# Non-Intrusive Load Disaggregation by Linear Classifier Group Considering Multi-Feature Integration
## 3 Methodology
### Steady-State Segment Based Event Detection  
One important characteristic of event-based load disaggregation is to detect the significant rising or falling edge in active power, and record the power value and occurrence time of events. This paper presents an event detection method based on steady-state segment. It has two parameters, one is noise  
Figure 4: Flowchart of the proposed algorithm.  
threshold \(d_{n}\), the other is power threshold \(d_{p}\). The schematic diagram of the event detection is shown in Figure 5.  
Each appliance can be represented by two states: (1) steady state, including ON and OFF state; and (2) transition state, i.e., the process of changing operation state of multi-state appliance. As long as the steady-state segments are identified, the duration of the power-on or power-off processes for different appliances can be determined adaptively. Load switching is successively based on the switch continuity principle [3], i.e., only one state transition can occur within the sampling time interval. It is feasible to use the step power variation in aggregated signal as the discriminant feature of event occurrence.  
The power grid noise exists in the actual electric environment all the time. Low-frequency data can largely avoid noise interference, because the sampling frequency is much less than the noise frequency. In order to further improve the accuracy of the algorithm, the noise threshold is introduced to minimize the possibility of noise impact. Considering the robust to the possible variation of power amplitude caused by the noise, an appropriate event extraction method is designed. The local mean and variance of power are used to capture the load steady state. Assuming \(P(k)\), \(k\) = 1,2,3,... \(L\) is a given aggregate power signal and \(T(k)\), \(k\) = 1,2,3,... \(L\) is the corresponding timestamp. By calculating the power changes at a certain time point, as well as before and after two time points, we can judge whether the household appliances are running steadily at that time. Two quantities are be calculated by Equations (3) and (4), where the former is the local mean power and the latter is the local variance.  
\[\mu_{P}(k)=\frac{1}{3}{\sum\
olimits_{i=-1}^{L}}P(k+i) \tag{3}\]  
\[\sigma_{P}(k)=\frac{1}{3}{\sum\
olimits_{i=-1}^{L}}(P(k+i)-\mu_{P}(k))^{2} \tag{4}\]  
The reason for choosing 1/3 is that it represents the mean and variance of three time points.  
Let \({\delta_{n}}^{2}\) denote the noise variation in power grid. If \(\sigma_{p}(k)<\delta_{n}\), \(P(k)\) is considered in a steady state and then two variables \(P_{\text{std}}(m)\) and \(T_{\text{std}}(m)\) are added to record the \(m\)th steady state, shown as follows.  
\[P_{std}(m)=\mu_{P}(k) \tag{5}\]  
\[T_{std}(m)=k \tag{6}\]  
After all the steady state segments are identified, the power difference between two consecutive steady states is calculated as Equation (7):  
\[P_{std}(m)=P_{std}(m)-P_{std}(m-1) \tag{7}\]  
Figure 5: Schematic diagram of the event detection.  
Set by users, the value of power threshold \(\delta_{p}\) depends on the load events they are interested in. For example, if users focus on the events with power change greater than 100 W, they can set \(\delta_{p}=100\). If abs(\(\Delta P_{\text{std}}(m)\))> \(\delta_{p}\), it indicates that a new event is detected. The power value and timestamp of this event can be obtained as:  
\[P_{\textit{ext}}(n)=\Delta P_{\textit{std}}(m) \tag{8}\]  
\[T_{\textit{e\_start}}(n)=T(T_{\textit{std}}(m-1)) \tag{9}\]  
\[T_{\textit{e\_end}}(n)=T(T_{\textit{std}}(m)) \tag{10}\]  
where \(n\) represents the \(n\)th event. \(P_{\textit{ext}}(n)\) stands for the power value of the \(n\)th event, \(T_{\textit{e\_start}}(n)\) and \(T_{\textit{e\_end}}(n)\) stand for the start time and end time of the event, respectively.