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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 16, NO. 4, NOVEMBER 2001
A Comparison Between Chronological and
Probabilistic Methods to Estimate Wind Power
Capacity Credit
Rui M. G. Castro and Luís A. F. M. Ferreira
Abstract—In this paper, the issue of the capacity credit provided by wind energy conversion systems (WECS) is addressed.
A chronological method of post-evaluation of the capacity credit
is presented and compared with a pre-evaluation probabilistic
method. The proposed chronological approach is based on the
computation of the WECS capacity factor (ratio between average
and total output) over some relevant time period. An appropriate
choice of the time interval, for instance the peak load hours,
will lead to a closer approximation of the capacity credit. The
comparison is illustrated with two case-studies, concerning
the Portuguese electric system. The analysis of the theoretical
background of both methods and the results obtained allow the
conclusion that chronological methods are best designed to assist
system operators, whereas probabilistic methods, which are
developed within the logic of the public system avoided resources,
are a helping tool for system planners.
Index Terms—Capacity credit, chronological methods, power
systems operation, power systems planning, power systems
reliability, probabilistic methods, wind power generation.
I. INTRODUCTION
I
N THE mid-1990s, a new structure of the electricity sector
was set-up in Portugal. In this novel framework (1995), the
coexistence of the following two electric energy sub-sectors was
established:
• a public sector, composed by separated operators for generation, transmission and distribution, and organized in a
logic of providing the public service;
• an independent sector, in which two subsystems take
place:
a market-oriented subsystem, with the aim of promoting the direct link between independent producers
and big consumers, the access to the public network
being guaranteed by the legislation
a “green” subsystem, formed by independent producers using either renewable energy sources (RIP)
or combined heat and power generation (CHP), and
regulated by specific legislation.
The main objective of the legal framework was to create the
adequate conditions for competition between the public and the
Manuscript received September 22, 2000. This work was performed at Instituto Superior Técnico (Technical University of Lisbon) under a research project
financed by ERSE—Entidade Reguladora do Sector Eléctrico (National Electricity Regulatory Authority).
The authors are with IST - Instituto Superior Técnico, Technical University
of Lisbon, Av. Rovisco Pais, 1049 Lisboa, Portugal.
Publisher Item Identifier S 0885-8950(01)08879-4.
market-oriented sectors, in order to increase the efficiency of the
overall electrical sector.
The competition was to be supervised by a Regulatory Authority, created in 1997. Further competences of the Regulatory
Authority comprise the establishment of the electrical sector
legislation including the public system tariffs.
Recently (1999), the government has recognized that the environmental benefits provided by the RIP and CHP producers
have different impacts. Therefore, they are separated in legislative terms, namely in what concerns the pricing of the energy
related services that these producers supply to the grid.
As far as the RIP are concerned, their specific legislation stipulates that the public sector is obliged to purchase the energy
they deliver to the grid at special tariffs, which are to be calculated following a novel method.
The general principle which is behind the new valuation
methodology is the unbundling of the costs avoided by the
public system as a consequence of the integration of these
producers in the grid.
The RIP are now paid accordingly to a sum of parcels regarding its contribution to:
• capacity credit;
• operation and maintenance costs reduction;
• electrical losses reduction;
• environmental benefits.
What is capacity credit provided by a particular renewable
source? In broad terms, one can say that it is the amount of conventional resources (mainly thermal) that could be “replaced”
by the renewable production, without making the system less
reliable. It is usually measured in terms of the installed capacity
of the renewable source.
If this capacity is zero, or is considered as zero, then conventional resources will be needed to guarantee the satisfaction of
peak demand. On the opposite case, some of those conventional
resources will not be needed, and, consequently, some savings
are to be expected, both from the operation and planning points
of view.
Capacity credit is proportional to the availability of the renewable energy technology. As the wind is hard to predict, the
evaluation of the capacity credit provided by wind energy conversion systems (WECS) is a rather interesting problem.
In fact, its assessment is still a matter of great concern both
from the public electrical system and the wind power producers
points of view. Moreover, it is becoming more and more relevant, because the wind power penetration in the generation mix
is increasing steadily for several years.
0885–8950/01$10.00 © 2001 IEEE
CASTRO AND FERREIRA: A COMPARISON BETWEEN CHRONOLOGICAL AND PROBABILISTIC METHODS
Wind is uncertain and, therefore, nondispatchable, which represents a significant drawback from the utilities’ point of view.
Furthermore, they claim that wind energy can never replace conventional resources, or remove the need for new of them to be
built, because the wind cannot be relied upon. So, utilities tend
to assign a low economic value to the capacity credit provided
by WECS.
On the other hand, wind power producers often overestimate
the value of its power. They say that no energy technology can
be relied upon 100% of the time nor the load demand has a
deterministic pattern.
The above mentioned situation fully justifies the need for
a correct assessment of the capacity credit value provided by
WECS.
In this paper, the issue of the capacity credit provided by the
WECS is addressed. A chronological method of post-evaluation
of the capacity credit is presented and compared with a preevaluation probabilistic method. The comparison is illustrated
with two case-studies, the data from which has been taken from
the Portuguese electric system.
II. STANDARD METHODS FOR CALCULATING WECS CAPACITY
CREDIT
Various approaches have been published in the literature concerning the issue of calculating the capacity credit provided by
WECS [1]–[4].
When a priori conclusions are intended, the most accurate
way of evaluating WECS capacity credit is to make use of probabilistic methods, based on some load duration curve. The basic
principles underlying the probabilistic methods of assessing the
capacity credit of a wind plant are standard techniques normally
used to evaluate the reliability of power systems. The evaluation
is based on some reliability measure, one of which is the loss of
load expectation (LOLE).
The LOLE indicates the expected number of hours within a
certain period, in which the utility is unable to meet its load, due
to some unplanned outage of any conventional generating unit.
Setting an acceptable value for the LOLE (for instance, one day
in ten years), allows for the management of the electric system,
in order to attain the desired reliability index.
Adding wind power to the grid, which roughly acts as a “negative load,” has the effect of increasing the reliability of the generating system; therefore, a reduction in conventional power can
be achieved. This reduction is taken as a measure of the capacity
credit of wind power.
Probabilistic methods are now a mature tool and new techniques are being proposed to further improve its performance.
However, they require a significant modeling effort and a major
computational burden.
III. THE CHRONOLOGICAL APPROACH
Wind speed varies widely along the time; therefore, to retain
as much chronological information as possible, is of utmost importance to capture the proper time-scale relationship between
the load and the WECS output.
Under these circumstances; it seems acceptable to use average values, which integrate the behavior of the whole wind
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park along a representative time interval, to account for its contribution to the availability of power in the grid.
In this sense, the load factor is a suitable index to evaluate
the WECS performance, in terms of the power supplied to the
grid over a time period. Let us remember that the load factor is
defined as the ratio between the average output and the rated
output, over a particular time period, for instance, a week, a
month, a year. Moreover, as this is a nondispatchable power, the
power supplied equals the power available.
Based on this idea, a simpler alternative approach to compute
WECS capacity credit is the use of a chronological method, that
computes the capacity factor (ratio between the average output
and the total output over some relevant time period) [5].
The capacity factor of a wind plant can be seen as the statistically expected output divided by the total output, and, in this
sense, it is an approximation to the capacity credit.
The calculation of the capacity factor may be performed over
various time periods. The selection of the appropriate time period is a key issue in this method.
The consideration of the whole year as the time period will
disregard an important matter: power is as much valuable, as
it is available whenever is required, and this is generally at
peak hours. On the other hand, if one takes only the top-peak
load hours, the results will appear hazardous, due to wind
fluctuations.
In broad terms, one can say that peak-hours occur at daylight
and night hours are considered as off-peak hours. Therefore, it
seemed reasonable to proceed as follows:
• to arrange the hourly load demand in a decreasing order;
• to compute chronologically the WECS capacity factor
against the hourly load demand;
• to retain the value of the capacity factor computed for the
top 50% of the load hours as a closer estimation of the
WECS capacity credit.
IV. APPLICATION OF THE CHRONOLOGICAL METHODOLOGY
The proposed chronological methodology was implemented
and applied to two case-studies built upon data available for the
Portuguese electric system [6].
A. Case-Study A—Fonte da Mesa Wind Park
A first application of the methodology was performed using
two sets of data corresponding to the year of 1998: the hourly
average power supplied by Fonte da Mesa wind park, and the
total national hourly load as seen from the public system.
Fonte da Mesa is a 10 MW wind park, located at the northern
part of the country and owned by the utility.
Two remarks worth to be mentioned:
• At the time of 1998, Fonte da Mesa wind park capacity
was around 20% of the total wind capacity installed in
Continental Portugal.
• The peak load of the national electrical system in 1998 was
slightly above 6000 MW.
Fig. 1 presents the results achieved by plotting the capacity
factor of Fonte da Mesa wind park against the total national
hourly load. It should be stressed that the hourly loads have been
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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 16, NO. 4, NOVEMBER 2001
Fig. 1.
Wind capacity credit for case-study A. Chronological method.
Fig. 2.
Wind capacity credit for case-study B. Chronological method.
arranged following a decreasing order, that is, from the maximum loads to minimum loads.
The 1998 Fonte da Mesa load factor, i.e., the capacity factor
computed for 100% of the hours, was about 26%, which may be
considered as a typical value.
Fig. 1 clearly shows that conclusions based on the consideration of only the top-peak hours (let’s say about 10%) are meaningless. In fact, the wind instability makes the results appear to
be casual.
Following the proposed criteria of retaining the top 50% load
hours, the capacity factor is reduced to 24%. Therefore, one can
say that 24% of the wind park installed capacity (2, 4 MW) may
be considered as an estimation of the capacity credit provided
to the public system, in 1998.
It should be stressed that an advantage of this kind of a posteriori analysis, is that it represents what has effectively happened. In fact, the chronological correspondence between the
wind park power output and the system’s load has been computed at the same hours. Moreover, the unexpected outages, both
of the park and the grid, have been naturally incorporated.
B. Case-Study B—Torres Vedras Virtual WECS
The same methodology was applied to perform another simulation, in different conditions.
A series of hourly wind speed data measured during the year
of 1998 at a location situated near Torres Vedras, in the central
part of Portugal, was taken. Correction to the hub height was applied and the resultant wind speed was converted to wind power
using a standard curve “electrical power output—wind speed”
of a 500 kW wind turbine.
This procedure intended to simulate a virtual WECS installed
at the mentioned location and connected to a particular rural
substation. Nevertheless, it should be pointed out that the resultant synthetic wind power output does not account for any
outages, nor from the WECS, nor from the grid.
The Torres Vedras virtual WECS capacity factor, computed
after the synthetic power output, was plotted against the total
national load, using the same approach as described above.
The results obtained are presented in Fig. 2.
The load factor of the virtual WECS is about 43%. This extremely high value is a result of two contributions:
• The mean wind speed at the WECS location was exceptionally high.
• A single WECS with 100% availability has been
considered.
When only the relevant hours are considered (50% of the total
number of hours) the capacity factor reduces to 41%.
CASTRO AND FERREIRA: A COMPARISON BETWEEN CHRONOLOGICAL AND PROBABILISTIC METHODS
907
Fig. 3. Normal distribution of the system load at peak hours.
The capacity credit that would have been provided by this
WECS in 1998 can therefore be overestimated in 40% of its
installed capacity (200 kW).
C. Remarks
It is apparent from Figs. 1 and 2 that the results obtained
from the simulations performed are very different. However, this
should not be viewed as a surprising result.
When only a few peak hours are considered, depending on
wind fluctuations the capacity factor may vary above or under
the load factor. If the number of hours is enlarged, then the capacity factor approaches the load factor.
This conclusion complies with the known conclusion of wind
specialists: “wind is random in the short-term, but almost predictable in the long-term.”
A limitation of the work presented so far is the shortness of
data used to calculate the capacity factor. Would the available
WECS power output cover an enlarged period of several years,
and more filtered results would be obtained, thus diminishing
the effects of wind randomness.
V. COMPARISON WITH A PROBABILISTIC METHOD
In order to assess the validity of the results obtained with
the proposed chronological methodology, a comparison with a
probabilistic method [7] was performed.
The method firstly assumes the following three hypotheses:
• The wind speed at the time of peak demand can be accurately described using a probabilistic Weibull distribution.
• The peak demand follows a probabilistic Normal
distribution.
• The conversion of wind speeds into electrical power
output is made through a typical power curve.
These hypotheses correspond to normal practices in wind energy probabilistic studies.
Considering that represents the capacity of conventional
the wind power output,
resources, the load peak demand,
the reliability level at which the peak demand should be satisfied, and the density of probability, it is possible to write:
Now, if
and
are, respectively, the values of
such that
and
the wind capacity credit, , can be computed as
The availability of the hourly average wind speed series at
both the sites A and B has allowed the computation of Weibull
parameters. Therefore, the Weibull distribution of the wind
speed at the two sites was obtained.
Moreover, a Normal distribution for the national load demand
was built, considering only the peak hours.
Fig. 3 displays the result achieved for the system load at peak
hours during 1998. It should be noted that the computed average
load demand was 4444 MW; this value was retained as the base
power for per unit conversions.
Also, the mapping of the wind speed into the wind power
output was performed at the two sites making use of a standard
500 kW turbine.
The described probabilistic method has been implemented
[6] and the results of its application to the above mentioned
case-study A and case-study B are shown in Figs. 4 and 5, respectively. It is worth to be mentioned that Figs. 4 and 5 show
both the computed data (marked thin line) and the respective
trend line (bold line).
All the calculations were performed in per unit values. This
procedure had the following implications:
• The computation of the wind capacity credit was performed in terms of the total installed wind capacity. This
index is shown in the vertical axis of Figs. 4 and 5.
• The definition of a quantity called “wind penetration
level” as the percentage ratio between the wind installed
capacity and the base power. This index is shown in the
horizontal axis of Figs. 4 and 5.
At the time of 1998, the wind penetration level was about
1%, since the wind installed capacity was around 45 MW in
Continental Portugal.
Analysis of Figs. 4 and 5 allows the conclusion that capacity
credit as estimated by the probabilistic method is around 26%
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Fig. 4.
IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 16, NO. 4, NOVEMBER 2001
Wind capacity credit for case-study A. Probabilistic method.
Fig. 5. Wind capacity credit for case-study B. Probabilistic method.
and around 39%, using Fonte da Mesa and Torres Vedras data,
respectively.
Although these results generally agree with the ones provided
by the chronological method, that is not the main issue here.
One that would like to know what is the capacity credit provided by installed WECS in Portugal, would find the results of
Figs. 4 and 5 very confusing. This is because an incorrect use of
the probabilistic method has been made.
The important conclusion that is strongly pointed out by
Figs. 4 and 5 may be enunciated as follows:
• Chronological methods are best suited for system operators. Providing that enough historical data is available, it
is possible to obtain a quick estimate of the capacity credit
provided by a particular wind park. This is important to account for the ability of the wind resources to satisfy peak
demands.
• Probabilistic methods are best suited for system planners.
The application of these methods is made from the point
of view of the public system avoided resources. They consider a big equivalent WECS generating wind power accordingly to an average national wind profile. This is very
useful in planning studies, to account for the statistically
expected capacity credit contribution of WECS.
VI. CONCLUSION
What is the value of the capacity credit provided by wind energy conversion systems to the public system? This question
was addressed in the paper, by means of a comparison of two
approaches to the problem: chronological methods and probabilistic methods.
The main conclusions of the work may be summarized as
follows:
• Chronological and probabilistic methods are not alternative, but are in fact complementary as they address different types of studies. The first are suitable to help the
system’s operation, whereas the later are a tool to assist
system planners.
• Capacity credit as calculated using a chronological
method was computed after the capacity factor over
the peak hours, whereas probabilistic capacity credit
is the amount of conventional resources that could be
“replaced” by the renewable production, without making
the system less reliable.
• For low levels of wind power penetration in the grid, the
WECS capacity credit can be approximated by the average
wind power.
CASTRO AND FERREIRA: A COMPARISON BETWEEN CHRONOLOGICAL AND PROBABILISTIC METHODS
ACKNOWLEDGMENT
The authors would like to thank REN, LTE, and ENERNOVA, all of them part of EDP Group, for their contributions
in supplying data for performing the simulations.
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[2] A. J. M. van Wijk, N. Halberg, and W. C. Turkenburg, “Capacity credit
of wind power in the Netherlands,” Electric Power Systems Research,
vol. 23, 1992.
[3] M. R. Milligan, “Variance estimates of wind plant capacity credit,” in
AWEA Windpower’96, Denver, CO, June 1996.
[4] R. Billinton, H. Chen, and R. Ghajar, “A sequential simulation technique
for adequacy evaluation of generating systems including wind energy,”
IEEE Trans. Energy Conversion, vol. 11, no. 4, Dec. 1996.
[5] M. Milligan and B. Parsons, “A comparison and case study of capacity
credit algorithms for intermittent generators,” in Solar’97, Washington,
DC, Apr. 1997.
[6] L. Pacheco, P. Oliveira, and T. Rodrigues, “Pricing the energy services
provided by the independent producers using renewable sources,” Graduation thesis (in Portuguese), IST, July 1999.
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[7] L. A. F. M Ferreira, “Capacity credit at the time of peak demand,”
in Planning for Large Wind Energy Penetrations: Contract no.
JOU2-CT92-0109 (DTEE), Electricidade de Portugal, Mar. 1994.
Rui M. G. Castro was born in Lisboa, Portugal, on January 17, 1961. He received the electrical engineering degree, and the M.Sc. and Ph.D. degrees from
Technical University of Lisbon (TUL), in 1985, 1989, and 1994, respectively.
In 1985, he joined the TUL, Power Systems Section, where he is currently an
Assistant Professor. His research interests are in the areas of power systems transients and control, renewable energies, energy pricing and open markets.
Luís A. F. M. Ferreira was born in Bombarral, Portugal, on June 22, 1953. He
received the electrical engineering degree from Technical University of Lisbon
(TUL), and the M.Sc. and Ph.D. degrees from GeorgiaTech—Georgia Institute
of Technology in 1977, 1983, and 1986, respectively. In 1977, he joined the
TUL, Power Systems Section, where he is currently an Associate Professor.
His research interests are in the areas of power systems control, distribution
planning.