 To address the overall behavior of the drivetrain, we'll go back to the overview that was provided at the beginning. We've seen how aerodynamic power is converted by the rotor and transmitted as mechanical power through the low-speed shaft, the gearbox and the high-speed shaft to the generator, where it is converted into electrical power. For the analysis of the behavior of the drivetrain, we will focus on the low-speed shaft and on the high-speed shaft, for which the power is determined by their rotational speed and torque. Their inputs come from the rotor and generator respectively and they connect through the gearbox. Therefore, we'll also look at the efficiency of the gearbox and how the gearbox changes speed and torque. As you have seen before, the mechanical power can be expressed as rotational speed times torque. When we relate the power in the high-speed shaft to the power in the low-speed shaft, we have to consider the efficiency of the gearbox. In the next step, we substitute the expressions for power to get the relation between torque and speed in both shafts. Furthermore, the rotational speeds are related through the transmission ratio of the gearbox. The efficiency of the gearbox has no effect on this expression, since it is a purely geometrical relation. Substituting this expression for the rotational speed in the energy balance leads to a relation between the torque in the high-speed shaft and in the low-speed shaft. This expression shows that the efficiency directly affects the torque in the high-speed shaft. This should not come as a surprise. The losses in the gearbox are caused by friction, which leads to a reduction in torque on the outgoing shaft. Here you see a recap of the torque speed characteristics of the different components. Neglecting losses in the main bearings, the aerodynamic CQ lambda curve can be directly translated to the speed torque curves in the low-speed shaft. Similarly, the speed characteristics of the generator can be directly translated to the speed torque characteristic in the high-speed shaft. However, the speed and torque levels in the two shafts differ several orders of magnitude due to the separation by the gearbox. Therefore we cannot directly judge from them how the system is going to behave. The next slide will show how the connection of speed and torque through the gearbox properties can help with this. The torque speed characteristics in the low-speed shaft and high-speed shaft are repeated here. For the next step it is good to realize what these characteristics actually mean. Let's first look at the low-speed shaft. These characteristics were based on the aerodynamic properties of the rotor, so it represents the behavior in the low-speed shaft when looking into the direction of the rotor. As a fault experiment, disconnect the low-speed shaft from the gearbox and connect it to a testing machine. This testing machine can be set at any rotational speed. If the wind speed is blowing at 10 meters per second and the testing machine would gradually increase the rotational speed in the low-speed shaft, the torque measured by the testing machine would follow the blue curve from left to right. Now we'll look at the high-speed shaft. In our fault experiment here, we disconnect the high-speed shaft from the gearbox and connect it to the testing machine. Let the testing machine apply a torque on the high-speed shaft and measure the rotational speed. It will be clear that the machine will measure the speed as it is set by the electrical frequency. Finally, we get to the crucial step. In the high-speed shaft, we have looked into the direction of the generator. With what are the torque speed characteristics if we look from the high-speed shaft into the direction of the rotor? In other words, what if we disconnect the high-speed shaft from the generator and connect it to the testing machine there? We can achieve these characteristics by using the gearbox properties. These tell us what happens to the torque and speed from the low-speed shaft when they are transferred to the high-speed shaft. Using these relations, we can translate the torque speed curve of the low-speed shaft to its equivalent in the high-speed shaft as shown here. Of course, they look similar in shape with the scale in both x and y-axis have been changed. Now that we know the characteristics in the high-speed shaft both looking in the direction of the rotor and in the direction of the generator we can determine from the combined graphs at which rotational speed and torque the system is going to settle. Remember that the blue curve for 10 m per second wind speed was obtained by replacing a generator by a testing machine. Now that the generator is back the generator takes the role of the testing machine. It sets the generator curve somewhere depending on the electrical frequency. The consequential torque in the high-speed shaft is where this curve crosses the blue curve. This is the point where the generator torque and rotor torque reach equilibrium in the high-speed shaft. If this generator was connected to the 50 Hz of the grid without back-to-back converter the operational point would always fall on this vertical line. For different wind speeds it would intersect at different heights with the relevant rotor curve. However, with the back-to-back converter the generator can also be controlled differently. It is also possible to set the torque in the generator and adjust the electrical frequency according to the demand. In this case the operational point is found at the intersection with the horizontal line and the demanded electrical frequency follows from the resulting rotational speed. This analysis shows that it is not the wind or the rotor air dynamics that determine the speed of the rotor. They do play a crucial role through the CQ lambda curve but it is the control of the generator that is decisive.