*2.1. Model of Wind Turbine*

Wind power generation is one of the important power generation units in the microgrid. As the objective of this paper is to optimize the microgrid, it is also necessary to predict the active power output by the wind turbine. The rotation speed of the hub is related to the wind speed, so the analysis of modeling the output power of the wind turbine is essentially an accurate measurement of the wind speed of the wind turbine hub [21]. Considering the measurement of the wind speed of the fan hub, the cut-in wind speed *Vci*, rated wind speed *Vr*, and cut-out wind speed *Vco* are often used. Three physical quantities are measured, and then the fan output power characteristic equation is obtained by curve fitting. All wind turbines have roughly the same wind speed power curve shape. Total extracted power from the wind turbines *Pwt* at any time can be calculated as follows [22]:

$$P\_{\rm wt}(\upsilon) = \begin{cases} 0 & 0 \le \upsilon \le \upsilon\_{\rm ci} \\\ a \cdot \upsilon^3 - b \cdot P\_{\rm wt-rate} & \upsilon\_{\rm ci} \le \upsilon \le \upsilon\_r \\\ P\_{\rm wt-rate} & \upsilon\_r \le \upsilon \le \upsilon\_{\rm co} \end{cases} \tag{1}$$

The constants *a* and *b* are given by the following equations [22]:

$$a = \frac{P\_{\text{wt}-\text{rat}}}{\upsilon\_r^3 - \upsilon\_{ci}^3} \quad b = \frac{\upsilon\_{ci}}{\upsilon\_r^3 - \upsilon\_{ci}^3} \tag{2}$$

where *a* and *b* respectively represent the fitting coefficients of the WT output power, and *Pwt*−*rate* is the rated power of the WT. Generally, in the standard test case, the wind speed power characteristic curve of the wind turbine is drawn, and then the wind speed power expression shown in the above formula is obtained by curve fitting, but there are certain errors in the actual environment, so the standard test environment is correct the wind speed power characteristic curve obtained below.
