## 2 Materials and Methods
### Optimization Method for Wind Turbine Health Region Based on Data Increment Inflection Points
At this point, the movement stops, and the vertical optimal upper (or lower) limit power curve is established. \[N_{d}{}^{\prime}=\frac{Lc_{n}{}^{\prime}-Lc_{\mathrm{Tc}}}{D}\times 100\% \tag{20}\]  
In Equation (20), \(\mathrm{Lc_{n}{}^{\prime}}-\mathrm{Lc_{Tc}}\) is the data volume between the n-th vertically moved wind power curve and the static optimal wind power curve. Multiple experimental validations have shown that the best data effect occurs at a specific \(\mathrm{N_{d}}^{{}^{\prime}}\approx 34.21\%\) value. Figure 2 illustrates the data volume change between the power curve, which has already been moved horizontally in step (4), and the static optimal power curve as it undergoes vertical movement. It is evident that when the step size accumulates a movement of approximately 20 kW, and the data volume \(\mathrm{N_{d}}\) reaches 34.21%, the absolute value of the slope begins to decrease, and the curve flattens, indicating that the path of movement has reached  
1. Rotational Speed Stability  
The stability of a wind turbine's rotational speed is quantifiable by its standard deviation--a statistical indicator used to measure the dispersion of data. In rotor speed data analysis, a smaller standard deviation indicates smaller changes in speed, more stable speed data, suggesting more stable wind turbine operation. In contrast, a higher standard deviation denotes significant speed variability, reflecting potential instability in turbine performance. Evaluating the standard deviation of rotational speed data over time can thus provide insights into the turbine's operational stability, with lower values indicating greater stability. This stability is crucial for consistent power output and efficiency in turbine operation. Higher stability helps the wind turbine to maintain a stable output power and has a positive impact on the speed control and operational efficiency of the wind turbine. 2. Power Performance Coefficient (CP)  
The power performance coefficient (CP) measures the alignment between a wind turbine's actual power output and its theoretical predictions. It is determined by comparing  
Figure 3: Wind turbine performance evaluation process. Figure 2: Changes in data volume caused by shifting the power curve. power outputs at various wind speeds, adjusted for air density, to theoretical values. The selection of sampling points between the turbine's cut-in wind speed and expected theoretical speeds, at intervals of 1 m/s, facilitates this comparison. Assessing the CP across these points allows for a comprehensive evaluation of the turbine's power efficiency in relation to theoretical models. \[Cp=1-\frac{SSR}{SST} \tag{21}\]  
In Equation (21), SSR denotes the sum of squares of residuals, representing the discrepancy between actual and theoretical power outputs. SST stands for the total sum of squares, quantifying the variance of actual power outputs from their mean value. A determination coefficient approaching 1 signifies a model's heightened ability to accurately represent actual power outputs, indicating superior model fitting. The power performance coefficient emerges as a pivotal metric in assessing wind turbine performance. 3. Efficiency of Power Generation  
\[PE=\frac{1}{60}\sum_{i=1}^{n}\frac{P_{r}}{P_{t}}T_{i}(KW\cdot h) \tag{22}\]  
Equation (22) articulates that \(\mathrm{P_{r}}\), the real-time power output recorded at 10 min intervals, and \(\mathrm{P_{t}}\) theoretical, the anticipated power output, alongside \(\mathrm{T_{i}}\) average, the mean duration of power production, serve as foundational elements. Power generation efficiency, typically ranging between 0 and 1, represents the ratio at which wind turbines convert wind energy into electrical power. Enhanced efficiency underscores a turbine's ability to optimize wind energy for electricity production, thus elevating energy conversion efficiency.