WFO_AIAA_FD2011 Souma


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This is my paper presentation at the AIAA Fluid Dynamics conference, 2011 in Hawaii

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  • Slowing down of growth rate might be due to various reasons, such as “limiting Gov. policies”, “lack of development in supporting infrastructure such a gridlines” – all these are restricting the spread of wind energy into the regions that are still untapped.
  • WPD: shows the resource potentialAEP: Represents the projected energy generation capacity or projected farm performanceCOE: Represents the economics of the wind farm
  • MCP is used, since onsite data is generally available only for a short time period (say 1 year), and such 1-year is not representative of the wind distribution at the site
  • Distinct advantages of the MMWD model are:1. It can represent the joint variation of wind speed, wind direction, and air density.2. It can represent multi-modally distributed data
  • The take away from this slide is: There are significant year-to-year variation in the wind distribution and the annual WPD
  • The overall point is:Assuming that the estimated distribution from recorded data is completely representative of the expected future distribution introduces significant uncertainties
  • Here we see how the WPD depends on the wind distribution p()Monte Carlo integration is used since it simple to implement, and provides a comparable or better accuracy relative to “repeated line integrals”.
  • Here we see how the Annual Energy Production depends on the wind distribution p()
  • PWU works with parametric wind distributions such as Weibull, Rayleigh, Gamma, Lognormal, etcNPWU works with parametric as well as non-parametric wind distributions such as MMWD
  • J is the Jacobian. It represents the sensitivity of the distribution to the distribution parameters
  • C_i represents the energy generated from the i-th wind condition
  • Showing that the frequency of any particular wind condition varies significantly from year to year
  • This formulation accounts for the correlation between the frequency of different wind conditions
  • This formulation neglects the correlation between the frequency of different wind conditions, but its application is practically more feasible, given the dimensions of the required stochastic model
  • Showing that the uncertainty in the distribution (blue line) forms a significant fraction of the distribution (green dashed line)
  • Shows which wind conditions are more uncertain and which ones less. In order to make reliable wind farms, the farm layout should be such that its performance is less sensitive to the more uncertain wind conditions.
  • “Underestimation”, since correlation terms are neglected.“Overestimation”, since a small data set (size =10) is used to fit a high dimensional stochastic model (dimensions=100)LND: lognormal distribution
  • The uncertainties in the payback period is also 4%. Such information is valuable when securing investment for project development, or when planning the installed capacity of the farm.
  • WFO_AIAA_FD2011 Souma

    1. 1. Modeling the Uncertainty in Farm Performance Introduced by the Ill-predictability of the Wind Resource Achille Messac#, Souma Chowdhury*, and Jie Zhang*# Syracuse University, Department of Mechanical and Aerospace Engineering* Rensselaer Polytechnic Institute, Department of Mechanical, Aerospace, and Nuclear Engineering 41st AIAA Fluid Dynamics Conference and Exhibit June 27 – 30, 2011 Sheraton Waikiki and the Hawaii Convention Center Honolulu, Hawaii
    2. 2. Wind Energy - Overview Currently wind contributes only 2.5% of the global electricity consumption (WWEA report). The 2010 growth rate of wind energy has also been the slowest since 2004 (WWEA report).. Large areas of untapped wind potential exist worldwide and in the US. NREL, 2011 2
    3. 3. Motivation One of the key factors restraining the development of wind energy is the ill-predictability of the actual power that will be generated. The power generated by a wind farm is a variable quantity that is a function of a series of highly uncertain parameters. A majority of these uncertainties are not well understood. Careful modeling of these uncertainties, together with their propagation into the overall system, will allow for 1. More credible wind resource assessment, and 2. Development of wind farms that have a reliable performance. 3
    4. 4. Uncertainties in Wind Energy Long Term Uncertainties Physical uncertainties in wind energy may be broadly classified into:Wind• Long Environmental Turbine Operational Term Uncertainties: Introduced by (i) theInterruptions Economic long term variation of Conditions Topography Factors Performance Factors wind conditions, (ii) turbine design, and (iii) other environmental, operational and financial factors Turbine Changes in Terrain/Surface Component Wind Speed Rain/Snow Component Utility Price Roughness Depreciation Breakdown ($/kWh) • Short Term Uncertainties: Introduced by boundary layer turbulence and other flow variations that occur in a small time scale (order of minutes) in Component Power Grid Changes Wind Direction Storms Vegetation Replacement Repair O&M Cost Installation of Man-made Changes is Govt. Air Density Additional Structures Policies Turbines Changes in Interest Rates & Insurance Rates 4
    5. 5. Presentation Outline• Research Objectives• Illustrating the ill-predictability of the wind distribution• Multivariate and Multimodal Wind Distribution model• Modeling the WPD, the AEP and the COE• Modeling the uncertainties in the wind distribution• Illustrating the estimated uncertainties for onshore and offshore wind sites• Concluding Remarks WPD: Wind Power Density; AEP: Annual energy Production; COE: Cost of Energy 5
    6. 6. Research Objectives Characterize the uncertainty in the predicted yearly variation of wind conditions (wind speed, wind direction and air density). Model the propagation of uncertainty from the wind distribution to the WPD, the AEP, and the COE. Validate the uncertainty models for onshore and offshore wind sites. WPD: Wind Power Density; AEP: Annual energy Production; COE: Cost of Energy 6
    7. 7. Variability of Wind Conditions The wind speed, the wind direction, and the air density at a given site vary significantly over the course of a year. The annual distribution of wind conditions also varies from year to year, although the overall pattern remains somewhat similar. The long term variation of wind conditions is generally represented using probability distribution models. These probability distribution models can be developed using previous years’ recorded wind data at the site. In a practical scenario, the Measure-Correlate-Predict (MCP) method is implemented to predict the long term distribution using short term (1-year) onsite data, and co-occurring long term data at nearby meteorological stations. Zhang et al, 2011 7
    8. 8. Uncertainties in Wind ConditionsUncertainty is introduced by: the assumption that, “The expected distribution of wind in the succeeding years of operation of the wind farm is deterministically equivalent to the wind distribution estimated from preceding years’ data, ”, and the inherent uncertainties in the MCP method.Factors that are often not explicitly considered are: A single year data at the site may not be representative of the wind pattern at the site; hence subsequent correlations may not be reliable. The wind data at the meteorological station is often recorded at lower heights (approx. 3-5 m). Extrapolation of this data using standard wind shear profiles that may be far from accurate, introduces further errors. 8
    9. 9. The Solution Economic and timeline constraints limit the feasibility of recording detailed onsite wind data over a longer time period. Uncertainties in wind predictions thus remain unavoidable. Therefore, if these uncertainties can at least be accurately quantified, a more credible farm resource assessment and a reliable farm performance projection/economic evaluation can be made. 9
    10. 10. Wind Distribution Model• In this paper, we use the non-parametric model called the Multivariate and Multimodal Wind Distribution (MMWD).• This model is developed using the multivariate Kernel Density Estimation (KDE) method.• Case studies: An onshore site and an offshore sites 26NDSU, North Dakota Agricultural Weather Network, online, 2010. 10 27NOAA, National Data Buoy Center, online, 2011.
    11. 11. Year-to-Year Variations (Onshore Site) Wind distributions estimated using the Multivariate and Multimodal model for a site at Baker, ND Zhang et al., 2011 11
    12. 12. Year-to-Year Variations (Offshore Site) Estimated Wind May not be the right Predicted Long Term Distribution way to account for Deterministic assumption Variation of Wind(preceding years’ data) wind variations (succeeding years) Zhang et al., 2011 12
    13. 13. Wind Distribution in Wind Power Density Wind Probability Distribution• WPD of a potential site is given by:• Using Monte Carlo integration, this integral equation can be numerically expressed as: Variability of Wind Uncertainty in Uncertainty in Conditions the Predicted the predicted Short time period of Yearly Wind Wind Power recorded data Distribution Density 13
    14. 14. Wind Distribution in Annual Power Generation Wind Probability Distribution• Annual Energy Production of a farm is given by: Wind Farm Power Generation• This integral equation can be numerically expressed as: Variability of Wind Uncertainty in Uncertainty in Conditions the Predicted the Annual Short time period of Yearly Wind Energy recorded data Distribution Production Kusiak and Zheng, 2010; Vega, 2008 14
    15. 15. Characterizing the UncertaintiesIn this paper, two different models have been proposed. Parametric Wind Uncertainty (PWU) Model: We consider the parameters of the wind distribution model to be stochastic - e.g. the k and c parameters in the Weibull distribution. Non-Parametric Wind Uncertainty (NPWU) Model : We consider the predicted yearly probability of a wind condition itself to be stochastic. 15
    16. 16. Parametric Wind Uncertainty (PWU) Model The uncertainty in the parameters of the wind distribution model is represented by their variance (in this paper). For a mp-parameter wind distribution model, the corresponding uncertainties in the predicted yearly probabilities of the sample wind conditions can be expressed in terms of a covariance matrix p as qk: kth parameter; q: Covariance of the distribution parameters; pi: frequency of the ith sample wind condition; 16
    17. 17. PWU Model continued… The uncertainty propagating into the AEP is modeled as a function of the uncertainty in the wind distribution. Uncertainty in Wind Distribution Subsequently, the Parameters uncertainty in the COE can be expressed as Uncertainty in the Predicted Yearly Probability of Sample Wind Conditions where Uncertainty in the Annual Energy Production Lindberg, 1999 17
    18. 18. Jacobian of Popular Univariate Wind Distribution Models 18
    19. 19. Non-Parametric Wind Uncertainty (PWU) Model : Concept Stochastic models of the wind distribution probabilities 5 Estimated probability of wind distribution, log(p(Ui, i)) The variability in the predicted yearly probabilities MMWD is directly 3 10-yr pi 2000 MMWD 1 represented by a stochastic model. 2001 MMWD 2002 MMWD -1 2003 MMWD Let us-3consider an example of the following five sample wind conditions 2004 MMWD 2005 MMWD 2006 MMWD -5 2007 MMWD 2008 MMWD -7 2009 MMWD sample-1 DPSWC -9 sample-2 DPSWC sample-3 DPSWC -11 Sample # Wind Speed (m/s) Wind Direction (deg) Air Density (kg/m3) sample-4 DPSWC sample-5 DPSWC -13 1 6.50 180 1.245 -15 2 9.75 90 1.323 3 3.25 270 1.168 -17 1 2 3 4 5 6 4 4.88 Sample number, i 135 1.284 5 11.38 315 1.129 DPSWC: Distribution of the yearly probability of the sample wind condition 19
    20. 20. NPWU Model: Formulation The probability of a given wind condition was observed to vary in orders of magnitude from year to year. To model this variability, a multivariate normal distribution of the logarithms of the predicted yearly wind probabilities is used. The uncertainty in the predicted yearly wind probabilities is then given by The uncertainty in the AEP and the COE can be determined as in PWU. 20
    21. 21. NPWU Model: Alternative The number of wind condition samples used (np) is significantly higher than the number of years for which wind data is available. The estimation of the probability pp thus requires fitting a high dimensional data with a significantly small number of data points. Alternatively, we can neglect the cross-covariance terms, thereby assuming the sample wind conditions to be independent random variables. The uncertainty in the AEP is then given by: ith diagonal element of the cov matrix Lindberg, 1999 21
    22. 22. Comparing the Two Uncertainty Models 22
    23. 23. Illustration of the Estimated UncertaintyUncertainty in the univariate distribution of wind speed: Using NPWUmodel without cross-covariance terms For a major portion of the wind distributions, there is approximately 20% uncertainty. 23
    24. 24. Illustration of the Estimated UncertaintyUncertainty in the bivariate distribution of wind speed and direction: UsingNPWU model without cross-covariance terms 24
    25. 25. Uncertainty in the WPD: Validation The uncertainty in the annual WPD can also be readily evaluated by its standard deviation over the ten years. WPD Uncertainty in the predicted WPD Reasonably accurate Underestimation Overestimation 25
    26. 26. Uncertainty in the Farm Performance• We consider a wind farm comprising 25 GE 1.5MW xle turbines at the onshore site.• Uncertainty is evaluated for the optimized farm layout, adopted from a recent publication*.• The AEP of the optimized wind farm was reported to be 4.4% higher than that of a reference wind farm having a 5x5 array layout.• The relative uncertainties in the AEP and in the COE, estimated using the NPUW model without cross-covariance, are each approximately 4%. *Chowdhury et al. 2011 26
    27. 27. Concluding Remarks This paper presents a methodology to characterize the uncertainties introduced by the ill-predictability of the long term variation in wind conditions. To the best of the authors’ knowledge, such an uncertainty model that provides a more credible assessment of the wind resource (WPD) and a more reliable prediction of the farm performance (AEP and COE) is unique in the literature. Two uncertainty models are developed: (i) Parametric Wind Uncertainty model (PWU), and (ii) Non-Parametric Wind Uncertainty model (NPWU). The relative uncertainty in the predicted yearly wind distribution was found to be as high as 20% (approx.) for the onshore and the offshore sites. 27
    28. 28. Concluding Remarks The parametric model provides a reasonably accurate estimation of the uncertainty in the WPD. Further advancement of the non-parametric model is necessary in order to provide accurate uncertainty quantification. Significant uncertainties were also observed in the AEP and the COE of a wind farm with an optimized layout. Therefore, an exploration of the trade-offs between optimal and reliable wind farm design is crucial in wind project planning. Future research should also investigate the interaction of “the uncertainties occurring due to year-to-year variations” with “the uncertainties introduced by the MCP method”. 28
    29. 29. Thank you Questions and Comments 29
    30. 30. UWFLO Cost Model• A response surface based cost model is developed using radial basis functions (RBFs).• The cost in $/per kW installed is expressed as a function of (i) the number of turbines (N) in the farm and (ii) the rated power (P) of those turbines.• Data is used from the DOE Wind and Hydropower Technologies program to develop the cost model. 30
    31. 31. Prediction of 5-year wind distribution 31
    32. 32. UWFLO Power Generation Model  Turbines locations are defined by a Cartesian coordinate system  Turbine-j is in the influence of the wake of Turbine-i, if and only if Avian Energy, UK Effectiveapproach allows us to consider turbines with differing rotor-  This velocity of wind  Power generated by Turbine-j: approaching Turbine-j: diameters and hub-heights 32
    33. 33. Wake Model We implement Frandsen’s velocity deficit model Wake growth Wake velocity – topography dependent wake-spreading constant Wake merging: Modeled using wake-superposition principle developed by Katic et al.: Frandsen et al., 2006; Katic et al.,1986 33