## 2 The Down-Regulation Control Problem  
The operation of the large wind turbine can be divided according to the wind speed in several regions, as shown in Figure 1 (see, for instance, [18; 19; 20; 21]). The first region is upper-limited by the cut-in value of the wind speed and characterised by an insufficient wind speed to deliver power. During the operation in the second region, delimited by the cut-in and the rated values, the machine delivers power without reaching its rated values. When the wind speed exceeds the rated value, the wind turbine enters Region III, where the rotational speed is regulated. If the wind speed exceeds the cut-out limit, the machine reaches Region IV, where it is shut down. The transition zones between regions are called Region I\({}^{\ddagger}\) and Region II\({}^{\ddagger}\), respectively.  
Figure 1: Operation regions of a modern wind energy converter.  
The general control strategies are constant generator speed, constant tip-speed ratio, i.e., tip speed/wind speed, and maximum generator speed. These control strategies are also valid for down-regulation control. The up-regulation problem is practically not treated in the literature, and therefore, it is not presented here.  
A down-regulated operation takes place when the machine is forced to operate, delivering less power than it can provide for the current wind speed. The correct operation using a down-regulation control (DRC) strategy presupposes the fulfilment of the following conditions:  
1. If the wind turbine is operated in Region III, the wind speed is always sufficient to carry out the down-regulation, but the up-regulation is limited to the maximum current wind speed;
2. If the wind turbine is working in Region II, the down-regulation requires that the given power reference \(P_{\textit{ref}}\) is lower than the maximum extractable power \(P_{\textit{max}}(v_{\textit{w}})\) for the current wind speed \(v_{\textit{w}}\). Up-regulation is not possible because the wind speed is not enough to scale up the power;
3. If the power reference \(P_{\textit{ref}}\) is greater than the maximum extractable power \(P_{\textit{max}}(v_{\textit{w}})\), the down-regulation is not available, but the power output should be as close as the current wind speed makes it possible to the power reference \(P_{\textit{ref}}\). As in condition 2, up-regulation is also not possible;
4. The power network is kept as constant and stable as possible. Hence, the power reference for the wind turbine does not change often, and it is provided by the wind farm control through the local supervisory control.  
A down-regulation approach can be implemented by adjusting the control strategy of either the torque control loop or the pitch control loop. Down-regulation by using the pitch control reduces the rotational speed first and then keep it constant, which means also a fatigue reduction, but also a lower reaction of the machine. Therefore, it is preferred in general to maintain the rotational speed constant as much as possible and to manipulate the generator torque in order to obtain the desired power output. The advantage of the technique is given by the fact that the control response is faster [9]. However, the rotational speed is normally high, affecting fatigue loads. Another strategy consists in minimising the thrust coefficient \(C_{t}\). In such case, the power output is reduced in the individual machine while improving the performance of the whole wind farm due to better management of the wake effects [22].  
The idea behind the present work is to combine torque and pitch control in order to obtain the advantages of both, by using the power tracking concept in both, including an additional power control loop. Furthermore, the up-regulation characteristic is simply an inherent feature of the power tracking control system used.