In Case B the effect of wind extractability is considered again as in Case A, but now the turbine operating points are adjusted or re-optimised taking into account the extractability, to reduce the negative impact of farm blockage and hence improve the power production.
4.3.1. Re-Optimising Turbine Operating Conditions
In this study we consider a simple adjustment of blade pitch angle and TSR only in Region 2b of turbine operation. This means that the turbine power coefficient in Region 2b will be lower than that used in Case A, but the turbine thrust coefficient will also be lower, leading to a reduction in and hence an increase in and the overall power production. The reason for focusing on Region 2b is because this wind speed range is low enough for the wind extractability to have a significant impact on but also high enough for the impact of power increase on the AEP to be substantial. Further adjustment of operating points in Regions 2a and 2c may result in some additional power increase, but this is not considered in the present study.
To find the new optimal operating point for Region 2b, first, we find possible combinations of blade pitch angle and TSR for a given
value, for example, 90%, 80%, 70%, 60% and 50% of the original
value (
) as shown in
Figure 11. Here we applied a two-dimensional linear interpolation to the original
and
tables to have more data points with smaller intervals of pitch angle and TSR (0.01 instead of 0.25). Secondly, we find the operating point that maximises
for a given
. As can be seen from
Figure 12, there is a single optimal point for a given
; for example, the optimal pitch angle increases from 0.75° to about 7° and the optimal TSR decreases from 8.0 to about 5.7 as the selected value of
decreases from
to 0.5
. Hence, now the question is how to find the optimal level of reduction in
.
The difficulty in finding the optimal reduction of
is that this depends on the wind speed and direction as well as the wind extractability, meaning that a number of FLORIS simulations would be required to find the true optimal point for each wind condition. To reduce the number of FLORIS simulations and the computational cost, here we attempt to find an approximately optimal point using an assumption that
is proportional to
; for example, if our trial
is 90% of the original value used in Case A, we assume that
is also 90% of the value obtained in Case A. This assumption allows us to estimate the value of
(by solving Equation (
7) for
) and then the farm-upstream wind speed from the following equation without running FLORIS simulations:
The above calculation of , and then a single FLORIS simulation using the calculated value, are performed for a range of trial values (between 1.0 and 0.5) to find the (approximately) optimal reduction of , for each of the 12 different wind directions (but only at = 10 m/s as a representative wind speed for Region 2b). This reduces the computational cost required to find a new optimal operating point for Region 2b (as otherwise we would need a handful of iterations of FLORIS simulations to obtain the correct , and values as we did in Case A, for each trial case). Note, however, that the above assumption/approximation is used only in the process of finding this new optimal operating point. The final AEP calculation for Case B is conducted using the same iterative process as in Case A.
Although the present re-optimisation method focuses on the adjustment of operating conditions only in Region 2b, we also adjust the upper-end wind speed for Region 2b. This adjustment is required as the turbine rotational speed should be at the maximum possible value in Region 2c (10 rpm) and the turbine power should be at the rated value in Region 3 (10 MW). Since TSR decreases as we reduce
in Region 2b, the maximum rotational speed is reached at a higher
value, increasing the upper-end wind speed for Region 2b. Similarly, since
decreases as we reduce
, the rated power may also be reached at a higher
than the original rated wind speed (if the reduction of
in Region 2b is large enough to eliminate Region 2c).
Figure 13 and
Figure 14 show some examples of how the
and
curves are adjusted depending on different levels of
reduction in Region 2b. It can be seen that the rated wind speed increases from the original value of 11.4 m/s to a higher value when
in Region 2b is reduced to less than about 80% of the original value.
4.3.2. Results
Figure 15 shows how the wind farm power at
= 10 m/s changes as we reduce the value of
from 1.0
to 0.5
, for the low (
= 10) and high (
= 20) extractability scenarios. Note that here the farm power has been normalised by the corresponding farm power obtained in Case A, for each of 12 different wind directions. It can be seen that the optimal reduction of
is about 0.8 and 0.85 (depending on wind direction) at
= 10, and about 0.9 at
= 20. The maximum increase in the farm power (compared to Case A) is about 3.5% to 4.5% at
= 10 (depending on wind direction) and about 1.5% at
= 20. As expected, the farm power becomes lower than Case A if we reduce
too much.
Figure 16 compares the farm-upstream wind speed reduction factor (
) between Case A and Case B (adopting the optimal
reduction at each wind direction) at
= 10 m/s. It can be seen that the
is higher in Case B than in Case A due to the reduced turbine thrust. The dependency of
on wind direction is similar between Case A and Case B, whilst the impact of wind extractability is still significant.
Finally, the AEP values calculated for Case B are summarised in
Table 5 for the three different extractability scenarios. The improvement of AEP from Case A (i.e., improvement due to the mitigation of farm blockage losses) depends on the wind extractability, varying between 2.0% at
= 10 and 0.6% at
= 20. These improvements are smaller than the improvements shown earlier for a fixed wind speed of
= 10 m/s (
Figure 15) but still promising, considering the simplicity of the mitigation method used in this study.