# Output Power Smoothing Control for a Wind Farm Based on the Allocation of Wind Turbines
## 2 Wind Energy Conversion System Description
### Wake Effect Model of the Wind Farm  
In a wind farm, the wind speed of downstream wind turbines was affected by the upstream turbines due to the air flow and the power loss that happened is called wake effect. The Jensen wake model is used commonly in the wind farm simulation due to its simplicity and validity for the far field [23; 24]. In this paper, the [PERSON] model was adopted to generate the wind speed of the downstream WTs as shown in Figure 3a. The basic [PERSON] wake effect model is shown in Figure 3 and the wind speed of downstream WTs is expressed as [23]:  
\[V_{x}=V_{in}\left[1-\left(1-\sqrt{1-C_{t}}\right)\left(\frac{d}{d_{x}}\right) ^{2}\right], \tag{11}\]  
where \(V_{x}\) is the downstream wind speed, \(V_{in}\) is the free stream wind speed, \(d\) is the diameter of the WT rotor, \(x\) is the distance between the WTs, \(k\) is the wake expansion coefficient which represents the effects of atmospheric stability, and \(d_{x}=d+2 kx\). In general, \(k\) is set as 0.075 for onshore wind farms and 0.05 for offshore wind farms. In this paper, \(k\) was set as 0.075. \(C_{t}\) is the thrust coefficient which is usually given by the wind turbine manufacturer or can be calculated according to the simulation software by giving the required data. In this paper, \(C_{t}\) was set as 0.8 when the wind speed was between 3 and 12 m/s by consulting the Vestas V80 type [24].  
The leeside speed can be obtained according to Equation (11) by assuming the \(x\) is zero as:  
\[V_{o}=V_{in}\sqrt{1-C_{t}} \tag{12}\]  
In practical wind farms, free wind speed can be affected by both obstacles and other WTs around which is called the wind shade effect [23]. Then the Equation (11) can be modified as by considering this effect:  
\[V_{x}=V_{in}\left[1-\left(1-\sqrt{1-C_{t}}\right)\left(\frac{d}{d_{x}}\right) ^{2}\left(\frac{A_{s}}{A}\right)\right], \tag{13}\]  
where \(A_{s}\) is the shade area caused by the other upstream WTs, and \(A\) is area of the downstream WT. Most wind farms consist of a large number of WTs, thus the cumulative shade effect of each WT should be considered. Thus, the Equation (13) is modified as  
\[V_{x}=V_{in}\left[1-\sum_{i}^{n}\left(1-\sqrt{1-C_{t}}\right)\left(\frac{d}{ d_{xi}}\right)^{2}\left(\frac{A_{si}}{A}\right)\right]: \tag{14}\]  
where \(n\) is the number of influencing upstream WTs, \(A_{si}\) is the shade area caused by upstream WT \(i\). The method for calculating the shade area is introduced in [24].  
The height of WTs and the wind direction are also important factors in the consideration of wake effect and the details can be seen in [23]. In this paper, the height of the nine WTs was the same and the wind direction was set as from west to east. The layout of the wind turbines was chosen according to the industry standards, as shown in Figure 3b, while the distance between the WTs in the west-east direction was \(6d\) and the distance between the WTs in the north-south direction was \(5d\)[24]. The WTs of the second row was affected by the first row WTs and the wind speed of the third row was affected by both the first and second row WTs. The wind speed deficit of WTs at the second row and third row can be calculated by the equations in [25; 26]. The [PERSON]'s wake effect model adopted in this paper was used to generate the wind speed for all WTs in the wind farm by giving the nature stochastic wind speed to the first row WTs.