IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 2, JUNE 2006
533
A Simplified Wind Power Generation Model
for Reliability Evaluation
Rajesh Karki, Senior Member, IEEE, Po Hu, Student Member, IEEE, and Roy Billinton, Life Fellow, IEEE
Abstract—Renewable energy sources, especially wind turbine
generators, are considered as important generation alternatives
in electric power systems due to their nonexhausted nature and
benign environmental effects. The fact that wind power penetration continues to increase has motivated a need to develop more
widely applicable methodologies for evaluating the actual benefits
of adding wind turbines to conventional generating systems. Reliability evaluation of generating systems with wind energy sources is
a complex process. It requires an accurate wind speed forecasting
technique for the wind farm site. The method requires historical
wind speed data collected over many years for the wind farm location to determine the necessary parameters of the wind speed
models for the particular site. The evaluation process should also
accurately model the intermittent nature of power output from
the wind farm. A sequential Monte Carlo simulation or a multistate wind farm representation approach is often used. This paper
presents a simplified method for reliability evaluation of power
systems with wind power. The development of a common wind
speed model applicable to multiple wind farm locations is presented and illustrated with an example. The method is further
simplified by determining the minimum multistate representation
for a wind farm generation model in reliability evaluation. The
paper presents a six-step common wind speed model applicable
to multiple geographic locations and adequate for reliability evaluation of power systems containing significant wind penetration.
Case studies on a test system are presented using wind data from
Canadian geographic locations.
Index Terms—Generation system, reliability evaluation, timeseries model, wind power.
I. INTRODUCTION
IND is one of the fastest growing energy sources, and is
regarded as an important alternative to traditional power
generating sources. Enhanced public awareness of the environment has led to rapid wind power growth throughout the world to
reduce greenhouse gas emissions associated with conventional
energy generation. An energy policy known as the renewable
portfolio standard (RPS) is being widely accepted around the
world. Acceptance of the RPS is a commitment to produce a
specified percentage of the total power generation from renewable sources within a certain date. In the North America, many
US states and Canadian provinces have agreed to generate between 5% and 25% of electrical power from renewable energy
resources by 2010–2015. Most of this renewable energy will
W
Manuscript received September 15, 2005; revised September 15, 2005. Paper
no. TEC-00177-2005.
The authors are with the Power System Research Group, Department
of Electrical Engineering, University of Saskatchewan, Saskatoon, SK
S7N 5A9 Canada (e-mail: Rajesh.Karki@usask.ca, poh591@mail.usask.ca,
Roy Billinton@engr.usask.ca).
Digital Object Identifier 10.1109/TEC.2006.874233
come from wind as other renewable sources are not suitable for
bulk power generation.
The development of comprehensive reliability and costevaluation techniques becomes more important as wind power
penetration levels in traditional power systems continue to increase in the near future. Both Monte Carlo simulation [1], [2]
and analytical methods [3]–[5] have been utilized in adequacy
assessment of generation systems containing wind power.
Simulation methods can recognize the chronology of wind
variation and its impact on a power system. Reference [6]
presents an algorithm to simulate the hourly wind speed using a time-series auto regressive and moving average (ARMA)
model. The method requires actual hourly wind speed data collected over a long period of time for the particular geographic
location to construct a wind speed simulation model for the
specific site. This model can reflect the true probabilistic characteristics of wind speed for the wind site.
The process for obtaining the proper ARMA model is quite
complex, and is specific to the geographic location of the wind
farm. Complex techniques are not readily applied in a practical
world. It would be very useful from a practical application point
of view if a common ARMA model could be developed that
would work for multiple wind farm locations [7]. It should also
be noted that historical wind data are not available for all potential wind farm locations. This paper presents the development of
a common wind speed model that can generate wind speed probability distributions for multiple wind farm sites if their annual
mean wind speed and standard deviation are known. Historical wind speed data from three Canadian sites (Swift Current,
North Battleford, and Toronto, which have different geographic
characteristics), are used in this paper to obtain the common
wind speed model. The wind speed distribution obtained from
the common wind speed model can then be used in an analytical
method for reliability evaluation of power systems containing
wind farms.
A wind turbine generator (WTG) is modeled as a multistate
unit in reliability evaluation using an analytical method [3]–[5].
The multistate model represents a WTG by a number of derated
power output states using the wind speed model for the wind
farm location and the power curve of the WTG. The model
appropriately reflects the fluctuating characteristics of the sitespecific wind.
Reliability studies using the Roy Billinton Test System
(RBTS) [8] are presented to determine the appropriate number
of states in the multistate WTG model, and develop a simplified model applicable to any wind farm connected to a power
system. The development of a simplified 6-step common wind
speed model that can be applied to any wind farm in power
0885-8969/$20.00 © 2006 IEEE
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 2, JUNE 2006
system reliability evaluation is presented. The validity of the
developed method and its practicality is illustrated by evaluating wind power penetration in the RBTS.
TABLE I
MAIN STATISTICAL CHARACTERISTICS OF SIMULATED
AND ACTUAL WIND SPEED DATA
II. SITE-SPECIFIC WIND DATA SIMULATION
Wind resource at a geographic location is highly variable.
Power generated from WTG depends on the wind speed, which
fluctuates randomly with time. Wind power studies, therefore,
require accurate models to forecast wind speed variation for
wind farm locations of interest.
Wind speed distributions are often characterized by Weibull
distributions, and methods using Weibull distributions [5] have
been previously used to estimate wind speed data in wind power
studies. Historical hourly data for the wind farm site collected
over significant time are normally required to obtain the shaping
parameters.
An ARMA time-series model has been used by researchers
[1], [2], [6] as an accurate method to forecast wind speed data
at any particular location. The wind speed at any given time for
a particular geographic location can be simulated using (1)
(1)
SWt = µt + σt . . . yt
where SWt is the simulated wind speed for hour t from historical mean wind speed µt and standard deviation σt . Timeseries values of yt can be obtained sequentially using (2), where
ϕi(i = 1, . . . , n) and θj(j = 1, . . . , m) are the auto-regressive
and moving average parameters of the model, respectively
yt = φ1 yt−1 + φ2 yt−2 + . . . + φn yt−n + αt
− αt−1 θ1 − αt−2 θ2 − . . . − αt−m θm
(2)
where {αt } is a normal white noise process with zero mean
and a variance of σa2 (i.e., αt ∈ NID(0, σa2 ), where NID denotes
normally independently distributed. The order [n, m] and the
values of the auto-regressive and moving average parameters
shown in (2) can be obtained from many years of collected
wind speed data using nonlinear least-square methods [9]. A
computer program was developed to estimate the parameters of
ARMA (n, m) models for geographic wind farm sites using the
algorithm provided in [9].
Historical wind data was obtained for three different locations
in Canada: Swift Current, North Battleford, and Toronto. Swift
Current lies in the southern part of the Saskatchewan province
and is home to one of the largest wind farms in Canada. North
Battleford lies to the north in the same province, but does not
have a good wind resource. Toronto lies at the great lakes and
has a coastal wind regime. These three locations have diverse
wind variation patterns and are therefore selected in the study.
Historical data on hourly wind speeds for three years (from
January 1, 2001 to December 31, 2003), and the hourly mean
and standard deviation of wind speeds from a 15-year database
(from January 1, 1989 to December 31, 2003) were obtained
from Environment Canada to determine the ARMA model for
the Swift Current location. The parameters are shown in (3)
yt = 0.8782yt−1 − 0.0066yt−2 + 0.0265yt−3
+ αt − 0.2162αt−1 + 0.0091αt−2
αt ∈ NID(0, 0.557922 ).
(3)
Equations (4) and (5) show the time-series ARMA models
obtained similarly for North Battleford and Toronto locations
respectively
yt = 1.7901yt−1 − 0.9087yt−2 + 0.0948yt−3
+ αt − 1.0929αt−1 + 0.2892αt−2
(4)
αt ∈ NID(0, 0.4747622 )
yt = 0.4709yt−1 + 0.5017yt−2 − 0.0822yt−3
+ αt + 0.1876αt−1 − 0.2274αt−2
(5)
αt ∈ NID(0, 0.5508 ).
2
Hourly wind speeds were repeatedly simulated for a large
number of yearly samples to obtain annual wind speed data for
the three sites. Table I shows the mean value and standard deviation of 20 years’ average actual collected data and simulated
wind speed data for a year for these sites. It can be seen that
the simulated values are very close to those obtained from the
actual data.
The entire range of the simulated data is equally divided into
Na intervals, and the SWai (i = 1, . . . , Na ) is the midpoint of
each interval. The probability Pai of a wind speed in an interval
SWai (i = 1, . . . , Na ) can be obtained using (6) by counting the
number Nai (i = 1, . . . , Na ) of simulated wind speed data in the
interval
Pai = Nai /(8760 × Ny )
(6)
where Ny is the number of sample years simulated.
The wind speeds SWai at each of the Na intervals and their
corresponding probabilities of occurrence Pai were calculated
for the three sites. Fig. 1 shows the probability distributions of
simulated wind speed data for these three sites.
Wind speed probability distributions are often represented by
Weibull distributions. Weibull distribution in general can have
various shapes depending on the shaping parameters. The wind
speed probability distributions obtained for the three diverse
geographic locations, however, are close to normal distribution
as shown in Fig. 1. It can however be seen that the three curves
are quite different, as the three selected sites have different
types of wind regimes. Time-series ARMA model generate both
positive and negative values of wind speeds as seen in Fig. 1.
Negative values have no physical meaning in this study, and are
set to zeros as recommended in [7].
KARKI et al.: A SIMPLIFIED WIND POWER GENERATION MODEL FOR RELIABILITY EVALUATION
Fig. 1.
Probability distributions of simulated wind data.
Fig. 2.
III. COMMON WIND SPEED MODEL FOR
MULTIPLE WIND SITES
The determination of a proper wind speed model for a wind
farm location is a complicated process as described in Section
II. The process also requires historical wind speed data collected
over a significant period of time. It would be very useful for practical applications, if a common wind speed model could be used
for benefit analysis of wind power sources located at different
geographic sites. This approach will prove useful for prospective wind farm locations lacking adequate historical data. The
objective is to determine a general model that can be used to
obtain power output from wind turbines located at different sites
with reasonable accuracy.
The probability distributions of wind speeds at the three selected geographic sites are shown in Fig. 1 in Section II. In
this section, the probability distributions are plotted in terms
of the annual mean wind speed value µ, and the standard deviation σ for the selected locations. The distribution considers wind speeds up to 10 σ to include extreme values despite
their low probability of occurrences. The distribution is divided into Nb number of interval steps, and each step has a
length of 10 σ/Nb , where the midpoint values of these steps are
SWbi (i = 1, . . . , Nb ), and one of the steps has a midpoint value
of µ. The steps SWbi are defined as in (7). For example, for a
100-step model, the midpoint values SWbi of the wind speed
steps will be as follows: µ–4.9σ, µ–4.8σ, . . . , µ–0.1σ, µ, µ +
0.1σ, µ + 0.2σ, . . . , µ + 5σ. The probability of each step
Pbi (i = 1, . . . , Nb ) can be calculated by (8)
SWbi = µ + (10σ/Nb ) × (i − 0.5 × Nb ) for even Nb , and
= µ + (10σ/Nb ) × (i − 0.5 × (Nb + 1))
for odd Nb
(7)
Pbi = Nbi /(8760 × Ny )
(8)
where Nbi is the number of simulated wind speed data in the
step SWbi (= 1 . . . , Nb ).
535
Combining wind speed models for different sites.
The probability distributions plotted in terms of µ and σ as
discussed above are shown in Fig. 2 for the three locations. It
can be seen that the three curves are very close. The three curves
for the three different wind regimes can be combined to obtain a
common wind speed model. The probability Pci (i = 1, . . . , Nb )
for each step in the common wind speed model is obtained by
taking the average value of Pbi (i = 1, . . . , Nb ) for these three
wind sites. Fig. 2 also shows the curve for the common wind
speed model.
The common wind speed model can be used to obtain the
wind speed probability distribution for any geographic location
with wind speed characteristics close to the selected Canadian
sites. The only data required are the annual mean wind speed µ
and the standard deviation σ for that site. Negative wind speed
values are converted to zeroes in this process. It is shown in
Section VI that the wind speeds and their probabilities obtained
for a specific site using the common wind speed model can be
used with reasonable accuracy in the reliability evaluation of
power systems containing wind power. Fig. 3 shows a common
wind speed model that can be used for multiple geographic
locations.
The application of the common wind speed model in Fig. 3
is illustrated in this paper by applying it to a site in Regina,
Saskatchewan. The µ and σ values for Regina wind data are
19.53 and 10.06 km/h, respectively. The common wind speed
model is used to obtain the wind speeds and their corresponding
probabilities for the example site. Table II shows the wind speeds
in km/h and their corresponding probabilities. Only 5 out of the
100 steps in the wind speed model are shown. It should be noted
that the negative values are converted to zeroes in Table II.
IV. COMMON WTG POWER GENERATION MODEL FOR
RELIABILITY EVALUATION
It is important to accurately assess the electric power generated by a WTG located at a particular geographic site in reliability analysis. The generated power varies with the wind
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Fig. 5.
Fig. 3.
Common wind speed model.
TABLE II
WIND MODEL FOR REGINA SASKATCHEWAN
Development of a WTG model.
Fig. 5 shows the development of the power generation model
of a WTG located at a particular geographic site. The annual
µ and σ wind speed data for the wind farm site is used in the
common wind speed model shown in Fig. 3 to obtain the sitespecific wind speed model. This site-specific wind speed model
is then combined with the WTG power curve to obtain the WTG
power generation model.
Equation (9) is the mathematical expression for the power
curve. The power generated Pi (i = 1, . . . , Nb ) corresponding
to a given wind speed SWbi (i = 1, . . . , Nb ) can therefore be
obtained from (9)
0 ≤ SWbi < Vci
Pi = 0,
= Pr (A + B × SWbi + C × SW2bi ),
Vci ≤ SWbi < Vr
Vr ≤ SWbi ≤ Vco
= Pr ,
= 0,
Vco < SWbi
(9)
where the constants A, B, and C are presented in [3].
Wind speeds less than Vci and greater than Vco produce zero
output power from the WTG. The wind speed model steps corresponding to these values can, therefore, be combined into a
cumulative step, and the zero output probability Pp0 can be obtained from (10). Similarly, wind speed steps between Vr and
Vco can be combined, and the probability of rated power output
Ppr can be obtained from (11)
Pci for 0 ≤ SWbi < Vci or Vco < SWbi
Pp0 =
Ppr =
Fig. 4.
(10)
Pci
for Vr ≤ SWbi ≤ Vco
(11)
Power curve of a WTG.
speed at the wind farm site. The power output of a WTG can
be determined from its power curve, which is a plot of output
power against wind speed. Fig. 4 shows a typical power curve
of a WTG. A WTG is designed to start generating at the cut-in
speed Vci (Vc ) and is shut down for safety reasons at the cut-out
speed Vco . Rated power Pr is generated when the wind speed is
between the rated speed Vr and the cut-out speed Vco . There is
a nonlinear relationship between the power output and the wind
speed when the wind speed lies within the cut-in speed Vci and
the rated speed Vr as shown in Fig. 4.
The application of the common WTG power generation
model is illustrated in this paper by applying it to a WTG
installed in Regina. WTG rated at 1.5 MW, and with cut-in,
rated, and cut-out wind speeds of 14.4, 45, and 90 km/h, respectively, are used in the studies. The site-specific wind speed
model shown in Table II is combined with the power curve to
obtain the WTG generation model. Table III shows the power
output levels and their corresponding probabilities. The 100step wind speed model in Table II is reduced to 33 steps in the
power generation model in Table III as different wind speeds
producing the same power level are aggregated into single
steps.
KARKI et al.: A SIMPLIFIED WIND POWER GENERATION MODEL FOR RELIABILITY EVALUATION
TABLE III
POWER GENERATION MODEL FOR A WTG IN REGINA
537
TABLE V
LOLE COMPARISON OF RBTS INCLUDING WECS LOCATED
AT DIFFERENT WIND SITES
TABLE IV
TRADITIONAL GENERATING UNIT RELIABILITY DATA (RBTS)
A wind farm usually consists of many WTG units subjected
to the same wind regime characterized by the geographic location. The total power generation model for the wind farm can
be obtained by summing up the individual WTG power levels
corresponding to each wind speed interval in the common wind
speed model.
V. VALIDITY OF THE COMMON WIND SPEED MODEL FOR
RELIABILITY STUDIES
The power generation model for a wind farm can be easily
obtained from the common wind speed model shown in Fig. 3
using only the site-specific µ and σ data and the WTG power
curve. The validity of this common model for practical reliability
applications is analyzed using a test system. Reliability studies
using analytical techniques were conducted on the RBTS [8] to
illustrate the practicality of a common wind speed model for
different sites.
The RBTS is a basic reliability test system that evolved from
the research and teaching program conducted at the University of
Saskatchewan. The RBTS consists of 11 traditional generating
units with a total capacity of 240 MW. The generating unit
ratings and reliability data are shown in Table IV. The system
peak load is 185 MW [8].
A wind farm with 18 WTG units was added to the RBTS.
WTG rated at 1.5 MW, and with cut-in, rated, and cut-out wind
speeds of 14.4, 45, and 90 km/h, respectively, was used in the
studies. The added wind capacity is 27 MW, which is almost
10% of the total installed system capacity.
The generating system adequacy of the test system was evaluated for three different cases, in which the wind farm was
considered at separate locations with North Battleford, Toronto,
and Swift Current wind regimes. Table I shows the mean wind
speed and the standard deviation for the three sites.
Table V shows the loss of load expectation (LOLE) [10]
for the RBTS before and after adding WTG at the different
locations. The LOLE results were obtained by convolving the
Fig. 6. LOLE comparison for North Battleford using its ARMA model and
the common wind speed model.
system generation model with the load model using an analytical
technique. The conventional generating units were represented
by a two-state model, in which the unit is either operating at
rated power output or on forced outage. To account for the
randomly varying power output from WTG units, they were
represented by 100-state model in the studies. The annual load
duration curve for the RBTS was used as the load model, and the
data are provided in [8]. The second row of Table V shows the
indices using the site-specific ARMA models shown in (3)–(5)
for the three locations. The third row shows the results obtained
using the common wind speed model in Fig. 3. It can be seen
that the results are very close. It can also be seen from Table V
that the adequacy of the RBTS is improved by adding the 27MW wind farm. The improvement with the Swift Current site
is more significant than that of the other two locations, as Swift
Current has a higher mean wind speed, and therefore, provides
a better wind resource.
Table V shows that the common wind speed model produces
accurate results for wind farm locations with different wind
regimes. Power system reliability is very sensitive to changes in
the system peak load. The accuracy of the common wind speed
model is therefore analyzed for different peak load levels at the
three geographic wind farm locations. Fig. 6 shows the system
LOLE for different peak load levels with the wind farm located
in North Battleford. The results obtained using the common
wind speed model is compared with those obtained using the
North Battleford ARMA model given in (4). Fig. 6 shows that the
common wind speed model also produces very close results at
different peak load levels. Fig. 7 shows similar results when the
wind farm is considered to be in the Toronto location. The results
show that the common wind speed model can be utilized in the
reliability evaluation of power systems containing wind farms,
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 2, JUNE 2006
Fig. 7. LOLE comparison for the Toronto Data using its ARMA model and
the common wind speed model.
Fig. 8. Swift Current wind site with a 10% wind power penetration level
(18 WTG).
and provide very close results compared to the site-specific
ARMA models for the different sites.
VI. SIMPLIFIED MULTISTATE WTG MODEL
A conventional generating unit is usually represented by a
two-state model in power system reliability evaluation. The two
states are the unit-operating state with rated power output, and
the unit-failure state with zero output. A WTG unit, however,
cannot be represented by a two-state model since the power
output can vary continuously and intermittently from zero to the
rated value depending on the wind speed at the wind farm site.
WTG units are therefore represented by multistate models in
analytical methods used in power system reliability assessment.
Accurate reliability assessment can be obtained by representing a wind farm by a large number of discrete output states.
This can be obtained from a wind speed model with a large
number of discrete wind speed steps. The model can be simplified by reducing the number of steps at the cost of accuracy. It
is, therefore, important to determine the minimum number of
steps that can be used in a simplified wind speed model to obtain
reasonable accuracy for all practical purposes.
Studies were done to evaluate the system LOLE with increasing peak load levels using different numbers of wind speed steps
in the common wind speed model. The wind farm is assumed
to be located in Swift Current. Fig. 8 shows the results of the
study. It can be seen that using six or more steps in the wind
speed model provides close results.
The reliability contribution of a wind farm highly depends on
the site wind regime. Studies similar to that shown in Fig. 8 were
also conducted for a wind farm site with a different wind regime.
Fig. 9 shows the system LOLE results for the case in which the
wind farm is assumed to be located in Toronto. Fig. 9 also shows
that a 6-step wind speed model is adequate for reliability studies
with reasonable accuracy.
It should be noted that 27 MW of wind capacity is added to the
RBTS in the above studies, which amounts to about a 10% wind
penetration. Since the reliability contribution of wind sources is
highly dependent on the wind penetration level, it is important to
determine the appropriate number of wind speed model steps at
practical wind penetration levels. The existing wind penetration
levels in most power systems are much lower than 10% for
Fig. 9. Toronto wind site with a 10% wind power penetration level (18 WTG).
Fig. 10. Swift Current wind site with a 15% wind power penetration level
(28 WTG).
which the above results are obtained. Studies conducted for
wind penetration of 1% showed that the number of steps had no
impact on the system LOLE results. When the penetration level
is insignificant, wind power has relatively little influence on the
total system reliability performance.
Reliability evaluation in power system planning should consider a long-term planning horizon. It is expected that wind
power penetration will grow to 10%–15% in the next 10–15
years. Fig. 10 shows the results obtained when the wind farm
added to the RBTS contains 28 WTG units, increasing the wind
penetration to 15% of the total installed system capacity. The
results show that a six-step wind speed model is adequate for
reliability studies with reasonable accuracy.
KARKI et al.: A SIMPLIFIED WIND POWER GENERATION MODEL FOR RELIABILITY EVALUATION
Fig. 11.
Six-step common wind speed model.
Fig. 12.
index.
539
Comparison of different models for WTG power output by LOLE
TABLE VI
Six-STEP WIND MODEL FOR REGINA SITE
using the simplified model in Table VII. The results obtained
from the simplified model are compared with those obtained
from a 100-step wind speed model derived from an accurate
ARMA (4, 3) model for Regina as shown in (13)
yt = 0.9336yt−1 + 0.4506yt−2 − 0.5545yt−3 + 0.1110yt−4
+ αt − 0.2033αt−1 − 0.4684αt−2 + 0.2301αt−3
(13)
αt ∈ NID(0, 0.409423 )
2
TABLE VII
SIMPLIFIED POWER GENERATION MODEL FOR
THE REGINA WIND FARM
The 6-step common wind speed model that can be used for
reliability studies of power systems with reasonable accuracy is
shown in Fig. 11. The model shows the six wind speed steps
and the corresponding probabilities. The wind speeds for a geographic site can be obtained from this model using (12), if µ
and σ for the site are known
SWbi = µ + (i − 3) × (5σ/3)
for (i = 1, . . . , 6).
(12)
The application of the six-step common wind speed model
is illustrated by applying it to a site in Regina. Table VI shows
the wind speeds in km/h and their corresponding probabilities. It should be noted that the negative values are converted
to zeroes.
A simplified multistate power generation model for a WTG
can be determined by combining the 6-step common wind speed
model with the power curve equation (9). This method can
be utilized to develop a simple but adequate multistate wind
generation model. The only data required are the wind farm site
annual µ and σ data, and the power-curve data for the WTG
units. For example, Table VII shows the simplified multistate
power generation model for a wind farm consisting of 18 WTG
units in Regina.
Fig. 12 shows the results of reliability assessment of the RBTS
system with 10% wind penetration coming from the 27-MW
Regina wind farm. The shaded bars show the LOLE results
It can be seen from Fig. 12 that the simplified multistate WTG
power generation model derived from the common 6-step wind
speed model can provide very close results when compared with
the 100-step model derived from the site-specific time-series
ARMA wind speed model for Regina. The simplified model
can therefore be used in the reliability evaluation of generating
system including wind power with reasonable accuracy.
VII. CONCLUSION
It becomes increasingly important to develop realistic reliability evaluation techniques that are practically useful for electric
power industries that are expected to include a rapidly growing
proportion of wind generation in the coming years. The benefits from wind sources are largely dictated by the wind regime
at the wind farm site. It is, therefore, very important to obtain
suitable wind speed simulation models and appropriate techniques to develop power generation model for WTG in reliability
evaluation.
It requires a significant amount of historical data and effort
to develop a realistic wind speed model for a geographic site.
Historical data from three Canadian sites with diverse wind
regimes were used to obtain a common wind speed model in
this paper. The common wind speed model can be applied to
obtain a wind farm power generation model for any geographic
location if the mean wind speed and standard deviation, and
the WTG power curve parameters are known. Results from
different analytical reliability studies are presented in this paper
to show that a wind power generation model can be greatly
simplified by using only 6 steps in the common wind speed
model. The technique to develop the simplified WTG multistate
model for any geographic location is presented and illustrated
with an example. The results show that the simplified method
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 2, JUNE 2006
can be used in the reliability evaluation of a generating system
including wind power with reasonable accuracy. This approach
will be very useful for wind farm locations lacking adequate
historical data. The presented simplified method can be easily
used for practical applications.
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1–4, 2005, pp. 541–544.
[8] R. Billinton and S. Kumar, “A reliability test system for educational
purposes—Basic data,” IEEE Trans. Power Syst., vol. 4, no. 3, pp. 1238–
1244, Aug. 1989.
[9] S. M. Pandit and S. M. Wu, Time Series and System Analysis With Application. New York: Wiley, 1983.
[10] R. Billinton and R. N. Allan, Reliability Evaluation of Power Systems,
New York: Plenum, 1996.
Rajesh Karki (S’98–M’00–SM’04) received the B.E. degree from Burdwan
University, Durgapur, India, in 1991, and the M.Sc. and Ph.D. degrees from
the University of Saskatchewan, Saskatoon, SK, Canada in 1997 and 2000,
respectively.
He was a Lecturer at the Tribhuvan University, Kathmandu, Nepal. He was
also an Electrical Engineer with Nepal Hydro & Electric, Butwal, Nepal; Udayapur Cement Industries, Udayapur, Nepal; Nepal Telecommunications Corporation, Kathmandu, Nepal; and General Electric Canada, Peterborough, ON,
Canada. Currently, he is an Assistant Professor in the Department of Electrical
Engineering at the University of Saskatchewan.
Po Hu (S’04) received the B.E. degree from the Chongqing University,
Chongqing, China, in 2001 and the M.Sc. degree from the University of
Saskatchewan, Saskatoon, SK, Canada in (2005). He is currently pursuing the
Ph.D. degree at the same University.
Roy Billinton (S’59–M’64–SM’73–M’78–LF’01) received the B.Sc. and M.Sc.
degrees from the University of Manitoba, Winnipeg, MB, Canada, in 1960 and
1963, respectively and the Ph.D. and D.Sc. degrees from the University of
Saskatchewan, Saskatoon, SK, Canada in 1967 and 1975, respectively. In 1964,
he joined the University of Saskatchewan. He was also with Manitoba Hydro,
Winnipeg, MB, Canada, in the System Planning and Production Divisions. He
is Formerly Acting Dean of Graduate Studies, Research and Extension of the
College of Engineering at the University of Saskatchewan. Currently, he is a
Professor Emeritus in the Department of Electrical Engineering. He is also
an author of power system analysis, stability, economic system operation, and
reliability papers.
Dr. Billinton is a Fellow of the EIC and the Royal Society of Canada.