3.2.2. Individual Pitch Control

One of the most common advanced pitch control strategies in wind energy research is the Individual Pitch Control (IPC) strategy [3,33]. Several studies have used this strategy as a comparison to other advanced pitch controller strategies [4,11,34]. It has also been used as a comparison or a complementary strategy for trailing edge flap controllers [7,9,10].

Figure 4 shows the graphical representation of the IPC strategy implemented in TUBCon.

**Figure 4.** Graphical representation of the Individual Pitch Control (IPC) strategy implemented in the controller. The Blade Root Bending Moments (BRBM) signals are transformed into a non-rotating coordinate system and filtered using a low-pass and a notch filter. The filtered signals are then used in a PI controller to calculate the control signals. These signals are transformed back into the rotating frame of reference to be used as input for the individual pitch angles.

The IPC uses as input signals the out-of-plane BRBM of the three blades (*M*BR *<sup>Y</sup>*<sup>1</sup> , *<sup>M</sup>*BR *<sup>Y</sup>*<sup>2</sup> , *<sup>M</sup>*BR *<sup>Y</sup>*<sup>3</sup> ) as well as the mean pitch angle *θmean* and the rotor azimuth angle *ϕ* (Figure 4(a)). The outof-plane BRBMs are transformed to the direct and quadrature axes using the once-perrevolution or 1P-Coleman transformation (Figure 4(b)). The 1P-Coleman transformation for a three bladed rotor takes the form

$$
\begin{pmatrix} d \\ q \end{pmatrix} = \frac{2}{3} \begin{pmatrix} \cos(\varrho) & \cos(\varrho + \frac{2\pi}{3}) & \cos(\varrho + \frac{4\pi}{3}) \\ \sin(\varrho) & \sin(\varrho + \frac{2\pi}{3}) & \sin(\varrho + \frac{4\pi}{3}) \end{pmatrix} \begin{pmatrix} M\_{Y1}^{\text{BR}} \\ M\_{Y2}^{\text{BR}} \\ M\_{Y3}^{\text{BR}} \end{pmatrix}, \tag{18}
$$

where *d* and *q* are the quantities expressed in the direct and quadrature axes respectively. The physical interpretation of these quantities is the rotor tilt and yaw moment in the non-rotating coordinate system.

These rotor moments are then passed through a second order low-pass filter (Equation (A2)) and a notch filter (Equation (A4)) Figure 4(c) to filter out unwanted high frequency content as well as the 1P component of the load signals in the non-rotating frame of reference. This step is needed as a 1P oscillation in the non-rotating frame of reference can lead to an increased 3P excitation of the turbine [35]. Following a concept presented in [9], a gain schedule is implemented using *θmean* to adapt the individual pitching action to the wind speed (Figure 4(d)). The gain schedule has the same mathematical expression as *ηθ* in Equation (16) but uses different parameter values. A PI controller is implemented with a zero set-point to reduce the rotor tilt and yaw moments (Figure 4(e)).

The control demand is transformed back to the demands of the individual pitch angles using the inverse 1P-Coleman transformation (Figure 4(f)). The inverse transformation is given by

$$
\begin{pmatrix} \theta\_1 \\ \theta\_2 \\ \theta\_3 \end{pmatrix} = \begin{pmatrix} \cos(\varphi') & \sin(\varphi') \\ \cos(\varphi' + \frac{2\pi}{3}) & \sin(\varphi' + \frac{2\pi}{3}) \\ \cos(\varphi' + \frac{4\pi}{3}) & \sin(\varphi' + \frac{4\pi}{3}) \end{pmatrix} \begin{pmatrix} D \\ Q \end{pmatrix} \tag{19}
$$

where the quantities *D* and *Q* represent the control signals in the non-rotating coordinate system and *θ*1, *θ*<sup>2</sup> and *θ*<sup>3</sup> the individual pitch angles for each blade (Figure 4(h)). The inverse Coleman transformation uses a modified azimuth angle *ϕ*- . Figure 4(g) shows that *ϕ*- = *ϕ* + *ϕlead*, where *ϕlead* is the lead angle. This constant angle helps decoupling the rotor yaw and tilt moments in the non-rotating frame of reference so that they can be treated as independent systems. As explained in [4], certain factors such as blade stiffness, collective pitch angle and pitch actuator response time introduce a dependency between the two rotor moments. Using the lead angle is a straightforward way to counter this problem.

It is possible to generalize this strategy to other frequencies by using *n*P Coleman transformations. In this case the rotor angle *ϕ* and the respective shift for each blade in Equations (18) and (19) are replaced by *n*-times their value. Using for example an IPC-like strategy with a 2P Coleman transform helps to reduce the 3P asymmetrical loads in the yaw bearing of the turbine [10].

The IPC pitch angles are limited to a maximum and minimum value (*θmax*−IPC and *θmin*−IPC) given by the user. Since the PI controller determines the quantities *D* and *Q* in the non-rotating coordinate system, the limits are transformed into this coordinate system:

$$\frac{\theta\_{\text{min}-\text{IFC}}}{\sqrt{2}} \le D, Q \le \frac{\theta\_{\text{max}-\text{IFC}}}{\sqrt{2}}.\tag{20}$$

As with the CPC strategy, an anti-windup procedure equivalent to Equation (3) is used to limit the increase of the integral part of the controller.

The pitch angle signal of the IPC strategy is added to the collective pitch signal to obtain the final pitch angle signal. The use of this strategy increases the pitch activity significantly. In order to limit this increase in pitch activity, the control strategy is phased out in the partial load regime. Bergami and Gaunaa show in [36] that the majority of fatigue loading that can be alleviated with this strategy occurs in the above-rated region. Phasing out the IPC strategy helps limit the pitch activity and optimizes energy capture by keeping the pitch angle constant in the below-rated region. The phasing out is done by multiplying the IPC PI-constants with a switch function (Equation (A5)) based on *θmean*. The switch limits used in this study are *x*<sup>0</sup> = 0.5◦ and *x*<sup>1</sup> = 3◦.
