**3. Results**

Figure 10a–d shows the results of the comparison between the measured electrical power, the electrical power predicted by WindSim, and the electrical power predicted by the dynamic model for four days in January, April, August, and November, respectively. The wind direction data measured from the met mast are also shown in the figure. The measured data and the data obtained from WindSim were 10-min averaged data, and therefore, the data from the dynamic model, which was originally in 1-s intervals, were converted to 10 min averaged data.

As shown in the figure, both predictions by WindSim and the dynamic model were close to the measured power; however, there are regions where relatively large discrepancies exist in Figure 10b,d. For these regions, the wind directions are between 110 degrees and 260 degrees. The reason for these relatively large discrepancies in these regions is that the met mast is located within the wake region of the wind turbines around the target wind turbine for those wind directions, and the wind speed implemented with WindSim to predict the wind speed for the target wind turbine is the wind speed reduced by the wake effect. To obtain the wind speed for the target wind turbine, WindSim again applies a wake model in the case where the wind direction corresponds to the direction causing the wake effect on the target wind turbine. Therefore, the wind speed obtained for the target wind turbine from WindSim in those wind directions becomes lower than the actual wind speed of the target wind turbine and the power output predicted by WindSim and the dynamic model becomes lower than the measured power.

To compare the results in more detail, small portions of Figure 10c,d corresponding to three hours are replotted in Figures 11 and 12, respectively. Figure 11 shows a mean wind speed lower than the rated wind speed, and Figure 12 shows a mean wind speed higher than the rated value. Figures 11a and 12a show the wind speed measured from the met mast and the wind speed of the target wind turbine predicted by WindSim. For both cases, the wind speed of the target wind turbine predicted by WindSim is slightly higher than the wind speed measured from a nearby met mast. This is partly due to the fact that the altitude of the target wind turbine location is slightly higher than that of the met mast location.

**Figure 10.** Comparison of the measured and predicted electrical power: (**a**) January, (**b**) April, (**c**) August, (**d**) November.

**Figure 11.** Comparison of the measured and predicted data for 3 h in August: (**a**) wind speed, (**b**) wind direction, (**c**) yaw mismatch, (**d**) electrical power, (**e**) generator torque, (**f**) pitch angle, (**g**) generator speed, (**h**) model switch.

Figures 11b and 12b show the wind direction measured from the met mast and the wind direction at the wind turbine position predicted by WindSim. The wind direction of the target wind turbine predicted by WindSim is basically consistent with the measured wind direction. They also show the turbine orientation predicted by the dynamic model. In Figure 11b, the yaw mismatch angle exceeded 11 degrees in the end, and the yaw system was activated to reduce the mismatch angle. In Figure 12b, the yaw orientation did not change because of the small yaw mismatch angles compared with the threshold. These are also shown in Figures 11c and 12c, which show the yaw mismatch angles. The mismatch angles are three-minute averaged values.

Figures 11d and 12d show the measured electrical power, the electrical power predicted by WindSim, and the electrical power predicted by the dynamic model. Figure 11d shows the electrical power when the wind speed is lower than the rated wind speed. Therefore, the blade pitch angle is fixed to be the fine pitch, and the generator torque is adjusted to maximize the power coe fficient. As shown in the figure, the power prediction from WindSim consistently overestimates the measured power. The power predicted by the dynamic model looks similar to the WindSim results but closer to the measured power. The generator torque and the blade pitch angle from the dynamic model is shown in Figure 11e,f. Figure 12d shows the electrical power when the wind speed is mostly higher than the rated wind speed. Therefore, the generator torque is fixed to the rated value, and the blade pitch angle is adjusted to maintain the rated wind speed and the rated power. Figure 12e,f shows the generator torque and the blade pitch angle from the dynamic model. In Figure 12d, there are a few downward spikes in the measured power. The dynamic model shows similar downward spikes but the power from WindSim does not. The reason for this is that WindSim does not consider wind turbine dynamics and yaw mismatch, and the power is solely dependent on the wind speed. Based on Figure 12a, the wind speed is maintained to be mostly higher than the rated wind speed, and therefore, the power prediction from WindSim is mostly close to the rated power. However, if we look at the results from the dynamic model in Figure 12e,h, the mode switch was turned o ff a few times between 4:00 and 5:00 o'clock, and the generator torque was reduced. As a result, the power decreased as a downward spike. The dynamic model includes wind turbine dynamics and could show similar measured power variations.

**Figure 12.** *Cont.*

**Figure 12.** Comparison of the measured and predicted data for 3 h in November (**a**) wind speed, (**b**) wind direction, (**c**) yaw mismatch, (**d**) electrical power, (**e**) generator torque, (**f**) pitch angle, (**g**) generator speed, (**h**) model switch.

Figures 11g and 12g show the generator speed obtained from the dynamic model. For Figure 11g, the generator speed varies between 550 rpm and 800 rpm to maximize the power coefficient; on the other hand, for Figure 12g, the generator speed is generally close to the rated value, which is about 1400 rpm.

Table 2 shows the relative percentage errors of the electrical energy production with respect to the measure values given in Figures 11d and 12d. As shown in the table, the relative errors of the energy production predicted by WindSim and the dynamic model for Figure 11d are 9.45% and 1.12%, respectively, which is the case when the wind speed is lower than the rated wind speed. The errors are reduced to 0.48% and −0.06%, respectively, for Figure 12d in which the wind speed is higher than the rated wind speed. For both cases, the errors from the dynamic model are smaller than those from WindSim, because the dynamic model considers the wind turbine dynamics and the yaw motion. In Table 2, the electrical energy production was normalized by the measured electrical energy production (MWh) of the corresponding period, respectively.

**Table 2.** Relative errors of electrical energy production prediction for the data shown in Figures 10d and 11d.


Table 3 shows the comparison between the measured AEP, the AEP predicted by the WindSim, and the AEP predicted by the dynamic model with and without yaw motion for the target wind turbine. As shown in the table, the relative error of AEP predicted by WindSim is 2.75%, and those of the dynamic model without and with the yaw system are 2.11% and 0.16%, respectively. Based on the results, the prediction error from ignoring yaw mismatch errors is larger than the prediction error from ignoring wind turbine dynamics. The annual energy production from the dynamic model is also about 2.52% smaller than that from WindSim. This result is similar to the result in Ref. [15], where the relative differences between WindPRO and the dynamic model for four different sites with the NREL 5 MW wind turbine were between 0.83% and 4.91%. In Table 3, the AEP is normalized by the measured AEP (MWh) for one year.


**Table 3.** The relative errors of the annual energy production (AEP) by the measured and other models.
