As an unsupervised learning process, clustering has a good effect on mining the

inner relations of unmarked data sets [13]. Compared with the k-means algorithm, the system clustering don’t need to set the number of clusters in advance, what is very suitable for processing such complex and unknown household electricity data and is one of the classical algorithms. This algorithm is divided into the cohesion method and the splitting method. Take the cohesion method as an example, each object is regarded as a cluster firstly. Then according to a similarity measure, two closest clusters are merged at every turn until all the clusters are merged into one and the affinity spectrum diagram is formed (specific principles are shown in Figure 2 ).The split rule is just the opposite.

Supposing the number of samples of household electricity consumption is s (10 ≤ s ≤ 15), global variables and phase variables are attribute parameters, and the kth sample can be described as: f_k = [f_kA,f_kB] = {A_k1, A_k2, ・・・, A_km, B_k1, B_k2, ・・・, B_kn} (k = 1, 2, ・・・, s), where A_ki (i = 1, 2, ・・・, m) is a global variable, B_kj (j = 1, 2,・・・ n) is a phase variable, and both of which are time series parameters. Assuming that there are qacquisition points in the sample period, A_ki = {, ,・・・, }, B_kj = {, ,・・・, }. Because of the existence of different dimensions between different variables, standardized processing is carried out by Z-score method:

where: μ is the sample mean of x, and τ is the sample standard deviation. For the convenience of writing, standardized variable symbols remain unchanged.

Choosing the global variables as the analysis parameters, s samples are clustered together to calculate the average distance between clusters by formula (2) and (3):

where: d(f_i, f_j) is the Euclidean distance between samples f_i and f_j, and I ≠ j, (i, j = 1, 2, ・・・, s), n_i and n_j are the number of objects of cluster C_i and C_j, respectively.

Merging the two clusters whose distance is the smallest, then updating the data,

the calculation above is repeated until all the clusters are merged into one. According to the complicated relationship, the situation of the combination of two samples, and the combination of a sample and a cluster is classified as a class. Taking into account that the mean is susceptible to the discrete points and extreme values, the household energy modes M₁, M₂, ・・・, M_p are obtained by utilizing the median eigenvalues to represent the general trend of a class of data sets:

where:, (I = 1, 2, ・・・, m; j = 1, 2, ・・・, n) are the medians of the corresponding variables in the pth class.

Gray relational analysis is used to quantitatively analyze and compare the dynamic development process of the system, and to excavate the main factors influencing its change, which is mainly composed of three elements as reference sequence, comparison sequence, and gray relational degree. Assuming that the reference sequence at the ith time is x₀(i), X₀ = (x₀(1), x₀(2), ・・・, x₀(n)). Comparison sequences are generally more than one, recorded as X₁, X₂, ・・・, X_k, where X_k = (X_k(1), X_k(2), ・・・, X_k(n)). The essence of gray relational analysis is to compare the similarity between the curves of X₁, X₂, ・・・, X_k and X₀ with time respectively. The gray relational degree represents the relative order of the similarity of each comparison reference sequence to the reference sequence, and the more similar, the similarity degree is greater.

Combined with phase data, the gray relational grade is applied to analyze the latent influencing factors of user’s power consumption modes, and the mode Mp is taken as an example:

1) The absolute difference between the phase and global variables is calculated by the formula (5):

where: k = 1,2, ・・・, m.

2) The gray relational coefficient of corresponding elements between the phase variables and the global variable is gotten by:

where: indicates the correlation between the ith variable and the global variable of mode M_p at the jth time point.

3) The relational degree of each phase variable to the global variable is computed by:

4) Comprehensive evaluation is applied to analyze and compare the relational degree of each variable in each mode finally.

This data is from the University of California, Irvine (UCI) database [17], mainly consists of four parts: 1) the total household electricity consumption, including global active power, global reactive power, average voltage, average current. 2) Kitchen power consumption, including a dishwasher, a microwave oven and oven. 3) Laundry power consumption, including a washing machine, a dryer, a refrigerator and a lamp. 4) Living area of electricity, including the water heater and air conditioner. The database contains the electricity consumption of the family from 2006 to 2010, measured once every minute. Because the analysis of household electricity consumption focuses on the information mining process, so although this paper uses foreign data that does not affect the final conclusion, and as China’s smart grid construction is maturing, household power split measurement is an inevitable trend.10 days ( 2010/8/2 to 2010/8/11 ) of electricity data were selected randomly as an analysis of samples to build data cube.

Considering the purpose of mining household electricity modes, and that household energy consumption is mainly based on active load, therefore, this paper chooses the daily load data as the analysis parameters, and uses the system clustering method in Section 2.2 to excavate the electricity consumption model to get the agglomeration schedule, as shown in Table 1.

The main purpose of clustering is to make the electricity consumption in the same mode as similar as possible, the electricity consumption of different modes as different as possible. Therefore, considering only the situation that the first agglomeration step is 0, agglomeration process of steps 7, 8, 9 are excluded. And the pedigree chart is shown in Figure 3.

From the figure above, we can see that, from 2010/8/2 to 8/11, the household electricity consumption can be roughly divided into four modes, and each mode is a clustering of days, which reflects the similarity of household electricity consumption in a short time. The median eigenvalue represents the corresponding modes, as shown in Figure 4. It can be seen that there are two peak powers in each household electricity consumption modes, where the peak period is gradually advanced from mode 4 to mode 1.

After analyzing a large number of sample data, it is found that the family has a basic load with amplitude of about 0.4 kW. The load fluctuation is small, which is the minimum basic energy loss of the household, while the user electricity

consumption load which is mainly related to the use of electrical appliances is fluctuated obviously. In order to distinguish the user’s electricity consumption load and household basic load, the load fluctuation threshold is set to be 0.5. Then the basic characteristics of the power consumption modes are obtained as shown in Table 2.

1) Experiment 1

In order to verify the short-term similarity of the household electricity consumption behavior, the electricity data of 8/12 are adopted to compare the correlation between each power consumption modes and the power consumption in 8/12. Besides, based on the electricity data from 8/12 to 8/16, this paper compares the relationship between the past 5 days’ power consumption and the most recent power consumption mode. Detailed data are shown in Table 3 and Table 4.

It can be seen from Table 3 and Table 4 that the gray relational degree between each mode with 8/12 household electricity consumption is basically reduced as the time interval larger, that is, the power characteristic of mode 1 is most similar to that of 8/12. In addition, the closer the date to mode 1, the greater the degree of correlation is, and the difference between the recent 3 days of

gray relational degree is not significant. The above shows that in the short term, the household electricity behavior has certain continuity and similarity. Through the large number of fitting experiments on the random number of days’ load, it is found that the similar electricity behavior cycle is 2 - 3 days, so utilizing the recent household electricity consumption model to predict this family 2 - 3 days power consumption is feasible.

2) Experiment 2

In this experiment, the data of phase parameter in each mode are taken to analyze the correlation between the phase variables. As the kitchen power consumption is zero, we select the two phase variables as the laundry and living area to analyze, and ultimately get the potential impact of each power model, as shown in Table 5.

It can be seen that in the mode 1 to mode 4, the gray relational degree of living area is greater than the laundry’s. Compared with the energy consumption of the laundry, the load curve of the living area is more similar to the characteristic curve in the corresponding mode, indicating that the electricity consumption habits of living area is more dominant than the laundry’s in the whole household.

From Table 2, we can see that the power peak hours is about 1.5 h, so taking the mode 3 for example, the living area’s peak time is delayed 1.5 h to get the curve shown in Figure 5, which shows that compared with the original load curve, living area electricity of mode 3 is mainly concentrated in the peak hours, after delaying the living area, the household peak load is obviously reduced and the load curve is relatively gentle. In summary, appropriate adjustment on the dominant phase variables is beneficial to improve the overall electricity load

fluctuation, is helpful to peak shifting and valley filling, and finally obtain some economic significance