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Capacity Value of Wind Power
Citation for published version:
Keane, A, Milligan, M, Dent, C, Hasche, B, D'Annunzio, C, Dragoon, K, Holttinen, H, Samaan, N, Soder, L &
O'Malley, M 2011, 'Capacity Value of Wind Power', IEEE Transactions on Power Systems, vol. 26, no. 2,
pp. 564-572. https://doi.org/10.1109/TPWRS.2010.2062543
Digital Object Identifier (DOI):
10.1109/TPWRS.2010.2062543
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IEEE Transactions on Power Systems
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Download date: 10. Aug. 2022
1
Abstract-- Power systems are planned such that they have
adequate generation capacity to meet the load, according to a
defined reliability target. The increase in the penetration of wind
generation in recent years has led to a number of challenges for
the planning and operation of power systems. A key metric for
generation system adequacy is the capacity value of generation.
The capacity value of a generator is the contribution that a given
generator makes to generation system adequacy. The variable
and stochastic nature of wind sets it apart from conventional
energy sources. As a result, the modeling of wind generation in
the same manner as conventional generation for capacity value
calculations is inappropriate. In this paper a preferred method
for calculation of the capacity value of wind is described and a
discussion of the pertinent issues surrounding it is given.
Approximate methods for the calculation are also described with
their limitations highlighted. The outcome of recent wind
capacity value analyses in Europe and North America, along with
some new analysis are highlighted with a discussion of relevant
issues also given.
Index Terms-- Wind power, capacity value, effective load
carrying capability, power system operation and planning
I. INTRODUCTION
P
OWER system reliability is divided into two basic aspects,
system security and system adequacy. A system is secure if it
can withstand a loss (or potentially multiple losses) of key
power supply components such as generators or transmission
links. Generation system adequacy refers to the issue of
whether there is sufficient installed capacity to meet the
electric load [1]. This adequacy is achieved with a
combination of different generators that may have
significantly different characteristics. Capacity value can be
defined as the amount of additional load that can be served
due to the addition of the generator, while maintaining the
existing levels of reliability. It is central to determining a
system’s generation adequacy. It is used by system engineers
to assess the risk of a generation capacity deficit [2].
Th
e work of this taskforce has been part conducted in the Electricity Research
Centre, University College Dublin which is supported by Bord Gáis, Bord na
Móna, Commission for Energy Regulation, Cylon, EirGrid, EPRI, Electricity
Supply Board (ESB) Networks, ESB Power Generation, ESB International,
Siemens, Gaelectric, SSE Renewables, SWS, and Viridian. This publication
has also emanated from research conducted with the financial support of
Science Foundation Ireland under Grant Number 06/CP/E005.
A. Keane and M. O’Malley are with University College Dublin, Ireland
(e-mail: andrew.keane@ucd.ie, mark.omalley@ucd.ie).
I
n recent years it has gained importance, in light of the
increased uncertainty arising from wind power availability,
which is a function of the local weather conditions.
The metrics that are used for adequacy evaluation include
the loss of load expectation (LOLE) and the loss of load
probability (LOLP). LOLP is the probability that the load will
exceed the available generation at a given time. This criterion
only gives an indication of generation capacity shortfall and
lacks information on the importance and duration of the
outage. LOLE is the expected number of hours or days, during
which the load will not be met over a defined time period. The
effective load carrying capability (ELCC) is the metric used in
this paper to denote the capacity value [3].
The topic of capacity value of wind power has been
attracting attention in recent times with a number of
publications dealing with this issue. In [4] methods for
capacity value are described, and classified as either
chronological or probabilistic. A range of methods for the
calculation of capacity value are assessed in [5, 6]. A
generalised version of [3] is presented in [7] with the key
innovation being a multi state representation of wind power. A
new approximate method for the adequacy assessment called
the Z method is given in [8]. The utilization of an
autoregressive moving average model of wind power along
with sequential Monte Carlo simulation is presented in [9-12].
In [13] a well being analysis framework is used to combine
deterministic and probabilistic approaches to determining
system adequacy. Currently a wide range of approaches have
been implemented in academia and industry, each with their
own inherent limitations and approximations. This paper is the
result of work undertaken by the Taskforce on Capacity Value
of Wind, which was proposed by the Wind Power
Coordination Committee and Power Systems Analysis,
Computing and Economics committee of the IEEE Power and
Energy Society (PES). The overall objective of the taskforce
has been to provide clarity on the calculation of capacity value
of wind. This paper is the outcome of the taskforce meeting
and panel session which took place at the IEEE PES General
Meeting in Pittsburgh, 2008.
The paper classifies the current approaches used for the
assessment of the capacity value of wind power generation. In
particular, a preferred method is recommended and described
in detail in Section II. Other approximate methods are
described in Section III, with the limitations of each
highlighted and recommendations made as to their usage. The
results of relevant international studies are described in
Section IV. A discussion of relevant issues is given in Section
Task Force on the Capacity Value of Wind Power, IEEE Power and Energy Society
Andrew Keane, Member, IEEE, Michael Milligan (Vice-Chairman), Member, IEEE, Chris Dent
Member, IEEE , Bernhard Hasche, Claudine D’Annunzio, Student Member, IEEE, Ken Dragoon,
Hannele Holttinen, Nader Samaan, Member, IEEE , Lennart Söder, Member, IEEE, and Mark
O’Malley (Chairman), Fellow, IEEE
Capacity Value of Wind Power
2
V, with conclusions and recommendations given in Section
VI.
II. P
REFERRED METHODOLOGY
A. Method Description
This method is based directly on the definition of capacity
value given above. Conventional thermal generation is still the
most common form of generation in power systems. They are
modeled by their respective capacities and forced outage rates
(FOR). Each generator capacity and FOR is convolved via an
iterative method to produce the analytical reliability model
(capacity outage probability table (COPT)) of the power
system. The COPT is a table of capacity levels and their
associated probabilities [1]. The cumulative probabilities give
the LOLP for each possible available generation state. Wind
power cannot be adequately modeled by its capacity and FOR
as wind availability is more a matter of resource availability
than mechanical availability. This leads to a different treatment
of wind generation in the traditional ELCC calculation method,
which is now summarized in the following three steps:
1. The COPT of the power system is used in
conjunction with the hourly load time series to
compute the hourly LOLPs without the presence of
the wind plant. The annual LOLE is then calculated.
The LOLE should meet the predetermined reliability
target for that period. If it does not match, the loads
can be adjusted, if desired, so that the target
reliability level is achieved.
2. The time series for the wind plant power output is
treated as negative load and is combined with the
load time series, resulting in a load time series net of
wind power. In the same manner as step 1, the LOLE
is calculated. It will now be lower (and therefore
better) than the target LOLE in the first step.
3. The load data is then increased by a constant ∆L
across all hours using an iterative process, and the
LOLE recalculated at each step until the target LOLE
is reached. The increase in peak load (sum of ∆Ls)
that achieves the reliability target is the ELCC or
capacity value of the wind plant.
B. Factors Influencing Capacity Value Calculation
For thermal units, the primary characteristics that influence
the overall system adequacy are the units’ available capacity
and FORs. Long-term FORs are typically available by type
and size of unit, compiled from a large data set of similar
units. Modelling wind power using 2-state distributions in this
manner is not recommended as wind is a highly variable
resource which cannot be adequately modeled by a two state
model.
With respect to wind power, the relationship between the
wind and the load is a key factor to be captured by the
calculation method. The correlation between wind and load is
site dependent. In some areas there is a diurnal and/or seasonal
wind pattern. Although the hourly correlation between wind
and load can be nearly zero, there may be a considerable
correlation among wind and load data when binned according
to rank. A physical mechanism for this may be that load
extremes are often due to relatively infrequent large-scale
high-pressure weather systems that typically bring calm
winds. This implies the existence of systematic patterns of
wind generation during system peaks and other time periods
that cannot be ignored. As an example, data used in the
Minnesota 20% Wind Integration Study [14] was used to
calculate correlation coefficients by deciles (10 equal
divisions) and vigiciles (20 equal divisions). Deciles are data
that is sorted into ten equal parts. Vigiciles refer to the same
concept where twenty equal parts are employed. The results
are shown in Fig. 1. The figure shows the relative ranking of
wind and loads by dividing them into deciles and vigiciles and
is based on the average wind or load within the grouping. The
annual correlation coefficient of the hourly wind and load data
is relatively small at -0.158. However, after computing the
midpoints of each decile and basing the calculation on those,
the correlation coefficient is considerable at -0.908, and the
corresponding vigicile correlation coefficient is -0.889.
Therefore, it is critical to use hourly wind and load data from
the same year so that the underlying relationship between
wind and load is implicitly captured in the modeling. The
linear correlation coefficients provide limited information
about the relationship between two variables, but are used here
as part of a simplified illustration.
Fig. 1. Correlation between wind and load based on deciles and
vigiciles
Although the key driver of wind capacity value comes from
the general correlation of wind and load, it is important to
remember that ELCC is a function of many different system
parameters. Some of these include hydro generation schedules
(generally highly correlated with load), import-export
schedules (often high imports are correlated with load), and
maintenance schedules for conventional units. This latter
impact can occur if maintenance outages have a significant
impact on LOLP during shoulder seasons, and if there is
significant wind generation during those times [15]. The
geographic dispersion of both wind and load will also impact
ELCC, as will the wind penetration level.
Fig. 2 illustrates the effect of an additional generator on the
reliability curve, where it is seen to move to the right. ELCC is
3
the contribution to overall adequacy, represented by the
movement of this curve. The case illustrated uses the common
LOLE target of 1 day/10 years. This target, although
commonly used, can be changed to reflect the acceptable risk
level of the region. The selected target reliability level can
have a large impact on the capacity value of both conventional
power and wind power [5]. When the target reliability level, is
lower, and LOLP higher, there is relatively more value in any
added capacity than in cases where LOLP is very low [15].
LOLE targets and calculations can be expressed in days per
year or hours per year. The relationship between hours per
year and days per year is not a factor of 24 and depends on the
generating system and load parameters. It is important to note
that there is a distinction between these calculation methods
that use daily LOLE values and hourly LOLE respectively.
The calculation of a daily LOLE based on peak load values
will be more pessimistic and is distinct from an hourly LOLE
calculation. Both daily and hourly LOLE are valid metrics, but
clarity regarding their application should be ensured.
A common approach is to estimate LOLE and related
indices for one balancing area of the whole interconnection,
e.g. for a utility, a state or a country. The interpretation of
LOLE is then not “Loss of Load Expectation”, but instead
expectation of requirement to import.
Fig. 2 Effect of generator addition on LOLE
In many systems where the calculations show a given
expectation of capacity deficit, the true expectation of capacity
deficit is much lower because there is a non-zero probability
of available imports which are not otherwise accounted for in
the analysis. The impact of imports could be modeled within
the preferred method if the data is available for the
interconnections into the system. For comparison of capacity
values between systems, the system is initially modified to
give a standard LOLE value such as 1 day in 10 years; this
then allows comparison of the capacity value of wind between
systems. This does not give a true measure of the adequacy of
the systems where LOLE values are different, but allows for
wind’s contribution to be assessed and compared against other
systems that used this standard value, as well as compared
against other energy sources.
The input data employed is a key factor in the calculation of
capacity value. It should be noted that regardless of the method
employed, if sufficient data of the required quality is not
available, the resulting answer cannot be relied upon. The
preferred method requires:
1) Load time series for the period of investigation (multi-year
of at least hourly resolution is preferable)
2) Wind power time series for the same period as the loads
3) A complete inventory of conventional generation units’
capacity, forced outage rates and maintenance schedules
The length of the period of investigation required is an open
question with wind power. For wind and other variable
generators, it has been common practice to use one or more
years of hourly generation data to calculate wind’s ELCC.
This approach, although a reasonable start, does not
adequately represent the long-term performance characteristics
of wind power plants in the same way that long-term
representations are made for conventional units. Multiple
years of time series data are preferred as there can be a
significant inter-annual variation of the wind resource [16]. If
the wind time series is only for a single year, then the
calculated LOLE will be simply a historical assessment rather
than a predictive one. The number required to provide a robust
answer is dependent on a number of factors including the size
of the system, load curve and penetration of wind power on
the system. The overall output for each year is important, but
the timing of the wind output is also a very important factor to
be captured. This reemphasizes the need for time synchronized
data with the load.
An important characteristic of wind power is its spatial
diversity. With respect to capacity value, weaker geographical
relationships are advantageous, as this results in a higher
capacity value of the whole wind fleet, due to the smaller
probability of very low output across the whole system. This
also means that the capacity value increases relatively with
larger region sizes. If in contrast the generation profiles are
perfectly correlated, the installation of additional capacity
does not compensate for the low wind hours; in this case,
while additional installed capacity would increase the MW
capacity value, the capacity value as a percentage of rated
capacity would decrease.
Wind data of the required quality and quantity has been
scarce to date due to many wind plants only being recently
installed. In addition, this time series data can be
commercially sensitive, making it harder to obtain. For other
energy resources such as hydro power, this is less of a
problem as it is a well established, mature technology with
decades of good quality data often being available. As noted
above, calculation of the “true” multi-area LOLE and related
indices should consider possibilities of import. This means
that representative time series for import levels and their
respective likelihoods in neighboring systems should be used.
Synthetic time series have been proposed in the literature as
a means of reconciling the sometimes limited availability of
historical wind time series [9-12]. This work has focused on
sequential Monte Carlo simulation to provide accurate
frequency and duration assessment of wind power. The wind
is modeled using an autoregressive moving average model,
which captures the correlation between different wind sites.
4
This approach is promising, provided that it can account fully
for the relationship between wind availability and load. A key
factor is capturing the effect of the underlying weather which
drives not only wind output but also the load.
III. A
PPROXIMATE METHODOLOGIES
This section outlines some of the approximate methodologies
that have been employed for calculation of capacity value.
They are included as a means of contrast with the preferred
method and also to highlight the approximations and
assumptions they make. The preferred method contains
approximations also but as it utilizes the datasets which
explicitly capture the full relationship between load and wind
it does provide the best assessment of wind’s capacity value.
It is important to note that with modern computing power
the preferred method is not overly time-consuming for
moderately sized systems; indeed, a multi-year calculation can
be run in a matter of seconds on a desktop PC. Approximation
methods must therefore be justified on grounds of ease of
coding, lack of data, or on grounds of greater transparency
which aids the interpretation of results.
A. Garver approximation based methods
Garver proposed a simplified, approximate graphical approach
to calculating the ELCC of an additional generator [3]. This
has been an important method in the calculation of capacity
values but has been superseded by advances in computing
power. Although the paper’s focus was on the graphical
approach, the same underlying methodology can be used to
estimate the ELCC of a wind generator added to a given
power system. Garver’s approximation and its extension to
multi-state units [6] are based on two main assumptions:
• The multi-state unit representation of wind described
below is used; the probability distribution for wind
availability is the same at all times.
• The LOLE before addition of the wind may be
approximated as
0
md
Be
, where
0
d
is the peak demand,
and
m
and
B
are fitting parameters.
The ELCC (
d
) of the wind generation is then calculated as
−=
∑
−
i
mw
i
i
ep
m
d ln
1
(1)
where
i
p
is the probability that the available wind capacity is
i
w
.
B. Multi-state unit representation
An alternative risk calculation to the preferred method is the
multi-state approach, which utilises a probabilistic
representation of the wind plant [7, 17, 18]. Similarly to
conventional units with de-rated states, the wind plant is
modeled with partial capacity outage states each of which has
an associated probability. To evaluate the LOLP at a given
time, the wind generation is included in a COPT calculation in
the same manner as a multi-state conventional unit. The ELCC
calculation then proceeds as described in the preferred
method, except using the modified calculation. A multistate
approach is adopted in [19] where a Markov model is
employed to model wind in discrete states.
The multi-state model for wind power is typically
constructed from a histogram of the wind power output for the
chosen period. A major concern associated with this approach
is the loss of information on wind/load correlation. In most
regions there is significant seasonal and diurnal variation in
wind energy availability, as well as effects of weather on
demand; these cannot be adequately described by a single
probability density function for all periods. This concern may
be addressed to some extent by using different probability
distributions for different categories of hours. The total LOLE
would then be evaluated by adding the LOLEs from the
various categories of hour. However, such a modification still
does not fully account for the correlation between demand and
wind availability. Such effects will be captured automatically
when the preferred methodology is employed.
C. Annual peak calculations
Loss of load probability at time of annual peak demand is
used as a proxy for system risk in some regions, for example
Great Britain has generally followed this practice [20, 21]. The
definition of ELCC for peak calculations remains the same as
for year-round risk calculations, except that the risk index
used is LOLP at time of annual peak. It follows that
probability distributions are required for the demand and
available wind capacity at time of annual peak (the
distribution for available conventional capacity is derived via
a COPT calculation, as in the preferred ELCC calculation
method.)
The requirement for a probability distribution for available
wind capacity is problematic, because peak demand by
definition occurs once a year, and hence by definition the
available data is very limited. Two approaches which have
been used in investigating the wind resource at annual peak
are:
1) Use a histogram of hourly load factors for the entire
peaking season. This has the disadvantage that many
days are not close to annual peak demand, so their
relevance is limited if the wind/demand correlation is
substantial.
2) Use a histogram of load factors from hours where
demand is within a certain percentage of that year’s peak.
This ensures greater relevance to peak demand, at the
expense of reducing the amount of data used.
The main criticisms of an annual peak calculation are that it
does not explicitly consider loss of load at other times of the
year, and that it is difficult to obtain appropriate probability
distributions for the wind resource at annual peak, and also for
the peak load.
D. Peak-period capacity factors
There has been considerable interest in using capacity
factors (average output) calculated over suitable peak periods
to estimate the capacity value of wind. Some of these
approximations are reasonably accurate [5]. In [22] a good
approximation was achieved only if hydro and import-export
transactions were ignored. As discussed previously, this is no
surprise because hydro and transaction schedules are often
positively correlated with load. Although capacity factor
![Fig. 5. ELCC as determined using peak and garver approximations compared to preferred method [24]](/figures/fig-5-elcc-as-determined-using-peak-and-garver-30j854n4.webp)
![Fig. 9. The ELCC values for 3 different levels of wind penetration for the Minnesota State study [14]](/figures/fig-9-the-elcc-values-for-3-different-levels-of-wind-amzb7vt7.webp)