Accurate Deep Model for Electricity Consumption Forecasting Using Multi-Channel and Multi-Scale Feature Fusion CNN–LSTM

Abstract

Electricity consumption forecasting is a vital task for smart grid building regarding the supply and demand of electric power. Many pieces of research focused on the factors of weather, holidays, and temperatures for electricity forecasting that requires to collect those data by using kinds of sensors, which raises the cost of time and resources. Besides, most of the existing methods only focused on one or two types of forecasts, which cannot satisfy the actual needs of decision-making. This paper proposes a novel hybrid deep model for multiple forecasts by combining Convolutional Neural Networks (CNN) and Long-Short Term Memory (LSTM) algorithm without additional sensor data, and also considers the corresponding statistics. Different from the conventional stacked CNN–LSTM, in the proposed hybrid model, CNN and LSTM extracted features in parallel, which can obtain more robust features with less loss of original information. Chiefly, CNN extracts multi-scale robust features by various filters at three levels and wide convolution technology. LSTM extracts the features which think about the impact of different time-steps. The features extracted by CNN and LSTM are combined with six statistical components as comprehensive features. Therefore, comprehensive features are the fusion of multi-scale, multi-domain (time and statistic domain) and robust due to the utilization of wide convolution technology. We validate the effectiveness of the proposed method on three natural subsets associated with electricity consumption. The comparative study shows the state-of-the-art performance of the proposed hybrid deep model with good robustness for very short-term, short-term, medium-term, and long-term electricity consumption forecasting.

1. Introduction

Accurate, reliable, and timely electricity consumption information is the key to ensure a stable and efficient electricity supply. However, the electricity consumption in daily life usually fluctuates with time, region, season, temperature, and society. Even in the same city, electricity consumption in different areas may vary. Typically, the power company arranges fixed personnel to provide the electricity supply of the fixed place. Once there is a surge of local electricity consumption, the electricity supply of the area will be affected, thus affecting the healthy life. Forecasting actual future electricity consumption can make corresponding adjustments in time to avoid this situation. There are three types of forecasts according to the forecasting duration: short-term forecast (STF), medium-term forecasting (MTF), and long-term forecasting (LTF). Generally, STF focuses on the time range from 24 h to one week; MTF focuses on the time range from one week to one month, and LTF focuses on the time range longer than the other two types [1,2].

Different types of electric power forecasting have different purposes: The short-term electricity consumption forecasting supports the personnel and equipment arrangement of the next day. The medium-term electricity consumption forecasting gives decision support for the human resource allocation of the power company. The long-term electricity consumption forecasting is a significant decision basis from the macro perspective. To deal with an emergency such as line damage, natural disasters, and so on, very short-term (VST) power consumption forecasting is also essential. We defined very short-term electricity forecasting in this paper is hourly.

Different methods have been carried out for power forecasting, which mainly contains three categories: regression-based, time series-based, and machine learning-based methods [3]. The regression-based method can be divided into two sub-classes: Normal regression such as simple linear regression, lasso regression, ridge regression, and autoregression methods such as vector auto-regression (AR) and vector moving average (MA). Especially, Tang et al. applied a LASSO-based approach to forecast the current solar power generation by using the past 30 days of data and achieve better results than the support vector machine-based method [4]. Yu et al. applied an improved AR-based method for short-term hourly load forecasting, which was tested on two kinds of real-time hourly data sets [5]. Ordinary regression only considers the relationship of current variables and needs additional related data. However, the dependent variables are affected by the relevant variables of the current and past periods. The autoregressive model takes into account the impact of the current and past points, but it requires data that must be stationary. To overcome the disadvantages that occurred in the regression-based method, a time series-based method is presented for energy consumption forecasting. Autoregressive integrated moving average model (ARIMA) is one of the most excellent time series-based models. It not only considers the impact of the current and past periods but also can be used for non-stationary data. The ARIMA model can be symbolized as $ARIMA\left(p,d,q\right)$, where $p$ is the parameter of lag $p^{th}$ order autocorrelation, $q$ is the parameter of lag $q^{th}$ order partial autocorrelation, and $d$ is the parameter for generating stationary time series. Usually, $d$ ranges from 1 to 2; $p$, $q$ range from 8 to 10 [3,6]. ARIMA has been employed for short-term power forecasting in [7,8]. Mitkov et al. [9] proved that ARIMA could be used for MTF and LTF for electricity forecasting.

The above regression-based and time series-based methods consider the relationship between the past and the current time is linear. However, most of the hidden relationships are nonlinear. The machine learning-based method can overcome this issue by using different nonlinear kernels such as support machine vectors (SVMs). Although some studies have successfully used SVM to predict energy consumption, there will be overfitting when data is broad [3,10]. Fortunately, the deep learning-based method can handle the overfitting problem very well with a good forecasting result. Recently, the convolutional neural network (CNN) [11], one of the mighty deep learning methods, has been widely applied for power forecasting due to its excellent feature extraction capacity. Li et al. [12] reshapes the data into two dimensions as an image and then applies CNN for short-term electrical load forecasting. A novel multi-scale CNN considering time-cognition was presented in [13] for multi-step short-term load forecasting. Suresh et al. developed a new sliding window algorithm to generate data to forecast solar PV using multi-head CNN in making STF and MTF [14]. Kim et al. applied CNN for VST photovoltaic power generation forecasting and compared it with the long short-term memory (LSTM) method, proving that the CNN-based method is better than LSTM for VSTF [15]. Another deep learning-based method LSTM was used for LTF and STF problems as it has long-term memory [16]. Ma et al. [17,18,19,20] employed LSTM for STF in the area of power. For LTF problems, Agrawal et al. presented a novel model by combining LSTM and recurrent neural network (RNN) to predict future five-year electricity loads [21]. An enhanced deep model was proposed in Han’s work [22] for STF and MTF of electric load. The attention mechanism was combined into LSTM for short-term photovoltaic power forecasting in Zhou’s work [23]. In order to overcome the shortcomings of a single model, some hybrid models are proposed for power forecasting, such asWang et al. [24] proposed ARIMA–LSTM for daily water level forecasting. It used LSTM to forecast the residuals through results and then utilized ARIMA to train the model with residuals. However, it is complex to build so many ARIMA models to get the residuals when the data size is massive. Another hybrid model, CNN–LSTM, is proposed in Kim’s work [25] for minutely, hourly, daily, and weekly electricity energy consumption forecasting using multi-variables as input. Hu et al. [26] also applied CNN–LSTM for daily urban water demand forecasting using related meteorological data. However, collecting such correlated variables is hard and time-consuming in reality. Although Yan et al. proposed a hybrid of CNN–LSTM to predict power consumption by using raw time series, it only focused on VSTF (minutely) [27]. Moreover, Yan et al. [28] proposed a hybrid LSTM model, in which wavelet transform (WT) is applied to preprocess the raw univariate time series firstly. Later, stationary parts of transformation are selected for VSTF (minutely). However, there is a problem that occurred in Yan’s work [28] is that we still need to select the stationary part by hand.

The limitations of current research for energy consumption forecasting are summarized as follows. On the one hand, most above methods only focused on one or two types of forecasts among VSTF, STF, MTF, and LTF. However, we need to master various types of future power consumption information to improve power supply efficiency and realize the smart grid. On the other hand, most existing methods refer to multi-variable regression, which requires collecting multiple related data. Motivated by this, we present a highly accurate deep model for various types of electricity forecasts by only using self-history data. We call this deep model multi-channels and scales CNN–LSTM (MCSCNN–LSTM). The proposed MCSCNN–LSTM employs dual channels as input to extract rich, robust feature representations from different domains of raw data. One channel is the raw sample, and the other is the information of statistics corresponding to the raw sample. We adopted the parallel structure of CNN–LSTM, which is different from conventional CNN–LSTM. At first, the CNN part in this structure extracts multi-scale and global features from the first channel using multi-scale and wide convolution technology. Then, the LSTM part guarantees to extract features that have a long-time dependency from the raw data. At last, combined with CNN, LSTM extracted features with statistics channels as comprehensive features to forecast the electricity consumption.

The biggest challenge is that the power consumption time series only has fewer time points rather than vibration signal, image, and video. It requires us to use CNN seriously due to the obtained data being relatively low dimensional. The strategy of this paper is to use a few pooling layers to reduce the loss of valuable information.

The main contributions of this paper are summarized as follows:

• To the best of our understanding, a few types of research focused on using one model for VSTF, STF, MTF, and LTF. This paper addresses this issue with MCSCNN–LSTM.
• The hybrid deep model MCSCNN–LSTM was designed, trained, and validated. The MCSCNN–LSTM obtains the highest performance compared to the current state-of-the-art methods.
• The proposed method can accurately forecast electricity consumption by inputting the self-history data without any additional data and any handcrafted feature selection operation. Therefore, it reduces the cost of data collection while simultaneously keeping high accuracy.
• The feature extraction capacity of each part has been analyzed.
• The excellent transfer learning and multi-step forecasting capacities of the proposed MCSCNN–LSTM have been proven.

The rest of the paper is arranged as follows. Section 2 formalizes our problem and gives the data generation method. Section 3 introduces the theoretical background of the proposed approach consisting of CNN, LSTM, and statistical components knowledge. Section 4 gives the proposed architecture for electricity forecasting. Each type of forecasting mission is defined in this section also. In Section 5, comparative experimental studies on three datasets are carried out. In Section 6, we discuss the proposed deep model. Section 7 presents the conclusions and feature work.

2. Problem Formulations

Our purpose is to forecast future power consumption using self-historical data. The self-historical data of power consumption could be expressed as a time series as follows:

$$T=\left(t_1,t_2,t_3,\dots ,t_i,\dots ,t_N\right)$$

(1)

where $T$ contains $N$ data points. Different types of forecasts have different elements in $T$. We defined four types of forecasts as shown in

Table 1. Defined four types of forecasts.

Forecasts Types	Length of Input History Data	Outputs
VSTF (hourly)	Previous $H$ hours	Next one hour
STF (daily)	Previous $D$ days	Next one day
MTF (weekly)	Previous $W$ weeks	Next one week
LTF (monthly)	Previous $M$ months	Next one month

and described follows.

• VSTF: Hourly forecasting, power consumption data of previous $H$ hours are employed for next-hour power consumption forecasting.
• STF: Daily forecasting, applying power consumption data of previous $D$ days to get the next day’s power consumption.
• MTF: Weekly forecasting, using power consumption data of previous $W$ weeks to forecast power consumption of the next week.
• LTF: Monthly forecasting, the power consumption data of previous $M$ months are employed to get the next one month.

The time series $T$ needs to reconstruct as Equation (2) to satisfy the input of the proposed deep model. The input matrix includes $N-L$ samples; the length of sample $x\left(t\right)$ is $L$. Different types of forecasts have different $L$, which corresponds to $H$, $D$, $W$, and $M$. The corresponding output is defined as Equation (3). Every output is the electricity consumption of the next duration.

$$Input=\left[\begin{array}{cccccc}{t}_1& t_2& t_3& \cdots & t_{L-1}& t_L\\ t_2& t_3& t_4& \cdots & t_L& t_{L+1}\\ ⋮& ⋮& ⋮& \ddots & ⋮& ⋮\\ t_{N-L}& t_{N-L+1}& t_{N-L+2}& \dots & t_{N-2}& t_{N-1}\end{array} \right]$$

(2)

$$Output=\left[\begin{array}{c}{t}_{L+1}\\ t_{L+2}\\ ⋮\\ t_N\end{array}\right]$$

(3)

3. Methods

3.1. CNN

CNN is a typical feedforward neural network. It virtually constructs various filters that can extract the characteristics of input data. Through these filters, the input data is convoluted and pooled, and the topology features hidden in the data are extracted step by step. With the deep entry of the network layer, the extracted features are abstracted. Therefore, the extracted features have translation, scaling, and rotation invariance. The sparse connection in CNN reduces the number of training parameters and speeds up the convergence; weight sharing effectively avoids algorithm overfitting; and downsampling makes full use of the features of the data and reduces the data dimension, optimizing the network structure [29,30]. CNN can deal with one-dimensional (1-D) signals and sequences, two-dimensional (2-D) images, and three-dimensional (3-D) videos. We apply CNN to extract features from 1-D sequences in this paper.

The essential components of CNN are convolutional operation and pooling operation. Through convolution operation, high-level local region feature representations are extracted with different filter kernels. The convolution process is described as follows:

$$x_j^l=f({\displaystyle \sum }_{i\in M_j}{x}_i^{l-1}\times k_{ij}^l+B_j^l)$$

(4)

where $x_j^l$ are the j feature maps of $l^{th}$ layer through convolution operation between $l-1^{th}$’s output $x_i^{l-1}$ and $j$ filters $k_{ij}^l$, $B_j^l$ is $j$ bias of each feature map; $i$ is in the range of $j$ input values $M_j$. After convolution operation, $x_j^l$ is processed with an activation function. The comprehensive result $a_j^l$ is the input of the next layer. Rectified Linear Unit (ReLU) was widely applied to accelerate and converge the CNN, which enabled a nonlinear expression of input signals to enhance the representation ability. Which is formalized as follows:

$$a_j^l=\max \left(0,x_j^{l-1}\right)$$

(5)

Another key component of CNN is the pooling operation, which is employed to reduce the dimension of input data and ensure scale invariance. Thus, obtained features are more stable, especially when data is acquired from a noisy environment. There are three types of pooling operations: maximum, minimum, and average pooling operation. We give an example of utilizing maximum pooling, which is expressed as follows:

$$p_j^l=max\left(q_j^{l-1}\left(t\right)\right),t\in \left[\left(j-1\right)w,jw\right]$$

(6)

where $p_j^l$ is the output of maximum value among $l-1^{th}$ layer obtained feature maps $q_j^{l-1}\left(t\right)$, $t$ is $t^{th}$ output neurons at $j^{th}$ layer in the network, $w$ is the width of pooling size. Further details of CNNs can be found in LeCun’s paper [11].

3.2. LSTM

The traditional feedforward neural networks only accept information from input nodes. They do not “remember” input to different time series [31]. Thus, it cannot extract the hidden features which have a long-time dependency from raw data. LSTM is proposed for overcoming this shortcoming as its long-term memory character [16]. It is a kind of special recurrent neural network (RNN). It implements memory function through gate structure in one cell as shown in Figure 1. The key point of the LSTM cell is the upper horizontal line, and it works like a conveyor belt; the information will not change during the transmission. It deletes old information or adds new information through three gate structures: forgot gate, input gate, and out gate. The output value of three gates and updated information are expressed using $f_t$, $i_t$, $o_t$, $\widehat{C_t}$ as shown in the following formulas:

$$f_t=\sigma \left(w_f·\left[h_{t-1},x_t\right]+b_f\right)$$

(7)

$$i_t=\sigma \left(W_i·\left[h_{t-1},x_t\right]+b_i\right)$$

(8)

$$\widehat{C_t}=\tan \mathrm{h}\left(W_C·\left[h_{t-1},x_t\right]+b_C\right)$$

(9)

$$C_t=f_t\ast C_{t-1}+i_{t\ast }\widehat{C_t}$$

(10)

$$o_t=\sigma \left(w_O·\left[h_{t-1},x_t\right]+b_O\right)$$

(11)

$$h_t=\sigma \left(w_O·\left[h_{t-1},x_t\right]+b_O\right)\ast \tan \mathrm{h}\left(C_t\right)$$

(12)

where $C_t$ represents the memory cell which integrates the old useful information $f_t\ast C_{t-1}$ and adds some new information $i_{t\ast }\widehat{C_t}$. $W_{f,i,o}$ represents the weight and bias vectors of the abovementioned gates. $\sigma$ is activation function $sigmoid$, $h_{t-1}$ is the LSTM value of the previous time step, and $x_t$ is input data.

3.3. Statistical Components

Statistics is a variable used to analyze and test data in statistical theory. It is the macro performance of data in the statistical domain. This paper creatively applied statistical components as one of the dual channels in the deep model to extract more features. The input matrix of raw time series we already defined as Equation (2). Each raw sample $x\left(t\right)ϵInput$ corresponds to six tuples named $Stati$stics, which contains $mean$, $max$, $min$, standard deviation ($Sd$), skewness ($Skew$), and kurtosis ($Kurt$), which are defined as Equations (13)–(18).

$$mean\left(t\right)=\frac{1}{M}{\displaystyle \sum }_{t=1}^{M}x\left(t\right)$$

(13)

$$\max \left(t\right)=\max \left(x\left(t\right)\right)$$

(14)

$$\min \left(t\right)=\min \left(x\left(t\right)\right)$$

(15)

$$Sd\left(t\right)=\sqrt{\frac{1}{M}{\displaystyle \sum }_{t=1}^M{\left(x\left(t\right)-mean\left(t\right)\right)}^2}$$

(16)

$$Skew\left(t\right)=E\left[{\left(\frac{x\left(t\right)-mean\left(t\right)}{sd\left(t\right)}\right)}^3\right]$$

(17)

$$Kurt\left(t\right)=E\left[{\left(\frac{x\left(t\right)-mean\left(t\right)}{sd\left(t\right)}\right)}^4\right]$$

(18)

4. Proposed Deep Model

We propose a deep model that has dual-channel inputs. One is raw data, and the other contains the six tuples of statistical components as we defined above. The overall architecture of the proposed deep model for electricity consumption forecasting can be seen from Figure 2 and a detailed configuration of the proposed deep model is shown in

Table 2. Detailed configuration information of the proposed deep model.

Layer	Output Shape	Connected To	Parameters
Input1 (Raw)	(None, 24, 1)	−	0
Input2 (Statistic)	(None, 6, 1)	−	0
Conv1_1	(None, 12, 16)	Input1	48
Conv1_2	(None, 8, 16)	Input1	64
Conv1_3	(None, 6, 16)	Input1	80
Conv2_1	(None, 12, 16)	Conv1_1	528
Conv2_2	(None, 8, 16)	Conv1_2	528
Conv2_3	(None, 6, 16)	Conv1_3	528
Concatenate_1	(None, 26, 16)	Conv2_1, Conv2_2, Conv2_3	0
Static_Conv	(None, 11, 10)	Concatenate_1	2570
Global_Maxpooling	(None, 5, 10)	Static_Conv	0
Flatten_1	(None, 50)	Global_maxpooling	0
LSTM_1	(None, 24, 20)	Input2	1760
LSTM_2	(None, 10)	LSTM_1	1240
Flatten_2	(None, 6)	Input2	0
Concatenate_2	(None, 66)	LSTM_2 Flatten_1 Flatten_2	0
Dense (Output)	(None, 1)	Concatenate_2	67

.

Modifying the hyperparameters such as number and size of filter can improve the performance of the model. We defined the configuration information of MCSCNN–LSTM empirically. Here, we defined $H,D,W,M$ as 24. The filter numbers of CNN decrease from 16 to 10 due to the shallow CNN layer being in charge of the detailed local feature extraction; the deeper CNN layer functions to capture abstract global feature representations. At the same time, LSTM is relatively time-consuming, so we defined proper output nodes in two LSTM layers as 20 and 10, respectively. From Figure 2, we can see six parts in our MCSCNN–LSTM: Input, CNN feature extraction, LSTM feature extraction, feature fusion, output, and weights updating. Every part is explained in detail as follows.

4.1. Input

The proposed deep model has double-channel inputs: raw sample $x\left(t\right)$ from the input matrix and six statistic components $Statistics\left(x\left(t\right)\right)$, which can be written as:

$$In=\left\{\left(x\left(t\right),Statistics\left(x\left(t\right)\right)\right)\right\}$$

(19)

Moreover, we transform the raw sample into one tensor with the shape of (24, 1), and six tuples $Stati$stics into tensor with the shape of (6, 1) to satisfy the input requirements of the deep model. The reshaped tensor is defined in (20).

$$Tenso{r}_{in}=\left\{Reshape\left(In\right)\right\}=\left\{\left(Reshape\left(x\left(t\right)\right),Reshape\left(Statistic\left(x\left(t\right)\right)\right)\right)\right\}$$

(20)

4.2. CNN Feature Extraction

Different from other CNNs, we adopted only one pooling layer to reduce the dimension of extracted features due to the data we used with lees dimensions, which is motivated by [31]. Firstly, CNN models the multi-scale local features from raw sample tensor $Reshape\left(x\left(t\right)\right)$ at three-scale convolution operations—Conv1_1, Conv1_2, and Conv1_3—using different size kernels with shapes of $1\times 2$, $1\times 3$, $1\times 4$. The convoluted results are activated by “ReLU”, as defined in Equation (5). In order to obtain more robust features, we applied one more convolutional layer to extract the abstract feature representations again; they are Conv2_1, Conv2_2, and Conv2_3. At last, extracted multi-local features are processed by one wide convolution layer “Global_Conv” to obtain global representations. CNN extracted features are expressed as Equation (21) and then are flattened for the next step, where $CNN()$ is the process of this sub-section.

$${\mathrm{CNN}}_{\mathrm{features}}=\mathrm{CNN}\left(\mathrm{Reshape}\left(\mathrm{x}\left(\mathrm{t}\right)\right)\right)$$

(21)

4.3. LSTM Feature Extraction

Although CNN extracted rich feature representations, we doubt whether CNN can extract some critical hidden features having a long-time dependency. Based on this point, we employed LSTM to extract those features. Two-stacked LSTM layers are employed in this deep model, and every LSTM layer contains some LSTM cells as shown in Figure 1. The features LSTM extracted are expressed as Equation (22). $LSTM()$ is the process of this sub-section.

$${\mathrm{LSTM}}_{\mathrm{features}}=\mathrm{LSTM}\left(\mathrm{Reshape}\left(\mathrm{x}\left(\mathrm{t}\right)\right)\right)$$

(22)

4.4. Feature Fusion

Conventional CNN–LSTM is a stacked structure, in which CNN extracted features are processed by LSTM again. Different from conventional CNN–LSTM, this paper adopted a parallel pattern of CNN–LSTM to extract the features and then merged the features they extracted with flattening statistics components. Therefore, we obtained fusion features that are multi-scale and multi-domain (time and statistic domains), which are expressed as:

$$FUSIO{N}_{features=}Concatenate(CN{N}_{features},LST{M}_{features},Flatten\left(Reshape\left(Statistic\left(x\left(t\right)\right)\right)\right)$$

(23)

4.5. Output

After obtaining the rich, robust feature representations, the output is given by using one full connection layer between the output nodes and the fusion features, which can be defined as:

$$Output=W·FUSIO{N}_{features}+B$$

(24)

where $W$ is the weight matrix and $B$ is the bias. This paper mainly focuses on power consumption forecasting of one duration unit (hourly, daily, weekly, and monthly). It is easy to extend the forecast of multi-duration units by setting the nodes of output; we will discuss this later.

4.6. Updating the Networks

Backpropagation [32] algorithm was employed for updating the weights of the hidden layer according to the loss function, and “Adam” [33] was selected as the optimizer for finding the convergence path. The loss function we applied in this deep model is Mean Squared Error (MSE) as shown in Equation (25), where $y_i$ is ground truth electricity consumption and ${\tilde{y}}_i$ is forecasting electricity consumption using the proposed hybrid deep model.

$$MSE=\frac{1}{N}{\displaystyle \sum }_{i=1}^N{\left(y_i-{\tilde{y}}_i\right)}^2$$

(25)

Electricity forecasting using the proposed model is formalized as Equation (26), where $MCSCNN\_LSTM()$ is our model, and $x{\left(t\right)}^{\prime }$ is new history electricity consumption data points.

$$consumption=MCSCNN\_LSTM\left(x{\left(t\right)}^{\prime },Statistic\left(x{\left(t\right)}^{\prime }\right)\right)$$

(26)

5. Experiment Verification

In order to verify the effectiveness of the proposed deep model, we designed the following experiments using three datasets. The experiments are based on the operating system of Ubuntu 16.04.3, 64 bits with 23.4 GB RAM, and Intel (R) i7-700 CPU of processing speed 3.6 GHz. We used Keras to implement our proposed deep model.

5.1. Dataset Introduction

The data we adopted for validating the priority of the proposed method is from Pennsylvania-New Jersey-Maryland (PJM), which is a regional transmission organization in the USA. It is a part of the Eastern Interconnection grid operating an electric transmission system serving all or parts of some states. Different companies supply different regions. This paper applies three data sets from three companies: American Electric Power (AEP), Commonwealth Edison (COMED), and Dayton Power and Light Company (DAYTON). The raw data set of those is hourly consumption in megawatts (MW), and detailed information is described in

Table 3. Induction of data sets.

Dataset	Start Date	End Date	Length
AEP	2004-12-31 01:00:00	2018-01-02 00:00:00	121,273
COMED	2011-12-31 01:00:00	2018-01-02 00:00:00	66,497
DAYTON	2004-12-31 01:00:00	2018-01-02 00:00:00	121,275

. The data is available on the website of kaggle.com/robikscube/hourly-energy-consumption.

The original data is utilized to validate the effectiveness of VSTF. For the other forecasting tasks, we use an overlapping sample algorithm to generate corresponding samples for each forecast, as shown in Algorithm 1. The stride of the algorithm we defined is one. Notably, we adopted the sample rate of 24 h, 168 h, and 720 h to generate each type of sample for STF, MTF, and LTF. One electricity consumption at different durations is given in Figure 3, in which different types fluctuate differently, respectively, VSTF and STF, which fluctuate frequently.

Algorithm 1: Overlapping sample algorithm

Input: Hourly electricity consumption historical time series $hourly$ Output: Daily, weekly, and monthly electricity consumption historical time series samples and labels. Define the length of samples $D,W,M$ as 24. Step 1: Integrating the original data for different forecasts     $daily<-sum\left(hourly,24\right)$   #adopt the sample rate of 24 h for STF     $weekly<-sum\left(hourly,168\right)$ #adopt the sample rate of 168 h for MTF     $monthly<-sum\left(hourly,720\right)$ #adopt the sample rate of 720 h for LTF Step 2: Generating the feature and label of each sample corresponding to the (2) and (3)     For $i$ in range ($length\left(daily/weekly/monthly\right)$): # different forecasts have different contents        $dail{y}_{features}<-daily\left[i:i+D\right]$        $dail{y}_{lables}<-daily\left[i+D+1\right]$        $weekl{y}_{features}<-weekly\left[i:i+W\right]$        $weekl{y}_{labels}<-weekly\left[i+W+1\right]$        $monthl{y}_{features}<-monthly\left[i:i+M\right]$        $monthl{y}_{labels}<-monthly\left[i+M+1\right]$     End for Return $dail{y}_{features}$, $dail{y}_{labels}$, $weekl{y}_{features}$, $weekl{y}_{labels}$, $monthl{y}_{features}$, $monthl{y}_{labels}$

A description of each data for different forecasts is shown in

Table 4. The description of each data set for different forecasts.

Forecasts	Dataset	Samples
VSTF (Hourly)	AEP	121,249
	COMED	66,473
	DAYTON	121,251
STF (Daily)	AEP	121,225
	COMED	66,449
	DAYTON	121,227
MTF (Weekly)	AEP	121,081
	COMED	66,305
	DAYTON	121,083
LTF (Monthly)	AEP	120,529
	COMED	65,753
	DAYTON	120,531

. The first 80% of samples are utilized for training the model; the last 20% of samples are utilized to validate. Before starting the experiment, we adopted Equation (27) to normalize each data to work out the impact of different sizes of units, where $x^{\prime }$ is the normalized data point of time series $T$ and $x$ is the raw data sample.

$$x^{\prime }=\frac{x-min\left(T\right)}{\max \left(T\right)-min\left(T\right)}$$

(27)

5.2. Evaluation Metrics

In order to fairly evaluate the effectiveness of the proposed MCSCNN–LSTM deep model, we adopted multiple evaluation metrics consisting of the root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE), as shown in Equations (28)–(30), where $N$ is the number of testing samples, the $forecast$ is the forecasted value, and $real$ is the ground truth. RMSE evaluates the model by the standard deviation of the residuals between real values and forecasted values; MAE is the average vertical distance between ground truth values and forecasted values and is more robust to the larger errors than RMSE. However, when massive data are utilized for training and evaluating the model, the RMSE and MAE increase significantly and quickly. Therefore, MAPE is needed, which is the ratio between residuals and actual values.

$$RMSE=\sqrt{\frac{{\sum }_{n=1}^N{\left(forecas{t}_n-rea{l}_n\right)}^2}{N}}$$

(28)

$$MAE=\frac{{\sum }_{n=1}^N\left|forecas{t}_n-rea{l}_n\right|}{N}$$

(29)

$$MAPE=\frac{100\%}{N}{\displaystyle \sum }_{n=1}^N\left|\frac{forecas{t}_n-rea{l}_n}{rea{l}_n}\right|$$

(30)

5.3. Performance Comparison with Other Excellent Methods

We compared our proposed method to other excellent deep learning-based methods: DNN- [34], NPCNN- [35], LSTM- [20], and CNN–LSTM-based [25] methods. The structure and configuration information of the above comparative methods are given in

Table 5. The structure and configuration information of comparative methods.

Method	Structure# Layer (Neurons)	Activation Function
[34] DNN	Input-Dense(24)-Dense(10)-Flatten-Output	Sigmoid
[35] NPCNN	Input-Conv1D(5)-Max1D(2)-Flatten(Dense(1))-Dense(10)-Output	ReLu
[20] LSTM	Input–LSTM(20)–LSTM(20)-Output	ReLu
[25] CNN–LSTM	Input-Conv1D(64)-Max1D(2)-Conv1D(2)-Flatten(Max1D(2))–LSTM(64)-Dense(32)-Output	ReLu

. Because the abovementioned methods employed other additional sensor data, we adopted the structure of them only. Conv1D is a convolutional layer with 1-D; Max1D is a max-pooling layer with 1D. We run 10 times of each deep learning-based method to overcome the impact of randomness, and every time runs at 50 epochs. Furthermore, we found the above NPCNN- [35], LSTM- [20], and CNN–LSTM-based [25] methods did not learn at some iterations. It means the loss does not decrease with the increase of training epochs. Instead, they keep one constant value from the first epoch. In summary, NPCNN, LSTM, and CNN–LSTM highly rely on initial processing. The results of this phenomenon are listed in

Table 6. The non-training times of each deep learning-based method among 10 times.

Dataset	Method	VSTF	STF	MTF	LTF
AEP	[34] DNN	None	None	None	None
	[35] NPCNN	2	3	2	2
	[20] LSTM	5	4	5	2
	[25] CNN–LSTM	2	2	3	2
	Proposed	None	None	None	None
COMED	[34] DNN	None	None	None	None
	[35] NPCNN	3	3	2	2
	[20] LSTM	5	4	5	4
	[25] CNN–LSTM	2	3	4	2
	Proposed	None	None	None	None
DAYTON	[34] DNN	None	None	None	None
	[35] NPCNN	2	2	3	2
	[20] LSTM	4	4	2	3
	[25] CNN–LSTM	2	2	1	2
	Proposed	None	None	None	None

, which gives the times of the above cases during 10-time training processes for each forecast. Notably, the term “None” means it always learns from raw data and is not sensitive to the random initial settings. For electricity consumption, we must avoid unpredicted and unexpected factors. However, NPCNN- [35], LSTM- [20], and CNN–LSTM-based [25] methods highly rely on initialization. The findings show only DNN [34], and the proposed method always learns so that they are considered as stable.

We compared the proposed method to the stable DNN [34] with averaged metrics of 10 times, and also compared averaged metrics of the proposed approach to the best results of three unstable methods: NPCNN [35], LSTM [20], and CNN–LSTM [25] in 10 times, as shown in

Table 7. The comparison results with RMSE.

Dataset	Method	RMSE (VSTF)	RMSE (STF)	RMSE (MTF)	RMSE(LTF)
AEP	[34] DNN	389.79	756.15	2864.03	15,387.72
	[35] NPCNN	476.38	1866.71	4220.96	40,393.06
	[20] LSTM	298.28	124.19	757.13	4876.94
	[25] CNN–LSTM	374.39	711.02	2408.09	20,060.97
	Proposed	294.03	424.14	665.29	3385.70
COMED	[34] DNN	310.69	765.16	3908.04	10,934.82
	[35] NPCNN	439.07	1090.17	6,274.38	14,900.91
	[20] LSTM	251.47	426.46	2925.53	30,407.07
	[25] CNN–LSTM	272.18	501.70	3082.33	4654.41
	Proposed	240.51	377.74	520.02	3122.94
DAYTON	[34] DNN	61.49	112.43	311.37	1299.99
	[35] NPCNN	71.16	183.90	390.88	1399.25
	[20] LSTM	43.84	142.49	107.87	444.95
	[25] CNN–LSTM	47.08	109.42	175.67	502.58
	Proposed	43.68	65.68	95.84	270.40

with RMSE,

Table 8. The comparison results with MAE.

Dataset	Method	MAE (VSTF)	MAE (STF)	MAE (MTF)	MAE (LTF)
AEP	[34] DNN	246.41	583.44	2052.89	10,384.48
	[35] NPCNN	332.21	1682.52	2506.76	16,803.83
	[20] LSTM	198.67	995.27	613.45	3732.41
	[25] CNN–LSTM	248.65	508.70	1705.03	11,723.84
	Proposed	180.94	250.15	494.04	2788.86
COMED	[34] DNN	198.20	611.87	2951.25	8023.53
	[35] NPCNN	333.18	813.53	5427.71	11,953.35
	[20] LSTM	156.24	316.02	2831.15	30,082.99
	[25] CNN–LSTM	179.20	405.19	1181.74	3274.47
	Proposed	142.60	244.50	345.84	2434.41
DAYTON	[34] DNN	39.93	88.92	244.97	1145.00
	[35] NPCNN	49.81	135.24	312.21	1247.53
	[20] LSTM	29.10	116.53	613.45	372.93
	[25] CNN–LSTM	28.82	79.36	131.67	392.52
	Proposed	27.12	38.68	70.04	212.64

with MAE, and

Table 9. The comparison results with MAPE.

Dataset	Method	MAPE (VSTF)	MAPE (STF)	MAPE (MTF)	MAPE (LTF)
AEP	[34] DNN	1.68	0.16	0.08	0.10
	[35] NPCNN	2.32	0.46	0.10	0.17
	[20] LSTM	1.65	0.27	0.03	0.03
	[25] CNN–LSTM	1.70	0.15	0.07	0.11
	Proposed	1.23	0.06	0.02	0.03
COMED	[34] DNN	1.79	0.23	0.16	0.10
	[35] NPCNN	3.02	0.30	0.29	0.15
	[20] LSTM	1.41	0.12	0.15	0.38
	[25] CNN–LSTM	1.68	0.15	0.07	0.04
	Proposed	1.30	0.09	0.02	0.03
DAYTON	[34] DNN	1.99	0.19	0.07	0.08
	[35] NPCNN	2.58	0.28	0.09	0.08
	[20] LSTM	1.36	0.23	0.03	0.03
	[25] CNN–LSTM	1.49	0.16	0.04	0.03
	Proposed	1.38	0.08	0.02	0.01

with MAPE. The findings reveal that our proposed method has absolute priority for different durations electricity forecasting at all evaluation metrics compared to DNN. Even when compared to the best results of the other three methods, the proposed MCSCNN–LSTM keeps the highest performance of all metrics for all data sets except for VSTF on the data set DAYTON with evaluation metric MAPE, and RMSE on data set AEP for STF. LSTM [20] performs a little better. In summary, the proposed MSCSNN–LSTM could forecast the electricity consumption of different durations accurately and stably.

The averaged improvements of MAPE on different data as shown in Figure 4. The results show that it improves a lot at all durations forecasts. Especially for STF, MTF, and LTF, which was beyond 50% compared to all the above methods. We select stable DNN as listed in Table 7 to compare the predicted results, as shown in Figure 5. The findings show both the proposed method and DNN [34] can predict the global trend of electricity consumption at VSTF, STF, and LTF. However, DNN cannot predict long-term electricity consumption. Moreover, the proposed method outperforms DNN; it can predict more detailed irregular trends for VSTF, STF, and LTF, respectively. We can see details from the marked deep-red box in VSTF and STF of Figure 5.

5.4. Feature Extraction Capacity of MCSCNN–LSTM

To better understand the feature extraction capacity of the proposed MCSCNN–LSTM, firstly, we compared it to some single models in MCSCNN–LSTM using the metric of MAPE: Multi-Scale CNN (MSCNN), Multi-Channel and Multi-Scale CNN (MCSCNN), and hybrid conventional stacked CNN–LSTM (SCNN–LSTM). The structure of LSTM is the same as [20], which is not stable. All configurations of those models are the same as MCSCNN–LSTM. The results are average of 10 times as shown in

Table 10. The comparison results for validating the feature learning capacity using averaged MAPE.

Dataset	Method	VSTF	STF	MTF	LTF
AEP	MSCNN	1.91	1.17	0.85	1.26
	MCSCNN	2.28	0.93	0.79	1.19
	SCNN–LSTM	1.84	0.64	0.57	0.75
	Proposed	1.23	0.06	0.02	0.03
COMED	MSCNN	2.36	1.02	0.79	0.86
	MCSCNN	2.31	0.87	0.89	0.58
	SCNN–LSTM	1.93	0.80	1.08	0.43
	Proposed	1.30	0.09	0.02	0.03
DAYTON	MSCNN	2.28	1.14	0.77	0.91
	MCSCNN	2.61	0.81	0.70	0.83
	SCNN–LSTM	2.08	0.63	0.45	0.45
	Proposed	1.38	0.08	0.02	0.01

.

Comparing the MSCNN with the NPCNN [35], we find that the proposed MSCNN is more stable than general CNN-based methods. The results indicate MSCNN with single input cannot extract satisfactory feature representations for different forecasts of electricity consumption by comparing MSCNN with MCSCNN, especially for STF, MTF, and LTF. By comparing SCNN–LSTM to LSTM, we can see the MCSCNN can extract elegant, robust features to avoid instability and improve performance. We computed the averaged improvement of MAPE on three data sets for different duration forecasts, as shown in Figure 6. MSCNN is selected as the baseline. The findings reveal that the proposed method promotes a lot for all kinds of forecasts. Attentively, the results show only the performance of the MCSCNN on data AEP for VSTF decreased. Furthermore, the level of feature extraction capacity is ranked as proposed: > SCNN–LSTM > MCSCNN > MSCNN.

Secondly, we have analyzed the inside features to confirm the productive feature extraction capacity of the proposed deep model. The visualization results using one VSTF sample shown in Figure 7a,b intimate double-channel inputs: one raw data sample and corresponding statistics components by using the normalized data sample of AEP. Figure 7c is a CNN-learned feature map through the raw data sample. Figure 7d is the feature map of LSTM and we marked it with a red box at the comprehensive feature map Figure 7f, and Figure 7e is a statistic feature map that is marked with the yellow box in Figure 7f. The unmarked part in Figure 7f is a CNN-learned feature map. Figure 7f is a comprehensive feature map. The findings reveal that CNN can learn multi-scale robust global features with less noise because it almost has no changes around 0. The feature map of LSTM ranges from −0.100 to 0.075, and the statistic feature map ranges from 0.00 to 1.75, which indicates statistic components are more useful to extract detailed patterns than LSTM. The comprehensive feature maps combined robust multi-scale global features and detailed features of different domains.

5.5. Transfer Learning Capacity Test

We have validated the transfer learning capacity of the proposed method to satisfy the needs in the real-life. For instance, one new company wants to predict electricity consumption, but they do not have enough historical data to train the model. It requires the model with an excellent transfer learning capacity. The following experiments are designed to test the transfer learning capacity of the proposed method, as described in

Table 11. Experiment design for transfer learning capacity test of the proposed deep model.

Forecasts	Training Sets	Testing Sets
VSTF	AEP	COMED, DAYTON
STF	COMED	AEP, DAYTON
MTF	DAYTON	AEP, COMED
LTF	DAYTON	AEP, COMED

. We adopted the training part of AEP as the training set to train the model for VSTF, the training part of COMED to train the model for STF, and the training part of DAYTON to train the model for MTF and LTF. The testing part of others is utilized to test.

The DNN [34] and the proposed MCSCNN–LSTM applied the same data to train and test are considered as comparative experiments to validate the transfer learning capacity. For example, we trained DNN and MCSCNN–LSTM with the training part of COMED, DAYTON, and tested on the testing part of the same data set for VSTF. The results as shown in Figure 8; the x-axis is the testing part of each data set. The results indicate the proposed method has a functional transfer learning capacity, which outperforms DNN [34] for all kinds of forecasts, and a little lower than the proposed method using the same data to train and test the model. We performed a t-test to quantify this difference. The results of the p-value are shown in

Table 12. The p-value of significance test using t-test.

Forecasts	Transfer vs. DNN [34]	Transfer vs. Proposed
VSTF	0.0380	0.4650
STF	0.4800	0.3600
MTF	0.3120	0.1840
LTF	0.1300	0.4230

. If a p-value is higher than 0.05, it means there is no significant difference. The results show there was no significant difference when we utilized different companies’ data for training the model. Moreover, even though DNN [34] employed the same source data to train and test model, its performance is worse than “transfer”. Notably, there is a significant improvement for the VSTF of electricity consumption compared to DNN. In summary, Figure 8 and Table 12 confirmed that the proposed method has an excellent transfer learning capacity against noisy data.

5.6. Multi-Step Forecasting Capacity Test

Accurate one-step forecasting enables decision-makers to create proper policies and measures of the power supply before one duration. Multi-step forecasting can provide multi-step future consumption information in advance. To validate the multi-step forecasting capacity of the proposed method for multiple forecasts, we designed a five-step forecasting experiment and compared it to [27], which tests the multi-step forecasting capacity of their model for VSTF. The input of the proposed MCSCNN–LSTM for multi-step forecasting in Figure 2 has the same shape with one-step forecasting, we only need to change the output into one vector with five elements regarding the five future consumption data points of each forecast. The comparative results using averaged RMSE, MAE, and MAPE of 10 times are shown in

Table 13. The multi-step forecasting capacity test results.

Metrics	RMSE		MAE		MAPE
Forecasts (Data)	Proposed	CNN–LSTM [27]	Proposed	CNN–LSTM [27]	Proposed	CNN–LSTM [27]
VSTF(AEP)	508.33	477.08	354.52	324.73	2.43	2.22
STF(COMED)	1.8311 $\times$ 103	1.8320 $\times$ 103	1.3592 $\times$ 103	1.3612 $\times$ 103	0.50	0.51
MTF(DAYTON)	4.6342 $\times$ 102	1.04$18\times$103	3.0828 $\times$ 102	$8.2458\times {10}^2$	0.11	0.23
LTF(AEP)	1.1251 $\times$ 104	3.0284$\times$104	$6.9459\times$ 103	2.35$23\times$ 104	0.07	0.22

. AEP is adopted for VSTF and LTF; COMED and DAYTON are adopted for STF and MTF. The results indicate the proposed MCSCNN–LSTM performs very well for STF, MTF, and LTF. Especially, the performance of MTF and LTF has increased tenfold compared to the method of [27] using RMSE, MAE, and MAPE. Only the VSTF is a little worse than [27], but they still are the same level. We also give one sample of five-step forecasting of different forecasts as shown in Figure 9. We can see the proposed MCSCNN–LSTM accurately predicts all types of trends from the raw data and it outperforms [27] CNN–LSTM in terms of handing details. Notably, the proposed method has an absolute advantage in terms of STF, MTF, and LTF.

6. Discussion

We have proposed a novel MCSCNN–LSTM that models different domain and multi-scale feature patterns to forecast the electricity consumption at different durations. The difficulty of feature extraction for different durations forecasts using one model, and different duration electricity consumptions have different patterns of the trend as shown in Figure 3, which requires a model with excellent feature extraction capacity with good robustness. Besides, collecting related data such as weather, the temperature is costly and time-consumption. Therefore, we developed MCSCNN–LSTM to extract multi-scale and multi-domain features by only inputting the electricity history data, as shown in Figure 2. We connected CNN and LSTM parallelly with dual inputs, Table 10 and Figure 6 shows it is more effective than conventional stacked CNN–LSTM.

We compared our proposed deep model with other excellent deep models in Table 6, which indicates our proposed model is stable. Furthermore, Table 7, Table 8 and Table 9 and Figure 4 show that we have improved the performance compared to the stable DNN [34] and the best results of NPCNN [35], LSTM [20], and CNN–LSTM [25]. Primarily, it has improved a lot for STF, MTF, and LTF. Figure 5 explained that the proposed method could predict the detailed irregular patterns of electricity consumption.

As can be seen from Table 10, we have analyzed the feature capacity of each part of the proposed MCSCNN–LSTM by comparing the averaged MAPE. In addition, we computed the averaged improvement ratio of the proposed MCSCNN–LSTM by using MCSCNN as the benchmark in Figure 6. It proved that each part of our proposed model has excellent feature extraction capacity. Moreover, we have analyzed the inside feature map of MCSCNN–LSTM as shown in Figure 7, it shows the CNN part of MCSCNN–LSTM can extract multi-scale robust global features, and statistic components are more effective in extracting detailed patterns than LSTM.

As shown in Figure 8, we have designed comparative experiments on three data sets to validate the transfer learning capacity of the proposed MCSCNN–LSTM. The findings from Figure 8 have proven that our proposed deep model has excellent transfer learning skills. In order to quantify the transfer learning capacity, we compared the p-value of the t-test with none-transfer learning methods in Table 12. Moreover, we have confirmed the proposed method could accurately forecast multi-step electricity consumption in advance in Table 13 and Figure 9, the results from Table 13 and Figure 9 indicate our proposed method outperforms CNN–LSTM which was developed in [27].

7. Conclusions

In conclusion, we proposed a novel MCSCNN–LSTM to forecast the electricity consumption at different durations accurately and robustly only by using the self-history data. The comparative analysis has shown that the proposed hybrid deep model MCSCNN–LSTM reaches state-of-the-art performance. The proposed model is compared to other excellent deep learning-based methods to confirm the efficiency and robustness. We run ten times for each model on three data sets to evaluate fairly. The results indicate that our proposed deep model is not sensitive to the initial settings and stable. We compare the forecasted results with other methods to prove that the proposed method can extract more detailed patterns. We also confirmed the necessity of each part in the proposed deep model by comparing the MAPE of each part for electricity forecasting at different durations. We proved that the parallel structure of CNN–LSTM is more potent than conventional stacked CNN–LSTM. We also analyzed the internal feature maps to confirm the feature extraction capacity of each part, and the results show CNN can extract global features; LSTM, and statistic components are in charge of detailed pattern extraction. Some individual experimental cases are designed to validate their excellent transfer learning capacity. We confirmed the proposed MCSCNN–LSTM has excellent multi-step forecasting capacity for STF, MTF, and LTF, respectively. The proposed MCSCNN–LSTM can accurately and stably predict the irregular patterns of electricity consumption at different durations by only using self-history data and have a good transfer learning capacity, which can be easy to extend to other forecasting tasks.

In this paper, we designed the networks empirically. Setting proper hyperparameters can effectively improve forecasting performance. In the feature, we will use deep reinforcement learning to automatically build the model and choose the better hyperparameters of MCSCNN–LSTM for electricity consumption forecasting.