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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
F. Spertino
Aerodynamics and Mechanical Aspects of
Wind Turbines
Filippo Spertino
Politecnico di Torino, Energy Department, Torino, Italy
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
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)
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
F.Spertino
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.
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
F.Spertino
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
F.Spertino
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
F.Spertino
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
F. Spertino
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
OPERATING PRINCIPLE OF A WIND TURBINE (4)
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
F.Spertino
OPERATING PRINCIPLE OF A WIND TURBINE (5)
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
F. Spertino
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
F. Spertino
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
F. Spertino
Electrical Aspects and Anemometry of Wind
Turbines
Filippo Spertino
Politecnico di Torino, Energy Department, Torino, Italy
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
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).
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
F.Spertino
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
F.Spertino
A SOLUTION FOR VARIABLE SPEED TURBINES (2)
-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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
F.Spertino
-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.
A SOLUTION FOR VARIABLE SPEED TURBINES (3)
power extraction
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
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.
A SOLUTION FOR VARIABLE SPEED TURBINES (4)
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
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.
A SOLUTION FOR VARIABLE SPEED TURBINES (5)
-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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
F.Spertino
CHARACTERIZATION OF THE SOURCE (2)
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
F. Spertino
CHARACTERIZATION OF THE SOURCE (3)
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
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).
CHARACTERIZATION OF THE SOURCE (4)
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
F. Spertino
CHARACTERIZATION OF THE SOURCE (5)
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
F. Spertino
Exercise Calculation of Productivity
from a Wind Turbine
Filippo Spertino
Politecnico di Torino, Energy Department, Torino, Italy
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
F. Spertino
Technical-Economic Issues affecting the Capacity
Factors of Wind Energy
Filippo Spertino
Politecnico di Torino, Energy Department, Torino, Italy
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
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
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
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%
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
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.
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
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.
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
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.
Summer School on Energy, Giacomo Ciamician, 17-21 June 2019
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.