## 5 Energy Management Strategy  
### MPPT Control Strategy for Wind Turbine  
Perturbation and observation method with variable step is used to achieve maximum power output of the wind turbine by adjusting the duty ratio. The method needs to estimate the position of the current maximum power point by real-time monitoring of the power difference between the two times, thereby determining the size of the duty cycle. If the difference is positive, the duty cycle will be decreased. Otherwise, the duty cycle will be increased. If it is zero, it indicates that the maximum power point has been reached. Since the wind speed in nature is randomly fluctuating, it may cause the power supply system to oscillate. Two step sizes are proposed in this study. The threshold of the power difference is set. If the difference is within the threshold, a small step will be used. If the difference is outside the threshold, a large step will be used to gradually approach the maximum power point. The mechanical energy produced by the wind turbine in this study can be expressed as follows. \[P_{WT}=\frac{1}{2}C_{p}(\lambda,\beta)S\sigma v^{3} \tag{15}\]  
where \(P_{WT}\) is the output of wind turbine (W); \(C_{p}(\lambda,\beta)\) is wind energy utilization factor; \(\lambda\) is tip speed ratio; \(\beta\) is pitch angle of blade; \(S\) is sweep area (m\({}^{2}\)); \(\sigma\) is air density (Kg/m\({}^{3}\)); \(\upsilon\) is wind speed (m/s). The sweep area of wind turbine can be described as follows. \[P_{WT}=\frac{1}{2}C_{p}(\lambda,\beta)S\sigma v^{3} \tag{16}\]  
where \(R\) is the impeller radius (m). The wind energy utilization factor can be described as follows. \[C_{p}(\lambda,\beta)=0.5176(116\lambda_{c}-0.4\beta-5)e^{-\frac{21}{\lambda_{ c}}}+0.0068\lambda \tag{17}\]  
Figure 7: The flowchart of the temperature control strategy. \(\lambda\) and \(\lambda_{c}\) in Equation (16) can be described as follows. \[\left\{ \begin{array}{l}\lambda=\frac{\omega R}{v}=\frac{2\pi nR}{60v}\\ \lambda_{c}=\frac{1}{\lambda+0.08g}-\frac{0.035}{\beta^{3}+1}\end{array} \right. \tag{18}\]  
where \(\omega\) is wind turbine angular velocity (rad/s); \(n\) is rotational speed of wind turbine (r/min). In the study of the MPPT strategy of the wind turbine, \(\beta\) (pitch angle of blade), \(v\) (wind speed) and \(\omega\) (wind turbine angular velocity) are set as input to the wind turbine power generation model. Air density is selected as 0.927 Kg/m\({}^{3}\). \(\beta\) is 0 in this study. For wind speed \(v\), we built a natural wind speed model. The wind speed model is considered as a combination of basic wind speed \(V_{b}\), gradual wind speed \(V_{r}\), and gust wind speed \(V_{g}\). The basic wind speed \(V_{b}\) is the average wind speed (7 m/s). The gradual wind speed \(V_{r}\) characterizes the slow change of the wind speed and can be expressed by follows. \[V_{r}=V_{r}(\max)\frac{t_{r1}-t}{t_{r1}-t_{r2}} \tag{19}\]  
where \(V_{r}(max)\) is maximum value of gradual wind speed (10 m/s); \(t_{r1}\) is start time of gradual wind (4 s); \(t_{r2}\) is end time of gradual wind (11 s); \(t\) is time of gradual wind. The gust wind speed \(V_{g}\) can characterize the degree of abrupt change in wind speed and can be expressed by follows. \[V_{g}=V_{g}(\max)/2\times\left[1-\cos 2\pi\left(\frac{t-t_{g1}}{T_{g}}\right)\right] \tag{20}\]  
where \(V_{g}(max)\) is maximum value of gust wind speed (6 m/s); \(t_{r1}\) is start time of gust wind (3 s); \(T_{g}\) is period of gust wind (6 s); \(t\) is time of gust wind. The model of natural wind speed can be described as follows. \[v=V_{b}+V_{r}+V_{g} \tag{21}\]  
We introduced the natural wind model into the wind power model, and the simulation results obtained by MATLAB Simulink of the wind speed, wind turbine output power and rotational speed of wind turbine are shown in Figure 8.  
As can be seen in Figure 8a, at the beginning, the wind speed was low (about 2-5 m/s), thus the output power of the wind turbine was also low (Figure 8b).