**2. Methodology**

#### *2.1. Target Wind Turbine*

In this study, a wind turbine in a commercial wind farm D in South Korea was used as a target wind turbine. As shown in Figure 1, wind farm D consists of 15 wind turbines. The met mast is at the north of the target wind farm. The target wind turbine is about 2.5 RD (Rotor Diameter) away from the met mast, which corresponds to 220 m in distance. The met mast and the target wind turbine are located in a relatively flat terrain, and they are about 1.7 km away from the sea.

**Figure 1.** The layout of wind farm D (Source: Google Maps).

Table 1 shows the general specification of the target wind turbine. As shown in the table, the hub height of the wind turbine is 80 m. The cut-in, rated, cut-out wind speeds are 3.5 m/s, 12 m/s, and 25 m/s, respectively. Figure 2 shows the power curve showing the power output with respect to the wind speed for the standard air density, which is 1.225 kg/m3.


**Table 1.** General specification of the target wind turbine.

**Figure 2.** The power curve of the target wind turbine.

#### *2.2. Wind Data*

In this study, the 10-min averaged data measured from 1 January 2017 to 31 December 2017 at the meteorological mast were used. The meteorological mast sensors comprise anemometers, wind direction vanes, a temperature sensor, a barometric pressure sensor, and a relative humidity sensor. The anemometers were installed at heights of 80 m, 78 m, and 40 m. The wind direction vanes were installed at heights of 78 m and 40 m. The temperature sensor, barometric pressure sensor, and relative humidity sensor were installed at a height of 75 m. The data measured with the 80 m anemometer and 78 m wind direction vane were used to predict the electrical power production of the target wind turbine in the wind farm. Figure 3a shows the Weibull distribution, and Figure 3b is the wind energy rose obtained using the met mast data. As shown in Figure 3, the average wind speed at a height of 80 m is 5.75 m/s, and the prevailing wind direction is 315 degrees in 16 sector-wise angles.

**Figure 3.** Measured wind data for the target wind turbine: (**a**) Weibull distribution; (**b**) total wind energy rose.

According to the equation for data normalization provided by the International Electrotechnical Commission (IEC) standards 61400-12-1 2nd edition [16], the air density at the target wind turbine can be calculated using the measured 10-min average data for temperature and air pressure of the mast at a height of 75 m. The 10-min average air density was calculated using Equation (1):

$$\rho\_{10\text{win}} = \frac{B\_{10\text{win}}}{R\_0 \times T\_{10\text{win}}}.\tag{1}$$

In the equation, ρ10*min* is the calculated 10-min average air density, *B*10*min* is the measured 10-min average air pressure, *T*10*min* is the measured 10-min average air temperature, and *R*0 is the gas constant of dry air, which is 287.05 J/(kg·K). The air density calculated at a height of 75 m at the met mast position is 1.076 kg/m3. The air density for the target wind turbine was assumed to be the same as the air density at the met mast.

#### *2.3. Terrain Modeling*

A terrain model that includes the information on both the topology and roughness was used for the CFD simulation analysis of the wind farm. The height contour map provided by the Korea National Spatial Information Portal and the land cover data provided by the Korea Ministry of Environment [17,18] were used to construct the terrain model.

The terrain model of the target wind farm was constructed by the geographic information system (GIS) software Global Mapper based on the height contour and the land cover data and implemented with the CFD simulation program, WindSim. Figure 4a,b shows the elevation and the roughness length information of the terrain model.

**Figure 4.** Terrain model of the target wind farm L (**a**) elevation; (**b**) roughness length.

The size and grid spacing of the terrain model has an impact on the prediction results of the power output [19]. Therefore, in this study, the size of the terrain model was determined to be 10 km by 10 km, and the horizontal grid spacing was 25 m by 25 m. The number of vertical grids was 40, and the number of grids below the wind turbine hub height was six, to accurately simulate the wind characteristics in the wind farm.

The wind field analysis was carried out using WindSim based on the Reynolds-Averaged Navier–Stokes (RANS) equation. Because the equation is nonlinear, the solution is solved with the use of multiple iterations until convergence is obtained [20]. This study uses the GCV (Convergence control with new solver) solver in the CFD simulation WindSim to solve the RANS equation. The GCV method uses a pressure-based separation solver strategy to control the mass flux on the control-volume faces, providing faster convergence [21]. It was assumed that the atmospheric boundary layer had a height of 500 m, that the atmospheric flow was stable, and that the wind speed above 500 m was constant with height [22]. The boundary condition at the top was "fixed pressure". The turbulence model used was the standard k-ε eddy viscosity turbulence model without considering temperature changes, where k is the turbulent flow energy and ε is the rate of turbulent dissipation.

Based on the results of the wind field analysis and the N.O. Jensen wake model [23], the 10-min averaged wind speed, wind direction, and electrical power of the target wind turbine were obtained from WindSim.

#### *2.4. The Wind Turbine Matlab*/*Simulink Dynamic Model with a Wind Turbine Controller*

In this study, the dynamic simulation model of a wind turbine was used for the prediction of the electrical power production by the target wind turbine. The model was developed in the previous study and modified for this study to be used to predict the power of an actual wind turbine [15].

Figure 5 shows the schematic of the dynamic model used for the target wind turbine. The dynamic model of the wind turbine is composed of four parts: the wind turbulence model, the yaw system model, the wind turbine controller, and the wind turbine model. The model requires 10-min average wind speed and direction data together with their standard deviations as inputs and calculates the electrical power output of the wind turbine with the power and yaw control algorithms. Detailed information on the model is available in Ref. [15].

**Figure 5.** The wind turbine dynamic model.

#### 2.4.1. The Wind Turbine Matlab/Simulink Dynamic Model

In this study, the wind turbine dynamic model was simulated by using Matlab/Simulink, and the block diagram of the dynamic wind turbine model is shown in Figure 6. As shown in the figure, the wind turbine dynamic model is composed of the aerodynamics model, the drive train model, the generator model, the pitch actuator model, and the control system model.

**Figure 6.** The block diagram of the wind turbine model.

The aerodynamic power can be simply modeled using Equation (2).

$$P\_{\rm area} = \frac{1}{2} \rho \pi R^2 \mathbb{C}\_P(\lambda, \beta) v^3,\tag{2}$$

where *Paero* is the aerodynamics power of the wind turbine, ρ is the air density, *R* is the wind turbine radius, *v* is the wind speed, and *CP* is the power coe fficient of the wind turbine which depends on the tip speed ratio (λ) and the blade pitch angle (β). The power coe fficients for various tip speed ratios and blade pitch angles are calculated from a BEMT (Blade Element Momentum Theory) software such as Bladed and used as a look-up table in the aerodynamics model.

The drive train model is composed of a low-speed shaft, a gearbox, and a high-speed shaft. The aerodynamics torque and generator torque are the inputs of the drive train model. The low-speed shaft and high-speed shaft can be modeled by the inertia, the sti ffness, and the damping. The drive train model was simulated using Equations (3) and (4). The relationship between the low-speed shaft and the high-speed shaft is shown in Equation (5) [24].

$$J\_r \frac{d\Omega\_\Gamma}{dt} = T\_a - k\_s \left(\theta\_r - \frac{1}{N} \theta\_\S\right) - c\_s \left(\Omega\_r - \frac{1}{N} \Omega\_\S\right) - B\_r \Omega\_{\S'} \tag{3}$$

$$J\_{\mathcal{S}} \frac{d\Omega\_{\mathcal{S}}}{dt} = \frac{k\_s}{N} (\theta\_r - \frac{1}{N} \theta\_{\mathcal{S}}) + \frac{c\_s}{N} \Big(\Omega\_r - \frac{1}{N} \Omega\_{\mathcal{S}}\Big) - B\_{\mathcal{S}} \Omega\_{\mathcal{S}} - T\_{\mathcal{S}'} \tag{4}$$

$$
\Omega\_{\mathbb{X}} = N \Omega\_{\mathbf{r}\prime} \tag{5}
$$

where *J* is the inertia, Ω is the rotation speed, *T* is the torque, *ks* is the torsional sti ffness, *cs* is the torsional damping, θ is the rotation angle, *B* is the damping, and *N* is the gear ratio. Moreover, *a* represents the aerodynamic, *r* and *g* mean the rotor and the generator, respectively.

The pitch actuator and the generator were modeled as 1st-order systems, which are shown in Equations (6) and (7), respectively [25].

$$\frac{\beta}{\beta\_{cmd}} = \frac{1}{1 + \tau\_{\beta}s},\tag{6}$$

$$\frac{T\_{\mathcal{S}}}{T\_{\mathcal{g,cmd}}} = \frac{1}{1 + \tau\_{\mathcal{S}}s}.\tag{7}$$

In Equations (6) and (7), β is the pitch angle, β*cmd* is the pitch angle command, and τβ is the time constant of the pitch actuator. *Tg* is the generator torque, *Tg*,*cmd* is the generator torque command, and <sup>τ</sup>*g* is the time constant of the generator torque.

#### 2.4.2. The Wind Turbine Control System

Figure 7 shows the wind turbine controller used in the dynamic wind turbine model. It consists of a basic torque and blade pitch control for power maximization and regulation and a peak shaving to use blade pitching to reduce thrust force by sacrificing power slightly near the rated wind speed region [26].

**Figure 7.** The wind turbine model control system.

To maximize the electrical power of the wind turbine in regions where the wind speed is lower than the rated wind speed, the pitch angle of the blade is fixed to be the fine pitch angle, and the optimal torque command is sent to the generator to maximize the power coefficient of the rotor [27]. To maintain the rated electrical power of the wind turbine in regions where the wind speed is higher than the rated wind speed, the torque is fixed to be the rated torque, and the blade pitch angle of the wind turbine is adjusted to keep the rated rotational speed of the rotor. The torque control algorithm in the control system used was a simple open-loop control using a look-up table with an input of measured generator speed and output of optimal generator torque. Moreover, the blade pitch control in the control system used the classical proportional–integral (PI) algorithm to minimize the error between the measured generator speed and the rated value.

#### *2.5. Conversion of Power Curve to Include Air Density E*ff*ect*

The power coefficient curve and thrust coefficient curve used for the wind turbine dynamic model are derived from Bladed under the condition of a standard air density of 1.225 kg/m3. However, the actual air density of a wind farm is different from the standard value, which causes a discrepancy between the prediction and the measured power output.

In this study, a novel method is proposed to match the power of a dynamic wind turbine model with that of a wind turbine with actual air density by tuning the controller. The first step of this method is to convert the power curve of the wind turbine based on the standard air density to that based on the actual mean air density of the site. This conversion is possible by using the correction method for wind turbines with active power control described in the standard, IEC 61400-12-1 [16].

Equation (8) represents the wind speed correction equation calculated based on the IEC standard.

$$V\_{10\text{min}} = V\_n / \left(\frac{\rho\_{10\text{min}}}{\rho\_0}\right)^{1/3}.\tag{8}$$

In Equation (8), *V*10*min* is the measured wind speed averaged over 10 min, *Vn* is the normalized wind speed, ρ10*min* is the derived 10-min average air density, and ρ0 is the reference air density, known to be 1.225 kg/m3. Through Equation (8), the wind speed of a power curve is converted to consider the mean air density at the site.

Figure 8 shows the comparison between the power curve with the standard air density and the power curve with the actual mean air density. It can be seen from the figure that when the power is lower than the rated power, the power with the standard air density is slightly higher than that with the actual mean air density.

**Figure 8.** Comparison of the power curve of standard air density and the power curve of actual air density.

*2.6. Tuning of the Wind Turbine Controller to Consider Actual Mean Air Density*

To consider the actual mean air density of the site in the dynamic model, the wind turbine controller needs to be tuned by considering the power curve with the actual mean air density as a target.

In the torque control region where the wind speed is lower than 10 m/s, the look-up table of the torque scheduling was tuned so that the power curve of the dynamic model is matched with the power curve with the actual mean air density. In the transition region where the wind speed is higher than 10 m/s and lower than the rated wind speed, the peak shaving algorithm and torque scheduling were used to match the target power curve. For the rated power region, the closed-loop PI control strategy was used, and no tuning was necessary because the algorithm is not affected by the change of air density.

Figure 9 compares the target power curve with the power curve obtained from the dynamic model after tuning the control algorithms. The two power curves are well matched.

**Figure 9.** Comparison of the measured power curve report and the power curve of different controllers at 1.076 kg/m3.
