Industrial users load pattern extraction method based on multidimensional electrical consumption feature construction

1 Introduction

In recent years, in order to solve the energy crisis and environmental pollution caused by traditional energy, the proportion of all kinds of renewable energy generation on the power supply side has been increasing (Gupta and Singh, 2022). Due to the intermittency and randomness of renewable energy power generation, the imbalance between power supply and demand in peak season is further aggravated. Therefore, it has become an urgent problem to explore the potential of demand side response (Zhang and Gu, 2016). Compared with other types of users such as residents and businesses, industrial users have advantage in large power consumption, stable load and easy management, so it is seen as an important demand side response resource of power grid (Hou and Xing, 2020; Jiang, et al., 2021). Industrial users can sign contracts with power companies to participate in load response, peak cutting and valley filling, etc., to help rational distribution of power resources and promote stable operation of the power grid (Xu and Lai, 2015; Dai et al., 2022). However, as there are a large number of industrial users with different power consumption characteristics and demand side response capabilities, it is difficult to achieve individual modeling analysis for every user. In order to solve this problem, it is necessary to extract the typical power consumption mode of industrial users from the massive load data, classify users with similar power consumption patterns into the same cluster, and formulate appropriate load control schemes for different groups, so as to improve the operational quality and efficiency of the power grid and promote the lean management of demand side (Shi, et al., 2017; Dehghan-Dehnavi, et al., 2020).

With the advance of the digital construction of power grid and the advanced measuring system, the popularization of advanced metering infrastructure (AMI), the power grid has stored massive load data of industrial users (Wang, et al., 2016). The emergence of a large amount of industrial electricity information provides data support for the research of load patterns, which is of great importance for load forecasting (Huang, et al., 2020), abnormal electricity detection (Zhang et al., 2020), demand side management (Bañales, et al., 2021), etc. Load clustering is an important method to extract typical electricity consumption patterns of users. It divides similar data into the same class and obtains several disjoint clusters by mining potential connections in load data (Deng, et al., 2021). According to different types of input, load clustering can be divided into direct clustering and indirect clustering. Direct clustering takes the original load data as the input of the clustering algorithm. (Al-Wakeel and Wu, 2016; Panapakidis, et al., 2017; Xu, et al., 2020). separately adopts the improved K-means algorithm, the improved fuzzy C-means algorithm and the improved spectral clustering algorithm respectively to achieve the clustering of daily load curve. Direct clustering method is simple and easy to interpret, but it challenges the computational efficiency by placing the clustering task in high dimensional space (Fang, et al., 2022).

Indirect clustering firstly uses dimensionality reduction technology to reduce user load data dimensionality and takes low dimensionality data as input for clustering algorithm. In indirect clustering, how to obtain the low dimensional features that can represent the power consumption characteristics of users through dimensionality reduction method is the focus of current research. In (Song, et al., 2019), six characteristic indicators of daily load curve were selected manually to reduce the dimensionality of daily load curve. However, the selection of such characteristic indicators is subjective and difficult to describe the temporal characteristics of load data. In (Lin, et al., 2017), piecewise aggregate approximation method was used to achieve data dimensionality reduction, and then spectral clustering was used in load classification. In (Koivisto, et al., 2012), Principal Component Analysis (PCA) and K-means algorithm were used for clustering. However, PCA belongs to linear dimension reduction method and is difficult to consider complex non-linear relations in time series data. In (Tian, et al., 2014; Ryu, et al., 2019; Duan, et al., 2021), autoencoder (AE) is used to learn the depth representation of load data, and then K-means or spectral clustering method takes it as the input to obtain clustering results.

K-means algorithm is a classic classification and clustering method, which has the advantages of simple operation, high efficiency and strong interpretability, and is widely used in electrical engineering. However, the K-means algorithm needs to manually set the clustering number and initial clustering center. If the initial clustering center is not selected properly, local convergence will be easily caused and the clustering effect will be affected (Si et al., 2021). In view of the above problems, Nikolaos et al. (2015) combines kernel method with K-means algorithm to improve the clustering effect, but there are problems such as long running time and artificial setting of kernel function parameters (Xu et al., 2015; Ai et al., 2020). Uses Hierarchical K-means to establish a hierarchical structure of massive data and select initial clustering centers for K-means to avoid the local convergence problem caused by random selection of initial clustering centers. Xu et al. (2017) selects the initial clustering center of K-means algorithm by calculating the data density, but the accuracy of selecting the initial clustering center only based on the data density is limited.

In order to extract the low dimensional characteristics of industrial users and effectively solve the local optimal solution in the traditional k-means method. This paper proposes a load pattern extraction method based on multidimensional electrical consumption feature construction (MECFC). Firstly, five indexes such as daily load rate and daily peak-valley difference number of industrial users were calculated, and each index was weighted with the improved entropy weight method to form an industrial load characteristic set indicating industrial users power consumption characteristics. In addition, Convolutional Auto-Encoder (CAE) is used to extract the temporal features of the industrial load data, and the multidimensional electrical consumption feature set of industrial users is constructed by combining the temporal features with industrial load characteristic set to solve the problem of high dimensionality of the industrial load data. Then, in order to solve the local optimal problem caused by the random selection of initial clustering center in the traditional K-means algorithm, the SK (SOM K-means) algorithm is proposed. The algorithm selects the initial clustering center of K-means algorithm by establishing Self-Organization Map (SOM) neural network to calculate the local density and distance attributes of nodes. Finally, taking the data set of industrial users in Zhejiang province as an example, the proposed method is compared with the traditional clustering method, which proves that the proposed method has certain advantages in clustering effect, operating efficiency and algorithm stability.

2 Industrial load characteristic set for industrial users

2.1 Load data preprocessing

Let ${\mathit{X}}_L=\left\{{\mathit{x}}_1,{\mathit{x}}_2,\cdots ,{\mathit{x}}_m\right\}$ be the industrial user load data set, where ${\mathit{x}}_i=\left\{x_{i,1},x_{i,2},\cdots ,x_{i,96}\right\}$. During data acquisition, data may be abnormal or missing due to measurement anomaly, communication interruption, and human error. Therefore, it is necessary to preprocess the original data. This paper preprocesses load data from missing data processing, outlier detection and filling, and data normalization.

2.1.1 Missing data processing

$x_t^{\left(i\right)}$ is assumed to be user(i)’s the load data of the tth sampling point. In the case of missing data values, in order to maintain the smoothness of load curve, this paper adopts the method of filling based on the mean value at the same time. The specific filling method is as follows:

$x_{j,t}^{\left(i\right)}=\frac{1}{N}{\displaystyle \sum _{j\in \vartheta }^N}{x}_{j,t}(1)$

Where $\vartheta$ is the set of dates with measured values at tth sampling point, $x_{j,t}$ represents the measured values of user at tth sampling point within date j, N is the number of dates in $\vartheta$. When the missing data accounts for more than 20% of the daily load data, it is considered as invalid data and is directly deleted.

2.1.2 Outlier detection

In addition to the condition of missing data, the load data may also be abnormal due to the failure of the measuring device. For this situation, this paper uses the horizontal similarity detection method to identify the bad data.

Assume that ${\mathit{x}}_i$ is the i^th daily load curve and $x_{i,j}$ is the load data of sampling point j to be detected. Firstly, calculate the load change rate ${\delta }_j$ of every sampling point j according to Formula 2, and then specify the normal range of load change rate of each node. Finally, determine whether the daily load change rate of each sampling point is abnormal. If there is abnormal value, Formula 3 is used to correct the abnormal value:

${\delta }_j=\frac{x_{i,j+1}-x_{i,j}}{x_{i,j}}\times 100\%(2)$

$x_{i,j}=\frac{{\displaystyle \sum _{a=1}^{a_1}}{x}_{i,j-a}+{\displaystyle \sum _{b=1}^{b_1}}{x}_{i,j+b}}{a+b}(3)$

where a₁ and b₁ respectively represent the number of points taken forward and backward. In this paper, a₁ = b₁ = 5.

2.1.3 Data normalization

Since the power values of loads of different industrial users may be quite different, in order to better quantify the similarity between data and improve the accuracy of subsequent multidimensional power characteristics acquisition, the load data should be processed by Min-Max standardization:

$x_{i,j}^{\prime }=\frac{x_{i,j}-\underset{1\le j\le N_j}{\mathit{min}}\left\{x_{i,j}\right\}}{\underset{1\le j\le N_j}{\mathit{max}}\left\{x_{i,j}\right\}-\underset{1\le j\le N_j}{\mathit{min}}\left\{x_{i,j}\right\}}j=1,\cdots N_j(4)$

where $N_j$ is the amount of industrial users daily load data.

2.2 Load characteristic indexes for industrial users

The power consumption characteristics of industrial users indicate the characteristics and properties of industrial users in the habit of using electricity, which can be described by the load characteristic indexes. In this paper, daily load rate $l_1$, daily peak-valley difference rate $l_2$ and daily maximum load utilization hours $l_3$ are selected to reflect the load variation characteristics and time utilization efficiency of industrial users. In addition, the electricity price of industrial users varies significantly in different periods. The load rate of peak period $l_4$ and valley period $l_5$ are selected to reflect the sensitivity of users to electricity price. Table 1 shows the specific calculation method of each index.

TABLE 1

TABLE 1. Load characteristic indexes of industrial users.

In Table 1, $P_{ave}$, $P_{\mathit{max}}$, $P_{\mathit{min}}$, $P_{ave,peak}$, $P_{ave,low}$ denotes the average daily load, daily maximum load, daily minimum load, average peak period load and average valley period load of industrial users, respectively, and the peak period is 9:00–12:00 and 17:00–22:00; valley period time is 23:00–0:00 and 0:00–8:00.

The above indexes describe the power consumption characteristics of industrial users from different degrees, and their degree of emphasis and importance varies. Therefore, it is necessary to set the weight coefficient of the load characteristic indexes so that they can objectively describe the importance of each index. In this paper, entropy weight method is used to determine the weights of different indexes. The specific steps are as follows: firstly, the entropy of each index needs to be calculated. Given that the index quantity to be weighted is 5 and the daily load data quantity is m, the entropy calculation formula of the c index is as follows:

$h_c=-\frac{1}{\mathit{ln}5}{\displaystyle \sum _{d=1}^m}{l}_{cd}\mathit{ln}{l}_{cd}(5)$

where $l_{cd}$ is the cth index value corresponding to the dth sample.

According to the calculated entropy value of each index, the improved entropy weight calculation formula is adopted to calculate the corresponding weight value of each index. The weight calculation formula of the cth index is as follows:

${\omega }_c=\frac{e^{{\displaystyle \sum _{d=1}^5}{h}_d+1-h_c}-e^{h_c}}{{\displaystyle \sum _{e=1}^5}\left(e^{{\displaystyle \sum _{d=1}^5}{h}_d+1-h_e}-e^{h_e}\right)}(6)$

The calculated weights are assigned to the above five power consumption characteristics indexes, and the above indexes are combined to form the industrial load characteristic set $\mathit{L}=\left\{{\omega }_1{l}_1,\cdots ,{\omega }_5{l}_5\right\}$ for industrial users.

3 Multidimensional electrical consumption feature construction for industrial users

The above five load characteristic indexes are artificially specified, which are subjective and difficult to represent the complex temporal relationship in the load curve. In order to improve the effect of industrial load clustering, it is necessary to consider the time sequence characteristics of load data and extract temporal features of industrial user load data. Traditional feature extraction method, such as Principal Component Analysis (PCA) or Independent Component Analysis (ICA), is difficult to mine the non-linear relationship between the data. Auto-Encoder (AE) is an unsupervised learning algorithm, which is composed of input layer, hidden layer and output layer, and belongs to a kind of neural network (Liu, et al., 2017). CAE uses convolution layer and pooling layer to replace the fully connected layer in traditional autoencoders, and its structure is shown in Figure 1. Due to weight sharing in the convolutional layer, the number of training parameters in CAE is less than that in the fully connected layer, which reduces the overfitting situation and speeds up the training speed, and is suitable for processing more complex high-dimensional data.

FIGURE 1

FIGURE 1. Convolutional auto-encoder network structure.

${\mathit{X}}_L=\left\{{\mathit{x}}_1,{\mathit{x}}_2,\cdots ,{\mathit{x}}_m\right\}$ is the load data set of industrial users, where m denotes the daily load data amount, ${\mathit{x}}_i$ is the i^th industrial load data, and each data dimension is 96. CAE includes encoder and decoder. In the process of encoding, the initial input vector ${\mathit{x}}_i$ first passes through the action of the convolution layer and the pooling layer in the encoder to obtain the feature vector h of the original vector in the hidden layer. In the decoding process, h in the hidden layer is reconstructed by the inverse convolutional layer and the upper sampling pooling layer in the decoder, and the output vector with the same dimension as the input vector ${\mathit{x}}_i$ is obtained. The process of encoding and decoding is shown in Eqs 7, 8:

$\mathit{h}={\varphi }_e\left(W_e\otimes \mathit{x}+{\delta }_1\right)(7)$

$\stackrel{\sim }{\mathit{x}}={\varphi }_d\left(W_d\otimes \mathit{h}+{\delta }_2\right)(8)$

Formula 7 represents the CAE encoding process. Where W_e represents the one-dimensional encoder convolution kernel; ${\delta }_1$ represents bias in the encoding process; $\otimes$ represents the convolution operator; h is the low dimensional feature vector of the hidden layer after encoding; ${\varphi }_e$ represents the activation function of encoder, and ReLU function is adopted in this paper.

Formula 8 represents the CAE decoding process. Where W_d represents the one-dimensional decoder convolution kernel; ${\delta }_2$ represents the bias in the decoding process; $\stackrel{\sim }{\mathit{x}}$ represents reconstructed input data; ${\varphi }_d$ represents the activation function of decoder, and Sigmoid function is adopted in this paper.

In this paper, Mean-square Error (MSE) is used as the CAE training loss function. CAE learns the optimal network parameters by minimizing the loss function, so that the reconstructed data $\stackrel{\sim }{{\mathit{x}}_i}$ is as close to the input ${\mathit{x}}_i$ as possible, and then obtains the low-dimensional feature vector h of the original input on the hidden layer, where the dimension of h is less than ${\mathit{x}}_i$. Thus, temporal feature extraction of industrial load data is realized while the dimension of input data is reduced.

The low-dimensional feature vector H in CAE hidden layer is extracted as the temporal feature of industrial user load data, and is combined with the industrial load characteristic set L to form the multidimensional feature set C, and finish the multidimensional electrical consumption feature construction, $\mathit{C}=\left\{\mathit{L},\mathit{H}\right\}=\left\{l_1,\cdots ,l_5,h_1,\cdots ,h_n\right\}$.

4 Industrial user load clustering based on SK algorithm

4.1 Introduction to SK algorithm

When traditional K-means method deals with clustering tasks, it will encounter two problems: 1) It is difficult to determine the initial clustering center; 2) The number of clustering k is difficult to determine. Rodriguez and Laio (2014) proposes two assumptions in the density peak clustering algorithm: 1) Clustering center generally has a large local density, that is, there are a large number of sample points around it; 2) The distance between different clustering centers is far. Based on the above two assumptions, this paper proposes a clustering algorithm based on SK algorithm. Firstly, SOM network is established to obtain the mapping relationship between daily load data and output layer nodes, then the local density of output layer nodes and the distance attribute of each node are calculated, and the initial clustering center of K-means algorithm is selected according to the two attributes of output layer nodes to improve the clustering performance of industrial users’ load.

4.2 Initial clustering center determination based on SOM network

SOM is an important unsupervised learning method, which is often used in clustering, high dimensional visualization, data compression, feature extraction and so on. SOM is essentially a double-layer neural network, consisting of an input layer and an output layer. The relationship between the output layer nodes and the input data is established through a competitive learning process, where each node competes to be the closest match to a given input data point. The output layer notes have the same dimension as the input data, and its network structure is shown in Figure 2.

FIGURE 2

FIGURE 2. SOM network structure.

In this paper, the specific steps to select the initial clustering center based on SOM are described as follows:

1) Establish self-organizing mapping neural network.

SOM network is constructed with multidimensional feature set C for industrial users as input. The number of samples is set as m, and the dimension of samples is set as f. Set the number of neurons in the input layer as m and the number of nodes in the output layer as M*N, and M = N = 4. And randomly initialize the weight of neurons in the output layer $\mathit{W}=\left[{\mathit{W}}_{\mathrm{1,1}},\cdots ,{\mathit{W}}_{\mathrm{4,4}}\right]$, and ${\mathit{W}}_{g,h}=\left[w_{g,h,1},w_{g,h,2},\cdots ,w_{g,h,f}\right]$.

2) Traversing every node in the output layer to find the winning node.

Read ${\mathit{C}}_o$ from multidimensional feature set of industrial users as input, and the Euclidean distance to each node $d_{o,g,h}$ is calculated, and the closest point ${\mathit{W}}_{g,h}$ is selected as the winning node.

3) Calculate the weight updating amplitude G of each node.

Set the weight update amplitude at the winning node as 1. Based on the Gaussian kernel function, the update amplitude of all nodes is calculated according to the distance between each node and the winning node. The calculation formula is as follows:

$g_{u,v}=\left\{\begin{array}{l}1,u=g,v=h\\ e^{-\frac{{\left(g-u\right)}^2}{2{\delta }^2}}\times e^{-\frac{{\left(h-v\right)}^2}{2{\delta }^2}},\text{else}\end{array}\right.(9)$

where $\delta$ is the distance parameter, indicating the sensitivity of g to the distance between nodes. As the number of iterations t increases, $\delta$ becomes smaller and smaller. Its updated formula is as follows:

${\delta }_t=\frac{{\delta }_0}{1+\frac{t}{\text{maxstep}/2}},t\in \left(0,\text{maxstep}\right)(10)$

where ${\delta }_0$ is the initial distance parameter, which is taken as ${\delta }_0=1$ in this paper; maxstep indicates the maximum number of iterations, $\text{maxstep}=T\times m$.

4) Update the weight W of each node.

After the weight updating amplitude G of each node is obtained, the weight value of the winning node and its domain node is updated. The node weight updating formula is as follows:

${\mathit{W}}_{u,v}={\mathit{W}}_{u,v}+\eta \cdot g_{u,v}\cdot \left({\mathit{C}}_o-{\mathit{W}}_{u,v}\right)(11)$

Where $\eta$ represents the learning rate, which is similar to $\delta$ and also becomes smaller as the number of iterations t increases. Its updated formula is as follows:

${\eta }_t=\frac{{\eta }_0}{1+\frac{t}{\text{maxstep}/2}},t\in \left(0,\text{maxstep}\right)(12)$

where ${\eta }_0$ is the initial learning rate, which is taken ${\eta }_0=1$ in this paper.

5) Repeat steps 2-4 until the number of iterations reaches maxstep, and the weight matrix of each node in the output layer is obtained after the training is completed.

6) Calculate the local density $\rho$ of each node.

According to the weight matrix of nodes ${\mathit{W}}_{4\times 4}$ in the output layer, the mapping relationship between input and output nodes is obtained, and the corresponding input quantity of each output node is counted, which is taken as the local density $\rho$ of nodes in the output layer.

7) Calculate the distance attribute $\gamma$ of each node.

In order to facilitate calculation, the weight matrix ${\mathit{W}}_{4\times 4}$ is changed into column vectors ${\mathit{W}}_{1\times 16}$ in order. If the node ${\mathit{W}}_r$ is not the node with maximum local density, its distance attribute is defined as the closest distance between nodes whose local density is higher than its. Calculate the distance between nodes ${\mathit{W}}_r$ and ${\mathit{W}}_s$, and then obtain the distance attribute $\gamma$ of each node. The calculation formula is as follows:

$d_{r,s}=dis\left({\mathit{W}}_r,{\mathit{W}}_s\right)=\sqrt{{\displaystyle \sum _{\eta =1}^f}{\left(w_{r,\eta }-w_{s,\eta }\right)}^2}(13)$

${\gamma }_r=\underset{{\rho }_r>{\rho }_s}{\mathit{min}}\left(d_{r,s}\right)(14)$

If the node ${\mathit{W}}_r$ is the node with maximum local density, then define distance attribute $\gamma$ as the Euclidean distance between the node ${\mathit{W}}_r$ and the node farthest away from it. And the calculation formula is modified as follows:

${\gamma }_r=\underset{r,s\in \mathbb{R}}{\mathit{max}}\left(d_{r,s}\right)(15)$

8) Select the K-means initial clustering center.

Calculate the local density $\rho$ and distance attributes $\gamma$ of each node in the output layer according to steps 6 and 7, k nodes with large $\rho$ and $\gamma$ are selected and their weights are set as the initial clustering centers of the k-means algorithm. k represents the number of clusters.

4.3 Determine the number of clusters

The K-means algorithm needs to set the clustering number k artificially. If the value of k is improperly selected, the clustering effect will be adversely affected. In this paper, by observing DBI and SC under different number of clusters, k value with smaller DBI value and larger SC index value is selected as the number of experimental clusters. DBI and SC calculation formulas are detailed in Section 4.4.

4.4 Clustering performance evaluation

Load clustering expects each type of curve to have high intra-class similarity and low inter-class similarity (Zhang, et al., 2015). In this paper, Calinski-Harabasz Index (CHI), Davies-Bouldin Index (DBI) and the Silhouette Coefficient (SC) are used as indicators to evaluate the load clustering performance.

4.4.1 Calinski-harabasz index (CHI)

The CHI calculates the ratio between the degree of inter-cluster dispersion and the degree of intra-class dispersion. The larger the CHI is, the greater the intra-class similarity and the smaller the inter-class similarity, that is, the better the clustering performance. The calculation formula of CHI is as follows:

$I_{CH}=\frac{S_B}{K-1}/\frac{S_W}{N-K}(16)$

where $S_B$ and $S_W$ stand for inter-class variance and intra-class variance respectively; K stands for cluster number; N stands for the number of data.

The calculation formulas of inter-class variance $S_B$ and intra-class variance $S_W$ are as follows:

$S_B={{\displaystyle \sum _{k=1}^K}{\displaystyle \sum _{j=1}^N}{\omega }_{k,j}‖c_k-\overline{x}‖}^2(17)$

$S_W={{\displaystyle \sum _{k=1}^K}{\displaystyle \sum _{j=1}^N}{\omega }_{k,j}‖x_i-c_k‖}^2(18)$

where $c_k$ represents the clustering center of the k^th cluster; $\overline{x}$ represents the center of all data samples; ${\omega }_{k,j}$ represents the membership relationship between the j^th object $x_j$ and the k^th cluster, If $x_j$ belongs to the k^th cluster, it takes 1, otherwise, it takes 0.

4.4.2 Davies-bouldin index (DBI)

DBI describes the tightness of data in the same cluster, and the smaller the value, the lower degree of dispersion and the better the clustering performance. The formula for calculating DBI is as follows:

$I_{DBI}=\frac{1}{k}{\displaystyle \sum _{i=1}^k}{\mathit{max}}_{i\ne j}\left(\frac{\overline{C_i}+\overline{C_j}}{d_{i,j}}\right)(19)$

Where $\overline{C_i}$ and $\overline{C_j}$ represents the average distance from the samples in the i^th and j^th cluster to the cluster center; $d_{i,j}$ is the distance between the i^th and j^th clustering centers.

4.4.3 Silhouette coefficient (SC)

SC combined with two factors of cohesion and separation degree, describes the definition of contour of each category after clustering, and the larger the value, the better the clustering performance.

$I_{SC}=\frac{1}{N}{\displaystyle \sum _{i=1}^N}\frac{b_i-a_i}{\mathit{max}\left\{b_i-a_i\right\}}(20)$

where $a_i$ represents the average distance between data i and other points in the same cluster; $b_i$ represents the minimum average distance between data i and samples in other clusters.

4.4.4 The overall process of industrial users load pattern extraction

Figure 3 is a detailed algorithm flow chart of the proposed load pattern extraction method of typical power consumption modes of industrial users based on multidimensional electrical consumption feature construction and SK algorithm.

FIGURE 3

FIGURE 3. Flow chart of industrial load clustering.

5 Example analysis

5.1 Experimental data

After data preprocessing, this paper selects the winter typical daily load data of 574 industrial users in a district of Zhejiang Province, China in 2020 for cluster analysis. The daily load data is collected every 15 min, that is, 96 points a day. The total daily load curve is shown in Figure 4. Experiments in this paper were carried out in python 3.8.5, AMD Ryzen 7 4800H with Radeon Graphics 2.90 GHz environment.

FIGURE 4

FIGURE 4. Total daily load curve of industrial users.

5.2 Construct multidimensional electrical consumption feature set

According to Table 1, the power consumption characteristic index of industrial users is calculated, and the weight vector W₁ of users is calculated with the entropy weight method. The CAE takes 96*1 daily load data as input. The encoder consists of five convolutional layers, the number of convolutional cores is 16, 32, 64, and 128, the size of convolutional kernel is 3, and the step size is 2, 1, 2, and 2. Finally, 12-dimensional sequences are output in the hidden layer. After that, five deconvolution layers are used to reconstruct the data. The number of deconvolution layers’ kernels is 64, 32, 16, and 1, the size of the convolution kernels is 3, and the step size is 2, 1, 2, and 2, respectively. Adam optimizer is used in the training process. The training times are 300 and the batch size is 8. CAE network parameters are shown in Table 2. After the training is completed, the hidden layer sequence is taken as the temporal feature of the load data of industrial users, and combined with industrial load characteristic set of industrial users, the multidimensional feature set of industrial users is obtained as the input of the SK algorithm.

TABLE 2

TABLE 2. Network structure of CAE.

5.3 Determination of optimal clustering number and selection of initial clustering center

In this paper, the number of clusters is changed from 2 to 12 to observe DBI and SC under different number of clusters. The change curve of DBI and SC is shown in Figure 5. When the number of clusters k = 4, the DBI value is small and the SC value is large, so the optimal cluster number of industrial users is taken as 4.

FIGURE 5

FIGURE 5. SC and DBI curve of industrial users.

SOM network is established and local density ρ and distance attribute γ of output layer nodes are calculated. In order to directly reflect the local density and distance attribute of each node in the output layer, the heat map of each node attribute is drawn in Figure 6. The darker the color in the figure, the larger the local density and distance attribute value of the node. The figure shows that the node W_1,4, W_3,4, W_4,1 and W_4,2 are the four nodes with large ρ and γ at the same time, so the four nodes are selected as the initial clustering center of the k-means algorithm.

FIGURE 6

FIGURE 6. Heat map of SOM output layer nodes: (A) Local density; (B) Distance attribute.

5.4 Analysis of typical load pattern of industrial users

Figure 7 shows the clustering result diagram of industrial users, indicating typical load patterns of industrial users in this area. According to the clustering results, it can be seen that there are four typical power consumption modes for users in this area, and the peak load time, peak-valley difference and fluctuation rate are different among all types. Therefore, it is necessary to analyze each power consumption mode and formulate appropriate load management strategies.

FIGURE 7

FIGURE 7. Industrial users daily load clustering result diagram: (A) Typical load pattern 1; (B) Typical load pattern 2; (C) Typical load pattern 3; (D) Typical load pattern 4.

Typical load pattern mode 1 of industrial users belongs to peak-avoiding load. This type of load pattern consumes less electricity in the peak period of the grid, but more electricity in the valley period, with high peak-valley difference, load rate of valley period and low load rate of peak period. The peak load time is 0:00–8:00 and 20:00–24:00, and the electricity consumption is very small between 8:00 and 20:00. Such users are greatly affected by TOU, and can well respond to the call of peak load shifting of the grid. They can actively use electricity in the off-peak hours of the grid load, and suspend production electricity in the peak hours.

Typical load pattern mode 2 of industrial users belongs to continuous load. This type of load pattern maintains a high level of electricity consumption throughout the day and requires high power continuity, with high daily load rate, daily maximum load utilization hour and low daily peak-valley difference. This kind of users generally have large power consumption and weak load transfer ability. Power companies need to have agreements with such customers in place to encourage them to use less electricity during tight months.

Typical load pattern mode 3 of industrial users belongs to daytime production load. This type of load pattern consumes more electricity in the peak period of the grid, but less electricity in the valley period, with high peak-valley difference, load rate of peak period and low load rate of valley period. The power consumption of these users is mainly from 8:00 to 17:00. During this time period, the load is stable, and the power consumption decreases slightly at noon. These users use electricity in concentrated and continuous hours, which affects the stable operation of the power grid. Such users should be encouraged to reduce their use of electricity during peak periods.

Typical load pattern mode 4 of industrial users belongs to daytime production load. This kind of user consumes more electricity in the daytime, but less electricity in the evening. The peak load appears between 9:00–11:00 in the morning and 14:00–16:00 in the afternoon, and the demand for electricity continuity is not high. For such users, power companies can contact users in advance to adjust the power consumption mode according to the actual demand of the power grid and the day-ahead dispatching requirements, so as to improve the operation level of the power grid.

5.5 Comparative analysis of clustering performance

In order to verify the effectiveness of multidimensional electrical consumption feature construction and SK algorithm (MECFC-SK) proposed in this paper, the performance of the proposed algorithm in industrial daily load clustering is compared with K-means, PCA + K-means, and Denoising Auto-Encoder (DAE) + K-means algorithms. CHI, DBI and SC are introduced to quantitatively analyze the clustering effect.

Table 3 records the evaluation indicators values of different algorithms in the data set. Compared with the above three algorithms, the algorithm proposed in this paper is better in each index, indicating that the MECFC-SK proposed in this paper is more effective than the traditional dimension reduction method, which can make the clustering has higher internal similarity and has greater external discrimination, and has better clustering performance.

TABLE 3

TABLE 3. Comparison of clustering performance of each method.

In addition, in order to visually display the differentiation of clusters of daily load data under various algorithms, this paper uses the t-distributed stochastic neighbor embedding (t-SNE) algorithm to reduce the multidimensional power feature set to 2 dimensions. Data visualization can be realized by drawing scatter plots on a plane (Van der Maaten and Hinton, 2008). The scatter diagram of daily industrial load data after dimension reduction in each algorithm is shown in Figure 8.

FIGURE 8

FIGURE 8. Scatter diagram after t-SNE dimension reduction: (A) K-means; (B) PCA + Kmeans; (C) DAE + Kmeans; (D) MECFC-SK.

Table 4 shows the average values of CHI, running time and iteration after 50 experiments using SK algorithm and tradition K-means in each simulation data set. Each simulation data set is built by adding different ratios of sample data and noise to the original data set. The purpose of adding sample data is to prove that SK algorithm can improve the running speed of traditional K-means algorithm, and the sample expansion ratio s varies from 100% to 600%. The purpose of adding noise is to prove that SK algorithm has better robustness in clustering performance, and the noise ratio r varies from 5% to 30%. When the noise ratio is small, there is a large gap between the two CHI, and the clustering effect of SK algorithm is obviously better than that of traditional K-means algorithm. As the ratio of sample expansion and noise continues to increase, SK has a small reduction in CHI compared with the traditional K-means algorithm, and it is significantly superior to the traditional K-means algorithm in terms of running time and iteration times, which proves that the SK algorithm proposed in this paper has a great improvement in operational efficiency.

TABLE 4

TABLE 4. Comparison of SK and traditional K-means clustering effect.

In order to prove that the initial clustering center selected by the algorithm in this paper can avoid the local optimal case and has better stability than traditional K-means, the coefficient of variation (CV) of CHI, operation time and iteration times obtained by the two algorithms on different simulated data sets are compared. CV is a normalized measure describing the degree of data dispersion, which is defined as the ratio of data standard deviation to the mean, which can effectively avoid the influence of the two groups of data dimensions and measurement scales. Table 5 shows the statistical table of CV collected on each simulation data set. It can be seen from the table that the CV of CHI of SK algorithm is much lower than that of traditional K-means, which proves that the clustering performance of SK algorithm in each experiment has little fluctuation, and effectively solves the problem that the traditional K-means algorithm is prone to fall into the local optimal solution. As shown in Table 5, CV of running time and the CV of iteration of the two algorithms are both low, indicating that the running time of the two algorithms does not fluctuate much in each clustering task. In addition, it can be seen from the experimental data recorded in Table 4 that the SK algorithm performs better in running time and iteration than traditional K-means. Therefore, it can be verified that SK algorithm is superior to Traditional K-means in running time and number of iterations in each experiment, which proves that SK algorithm has good stability and accelerates the speed of clustering.

TABLE 5

TABLE 5. Coefficient of variation table.

6 Conclusion

Mining typical load patterns of industrial users can classify industrial users according to their power consumption habits and group users with similar power consumption characteristics into one category for demand-side management. In order to extract the typical load patterns of industrial users accurately, this paper proposes an extraction method of typical load patterns of industrial users based on multidimensional electrical consumption feature construction and SK algorithm, which intends to solve the problems of high dimension and complex non-linear relationship of industrial users load data, and local convergence in traditional k-means algorithm. The data set of industrial users in Zhejiang Province, China is taken as an example. Compared with other clustering algorithms, the effectiveness of this method is proved, and the conclusions are as follows:

(1) In this paper, temporal features of industrial daily load data are obtained based on CAE and combined with industrial load characteristic set to construct multidimensional feature set of industrial users, which can effectively extract low-dimensional vectors of original data to achieve data dimension reduction and improve clustering performance.

(2) The SK clustering algorithm proposed can effectively solve the local optimal problem caused by the random selection of initial clustering center by traditional K-means method, improve the stability of the algorithm, speed up the algorithm running speed, and improve the clustering accuracy.

(3) By clustering the daily load data of industrial users, typical load patterns of users can be extracted, users can be classified according to their power consumption habits, and appropriate management schemes can be formulated for various users, which plays a positive role in promoting lean management and safe and reliable operation of the power grid.

Data availability statement

The raw data supporting the conclusion of this article will be made available by the authors, without undue reservation.

Author contributions

The author’s personal contributions are as follows: Manuscript writing, LW; writing instruction, JZ and XX. Data collection and interpretation JL, YL, and LZ; content and format correction, LW, JZ, and XX. All authors have read and agreed to the published version of the manuscript.

Funding

This work is sponsored by “Chenguang Program” supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission (19CG61). The funder was not involved in the study design, collection, analysis, interpretation of data, the writing of this article, or the decision to submit it for publication.

Conflict of interest

XX was employed by the company China Coal Technology and Engineering Group Shanghai Company Limited.

JL, YL, and LZ were employed by the company Huzhou Power Supply Company of State Grid Zhejiang Electric Power Company Limited.

The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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