MP3001/MA3005 Continuous Assessment 1 7 February 2013 MP3001 – Dynamics and Control /MA3005 – Control Theory Continuous Assessment Exercise AY 2012/2013 S2 Deadline: Week 11 (1 – 5 April 2013) Figure 1 shows the wind turbine drivetrain in direct-drive configuration. The turbine blades are rotatable around its own axis to a certain pitch angle?. The incoming wind having a mean wind speed of V, delivers a certain amount of aerodynamic torque Taero that drives the rotor. This aerodynamic torque is a function of the wind speed V, the pitch angle?, and the drivetrain rotational speed?, i.e. Taero(V, ?, ?). Figure 1: Configuration of the direct drive wind turbine drivetrain 1. Transfer Function and Open-Loop Block Diagram Representation (10 marks) As Taero(V, ?, ?) is a nonlinear function, the function needs to be linearized prior to designing a linear controller for the drivetrain system. The linearized equation of motion takes the form of: ??? ? ??? ???V ???? ???Tgen where ?, ?, and ? are coefficients that depend on the desired operating point (Vo, ?o, ?o) and ? refers to the change of variable from that operating point, i.e. ?? = ? ? ?o, ?V = V ? Vo, ?ß = ß ? ßo, and ?Tgen = Tgen ? Tgen,o. Express the above equation in Laplace domain, then determine the open-loop transfer functions: (i) from ?V to ??, (ii) from ?ß to??, and (iii) from ?Tgen to??. Draw a single open-loop block diagram representation of the linearized equation of motion showing all the three inputs (?V, ?ß, ?Tgen) and the output ??.
MP3001/MA3005 Continuous Assessment 2 7 February 2013 Figure 2: Power curve of the wind turbine 2. Open-Loop Response (10 marks) Figure 2 shows the operating curve of the wind turbine. It relates the output power of the generator to the incoming wind speed. For analysis, the drivetrain model can be linearized at the operating point indicated by the point A in Fig. 2, in which ? =?0.194, ? =0.069, ? =?2.65, and ? =0.000112. If the pitch angle and the generator torque are…