Electricity is one irreplaceable form of energy in modern production and daily life. Research related to its generation, transmission, storage, and utilization is increasingly the focus of researchers and applications on electric grids, power supply, distribution, renewable energy, and energy efficiency management (Hou et al., 2024; El-Sayed et al., 2024; Ahmed et al., 2024; Naidu et al., 2024; Gennitsaris et al., 2023; Hasanvand et al., 2024; Yang et al., 2024; Chen et al., 2023; Kumar et al., 2023a; Kumar, 2024; Kumar et al., 2023b). With the popularization of Internet of Things (IoT) technology, an increasing number of applications and research have focused on precisely monitoring and managing electricity usage processes at the user end (Ahammed et al., 2021; Abhishek et al., 2021; Fabricio et al., 2020; Ramson et al., 2022; Balakumar et al., 2023; Solatidehkordi et al., 2023; Caldera et al., 2023; Çimen et al., 2021; Chen et al., 2020; Avancini et al., 2021; Chou and Truong, 2019; Diawuo et al., 2020; Saleem et al., 2021; Sayed et al., 2022; Rago et al., 2021; Himeur et al., 2023; Mohi-Ud-Din et al., 2021; Priyadharshini et al., 2021; Ullah et al., 2022; Zhou et al., 2022; Zhu et al., 2020). Currently, most research on electricity consumption on the user demand side is based on features such as voltage, current, power, and other characteristics of appliances. The steady-state analysis, transient analysis, and a combination of both have received attention. Data used in those research works are electricity consumption situation data acquired through smart meters (Avancini et al., 2021; Priyadharshini et al., 2021; Wang et al., 2013; Swindiarto et al., 2018). Because the time granularity of the observed electricity consumption situation data is relatively large when electricity consumption situations are collected through smart meters, it is insufficient to support the timely identification of the types of appliances in use and their running state. The precise perception and online monitoring of electricity consumption situations on the user side not only can help understand details of the user-side power consumption but can also contribute to enhancing the safety and efficient management of user-side energy (Chou and Truong, 2019; Phangbertha et al., 2019; Wang and Zhang, 2022): On the one hand, the online monitoring and precise perception of electricity consumption situations enable users to promptly monitor the operation state of their appliances and detect any abnormal issues, ensuring the safety of their electricity usage; on the other hand, the online monitoring and precise perception of electricity consumption situations on the user side also contribute to a more accurate understanding of the electricity consumption process, providing detailed evidence for optimizing electricity usage behavior and adjusting electricity consumption habits.

There are two methods for running-state monitoring of electrical appliances. One is intrusive appliance load monitoring (ILM), and the other is nonintrusive appliance load monitoring (NALM). The ILM method generally utilizes devices such as smart plugs to collect data on the electric consumption situation of individual appliances (Chou and Truong, 2019; Phangbertha et al., 2019; Wang and Zhang, 2022; Ridi et al., 2013; Yan et al., 2019). The ILM method typically conducts further research based on the current and power data from the electric consumption situation. By analyzing and modeling those data, the ILM method can reveal the electricity consumption patterns of users, electrical load characteristics, and other potential measures for improving energy efficiency (Chou and Truong, 2019; Wang and Zhang, 2022). Based on the typical ILM system architecture and commonly used feature extraction and machine learning algorithms in ILM systems, methods based on the K-nearest neighbor algorithm and the Gaussian mixture model (GMM) are used to classify appliances based on smart plugs (Ridi et al., 2013). This method extracts dynamic features of current data sequences by utilizing the first and second derivatives of the electric data sequence. A household appliance identification algorithm based on the Bayesian classification model is proposed based on the electric consumption situation data collected through smart plugs (Yan et al., 2019), which can summarize and extract the electricity consumption behavior and energy consumption characteristics of typical household appliances from the load power sequence samples.

The NALM method samples electricity consumption data such as voltage, current, load, or power of the total load at the power entrance. By decomposing the electricity consumption data, the NALM method can infer the operational state of various electrical appliances. In general, NALM utilizes devices such as electric meters for electricity consumption data collection and can be used to monitor and identify individual electrical appliances within households or buildings in time (Hart, 1992; Kong et al., 2018; Himeur et al., 2020; Chen et al., 2022; Aslan and Nur, 2022; Liu et al., 2019). The NALM method can determine the energy consumption of an appliance when the appliance is working within an electrical load by conducting a detailed analysis of the total load current and voltage measured at the power interface (Hart, 1992).

To offer an improved solution for accurately identifying appliances such as washing machines and dishwashers with diverse modes and varying energy consumption patterns, a novel framework based on hierarchical hidden Markov models (HHMM) is given for modeling the problem of appliance identification (Kong et al., 2018). An appliance identification system based on the NALM method utilizes multi-scale wavelet transform to extract features from data sequences and employs an integrated bagging tree classifier for data sequence classification (Himeur et al., 2020), which presents a novel and reliable event detection scheme. Based on the NALM method, a two-stream convolutional neural network (TSCNN) is used to extract temporal and spectral load characteristics from current sequences and perform classification tasks (Chen et al., 2022). This approach effectively captures and uses the time-domain and frequency-domain features of the load signals for accurate classification. The K-nearest neighbors rule (k-NNR) and support vector machines (SVMs) for load identification are employed to extract ten features on the time domain and the steady state from electrical current sequences (Aslan and Nur, 2022). Additionally, principal component analysis (PCA) is combined with k-NNR and SVM separately to evaluate the effectiveness of the ten features and select the most useful ones. Meanwhile, S-transform extracts device features and employs an SVM classifier to identify each electrical device (Liu et al., 2019).

With high-frequency online monitoring of the electricity consumption situation on the user side, this article proposes the current pattern-based appliance running state identification model (CPARSIM) to promptly identify the running state of electrical appliances on the user side. By analyzing the electrical current state, the model can accurately determine the running state of appliances in real time. This approach can enable efficient monitoring and management of user-side electrical appliances. To extract the current patterns corresponding to different running states of electrical appliances from a massive amount of high-frequency monitoring data of user electricity consumption, with definitions of the current transfer state and current steady state, CPARSIM represents each piece of the current sequence using a univariate regression feature. In CPARSIM, each cluster of the entire set of univariate regression features of all current pieces is treated as one current pattern, and the DBSCAN algorithm is used to cluster the univariate regression feature set. In CPARSIM, each current pattern corresponds to a specific running state of an electrical appliance. According to the current state of the univariate regression features of the current piece, CPARSIM asserts the running state of the appliance when the electricity consumption situation is monitored online.

The rest of this article is organized as follows. The univariate regression features of the current sequence piece and its construction methods are presented in Section 2; Section 3 proposes a current-state pattern mining method based on the DBSCAN algorithm, and experimental results and analysis are provided in Section 4. Finally, Section 5 summarizes the research of the entire article. The main contributions of this article are as follows:

(1) Introducing CPARSIM. We propose the current pattern-based appliance running state identification model (CPARSIM), which enables the identification of running states of electrical appliances using univariate regression features of current pieces and current patterns.

The running state of one electrical appliance often changes from one state to another when the appliance is working. Usually, when the running state of an appliance is in a specific stable condition, the electric consumption data on the power line remain relatively stable. However, when the running state of the appliance changes, the electric consumption data on the power line also change.

If an appliance is running stably, the running state of the appliance is called the steady state. Correspondingly, the online monitoring data sequence of the steady state of the appliance is referred to as the steady-state sequence. As to two adjacent steady states in time of one appliance, the running states of an appliance generally cannot instantaneously transfer from one steady state to the next. In general, the transition requires some time from the first to the next. The data sequence collected at the time interval from the ending of the first steady state to the beginning of the following steady state is referred to as the transfer-state sequence, and the running state of the appliance at that time interval is the transfer state. From the perspective of electricity consumption, the running of an electrical appliance is a continuous transfer process between a steady state and a transfer state. During a steady state, the electrical current of the appliance remains relatively stable. However, the electrical current undergoes variations during the transfer, including momentary peaks or sustained fluctuations. This transfer process reflects the appliance energy consumption and dynamic characteristics under different running states.

The timely identification of the running state of an electrical appliance based on high-frequency current data is a common challenge in appliance running state identification. The CPARSIM framework is depicted in Figure 1.

The CPARSIM framework depicted in Figure 1 consists of Parts A and B. Part A utilizes high-frequency collected data from historical records to construct a set of current-state patterns. On the other hand, Part B uses the current pattern set built in Part A to perform an online analysis of the current sequence piece, thereby identifying the running state of the appliance. In Figure 1, Module 1 performs a deep analysis of the current sequence, decomposing it into some individual steady-state sequence pieces. Module 2 extracts all current transfer state sequences from the current sequence with the steady-state sequences outputted by Module 1 and the original current sequence as inputs. All current steady-state sequences outputted by Module 1 and current transfer-state sequences outputted by Module 2 are converted into current-state features by Module 3. Module 4 takes the current-state feature set as input and generates the current-state pattern set.

As shown in Figure 1, Module 5 is responsible for storing, querying, and visualizing all current-state patterns. Module 6 generates feature representations for the current sequence pieces. With the construction of the running state identification model based on the current-state pattern set in Model 5, Module 7 identifies the running state of the electrical appliance on the circuit with the output of Model 6 as input.

Changes in the operational state of electrical loads in a circuit can cause rapid alterations in the current sequence state. These rapid changes in the current sequence state can be effectively captured when monitoring user electricity usage patterns at a fine-grained level. Based on this concept, the CPARSIM model first derives feature representations of all current transitional and steady states from the sample dataset. It can then determine the state of the load corresponding to the observed current sequence state based on these feature datasets, thus achieving recognition of the appliance’s operational state. This model has a framework structure, and the design and implementation of each module within this structure are topics of interest in related research. Overall, the construction and identification processes of the CPARSIM model are as follows.

a) As shown in Part A of Figure 1, when constructing the feature set of all current steady states, the CPARSIM model first uses Module 1 to extract all steady-state sequence segments from the entire sequence data. Then, Module 2 extracts all steady-state sequence segments from the complete sequence data based on the segments obtained by Module 1. Next, Module 3 performs a feature representation of the current sequence segments constructed by Modules 1 and 2, while Module 4 conducts an in-depth analysis of the feature representation of all current sequence segments to obtain current patterns based on the feature representation. Finally, Module 5 stores and manages all current patterns and provides access support.

The electrical data sequence used in our experiment is from the observation data of the lighting line in Anhui Province Key Laboratory of Intelligent Building & Building Energy Saving. The period for the current observation data collected spans from 2023-02-01 00:00:00 to 2023-05-31 23:59:59. During those 10,368,000 s, data were collected 8,098,039 times, and duplicate data collections (where two or more collections occurred in one second) occurred 1,024 times. Moreover, data were missed 2,062,229 times, and power outages occurred 138 times, while the data collection program was terminated once at 206,570 s.

With ε = 0.08, ∆ = 0.3, for the current sequence as above, there are 339 current sequence pieces corresponding to the transfer state and 348 current sequence pieces corresponding to the steady state. That is, there are 687 current sequence pieces in our experiment. Figure 2A illustrates the time-domain morphology of the current sequence and the 687 current sequence pieces. Figure 2B presents the time-domain morphology of the current sequence from 2023-02-10 14:33:19 to 2023-02-11 01:39:59 within five current sequence pieces (three steady-state sequence pieces and two transfer sequence pieces). In Figures 2A, B, the curve for the current sequence piece of the steady state is marked in red, while blue marks the curve for the current sequence piece of the transfer state. According to curves in Figures 2A, B, each piece of the current transfer state corresponds to the current sequence piece with relatively rapid ascent or descent. In contrast, the current steady-state pieces fit into the current sequence piece with minimal fluctuations. In Figures 2A, B, the missing current data within each non-power outage time interval are estimated using the observed value or estimated value (when data are missing) of the previous second’s current.

Figure 3 illustrates the time-domain morphology of the current sequence in 1 min intervals from 2023-02-10 17:45:34 to 2023-02-10 17:46:33. In Figure 3, the horizontal axis represents the sampling time, and the vertical axis represents the collected current values. A point in Figure 3 represents a current value collected at a specific time. Theoretically, the points in Figure 3 should have equal horizontal intervals due to the electricity state being sampled per second. However, it can be observed from Figure 3 that the points are not evenly spaced horizontally. This phenomenon indicates that not every moment of current data is collected and implies that the model and method used to construct the feature of the current sequence must be able to handle or tolerate missing data.

The PSO algorithm is used to construct the univariate regression feature of the current sequence piece defined by Equation 3. In our experiment, the particle number of the PSO algorithm is 400, the values of learning factors c1 and c2 are 2, and the value of inertia factor ω is 0.8. Because each particle represents a candidate solution to the corresponding optimization problem in the PSO algorithm for solving optimization problems, Table 1 presents the minimum, maximum, mean, median, Q1, Q3, and variance of the feasible solution fitness values corresponding to all 400 particles when the PSO algorithm is used to construct all univariate regression features for 687 current sequence pieces. As the experiment was repeated 20 times, Table 1 contains 20 rows. Across all 20 experiments, the fitness value of the optimal solution had a minimum of 8.11E−20, a maximum of 1.71E−15, and a variance of 3.9474−16. These values are all very close to 0. Because the PSO algorithm uses the feasible solution with the smallest fitness value as the estimated optimal solution, and each data point in the minimum column of Table 1 is approximately 0, it can be asserted that the PSO algorithm is suitable for accurately solving the univariate regression features of the current sequence piece. The time used by the PSO algorithm is also given in Table 1. When the PSO algorithm is used to solve the univariate regression features of all 687 current sequence pieces, the minimum time used is 3,748.056 s, the maximum is 4,566.583 s, the mean is 4,118.558 s, the variance is 240.122 s, and the total time is 82,371.151 s over 20 repetitions. Given that the average time required to solve the univariate regression feature of each current sequence piece is 5.995 s, attention should be paid to the associated time constraints when the PSO algorithm is used to construct the univariate regression features of the current sequence piece in practice.

Two sets of lighting appliance fixtures are used in the experiment. Manual annotation determined that the 687 current sequence pieces in the experimental current sequence data corresponded to 13 different electricity states for the two lighting appliances. Table 2 describes those 13 electricity states. Because the missing data phenomena happened randomly during power data acquisition, the PSO algorithm was employed to construct the univariate regression features of the current sequence pieces specified in Equation 3.

First, all 687 current sequence pieces, where each current sequence piece is represented with its univariate regression feature, are partitioned into some clusters by Algorithm 1. Each cluster is treated as one current-state pattern corresponding to one electricity state in Table 2. Figure 4 illustrates the precision of Algorithm 3 for current-state pattern mining, while Figure 5 illustrates the silhouette coefficients. Because the implementation of Algorithm 1 takes reference from the DBScan algorithm, epsilon, the neighborhood radius parameter in Figure 4 varies from 0.001 to 1, incrementing by 0.001. Meanwhile, minPts, the minimum number of sample parameter for the density threshold, ranges from 1 to 20, incrementing by 1. Figure 4 illustrates the fluctuations in precision, as defined by Equation 9, with variations in the parameters epsilon and minPts. According to Figure 4, the precision of current-state pattern mining by Algorithm 3 exhibits significant variability when epsilon and minPts vary: the minimum precision is 0.1913, the maximum precision is 0.7824, the median precision is 0.6697, and the average precision is 0.5010 with 0.2561 as the standard deviation. When epsilon ranges from 0.001 to 0.006 and minPts is set to 1, the precision reaches its maximum. In Figure 4, the purple point indicates the corresponding data point representing the maximum precision value.

Because Algorithm 1 is implemented based on the DBScan algorithm, the silhouette coefficient can also be used to evaluate the performance of current-state pattern mining by Algorithm 1. Figure 5 illustrates the variation of the average silhouette coefficient concerning changes in the values of epsilon and minPts. In Figure 5, because Algorithm 1 clusters all the current sequence pieces into one cluster when epsilon exceeds 0.875, the neighborhood radius parameter, epsilon, varies from 0.001 to 0.875, incrementing by 0.001; meanwhile, minPts, varies uniformly from 1 to 20, incrementing by 1. It is evident that the silhouette coefficient of current-state pattern mining by Algorithm 1 exhibits significant variability when epsilon and minPts vary. For the average silhouette coefficient, the minimum is −0.3425, the maximum is 0.9379, the mean is 0.6142, the median is 0.6582, and the standard deviation is 0.1573. When epsilon is set to 0.005, and minPts is set to 1, the average silhouette coefficient reaches its maximum of 0.9379. In Figure 5, the maximum of the average silhouette coefficient is highlighted in purple. According to Figures 4, 5, it is easy to assert that the performance of current state pattern mining by Algorithm 1 is optimal when the value of epsilon is set to 0.005 and minPts is set to 1.

The k-means algorithm is a widely used clustering algorithm. For comparison, Figures 6, 7 illustrate the variations in precision and average silhouette coefficient of current-state pattern mining by the k-means algorithm based on the univariate regression feature set of current sequence pieces. When current-state patterns are mined by the k-means algorithm, for each possible value of parameter k, the process is repeatedly executed 400 times, and the precision and silhouette coefficient are recorded each time in our experiment. Figure 6 illustrates the variation of precision with increasing k. In Figure 6, k uniformly increases from 1 to 30, incrementing by 1. As k increases, some indicators for the precision of the current-state pattern constructed by the k-means algorithm, such as minimum, maximum, average, or median, tend to stabilize. Moreover, when k ≥ 13, the minimum, maximum, average, and median values are all approximately 0.77, and the values of these indicators are gradually approaching consistency. Because the k-means algorithm considers all data as one cluster when k = 1, the silhouette coefficient for the clustering cannot be calculated; therefore, in Figure 7, the value of k varies from 2 to 30, incrementing by 1. In Figure 7, when k ≥ 13, the mean and median of the silhouette coefficients for the current-state patterns constructed by the k-means algorithm converge and approach stability. Furthermore, when k = 14, 15, and 16, both the mean and the median reach their highest levels, and the average silhouette coefficient values are 0.8431, 0.8430, and 0.8422; meanwhile, the median values are 0.8505, 0.8499, and 0.8490, respectively. According to information in Figures 6, 7, the best value of parameter k is 14, 15, or 16 when the k-means algorithm is used to mine the current-state patterns.

The SOM neural network is one kind of unsupervised learning artificial neural network that is extensively used in domains such as data clustering, feature extraction, and data visualization. The experiment utilized an SOM neural network to perform cluster analysis on the univariate regression feature set of all current sequence pieces to obtain current sequence patterns. In the experiment, the SOM neural network consisted of 30 neurons arranged in five rows and six columns. Parameter epochs, representing the number of training iterations, varied uniformly from 50 to 1,000, incrementing by 50. For each value of epochs, the current-state patterns are constructed 400 times, and the precision and silhouette coefficient of the partition of the feature set of current sequence pieces are recorded each time. Figures 8, 9 illustrate the variations of precision and the average silhouette coefficient across different epochs.

Figure 8 illustrates the variation curve of precision of cluster partition of current state pattern mining by SOM with epoch increases. Obviously, the average precision remains relatively stable at approximately 0.78, and the median of precision aligns with the maximum precision and stabilizes at 0.7824 when epochs ≥ 100. Figure 9 illustrates the variation curve of the silhouette coefficient of cluster partition of current state pattern mining by SOM with epochs increases. The average silhouette coefficients remain relatively stable at around 0.82, and the median silhouette coefficients remain relatively stable at around 0.83 when epochs ≥ 150. According to Figures 8, 9, it can be concluded that the performance of cluster partition of current-state pattern mining by SOM is better when epochs = 150 or 200.

The optimal precision and silhouette coefficient of the current-state pattern constructed by the DBSCAN algorithm, k-means algorithm, and SOM neural network are given in Table 3. In the row for the DBSCAN algorithm of Table 3, the precision value at the precision column is the maximum precision when the current-state pattern is constructed by Algorithm 1 as above, and the silhouette coefficient value at the silhouette coefficient column represents the maximum average silhouette coefficient of the current-state pattern is built by Algorithm 1 as above. In the row for the k-means algorithm of Table 3, the precision value at the precision column is the maximum of average precision when the current-state pattern is constructed by the k-means algorithm 400 times as above, and the silhouette coefficient value at the silhouette coefficient column represents the maximum of average silhouette coefficient of the current-state pattern is constructed by the k-means algorithm 400 times. In the row for the SOM neural network of Table 3, the precision value at the precision column is the maximum of average precision when the current-state pattern is constructed by the SOM algorithm 400 times as above, and the silhouette coefficient value at the silhouette coefficient column represents the maximum of average silhouette coefficient of the current-state pattern is constructed by the SOM 400 times. Based on the information provided in Table 3, it can be concluded that Algorithm 1 demonstrates superior performance in partitioning current-state patterns than the k-means algorithm and SOM neural network. Thus, Algorithm 1 is deemed more suitable for current-state pattern mining.

The computer used for current-state pattern mining in this experiment is a Dawn W760-g20 server with dual Intel^® Xeon^® CPU E5-2637 v3 processors and 192 GB ECC memory. The operating system is Windows 10, and the program environment is MatLab R2017a.

This study introduces the CPARSIM framework, designed to efficiently identify electrical current-state patterns and the running states of appliances by analyzing current sequence pieces. In the CPARSIM framework, the two coefficients of the univariate regression equation for each current sequence piece are treated as its features, and the PSO algorithm is applied to solve the univariate regression equation for a current sequence piece where some data may be missing. The challenge of mining current-state patterns is approached as a cluster analysis problem, with each cluster representing a distinct current-state pattern. A novel current-state pattern mining method is proposed based on the DBSCAN algorithm. In our experiments, clustering analysis algorithms, such as the k-means algorithm, DBSCAN algorithm, and SOM neural network, are individually used to cluster the feature set of current sequence pieces. Experimental results show that the current-state pattern mining by the DBSCAN algorithm is more suitable for identifying running states of appliances based on online current sequence pieces in real scenarios.

In this article, the tactics of adjacent data differencing are used to identify pieces of the online current sequence. The online data may exhibit more significant fluctuations if there is significant interference on the circuit, and those fluctuations may result in a single current sequence piece being identified as multiple pieces, as well as significant drifting of the features of these pieces. To ensure the completeness and stability of the current sequence pieces for the same event, techniques such as applying sliding windows, fixed time interval sampling, event triggering, and methods based on load switching points are exciting topics. Additionally, the standardization and normalization of data and the analysis and interpretation of appliances running states corresponding to various current-state patterns based on cluster analysis results are valuable topics for future research.

Furthermore, this article uses univariate regression features to represent variable-length current sequence pieces, and each sequence piece is treated as one point within the two-dimensional feature space. In the future, Fourier transformation can extract the spectral features of the current sequence pieces, or statistical features such as mean, variance, and peak value could be used to represent variable-length current sequence pieces in a unified dimension. Representing variable-length current sequence pieces in a suitable dimension is worth attention in different application scenarios.