# Optimal Strategy to Select Load Identification Features by Using a Particle Resampling Algorithm
## 2 Materials and Methods
### Identification Feature Extraction and Resampling  
Since the change point was found by the above method, the feature of the load could be obtained by using the load characteristics of the changes [14]. Usually, the load event is determined based on physical changes in current, voltage, and other power information. Therefore, the load characteristics of these changes can be considered as the characteristics of the switching of the electrical device. For example, Figure 3 illustrates three types of load, named resistive load, capacitive load, and inductive load, which have different current phases for their capacitive reactance and opposite impedance performances. We can figure out the active power P by the voltage \(U\), current \(I\), and their phase difference \(\varphi\) that:  
\[P=Ul\text{cos}\varphi. \tag{5}\]  
Similarly, the reactive power Q can be described as:  
\[Q=Ul\text{sin}\varphi. \tag{6}\]  
Active power and reactive power can be calculated by Equations (5) and (6), and they can distinguish between the different types of loads according to their values. Moreover, active power and reactive power can be captured by low-frequency meters. In this paper, active power P and reactive power Q were adopted as the features. Figure 3: Current of the linear load. In order to clearly illustrate the extraction of the load features, including the active and reactive characteristics, let \(P(t)\) denote the active power variation with time \(t\) for an example. Usually, it is statistically stable. However, once the load changes the status, the \(P(t)\) may undergo large changes at that time. So, the difference of \(P\) can represent the change of the status of the device, thus the value of \(P(t)\) can be disaggregated. Here, we denote the \(\Delta P=P(t+\Delta t)-P(t)\) as the difference of \(P\), and the \(P(t)\) satisfies the condition as follows:  
\[ \begin{array}{l}\min\left|P(t)-\sum\limits_{i=1}^{m}a_{i}(t)P_{i}\right|\\ \min\limits_{\Delta t=T}\left|P(t+\Delta t)-\sum\limits_{i=1}^{m}a_{i}(t+ \Delta t)P_{i}\right|\end{array} , \tag{7}\]  
where \(P(t)\) is the active power at time \(t\); \(m\) is the total number of load in the database; \(a_{i}\) is the mark of the state of load, where \(a_{i}=1\) indicates the running state and \(a_{i}=0\) means turned off; and \(T\) is the time interval. Similarly, the reactive characteristic (or called the difference of Q) \(\Delta Q=Q(t+\Delta t)-Q(t)\) at time \(t\) satisfies the condition as follows:  
\[ \begin{array}{l}\min\left|Q(t)-\sum\limits_{i=1}^{m}a_{i}(t)Q_{i}\right|\\ \min\limits_{\Delta t=T}\left|Q(t+\Delta t)-\sum\limits_{i=1}^{m}a_{i}(t+ \Delta t)Q_{i}\right|\end{array} . \tag{8}\]  
From Equations (7) and (8), it can be observed that the extraction of load characteristics from power load switching is related to the time of change point, i.e., the time interval \(T\). Although the change point is found according to the rules of the minimum inner-class variance, the voltage and current fluctuations make it difficult to determine this time interval \(T\). Usually, the different time \(T\) can obtain the different P and Q features. In some papers [15; 16; 17], the time \(T\) is selected as the point after the change point. For some situations, the changes in P and Q may mismatch the load during load identification. So, in this paper, the importance resampling method was proposed to avoid the uncertainty of time interval \(T\) and the influence of power load information fluctuation. The resampling algorithm is often used to solve the sequential importance sampling algorithm [18]. At present, there are many kinds of resampling algorithms [19; 20]. In this paper, the importance resampling algorithm is adopted. To further explain, Figure 4 describes the process of resampling. It can be seen that this method regards the characteristics at each time as a particle and resamples the importance of each particle according to the distribution of particles before and after the change point.