WIND ENERGY TECHNOLOGY Theory & Practice Siraj Ahmed Professor & Former Head Department of Mechanical Engineering Maulana Azad National Iinstitute of Technology Bhopal (An Institute of National Importance) [email protected]
Wind Energy Technology State of Art Indian Perspective June 2022
Wind @ sea
Wind & nature
Wind in desert
Contents Introduction Wind Resource Site Characterization Wind Turbines Energy Calculations Optimization Opportunities Challenges of Integration Re-Powering
…Contents Current Research Areas WRA & Remote Sensing Remote Sensing Applications Siting Environmental Impact Economics Wind Farm Development Steps
Wind is air in motion Earth is tilted 23 1/2 o of its axis to plane of rotation results in Differential Heating from sun and causes pressure difference on earth Rotation of Earth Geographical factors: global as well as local Kinetic Energy in Wind around the Globe is about 0.7x10 21 J What causes wind?
Wind Power Density (WPD)
Wind Power Density (WPD) Truer Indication 24 X 365 = 8760
Fuel is wind Less than 2% of land area is needed Wind turbines design life is 20-25 years Turbines are modular and quick to install for rapid increase in generation Require no water Boost to regional economy, employment Wind Energy
Wind Energy Arrests Climate Change, Global Warming Complements other sources during high wind Conserve fossil fuels Significant role in overall energy mix Perennial Energy Resource
Wind Energy Wind is not mined Wind resource cost is constant ( Free ) Wind is not transported Wind need not be stored Wind is abundant, giving Green Power Wind is freely owned Wind is completely renewable by NATURE
WIND IN NUMBERS 600 more than million tonnes of CO 2 emissions avoided globally every year 8,000 parts in a wind turbine 270,000 more than number of wind turbines in world today 2,000 water in liters per MWh saved 3 to 6 months to recoup the energy that goes into producing a wind turbine 25 Years Life of wind turbine
WIND IN NUMBERS 3% more than global electricity by wind 17-19% global electricity by wind in 2030 8 MW Vestas largest wind turbine with rotor diameter of 164 meters > 1 million people employed worldwide in wind industry today
Wind is air in motion Wind Vector Steady Value Fluctuating Value
Stochastic in Nature Apart from the seasonal and daily variations, the wind pattern may change from year to year, even to the extent of 10 to 30 per cent
Wind Rose
Frequency Cumulative time the wind blows at prescribed values of velocity on an annual basis Persistence Continuous time the wind maintains a particular speed
Typical Wind Rose and Frequency Distribution for a Site
Vertical Profile
Turbulence Rapid disturbances in wind speed, direction, and vertical component Turbulence Intensity (TI) Relative Indicator Low, Medium or High Levels on Different Sites = Standard Deviation V = Mean Wind Speed
Wind Resource Main Parameters Annual average wind speed (U ave ) Wind Power Density (WPD) Wind Rose Prevailing Wind Direction Speed Frequency Distribution and Persistence
Wind Resource Vertical Wind Speed Profile Wind Shear Exponent ( ) Weibull Parameters: Shape Parameter (k) Scale Parameter (C) Turbulence Intensity (TI) Wind Density ( ) and its Variation Vertically and Seasonally Historical Wind Data (Fequency & Intensity of Storms)
Site Characterization Longitude, Latidute, Average Mean Sea Level Available Land Area, Soil Type Positions of Existing Roads and Dwellings Type of Land Cover (e.g. Forests, Desert etc.) Political/Administrative Boundaries National Parks, Forest Reserves, Restricted Areas Proximity to Transmission Lines Location of Obstructions Potential Impact on Local Aesthetics Cellular Phone Service for Remote Data Transfers
Topographic Screening Ridges oriented perpendicular to the prevailing wind direction Highest Elevations within a given area Locations where Local Wind can Funnel
Other Associated Parameters Power Curve of Turbine Capacity Factor (CF) Annual Energy Production (AEP) Economics Topographical Map, Contour Map Roughness Class of the Site Grid Related Studies Transmission Line Map Approach Road Other Infrastructural Facilities
Wind Turbines Small ( 100 kW) Homes (Grid-connected) Farms Remote Applications (e.g. Battery Changing, Water Pumping, Telecom Sites) Intermediate (1 00- 1000 kW) Village Power Hybrid Systems Distributed Power Large (> 1 MW) Central Station Wind Farms Distributed Power Offshore Wind
basic research into wind turbine technology Wind Turbines 1994 0.5 MW 2020 6.5 MW Average size (Onshore) Europe 3.3 MW India 2.0 MW Rotor Diameters (Current) 220 m for GE 222 m for SGRE 236 m for Vestas 242 m for MingYang
Capacity Factor Offshore 58% 2030 60% 2050 Onshore (India) 35% presently (Rotor Diameter 120 m Hub Height 140 m)
Lower specific power ratios (SP) presently in the range of 175 to 250 (W/m^2) Low Wind Turbine Concept (SP) of 100 W/m^2.
Blade Tip Rotor New turbine concept called WTx2 Two stage wind-turbine conversion Lightweight rotor mounted at the tips of the main rotor blades
Floating System Using Multiple Rotors Wind Catching System using several small rotors Slash costs for offshore wind energy Significantly larger swept area Output many times higher than a single turbine
Rotors Upscaling of rotor sizes (Offshore) Design for low wind conditions (Onshore) Advanced materials Aero-elastic design technologies such as load alleviation combined with advanced controls Modularity Compatible blade segments for optimal site-specific performance
Drive Train Geared drive trains for the onshore turbines Direct drive train for offshore ( permanent magnets)
Sustainability in the Wind Industry Total Life Cycle Emissions Global Wind Report 2021 Carbon emissions payback period 5.4 months for a 2 MW onshore 7.8 months for a 6 MW offshore turbine
Total Lifecycle Emissions NREL DATA Onshore wind 13 g CO2e/kWh Solar PV 43 g CO2e/kWh Solar CSP 28 g CO2e/kWh
Recycling About 80% turbine mass (steel, iron, copper and aluminium ) is recyclable 11-16% carbon fibre or fibreglass composites, plastics and resin, (rotor blades) difficult to recycle 65% of the blade materials can be added to the kiln to create the cement
USED BLADES old, discarded blades can be used sed to construct pedestrian bridges bus stop shelters etc.
Pause for Video on Modern Wind Turbine 3 MW Turbine to become standard for onshore (GWEC)
Energy Calculation Wind Kinetic Energy Wind Power Electrical Power C b 0.35 <0.593 “Betz limit” N g 0.75 generator efficiency N t 0.95 transmission efficiency
Wind V and E Match
Optimization Opportunities Site selection Altitude, Wind Frequency, Consistency, Grid Access, etc Turbine Selection Design (HAWTs vs VAWTs), vendor, size, quantity, Turbine Height: “7 th root law” Greater precision for local conditions Local topography (hills, ridges, …) Turbulence caused by other turbines Prevailing wind direction, wind rose, Turbulence Intensity Ground stability (support massive turbines) Grid upgrades: extensions, surge capacity, … Non-power constraints/preferences Environmental (birds, aesthetics, power lines, …) Cause radar clutter (e.g. near airports, air bases)
Economic Optimization MW Capacity Questions Economy of scale? Life? Interest rate? Operational costs? Price of Storage or Battery Bank Price of Electricity
Optimization To Date Turbine Blade Design Huge Literature Generators Already near Optimal Wind Farm Layout Modeling & Simulation Topography Alternative Site + Transmission + Storage New Challenges
Challenges of Grid Integration Growth of Wind Power: Challenge for Utilities and Grid Managers Intermittent Electricity Challenge: Integrating Large Variable Power Expected to Ride Through Disturbances Increased Transmission Capacity
How Wind Power is being Reliably and Cost-Effectively Integrated? Advanced Turbine Technology Forecasting Techniques based on Probabilistic Models Predicting Wind Power Output Hours and Days in Advance with Increasing Accuracy and Confidence Spread Wind Farms in Larger Geographical Regions
Spread Wind Farms in Larger Geographical Regions
Re Powering Replacing Older, Less Efficient Turbines with a Smaller Number of More Adavancd Models Re Power where the wind farm is commissioned in last fifteen years or more Old Turbines can be Refurbished for Re-use Before Repowering After Repowering
Current Research Areas Integration of Wind Turbines with Large Buildings Forecasting Model, Short and Long Term Penetration Limits in Grid System Integration of Wind Farms Lightning Protection of Blade and Tower Structure Numerical & Observed Wind Atlas – Modeling, Verification & Application
….Current Research Areas Stand-Alone and Non-Grid Applications Wind – Solar Hybrid Systems VAWT – Aerodynamic Studies of Different Configurations Offshore – Foundation, Cable & Peculiar Issues of Marine Operation Repowering, Techno-Economic Analysis Wind Farm Design and Flow Modelling
….Current Research Areas Nano -Composite Materials for Blade in different Environmental Conditions Complex Terrain Wind Modelling Application of Remote Sensing Wind Energy for Hydrogen Production Smart Grid, Net Metering ………………..
Wind Resource Potential Assessment
Anemometry ? Study of measuring,recording and analysing the direction and speed of the wind
Objectives of Anemometry Wind speed Wind direction Air temperature Barometric pressure Precipitation Finally, Assessing the Power in the flow of wind.
Steps in anemometry Setting up a wind-monitoring tower Installing anemometers at three or more heights Installing data logger and programming Collection & Recording of data Analysis of data
ANEMOMETER
WIND VANE or Direction Sensor
DATA LOGGER A data logger is an electronic instrument that records measurements over time. They are small, battery-powered devices that are equipped with a microprocessor, data storage and sensor.
TUBULAR WIND MAST
LATTICE WIND MAST
A three level monitoring tower
Typical Wind Monitoring Station
Tower Lightning protection Secured against vandalism Clearly marked to avoid collisions Protected against corrosion Protected from grazing animals
Obstruction Effects on Airflow
Average wind speed ?? No V, m/s 1 4.3 2 4.7 3 8.3 4 6.2 5 5.9 6 9.3 Average wind speed = 6.45 m/s
No V, m/s V 3 P, W/m 2 1 4.3 79.51 49.29 2 4.7 103.82 64.37 3 8.3 571.79 354.51 4 6.2 238.33 147.76 5 5.9 205.38 127.33 6 9.3 804.36 498.70 Average Power = 207 W/m 2
Time Series Profile of Wind Speed
Wind Speed & Wind Power Density Site: Dhanuskodi off-coast Rameshwaram (TN)
Monthly Wind Profile Diurnal Wind Profile
Wind Speed Annual Histogram @ 100m
Wind Rose at 100 m with wind speed classes
Vertical Wind Shear Profile
Inter-Annual Variation Graph for Dhanuskodi Measurement at 102m
Indian Scenario Two seasonal winds South-west monsoon (June to Sept) [Major areas in India] North-east monsoon (Oct to Dec) [Tamil Nadu]
Wind Resource Installed capacity all over World > 500 GW (2019) India 4 th > 34 GW (MNRE , 2019) Estimated gross potential at 50 m is 49 GW, 2% land availability With hub height of 100 m, rotor diameter > 100 m, projected wind potential is > 300 GW WPD cap of 200 W/m 2 at 50 m removed by MNRE for techno-economic viability of the projects since April 2011 Initiative opens up opportunity to set up wind power in low or moderate wind regime areas with higher hub height of 80-120 m
Estimation of Wind Power Potential at 50 meter and 80 Meter hub-height (Source NIWE) States / Uts Estimated potential (MW)@ 50 m @ 80 m Andaman & Nicobar 2 365 Andhra Pradesh 5394 14497 Arunachal Pradesh* 201 236 Assam* 53 112 Bihar - 144 Chhattisgarh* 23 314 Dieu Damn - 4 Gujarat 10609 35071 Haryana - 93 Himachal Pradesh * 20 64 Jharkhand - 91 Jammu & Kashmir * 5311 5685
Estimation of Wind Power Potential at 50 meter and 80 Meter hub-height (Source NIWE) States / Uts Estimated potential (MW)@ 50 m @ 80 m Karnataka 8591 13593 Kerala 790 837 Lakshadweep 16 16 Madhya Pradesh 920 2931 Maharashtra 5439 5961 Manipur* 7 56 Meghalaya * 44 82 Nagaland * 3 16 Orissa 910 1384 Pondicherry - 120 Rajasthan 5005 5050
Estimation of Wind Power Potential at 50 meter and 80 Meter hub-height (Source NIWE) States / Uts Estimated potential (MW)@ 50 m @ 80 m Sikkim * 98 98 Tamil Nadu 5374 14152 Uttarakhand * 161 534 Uttar Pradesh * 137 1260 West Bengal* 22 22 Total 49,130 1,02,788 * Estimation is based on meso scale modelling. To be validated with actual measurements
INDIAN WIND ATLAS: GIS Based @ 100 m AGL
INSTALLABLE WIND POTENTIAL @ 100m (MW) State Rank I Rank II Rank III Total Andaman & Nicobar 4 3 1 8 Andhra Pradesh 22525 20538 1165 44229 Chhattisgarh 3 57 16 77 Goa 0 0 1 1 Gujarat 52288 32038 106 84431 Karnataka 15202 39803 852 55857 Kerala 333 1103 264 1700 Lakshadweep 3 3 1 8 Rank I Waste Land Rank II Cultivated Land Rank III Forest Land
INSTALLABLE WIND POTENTIAL @ 100 m (MW) Madhya Pradesh 2216 8259 9 10484 Maharashtra 31155 13747 492 45394 Odisha 1666 1267 160 3093 Puducherry 69 79 4 153 Rajasthan 15415 3343 13 18770 Tamil Nadu 11251 22153 395 33800 Telangana 887 3348 9 4244 West Bengal 0.034 2.042 0 2 Total in MW 153020 145743 3489 302251 Total in GW 153 146 3 302
At a Galance : INSTALLABLE WIND POTENTIAL @ 100 m (MW)
INSTALLABLE WIND POTENTIAL @ 100m MNRE Targets 100 GW by 2030 NIWE 100 m height meso-scale derived wind maps and micro-scale measurement. Spatial resolution of 500 m numerical wind flow model corroborated with 1300 met-mast
INSTALLABLE WIND POTENTIAL @ 100 m GIS for regional and local wind potential with annual average wind speed, WPD and capacity utilization factor (CUF) calculated for an average 2 MW wind turbine of 100 m hub height. Weibull k and C, air density, temperature, and frequency distribution are additional wind parameters estimated
INSTALLABLE WIND POTENTIAL @ 100m Potential based on actual land use Land Use Land Cover (LULC) in GIS format Rank I Waste Land Rank II Agricultural Land Rank III Forest land Land availability estimation assuming 2 percent for windy states 0.2 percent for non-windy states
INSTALLABLE WIND POTENTIAL @ 100m Zones with 20 percent and above CUF are considered for potential estimtes Installable wind power capacity estimated by considering 6 MW per km 2 assuming 5 D X 7 D micro-siting configuration
Offshore Development
Off-Shore Development Pressure of space Greater productivity from a better wind regime Stronger Foundations Long under water cables Larger individual turbines Incubation period is about 5 years 8 MW Turbine to become standard for Offshore (GWEC)
Coastal Mast Locations
Off-Shore Higher in Indian context (> 7,500 km shore-line) Needs to be quantified with advanced techniques at Coastal Gujarat (Bay Khambat area etc.) Coastal Tamilnadu (near Rameshwaram area) Arabian sea (Coastal Gujarat) Bay of Bengal around Andamans and Nicobar and Lakshadeep and other areas
Dhanuskodi Mast Location off coast Rameshwaram (TN)
Image of Dhanushkodi 100m Mast
Offshore mean simulated wind power density at 80 m agl
Source: GWEC
Remote Sensing Application in Wind Resource Estimation
Recenet times, wind turbines are installed with increasing hub heights Hilly Regions Forested Regions Complex Moutaneous Terrain Off-shore sites Due to increasing hub height of wind turbine the cost of met towers are increasing approximately to the third power of height Cost [Height] 3 Licencing permission of installation of high met mast is time consuming
Example Measurement of wind speed at 100 m height for a modern 5 MW wind turbine hub level at a single point by cup-anemometer is not a representative speed of wind for a rotor diameter spanning > 120 m. Cup anemometer: A point measurement device The rotor blade tip from lower most point to upper most point for such wind turbine will be at a height from 40 m to 160 m
120 m mast with 2 MW Turbine (Kenersys) at Kayathar (TN)
…Example For a wind turbine of rotor diameter 120 m, the wind field over the entire plane can not be represented by a single point measurement that too especially in mountaneous and complex terrain Wind flow over the entire rotor plane, multi-point and multi-heigh t wind measurement will be required Remote Sensing Application is now available for above requirement.
Remote Sensing Application S upplements and R eplaces Tall Met Mast Wind Resource Assessment Global Wind Resource Plains Over Hilly and Mountainous Terrain Coastal Area Off-Shore Evaluating various Wind Flow Models
…Remote Sensing Application Developing Wind Atlases, Mapping Micro Level Macro Level Global Scale Power Curve Verification of wind turbines Wind turbine online and forward-feed controls
…Remote Sensing Application Wind Profiling (Vertically and Horizontally) Wind Scanning (In a plane and in a volume) Determination of Wind Loads SODAR or LIDAR at 100 m height probes a sampling volume in order of 1000 m 3
Method of obtaining information about of an object without physical contact
Met-tower and Remote Sensing Instrument with Wind Turbine Modern Turbine Remote Sensing instrument
Pause for Video on Remote Sensing
SODAR (Sonic Detection And Ranging ) Remote sensing technique Sound waves propagation and backscatter detection and ranging Sodar is direct measurement of wind speed and direction based on Doppler shift
…SODAR Based on audio-frequency technology A ground based instrument transmits sequence of short bursts of sound waves of audible range frequencies from 2000 to 4000 Hz aloft at various heights in the atmosphere in three directions
…SODAR Height at which wind speed is measured, will be determined by the delay in time in the back scatter of transmitted pulse
…SODAR Example In standard atmospheric conditions the speed of sound propagation is about 340 m/s For Example the back scatter of sound wave from a height of 170 m above the ground will be received back into the detector after delay of 1 s
…SODAR The wind speed is determined as a fuction of Doppler shift observed from the frequncy difference between the transmitted sound wave and frequncy of back scattered received by the sodar instrument
…SODAR Can work as gust warning system and for power optimization Two types of sodar systems available: mono-static and bi-static
…SODAR The carrier to noise ratio (C/N) is higher for bi-static system Bi-static continuous wave (CW) sodar system is preferred due to higher accuracy
…SODAR Sodar measurement is within accuracy of ± 3 percent as compared to cup-anemometer 1 percent uncertainty in mean wind speed results in 3 percent uncertainty in mean wind power Relatively cheaper compared to lidar with low power consumption of about 10 W per unit
SODAR AVAILABLE AT KAYATHAR
S.No. Parameter Value/Dimension 1. Maximum height 200 m 2. Wind data capture heights 40, 50, 60, 80, 100, 120, 140, 160, 180, 200 m 3. Wind speed range 0–25 m/s (0–55 mph) 4. Data upload rate Every 10 minutes, via communications link 5. SD memory card socket 2 GB SD card records a minimum of 2 years of 10 minute data. 6. Power consumption 7 W (average) 7. Solar panels 2 panels, each rated @ 85 W 8. Internal batteries Leak-proof AGM marine batteries, rated 12V, 92 Ah. 9. Footprint 2 m x 3 m (6’ x 9’) with solar panels fitted 10. Ambient temperature 40°C to +65°C (–40°F to +150°F) 11. Frequency of sound beams 4,500 Hz (nominal), with automatic temperature correction. 13. Data sampling rate 100 ‘chirps’ per sound beam per 10 minute period 14. Duration of sound ‘chirp’ 60–100 milliseconds 15. Sound level at ear level 87 dBa at 0m; 63 dBa at 50m (intermittent sound source) 16. Weight 350 to 450 kg (750 to 1000 lbs.) SPECIFICATION OF SODAR AT KAYATHAR
Measurement over the Rotor Plane
LIDAR (Light Detection And Ranging) Light waves propagation and backscatter detection and ranging using Laser beam Direct measurement of speed, direction and turbulence based on Doppler shift Back scattering of light from small aerosols suspended and moving in Atmosphere
…LIDAR Doppler shift is directly proportional to wind speed in beam direction Laser of wavelength of about 1.5 µm near infra-red is used in LIDAR Buoy mounted are useful for off shore applications
…LIDAR Two measurement principles: Continuous Wave (CW) LIDAR, and Pulsed LIDAR CW LIDAR showed higher spatial resolution and faster data acquisition and preferred for turbulence measurements Pulsed LIDAR is preferred for wind speed measurements at multiple heights simultaneously with higher ranges
WIND PROFILER Ground based system transmitting a continuous or pulsed laser beam Measures average parameters aloft in the atmosphere: vertical wind speed profiles vertical direction profiles vertical turbulence profiles It has transmition and receiving antennas combined in a single optical telescope
LIDAR FEATURES Higher accuracy: Laser is 10 6 times faster than a sound wave Antenna aperture size is based on the wave length of light. Ratio of its lense diameter to wavelength is more which results in better beam control and higher data sampling rate
…LIDAR FEATURES Can be mounted in spinner or in blades and sense the wind front 300 m to 400 m ahead of rotor and by the time wind strikes the blades it can activate the pitch of the blade Active nacelle yaw movement as forward-feed control strategy Improve power performance results due to enhanced yaw control and lead-time control of blade pitching for approaching wind front Reduces the fatigue damage from extreme wind speeds and wind shear due to forward-feed control to prolong blade life
…LIDAR FEATURES Based on volume-averaged measurement, more representative than point based cup-anemometer Mobile instruments and better suited for onshore as well as offshore applications
Mast wind speed Lidar wind speed Sodar wind speed
SCATTEROMETRY Remote sensing technique to sense wind charactristics like speed, direction and turbulence aloft the sea surface Scaterrometers are active radards that send micro-wave pulses towards the surface of sea and measure the back scattered signal due to small scale waves in the order of 20 mm Sun synchronous satellite over the ocean fitted with radar scatterometers operating at different sub-bands of micro-wave are widely used to measure near-surface wind speed and direction
SAR Satellite based sea surface micro-wave scatterometry and Synthetic Aperure Radar (SAR) find useful replacement of expensive met mast based sensors
…SAR It replaces time consuming installation of high met mast SAR is based on proxy-empirical calibration methods.
Ranges SODAR technique can be used for measurement in the range of 200 m to 600 m and LIDAR technique can be used upto 2000 m
Signal processing in remote sensing involves Doppler shift Time to travel Pattern matching Fast Fourier Transform Strength of scattering, etc. Signal Processing
Concept of REWS is more realistic than hub height single point reference wind speed for power curve verification as well as for assessment and quantification of kinetic energy in wind Rotor Equivalent Wind Speed (REWS)
Studies of mixing layer height in the atmospheric boundary layer is very important due to low level jet effects at different times of the day due to synoptic situation changes in 12 hours period For Example the difference in wind shear profile above and below 160 m level is significant for multi-MW wind turbine …REWS
LIDAR/SODAR is used with a met mast for initialization and calibration for measuring wind characteristics even upto the tip of blade in vertical position …REWS
LIDAR and Met Mast at Dhanuskodi
Time Series Comparison between Met Mast and LIDAR data Correlation Plot between Met. Mast and LIDAR data
Remote Sensing Advances Technology is developing to model the air flow over the entire wind farm offshore using Doppler radar
MICRO-SITING Art of positioning WEGs in a wind farm for maximizing its annual energy output Considering Wind regime Wind rose of the site Wake effect WEG parameters Topographic features of the terrain etc.
GEOGRAPHICAL Factors Earth quake Floods Any other calamitous conditions Terrain features
TURBINE Factors Power curve Thrust curve Class of wind turbine to match with the site conditions
Typical Layout Turbine Spacing 7 or 8 times diameter in prevailing wind direction Turbine Spacing 4 or 5 times diameter perpendicular to wind direction
Wind Turbines in a Single Row
Kayathar Location of Wind Turbine at Kayathar (TN)
Wind Farm Production Predicted Wind Climate + WTG Characteristics Gross AEP of Wind fFarm Predicted Wind Climate + WTG Characteristics + Wind Farm Layout Wind Farm Wake Losses Gross AEP of Wind Farm - Wake Losses Net AEP of Wind Farm
ECONOMICS Annual Energy Production Capital Cost Interest Rate Pay-Back Period Operation & Maintenance Cost, Insurance, Land-Lease etc. Life Cycle Cost Analysis ANNUAL ENERGY PRODUCTION DEPENDS Wind Speed Frequency Distribution of Site Power Curve of Wind Turbine Availability of Wind Turbine
Steps of Development Analyze the Wind Resource Conduct Site Analysis Establish Economics of the Project Analyze Critical Environmental Issues Identify Regulatory Frame Work Conduct Transmission Capacity Analysis
…Steps of Development Master Plan Approach (Futuristic) Maximize Energy Capture Reduce Unit Cost of Generating Electricity Re-powering
Thanking You
Weibull Distribution
The Weibull model closely mirrors the actual distribution of hourly wind speeds
Weibull Function The Weibull distribution fits quite well to frequency distribution of wind speeds v = wind speed k = shape parameter C = scale parameter
Weibull Function Cumulative distribution function Probability function
Weibull Function Average wind speed Let and
Weibull Function Average wind speed Standard deviation
Three Rayleigh distribution (k =2) are shown with same area under the curve but with different scale parameters and average wind speeds
Three Weibull distribution with same Scale Parameter C =7 and same Average Wind Speed are shown with same area under the curve but with different Shape Param eters