DIRECTRICES DE GESTIÓN A SEGUIR POR EL PROPIETARIO O GESTOR

There are many possible TST configurations. The designer can choose between a direct-drive system or a geared system; the generator can be synchronous or asynchronous and connection to the grid can be through a full-power converter, a partially rated converter or directly connected. As discussed in Section 1.2.7 the use of a PMSG in a direct drive configuration is an attractive solution. When used in conjunction with a full-power converter, the generator is decoupled from the grid and full variable speed operation can be achieved. Variable speed operation increases the energy yield of the turbine by allowing it to operate at its maximum power coefficient over a wide range of flow speeds. Figure 2.1 shows the system considered in this thesis.

Figure 2.1: Block diagram of PMSG based TST.

The system consists of a PMSG and a full-power converter, consisting of back-to-back voltage source converters. Use of two, six switch converters connected in a back-to-back configuration with an intermediate DC link capacitor has the advantage of allowing for vector control on both the generator and grid-side converters (Pena, Clare & Asher, 1996). This topology allows bi- directional current flow and one has full control over the generator power factor and torque. An alternative is to use a diode rectifier on the generator-side, which simplifies the control and reduces the cost. The disadvantages of using a diode rectifier are mostly related to efficiency. The diode rectifier has been reported as introducing high levels of harmonic distortion in the generator (Huang et al., 2008), which affects efficiency and can introduce pulsating torques. For these reasons the full-power converter with active rectifier is used in this work.

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Hydrodynamic Model

The hydrodynamic torque developed by the turbine rotor of Figure 2.1 is (Burton et al., 2002):

(2.1)

The block diagram of the hydrodynamic system is shown in Figure 2.2. For modelling purposes, is a mapping function which isexpressed through a look-up table (Heir, 2006). This model simply converts the flow incident on the turbine rotor into hydrodynamic torque and does not include any structural dynamics or any dynamic inflow effects, such as shear or tower shadowing. Models that do include these dynamic effects are developed in Chapter 4. For the work in this section the simplified model of Figure 2.2 is sufficient.

Figure 2.2: Model of hydrodynamic system.

The tip speed ratio (TSR) is calculated based on the flow speed and the rotor speed. An initial condition is set such that the rotor speed is non zero at the start of the simulation. The calculated TSR and the blade pitch angle are then mapped to the appropriate value using the lookup table.The look-up table is for a generic 1 MW TST rotor. The parameters of the rotor are given in Appendix A.1. Having obtained the value the hydrodynamic torque was calculated.

Drive-Train Model

The hydrodynamic torque generated by the rotation of the rotor is transferred to the generator via the drive-train. In this case a direct-drive system is used, meaning the rotor is connected directly to the generator via a single shaft. To model the TST drive-train a two-mass model is used whereby the rotor and hub are considered to be one lumped mass and the generator is considered to be another lumped mass. The two masses are connected together via a flexible shaft which has a stiffness and damping . The model is shown in Figure 2.3 where

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one end of the shaft is driven by the turbine rotor, generating a torque . The other end of

the shaft is loaded by the generator, which generates a torque .

Figure 2.3: Two-mass drive-train model without gearbox.

The drive-train is described by the following set of equations (Florin et al, 2004):

(2.2) (2.3) = , (2.4)

where and are the angular positions of the rotor shaft and generator shaft, and are the speeds of the rotor shaft and generator shaft. and are moments of inertia for the rotor and generator respectively. The drive-train parameters are given in Appendix A.2.

Generator Model

The electrical equations used to model the PMSG are represented in the rotating reference frame, in which the -axis is oriented along the rotor flux vector position and the -axis leads the -axis by 90 degrees (Figure 2.4). Expressing the electrical equations in this way allows the torque producing and magnetising flux components of the machine to be separated; therefore, allowing for the development of a control strategy that provides independent control of the torque. In this model the three phase quantities of the machine (voltages, currents and magnetic

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flux) can be described using just two complex vectors. This means that a three phase machine can be modelled as a two phase machine.

Figure 2.4: Representation of PMSG in the rotating reference frame where the three-phase winding has been replaced by a two-phase rotating winding. The -axis is aligned with the rotor flux field and the -

axis leads the -axis by 90 degrees. and are the stator currents and and are the stator voltages. and are the rotor field current and voltage. is the electrical rotor position angle measured

relative to the stationary magnetic axis of phase . and represent the stationary (or stator) reference frame. Where is aligned with the magnetic axis of phase and leads by 90 degrees.

The equations of the PMSG in the , reference frame are given as follows (Krishnan, 2010):

(2.5)

(2.6)

where and are the stator currents, is the stator resistance, is the electrical PMSG

rotor speed, and are the equivalent self inductances of the stator and is the flux

produced by the permanent magnets. The full derivation of the PMSG model of Figure 2.4 is given in Appendix B.1. It is assumed that the PMSG used in this work is of the surface-mounted type and exhibits no saliency .

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Power Converter Model

The voltage source converters and DC link capacitor are modelled using blocks from the SimPowerSystems library within Simulink® _{(The MathWorks Inc., 2010). The grid is modelled}

using an AC voltage source from the SimPowerSystems library in series with an impedance .