 2010.

35.

Verma

, Sarangi

and Kolekar

M.H.

, Stator winding fault prediction of induction motors using multiscale entropy and grey fuzzy optimization methods, Computers & Electrical Engineering 40(7) (2014), 2246–2258.

36.

Karaboga

and Basturk

, On the performance of artificial bee colony (ABC) algorithm, Applied Soft Computing 8(1) (2008), 687–697.

37.

Karaboga

and Akay

, A comparative study of artificial beecolony algorithm, Applied Mathematics and Computation 214(1) (2009), 108–132.

38.

Zhu

and Kwong

, Gbest-guided artificial bee colony algorithmfor numerical function optimization, Applied Mathematics andComputation 217(7) (2010), 3166–3173.

39.

Karaboga

and Akay

, A modified artificial bee colony (ABC) algorithm for constrained optimization problems, Applied Soft Computing 11(3) (2011), 3021–3031.

40.

Akay

and Atak

, Grey prediction with rolling mechanism for electricity demand forecasting of Turkey, Energy 32(9) (2007), 1670–1675.

41.

Wang

, Du

, Lu

et al. An improved grey model optimized by multi-objective ant lion optimization algorithm for annual electricity consumption forecasting, Applied Soft Computing 72 (2018), 321–337.

42.

Liu

, Tian

, Liang

et al. Wind speed forecasting approach using secondary decomposition algorithm and Elman neural networks, Applied Energy 157 (2015), 183–194.

43.

, Wang

and Goel

, Short-term load forecasting by wavelet transform and evolutionary extreme learning machine, Electric Power Systems Research 122 (2015), 96–103.

44.

Yang

, Hao

and Hao

, Innovative ensemble system based on mixed frequency modeling for wind speed point and interval forecasting, Information Sciences 622 (2023), 560–586.

45.

Zhang

, Yin

and Yang

, Predicting bioenergy power generation structure using a newly developed grey compositional data model: A case study in China, Renewable Energy 198 (2022), 695–711.

46.

Yang

and Sun

, Tourism demand forecasting and tourists’ search behavior: evidence from segmented Baidu search volume, Data Science and Management 4 (2021), 1–9.

47.

, Wang

and Hao

, Deterministic and uncertainty crude oil price forecasting based on outlier detection and modified multi-objective optimization algorithm, Resources Policy 77 (2022), 102780.

48.

Tian

, Luan

, Li

et al. Interval prediction of bending force in the hot strip rolling process based on neural network and whale optimization algorithm, Journal of Intelligent & Fuzzy Systems 43(6) (2022), 7297–7315.

49.

Bharathi

P.D.

, Narayanan

V.A.

and Sivakumar

P.B.

, Fog computing enabled air quality monitoring and prediction leveraging deep learning in IoT, Journal of Intelligent & Fuzzy Systems 43(5) (2022), 5621–5642.

50.

, Yu

, Wang

et al. A short-term building energy consumption prediction and diagnosis using deep learning algorithms, Journal of Intelligent & Fuzzy Systems 43(5) (2022), 6831–6848.

An innovative model for electrical load forecasting: A case study in Australia

Abstract

Keywords

1 Introduction

2 Methodology

2.1 Data preprocessing

Table 1 Four threshold selection algorithms [33] Name Description Minimax Minimax thresholding principle Rigrsure Adaptive threshold selection by the principle of SURE Sqtwolog Threshold equals sqrt (2*log(length(X))) Heursure Heuristic variant of Rigrsure and Sqtwolog

2.3 Artificial intelligence optimization algorithm

2.3.1 Original artificial bee colony algorithm

3.3 Part three: Determine the optimization techniques

3.4 Part four: Building the model and evaluation

4 Experiments and analysis

4.1 Data selection

4.2 The performance metric

Footnotes

Acknowledgments

References

Table 1
Four threshold selection algorithms [33]

Name Description

Minimax Minimax thresholding principle

Rigrsure Adaptive threshold selection by the principle of SURE

Sqtwolog Threshold equals sqrt (2**log(length(X)))

Heursure Heuristic variant of Rigrsure* and Sqtwolog