## 2 Materials and Methods
### Health Index of Wind Turbine Operating State
#### 2.2.2 Discussion on Health Indicators of Wind Turbine Operation  
The relationship between the wind speed and power is the most important relationship among wind turbine operating conditions. A change in the wind turbine operating state is reflected in a difference between its wind speed and power curve; thus, many researchers identify the operating health state of the wind turbine by quantifying the difference between wind speed and the power curve at different times.  
Under normal operation, a data relation standard model is:  
\[P_{\text{std}}(v)=a_{\text{std},0}+a_{\text{std},1}v+\ldots+a_{\text{std},n}v^{n} \tag{10}\]  
Let the \(t_{k}\) time data relation model be:  
\[P_{k}(v)=a_{k,0}+a_{k,1}v+\ldots+a_{k,n}v^{n} \tag{11}\]  
Let the state health indicator \(C_{\text{power}}\) be defined based on the output power attenuation as:  
\[C_{\text{power}}=\frac{\int_{v_{\min}(k)}^{v_{\max}(k)}\sum\limits_{j=0}^{3} \left[a_{j}(k)-a_{j}\right]v^{j}}{v_{\max}(k)-v_{\min}(k)}\text{d}v \tag{12}\]  
The state health index \(C_{\text{eu}}\) based on Euclidean distance is defined as:  
\[C_{\text{eu}}=\frac{\sqrt{\int_{v_{\min}(k)}^{v_{\max}(k)}\sum\limits_{j=0}^{3 }\left[(a_{j}(k)-a_{j})v^{j}\right]^{2}\text{d}v}}{v_{\max}(k)-v_{\min}(k)} \tag{13}\]  
State health indicators proposed by [PERSON] (2018) and others are:  
\[C_{\text{Y}}=\frac{\int_{v_{\min}(k)}^{v_{\max}(k)}\left|\sum\limits_{j=0}^{3 }\left(a_{j}(k)-a_{j}\right)v^{j}\right|\text{d}v}{v_{\max}(k)-v_{\min}(k)} \tag{14}\]  
With a 24 h window width and a 1 h increment, the wind speed and power data of wind turbine SCADA for 72 h are processed, and three state health indicators based on data relations were compared and analyzed. The results of these analyses are shown in Figure 4. The three health indicators changed markedly after 40 h, indicating that the health status of the wind turbine generator sets was abnormal.  
Figure 4: Comparison of the health indicators of wind turbine operating conditions (total time step \(n=73\)).  
The operating health of wind turbines can also be evaluated by the real-time wind energy utilization efficiency. Because wind speeds can change rapidly and the mechanical energy stored on the wind wheel of the wind turbine can only change slowly due to the inertia of the wind wheel, the value of the transient wind power coefficient is inconsistent with the actual situation. As shown in Figure 5, the minimum value was 0.18, and the maximum value was 1.95, which was much larger than the theoretical maximum value of 0.593 of the wind power coefficient.  
Using the ratio of the total energy of the airflow flowing through the wind wheel in a period of time to the total electrical energy output in that time period and considering the energy stored on the wind wheel [21], the wind power efficiency can be obtained as follows:  
\[C_{\text{P}}=\frac{\int_{0}^{t_{2}}Pdt-\int_{0}^{t_{1}}Pdt+\frac{1}{2}J\omega ^{2}\big{|}_{t=t_{2}}-\frac{1}{2}J\omega^{2}\big{|}_{t=t_{1}}}{\int_{0}^{t_{2}} \frac{1}{2}\rho\pi R^{2}v^{3}dt-\int_{0}^{t_{1}}\frac{1}{2}\rho\pi R^{2}v^{3}dt} \tag{15}\]  
where \(t_{2}>t_{1}\) and \(J\) is the moment of inertia of the wind wheel. Figure 6 shows the wind power efficiency of wind turbines at different times. The wind turbine generator power coefficient began to drop after 24 h, which is different from the change rule of the first three health indicators.