corso di impianti eolici - politecnico di milano · mi tecnico lano corso di impianti eolici ......

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Impianti Eolici

Alessandro Croce Dipartimento di Scienze e Tecnologie Aerospaziali

Politecnico di Milano Milano

Anno Accademico 2015-16

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2 POLI-Wind Research Lab

The Wind Resources

Understanding the characteristics of the wind resource is critical to all aspects of wind energy:

• Identification of suitable sites (siting);

• Prediction of the economic aspect ;

• Design of wind turbine;

• Evaluation of the grid effects.

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Wind Variability

Wind exhibits variability in space and time over very broad scales

Spatial variability:

• Hemispheres

• Climatic regions

• Physical geography (land, see, mountains, plains, …)

• Local orography

• Vegetation (influence roughness, moisture, absorption/reflection of solar radiation)

Temporal variability:

• Long term (poorly understood)

• Yearly (El Niño/La Niña, North Atlantic Oscillation, …)

• Synoptic (due to large scale weather patterns, high/low pressure, cold/warm fronts, …)

• Diurnal

• Turbulence

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Temporal Variability

van der Hoven wind spectrum

Synoptic peak

Diurnal peak

Turbulent peak Spectral gap (little energy between 10min and 2h)

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Probability distribution function, used to describe the distribution of wind speeds over an extended period of time

Weibull distribution:

cumulative probability function (i.e. probability that: ):

probability density function:

where:

scale parameter of the Weibull function [m/s]

shape parameter of the Weibull function [-]

wind speed

average wind speed

gamma function

Wind Speed Distribution

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Gamma function

𝑘 = 2 ⟹ Γ 1 +1

𝑘= Γ

3

2=

𝜋

2

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Weibull distribution

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A special case of the Weibull distribution is with k=2 which is a fairly typical value for many locations

Rayleigh distribution:

cumulative probability function (i.e. probability that: ):

probability density function:

where:

(annual) average wind speed (at hub height).


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Rayleigh distribution

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Annual energy yield given power curve P=P(V) :

where: Y=8760 hours/year

Power plants do not work at full power at all times

Wind turbines:

• Environmental variability (wind and air density)

• Availability (fraction of time WT is able to produce electricity, i.e. not down for scheduled or unscheduled maintenance) (typically > 95%)

Capacity factor:

ratio between the produced energy in given period and the theoretical max energy (i.e. the nameplate power times the period length):

Equivalent hours:

hours required to produce same energy in a given period if operating at nameplate power:

AEP VS Capacity Factor

𝐶𝐹 = 𝐴𝐸𝑃

𝑌 ∙ 𝑃𝑟𝑎𝑡𝑒𝑑

𝐸𝑞𝑣𝐻 = 𝐴𝐸𝑃

𝑃𝑟𝑎𝑡𝑒𝑑= 𝑌 ⋅ 𝐶𝐹

𝐴𝐸𝑃 = 𝑌 𝑃(𝑉)𝑓𝑟 𝑉 𝑑𝑉𝑉𝑜𝑢𝑡

𝑉𝑖𝑛

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Example 1:

VAVE = 7.5m/s (class III)

Vrated = 12m/s

Example 2:

VAVE = 7.5m/s (class III)

Vrated = 10m/s

Example 3:

VAVE = 10.5m/s (class I)

Vrated = 12m/s

AEP VS Capacity Factor

CF = 34.98%

EqvH = 3064 h/yr

CF = 43.47%

EqvH = 3808 h/yr

CF = 50.65%

EqvH = 4437 h/yr

Y = 8760 h/yr

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Example:

Wind speed measured at 80m;

Period: 01 January 2011 – 31 December 2011

Data available: 99.6 % (3352bins on a tot of 3365);

Location: South of Italy.


time stamp [GMT+00:00] Met Mast 1: Wind speed 10min [m/s]

Met Mast 1: Abs. wind direct. 10min [°]

Met Mast 1: Outd.temp. nacelle 10min [°C]

Met Mast 2: Wind speed 10min [m/s]



time stamp [GMT+00:00] Met Mast 1: Wind speed 10min [m/s]



Met Mast 2: Wind speed 10min [m/s]



01/01/2011 00:00 1,1 306 7 0,5 204 6 […] […] […] […] […] […] […]

01/01/2011 00:10 0,7 297 7 1,3 204 6 31/12/2011 22:30 7 229 7 7,8 309 7

01/01/2011 00:20 1,3 293 7 1,1 204 6 31/12/2011 22:40 7,1 229 7 7,9 309 7

01/01/2011 00:30 1,3 265 7 0,7 204 6 31/12/2011 22:50 6,8 227 7 7,8 308 7

01/01/2011 00:40 1,0 300 7 1,0 357 6 31/12/2011 23:00 6,8 226 7 7,6 305 7

01/01/2011 00:50 1,8 303 7 0,6 355 6 31/12/2011 23:10 6,5 224 7 7 303 7

01/01/2011 01:00 1,6 14 7 1,2 334 6 31/12/2011 23:20 6,1 223 7 6,7 302 7

01/01/2011 01:10 1,1 37 7 1,1 299 7 31/12/2011 23:30 6,2 221 7 7 301 7

01/01/2011 01:20 0,9 10 7 1,1 299 7 31/12/2011 23:40 6,3 219 7 7,3 300 8

01/01/2011 01:30 1,3 338 7 0,8 304 7 31/12/2011 23:50 6,7 219 7 7,8 299 8

[…] […] […] […] […] […] […] 01/01/2012 00:00 6,4 217 7 7,4 296 8

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◀ Measured data

▼Measured data

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◀ Measured data

▼ Probability density function

Weibull parameters

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Weibull parameters

◀ Probability density function

▼ Probability density function and complementary cumulative probability function

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Example:

Wind speed measured at 80m;

Period: 07 May 2008 – 31 Nov 2008 (208 days);

Data available: 99.07 % (29617 bins on a tot of 29895);

Location: Calabria (south Italy).


Complementary cumulative distribution function

Probability function

Weibull parameters

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Wind rose diagram:

• Speed

• Direction

• Frequency

Wind Direction Distribution

(30 year data for April in Fresno, CA, source: http://www.wcc.nrcs.usda.gov/)

(La Guardia, NY, source: http://www.breeze-software.com)

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Turbulence

Dissipation of kinetic energy into thermal energy via the creation and destruction of eddies in the flow

• Decomposition of velocity components:

• Short term mean: (> than turbulent fluct’s, < than diurnal variations, spectral gap suggests 10 min)

• Zero mean fluctuations:

• Standard deviation:

• Turbulence intensity (TI):

Typical values: TI≈0.1 ÷ 0.4 (high TI/low U and low TI/high U)

Dependence on terrain features

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Vertical Wind Profile (Shear)

Wind speed increase with height within the atmospheric boundary layer Strong effect on power production and fatigue loading

Turbulence intensity s1= 5%

Actual wind can be seen as superposition of vertical shear

and turbulent fluctuations ▶

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Vertical Wind Profile (Shear)

Profile models: • Logarithmic (derived from BL theory):

• Power law (flat plate, but also empirical):

𝒛𝒓= reference height

𝒛𝟎= surface roughness length

(crops, trees, buildings, waves, …)

𝜶 = wind shear (power law) exponent

(stability, terrain features, wind speed, …)

(typically 0.2 on-shore, 0.14 off-shore)

Normal Wind Profile (NWP):

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Extreme Wind Conditions

Deterministic extreme conditions (IEC 61400 Ed. 2):

• Gust models

• Wind shear events

• Rapid changes in wind speed and direction

(assumed models, bear little resemblance with actual wind events)

Extreme wind speed model:

Normal Turbulence Model (NTM)

Turbulence standard deviation:

𝑰𝒓𝒆𝒇 = turbulence intensity at 15 m/s

𝑽𝒓𝒆𝒇 = 10 min avrg reference wind speed

𝑽𝒉𝒖𝒃 = 10 min avrg hub speed

Class I II III S

Vref (m/s) 50 42.5 37.5

Values specified by designer

A Iref 0.16

B Iref 0.14

C Iref 0.12

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Extreme Operating Gust (EOG):

𝝈𝟏 = turbulence standard deviation

𝝺𝟏 = turbulence scale parameter

𝑫 = rotor diameter

𝑻 = gust duration (𝑻 = 𝟏𝟎. 𝟓 𝒔) )


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Extreme Direction Change (EDC):

Duration 𝑻 = 𝟔 𝒔

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Extreme coherent gust with direction change (ECD):

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Extreme wind shear (EWS):

Vertical shear:

Horizontal shear:

𝜶 = 𝟎. 𝟐 𝜷 = 𝟔. 𝟒 𝑻 = 𝟏𝟐 𝒔

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Effects of Roughness

Changes smooth-rough and rough-smooth:

(source: Wegley et al., PNL-2521 rev. 1, 1980)

In equilibrium with local roughness

conditions

Transition and equilibrium heights depends on type of and distance from change

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Effects of Obstacles

Obstacles generate speed deficit, turbulence increase, change in shear


Recirculation region

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Topographical Effects, Complex Terrains

Flat terrain: • No 𝒉/𝒍>1/50 within 4 km • Rotor lowest point > 𝟑𝒉 within 4 Km • 𝑯 < 𝟔𝟎 m within 11.5 Km Complex otherwise Orientation and shape of ridges can be exploited to improve energy capture:

ℎ

𝑙 > 3ℎ

𝐻


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Complex Terrains

Acceleration effects of ridges:


Ideal triangular ridge shape

Fluctuations not much affected, but mean speed increases (hence TI decreases)

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