# Output Power Smoothing Control for a Wind Farm Based on the Allocation of Wind Turbines
## 4 Simulation Results
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Wind Turbine** & & **PMSG** & \\ \hline Blade radius (m) & 35 & Stator resistant (\(\Omega\)) & 0.01 \\ Air density (kg/m\({}^{3}\)) & 1.225 & Inductance (mH) & 0.835 \\ Optimum TSR & 8.1 & Rotor inertia (kg\(\cdot\)m\({}^{2}\)) & 8500 \\ Optimum power coefficient & 0.48 & PM linkage (Wb) & 8.76 \\ Rated wind speed (m/s) & 12 & Pole pairs & 32 \\ Rated power (MW) & 2 & Rated power (MW) & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the simulation. Figure 10: _Cont._  
Figure 9: Time histories of the wind speed and rotor speed in the wind farm under the maximum power point tracking (MPPT) control. (**a**) Wind speed of the first group WTs (1–3). (**b**) Wind speed of the second group WTs (4–6). (**c**) Wind speed of the third group WTs (7–9). (**d**) Rotor speed of the first group WTs (1–3). (**e**) Rotor speed of the second group WTs (4–6). (**f**) Rotor speed of the third group WTs (7–9). The second working mode of the wind farm was to output the smoothing power and the simulation results are shown in Figures 11 and 12. At this time, the proposed power smoothing control strategy based on the allocation and rotor inertia of wind turbines was adopted. The MPPT method combing the rotor inertia control was applied to the PWTs 1-6, while the given power control was adopted for the CWTs 7-9. The sampling period of the kinetic energy based power smoothing strategy for PWTs was 0.001. The cut off frequency of the low-pass filter was 10 Hz. The simulation waveforms of the PWTs are shown in Figure 11 including the rotor speed, torque, and output power. The rotor speed of PWTs shown in Figure 11a,d did not follow the optimum MPPT speed, which are shown in Figure 9d,e. It can be seen from Figure 11b,e that the torque of the PWTs was almost straight with very tiny fluctuations. Then, the mechanical stress of WTs was reduced effectively. By comparing the output power Figure 11c,f with Figure 10d,e, it can be observed that the output power of PWTs under the proposed rotor inertia based method was smoother than the power under MPPT control. Thus, the effectiveness of power smoothing method for PWTs based on the rotor inertia control was verified. Figure 10: Time histories of the torque, power of WTs in the wind farm under the maximum power point tracking (MPPT) operation mode. (**a**) Torque of the first group WTs (1–3). (**b**) Torque of the second group WTs (4–6). (**c**) Torque of the third group WTs (7–9). (**d**) Output power of the first group WTs (1–3). (**e**) Output power of the second group WTs (4–6). (**f**) Output power of the third group WTs (7–9). (**g**) Total output power. (**h**) DC link voltage. (**i**) Power of the BESS. The output power of the three CWTs is shown in Figure 12a-c respectively. The reference power calculated according to the block diagram in Figure 4 was given to CWTs after 1s, while the maximum power was given to the PWTs before 1s. The power of each CWT was allocated according to the wind speed relationship which was obtained by calculating the wake effect. As shown in Figure 12a-c, the output power of CWTs was different from that under the MPPT control mode which is shown in Figure 10f and the actual output power of the three CWT can match the reference given power well. It can be seen from Figure 12e that the output power of WTs was smoothed through the proposed control strategy by comparing with the MPPT power. However, the output power of WTs could not be smoothed when the needed smoothing power exceeded the maximum output power of CWTs. In this case, the BESS was joined in to smooth the rest power and the power of BESS is shown in Figure 12d. Thus, the output power of the wind farm was smoother than the output power of WTs. Figure 12d shows that the BESS was not working all the time and then the charge and discharge times was reduced significantly compared to that using the traditional power smoothing method (shown in Figure 10i). Thus, the battery lift would be extended greatly.