WIND POWER Technical-economic issues affecting the

Summer School on Energy, Giacomo Ciamician, 17-21 June 2019

Filippo SpertinoDepartment Energy, Politecnico di Torino

Kreuzbergpass (BZ), Italy

June 18th 2019

WIND POWERTechnical-economic issues affecting the

capacity factors of wind energy

Summer School on Energy Giacomo Ciamician


F. Spertino

Aerodynamics and Mechanical Aspects of

Wind Turbines

Filippo Spertino

Politecnico di Torino, Energy Department, Torino, Italy


F.Spertino

ENERGY CONVERSION IN A WIND TURBINE (1)

The energy conversion efficiency depends on the wind turbine

velocity with respect to the wind speed (tip speed ratio)

The most efficient

WT is the 3 blade

rotor with lower tip

speed ratios (5-10)

The efficiency limit is provided by the actuator disc theory: it is defined

as the power coefficient Cp =16/27≈0.59 (from Betz)

The Horizontal Axis Wind

Turbines (HAWTs) are more

efficient than the Vertical Axis

Wind Turbines (VAWT)


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ENERGY CONVERSION IN A WIND TURBINE (2)

Regarding a horizontal-axis wind turbine, these phenomena occur

in a stream tube with stationary flow:

u1

u2 < u1

p1 p2 = p1

u1

u2 < u1

p1 p2 = p1

1. surface expansion

2. kinetic energy reduction

3. pressure increment before and after the blades

By applying Bernoulli’s principle (not

turbine section):

m is mass, u wind speed, g gravitational

acceleration, h height, p pressure and Vol

is volume

Continuity equation for mass

flow rate = dm/dt = u A = const

energy = 0.5 m u2 + m g h + p Vol

is air density, and A is area of

cross section

EBern=const1

EBern =const2<const1

const.


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STRUCTURE OF A HA WIND TURBINE

Turbines are placed at heights up to 100m with respect to the ground bytowers. The blades of fiberglass orcarbon-fiber (3 with diameters from 30to 100 m) are designed so as tomaximize the lift. The hub does rotatethe low-speed shaft (10-30 rpm): thegearbox does rotate the high-speedshaft (1000-1500 rpm).

The high-speed shaft provides the torque to the electric generator.

All the components are into the nacelle.

Typical mechanical regulations are: pitch control of the blades, yaw

control. The pitch control can be towards the stall or the feather. The

yaw control allows to track the wind direction.

A brake can shut down the wind turbine in extreme wind conditions.

Hub with pitch

mechanism

Rotor

Tower

Yaw system

Nacelle

Brake

Gearbox

Generator

Electric Control


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OPERATING PRINCIPLE OF A WIND TURBINE (1)For a blade (non-inertial reference frame) the aerodynamics is

described by the following quantities, velocities and forces applied to

the centre of pressure:

angular velocity of rotation;

U unperturbed wind speed; V peripheral speed; W relative speed;

angle of attack and pitch angle measured with respect to the chord lineof the profile;

FL lift and FD drag forces; FC torque and FS thrust components; centrifugalforce not represented.

U

Vx = Rx

Wx

FL

FD

Fris

FC

FS

U

Vx = Rx

Wx

FL

FD

Fris

FC

FS

S S’

U

Rx

S S’

U

Rx

Lift contribution is one order of magnitude higher than drag


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OPERATING PRINCIPLE OF A WIND TURBINE (2)

2

2

1WA

FC L

L

Within the low-mid wind speed, the goal is to maximize the ratio “lift to

drag”. It is possible to achieve this by appropriate angles of attack in

the range 5°—15°.

2

2

1WA

FC D

D

cossin DLC FFF

sincos DLS FFF

Feather

Stall


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0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 2 4 6 8 10 12 14 16

Co

eff

icie

nt o

f P

ow

er C

p

Tip speed ratio l

= 0 = 6

= 4

= 2


Each turbine is characterized by a performance curve which links thecoefficient of power Cp and the tip-speed ratio l.

The pitch regulation toward feather is used to reduce the powerincrement, after the centrifugal limit, even if wind speed is increasing

U

R

U

Vctg

l

3

2

1UA

PC mec

P

V = R

U

W

FC

FL V = R

U

W

FC

FL


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0

200

400

600

800

1000

0 5 10 15 20 25 30 35 40 45 50

B lade s peed (rpm)

Me

ch

an

ica

l p

ow

er

(kW

)

U = 5 m/s

U = 7 m/s

U = 9 m/s

U = 11 m/s

U = 13 m/s

P = P max

= const.

Centrifugal limit

It is advisable to track the maximum power points with the variations of

the wind speed: the variable speed control allows to achieve this goal


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The gearbox is composed of some stages (often 3 with ratios 1:2,

1:3, 1:5), ensuring its mechanical conversion efficiency higher than

90% within the useful range of wind speeds.

STRUCTURE OF A GEARBOX


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STRUCTURE OF AN INDUCTION GENERATOR

An electric machine is characterized by an external stator and an

internal rotor. The mutual magnetic flux enables the power exchange

between stator winding and rotor winding through the airgap

stator

stator yoke

rotor yoke

rotor slot

stator slot

shaft

statortooth

wings of the case(heat sink)

rotor tooth squirrel cage rotor

main fluxleakage flux (stat.) (rot.)

airgap


F. Spertino

Electrical Aspects and Anemometry of Wind

Turbines

Filippo Spertino



F. Spertino

EQUIVALENT CIRCUITS OF ELECTRIC MACHINES

E

XS

+

U

I+

E

XS

+

I+

Single-phase circuit for induction machine(IM) as a generator with negative slip

Synchronous generator (SG)

+

E(s)

I

U

+

RFXM

RCuXD

+

E(s)

I

U

+

RFXM

RCuXD

For IM it is possible to calculate thecurrent responsible for the torque, themechanical power and the rotor joulelosses

The electric generators, used in the fixed-speed and the variable-

speed wind turbines, are asynchronous and synchronous machines

p

ps

mec

0

0

slip s measures the deviation of magnetic-field speed 0/p

w.r.t. the rotor speed mec

2

2'

Drot

stat

T

Xs

RR

UI

2'13 Trotmech IR

s

sP

2'3 Trotjrot IRP

mech

Fjrotjstatmechelectr

P

PPPP

23 Tstatjstat IRP

S

TjX

UEI


F. Spertino

OPERATION OF AN INDUCTION GENERATOR

An induction machine is characterized by different

mechanisms of losses and non-idealities:

1. Joule losses in the stator and rotor windings(resistance in series).

2. Leakage fluxes (inductive reactance in series).

3. Iron losses due to hysteresis and eddy currents(resistance in parallel).

4. Remarkable magnetizing current (inductivereactance in parallel).


F.Spertino

GB: gearbox - IG: induction generator with squirrel cage – IGpermits slightly variable speed with respect to the rotating field (slip =-1% up to -10% with wind gusts)

SCHEMES OF WIND TURBINES ON THE MARKET

Fixed-speed scheme

(sites with strong wind, IEC classes I and II)

PMSG, Permanent Magnet Synchronous Generator with Full ScalePower Converter (FSPC) with wide slip: 30% and separate

regulation of active power P and reactive power Q; otherwise theDFIG solution equipped with gearbox

3

==

3

PMSG

Grid

= 15-55%

= 95-99%

Variable-speed scheme

(sites with moderate wind, IEC class III)

IGGB3 power

transformer

Grid

= 8-50% = 90-98%

= 95%

3 power

transformerFSPC


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IM

T3

BEC

RC GC

L-C filter

DC link

CRC CGC

A SOLUTION FOR VARIABLE SPEED TURBINES (1)

The use of bidirectional electronic converter (BEC) optimizes the

efficiency with variable speed concept in a wound rotor IM: the

electric torque is adjusted apart from the aerodynamic torque.

power flow

dt

dJTT rot

electblade

DFIG (Doubly Fed Induction

Generator) concept

rot

rotor converter commands

grid converter commands

MV/LV transformer


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-40

-30

-20

-10

0

10

20

30

40

1200 1300 1400 1500 1600 1700 1800

Rotor speed (rpm)

Ele

ctr

o-m

echanic

al to

rque (

kN

m)

R'app = 0

R'app > 0

Pgap Pjr

PBEC

The rotor speed can be increased, recovering power into the grid (super-

synchronous speed) with extended range up to 30%: the efficiency is high

due to the low losses in BEC

2

2''

D

approt

stat

T

Xs

RRR

UI

2''13 Tapprotmech IRR

s

sP

2'3 TappBEC IRP

2'3 Trotjrot IRP

mech

Fjrotjstatmechelectr

P

PPPP

2

''

3 T

approt

gap Is

RRP

23 Tstatjstat IRP

power recovery


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-40

-30

-20

-10

0

10

20

30

40

1200 1300 1400 1500 1600 1700 1800

Rotor speed (rpm)

Ele

ctr

o-m

echanic

al to

rque (

kN

m)

R'app = 0

R'app < 0

Pmec

Pjr PBEC

On the other hand, the rotor speed can be also decreased, extracting

power from the grid (sub-synchronous speed) with extended range

down to 30%: that gives high efficiency with low wind speed.


power extraction


F.Spertino

The dependence of blade/mechanical powers and generator speed on

the wind speed are the most important figures of a WT. The thrust limit

at wind speed =25 m/s is not shown.


0

300

600

900

1200

1500

1800

4 6 8 10 12 14 16

wind speed (m/s)

me

ch

an

ica

l p

ow

er

(kW

),

roto

r s

pe

ed

(rp

m)

0

3

6

9

12

15

18

pit

ch

an

gle

(

°)

P blade

rot

P mec

β

centrifugal limit

bending moment

limit


F.Spertino

The suitable BEC control by the apparent resistance R’app permits to

obtain the desired electrical power in a 850-kW wind turbine.


-100

0

100

200

300

400

500

600

700

800

900

4 6 8 10 12 14 16

wind speed (m/s)

ele

ctr

ica

l p

ow

er

(k

W)

-2.7

-2.4

-2.1

-1.8

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

ap

pa

ren

t re

sis

tan

ce

(Ω

)

P BEC

R' app P el


F. Spertino

CHARACTERIZATION OF THE SOURCE (1)

An air mass, with density 1,225 kg/m3 (sea level, 15 °C), speed U

(m/s) through a cross section of area A (m2), has a power density inW/m2 (from derivative of kinetic energy):

Within speed values of 8-10 m/s, the power density is within 300-600W/m2, whereas with 20 m/s a power density of 5 kW/m2 can beachieved.

The air density is function of temperature T and pressure B; decreases

with rises in height with respect to the ground (e.g., 1.11-1.12 kg/m3 at1200-1300 m of altitude)

3

2

1U

A

P

TR

B

0

R0 = 287.05 J/(kgK) is the gas constant of dry air


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Wind parameters are speed and direction (cup and vane anemometersinstalled at height of 10-15 m on a mast). The experimental datathrough 1 year should be collected with a sampling rate of 1 Sa/s andevery 10 min the statistics include:

mean value Umean

standard deviation Umean

maximum value

minimum value0

2

4

6

8

10

12

N

N-NE

NE

NE-E

E

E-SE

SE

SE-S

S

S-SW

SW

SW-W

W

W-NW

NW

NW-N

NE and SW arethe maindirections

Turbulence intensityderived by the first twoparameters


F. Spertino


Data are transferred at the hub height, since wind speed dependson height (with positive increment, wind shear) and on terrain(roughness height Z0: low values for flat surfaces, e.g., sea).

0

20

40

60

80

100

2 3 4 5 6 7 8 9 10

wind speed (m/s)

Heig

ht

wit

h r

esp

ect

to t

he

gro

un

d (

m)

Zo

0

0

0

ln

ln

,

Z

h

Z

h

uZhuref

ref


F. Spertino

The data are arranged in bins of 0,5 m/s in order to calculate meanvalue and standard deviation. The Weibull distribution is the best choicerather than the Gauss distribution: it is function of 2 parameters (shapefactor k and scale factor c).


0

0,01

0,02

0,03

0,04

0,05

0,06

0,07

wind speed (m/s)

pro

bab

ilit

y d

en

sit

y

0 5 10 15 20 25 30 35

k

c

Uk

ec

U

c

kUf

1


F. Spertino


If k = 2, Weibull distribution becomes the Rayleigh distribution withonly one parameter (average wind speed).

The statistic analysis is required because the turbine efficiency isstrongly variable with the speed variations.

0

0,1

0,2

0,3

0,4

0,5

0 2,5 5 7,5 10 12,5 15 17,5 20 22,5 25

wind speed (m/s)

Weib

ull d

istr

ibu

tio

n

0

0,2

0,4

0,6

0,8

1

Cu

mu

lati

ve p

rob

ab

ilit

y

k = 2 ; C = 5,5

k = 2,4 ; C = 8,5

k

c

U

eUF

1


F.Spertino

The calculation of energy production is performed by the product, for

a wind speed at hub height, of the “electric power vs. speed” curve

and the wind frequency curve (usually the Weibull distribution)

CALCULATION OF ENERGY PRODUCTION

0

100

200

300

400

500

600

700

800

900

0%

3%

6%

9%

12%

15%

18%

21%

24%

27%

0 2 4 6 8 10 12 14 16

ele

ctri

c p

ow

er

Pel

(kW

)

We

ibu

ll fr

eq

ue

ncy

in p

erc

en

t

wind speed U (m/s)

964 h -> 11% of 1 year

100 kW -> bin [5-6] m/s with 5.5 m/s as central value

Pel(U)

fW(U)

A 850-kW turbine produces ≈765

MWh/year with final yield = EAC /Prated

≈ 900 h/year

Capacity factor is the ratio of final

yield to the hours of 1 year

EAC /(8760Prated) Here ≈ 0.1, very

low


F.Spertino

Advantages

– Renewable source

– Absence of atmospheric pollution

– High energy density

– Costs similar to conventional technologies

Drawbacks

– Intermittent production: impact on the grid stability

– Noise and aesthetic impact: installation away from cities and towns

– investments on the transmission system specially for off-shore wind farms

ADVANTAGES AND DRAWBACKS OF WIND ENERGY


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Exercise Calculation of Productivity

from a Wind Turbine

Filippo Spertino



F. Spertino

During the exercise, we use the following equation tocalculate the productivity EAC of a wind turbine.The power curve of WT is given in terms of a sequence ofelectric power values, each one corresponding to aspecific wind speed from cut-in to cut-out wind speeds.The relative frequency of wind resource is computed atthe height of the WT hub:

where:Pk (U) value of electric power corresponding to a value of U;fk (U) relative frequency of wind resource for a value of U.

Calculation of Productivity

EAC = 8760 h k Pk(U) fk(U)

http://www.soda-pro.com/web-services/meteo-

data/merra;jsessionid=009CC3C653AB076BB458FC164CB5CD31

http://www.soda-pro.com/web-services/meteo-data/merra;jsessionid=009CC3C653AB076BB458FC164CB5CD31


F. Spertino

Technical-Economic Issues affecting the Capacity

Factors of Wind Energy

Filippo Spertino



F. Spertino

ECONOMIC SITUATION OF WIND ENERGY

50-60 GW of new wind power per year in the last 5 years

Five countries have >20,000 MW: China (220 GW with feed-intariffs), USA (96 GW with investment/production tax credits),Germany (59 GW), India (35 GW), Spain (23 GW)

Cost of installation: 1200 – 2000 €/kW ; cost of energy: 3 – 12 c€/kWh


F. Spertino

http://atlanteeolico.rse-web.it/

A free software for estimation of wind energy is available in the

website of RSE (an Italian research centre). It provides a database

of the Italian windy sites with their productivity

SOFTWARE FOR WIND PRODUCTIVITY


F. Spertino

OPTIMAL CHOICE OF WTs AND MUTUAL SPACING

The best WT in a windy site maximizes CF (up to 15% of gain)

If more than one WT is installed, it is important to take into accountthe wake effect with linearly expanding diameter and conic profile(Jensen). Wake depends on thrust coefficient CT

250hswz

T

TUA.

FC

velocity in the wake at the distance x from the upwind WT is expressed

2

0

0011

x

Txr

rCUUU

U0 wind speed in front of the upwind WT, rx radius of the slipstream at thedistance x, r0 radius of the rotor and scalar coefficient indicating howquickly the trail expands. Normally =0.075 for onshore and =0.04—0.05for offshore WT plants

xrrx

0

Only 4 WTs can be placed in

a little island with flat terrain:

CF=0.31 and wake losses

≈5%


F. Spertino

AVAILABILITY ASPECTS

Failure rate: number of failures per turbine and per year, and itspartitioning by component and by failure cost category.

For fixed-speed WT, the failure rates for drive train components (gearbox,blades) are remarkable.For variable-speed WT, the failure rates of drive train are greatly reduced,but the failure rates of control and electric components (pitch regulation,sensors) are increased.The useful interval Tw is obtained excluding when wind is negligible (<4m/s) or excessive (>25 m/s). Tf is the time of outage conditions, theduration of actual production Ta=Tw–Tf.

The time-based availability indicator

w

aT

T

TA

A wind farm, in complex terrain, consists of 32 WTs (wind parks of 11, 11and 10 WTs, respectively). The experimental values of time-basedavailability are 0.69, 0.62 and 0.71.For a wind farm in ideal terrain the availability indicator may be >95%.The production-based availability indicator is consistent with CF.


F. Spertino

DEVIATIONS FROM MANUFACTURER POWER CURVE

During field operation, WTs exhibit actual powers different each otherfor the same average wind speed

The powers produced in real conditions (It

up to 0.2) are much lower than thepowers in case of negligible turbulence(<0.1).The wind speed sensors by SCADA of WTsare placed on the nacelle after thepassage of the air stream through theblades.

After correction of data, the real WT behavior in field operation is comparedwith the manufacturer’s power curve.Considering all the data points available, the underperformance of wind farm isestimated within 25—35% in a very complex terrain.

The estimation of input UhIN from output UhOUT, needed for the comparison withthe manufacturer power curve, is carried out by a method based on thecalibration procedure of instruments.


F. Spertino

0,00

0,10

0,20

0,30

0,40

0,50

0

100

200

300

400

500

600

700

800

900

1000

0 5 10 15 20 25

Eff

icie

ncy

Ele

ctri

c p

ow

er (

kW

)

Wind speed (m/s)

raw data WT#21

corrected data WT#21

manufacturer power

manufacturer efficiency

underperformance

DEVIATIONS FROM MANUFACTURER POWER CURVE

For these three mentioned wind parks, CF =0.168, 0.145 and 0.163,respectively. These figures correspond to about 16% in average,which is a capacity factor close to the national value in China

Wind farm with #32 WTs in very complex terrain

Underperformance of -34%: the mean power on the manufacturer’s curve is564 kW at 10 m/s, with respect to the worst corrected mean power of 370kW from SCADA.


F. Spertino

CURTAILMENT OF WIND ENERGY

The TSOs and DSOs tasks to manage the grid in presence of

frequency and voltage fluctuations, consequent to the intermittent

production of wind farms, are easier in case of voltage variations

rather than frequency variations.

Frequency variations depend on the continuous balance of

generated and absorbed active powers at HV level.

The wind intermittency imposes constraints to TSOs: a typical case

occurs when the summation of generated powers overcomes the

summation of absorbed powers.

In China, sometimes, TSO curtails wind power rather than shut

down coal-based power stations. This curtailment accounts for -10%

in average.

Documents

WIND POWER Technical-economic issues affecting the