This document summarizes research exploring uncertainties in wind project planning due to variable wind resources. The researchers developed multivariate, multimodal models to characterize joint distributions of wind speed, direction and density. They quantified uncertainties in yearly wind distributions and proposed two models to represent these uncertainties - a parametric model considering uncertainties in distribution parameters, and a non-parametric model treating predicted wind probabilities as stochastic. The goal is to model how wind distribution uncertainties propagate into uncertainties in predicted annual energy production and cost of energy for wind projects.
This document discusses modeling uncertainty in wind farm performance caused by the unpredictable nature of wind resources. It introduces uncertainty models to characterize variability in wind speed, direction and air density over time. These uncertainty models are used to predict the range of possible annual wind power density, energy production and cost of energy for a wind farm, given uncertainties in estimating long-term wind distributions from short-term recorded data. The models aim to provide more reliable wind resource assessments and economic evaluations of wind farm projects.
Esta presentación sintetiza los fundamentos de los lenguajes de programación. Espero los sea de mucha utilidad para comprender la importancia de estos programación.
The document provides several potential holiday activity recommendations for 2009, including swimming at a new beach resort in Japan, visiting the Grand Canyon Skywalk, going to a theme park in Las Vegas, seeing a tennis match in Dubai, mountain trekking, or biking. It wishes the reader a wonderful holiday season and notes that the presentation was shared among friends to spread holiday cheer, with some images attributed to Victor Lucas in 2006.
This document summarizes research exploring uncertainties in wind project planning due to variable wind resources. The researchers developed multivariate, multimodal models to characterize joint distributions of wind speed, direction and density. They quantified uncertainties in yearly wind distributions and proposed two models to represent these uncertainties - a parametric model considering uncertainties in distribution parameters, and a non-parametric model treating predicted wind probabilities as stochastic. The goal is to model how wind distribution uncertainties propagate into uncertainties in predicted annual energy production and cost of energy for wind projects.
This document discusses modeling uncertainty in wind farm performance caused by the unpredictable nature of wind resources. It introduces uncertainty models to characterize variability in wind speed, direction and air density over time. These uncertainty models are used to predict the range of possible annual wind power density, energy production and cost of energy for a wind farm, given uncertainties in estimating long-term wind distributions from short-term recorded data. The models aim to provide more reliable wind resource assessments and economic evaluations of wind farm projects.
Esta presentación sintetiza los fundamentos de los lenguajes de programación. Espero los sea de mucha utilidad para comprender la importancia de estos programación.
The document provides several potential holiday activity recommendations for 2009, including swimming at a new beach resort in Japan, visiting the Grand Canyon Skywalk, going to a theme park in Las Vegas, seeing a tennis match in Dubai, mountain trekking, or biking. It wishes the reader a wonderful holiday season and notes that the presentation was shared among friends to spread holiday cheer, with some images attributed to Victor Lucas in 2006.
This document is a curriculum vitae for Ashok Holmukhe summarizing his professional experience and qualifications. He has over 16 years of experience in supply chain management and logistics, currently working as a warehouse manager. He holds a Master's degree in Arts and Bachelor's degree in Arts. His roles have included managing warehouse operations, inventory, logistics scheduling, and liaising with vendors.
This work was presented at 51st AIAA/SDM conference, Apr 14, 2010 in Orlando. The work presented in this paper was performed in collaboration with Prof. Achille Messac and Dr. Ritesh Khire.
Master of Science Thesis Defense - Souma (FIU)Souma Chowdhury
The document summarizes Souma Chowdhury's Master's thesis defense on developing a modified predator-prey algorithm to solve single- and multi-objective optimization problems. The predator-prey algorithm imitates interactions between predators and prey in nature. Chowdhury substantially modified the basic algorithm to make it robust and computationally inexpensive for handling optimization problems involving multiple objectives and design variables. The modified predator-prey algorithm was developed to produce well-distributed Pareto optimal solutions with fewer function evaluations compared to other evolutionary algorithms.
The planning of a wind farm, which minimizes the lifecycle project costs and maximizes the reliability of the expected power generation, presents significant challenges to today’s wind energy industry. An optimal wind farm planning strategy that simultaneously (i) accounts for the key engineering design factors, and (ii) addresses the major sources of un- certainty in a wind farm, can offer a powerful solution to these daunting challenges. In this paper, we develop a new methodology to characterize the long term uncertainties, partic- ularly those introduced by the ill-predictability of the annual variation in wind conditions (wind speed and direction, and air density). The annual variation in wind conditions is rep- resented using a non-parametric wind distribution model. The uncertainty in the predicted annual wind distribution is then characterized using a set of lognormal distributions. The uncertainties in the estimated (i) farm power generation and (ii) Cost of energy (COE) are represented as functions of the variances of these lognormal distributions. Subsequently, we minimize the uncertainty in the COE through wind farm optimization. To this end, we apply the Unrestricted Wind Farm Layout Optimization (UWFLO) framework, which provides a comprehensive platform for wind farm design. This methodology for robust wind farm optimization is applied to design a 25MW wind farm in N. Dakota. We found that layout optimization is appreciably sensitive to the uncertainties in wind conditions.
In the past decade or so, there has been appreciable progress in developing renewable energy resources; among them, wind energy has taken a lead, and is currently contributing towards 2.5% of the global electricity consumption (WWEA, 2011). On the downside, the variability of this resource itself has been one of the major factors restricting its potential growth – wind speed and direction show strong temporal variations. In addition, the distribution of wind conditions varies significantly from year to year. The resulting ill-predictability of the annual distribution of wind conditions introduces significant uncertainties in the estimated resource potential and the predicted performance of the wind farm.
A wind farm planning strategy that simultaneously accounts for the key engineering design factors, and addresses the major sources of uncertainty in a wind farm, can offer a powerful impetus to the development of wind energy. The distribution of wind conditions, including wind speed, wind direction, and air density, vary significantly from year to year. The resulting ill-predictability of the annual distribution of wind conditions introduces significant uncertainties in the estimated resource potential as well as in the predicted performance of the wind farm. In this paper, a new methodology is developed (i) to char- acterize the uncertainties in the annual distribution of wind conditions, and (ii) to model the propagation of uncertainty into the local Wind Power Density (WPD) and the farm performance: Annual Energy Production (AEP) and Cost of Energy (COE). Both para- metric and non-parametric uncertainty models are formulated, which can be leveraged in conjunction with a wide variety of stochastic wind distribution models. The AEP and the COE are evaluated using advanced analytical models, adopted from the Unrestricted Wind Farm Layout Optimization (UWFLO) framework. The year-to-year variations in the wind distribution and the quantified uncertainties are illustrated using two case studies: (i) an onshore wind site at Baker, ND, and (ii) an offshore wind site near Boston, MA. Appreciable uncertainties are observed in the estimated yearly WPDs over the ten year period - approximately 11% for the onshore site, and 30% for the offshore site. Likewise, an appreciable uncertainty of 4% is observed in the performance of an optimized wind farm layout at the onshore site.
IRJET- A Revieiw of Wind Energy Potential in Kano State, Nigeria for the ...IRJET Journal
This document reviews the wind energy potential in Kano State, Nigeria for electricity generation. It summarizes previous studies that found average wind speeds in Kano ranging from 4.3 to 9.39 m/s, indicating potential for wind energy. The document outlines methods for estimating wind energy potential based on wind speed data, height variations, power density functions, and Weibull distribution analysis. It provides context on wind turbines and the conversion of kinetic wind energy to electrical energy.
This document compares the economics of wind electricity to conventional electricity sources for captive power plants and utility companies. It presents the capital and operating costs of a 15 MW wind farm and different conventional options. Scenario I compares the levelized cost of electricity for wind vs. coal cogeneration, natural gas engines, and fuel oil engines for captive power plants over 20 years. Scenario II evaluates the costs for utility-scale coal, gas, and fuel oil plants vs. a 150 MW wind farm. The wind farm has lower lifetime costs per MWh than all fossil fuel options considered for both scenarios.
Wind Energy Technology & Application of Remote SensingSiraj Ahmed
This document discusses wind energy technology and the application of remote sensing techniques. It provides an overview of topics including wind resource assessment, site characterization, wind turbines, energy calculations, optimization opportunities, and challenges of grid integration. Remote sensing techniques like SODAR and LIDAR are described as useful tools for wind resource mapping, profiling, scanning, power curve verification, and aiding wind turbine control. Key issues discussed include the need for remote sensing at higher hub heights and offshore, its advantages over meteorological towers, and applications in areas like proactive wind turbine control.
This document describes a visually-informed decision-making platform (VIDMAP) for model-based design of wind farms. It aims to quantify and illustrate the criticality of information exchanged between different models in the wind farm layout optimization process. The platform consists of three main components: (1) uncertainty quantification to quantify variability in inputs and uncertainties introduced by upstream models, (2) sensitivity analysis to analyze sensitivity of downstream models, and (3) information visualization to visualize uncertainties and inter-model sensitivities. Sensitivity analysis is performed to quantify the sensitivity of an energy production model to first-level inputs and errors in upstream models like wind distribution, shear, turbine power response, and wake models.
This paper presents a new method to accurately char- acterize and predict the annual variation of wind conditions. Estimation of the distribution of wind conditions is necessary (i) to quantify the available energy (power density) at a site, and (ii) to design optimal wind farm configurations. We develop a smooth multivariate wind distribution model that captures the coupled variation of wind speed, wind direction, and air density. The wind distribution model developed in this paper also avoids the limiting assumption of unimodality of the distribution. This method, which we call the Multivariate and Multimodal Wind distribution (MMWD) model, is an evolution from existing wind distribution modeling techniques. Multivariate kernel density estimation, a standard non-parametric approach to estimate the probability density function of random variables, is adopted for this purpose. The MMWD technique is successfully applied to model (i) the distribution of wind speed (univariate); (ii) the distribution of wind speed and wind direction (bivariate); and (iii) the distribution of wind speed, wind direction, and air density (multivariate). The latter is a novel contribution of this paper, while the former offers opportunities for validation. Ten-year recorded wind data, obtained from the North Dakota Agricultural Weather Network (NDAWN), is used in this paper. We found the coupled distribution to be multimodal. A strong correlation among the wind condition parameters was also observed.
Variable solar generation does not inherently present a barrier to connecting to the grid. While solar output can fluctuate rapidly at a single site, geographical diversity reduces fluctuations across multiple sites. Short-term variability is reduced and has minimal system impacts when forecast and accounted for properly. As solar penetration increases, additional flexibility will be required from generation, transmission, demand response and storage to integrate variable output cost-effectively. With changes to planning and market practices, high levels of solar can be accommodated without overbuilding of conventional generation.
Wind Force Newsletter July, Edition, 2012rupeshsingh_1
This document summarizes regulatory developments related to wind power projects in India. It discusses changes to transmission tariffs in Maharashtra and retail tariffs in Gujarat that impact project viability. It also outlines draft wind power tariffs in Rajasthan and issues raised in stakeholder hearings in Tamil Nadu regarding banking of electricity and tariff rates. The document provides an overview of guidelines from MNRE on installing prototype wind turbines and a new methodology from the Ministry of Power for rating distribution companies that includes RPO fulfillment as a criteria.
In developing complex engineering systems, model-based design approaches often face critical challenges due to pervasive uncertainties and high computational expense. These challenges could be alleviated to a significant extent though informed modeling decisions, such as model substitution, parameter estimation, localized re-sampling, or grid refine- ment. Informed modeling decisions therefore necessitate (currently lacking) design frame- works that effectively integrate design automation and human decision-making. In this paper, we seek to address this necessity in the context of designing wind farm layouts, by taking an information flow perspective of this typical model-based design process. Specif- ically, we develop a visual representation of the uncertainties inherited and generated by models and the inter-model sensitivities. This framework is called the Visually-Informed Decision-Making Platform (VIDMAP) for wind farm design. The eFAST method is used for sensitivity analysis, in order to determine both the first-order and the total-order in- dices. The uncertainties in the independent inputs are quantified based on their observed variance. The uncertainties generated by the upstream models are quantified through a Monte Carlo simulation followed by probabilistic modeling of (i) the error in the output of the models (if high-fidelity estimates are available), or (ii) the deviation in the outputs estimated by different alternatives/versions of the model. The GUI in VIDMAP is cre- ated using value-proportional colors for each model block and inter-model connector, to respectively represent the uncertainty in the model output and the impact (downstream) of the information being relayed by the connector. Wind farm layout optimization (WFLO) serves as an excellent platform to develop and explore VIDMAP, where WFLO is generally performed using low fidelity models, as high-fidelity models (e.g. LES) tend to be compu- tationally prohibitive in this context. The final VIDMAP obtained sheds new light into the sensitivity of wind farm energy estimation on the different models and their associated uncertainties.
This document is a curriculum vitae for Ashok Holmukhe summarizing his professional experience and qualifications. He has over 16 years of experience in supply chain management and logistics, currently working as a warehouse manager. He holds a Master's degree in Arts and Bachelor's degree in Arts. His roles have included managing warehouse operations, inventory, logistics scheduling, and liaising with vendors.
This work was presented at 51st AIAA/SDM conference, Apr 14, 2010 in Orlando. The work presented in this paper was performed in collaboration with Prof. Achille Messac and Dr. Ritesh Khire.
Master of Science Thesis Defense - Souma (FIU)Souma Chowdhury
The document summarizes Souma Chowdhury's Master's thesis defense on developing a modified predator-prey algorithm to solve single- and multi-objective optimization problems. The predator-prey algorithm imitates interactions between predators and prey in nature. Chowdhury substantially modified the basic algorithm to make it robust and computationally inexpensive for handling optimization problems involving multiple objectives and design variables. The modified predator-prey algorithm was developed to produce well-distributed Pareto optimal solutions with fewer function evaluations compared to other evolutionary algorithms.
The planning of a wind farm, which minimizes the lifecycle project costs and maximizes the reliability of the expected power generation, presents significant challenges to today’s wind energy industry. An optimal wind farm planning strategy that simultaneously (i) accounts for the key engineering design factors, and (ii) addresses the major sources of un- certainty in a wind farm, can offer a powerful solution to these daunting challenges. In this paper, we develop a new methodology to characterize the long term uncertainties, partic- ularly those introduced by the ill-predictability of the annual variation in wind conditions (wind speed and direction, and air density). The annual variation in wind conditions is rep- resented using a non-parametric wind distribution model. The uncertainty in the predicted annual wind distribution is then characterized using a set of lognormal distributions. The uncertainties in the estimated (i) farm power generation and (ii) Cost of energy (COE) are represented as functions of the variances of these lognormal distributions. Subsequently, we minimize the uncertainty in the COE through wind farm optimization. To this end, we apply the Unrestricted Wind Farm Layout Optimization (UWFLO) framework, which provides a comprehensive platform for wind farm design. This methodology for robust wind farm optimization is applied to design a 25MW wind farm in N. Dakota. We found that layout optimization is appreciably sensitive to the uncertainties in wind conditions.
In the past decade or so, there has been appreciable progress in developing renewable energy resources; among them, wind energy has taken a lead, and is currently contributing towards 2.5% of the global electricity consumption (WWEA, 2011). On the downside, the variability of this resource itself has been one of the major factors restricting its potential growth – wind speed and direction show strong temporal variations. In addition, the distribution of wind conditions varies significantly from year to year. The resulting ill-predictability of the annual distribution of wind conditions introduces significant uncertainties in the estimated resource potential and the predicted performance of the wind farm.
A wind farm planning strategy that simultaneously accounts for the key engineering design factors, and addresses the major sources of uncertainty in a wind farm, can offer a powerful impetus to the development of wind energy. The distribution of wind conditions, including wind speed, wind direction, and air density, vary significantly from year to year. The resulting ill-predictability of the annual distribution of wind conditions introduces significant uncertainties in the estimated resource potential as well as in the predicted performance of the wind farm. In this paper, a new methodology is developed (i) to char- acterize the uncertainties in the annual distribution of wind conditions, and (ii) to model the propagation of uncertainty into the local Wind Power Density (WPD) and the farm performance: Annual Energy Production (AEP) and Cost of Energy (COE). Both para- metric and non-parametric uncertainty models are formulated, which can be leveraged in conjunction with a wide variety of stochastic wind distribution models. The AEP and the COE are evaluated using advanced analytical models, adopted from the Unrestricted Wind Farm Layout Optimization (UWFLO) framework. The year-to-year variations in the wind distribution and the quantified uncertainties are illustrated using two case studies: (i) an onshore wind site at Baker, ND, and (ii) an offshore wind site near Boston, MA. Appreciable uncertainties are observed in the estimated yearly WPDs over the ten year period - approximately 11% for the onshore site, and 30% for the offshore site. Likewise, an appreciable uncertainty of 4% is observed in the performance of an optimized wind farm layout at the onshore site.
IRJET- A Revieiw of Wind Energy Potential in Kano State, Nigeria for the ...IRJET Journal
This document reviews the wind energy potential in Kano State, Nigeria for electricity generation. It summarizes previous studies that found average wind speeds in Kano ranging from 4.3 to 9.39 m/s, indicating potential for wind energy. The document outlines methods for estimating wind energy potential based on wind speed data, height variations, power density functions, and Weibull distribution analysis. It provides context on wind turbines and the conversion of kinetic wind energy to electrical energy.
This document compares the economics of wind electricity to conventional electricity sources for captive power plants and utility companies. It presents the capital and operating costs of a 15 MW wind farm and different conventional options. Scenario I compares the levelized cost of electricity for wind vs. coal cogeneration, natural gas engines, and fuel oil engines for captive power plants over 20 years. Scenario II evaluates the costs for utility-scale coal, gas, and fuel oil plants vs. a 150 MW wind farm. The wind farm has lower lifetime costs per MWh than all fossil fuel options considered for both scenarios.
Wind Energy Technology & Application of Remote SensingSiraj Ahmed
This document discusses wind energy technology and the application of remote sensing techniques. It provides an overview of topics including wind resource assessment, site characterization, wind turbines, energy calculations, optimization opportunities, and challenges of grid integration. Remote sensing techniques like SODAR and LIDAR are described as useful tools for wind resource mapping, profiling, scanning, power curve verification, and aiding wind turbine control. Key issues discussed include the need for remote sensing at higher hub heights and offshore, its advantages over meteorological towers, and applications in areas like proactive wind turbine control.
This document describes a visually-informed decision-making platform (VIDMAP) for model-based design of wind farms. It aims to quantify and illustrate the criticality of information exchanged between different models in the wind farm layout optimization process. The platform consists of three main components: (1) uncertainty quantification to quantify variability in inputs and uncertainties introduced by upstream models, (2) sensitivity analysis to analyze sensitivity of downstream models, and (3) information visualization to visualize uncertainties and inter-model sensitivities. Sensitivity analysis is performed to quantify the sensitivity of an energy production model to first-level inputs and errors in upstream models like wind distribution, shear, turbine power response, and wake models.
This paper presents a new method to accurately char- acterize and predict the annual variation of wind conditions. Estimation of the distribution of wind conditions is necessary (i) to quantify the available energy (power density) at a site, and (ii) to design optimal wind farm configurations. We develop a smooth multivariate wind distribution model that captures the coupled variation of wind speed, wind direction, and air density. The wind distribution model developed in this paper also avoids the limiting assumption of unimodality of the distribution. This method, which we call the Multivariate and Multimodal Wind distribution (MMWD) model, is an evolution from existing wind distribution modeling techniques. Multivariate kernel density estimation, a standard non-parametric approach to estimate the probability density function of random variables, is adopted for this purpose. The MMWD technique is successfully applied to model (i) the distribution of wind speed (univariate); (ii) the distribution of wind speed and wind direction (bivariate); and (iii) the distribution of wind speed, wind direction, and air density (multivariate). The latter is a novel contribution of this paper, while the former offers opportunities for validation. Ten-year recorded wind data, obtained from the North Dakota Agricultural Weather Network (NDAWN), is used in this paper. We found the coupled distribution to be multimodal. A strong correlation among the wind condition parameters was also observed.
Variable solar generation does not inherently present a barrier to connecting to the grid. While solar output can fluctuate rapidly at a single site, geographical diversity reduces fluctuations across multiple sites. Short-term variability is reduced and has minimal system impacts when forecast and accounted for properly. As solar penetration increases, additional flexibility will be required from generation, transmission, demand response and storage to integrate variable output cost-effectively. With changes to planning and market practices, high levels of solar can be accommodated without overbuilding of conventional generation.
Wind Force Newsletter July, Edition, 2012rupeshsingh_1
This document summarizes regulatory developments related to wind power projects in India. It discusses changes to transmission tariffs in Maharashtra and retail tariffs in Gujarat that impact project viability. It also outlines draft wind power tariffs in Rajasthan and issues raised in stakeholder hearings in Tamil Nadu regarding banking of electricity and tariff rates. The document provides an overview of guidelines from MNRE on installing prototype wind turbines and a new methodology from the Ministry of Power for rating distribution companies that includes RPO fulfillment as a criteria.
In developing complex engineering systems, model-based design approaches often face critical challenges due to pervasive uncertainties and high computational expense. These challenges could be alleviated to a significant extent though informed modeling decisions, such as model substitution, parameter estimation, localized re-sampling, or grid refine- ment. Informed modeling decisions therefore necessitate (currently lacking) design frame- works that effectively integrate design automation and human decision-making. In this paper, we seek to address this necessity in the context of designing wind farm layouts, by taking an information flow perspective of this typical model-based design process. Specif- ically, we develop a visual representation of the uncertainties inherited and generated by models and the inter-model sensitivities. This framework is called the Visually-Informed Decision-Making Platform (VIDMAP) for wind farm design. The eFAST method is used for sensitivity analysis, in order to determine both the first-order and the total-order in- dices. The uncertainties in the independent inputs are quantified based on their observed variance. The uncertainties generated by the upstream models are quantified through a Monte Carlo simulation followed by probabilistic modeling of (i) the error in the output of the models (if high-fidelity estimates are available), or (ii) the deviation in the outputs estimated by different alternatives/versions of the model. The GUI in VIDMAP is cre- ated using value-proportional colors for each model block and inter-model connector, to respectively represent the uncertainty in the model output and the impact (downstream) of the information being relayed by the connector. Wind farm layout optimization (WFLO) serves as an excellent platform to develop and explore VIDMAP, where WFLO is generally performed using low fidelity models, as high-fidelity models (e.g. LES) tend to be compu- tationally prohibitive in this context. The final VIDMAP obtained sheds new light into the sensitivity of wind farm energy estimation on the different models and their associated uncertainties.
The document discusses setting up a wind power plant in Madhya Pradesh, India. It provides an overview of wind energy potential and capacity in the state. It then outlines the essential requirements for a wind farm and reasons for lack of investment. The document also describes the steps involved in building a wind farm and choosing turbine components. Finally, it presents a financial model analyzing the profitability of a potential wind power project.
IRJET - Design & Construction of Combined Axis Wind Turbine with Solar Power ...IRJET Journal
This document describes the design and construction of a combined horizontal and vertical axis wind turbine with solar panels. It begins with an introduction to renewable energy sources and the benefits of wind and solar power. It then provides details on the components and operation of horizontal axis wind turbines, followed by vertical axis wind turbines. The materials and components used in this combined design are outlined. Diagrams and tables showing the setup and power generated from each energy source are included. The conclusions discuss the results and benefits of generating clean electricity from renewable wind and solar energy.
This document discusses wind resource assessment in Meghalaya, India. It provides an overview of wind studies conducted in Meghalaya, including wind monitoring stations that have been set up. It discusses the process of wind resource assessment, including anemometry to measure wind speed and direction. Metrics used to characterize the wind resource such as wind shear, Weibull parameters, and turbulence intensity are presented. The document also discusses stand-alone and hybrid wind-solar energy systems, including specifications and costs. It proposes adding more wind-solar hybrid capacity and additional wind monitoring stations in Meghalaya over the next few years.
The planning of a wind farm, which minimizes the project costs and maximizes the power generation capacity, presents significant challenges to today’s wind energy industry. An optimal wind farm planning strategy that accounts for the key factors (that can be designed) influencing the net power generation offers a powerful solution to these daunting challenges. This paper explores the influences of (i) the number of turbines, (ii) the farm size, and (iii) the use of a combination of turbines with differing rotor diameters, on the optimal power generated by a wind farm. We use a recently developed method of arranging turbines in a wind farm (the Unrestricted Wind Farm Layout Optimization (UWFLO)) to maximize the farm efficiency. Response surface based cost models are used to estimate the cost of the wind farm as a function of the the turbine rotor diameters and number of tur- bines. Optimization is performed using a Particle Swarm Optimization (PSO) algorithm. A robust mixed-discrete version of the PSO algorithm is implemented to appropriately account for the discrete choice of feasible rotor diameters. The use of an optimal combi- nation of turbines with differing rotor diameters was observed to significantly improve the net power generation. Exploration of the influences of (i) the number of turbines, and (ii) the farm size, on the cost per KW of power produced, provided interesting observations.
The document proposes a flexible optimization framework to maximize the annual energy production of wind farms by simultaneously optimizing turbine layout and turbine type selection. It develops models for wind distribution, power generation, cost, and uses a mixed-discrete particle swarm optimization method. The framework is tested on a case study wind farm and results show up to a 6% increase in energy production over a conventional array layout approach by allowing optimization of turbine types.
This document provides a review of techniques for modelling wind turbine power curves. It discusses the need for accurate power curve models in applications like wind power assessment, turbine selection and performance monitoring. Various factors that influence power curves are outlined, including wind conditions, air density, turbine condition and IEC standard measurement methods. The paper then reviews different power curve modelling methods in the literature, including those using manufacturer data and measured turbine data. It identifies issues like differences between individual and grouped turbines. Overall the document aims to critically analyse existing modelling approaches and identify areas for further research to develop more accurate site-specific power curve models.
This paper presents a new method (the Unrestricted Wind Farm Layout Optimization (UWFLO)) of arranging turbines in a wind farm to achieve maximum farm efficiency. The powers generated by individual turbines in a wind farm are dependent on each other, due to velocity deficits created by the wake effect. A standard analytical wake model has been used to account for the mutual influences of the turbines in a wind farm. A variable induction factor, dependent on the approaching wind velocity, estimates the velocity deficit across each turbine. Optimization is performed using a constrained Particle Swarm Optimization (PSO) algorithm. The model is validated against experimental data from a wind tunnel experiment on a scaled down wind farm. Reasonable agreement between the model and experimental results is obtained. A preliminary wind farm cost analysis is also performed to explore the effect of using turbines with different rotor diameters on the total power generation. The use of differing rotor diameters is observed to play an important role in improving the overall efficiency of a wind farm.
1. Characterizing the Uncertainty Propagation from the
Wind Conditions to the Optimal Farm Performance
Souma Chowdhury*, Jie Zhang*, Achille Messac#, and Luciano Castillo*
# Syracuse University, Department of Mechanical and Aerospace Engineering
* Rensselaer Polytechnic Institute, Department of Mechanical, Aerospace, and Nuclear Engineering
52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and
Materials Conference
7th AIAA Multidisciplinary Design Optimization Specialist Conference
April 4 – 7, 2011
Sheraton Denver
Denver, Colorado
2. Wind Energy - Overview
Currently wind contributes only 2% of the total electricity
consumption (worldwide and in the US).
Wind energy is planned to account for 20% of the U.S. electricity
consumption by 2030.
Steady improvement of wind energy technologies, particularly
for offshore wind farms would help accomplish this target.
www.prairieroots.org
NREL, 2011 2
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.
Quantification of these uncertainties become all the more important
for offshore wind farms that generally require a higher investment
upfront.
Careful modeling of these uncertainties, together with their
propagation into the overall system, will allow for more credible
planning of wind projects.
3
4. Presentation Outline
• Research Objectives
• Illustrating the Uncertainties in Wind Conditions
• Modeling the Uncertainties in Wind Conditions
• Multivariate and Multimodal Wind Distribution
• Robust Wind Farm Optimization
• Concluding Remarks
4
5. Uncertainties in Wind Energy
Long Term
Uncertainties
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
5
6. Research Objectives
Characterize the uncertainty in the predicted long term
variation of wind conditions.
Model the propagation of uncertainty from the wind
conditions to the power generated by the farm.
Develop and apply a robust wind farm optimization
framework using the new uncertainty model and the
Unrestricted Wind Farm Layout Optimization (UWFLO)
method.
6
7. Uncertainties in 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 long term variation of wind conditions is generally represented using
probability distribution models.
• These probability distribution models are developed using previous
years’ recorded wind data (e.g. wind data from 2000 – 2009).
• Uncertainty is mainly introduced by the assumption, “the annual
distribution of wind conditions, estimated from preceding years’ data,
will directly apply to the succeeding years of operation of the wind farm
(being designed).”
• More often than not, the number of years for which credible wind data is
available is (for a particular site) significantly less than the designed
lifetime of the wind farm (15 – 20 years or more).
Zhang et al, 2011 7
8. Wind Distribution in Annual Power Generation
Wind Probability Distribution
• Annual Energy Production of a farm is given by:
• In farm power generation models this integral equation is expressed as:
Uncertainty in Uncertainty in
Uncertainty in
the Predicted the Annual
Wind
Yearly Wind Energy
Conditions
Distribution Production
Kusiak and Zheng, 2010; Vega, 2008 8
9. Year-to-Year Variations
Estimated Wind May not be the right Predicted Long Term
Distribution way to account for
Deterministic assumption Variation of Wind
Wind distributions estimated using the Multivariate and years)
(preceding years’ data) wind variations (succeeding
Multimodal model for a site at Baker, ND
Zhang et al., 2011 9
11. Characterizing the Uncertainties
In this paper, we model the uncertainty in the wind conditions as a
function of the uncertainty in the predicted wind distribution.
Two different models have been proposed.
Model 1: We consider the parameters of the predicted wind distribution
to be stochastic (e.g. the k and c parameters in the popularly used Weibull
distribution).
Model 2: We consider the predicted yearly wind probability value itself
to be stochastic.
11
12. Uncertainty Model 1
The uncertainty in the parameters of the wind distribution model is
represented by their variance (in this paper).
The variability in the predicted yearly probability pi of wind coming at
speed Ui, direction i, and air density ri can thus be represented as a
function of the variance of the wind distribution parameters.
qk: kth parameter; Sq: Covariance of the distribution parameters;
12
13. Uncertainty Propagation Model 1
The uncertainty propagating into the annual energy production is
modeled as a function of the variance of the wind distribution.
Uncertainty in the predicted yearly
probabilitiesin Wind Distribution
Uncertainty of the sample wind conditions
Parameters
Uncertainty in the Predicted
Yearly Probability of Sample
Wind Conditions
Uncertainty in the Annual Energy
Production
Lindberg, 1999
13
14. Uncertainty Model 2
The variability in the predicted yearly probabilities pi is directly
represented by a stochastic model.
This approach has three key advantages:
Stochastic models of the wind distribution probabilities
5
Estimated probability of wind distribution, log(p(Ui,i))
1. Can be applied to both parametric and non-parametric10-yr MMWD distribution
3 wind
2000 MMWD
models
1 2001 MMWD
2002 MMWD
-1 2003 MMWD
2. Can -3 readily applied to univariate, bivariate and multivariate wind
be 2004 MMWD
2005 MMWD
distributions
-5
2006 MMWD
2007 MMWD
2008 MMWD
3. Avoids the bias that might be introduced by the estimation of the
-7 2009 MMWD
sample-1 DPSWC
nonlinear uncertainty propagation
-9 sample-2 DPSWC
sample-3 DPSWC
-11 sample-4 DPSWC
sample-5 DPSWC
Robust wind farm optimization in this paper has been performed using
-13
-15
this model.
-17
1 2 3 4 5 6
Sample number, i
14
15. Uncertainty Model 2: Formulation
The probability of a given wind condition was observed to vary in orders
of magnitude from year to year.
We used lognormal distribution to represent the variation in the yearly
probabilities (over years) of a given sample wind condition.
We call this model the Distribution of the Probability of a Sample Wind
Condition (DPSWC).
The DPSWC model and the uncertainty in the predicted yearly wind
probability is given by
15
16. Uncertainty Propagation Model 2
The uncertainty in the annual energy production can be determined by
where
Subsequently, the uncertainty in the Cost of Energy (COE) can be
expressed as
where
Lindberg, 1999 16
17. 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.
• In this paper, we use 10-year wind data for a site at Baker, ND.
17
19. Motivation for Wind Farm Optimization
The net power generated by a wind farm is reduced by the wake effects, which
can be offset by optimizing the farm layout.
Optimally selecting the turbine-type to be installed may further improve the
power generation capacity and the economy of a wind farm.
Turbine
Rated Rotor Hub Power
Power Diameter Height Curve
www.wind-watch.org
19
20. Existing Wind Farm Optimization Methods
Array layout approach Grid based approach
Computationally less expensive. Allows the exploration of different farm
Restricts turbine locating and introduces configurations.
a source of sub-optimality Results might be undesirably sensitive
to the pre-defined grid size
• Do not simultaneously optimize the selection of wind turbines
• Majority of them do not consider an appropriate multivariate wind
distribution model
• Do not explicitly account for the uncertainties in wind conditions
Sorenson et al., 2006; Mikkelson et al., 2007; Grady et al., 2005; 20
Sisbot et al., 2009; Gonzleza et al., 2010
21. Unrestricted Wind Farm Layout Optimization (UWFLO)
Develops and uses a computationally inexpensive analytical power
generation model.
Uses a response surface based wind farm cost (RS-WFC) model.
Simultaneously optimizes the farm layout and the selection of the
turbine-type to be installed.
Accounts for the annual distribution of wind speed and direction.
The robust wind farm optimization framework, which is an evolution
from the UWFLO method, accounts for the uncertainties in wind
conditions.
Chowdhury et al., 2011 21
22. 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
22
23. Wake Model
We implement Frandsen’s velocity deficit model
Wake growth Wake velocity
a – 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 23
24. Problem Definition
We apply a 2-step optimization process:
Step-1: Minimize the Cost of Energy (COE).
Step-2: Minimize the uncertainty in the COE. The minimum COE
obtained in Step-1 is relaxed (increased) by 5%, and applied as an
additional constraint.
Farm Boundaries
Inter-Turbine Spacing
COE Constraint
24
25. Optimized Farm Layouts
Minimizing the COE has produced a well spread out farm layout, thereby
seeking to minimize the wake losses for wind coming from all directions.
Minimizing the uncertainty in COE has biased the layout towards a
North-South spread, which probably seeks to extract more power from
relatively less uncertain wind conditions.
25
26. Performance of the Optimized Farms Designs
Parameter Step 1: Minimizing COE Step 2: Minimizing
Uncertainty in COE
Overall Farm Efficiency 0.776 0.752
COE ($/kWh) 0.0185 0.0191
Uncertainty in COE 3.7% 3.6%
As expected, the reduction in the uncertainty of COE comes at the
expense of farm performance.
Expectedly, robust optimization of wind farms presents conflicting
objectives.
26
27. Concluding Remarks
This paper presents a model 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 quantification of the distribution of wind
conditions compared to traditional wind distribution models is unique in the
literature.
A generalized uncertainty model is developed by considering the predicted
yearly wind probabilities themselves to be stochastic parameters.
This generalized model can be used in conjunction with parametric/non-
parametric and univariate/bivariate/multivariate wind distribution models.
27
28. Concluding Remarks
Robust wind farm optimization was performed by (i) minimizing the
COE and (ii) minimizing the uncertainty in COE in series.
Interestingly, when we are minimizing the uncertainty, layout
optimization seeks to reduce the sensitivity of the farm power generation
to the relatively more uncertain wind speeds and wind directions.
Expectedly, it is observed that farm performance and the uncertainty in
the farm performance are conflicting objectives.
A multiobjective optimization scenario should be investigated in the
future.
Applicability of the two different uncertainty models would be explored
and compared using a parametric wind distribution model.
28
29. Acknowledgement
• I would like to acknowledge my research adviser
Prof. Achille Messac, and my co-adviser Prof.
Luciano Castillo for their immense help and
support in this research.
• I would also like to thank my friend and colleague
Jie Zhang for his valuable contributions to this
paper.
29
31. Mixed-Discrete Particle Swarm Optimization (PSO)
This algorithm has the ability to
deal with both discrete and
continuous design variables, and
The mixed-discrete PSO presents
an explicit diversity preservation
capability to prevent premature
stagnation of particles.
PSO can appropriately address the
non-linearity and the multi-
modality of the wind farm model.
31
32. 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.
32