# Output Power Smoothing Control for a Wind Farm Based on the Allocation of Wind Turbines
## 3 Power Smoothing Control Strategy
### Control Strategy for the PWTs  
The control purpose of the PWTs was to output the relatively smoother maximum power. Then the power given MPPT control with the rotor inertia based power smoothing control was adopted. The rotor inertia based power smoothing method can reduce the rotor torque ripple and then reduce the mechanical stress of the generator. The idea of the rotor inertia control was to use the kinetic energy in the rotor inertia of the wind turbine to smooth the output power of the system, especially when the inertia was significant, it can be regarded as an energy storage device [27]. The kinetic energy of the wind turbine will increase due to the acceleration of the rotor speed when the wind speed increases  
Figure 4: Block diagram of the power allocation. fast. Otherwise, the kinetic energy will release due to the decline of the rotor speed when the wind speed decreases. The average value of the maximum wind power in Equation (5) can be calculated as [5]:  
\[P_{avg}=\frac{1}{T}\int_{t-T}^{t}P_{wopt}dt, \tag{15}\]  
where \(t\) is the real time and \(T\) is the sampling period. The power difference of the optimum value and the average value determines the storing and restoring power in inertia of the wind turbine. Then the integral of the difference power is the redundant kinetic energy. The kinetic energy of the wind turbine can is calculated as [5]:  
\[E=\frac{1}{2}J\omega^{2}. \tag{16}\]  
Thus, the reference kinetic energy can be given as:  
\[E^{*}=\frac{1}{2}J\omega^{2}+\int{(P_{wopt}-P_{avg})}. \tag{17}\]  
Then the reference rotor speed is  
\[\omega^{*}=\sqrt{2E^{*}/J}. \tag{18}\]  
Finally, the output power smoothing by using the kinetic energy can be realized by giving the reference wind turbine rotor speed shown in Equation (18). The power smoothing effect relies on parameters, such as the wind turbine rotor inertia J and the sampling period T. The greater the rotor inertia is, the better the smoothing effect is. However, the big rotor inertia will bring a lot of difficulties for the system control, such as reducing the control response speed. As shown in Equation (17), the traditional kinetic energy control compares the optimum power and the average value of the optimum power in a period to obtain the needed smoothing power. The principle of taking an average is simple, but the sampling period and system sampling precision are very important in the process. The low-pass filter is used widely in the wind power smoothing filed combing with the energy storage devices. In this paper, the low-pass filter is used to replace the averaging step to simplify the control process and then the Equation (17) will be changed as:  
\[E^{*}=\frac{1}{2}J\omega^{2}+\int{(P_{wopt}-P_{filter})}, \tag{19}\]  
where \(P_{filter}\) is the maximum power after low-pass filtering. The rotor inertial power smoothing based MPPT control by adopting the low-pass filter is shown in Figure 5. The cut-off frequency of the low-pass filter is set according to the power smoothing demand of the grid. The lower the cut-off frequency is, the smoother the output power is. \(T_{s}\) is the sampling time of the kinetic energy. After calculating the reference rotor speed \(\omega^{*}\), the actual speed \(\omega\) is compared with \(\omega^{*}\) and the difference was imported to a Proportional Integral (PI) controller. For realizing the vector control of the PMSG, the real three phase currents (\(i_{a}\), \(i_{b}\), \(i_{c}\)) were transformed into direct axis (\(d\)-axis) current \(i_{ds}\) and quadrature axis (\(q\)-axis) current \(i_{qs}\) through the combination of the Clark transformation and Park transformation (\(abc/dq\)) using the rotor position \(\theta\). The reference \(q\)-axis current \(i^{*}_{qs}\) was obtained from the speed PI loop. \(i_{d}\) = 0 control was adopted widely due to its simplicity and practicality [28]. Thus, the reference \(d\)-axis current \(i^{*}_{ds}\) was set to zero to simplify the control.