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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 3, SEPTEMBER 2011
987
Power Engineering Letters
A Modular Approach to Enhance Capacity Factor Computation of Wind Turbine
Generators
Shyh-Jier Huang and Hsing-Ho Wan
Abstract—In this letter, a modular approach is proposed to compute the capacity factor of wind turbine generators, with which
the systematic calculation under manufacturing data can be performed with a higher flexibility. This proposed approach has been
compared with existing methods through site wind speed data. Test
results help confirm the feasibility of the method for wind source
assessment applications.
Index Terms—Capacity factor, computing module, wind turbine
generator (WTG).
sistent. Although the CF computation based on either quadratic
function [3], [7] or cubic model [2] has been proposed, however, because the wind energy assessment may move away from
assumption in favor of direct experimental fits to actual data, a
modular CF computation method is proposed in this letter that is
mainly based on manufacturer’s power curves. The new method
is flexible and data driven. By using CF computations for WTGs
under real wind conditions collected in Taiwan, the method is
being considered an effective alternative in addition to several
existing methods.
I. INTRODUCTION
O EVALUATE the performance of wind energy conversion system at sites, power curve modeling of wind turbine generators (WTGs) is often deemed one of important tasks.
However, it requires an arduous effort to formulate an appropriate model between power output and wind speed at nonrated
operation region of WTGs. Some previously published literature have reported their study in this direction of research. A
cubic function model was suggested for the site matching with
WTG in [1], by which it was also applied to find optimum speed
parameters in [2]. Then, a quadratic function model containing second-degree and constant terms was developed as well
for energy estimation and turbine-site pairing performance [3].
Besides, a quadratic function model along with second-degree,
one-degree, and constant terms was utilized to reliability evaluation [4] and cost-effective assessment [5]. Through aforementioned literature review, it is found that the modeling of nonrated
region on power curve of a WTG can be made based on cubic,
quadratic, or linear functions. Apart from mathematic functions,
a nonparameter model of wind turbine based on a neural network
was meanwhile suggested [6], yet its effectiveness was highly
hinged on a large number of data set as well as an appropriate
training strategy.
Recently, the concept of capacity factor (CF) of a WTG has
become more important to assess the amount of energy delivered
than ever since the wind resource is known to be seldom con-
T
Manuscript received March 11, 2010; revised September 8, 2010; accepted
May 12, 2011. Date of publication August 2, 2011; date of current version
August 19, 2011. Paper no. TEC-0028-2010.
The authors are with the Department of Electrical Engineering, National Cheng Kung University, Tainan 70101, Taiwan (e-mail: [email protected]
ncku.edu.tw; [email protected]).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TEC.2011.2158022
II. PARADIGM
In this section, a modular approach for computing CF of
WTGs is derived. The power curve of a WTG is characterized
by cut-in vc , rated vr , and cut-out vf speeds. Based on the
manufacturing data of WTGs, the nonrated operation region of
the power curve can be modeled by an n-degree polynomial,
through which the CF can be expressed as
n
1 αi ψi + ψR
(1)
CF =
PR i=0
where PR is the rated output, αn , . . . α0 are the curve-fitting coefficients, and Ψn and ΨR are computing modules for nonrated
and rated regions which are derived as
n
n
k
k
ψn = cn pn e−p − q n e−q + Γ
k
k
n
n
× γ qk ,
− γ pk ,
k
k
ψ0 = e−p − e−q
k
ψR = e−q − e−s
k
k
k
(2)
where p = vc /c; q = vr /c; s = vf /c; k and c are Weibull shape
and scale factors, respectively, and γ is the incomplete gamma
function. From the aforementioned derivations, the CF computation is seen to perform with the product of various coefficients
based on the models concerned. As an example, when the machine output power P is characterized by the wind speed v with
a polynomial expression of P(v) = α3 v 3 + α2 v 2 + α1 v + α0 ,
the CF can be accordingly presented along with the modules of
Ψ3 , Ψ2 , Ψ1 , and Ψ0 to construct a generalized form of CF =
(α3 Ψ3 +α2 Ψ2 +α1 Ψ1 +α0 Ψ0 )/PR +ΨR , thereby realizing the
0885-8969/$26.00 © 2011 IEEE
988
IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 3, SEPTEMBER 2011
Table III
CF COMPUTATION OF GE-1.5SE AT MAILIAO WIND FARM
Table IV
CF COMPUTATION OF GE-1.5SE AT SIHHU WIND FARM
Fig. 1. Power curves of the WTG under manufacturing data and different
models.
Table I
PARAMETERS OF MAILIAO AND SIHHU WIND FARMS IN TAIWAN
Table V
CF COMPUTATION OF NEG-MICON2000 AT MAILIAO FARM
Table II
SPECIFICATIONS OF THE CONSIDERED WIND TURBINE GENERATORS
systematic and modular approach for wind source assessment
applications considered.
Table VI
CF COMPUTATION OF NEG-MICON2000 AT SIHHU FARM
III. METHOD COMPARISONS
In preliminary wind energy evaluation, power curves of
WTGs are often characterized by different models [1], [3], [4],
[8]. Fig. 1 presents manufacturing data [9] and four existing
models of the power curve on the same graph for WTGs. To
validate the effectiveness of the method, it is employed to investigate the CF for the WTG of wind farms located at Mailiao
and Sihhu Township located near central Taiwan. Table I lists
Weibull parameters of these two wind farms, which are obtained
by the long-term wind data recorded in the Central Weather Bureau, Taiwan. The total number of hours recording the mean
wind speed of Mailiao and Sihhu wind farms are 32 443 and
35 013, respectively, which was collected from the monitoring
lasting over 4 years. Table II lists the specifications of two WTGs
considered in this letter. Efforts on CF computations using existing models have been made and proposed in [2], [3], and [7].
Among these methods, the method in [2] was derived from the
model in [1], while the methods in [3] and [7] were developed
from the model in [3]. Each existing method is applicable for a
specific model only. In this letter, the proposed approach is compared with existing methods through real wind farm data, where
the CF using different models [1], [3], [4], [8] as well as [9]
(manufacture data) is individually shown in Tables III–VI.
As the table lists, the proposed methods and several existing
methods are applied to compute the CF under different models,
where the symbol “” means not applicable. As an example,
when the model of a WTG in [1] is considered for CF estimation, only the method proposed in [2] would present a closed
form for CF computation. Then, as for the model in [3] is employed, only methods proposed in [3] and [7] are applicable,
while others are not. Note that the acronym “Manu.” used in
the cell stands for the manufacturer. Now, from the tabulations
of these tables, it is found that for all these five cases, the proposed method is applicable and reaches good agreement with
previously published techniques whenever the test outcome is
available for the comparison. It is also observed that the model
using manufacturing data would yield a highest CF, implying
that the model per se seems to own a higher potential to provide larger energy than several existing models, which may be
a useful reminder in the evaluation of wind projects.
IV. CONCLUSION
This letter presents a modular approach to estimate the
CF of WTGs, offering a quick grasp of scenarios considered
and benefiting the engineers for wind resource assessment in
wind power projects. Currently, with the technical support
IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 3, SEPTEMBER 2011
of utility engineers, the method is being extended to evaluate more wind sites in Taiwan. The estimation reliability has
become the major concern that will be reported in the near
future.
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