AckermannTh. (ed) Wind Power in Power Systems
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be assumed to be an ideal economic system where the value is equal to the decrease of
total costs. The numerical examples refer to the Swedish power system, with a compara-
tively high proportion of hydropower (50 %) but with strong connections to neigh-
bouring power systems. The neighbouring systems use hydropower (Norway) and
thermal power (Denmark, Finland, Germany and Poland). The value in the ‘real world’
(i.e. the existing market) is described in Section 9.4, where the Swedish deregulation
framework is considered (for other markets, see Milligan et al., 2002).
9.3.1 The operating cost value of wind power
The operating cost value considers the capability of wi nd power to decrease the operat-
ing costs of other power sources. The value means in reality that each kilowatt-hour that
is produced by wind power will replace one kilowatt-hour that otherwise would have
been produced from another power source. In the Swedish hydro system, hydro energy
is (almo st) never replaced by wind power production, since water that is store d in
reservoirs during periods with high wind production can be used later for power
production. There is one exception, though, during high inflows, when hydro produc-
tion has to be very high in order to avoid spillage. If this coincides with very low load
and very high winds it may happen that water has to be spilled because of the high wind
power production. These situations are probably rather rare and in such cases excess
power might also be sold to neighbouring systems.
The common situation is that wind power production replaces fuel-based generation
in thermal power stations. The generation can be replaced directly (i.e. the production in
thermal power stations is reduced if there is wind power production). An indirect way of
replacing fuel-based generation in thermal power stations is to store water during good
wind conditions and late r use this ‘stored hydro power’ to replace fuel-based generation.
In the thermal power part of the power system, the low-cost units are used first and
those with higher operating costs are used later. This implies that wind power normally
replaces fuels in the units with the highest operating costs, since one of the aims of a
power system is to operate at the lowest cost possible.
9.3.2 The capacity credit of wind power
The capacity credit of wind power refers to the capability of wind power to increase the
reliability of the power system. For defining the capacity credit we use the same method as
for other types of power plants (e.g. see IEEE, 1978; the capacity credit of wind power is
also included in Milligan, 2002). Figure 9.1 illustrates an example of weekly load. The
available capacity is set to 3250 MW and the load is the real hourly load in the western part
of Denmark during the week starting 2 January 2003. The available capacity is not the real
one but has been chosen in order to illustrate the capacity credit of a certain amount of wind
power. In this situation, there would have been a capacity deficit during 40 h of that week.
If, now, wind power is introduced into this system, the available capacity is increased
(Figure 9.2). This figure includes the real wind power production during the same week
illustrated in Figure 9.1. During this week, mean wind power production was 392 MW.
On 31 December 2002, total installed wind power capacity was 1994 MW. During 2002,
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the mean wind power production in this area was 396 MW (i.e. the selected week is
representative regarding the total energy). This amount of wind power resulted in a
decrease in the number of hours with a capacity deficit, falling from 40 h to 27 h. This
means that the reliability of the power system has increased as a result of the installed
wind power. If the reliability was acceptable before the instalation of wind power, wind
power production will enable the power system to meet a higher demand at the same
reliability level.
Figure 9.3 shows that if the load increases by 300 MW during each hour (compared
with the load shown in Figure 9.2) the number of hours with a capacity deficit increases
to 40. This means that the capacity credit measured as the equivalent load-carrying
capability is 300 MW. In this example, the capacity credit for an installed wind power
capacity of 1994 MW is 300 MW, corresponding to 15 % of installed capacity. This is
slightly lower than results from other studies, which indicate capacity credits in the
range of 18–24 % of installed capacity (Munksgaard, Pedersen and Pedersen, 1995; van
Wijk, 1990).
0 20 40 60 80 100 120 140 160
0
1000
2000
3000
4000
5000
Available capacity
Total load
Deficit time
Time (h)
Duration of deficit
(total deficit duration = 40 h)
MW
Figure 9.1 Denmark, week starting 2 January 2003: capacity deficit without wind power
0 20 40 60 80 100 120 140 160
0
1000
2000
3000
4000
5000
Wind power
production
Time (h)
MW
Available capacity
Total load
Deficit time
Duration of deficit
(total deficit duration = 27 h)
Figure 9.2 Denmark, week starting 2 January 2003: capacity deficit with wind power
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There remains the question of how wind power can have a capacity credit when there
are situations with no wind? It has to be kept in mind that for any power source there is
a risk that it is not available during peak loads. The method used here to define capacity
credit is exactly the same as the method that is used to define the capacity credit for
other sources (IEEE, 1978). The example above shows that the number of hours with
capacity deficit decreases, but not to zero, when the amount of wind power increases.
During hour 60, for instance, there is no wind, and it does not matter whether the
amount of wind power increases during this hour, since there is no wind. But the figures
also show that during peak hours there is sometimes wind, which means that wind
power can decrease the risk of a capacity deficit. In the figures, one week is used for
illustrative purposes, but the data of a longer period, probably over several years, have
to be used to be able to draw general conclusions.
We can compare the capacity credit of wind power production with that of generation
from a thermal plan. The mean weekly wind power production for 2002 was 396 MW;
thus the yearly production was as follows:
Power production in one year ¼ð396 MWÞð365 24 hÞ¼3469 GWh:
Assume the thermal plant is available 92 % of the time and that it shuts down for 4
weeks for maintenance. In order to produce the same amount of energy as the wind
power system (3469 GWh):
3469 GWh ¼ (thermal power production)
92
100
48
52
8760 h
:
Therefore, rearranging, we obtain:
thermal power production ¼ 3469 GWh
100
92
52
48
1
8760 h
¼ 0:466 GWh
¼ 466 MW:
0 20 40 60 80 100 120 140 160
0
1000
2000
3000
4000
5000
Deficit time
Time (h)
Wind power
production
Available capacity
Total load
MW
Duration of deficit
(total deficit duration = 40 h)
Figure 9.3 Denmark, week starting 2 January 2003: capacity deficit with wind power and with
load þ300 MW compared with situation illustrated in Figure 9.2
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The capacity credit for this thermal power plant is around 429 MW (92 % of 466 MW).
This means, for this example, that the capacity credit of wind power production
(300 MW) corresponds to approximately 70 % of the capacity credit for a thermal
power plant with the same yearly energy production.
9.3.3 The control value of wind power
The control value of wind power considers the capability of wind power to participate in
balancing production and consumption in the power system. Since electric power
cannot be stored it is necessary to produce exactly as much power as is consumed, all
the time. The balancing problem is handled differently depending on the time frame:
9.3.3.1 Primary control
Primary control considers the capability of the power system to keep a balance between
production and consumption from second to second up to about a minute. Primary
control can be summarised as follows: most of the generators in a power system are
normally of a synchr onous type. In these generators, there is a strong connection
between the rotational speed of the axis and the electric frequency. When the rotational
speed decreases, the electric frequency decreases, too. This means that if too little power
is produced in a power system, the frequency decreases since the required extra power is
taken from the rotational energy in the synchronous machines. When the rotational
energy is used up, the rotational speed decreases, which also decreases the electric
frequency. In some power plants (e.g. in Swedish hydro power plants) the frequency is
measured and if it decreases the power production is increased until the frequency is
stabilised. In this way, the short-term balance of the system is maintained.
Wind power plants do not contribute to primary control since they cannot keep any
margins in their production units, which then could be used if frequency decreased.
Wind power units normal ly produce at the maximum possible. That means that wind
power generation increases the need of primary control reserve margins since additional
variations are introduced into the system. There are two types of variations that are
essential.
The first type is when the wind speed varies between cut-in wind speed and rated wind
speed, v
R
, as shown in Figure 9.4. Wind speed variations from second to second in
different wind power plants can, on this time scale, be considered as independent
variables. In So
¨
der (1992), I provided an example with 3530 MW of wind power in a
system with a total installed capacity of 15 589 MW (i.e. wind power corresponds to
23 % of installed capacity, and 15 % of yearly energy). This amount of wind power
requires additional primary control reserve margins of 10 MW. The amount is so small
because the load variations already require a rather large reserve (250 MW), and the
10 MW refers to the increase in these requ irements.
The second type of variation refers to a situation wher e a storm front approaches a
coast and may cause a sudden decrease in wind power production. During such a storm
front, the wind speed may exceed the cut-out wind speed (25 m/s in Figure 9.4) in many
wind turbines at the same time. However, the probability of that the amount of suddenly
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stopped wind capacity reaches 1000 MW (equivalent to the production decrease if a
large nuclear power station is stopped) is so low that the required amount of reserves
will not have to be increased. The reason is that 1000 MW of wind power in reality
means 500 2 MW, for instance, and the probability that these 500 units will be hit by
the same storm front within 1 minute is extremely low. Table 9.1 shows examples of
maximum wind gradients in two grids, E.ON Netz and Eltra.
The final conclusion is that the primary control value of wind power is negative, but
the size of this value is rather low.
9.3.3.2 Secondary control
Secondary control refers to the capability of the power system to keep the balance
between production and consumption during the time following primary control and up
to one hour. A consequence of primary control is that the frequency is no longer 50 Hz
and that reserve margins are used. This is handled by increasing the production in some
units in the case of a frequency decrease. This means that some units have to be used as
secondary reserve plants that can be started if the frequency is too low.
Wind power does not contribute to secondary control margins but instead requires
extra secondary reserve margi ns, as it introduces additional variations in the period of
up to one hour. That means that the secondary control value of wind power is negative.
In So
¨
der (1988), I provided an example with 3530 MW of installed wind power. The
0 10 20 30
0
1
2
3
P
R
v
R
v
ci
Wind speed (m/s)
Type 1
Power (MW)
0 5 10 15 20 25
0
200
400
600
800
1000
Wind speed (m/s)
Type 2
Power (MW)
v
ci
Figure 9.4 Wind speed power transfer function for a pitch-controlled wind power plant
Table 9.1 Comparison of maximum wind power gradients
E.ON Netz Eltra
For 4000 MW Per 1000 MW For 2300 MW Per 1000 MW
Increasing 250 MW per 15 min 4.1 MW per 1 min 8 MW per 1 min 3.5 MW per 1 min
Decreasing 400 MW per 15 min 6.6 MW per 1 min 15 MW per 1 min 6.5 MW per 1 min
Source: compiled by T. Ackermann, based on data published by Eltra and E.ON Netz.
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example uses the the same system as in the example of primary control (i.e. a system
with a total installed capacity of 15 589 MW, with wind power corresponding to 23 % of
installed capacity and 15 % of yearly energy). With this amount of wind power,
secondary control reserves require an additional 230 MW, which is more significant
than the increase in primary reserve requirements. The reason for the increase is, on the
one hand, that wind speed can vary more within one hour than within 10 minutes, and,
on the other hand, that wind speed variations at different sites are correlated to a larger
extent.
9.3.3.3 Daily and weekly contr ol
During a period of 24 hours, the control requirements are large, because power con-
sumption is higher during days than during nights. Some wind power locations have
higher wind speeds during the day than during the night. If this is the case, wind power
contributes to the necessary daily control in the system. However, sometimes there may
be higher winds during the night than during the daytime. If this is the case the daily
control value is negative.
With increased daily (and weekly) variations in the power system, the other produc-
tion units have to be controlled to a larger extent. Additional control in these units
may decrease the efficiency of the controlled units. This issue is studied more thor-
oughly in So
¨
der (1994). The simulation results show that, in Sweden, wind power
plants of about 2–2.5 TWh per year do not affect the efficiency of the Swedish hydro
system. At wind power levels of about 4–5 TWh per year, the installed amount of wind
power has to be increased by about 1 % to compensate for the decreased efficiency in
the hydro system. At wind power levels of about 6.5–7.5 TWh per year, the necessary
compensation is probably about 1.2 %, but this figure has to be verified with more
extended simulations. Larger amounts of wind power were not studied in this report.
In that study, I found that the main reason for the decreased efficiency was that wind
power variations caused larger variation in the hydro system, and, at very high
production, the efficiency of hydro power plants (kWh per m
3
of water) in the studi ed
hydro system decreased by several percent, compared with best efficiency operation
point. However, correct conclusions can be drawn only if a large number of possible
scenarios, including cases with decreased efficiencies (high load, low wind, high hydro)
and increased efficiencies (high load, high wind, lowered hydro) are compared with the
nonwind power system.
The consequence is that the daily (and weekly) control value of wind power is
negative, but this value is not large, at least not for minor amounts of wind power.
9.3.3.4 Seasonal control
Seasonal control is needed in a power system where there are hydro reservoirs that can
store water from one part of the year to another part. In this type of system, such as in
Sweden and Norway, it is important to carry out this seasonal planning and scheduling
in an economically efficient way. The uncertainty in the inflow forecasts has to be taken
into account for this.
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In Sweden, the load is higher in the winter than in the summer. Variations in wind
power production follow the same pattern (i.e. production during the winter is higher
than in the summer). This control value is therefore positive, in contrast to the other
wind power control values. This value can be included in the operating cost value, unless
the changes that wind power production causes to seasonal planning are not included in
the method for determining this value.
9.3.3.5 Multiyear control
Multiyear control is needed in power systems with a large share of hydro power since the
inflow is different during different years. This implies that water has to be stored
between different years. However, the future inflow is uncertain, which means that it
is not trivial to decide how much water should be stored, and having knowledge
regarding this uncertainty is desirable. Especially, during dry years there is a certain
risk that there will not be enough energy available to cover the load. At that point, the
question is whether wind power is able to produce energy during years with low inflow.
Here, it is important to look at the correlation between river inflow and wind energy
production, as in So
¨
der (1997, 1999b); in which I included an example that shows that
the correlation between three different Swedish wind power sites and hydro inflow were
0.14, 0.15 and 0.44, respectively. This means that there is a slight tendency to lower
winds during dry years compared with the multiyear mean value. This implies that wind
power has a slightly negative impact on the requirement for multiyear control compared
with thermal power stations, for example, which have the same potential during all
years. But new wind power is doing slightly better than new hydro power, since the
correlation between new hydro and old hydro power is much higher than the correlation
between new wind power and old hydro power. The reason is that new hydro produc-
tion will be located close to old hydro generation (high correlation in inflow), whereas
new wind power generation will not necessarily be located in the same region as hydro
production, and there is a limited correl ation between wind in one region and inflow in
another. Section 9.4.3 gives an example of the market value of multiyear variations in
wind power.
9.3.4 The loss reduction value of wind power
The loss reduction value concerns the capability of wind power to reduce grid losses in
the system. Wind power plants are often located rather far out in the distribution grid on
a comparatively low voltage level. This is different from large power stations, which are
located close to the transmission network. If the load close to the wind power plants is of
the same size as the wind power plant, the power does not have to be transported far,
which means that the losses are reduced as a result of wind power generation. In that
case, the loss reduction value of wind power is positive. How ever, it could also happen
that losses increase if there is no local load close to the wind power generation, which
means that the power produced in the wind power plant has to be transported to the
load centres on lines with comparatively high losses. If this is the case, the loss reduction
value is negative.
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An important issue here is that the marg inal losses are changed. The losses on a power
line can be calculated with use of the following equation:
P
L
¼ 3RI
2
¼ R
P
2
þ Q
2
U
2
¼ R
1 þ tan
2
’
U
2
P
2
¼ kP
2
; ð9:1Þ
where
P
L
¼ power losses on the line;
R ¼ line resistance;
I ¼ current on the line;
P ¼ total transmitted active power on the line;
Q ¼ total transmitted reactive power on the line;
U ¼ voltage;
’ ¼ phase shift between line voltage and current;
and
k ¼
Rð1 þ tan
2
’Þ
U
2
:
Assuming the approximation that U and ’ are constant, the losses are proportional to
the square of transmitted power. Assuming that a line has a transmitted power P
0
, this
results, according to Equation (9.1), in the losses (see also Figure 9.5):
P
L0
¼ kP
2
0
: ð9:2Þ
For this transmission, the losses, as a percentage, can be calculated as follows:
P
L0
ð%Þ¼100
P
L0
P
0
¼ 100kP
0
: ð9:3Þ
50
40
30
20
10
0
100 200 300 400 500 600 700 800 900 10000
Losses (kW)
Transmission (kW)
P
L0
P
L1
P
L
= kP
2
dP
L
dP
P
0
P
1
Figure 9.5 Impact of marginal losses
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If a local power source now causes the transmission to decrease to P
1
, losses decrease to
P
L1
. If the change in transmission is small, the new loss level can be calculated from a
linearisation of the losses according to Figure 9.5:
P
L1
P
L0
dP
L
dP
ðP
0
P
1
Þ¼P
L0
2kP
0
ðP
0
P
1
Þ: ð9:4Þ
The local production P, equal to P
0
P
1
, thereby causes a reduction in the losses of
P
L
, equal to P
L0
P
L1
. The loss reduction as a percentage becomes
P
L
ð%Þ¼100
P
L
P
¼ 100
P
L0
P
L1
P
0
P
1
100 2kP
L0
¼ 2P
L0
ð%Þ:
ð9:5Þ
This means that the marginal losses, and thereby the marginal loss reduction, are twice
as large as the mean losses. Whether wind power de creases or increases the losses in the
system depends on the location of the wind power, the location of the load and the
location of the power source that is replaced by the wind power. It is important to take
into account the losses in the whole grid, and not simply a part of it.
In So
¨
der (1999a) I studied an example of the loss reduction caused by 90 GWh of
wind power on the Swedish island of Gotland. Table 9.2 summarises the results,
comparing a wind farm with the alternatives where the same amount of yearly energy
is produced at locations in Karlshamn and Gardikforsen. At both locations, the wind
farms are connected directly to the transmission grid.
Table 9.2 shows that the wind power production on Gotland is the alternative that
reduces the losses among the three studied alternatives the most. The difference com-
pared with Karlshamn – 2.4 GWh (i.e. 4.6 GWh 2:2 GWh) – is 2.7 % of the produc-
tion of 90 GWh. The difference compared with Gardikforsen – 10.8 GWh [i.e. 4.6 GWh
( 6:2 GWh)] – corresponds to 12 % of production. Even though wind power on
Gotland increases the losses in the local grid on Gotland, this is compensated by
decreased losses in the regional and transmission grids. The hydro power station at
Gardikforsen is located in the northern part of Sweden, and the other sites are in the
Table 9.2 Loss reduction value of 90 GWh production at three different sites (Gotland,
Karlshamn and Gardikforsen)
Grid Loss (GWh)
Wind power, Gotland Oil unit, Karlshamn Hydro power, Gardikforsen
Local grid 2.8 — —
Regional grid 4.6 — —
Transmission grid 2.8 2.2 6:2
Total 4.6 2.2 6:2
— Not applicable.
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southern part. In Sweden, the dominating direction of power flow is from north to
south. Therefore, Gardikforsen causes comparatively large losses.
9.3.5 The grid investment value of wind power
The grid invest ment value refers to the capability of wind power to decrease the need of
grid investments in the power system. In order to be able to study this value it is first
necessary to study how the grid is dimensioned without wind power and then to look at
how the dimensioning changes if wind power is introduced. It is rather difficult to draw
any general conclusions concerning this item. An important issue are the costs that are
part of the required grid investments but that are also included in the cost of the wind
farm. An example would be a medium-sized offshore wind farm with the costs for the
transmission line from the wind farm to the transmission system being included in the
total cost of the wind farm. The grid investment value is then probably comparatively
small, if no other grid investments are needed.
I analysed this question in a more general way in So
¨
der (1997), and an example of the
market grid investment value of wind power is provided in Section 9.4.5.
9.4 The Market Value of Wind Power
In Sweden, new rules for the electricity market were introduced 1 January 1996. Some
important changes included the following:
.
All networks at all levels had to be opened;
.
All network services had to be unbundled from generation and electricity sales;
.
A transmission system operator (TSO) is responsible for the short-term power balance.
If a production source has a certain value, it is reasonable that the market be organised
in a way that the owner of the production source is paid according to this value. This
point will be discussed below in relation to the different values outlined in Section 9.3
and the deregulated market that has been introduced in Sweden, where wind power
production can receive support from the state (e.g. through tax reductions and invest-
ment support). Currently, in Sweden there is also a system of certificates that supports
owners of wind power plants. These issues will not be treated in detail, though.
9.4.1 The market operation cost value of wind power
In the Nordic market, power can be sold in three different ways:
.
Sold bilaterally to consumers: if wind power is to be sold, this means in practice that
someone has to handle the balance between wind power production and consumption;
that is, the wind power control value has to be considered and a trader has to be involved.
.
Sold bilaterally to traders: this means that the trader buys wind power and then sells
this power, together with other production, directly to consumers and traders and/or
180 The Value of Wind Power