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Validation of a Quasi-Steady Wind Farm Flow Model in the Context of Distributed Control of the Wind Farm

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Validation of a Quasi-Steady Wind Farm Flow Model in the Context of Distributed Control of the Wind Farm Validation of a quasi-steady wind farm flow model in the context of distributed control of the wind farm A.J. Brand J.W. Wagenaar Presented at: Torque 2010, 28-30 June 2010, Crete, Greece ECN-M--10-058 JULY 2010 2 ECN-M-10-058 Validation of a quasi-steady wind farm flow model in the context of distributed control of the wind farm A J Brand J W Wagenaar ECN Wind Energy ECN Wind Energy P.O. Box 1, NL 1755 ZG Petten, P.O. Box 1, NL 1755 ZG Petten, Netherlands Netherlands [email protected] [email protected] wind farm flow model, and presents load Abstract quantifiers calculated by the model. First, the research objectives of the FP7 project This work presents validation of an Aeolus are described (section 2) and the intermediate version of a quasi-steady quasi-steady wind farm flow model is wind farm flow model which will be part of introduced (section 3). Next, a comparison distributed control of a wind farm. In is presented between model output for and addition power and three load quantifiers measured data from the ECN Wind turbine as calculated by the model are Test site Wieringermeer EWTW (section demonstrated. It is concluded that 4). In addition power and three short-term differences between measurement and load quantifiers as calculated for the prediction are smaller than 2 m/s (wind considered cases are presented (section speed) and 200 kW (power), measured 5). Finally, a summary of the work and an minimum in wind speed and aerodynamic outlook to future work are given (section power at second or third turbine is not 6). predicted, and main differences originate from un-modelled spatial variations in wind speed and too gradually modelled decay 2. Objectives and approach of wind speed. The general objectives of the FP7 project Keywords: Model predictive control, Aeolus are to develop models that allow Wind farms, Offshore wind energy real-time predictions of flow in a wind farm and incorporate data from a network of 1. Introduction sensors, and to develop control paradigms that acknowledge the uncertainty in the In Europe wind farms are being developed modelling and dynamically manage the at a large scale. These installations are flow resource in order to optimize specific expected to operate similar to control objectives. conventional power plants and to provide Specific objectives of the project, quality power at the lowest possible cost. contained in the two flow modelling work During operation this is achieved by packages, include the development of a addressing three control objectives at wind quasi-steady and a dynamic flow model. farm level: maximum power production, The quasi-steady flow model relates single minimum structural loads and optimal turbine production and loading to a map of integration into the power system. wind speeds [4, 5, 6], in contrast to the The EU project FP7-ICT STREP dynamic flow model which describes 22548 / Aeolus is aimed at the deviations from the steady model due to development of distributed control of large rapidly changing flow effects [7]. offshore wind farms [1, 2]. In this context a quasi-steady wind farm flow model is The quasi-steady flow model is derived developed, which is to be part of the from fluid dynamics principles and is supervisory control algorithm [3]. based on a database of meteorological This paper addresses validation of an and wind turbine related measurements. It intermediate version of the quasi-steady is developed in two stages: first a preliminary version (finished April 2009 theory the aerodynamic state of a wind and reported separately [4, 5, 6]) and next turbine is expressed in terms of an axial the final version (finished February 2010, induction factor. Relations for the mean also reported separately [8, 9] and partly and the standard deviation of the axial covered in this paper). induction factor both bring the effect of In fact the quasi-steady flow model is turbulence into account. Subsequently a model of the control object "wind farm"; aerodynamic power, tower bending where "model" means a mathematical moment, blade bending moment and rotor map/function in the form of equations (or shaft torque are calculated. In addition initially look-up tables) which relates farm velocity deficit and extra turbulence due to output (power and load quantifiers) to the single wind turbine are calculated. measured quantities (e.g. rotor speed, The model treats a cluster of wind blade pitch angle, wind speed), references turbines by linking individual wind turbines (e.g. power set point) and disturbances via their wakes. For the given wind (unmodelled system inputs). Figure 1 direction, for all wind turbines in the cluster shows the basic structure. The model is the streamwise and the spanwise distance steady in the sense that it is valid over downstream each wind turbine is averaging periods of 10 minutes, in determined. Subsequently, this infomation contrast to the dynamic flow model which is employed in order to calculate all local is dynamic in the sense that it describes values of velocity deficit and added deviations from the mean. The model is turbulence by using decay laws. quasi steady because it gives mean as 3.2 Load quantifiers well as standard deviation of a quantity, and by doing so provides information on The quasi-steady wind farm flow model variations which are translated into load translates wind speed mean values and quantifiers. standard deviations into mean values and standard deviations of mechanical loads. 3. Quasi steady wind farm Subsequently the model translates this information into load quantifiers. In this flow model section the approach is presented. 3.1 Flow model First, as described in preceding The quasi-steady wind farm flow model publications [4, 8], it is assumed that load allows the wind farm controller to calculate mean μL as well as load standard deviation in real time maps of wind, loads and σL depend on wind speed mean μU and energy, or to be more specific, wind speed wind speed standard deviation σU: at each turbine in a wind farm plus tower bending moment, blade bending moment, , and , . rotor shaft torque and aerodynamic power L L U U L L U U of each turbine as a function of "ambient" This crucial assumption is motivated by wind speed, wind direction and turbulence experimental and modelling based intensity. The corresponding flow chart is identification of the parameters that shown in figure 2. influence equivalent loads [14, part 1, sub B, section 5.4]. The conclusions in the The structure and the details of the flow referred work are that: model, which are described in preceding publications [5, 6], are summarized in this The primary fatigue load parameter is the standard deviation of the longitudal section. 1 Apart from sub-models based on wind speed component , and classic momentum theory [10], inspired by The equivalent load is a function of the the literature on wind turbine wakes [11, wind speed standard deviation σU and, 12, 13, 14 part 1 sub A section 2.4, 15, because at higher wind speeds a 16], this model includes specially constant value of the turbulence developed sub-models for creation and intensity may be assumed, the mean decay of velocity deficit, creation and wind speed μU. decay of added turbulence, impact of turbulence on average values, and standard deviation of all quantities. The model treats individual wind 1 The second important parameter is yaw turbines separately. By using momentum misalignment, and the third important parameter is turbulence structure Secondly, it is assumed that loads are normally distributed. This assumption is Section 5 demonstrates the equivalent fair in a short-term assessment of wind load concept on basis of measured data. turbine components because: Future work is aimed at relating equivalent In a short time period (10 minutes) the load to fatigue load. number of observations or revolutions is high (600 resp. ~200), and 4. Model output versus Under normal operation during a 10- minute period wind turbine loads have measured data comparison experimentally been found to vary with 4.1 Overview well-defined mean and standard deviation. In this section output from an intermediate version of the quasi-steady flow model is The load quantifier selected is the compared to measured data from the ECN Wind turbine Test site Wieringermeer equivalent load Leq [e.g. 17, page 80] of a EWTW. (The EWTW consists of a row of series of loads Lj (j = 1, 2, 3, …, N): five 2.5 MW wind turbines plus a meteo 1 1 mast.) Various wind speed and direction m m m cases are presented and discussed, see Leq niLi L j N i N j figure 3 for a definition sketch, and = m-th raw moment of the observed loads. modelling issues are identified in the light of the modelling objective. Here L indicates the load, m is the slope of the SN-curve of the material and N is the 4.2 Inflow perpendicular to turbine row number of load observations in the time In this section inflow perpendicular to the period. Furthermore ni is the number of row of turbines (wd2) together with four loads with value Li, whereas j indicates an wind speed cases is considered. This wind individual load in the series Lj. direction case is relevant because it shows to what extent the state of each turbine is If the load is a moment (e.g. tower bending predicted if all turbines have the same moment, or blade bending moment), ni is inflow. The wind speed cases are relevant the number of load observations of level Li because they correspond to near cut-in in the time period and N = Σi ni is the (ws1), halfway nominal power (ws2), near number of load observations in that period nominal power (ws3) and constant power [e.g.
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