WFO TIERF2011 Souma

Exploring and Quantifying the Role of Resource Uncertainties in Wind Project Planning Achille Messac#, Souma Chowdhury*, Jie Zhang*, and Luciano Castillo**# Syracuse University, Department of Mechanical and Aerospace Engineering* Rensselaer Polytechnic Institute, Department of Mechanical, Aerospace, and Nuclear Engineering**Texas Tech University, Department of Mechanical Engineering 1000 Islands Energy Research Forum Nov 11 – 13, 2011 Alexandria Bay, NY

Wind Energy - Overview Currently wind contributes 2.5% of the global electricity consumption. The growth rate of wind energy has however not been consistent (WWEA report). One of the primary factors affecting its growth is the variability of the resource itself. www.prairieroots.org 2

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 3

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. Zhang et al, 2011 4

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”. Further uncertainties can also be introduced by the assumptions in the Measure-Correlate-Predict (MCP) method used for long term wind resource modeling.[MCP: It is a method implemented to predict the long term wind data/distribution atthe site using short term (1-year) onsite data, and the co-occurring data at nearbymeteorological stations (that also have long term data).] 5

Presentation Outline• Research Objectives• Wind Distribution Modeling• Uncertainties in the Yearly Wind Distribution• Modeling the Wind Uncertainties• Quantifying and Illustrating the Resulting Uncertainties in the farm AEP and COE.• Concluding Remarks AEP: Annual Energy Production; COE: Cost of Energy 6

Research Objectives Model the yearly (and long term) joint distribution of wind speed, wind direction, and air density, using recorded site data. Characterize the uncertainty in the yearly distribution of wind conditions. Model the propagation of the wind distribution uncertainty into the predicted Annual Energy Production (AEP) and Cost of Energy (COE). 7

Wind Distribution 8

Existing Wind Distribution Models Popular wind distribution models include variations of Weibull, Lognormal, Rayleigh, Beta, inverse-Gaussian and Gamma distributions. These models can be broadly classified into:  univariate and unimodal distributions of wind speed  bivariate and unimodal distributions of wind speed and wind direction These wind distribution models make limiting assumptions regarding the correlativity and the modality of the distribution of wind conditions. 9

Multivariate and Multimodal Wind Distribution (MMWD) Model• MMWD can capture the joint variation of wind speed, wind direction, and air density.• MMWD allows representation of multimodally distributed data.• MMWD is developed using Kernel Density Estimation.• Case studies: 26NDSU, North Dakota Agricultural Weather Network, online, 2010. 10 27NOAA, National Data Buoy Center, online, 2011.

Kernel Density EstimationUnivariate Kernel Density EstimationMultivariate Kernel Density EstimationOptimal Bandwidth Matrix Selection MISE: Minimum Integrated Squared Error 11

Wind Distribution Results Onshore Offshore Wind data is observed to be multimodal 12

Comparison of Distribution Accuracies To compare the distributions, we use coefficient of determination, (R2) that is a measure of the agreement between an estimated distribution and the recorded data. Higher the value of R2, better the distribution 13

Uncertainties in the Yearly Wind Distribution 14

Year-to-Year Variations (Onshore 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 15

Wind Distribution in Annual Power Generation Wind Probability Distribution• Annual Energy Production of a farm is given by:• This integral equation can be numerically expressed as: Kusiak and Zheng, 2010; Vega, 2008 16

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. 17

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; 18

PWU Model (continued…) The uncertainty propagating into the AEP is modeled as a function of the uncertainty in the wind distribution. Subsequently, the uncertainty in the COE can be expressed as where Lindberg, 1999 19

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

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 10% uncertainty. 21

Illustration of the Estimated Uncertainty Uncertainty in the bivariate distribution of wind speed and direction, using NPWU model without cross-covariance termsUncertainty in Yearly Wind Distribution Wind Distribution Offshore Onshore 22

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 23

Concluding Remarks This research developed a distribution model that represents the joint variation of wind speed, wind direction, and air density. However, the predicted annual distribution of wind conditions themselves varied significantly from year to year. A novel methodology to characterize these yearly wind distribution uncertainties was therefore developed. Uncertainty propagation models were developed to quantify the resulting uncertainties in the farm AEP and COE. The relative uncertainty in the predicted yearly wind distribution was found to be as high as 10% (approx.) for the sites considered. The uncertainty in the AEP and COE of an optimized farm layout was found to be as high as 4% of their nominal values. 24

Future Research• Future research would investigate the impact of the wind resource uncertainties on farm layout 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”. 25

Thank you Questions and Comments 26

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. 27

Prediction of 5-year wind distribution 28

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 29

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 30

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. 31

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. 32

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 33

Jacobian of Popular Univariate Wind Distribution Models 34

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 35

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 36

Comparing the Two Uncertainty Models 37

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 38

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: 39

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”. 40

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