Wind Farm – Impact in Power System and Alternatives to Improve the Integration 264 10 20 30 40 50 60 20 40 60 0 0.2 0.4 0.6 0.8 1 Original State Next State Transition Probability Fig. 15. Gaussian transition probabilities for M = 64 states 10 20 30 40 50 60 20 40 60 0 0.2 0.4 0.6 0.8 1 Original State Next State Transition Probability Fig. 16. Weibull transition probabilities for M = 64 states Modeling Wind Speed for Power System Applications 265 0 2 4 6 8 10 12 14 16 18 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Wind speed m/s State Probability Theoritical Statistical Fig. 17. Weibull state probabilities for M = 16 states -3 -2 -1 0 1 2 3 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Normalized wind speed m/s State probability Theoritical Statistical Fig. 18. Gaussian state probabilities for M = 16 states Wind Farm – Impact in Power System and Alternatives to Improve the Integration 266 Applying the quantization process and Markov state model to the decomposed wind speed signals presented in Figure 10 (16-year time series in hourly resolution) results in log normal distribution of wind speed state probabilities. The final results of the state probabilities are shown in Figures 19 - 21. Figures 22 – 24 show the transition probabilities for each decomposed wind speed signal. It is shown that smooth transitions appear in medium and low frequency component signals (i.e., centered around the diagonals), while high frequency component transition probabilities exhibit significant non-uniformities and disruptions due to fast changes and high frequencies variations driving the high frequency decomposed wind speed signal. Fig. 19. Lognormal state probabilities (M = 128) for high frequency wind signal. Modeling Wind Speed for Power System Applications 267 Fig. 20. Lognormal state probabilities (M = 128) for medium frequency wind signal. Fig. 21. Lognormal state probabilities (M = 128) for low frequency wind signal. Wind Farm – Impact in Power System and Alternatives to Improve the Integration 268 Fig. 22. Lognormal transition probabilities (M = 128) for high frequency wind signal. Fig. 23. Lognormal transition probabilities (M = 128) for medium frequency wind signal. Modeling Wind Speed for Power System Applications 269 Fig. 24. Lognormal transition probabilities (M = 128) for low frequency wind signal. 5. Conclusion This chapter characterizes wind speed signal using stochastic time series distribution models. It presents a short term wind speed prediction model using a linear prediction method by means of FIR and IIR filters. The prediction model was based on statistical signal representation by a Weibull distribution. Prediction accuracies are presented and they show independencies on past value expect for the most recent one. These in turn validate a Markov process presentation for stationary wind speed signals. The chapter also studies the integration of a complete wind speed pattern from a decomposition model using Fourier Transform for different wind time series models defined by different frequencies of each wind pattern. Uniform quantization and discrete Markov process have been applied to the short, medium and long term wind speed time series signals. The actual state and transition probabilities have been computed statistically based on the counting method of the quantized time series signal itself. Theoretical state probabilities have been also computed mathematically using the fitted PDF model. A comparison of the statistical and theoretical state probabilities shows a good match. Both low and medium frequency signals exhibit smooth variation in state transition probabilities, while the high frequency component exhibit irregularity due to fast, short term variations. 6. References [1] GE Energy, (March 2005), Report on “The Effects of Integrating Wind Power on Transmission System Planning, Reliability, and Operations” Prepared for:The New York State Wind Farm – Impact in Power System and Alternatives to Improve the Integration 270 Energy Research and Development Authority. Available online: http://www.nyserda.org/publications/wind_integration_report.pdf [2] C. Lindsay Anderson, Judith B. Cardell, (2008), “Reducing the Variability of Wind Power Generation for Participation in Day Ahead Electricity Markets,” Proceedings of the 41 st Hawaii Inter national Conference on System Sciences, IEEE. [3] Kittipong M., Shitra Y., Wei Lee, and James R., (Nov. 2007), “An Integration of ANN Wind Power Estimation Into Unit Commitment Considering the Forecasting Uncertainty,” IEEE Transactions On Industry Applications, Vol., 43, No. 6, [4] Marcos S. Miranda, Rod W. Dunn, (2006), “One-hour-ahead Wind Speed Prediction Using a Bayesian Methodology,” IEEE. [5] D. Hawkins, M. Rothleder, (2006), “Evolving Role of Wind Forecasting in Market Operation at the CAISO,” IEEE PSCE, pp. 234 -238, [6] Alberto F., Tomas G., Juan A., Victor Q., (Aug. 2005), “Assessment of the Cost Associated With Wind Generation Prediction Errors in a Liberalized Electricity Market,” IEEE Transactions on Power Systems, Vol. 20, No. 3, pp. 1440-1446,. [7] Dale L. Osborn, (2006), “Impact of Wind on LMP Market,” IEEE PSCE, pp. 216-218. [8] Cameron W. Potter, Micheal Negnevistsky,(2005) “Very Short-Term Wind Forecasting for Tasmanian Power Generation”, IEEE, TPWRS Conference. [9] National weather station, available online, http://www.ndbc.noaa.gov/data/5day2/DBLN6_5day.cwind [10] B. A. Shenoi, (2006), “Introduction to Digital Signal Processing and Filter Design” John Wiley & Sons, Inc. [11] F. Castellanos, (Aug. 2008), ” Wind Resource Analysis and Characterization with Markov’s Transition Maatrices,” IEEE Transmission and Distribution Conf., Latin America, [12] Noha Abdel-Karim, Mitch J. Small, Marija Ilic, (2009), “Short Term Wind Speed Prediction by Finite and Infinite Impulse [13] Response Filters: A State Space Model Representation Using Discrete Markov Process”, Powertech Conf. Bucharest, 2009. [14] P. P. Vaidyanathan, (2008), The Theory of Linear Prediction, California Institute of Technology, 1 st ed., Morgan & Claypool, 2008 [15] Yang HE, (2010), Modeling Electricity Prices for Generation Investment and Scheduling Analysis., Thesis proposal, University of Hong Kong. 12 Modelling and Simulation of a 12 MW Active-Stall Constant-Speed Wind Farm Lucian Mihet-Popa 1 and Voicu Groza 2 1 Politehnica University of Timisoara 2 University of Ottowa 1 Romania 2 Canada 1. Introduction The conventional energy sources such as oil, natural gas, or nuclear are finite and generate pollution. Alternatively, the renewable energy sources like wind, solar, tidal, fuel cell, etc are clean and abundantly available in nature. Among those the wind energy has the huge potential of becoming a major source of renewable energy for this modern world. In 2008, 27 GW wind power has been installed all over the world, bringing world-wide install capacity to 120.8 GW (GWEC publication, 2009). The wind energy industry has developed rapidly through the last 20-30 years. The development has been concentrated on grid connected wind turbines (wind farms) and their control strategies. Conventional stall wind turbines are equipped with cage rotor induction generators, in which the speed is almost constant, while the variable speed and variable pitch wind turbines use doubly-fed induction generators or synchronous generators in connection with a power converter (partial rate or full rate). The variable speed wind turbine has a more complicated electrical system than the fixed-speed wind turbine, but it is able to achieve maximum power coefficient over a wide range of wind speeds and about (5- 10) % gain in the energy capture can be obtained (Hansen, A.D. et.al, 2001). In this paper a complete simulation model of a 6 x 2 MW constant-speed wind turbines (wind farm) using cage-rotor induction generators is presented using data from a wind farm installed in Denmark. The purpose of the model is to simulate the dynamical behaviour and the electrical properties of a wind turbine existing in a wind farm. The wind farm model has also been built to simulate the influence on the transient stability of power systems. The model of each wind turbine includes the wind fluctuation model, which will make the model useful also to simulate the power quality and to study control strategies of a wind turbine. 2. Wind turbine modelling In order to simulate the wind turbine as a part of a distribution system, models have been developed for each element and implemented in the dedicated power system simulation tool DIgSILENT Power Factory. The purpose of the model is to simulate the dynamical behaviour and the electrical properties of a wind turbine. The modelling of the wind turbine should create a model as Wind Farm – Impact in Power System and Alternatives to Improve the Integration 272 simple as possible from a mechanical point of view, but capable of providing a good description of the electrical characteristics of a wind turbine. The wind turbine model consists of different component models: wind model, aerodynamic model, transmission model and of the electrical components such as induction generator, soft-starter, capacitor bank and transformer model (Mihet-Popa, 2004). Aerodynamics is normally integrated with models for different wind conditions and structural dynamics. The wind turbine is characterized by the non-dimensional curves of the power coefficient C p as a function of both tip speed ratio λ, and the blade pitch angle, θ pitch . The tip speed ratio is the ratio of linear speed at the tip of blades to the speed of the wind. As shown in Fig. 1, the wind model generates an equivalent wind speed u eq , which, together with the blade pitch angle θ blade and rotor speed ω rot , are input to the aerodynamic block. The output of the aerodynamic model is the aerodynamic torque T rot , which is the input for the transmission system together with the generator speed ω gen . The transmission system has as output the mechanical torque T hss on the high-speed shaft, which is used as an input to the generator model. Finally, the blade angle control block models the active control loop, based on the measured power and the set point. A simplified block diagram of the wind turbine model is presented in Fig. 1. 2.1 The wind speed model The wind models describe the fluctuations in the wind speed, which influence the power quality and control characteristics of the wind farm. Thus, the wind speed model simulates the wind speed fluctuations that influence the fluctuations in the power of the wind turbines. The wind acting on the rotor plane of a wind turbine is very complex and includes both deterministic effects (mean wind, tower shadow) and stochastic variations due to turbulence (Mihet-Popa, 2003). Fig. 1. The block diagram of a simplified model for a constant-speed wind turbine using induction generator. The simulations shown in Fig. 2 illustrate the effect of the rotational sampling. This hub wind speed is used as input to the rotor wind model to produce an equivalent wind speed Modelling and Simulation of a 12 MW Active-Stall Constant-Speed Wind Farm 273 (u eq ), which accounts for the rotational sampling on each of the blades. The wind speed (wspoint), which influences the power quality, should be filtered to generate a hub wind speed (wsfic). Figure 2 shows a simulation result for one wind turbine, based on a look-up table, at an average wind speed of 10 m/s. As expected, both wind speed models fluctuate with three times the rotational frequency (3p). 2.2 The aerodynamic model A wind turbine is essentially a machine that converts the kinetic energy of the moving air (wind) first into mechanical energy at the turbine shaft and then into electrical energy (Heier S., 1998). Fig. 3 describes the conversion of wind power (P WIND ) into mechanical (P MEC ) and thereafter into electrical power (P EL ). Fig. 2. Rotor wind speed and hub wind speed model. The interaction of the turbine with the wind is complex but a reasonably simple representation is possible by modelling the aerodynamic torque or the aerodynamic power as described below. Aerodynamic modelling also concerns the design of specific parts of wind turbines, such as rotor-blade geometry and the performance prediction of wind farms. The force of the wind creates aerodynamic lift and drag forces on the rotor blades, which in turn produce the torque on the wind turbine rotor (Hansen et. al, 2003). [...]... thus wasting the excess energy in the wind 4 Wind farm modelling The wind farm contains 6 wind turbines of 2 MW each of them The model of wind turbine, presented before, was implemented for each wind turbine The layout of the active-stall wind farm is shown in Fig 14 and a load flow simulation for one wind turbine in Fig 15 Each wind turbine is connected to a 10 kV bus bar The induction generators, soft-starters,... system is based on the measured generator power (Pm) and the aerodynamic power (Paero) of wind turbine as a function of measured wind speed (vwind) at different pitch angles (θ) 284 Wind Farm – Impact in Power System and Alternatives to Improve the Integration Fig 11 Block diagram of an active-stall controlled wind turbine with constant speed using a cage-rotor induction generator Fig 12 The block diagram... while the wind turbine will pitch the blades a few degrees every time when the wind changes in order to keep the rotor blades at the optimum angle When the wind turbine reaches its rated power, and the generator is about to be overloaded, the turbine will pitch its blades in the opposite direction In this way, it will increase the angle of attack of the rotor blades in order to make the blades go into... control the active power more accurately than with passive stall, so as to avoid overshooting the rated power of the turbine at the beginning of a gust of wind Another advantage is that the wind generator can be run almost exactly at the rated power of the machine at all high wind speeds 3.4 Rotor efficiency under stall and pitch controlled wind turbines The output power of wind turbines varies with wind. .. capacitor banks for reactive power compensation and the step-up transformers are all palaces in nacelle and thus the transformer is considered part of the wind turbine The control of active and reactive power is based on measured reactive power at the point of common coupling The wind turbine controller must be able to adjust the wind turbine production to the power reference computed in the wind farm. .. 0 0 2 4 6 8 10 12 0 -1 -2 -3 14 lambda b) Fig 13 Power coefficient (Cp) of a 2MW wind turbine versus wind speed (a), and the tip speed ration (λ), (b) at different pitch angles 286 Wind Farm – Impact in Power System and Alternatives to Improve the Integration In order to achieve maximum power yield for each wind speed the maximal Cp and the corresponding θ has to be found In fact, the control strategy... to it, as the energy that the wind contains increases with the cube of the wind speed At low wind speeds (1-3 m/s), wind turbines are shut down, as they would be able to generate little or no power (Fig 9) Wind turbines only start-up at wind speeds between 2.5 and 5 m/s, known as the “cut -in wind speed “Nominal” or “rated” wind speed, at which nominal output power is reached, is normally between 12. .. system, according to the demands imposed by the system operator In case of normal operation conditions the wind turbine has to produce maximum power In power limitation operation mode the wind turbine has to limit its production to the power reference received from the wind farm controller 4.1 Electrical diagram The Fig 14 contains the grid representation from 50 kV double bus-bar systems down to the. .. slightly out of the wind Conversely, the blades are turned back into the wind whenever the wind drops again The rotor blades thus have to be able to turn around their longitudinal axis (to pitch) During normal operation the blades will pitch a fraction of a degree at a time - and the rotor will be turning at the same time Designing a pitch-controlled wind turbine requires some clever engineering to make sure...274 Wind Farm – Impact in Power System and Alternatives to Improve the Integration PMEC PWIND n1 PEL n2 IG 3 Fig 3 A block diagram of the power conversion in a wind turbine The aerodynamic torque is given by: Trot  Paero rot  1   R 3 C p (  ,  pitch ) 2 (1) Where Paero is the aerodynamic power developed on the main shaft of a wind turbine with radius R at a wind speed ueq and air density . fluctuations in the power of the wind turbines. The wind acting on the rotor plane of a wind turbine is very complex and includes both deterministic effects (mean wind, tower shadow) and stochastic. of a wind turbine existing in a wind farm. The wind farm model has also been built to simulate the influence on the transient stability of power systems. The model of each wind turbine includes. of the model is to simulate the dynamical behaviour and the electrical properties of a wind turbine. The modelling of the wind turbine should create a model as Wind Farm – Impact in Power System