*4.1. Steady Wind Simulations*

Figure 7 shows the behavior of both controllers in the steady wind simulation.

**Figure 7.** Validation of the controller in steady wind simulations. Pitch angle *θ* and rotor speed Ω of both controllers are compared for ascending wind steps.

This simulation features a series of wind speed steps from 4 m/s to 24 m/s with a 2 m/s step height. Between two steps, the wind speed is held constant for 30 s. It can be seen that both controllers behave in an almost identical manner. This is due to the fact that the collective pitch and torque controllers from TUBCon were directly adapted from the Basic DTU Controller. With the chosen parameters, TUBCon manages to stabilize the turbine without large overshoots in the pitch and rotor speed signals in spite of the sudden increases in wind speed. This is true for all simulated wind speeds.

#### *4.2. Turbulent Wind Simulations*

The turbulent wind simulations were done using the Normal Turbulent wind Model (NTM) from [21]. Because of this, the controller validation has to be done in a statistical manner. The setup is given in Table 4 under the column "Turbulent calculations". For each wind speed bin, we did six simulations with three different yaw angles of the turbine and two turbulence seeds. In total, there were 66 simulations, each 600 s in length for each controller. Because we are using QBlade's LLFVW method, the wake needs to first develop behind the rotor in order to have accurate results. We added 200 s of pre-simulation time to allow the wake to develop. This time was discarded in the analysis. Figure 8 shows an example of an aero-servo-elastic simulation of the DTU 10 MW RWT within QBlade. The incoming turbulent wind speed has an average hub-height value of 14 m/s and is shown on the left. The wake is modeled by vortex elements that are allowed to convect freely downstream of the turbine.

**Figure 8.** Turbulent wind aero-servo-elastic simulation with QBlade's Lifting Line Free Vortex Wake (LLFVW) aerodynamic model. The DTU 10MW Reference Wind Turbine (RWT) is simulated in a turbulent wind field with an average hub-height wind speed of 14 m/s.

To compare the controllers we chose a selection of turbine sensors that are summarized in Table 5. These sensors give a good estimate of the overall loading of the turbine blades, tower top and tower bottom.

**Table 5.** Considered sensors for turbulent wind simulations


We used two metrics to analyze the performance of the controllers, depending on the nature of the sensor. For the load sensors our metric is the lifetime Damage Equivalent Loads (DELs). These are calculated using the rainflow counting algorithm combined with the Palmgren-Miner linear damage accumulation hypothesis, as described in [39]. The rainflow count was done using the software Crunch [40]. For the controller signals, we use the averaged standard deviation of each signal. The average is taken from the individual standard deviations of all simulations in each of the wind speed bins. To calculate the lifetime DELs we used a wind speed distribution that corresponds to a wind class IA turbine [21], which is the design wind class of the DTU 10MW RWT.
