AckermannTh. (ed) Wind Power in Power Systems
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With voltages (RMS values of line-to-line voltages) on each side of the impedance
(which may represents a transmission line, for instance), and the current (RMS value of
the phase current), the voltage drop over the impedance can be calculated as:
U
1
U
2
¼
ffiffiffi
3
p
IZ: ð3:7Þ
Figure 3.3 shows the basic problem of the grid connection of a wind farm. The grid
can be seen as a voltage source, U
1
, next to the impedance, Z. The impedance represents
the impedance in all transmission lines, cables and transformers in the feeding grid. At
the point of conn ection of the wind farm, there is also a local load. The short circuit
power, S
k
, in the wind power connection point can be calculated as
S
k
¼
U
2
1
Z
: ð3:8Þ
Changes in wind power production will cause changes in the current through the
impedance Z. These current changes cause changes in the voltage U
2
.IfZ is large (in
a weak grid, S
k
is small) there is not as much room for wind power as there is in a
situation where Z is small (in a strong grid, S
k
is large).
In Figure 3.3, wind power production and load are represented as P þ jQ. P he re is
the active power, and Q is the reactive power. The reactive power depends on the phase
shift, ’, between the voltage and the current, such as:
Q ¼
sin ’
cos ’
P; ð3:9Þ
see Equation (3.2).
The vo ltage U
2
in the figure can be calculated as:
U
2
¼
2a
1
U
2
1
2
þ
2a
1
U
2
1
3
2
a
2
1
þ a
2
2
"#
1=2
8
<
:
9
=
;
1=2
; ð3:10Þ
Z
U
2
U
1
I
Figure 3.2 Voltages U
1
and U
2
either side of an impedance, Z, with current I
Grid
Load
Wind powe
r
U
1
U
2
Z = R + jX
P
W
+jQ
W
P
LD
+ jQ
LD
Figure 3.3 Grid connection of wind power. U
1
, U
2
¼ voltage either side of impedance Z;
P
w
, P
LD
¼ active power from wind power and of load; Q
w
, Q
LD
¼ reactive power of wind power
and load
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where
a
1
¼RðP
W
P
LD
ÞXðQ
W
Q
LD
Þ;
a
2
¼XðP
W
P
LD
ÞþRðQ
W
Q
LD
Þ:
This equation shows that the reactive power production in the wind farm, Q
W
, has an
impact on the voltage U
2
. The impact is dependent on the local load and on the feeding
grid impedance. We will now look at the different possibilities of generating wind power:
An asynchronous generator consumes reactive power and the amount is not con-
trollable. The reactive consumption is normally partly compensated with shunt capaci-
tors, the so-called phase compensation (which produces reactive power and reduces ’).
If there are severa l capacitors, the voltage can be controlled stepwise by changing the
number of connected capacitors.
In synchronous generators (not with permanent magnets) and in converters it is
possible to control the reactive generation or consumption. This makes it possible to
control the voltage as shown in Equation (3.10).
3.6 Characteristics of Wind Power Generation
In the following section we will discuss in more detail wind as a power generation source,
including its fluctuating character and the physical limitations for utilising this natural
resource. After that, the typical characteristics of wind power generation will be analysed.
3.6.1 The wind
Air masses move because of the different thermal conditions of these masses. The
motion of air masses can be a global phenomenon (i.e the jet stream) as well as a
regional and local phenomenon. The regional phenomenon is determined by orographic
conditions (e.g. the surface structure of the area) as well as by global phenomena.
Wind turbines utilise the wi nd energy close to the ground. The wind conditions in this
area, known as bounda ry layer, are influenced by the energy transferred from the
undisturbed high-energy stream of the geostrophic wind to the layers below as well as
by regional conditions. Owing to the roughness of the ground, the local wind stream
near the ground is turbulent.
The wind speed varies continuously as a function of time and height. The time scales
of wind variations are presented in Figure 3.4 as a wind frequency spectrum. The
turbulent peak is caused mainly by gusts in the subsecond to minute range. The diurnal
peak depends on daily wind speed variations (e.g. land–sea breezes caused by different
temperatures on land and sea) and the synoptic peak depends on changing weather
patterns, which typically vary daily to weekly but include also seasonal cycles.
From a power system perspective, the turbulent peak may affect the power quality of
wind power production. As discussed in Chapters 5, 6 and 16, the impact of turbulences
on power quality depends very much on the turbine technology applied. Variable speed
wind turbines, for instance, may absorb short-term power variations by the immed iate
storage of energy in the rotating masses of the wind turbine drive train. That means that
the power output is smoother than for strongly grid-coupled turbines. Diurnal and
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synoptic peaks, however, may effect the long-term balancing of the power system as
discussed mainly in Chapters 10 and 11. Wind speed forecasts play a significant role for
the long-term balancing of the power system, see also Chapter 17.
Another important issue is the long-term variations of the wind resources. There are
several studies regarding this issue (see Petersen et al., 1998; So
¨
der, 1997; 1999). Based on
these studies, it has been estimated that the variation of the yearly mean power output
from one 20-year period to the next has a standard deviation of 10 % or less (see also
Chapter 9). Hence, over the lifetime of a wind turbine, the uncertainty of the resource
wind is not large, which is an important factor for the economic evaluation of a wind
turbine. In many locations of the world, the uncertainty regarding the availability of water
of a longer time period (more than 1 year) for hydropower generation exceed that of wind
power (Hills, 1994).
3.6.2 The physics
The power of an air mass that flows at speed V through an area A can be calculated as
follows:
power in wind ¼
1
2
AV
3
ðwattsÞ; ð3:11Þ
where
¼ air density (kg m
3
);
V ¼ wind speed (m s
1
).
Synoptic peak
Diurnal peak
Turbulent peak
10 days 4 days 24 h 10 h 2 h 1 hr 30 min 10 min 3 min 1 min 30 s 10 s 5 s
Frequency, lo
g
(f )
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
Spectrum, f S(f )
Figure 3.4 Wind spectrum based on work by van Hoven (Reproduced from T. Burton, D.
Sharpe N. Jenkins and E. Bossanyi, 2001, Wind Energy Hand book, by permission of John Wiley
& Sons, Ltd.)
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The power in the wind is proportional to the air density , the intercepting area A
(e.g. the area of the wind turbine rotor) and the velocity V to the third power. The air
density is a function of air pressure and air temperature, which both are functions of the
height above see level:
ðzÞ¼
P
0
RT
exp
gz
RT
; ð3:12Þ
where
(z) ¼ air density as a function of altitude (kg m
3
);
P
0
¼ standard sea level atmospheric density (1:225 kg m
3
);
R ¼ specific gas constant for air (287:05 J kg
1
K
1
);
g ¼ gravity constant (9:81 m s
2
);
T ¼ temperature (K);
z ¼ altitude above sea level (m).
The power in the wind is the total available energy per unit of time. The power in the
wind is converted into the mechanical–rotational energy of the wind turbine rotor,
which results in a reduced speed in the air mass. The power in the wind cannot be
extracted completely by a wind turbine, as the air mass would be stopped completely in
the intercepting rotor area. This would cause a ‘congestion’ of the cross- sectional area
for the following air masses.
The theoretical optimum for utilising the power in the wind by reducing its velocity
was first discovered by Betz, in 1926. According to Betz, the theoretical maximum
power that can be extracted from the wind is
P
Betz
¼
1
2
AV
3
C
P Betz
¼
1
2
AV
3
0:59: ð3:13Þ
Hence, even if power extraction without any losses were possible, only 59 % of the wind
power could be utilised by a wind turbine (Gasch and Twele, 2002)
3.6.3 Wind power production
In the following subsect ions typical charact eristics of wind power production are briefly
discussed.
3.6.3.1 Power curve
As explained by Equation (3.11), the available energy in the wind varies with the cube of
the wind speed. Hence a 10 % increase in wind speed will result in a 30 % increase in
available energy.
The power curve of a wind turbine follows this relationship between cut-in wind speed
(the speed at which the wind turbine starts to operate) and the rated capacity, approxi-
mately (see also Figure 3.5). The wind turbine usually reaches rated capacity at a wind
speed of between 1216 m s
1
, depending on the design of the individual wind turbine.
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At wind speeds higher than the rated wind speed, the maximum power production will
be limited, or, in other words, some parts of the available energy in the wind will be
‘spilled’. The power output regulation can be achieved with pitch-control (i.e. by feather-
ing the blades in order to control the power) or with stall control (i.e. the aerodynamic
design of the rotor blade will regulate the power of the wind turbine). Hence, a wi nd
turbine produces maximum power within a certa in wind interval that has its upper limit
at the cut-out wind speed. The cut-out wind speed is the wind speed where the wind
turbine stops production and turns out of the main wind direction. Typically, the cut-
out wind speed is in the range of 20 to 25 m s
1
.
The power curve depends on the air pressure (i.e. the power curve varies depending on
the height above sea level as well as on changes in the aerodynamic shape of the rotor
blades, which can be caused by dirt or ice). The power curve of fixed-speed, stall-regulated
wind turbines can also be influenced by the power system frequency (see also Chapter 15).
Finally, the power curve of a wind farm is not automatically made up of the scaled-up
power curve of the turbines of this wind farm, owing to the shadowing or wake effect
between the turbines. For instance, if wind turbines in the first row of turbines that
directly face the main wind direction experience wind speeds of 15 m s
1
, the last row
may ‘get’ only 10 m s
1
. Hence, the wind turbines in the first row will operate at rated
capacity, 1500 kW for the turbine in Figure 3.5, whereas the last row will operate at less
than rated capacity (e.g. 1100 kW for the same turbines).
3.6.3.2 Hysteresis and cut-out effect
If the wind speed exceeds the cut-out wind speed (i.e. 25 m s
1
for the wind turbine in
Figure 3.5) the turbine shuts down and stops producing energy. This may happen during
a storm, for instance. When the wind drops below cut-out wind speed, the turbines will
0
200
400
600
800
1000
1200
1400
1600
1 2 3 4 5 6 7 8 9 10111213141516171819202122232425
Wind speed (m s
–1
)
Power output (kW)
Figure 3.5 Typical power curve of a 1500 kW pitch regulated wind turbine with a cut-out speed
of 25 m s
1
(the broken line shows the hysteresis effect)
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not immediately start operati ng again. In fact, there may be a substantial delay,
depending on the individual wind turbine technology (pitch, stall and variable speed)
and the wind regime in which the turbine operates. The restart of a wind turbine, also
referred to as the hyster esis loop (see the broken line in Figure 3.5), usua lly requires a
drop in wind speed of 3 to 4 m s
1
.
For the power system, the production stop of a significant amount of wind power
arising from wind speeds that exceed the cut-out wind speed may result in a compara-
tively sudden loss of significant amounts of wind power. In European power systems,
where wind power is installed in small clusters distributed over a significant geographic
area (for more details, see Chapters 10 and 11), this shut down of a significant amount
of wind power as a result of the movement of a storm front usually is distributed
over several hours. However, for power systems with large wind farms installed in a
small geographic area, a storm front may lead to the loss of a significant amount of wind
power in a shorter period of time (less than 1 hour). The hysteresis loop then determines
when the wind turbines will swi tch on again after the storm has passed the wi nd farm.
To reduce the impact of a sudden shutdown of a large amount of wind power and to
solve the issues related to the hysteresis effect, some wind turbine manufacturers offer wind
turbines with power curves that, instead of an sudden cut out, reduce power production
step by step with increasing wind speeds (see Figure 3.6). This certainly reduces the
possible negative impacts that very high wind speeds can have on power system operation.
3.6.3.3 Impact of aggregation of wind power production
The aggregation of wind power provides an important positive effect on power system
operation and power quality. Figure 3.7 shows the principal of aggregated wind power
production. The positive effect of wind power aggregation on power system operation
has two aspects:
1 2 3 4 5 6 7 8 910 11121314151617181920212223242526272829303132333435
Wind Speed (m s
–1
)
Power (kW)
1400
1200
1000
1600
800
600
400
200
0
Figure 3.6 The power curve of a 1500 kW pitch-regulated wind turbine with smooth power
reduction during very high wind speeds
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1 Wind
turbine
30 Wind turbines 150 Wind turbines 300 Wind turbines
Power (p.u.) Power (p.u.) Power (p.u.) Power (p.u.)
Figure 3.7 Impact of geographical distribution and additional wind turbines on aggregated power production. Time scale on graphics: seconds.
Based on simulations by Pedro Rosas (Reproduced from P. Rosas, 2003, Dynamic Influences of Wind Power on the Power System (PLD thesis,
Ørsted Institute and Technical University of Denmark), by permission of Pedro Rosas.)
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.
an increased number of wind turbines within a wind farm;
.
the distribution of wind farms over a wider geographical area.
Increased number of wind turbines within a wind farm
An increased number of wind turbines reduces the impact of the turbulent peak (Figure
3.4) as gusts do not hit all the wind turbines at the same time. Under ideal conditions,
the percentage variation of power output will drop as n
1/2
, where n is the number of
wind generators. Hence, to achieve a significant smoothing effect, the number of wi nd
turbines within a wind farm doe s not need to be very large.
Distribution of wind farms over a wider geographical area
A wider geographical distribution reduces the impact of the diurnal and synoptic peak
significantly as changing weather patterns do not affect all wind turbines at the same
time. If changing weather patte rns move over a larger terrain, maximum up and down
ramp rates are much smaller for aggregated power output from geographically dispersed
wind farms than from a very large single wind farm. The maximum ramp rate of the
aggregated power output from geographically dispersed wind farm clusters in the range
of 10 to 20 MW with a total aggregated capacity of 1000 MW, for instance, can be as
low as 6.6 MW per minute (see also Chapter 9), and single wind farms with an installed
capacity of 200 MW have shown ramp rates of 20 MW per minute or more. The precise
smoothing effect of the geographical distribution depends very much on local weather
effects and on the total size of the geographical area (see also Chapter 8). It must be
emphasised that a distribution of wind farms over a larger geographi cal area usually has
a positive impact on power system operation.
3.6.3.4 Probability density function
As explained in Section 3.6.1, the power production of a wind power plant is related to
the wind speed [see Equation (3.11)]. Since wind speed varies, power production varies,
too. There are two exceptions, though. If the wind speed is below the cut-in wind speed
or is higher than the cut-out wind speed then power production will be zero.
Figure 3.8 shows the structure of the probability density function (pdf), f
P
(x), of the
total wind power from several wind power units during a specific period (e.g. one year).
0
0
x (MW)
C
IC
f
p
(x)
Figure 3.8 Probability density function for the available power production from several wind
power units
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The total installed capacity (IC) is assumed to be C
IC
. There is one discrete probability of
zero production, p
0
, when the wind speed is below the cut-in wind speed for all wind
turbines or when the wind turbines are shut down because of too high winds. There is also
one discrete probability of installed capacity, p
IC
, when the wind speed at all pitch-
controlled units lies between the rated wind speed and cut-out wind speed, and when
for all stall-controlled turbines the wind speed lies in the interval that corresponds to
installed capacity. Between these two levels there is a continuous curve where for each
possible production level there is a probability. There is a structural difference between
wind power production and conventional power plants, such as thermal power or hydro-
power. The difference is that these power plants have a much higher probability, p
IC
,that
the installed capacity is available and a much lower probability, p
0
, of zero power
production. For conventional power plants, there are normally only these two probabil-
ities, which means that the continuous part of the pdf in Figure 3.8 will be equal to zero.
The values of p
0
and p
IC
decrease with an increasing total amount of wind power. This
is owing to the fact that if there is a larger amount of wind power, the turbines have to
be spread out over a wider area. This implies that the probability of zero wind speed at
all sites at the same time decreases. The probability of high (but not too high) wind
speeds at all sites at the same time will also decrease.
The mean power production of all units can be calculated as
P
m
¼
Z
C
IC
0
xf
P
ðxÞdx: ð3:14Þ
3.6.3.5 Capacity factor
The ratio P
m
/C
IC
is called the capacity factor (CF) and can be calculated for individual
units or for the total production of several units (for a more detailed discussion on the
capacity factor, see Chapter 9). The capacity factor depends on the wind resources at the
location and the type of wind turbine, but lies often in the range of about 0.25 (low wind
speed locations) to 0.4 (high wind speed locations). The utilisation time in hours per year
is defined as 8760 P
m
/C
IC
. This value lies, then, in the range of 2200–3500 hours per
year. In general, if the utilisation time is high, the unit is most likely to be operating at
rated capacity comparatively often.
The yearly energy production, W, can be calculated as
W ¼ P
m
8760 ¼ C
IC
8760 CF
¼ C
IC
t
util
ð3:15Þ
where
CF ¼ capacity factor;
t
util
¼ utilization time.
Occasionally, the utilisation time is interpreted as ‘equivalent full load hours’, and this
is correct from an energy production perspective, but it is sometimes even misunder-
stood and assumed to be the operating time of a wind power plant.
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Compared with base-load power plants, such as coal or nuclear power plants, the
utilisation time of wind power plants is lower. This implies that in order to obtain the
same energy production from a base-load power plant and a wind farm, the installed wind
farm capacity must be significantly larger than the capacity of the base-load power plant.
3.7 Basic Integration Issues Related to Wind Power
The challenge that the integration of wind power poses can be illustrated using
Figure 3.9. In this power system, there are industries and households that consume
power P
D
and a wind power station that delivers power P
W
. The additional power, P
G
,
is produced at another location. The impedances Z
1
–Z
3
represent the impedances in the
transmission lines and transformers between the different components.
In an electric power system, such as the one illustrated in Figure 3.9, power cannot
disappear. This means that there will always be a balance in this system, as
P
G
¼ P
D
þ P
L
P
W
; ð3:16Þ
where
P
G
¼ additional required power producti on;
P
D
¼ power consumption;
P
L
¼ electrical losses in the impedances Z
1
–Z
3
;
P
W
¼ wind power production.
Equation (3.16) is valid for any situation; it does not matter whether we look at a
short time period (e.g. minutes) or a long period (e.g. a year). Equation (3.16) also
implies that electricity cannot be stored within an electric power system. Hence any
change in electricity demand (or wind power) must be simultaneously balanced by other
generation sources within the power system.
3.7.1 Consumer requirements
As mentioned in Section 3.4, the main aim of a power system is to supply consumers
with the required electricity at any given time at a reasonable cost. From the consumer’s
perspective, three main requirements can be defined:
Z
3
Z
1
U
0
U
1
P
W
I
1
I
2
I
3
U
3
P
D
Z
2
U
2
P
G
Wind
Demand
Generation
Figure 3.9 Illustrative power system
40 Wind Power in Power Systems: Introduction