Wind Turbines Part 16 docx

Wind Turbines 590 5 10 15 0 1 2 Wind speed [m/s] Turbine power P t [MW] 5 10 15 0 100 200 300 Wind speed [m/s] Vr' [V] 5 10 15 0 0.1 0.2 0.3 0.4 Wind speed [m/s] C p [-] 5 10 15 5 10 15 20 Ω turb [rpm] Wind speed [m/s] sr=0.15 sr=0.41 sr=0.8 3 3.5 4 0 1 2 zoom (a) (b) (c) (d) Fig. 20. Turbine power P t , rotor voltage V r ’(rotor side), turbine power coefficient C p and turbine rotating speed Ω turb versus wind speed for three different stator to rotor turns ratios (G r =68.1). 5 10 15 0 10 20 30 40 50 Wind speed [m/s] Power converters losses [kW] 5 10 15 0 500 1000 1500 Wind speed [m/s] DFIG rotor current I r ' [A] sr=0.41 sr=0.8 sr=0.15 Fig. 21. DFIG rotor current and total power converters losses (RSC+GSC) versus wind speed, for three different stator to rotor turns ratios. From simple analytical relations, neglecting stator and rotor losses and mechanical losses, it is possible to derive the well known rotor active power balance: 1 rt s PP s = − (22) With P r the DFIG rotor active power. Since for the stator to rotor turns ratio analysis the gearbox ratio is maintained fixed, the super-synchronous maximal slip is the same between Optimal Selection of Drive Components for Doubly-Fed Induction Generator Based Wind Turbines 591 solution with sr=0.41 and sr=0.8, as it can be understood from Fig. 20 (d) (same maximal rotating speed). Therefore, referring to eq. (22), the rotor active power flow P r is the same for both solutions on a wide operating wind speed (a difference can be noticed in the wind speeds region below 6 m/s as shown in Fig. 20 (d)). Neglecting the reactive power, the active power is the product of the rotor voltage and rotor current. However in one case (Gr=0.41) the rotor voltage is higher than in the other case (Gr=0.8), leading to a remarkable difference between the rotor currents behaviors, as presented in Fig. 21. This difference in currents produces a difference in the power converter losses which are strongly dependent on the currents. Therefore the global efficiency of the system decreased when sr is increased, explaining the annual production degradation illustrated in Fig. 19 for sr values above sr=0.41. Furthermore the increase in the RSC currents with the increase of sr, explains the increase of the power converter ratings presented in Fig. 19. The gearbox mass issue was not considered here because its value is constant in the range of ratios used in these examples (according to the model presented in (4) and (5)). However the model can be very useful when the designers are exploring new topologies considering a wide range of gearbox ratios and stages (Aguglia et al., 2009). The objective of the analysis presented in this section was mainly to give a flavor of the complex selection process of some key variables of wind turbines DFIG drive systems. This complex process can be handled by use of a non-linear constrained optimization program, which can be used to select the optimal compromises between DFIG, power converter and gearbox performance/cost to maximize the annual production. The dimensional design of the DFIG itself, which consists in finding the optimal mechanical dimensions of the active materials (iron & copper), can be easily integrated in this global environment as presented by the authors in (Aguglia et al., 2009). 6. Conclusion The DFIG drive components selection process, or design process, needs a global approach of the system in order to optimize its global performances. In the case of a wind turbine plant, such global performances are represented by the annual production, the overall mass and the initial cost. For this purpose the designer needs a model of each sub-component. In this chapter only a few key variable for the DFIG drive design were considered for a sensitivity analysis with respect to the annual production and size of the converter. It is demonstrated that every choice of drive components (gearbox, DFIG and power converter) has an influence on the annual energy production and power converter cost. This powerful design methodology can be used to design the DFIG mechanical geometry as well. With this approach it is possible to integrate into the design process the wind probability distribution. Therefore, the plant is not optimized for a given operating point only, but for the global operation spectrum. This methodology is very useful for every electrical drive design in the variable speed application area, where all operating points must be considered and weighted with a certain probability of operation (e.g. typical torque vs. time behavior of an electric vehicle or typical cyclic operation of a fan). The selection, or design, process can be coupled with a non-linear optimization algorithm, which can help in the complex task of selecting the optimal variables. In such an iterative process it is essential to have efficient models which allow to quickly obtaining all global performances. Analytical formulations of these models are well adapted for this purpose. The presented results for DFIG wind turbines drives have been obtained thank to the proposed analytical determination of the rotor power converter control laws. The most Wind Turbines 592 important variable influencing the annual production are the gearbox ratio and the DFIG stator to rotor turns ratio. It is important to mention that this sensitivity to these two variables is strongly dependent on the rotor side converter voltage limit. Therefore it is of extreme importance to take into account this limitation during the design process. 7. References Aguglia D., Viarouge P., Wamkeue R., Cros J. (2007a). Selection of Gearbox Ratio and Power Converters Ratings for Wind Turbines Equipped With Doubly-Fed Induction Generators, IEEE conference “Electrical Machines and Drives – IEMDC”, Vol. 1, 3-5 May 2007, pp. 447-452. Aguglia D., Wamkeue R., Viarouge P., Cros J. (2007b). Optimizing the Annual Energy Production of Doubly-Fed Induction Generator Based Wind Turbines, IEEE Conference “Electrical Power Conference–EPC”, Montreal, 25-26 October 2007, pp. 248-255. Aguglia D., Viarouge P., Wamkeue R., Cros J. (2008). Analytical determination of steady- state converter control laws for wind turbines equipped with doubly fed induction generators, IET. Journal on Renewable Power Generation, Vol. 2, no 1, March 2008, pp. 16 -25. Aguglia D., Viarouge P., Wamkeue R., Cros J. (2009). Doubly-Fed Induction Generator Drive Optimal Design for Wind Turbines with Reduced Gearbox Stages Number, “European Wind Energy Conference (EWEC)”, 16-19 March 2009, pp. 1-10. Çadirici I., and Ermis M.: ‘Double-output induction generator operating at sub synchronous and super synchronous speeds: steady-state performances optimization and wind- energy recovery’, IEE Proceedings-B, Vol. 139, No. 5, 1992 Cotrell J.R., “A preliminary evaluation of a multiple-generator drivetrain configuration for wind turbines,” in Proc. 21st ASME Wind Energy Symp., 2002, pp. 345-352. Flender “Planurex® 2, Planetary gear units”, Brochure, [Online]. Available: http://www.flender.com/_upload/k256en.pdf Generation Using Doubly Fed Wound Rotor Induction Machine – A comparison With Alternative Schemes,” IEEE Trans. Energy Convers., Vol. 17, No. 3, 2002. Grauers A., “Efficiency of three wind energy generator systems,” IEEE Trans. Energy Convers., Vol. 11, No. 3, September 1996. Heier S.: “Grid integration of Wind Energy Conversion Systems, Second edition,” John Whiley & Sons, Ltd, 2006, pp. 31-44. Li H., Chen Z., Polinder H. : ‘Optimization of multibrid permanent-magnet wind generator systems’, IEEE Trans. on energy conv., Vol. 24, No. 1, March 2009, pp 82-92. Pena R., Clare J. C., Asher G. M. (1996). Doubly fed induction generator using back-to-back PWM converters and its application to variable-speed wind–energy generation, IET Journal on Electric Power Applications, pp. 231-241, Vol. 43, no. 3 Petersson A., ‘Analysis, modeling and control of doubly-fed induction generators for wind turbines’, Ph.D. Thesis, Chalmers University of Technology, Sweden 2005. Smith S., Todd R., Barnes M., and Tavner P. J.: ‘Improved Energy Conversion for Doubly- Fed Wind Generators’, IEEE IAS Conference, Vol. 4, 2005 Nordex N80/2500kW wind turbine Brochure, Online, Available: http://www.nordex-online.com/en/nordex/downloads.html, accessed November 2007 Zinger D. S. and Mulijadi E.: “Annualized Wind Energy Improvement Using Variable Speeds,” IEEE Trans. Ind. Appl., Vol. 33, No. 6, 1997. 26 Wind Turbine Model and Maximum Power Tracking Strategy Hengameh Kojooyan Jafari and Ahmed Radan Islamic Azad University-Islamshahr Branch, K.N. University of Technology Iran 1. Introduction Today doubly fed induction generators (DFIG) are used for modern wind turbines to deliver electrical power to the grid. A speed variation of ±30% around synchronous speed can be obtained by the use of power converter of ±30% of nominal power. Furthermore, it is possible to control active and reactive power, which gives a better performance, and the power electronics enables the wind turbine to act as a more dynamic power source to the grid. The DFIG does not need either a soft starter or a reactive power compensator. This system is naturally a little bit more expensive compared to the classical systems; however, it is possible to save money on the safety margin of gear and reactive power compensation units, and it is also possible to capture more energy from the wind (Blaabjerg & Chen, 2006). A wind turbine with maximum power tracking is a very suitable power source to the grid. This new model, as a dynamic power source to the grid, comprises a maximum power tracking wind turbine, a doubly fed induction machine with winding configuration, external rotor resistance and external rotor source which has a variable phase and amplitude. In this chapter its simulation, effects of important parameters, design of a special kind of voltage controller and a new combined controller for it and comparison of these controllers are presented. 2. Key words Doubly fed machine, Wind turbine, Voltage controller, Combined controller 3. Maximum power tracking wind turbine Maximum power tracking wind turbine can deliver maximum power to the grid in low and high wind speeds. Turbine torque via wind is inferred from following equations (1) to (3): M wind R V ω λ × = (1) 3 5 3 1 2 M MP PRC ω ρπ λ = (2) Wind Turbines 594 2 5 3 1 2 MM MP M P TRC ω ρπ ω λ == (3) Where, V wind , the wind speed, is measured in m/s, R, the blade radius is measured per m, ρ (1.24kg/m 3 [4]), air density is measured in kg/m 3 , ω M , turbine mechanical speed, is measured in rad/sec, λ is tip-speed ratio (TSR) and C p is power coefficient, i.e. ratio of turbine power (power extracted) to wind power (power available) and it depends on aerodynamics specifications of blades (Hoseinpur, 2001), (Burter et al., 2001). C p is function of λ (Burter et al., 2001): 3 10.035 12.5( ) 0.08 1 3 1 0.035 0.22 116( ) 0.4 5 0.08 1 P Ce λβ β β λβ β −− + + ⎡⎤ =−−− ⎢⎥ + + ⎣⎦ (4) Where β is blade pitch angle. Simulation of turbine for two typical wind speed, 4 and 5m/s that are in valid range of speed between low-shutdown speed and high stopped speed, has been performed for improved turbine parameters according to table1 (Hoseinpur, 2001): Nominal power 15kw Blade radius 5.5m Blade pitch angle 0° Table 1. Turbine parameters In a fixed wind speed, maximum power of turbine can be achieved from C Pmax function considering improved λ. Improved parameters from equation (8) are presented in table2 (Hoseinpur, 2001). λ i or Improved TSR C pmax or Maximum power coefficient 8.636 0.48 Table 2. Improved parameters of turbine Then, by using equations (1), (2), maximum turbine power is calculated. 4. Doubly fed induction machine Most of wind turbine generators are induction generators that are very reliable and costs of them are low (Ehernberg et al., 2001). Induction generators are not complicated. These generators can give active power to grid however they take reactive power from it. In these generators at 50HZ frequency, the angular frequency is usually among 1200rpm to 1800rpm (relative to number of poles) and gear ratio is among 30 to 50 (Burter et al., 2001). Recently use of doubly-fed induction generators in wind turbines has become more common; however, they are more complicated than ordinary induction machines. Voltage equations of an induction generator in ABC system are given by equation (5) (Krause, 1986): Wind Turbine Model and Maximum Power Tracking Strategy 595 () ,,, ,Sr Sr Sr Sr d VRi Li dt =•+ • (5) And n, the ratio of equivalent stator turns to equivalent rotor turns is unit (Krause, 1986): 1 2 3 ms m ms mr n LL LL = = = (6) And electromagnetic torque is according to equation (7) (Krause, 1986): () () '' T e abcS sr abcr m d Ti L i d θ =• (7) And rotor mechanical speed can be obtained from equation (8) (Krause, 1986): m em m d TT J D dt ω ω −= + (8) Where T m is mechanical torque, T e is generator torque, D is system drag (friction) coefficient and J is total inertia. In induction machine with rotor configuration that is referred to as a winding rotor, rotor external resistance is used to increase slip and its amount is usually low and is nearly one over ten percent of rotor resistance per phase. In doubly-fed induction generator, an external source with adjustable amplitude and phase is used to control induction generator speed and power (Ehernberg et al., 2001). According to table 3 and by using induction machine model of MATLAB-SIMULINK the simulation has been performed. Nominal power 15 kW Line to line nominal voltage 460 V Nominal frequency 60 HZ Number of pair poles 4 Stator resistance, R S 0.2761 Ω Stator inductance, L ls 2.2 mH Rotor resistance, R r 0.1645 Ω Rotor inductance, L lr 2.2 mH Magnetizing inductance, L m 76.14 mH Inertia, J 0.1 kg.m 2 Friction coefficient, F 0.018 N.m.s Table 3. Induction machine parameters in side of stator (Hoseinpur et al., 2001) Wind Turbines 596 5. Machine simulation results Results of simulation of fig.1 are presented in table 4 (Kojooyan Jafari & Radan, 2008). Simulation has been performed for 2 seconds, using MATLAB-SIMULINK. In table4, the polarity of input power to machine is considered negative and that of output from machine is considered positive. Fig. 1. Model of doubly-fed machine with improved wind turbine In simulation, the gearbox effect is considered and output torque of gearbox is multiplied by inverse of gear ratio where gear ratio is the ratio of generator shaft speed to low-speed shaft speed in relation to equation (9): mr GB T N ω ω = (9) V wind k θ r ex ω T ω mr N g P T3Ф P S3Ф 4 5 -0.02 0.016 6.28 94.5 15 -1.8k 1.4k 4 5 -0.78 0.016 6.28 94.5 15 -1.8k 1.4k 4 10 -0.02 0.016 6.28 94.5 15 -1.8k 1.4k 4 10 -0.78 0.016 6.28 94.5 15 -1.8k 1.4k 5 15 -0.02 0.016 7.85 95 12 -3.53k 3k 5 15 -0.78 0.016 7.85 95 12 -3.53k 3k 5 20 -0.02 0.016 7.85 95 12 -3.53k 3k 5 20 -0.78 0.016 7.85 95 12 -3.53k 3.53k Table 4. Simulation results of wind turbine and doubly-fed generator Wind Turbine Model and Maximum Power Tracking Strategy 597 V wind k r ex P r3Ф P loss Q S3Ф Q r3Ф 4 5 0.016 6 394 -7.5k 11.5 4 5 0.016 6 394 -7.5k 11.5 4 10 0.016 10 390 -8.5k 47 4 10 0.016 10 390 -8.5k 47 5 15 0.016 7 523 -8k 21 5 15 0.016 7 523 -8k 21 5 20 0.016 10 480 -8.5k 40 5 20 0.016 10 480 -8.5k 40 Table 4. (continue) Where k and θ are amplitude and phase of external rotor source, r ex is external rotor resistance, Q S3Ф and Q r3Ф are 3-phased reactive power of rotor and stator in VAR, P T3Ф is maximum turbine power, P r3Ф and P S3Ф are 3-phased active power of rotor and stator and P loss is power losses of machine that all are in watt, ω T is turbine speed in rad/sec, V wind is wind speed in m/s, ω mr is mechanical speed of rotor in rad/sec and Ng is ratio of gear Table5 shows the results of simulation for two amounts of external rotor resistance. V wind k θ r ex ω T ω mr Ng Q r3Ф 4 10 -0.78 0.016 6.28 94.5 15 47 4 10 -0.78 3 6.28 96.7 15.4 -1 5 15 -0.78 0.016 7.85 95 12 21 5 15 -0.78 3 7.85 99 12.6 -0.5 Table 5. Simulation results of wind turbine with doubly-fed generator for two different r ex V wind k Q S3Ф P T3Ф P S3Ф P r3Ф P loss 4 10 -8.5k -1.8k 1.4k 10 390 4 10 -7.2k -1.8k 1.5k -0.5 300.5 5 15 -8k -3.53k 3k 7 523 5 15 -7.3k -3.53k 3.1k 2 428 Table 5. (continue) The curves of simulation are presented in the following figs.2 to 17 (Kojooyan Jafari & Radan, 2009). Wind Turbines 598 Fig. 2. Curve of torque-speed for k=15, r ex =0.016, V wind =5, θ=-0.78 and Ng=12 Fig. 3. Curve of electromagnetic torque-time for k=15, r ex =0.016, V wind =5, θ=-0.78 and Ng=12 Fig. 4. Curve of mechanical torque-time for k=15, r ex =0.016, V wind =5, θ=-0.78 and Ng=12 [...]... Curve of mechanical rotor speed-time for k=10, rex=0. 016, Vwind=4, θ=-0.78 and Ng=15 602 Wind Turbines Fig 14 Curve of torque-speed for k=10, rex=3, Vwind=4, θ=-0.78 and Ng=15 Fig 15 Curve of electromagnetic torque-time for k=10, rex=3, Vwind=4, θ=-0.78 and Ng=15 Fig 16 Curve of mechanical torque-time for k=10, rex=3, Vwind=4, θ=-0.78 and Ng=15 Wind Turbine Model and Maximum Power Tracking Strategy... mechanical rotor speed-time for k=15, rex=3, Vwind=5, θ=-0.78 and Ng=12 Fig 10 Curve of torque-speed for k=10, rex=0. 016, Vwind=4, θ=-0.78 and Ng=15 Wind Turbine Model and Maximum Power Tracking Strategy 601 Fig 11 Curve of electromagnetic torque-time for k=10, rex=0. 016, Vwind=4, θ=-0.78 and Ng=15 Fig 12 Curve of mechanical torque-time for k=10, rex=0. 016, Vwind=4, θ=-0.78 and Ng=15 Fig 13 Curve of mechanical.. .Wind Turbine Model and Maximum Power Tracking Strategy 599 Fig 5 Curve of mechanical rotor speed-time for k=15, rex=0. 016, Vwind=5, θ=-0.78 and Ng=12 Fig 6 Curve of torque-speed for k=15, rex=3, Vwind=5, θ=-0.78 and Ng=12 Fig 7 Curve of electromagnetic torque-time for k=15, rex=3, Vwind=5, θ=-0.78 and Ng=12 600 Wind Turbines Fig 8 Curve of mechanical torque-time for k=15, rex=3, Vwind=5, θ=-0.78... current ira for typical vwind=6m/s, k=10, Ng=34 and P controller Wind Turbine Model and Maximum Power Tracking Strategy Fig 49 Curve of torque-speed for typical vwind=6m/s, k=2, Ng=34 and P controller Fig 50 Curve of rotor speed for typical vwind=6m/s, k=2, Ng=34 and P controller Fig 51 Curve of stator powers for typical vwind=6m/s, k=2, Ng=34 and P controller 615 616 Wind Turbines Fig 52 Curve of... torque-speed for typical vwind=6m/s, k=2, Ng=34 and PI controller Fig 26 Curve of rotor speed for typical vwind=6m/s, k=2, Ng=34 and PI controller Fig 27 Curve of stator powers for typical vwind=6m/s, k=2, Ng=34 and PI controller 607 608 Wind Turbines Fig 28 Curve of rotor current ira for typical vwind=6m/s, k=2, Ng=34 and PI controller Fig 29 Curve of torque-speed for typical vwind=6m/s, k=10, Ng=17... speed for typical vwind=6m/s, k=10, Ng=17 and PI controller Wind Turbine Model and Maximum Power Tracking Strategy Fig 31 Curve of stator powers for typical vwind=6m/s, k=10, Ng=17 and PI controller Fig 32 Curve of rotor current ira for typical vwind=6m/s, k=10, Ng=17 and PI controller Fig 33 Curve of torque-speed for typical vwind=6m/s, k=2, Ng=17 and PI controller 609 610 Wind Turbines Fig 34 Curve... Fig 39 Curve of stator powers for typical vwind=6m/s, k=10, Ng=3.8 and PI controller 611 612 Wind Turbines Fig 40 Curve of rotor current ira for typical vwind=6m/s, k=10, Ng=3.8 and PI controller Fig 41 Curve of torque-speed for typical vwind=6m/s, k=2, Ng=3.8 and PI controller Fig 42 Curve of rotor speed for typical vwind=6m/s, k=2, Ng=3.8 and PI controller Wind Turbine Model and Maximum Power Tracking... stator powers for typical vwind=6m/s, k=2, Ng=3.8 and PI controller Fig 44 Curve of rotor current ira for typical vwind=6m/s, k=2, Ng=3.8 and PI controller Fig 45 Curve of torque-speed for typical vwind=6m/s, k=10, Ng=34 and P controller 613 614 Wind Turbines Fig 46 Curve of rotor speed for typical vwind=6m/s, k=10, Ng=34 and P controller Fig 47 Curve of stator powers for typical vwind=6m/s, k=10, Ng=34... form Fig 21 Curve of torque-speed for typical vwind=6m/s, k=10, Ng=34 and PI controller 606 Wind Turbines Fig 22 Curve of rotor speed for typical vwind=6m/s, k=10, Ng=34 and PI controller Fig 23 Curve of stator powers for typical vwind=6m/s, k=10, Ng=34 and PI controller Fig 24 Curve of rotor current ira for typical vwind=6m/s, k=10, Ng=34 and PI controller Wind Turbine Model and Maximum Power Tracking... controller Fig 57 Curve of torque-speed for typical vwind=6m/s, k=2, Ng=17 and P controller 617 618 Wind Turbines Fig 58 Curve of rotor speed for typical vwind=6m/s, k=2, Ng=17 and P controller Fig 59 Curve of stator powers for typical vwind=6m/s, k=2, Ng=17 and P controller Fig 60 Curve of rotor current ira for typical vwind=6m/s, k=2, Ng=17 and P controller Wind Turbine Model and Maximum Power Tracking . 2009). Wind Turbines 598 Fig. 2. Curve of torque-speed for k=15, r ex =0. 016, V wind =5, θ=-0.78 and Ng=12 Fig. 3. Curve of electromagnetic torque-time for k=15, r ex =0. 016, V wind =5,. torque-time for k=10, r ex =0. 016, V wind =4, θ=-0.78 and Ng=15 Fig. 13. Curve of mechanical rotor speed-time for k=10, r ex =0. 016, V wind =4, θ=-0.78 and Ng=15 Wind Turbines 602 Fig -0.02 0. 016 7.85 95 12 -3.53k 3k 5 15 -0.78 0. 016 7.85 95 12 -3.53k 3k 5 20 -0.02 0. 016 7.85 95 12 -3.53k 3k 5 20 -0.78 0. 016 7.85 95 12 -3.53k 3.53k Table 4. Simulation results of wind turbine