## 4 Separation Methodology
### The Case of Identifying Abnormal Conditions for Daily Data  
From April to August 2018, Building A is selected to verify the results for identifying and separating the normal data by the above methodology. The parameter \(a\) is used to evaluate the results, as follows:  
\[a=\frac{n}{N} \tag{2}\]  
For the OATPM method, taking daily power consumption as the ordinate and the daily average outdoor temperature as the abscissa, the model of daily average outdoor temperature and daily power consumption of lighting sockets (mixed with power consumption of air-conditioning) is shown in Figure 10. The three clusters are displayed in three colors. The data are fitted into a curve, and the second derivative is calculated to obtain the inflection point (24 \({}^{\circ}\)C, 1445 kWh). The average outdoor temperature and power consumption are, respectively, represented by black dotted lines. As shown in Figure 10, when the outdoor temperature is lower than 24 \({}^{\circ}\)C the daily power consumption is within the range of 750-1500 kWh, and the maximum value is 1445 kWh. Figure 10: Model of average outdoor temperature versus daily electricity consumption. Figure 9: Identification method of air-conditioning usage condition on the designated day. When the outdoor temperature is higher than 24 \({}^{\circ}\)C, the daily cumulative electricity consumption is higher than 1445 kWh. According to the properties of the second derivative, at 24 \({}^{\circ}\)C, the plus and minus signs of the first derivative change, that is, the local extreme value appears. Therefore, 24 \({}^{\circ}\)C is presumed to be the point of the power consumption characteristic change. At the same time, analyzing this point by the correlation coefficient, the power consumption of the lighting socket equipment is weakly correlated with the outdoor temperature, but the power consumption of the air-conditioning is strongly correlated with outdoor meteorological conditions. The conditions when \(\overline{T_{i}}\) is higher than 24 \({}^{\circ}\)C and \(\overline{T_{i}}\) is lower than 24 \({}^{\circ}\)C are calculated, respectively, about the correlation coefficient between the average outdoor temperature and the daily power consumption, as follows:  
\[r_{XY}=\frac{cov(X_{i},Y)}{\sqrt{var(X_{i})var(Y)}} \tag{3}\]  
where \(X_{i}\) is the average daily outdoor temperature and \(Y\) is the power consumption of the lighting socket (mixed with the power consumption of air-conditioning). The value of the correlation coefficient \(R\) ranges from 0 to 1. The closer it is to 1, the stronger the correlation between variables; the closer it is to 0, the weaker the correlation. After the calculation, \(R\left(\overline{T_{i}}\geq 24\ ^{\circ}\text{C}\right)=0.709\); \(R\left(\overline{T_{i}}\leq 24\ ^{\circ}\text{C}\right)=0.196\). Therefore, when the average outdoor temperature is lower than the judgment temperature (24 \({}^{\circ}\)C), the power consumption is small, and the relationship between the average outdoor temperature and the lighting socket power consumption is relatively weak, so it can be considered that the air-conditioning power consumption is not mixed with the lighting socket power consumption. When the average outdoor temperature is higher than the judgment temperature (24 \({}^{\circ}\)C), the power consumption increases suddenly, and the maximum value of the power consumption curve appears. The relationship between the average daily outdoor temperature and the power consumption is relatively large. Thus, it can be considered that the air-conditioning power consumption is mixed with the lighting socket power consumption. Regarding the KNN method, it is calculated by the k-means algorithm, of which the parameter \(K\), the number of clusters, is also evaluated at 3, as discussed above. That is, closed (\(p<40\%\)), slightly open (40% \(<p<70\%\)), and fully open (\(p>70\%\)).