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Energies 2019, 12, 2949; doi:10.3390/en12152949 www.mdpi.com/journal/energies
Article
Determining the Optimized Hub Height of
Wind Turbine Using the Wind Resource
Map of South Korea
Jung-Tae Lee, Hyun-Goo Kim *, Yong-Heack Kang and Jin-Young Kim
New and Renewable Energy Resource & Policy Center, Korea Institute of Energy Research, 152 Gajeong-ro,
Yuseong-gu, Daejeon 34129, Korea
* Correspondence: hyungoo@kier.re.kr; Tel.: +82-42-860-3376
Received: 11 July 2019; Accepted: 29 July 2019; Published: 31 July 2019
Abstract: Although the size of the wind turbine has become larger to improve the economic
feasibility of wind power generation, whether increases in rotor diameter and hub height always
lead to the optimization of energy cost remains to be seen. This paper proposes an algorithm that
calculates the optimized hub height to minimize the cost of energy (COE) using the regional wind
profile database. The optimized hub height was determined by identifying the minimum COE after
calculating the annual energy production (AEP) and cost increase, according to hub height increase,
by using the wind profiles of the wind resource map in South Korea and drawing the COE curve.
The optimized hub altitude was calculated as 75~80 m in the inland plain but as 60~70 m in onshore
or mountain sites, where the wind profile at the lower layer from the hub height showed relatively
strong wind speed than that in inland plain. The AEP loss due to the decrease in hub height was
compensated for by increasing the rotor diameter, in which case COE also decreased in the entire
region of South Korea. The proposed algorithm of identifying the optimized hub height is expected
to serve as a good guideline when determining the hub height according to different geographic
regions.
Keywords: hub height; rotor diameter; wind turbine; cost of energy; optimization
1. Introduction
As two of the core factors in wind tu rbine design, hub height (HH) and rotor diameter (RD) have
significant impact on power output and facility cost, thereby determining the cost of energy (COE) [1].
Theoretically, as HH increases, wind speed increases. Likewise, longer RD means that the area
absorbing wind momentum increases, thereby increasing power output [2]. The effect of surface
roughness diminishes with height, so wind speed increment occurs within a mixed layer and
mitigates as the height approaches the boundary layer height. Since the overall cost increases with
the increase in HH, however, the optimal hub height (OHH) that ensures minimum COE should be
at a certain HH for investment efficiency.
Wind power projects aim to minimize capital expenditure (CAPEX) and operation expenditure
(OPEX), and to maximize annual energy production (AEP) as with other profit-oriented projects. In
other words, the goal of a wind farm design is to minimize COE as a function of CAPEX, OPEX, and
AEP, and various studies have been conducted to reduce COE by minimizing wake loss through the
optimization of wind turbine layout in a large wind farm [3–6]. Studies have also been conducted to
determine the optimal HH and RD, as the control of HH and RD is more influential in reducing COE
than optimizing the layout in a small wind farm.
Energies 2019, 12, 2949 2 of 13
Lee et al. [7] calculated OHH to maximize the power generation profit, but it was excessively
high (150~220 m). They also calculated profit according to the electricity price, so OHH could change
if the electricity price or government incentive policy changed. Rehman et al. [8] presumed OHH to
be an intersection where the total cost function of HH and a gradient curve of the AEP function were
crossed, but they did not present sufficient rationale that the calculated intersection was theoretically
OHH, rather they applied their own method to regions with a few observation data. Maki et al. [9]
and Mirghaed et al. [10] calculated the minimized COE iteratively with regard to all cases by
controlling a variety of variables, including generator’s revolutions per minute (RPM) and turbine
pitch, in addition to HH and RD. This was not only complicated, but also incurred high calculation
cost. Moreover, these studies do not guarantee a reliable AEP because they used constant wind speed
and shear exponent, which hardly makes COE credible for the specific site. Since, Stanley et al. [11]
used a gradient-based method, which was also iterative to calculate the optimum value, and it
remained site-specific (one site).
In sum, the technical problems of the previous studies were: (1) Variability of OHH due to
external factors (government policy or electricity price, etc.); (2) cases that were limited to a few
regions only, and; (3) complicated calculations that take a long time as a large number of variables
were considered, so it was hard to calculate OHH for a large area.
To overcome the aforementioned problems and limitations of the previous studies, this paper
proposes a method that generates the COE curve according to HH, and searches OHH that minimizes
COE. This method has nothing to do with government policies and external factors, such as incentive
programs or electricity price, and the calculated OHH is dependent only on AEP and COE according
to the characteristics of wind resources in the target region. In other words, since all cost information
are summed and dealt with as a single variable, OHH can be calculated with fewer computations
than other methods that consider a number of variables. This study not only calculated the COE curve
accurately using the wind resource map provided by the Korea Institute of Energy Research (KIER),
which re-distributed AEP into a 1 km horizontal and 10 m vertical distance grid, but also observed a
correlation between OHH and geographical characteristics spatially. In other words, the proposed
method can identify the pattern of OHH according to geographical characteristics, such as coast,
inland, or mountain regions in South Korea, through the mapping of OHH [12]. Note that this study
was limited to onshore wind turbines since the cost information of offshore wind turbines was not as
sufficient as that of onshore.
The proposed method produced OHH that was lower than 80 m as the general hub height (GHH)
of MW-capacity wind turbines in high wind sites. This may degrade AEP. If sufficient power
production is one of the critical goals of the wind power project, it is necessary to have a measure for
compensating for the degraded AEP due to the calculated OHH. This study proposed a measure for
compensating for the AEP loss by increasing RD. Specifically, the power generation loss due to OHH
was compensated for by increasing RD, but COE did not increase even with such compensation.
2. Data and Methods
The following procedure determines the OHH proposed in this study:
(1) Step to prepare wind profile data
(a) The time-series wind profile data are fetched from the grid points in the wind resource map.
(2) Steps to calculate OHH
(a) AEPs are calculated by increasing HH from 40 m to 100 m with 10 m increments.
(b) The COE curve is produced through regression analysis with the calculated AEPs and cost
data.
(c) OHH is searched when the COE curve is minimum using a numerical analysis method.
(3) Steps to calculate RD
(a) The AEP loss is calculated when GHH is changed to OHH.
Energies 2019, 12, 2949 3 of 13
(b) The AEP increase is calculated by raising RD to 70 m, 80 m, 90 m, and 97 m.
(c) The RD that can compensate for the AEP loss due to OHH is determined.
The procedure above is performed with regard to the entire onshore in South Korea.
2.1. Wind Resource Map
As a high-resolution wind resource map produced by KIER, KIER-WindMap was used to
employ the time-series data of the wind profile, which were needed to calculate AEP per region.
KIER-WindMap was produced by Weather Research and Forecasting (WRF) v3.7.1, a mesoscale
numerical weather prediction model. Table 1 presents the configuration of the model in detail. For
the initial and boundary conditions, the Regional Data Assimilation and Prediction System (RDAPS),
a regional model of 12 km spatial resolution produced by the Korea Meteorological Administration
(KMA), was used. The final domain was discretized as a 933 (east-west) × 1332 (south-north) grid,
having 1 km × 1 km spatial resolution in a horizontal plane covering the Korean Peninsula (Figure 1),
and the vertical layer consisted of 37 layers. The lower layer where the wind turbine is to be located
was re-distributed with 10 m interval. The Mellor-Yamada-Janjic scheme was used as the planetary
boundary layer parameterization scheme, and the WRF single moment 3-class ice scheme was used
as cloud microphysics parameterization [13,14]. The land surface model calculated the physical
process of the surface boundary layer (SBL) using the WRF-combined Noah-MP land surface model [15].
To improve the accuracy of KIER-WindMap, observation data (AWS/ASOS, Sonde/Wind profiler,
Buoy) of KMA and related institutions were assimilated into the background field using the four-
dimensional data assimilation technique. The accuracy of the final wind resource map was proven
through various verification studies [16,17].
Table 1. Model configuration of Weather Research and Forecasting (WRF).
Model Advanced Research WRF (v3.7.1)
Period 2010~2012
Input data Unified Model 12 km/WRF 3 km
Sea-surface temperature OSTIA Sea Surface Temperature (SST)
Terrain Shuttle Radar Topography Mission (3 arc-seconds)
Land cover Ministry of Environment (South Korea)
Grid 933 × 1332 (1 km × 1 km)
Vertical levels 37 levels
Data assimilation Four-Dimensional Data Assimilation (FDDA)
Surface physics Mellor-Yamada-Janjic scheme (MYJ)
Cloud micro physics WRF single moment 3-class ice scheme (WSM3)
Cumulus physics No cumulus physics
Land surface Noah-MP land surface model
Energies 2019, 12, 2949 4 of 13
Figure 1. Terrain elevation of the analysis domain (South Korea).
2.2. COE Curve as a Function of HH
OHH in this study refers to a height that produces the minimum value of COE, which is
calculated by dividing the total investment cost (TIC) in a year (Equation (1)) by AEP (Equation (2)).
Since coefficient α of the highest order term in the COE function (Equation (3)) is larger than zero, it
has a convex curve shape in the downward direction (Figure 2). In the condition of HH 𝑝, the COE
function has minimum value 𝑞, and 𝑝 is calculated as OHH. In other words, OHH is understood to
be a value wherein the derivative of the COE function is 0 (COE
𝑝 0). Using the polynomial
regression equations shown in Equations (1)–(3), the downward convex shape of the COE curve can
be clearly expressed mathematically. Therefore, the point of OHH where the derivative of the COE
curve becomes 0. The 𝛼
and 𝛼
in Equation (2) and 𝛼
in Equation (3) are coefficients that are
changed depending on the region, with the coefficients in Equation (1) as constants: 𝛼
18.7, 𝛼
15.310
, 𝛼
12.610
. The coefficients of polynomial regression equations are determined
using a least square method.
To find OHH, the COE equation is calculated first. AEP and TIC are calculated by changing a
10-m-long HH with 1 m increments through polynomial regression to produce a smooth COE curve.
AEP is calculated using the wind turbine performance curve and time-series wind profile data
provided by the wind resource map database KIER-WindMap. The South Korea-made STX72-2.0
MW was used as the reference wind turbine, and the rotor equivalent wind speed (REWS) was
applied to reflect the characteristics of the regional wind profile correctly (Equation (4)). For the TIC
for one year, the cost increase data according to HH proposed in a previous study was used [8]. In
other words, it was a divided cost for over one year with regard to the facility cost, construction cost,
and maintenance cost across the 20-year service life of the wind turbine.
TIC
𝑓
HH𝛼
HH
𝛼
HH 𝛼
(1)
AEP 𝑔HH 𝛼
lnHH 𝛼
(2)
COE
𝛼
HH𝑝
𝑞, (𝛼
0 (3)
AEP
𝑃REWS𝑡
(4)
Energies 2019, 12, 2949 5 of 13
Figure 2. Cost of energy (COE) curve as a function of hub height hub height (HH). OHH, optimal hub
height.
REWS, which was used instead of HH wind speed in order to avoid overestimating AEP and to
consider the regional wind speed characteristics, was calculated by dividing the rotor area by 5 as
shown in Figure 3 and area-weighting the wind speed at mid-height of each segment [18–20].
REWS
∑
𝑤
∙𝑉
/
, 𝑤
𝐴
𝐴
⁄ (5)
where 𝑉
refers to the wind speed at the i-th segment center, 𝐴 is a rotor area, and 𝐴
refers to the
i-th segment area.
Figure 3. Rotor area fraction and corresponding weights for rotor equivalent wind speed (REWS)
calculation.
2.3. Calculation of RD to Compensate for AEP
The AEP loss, which occurs if OHH is lower than GHH, is compensated for by increasing RD.
This is equivalent to Equation (6).
ΔAEP AEPGHHAEPOHH𝑑AEPRD
𝑑RD ΔRD (6)
where ∆AEP and ∆RD refer to the AEP loss and increase in RD length, respectively. This study
considered three RD lengths: 80 m, 90 m, and 97 m among many rotor lengths in the Gamesa 2 MW
model as the wind turbine model (Table 2). Thus, the maximum ∆RD was limited to 27 m. Figure 4
Energies 2019, 12, 2949 6 of 13
shows the performance curves of the reference wind turbine (WT0) and three other wind turbines
(WT1~WT3) with increased RDs.
Table 2. Wind turbines considered in this study.
Wind Turbine Manufacturer Rotor Diameter (m)
WT0 STX (STX72-2.0MW) 70.6
WT1 Gamesa (G80-2.0MW) 80
WT2 Gamesa (G90-2.0MW) 90
WT3 Gamesa (G97-2.0MW) 97
Figure 4. Power curves of 2 MW wind turbines.
2.4. Cost of Tower and Rotor
The investment and operation costs according to HH are presented in Table 3. The costs were
evaluated based on the 1 MW wind turbine and used in the TIC calculation of COE. The cost increase
due to RD increase is presented in Table 4. The blade cost is determined considering the materials
used, labor, profit and overhead, tooling, and transportation and is sensitive to the labor cost (LC)
and material cost (MC) [21]. Other factors (overhead, tooling, and transportation) are fixed
proportions accounting for 28% of the total rotor-related cost. Thus, only the costs of material
(Equation (8)) and labor (Equation (9)), which were variable proportions, were considered, and 72%
of the variable proportion except the fixed proportion out of the total cost was calculated using
Equation (7).
Blade cost MC LC/1 0.28 (7)
MC 0.4019𝑅
955.24 (8)
LC 2.7445𝑅
.
(9)
Table 3. Incremental cost of the 1 MW wind turbine. Source: Rehman et al. [8].
Hub Heights (m) Total Capital and Installation Cost (€)
40 900,000
50 954,000
60 1,020,780
70 1,112,650
80 1,235,000
90 1,395,500
100 1,618,900
Energies 2019, 12, 2949 7 of 13
Table 4. Costs of material and labor and total blade cost with rotor diameter. Source: Fingersh et al. [21].
Rotor Diameter (m) Material Cost (€) Labor Cost (€) Total Blade Cost (€)
70 124,075 103,066 315,474
80 185,635 143,959 457,770
90 264,680 193,307 542,193
97 363,394 221,314 636,093
3. Results
3.1. Regional Characteristics of OHH
OHH was calculated throughout all regions in South Korea, and its distribution is shown in
Figure 5. Figure 5 shows a clear difference in OHH distribution according to the geographical
conditions; the calculated OHH in the inland plain was 75 m~82 m, whereas that in the mountain or
onshore sites was 60 m~70 m.
Figure 6 shows the COE curves at three typical sites (inland, onshore, and mountain) where the
wind farms are currently operating, with the OHH, minimum COE, and wind profile exponent at
each site presented in Table 5. For the inland site (S1), the highest OHH among the three sites was 74
m, followed by the onshore site (S2) with 63 m and the mountain site (S3) with 61 m. The calculated
OHH in most sites was lower than the GHH of the MW-capacity wind turbine. In particular, OHHs
in onshore and mountain sites were approximately 10 m lower than that of inland. If the onshore TIC
is applied to that of offshore for approximation, for which calculating the construction cost is difficult
due to the lack of cost information, OHH offshore is calculated to be 40 m or lower, which is fairly
lower than that of onshore. Note, however, that this OHH is neither valid nor realistic considering
the rotor length.
The reason for the difference in OHH by site can be found in the wind profile of each site (Figure 7).
Specifically, the wind profile at (S1) (inland site) showed that the mean wind speed was lower than
4 m s−1, which is almost the cut-in speed of wind turbine WT0 at an approximate height of up to 50
m, followed by low AEP at 50 m or lower. Since the mean wind speed was higher than the cut-in
speed at a height above 50 m, AEP increased, with the minimum COE found at a relatively high HH
compared to that of other sites. In the inland site, the lower layer in the wind profile had a low wind
speed due to the surface friction, which did not produce sufficient AEP. This was why OHH had to
be high. In contrast, the mean wind speeds in the onshore (S2) and mountain (S3) sites exceeded the
cut-in speed at a height below 50 m. Since S2 had the highest mean wind speed among the three sites,
the minimum COE was also the lowest at 24.7 € MWh−1.
Energies 2019, 12, 2949 8 of 13
Figure 5. Distribution of optimal hub height for WT0.
(a) (b)
Figure 6. COE curves by hub height and OHH (points) at the three sites. (a) S1; (b) S2 and S3.
Table 5. Comparison of the calculated results at the three sites. OHH, optimal hub height; GHH,
general hub height.
Sites S1 (Inland) S2 (Onshore) S3 (Mountain)
OHH (m) 74 63 61
COE (€ MWh
−1
) 51.7 24.7 27.2
Mean wind speed at GHH (m s
−1
) 4.1 7.3 6.9
Wind profile exponent 0.33 0.12 0.15
Energies 2019, 12, 2949 9 of 13
Figure 7. Mean wind speed profile at the three sites (S1, S2, and S3).
3.2. Calculation of RD to Compensate for AEP
The calculated OHHs in most regions in South Korea were less than GHH. If wind turbines are
installed according to the calculated OHH, it can reduce the cost required to construct a tower, which
then leads to the minimization of COE; thus resulting in improvements in terms of economic
feasibility. Note, however, that the reduction in HH will result in loss of AEP according to the
reduction of wind speed in a rotor area. A power production loss of 5% is expected to occur if the
OHH of the S1 site is changed to 74 m instead of using GHH. In the same manner, S2 and S3 will
experience loss of AEP by 13% and 12%, respectively. In other words, lower HH means larger loss of
AEP. This correlation is also applied to onshore and mountain sites where the mean wind speed is
relatively stronger than that of inland.
This can be a drawback of the OHH calculation algorithm, which minimizes COE. If the goal is
to maximize AEP, it is necessary to have a method of compensating for the loss of AEP due to OHH.
This study derived a linear regression equation between RD and AEP after calculating the AEP of
three types of wind turbines (WT1, WT2, WT3), which had longer RD than that of WT0 as the
reference wind turbine to compensate for the lost AEP due to OHH (Figure 8). Figure 8 confirms that
an increase in RD by 1 m at HH of 60 m~100 m improves AEP by 54 MWh to 64 MWh, and this trend
is common in all regions in South Korea.
Energies 2019, 12, 2949 10 of 13
Figure 8. Increment of annual energy production (AEP) with increment of rotor diameter at different
hub heights.
Figure 9 shows the mapping of RD increment in South Korea to compensate for AEP loss due to
OHH. Compared to Figure 5, Figure 9 indicates that a large RD increment is needed because of the
large AEP loss in onshore and mountain sites where OHH was calculated to be lower than GHH. The
RD increments at the three sites for AEP loss compensation, as analyzed above, were 2.1 m, 5.8 m,
and 6.6 m, respectively (Table 6).
Table 6. AEP loss due to decreased hub heights and gain owing to increased rotor diameter at the
three sites. RD, rotor diameter.
Sites AEP Loss (MWh m
−1
) by OHH AEP Gain (MWh m
−1
) by ∆𝐑𝐃 Increment of RD (m)
S1 17.2 39.3 2.1
S2 24.7 77.9 5.8
S3 29.5 91.6 6.6
Figure 9. Distribution of increment rotor diameter for compensating for AEP loss.
Energies 2019, 12, 2949 11 of 13
3.3. Discussions
The OHHs in South Korea were distributed within 50 m~90 m, and a regional difference existed
according to the geographical characteristics. OHH was also calculated to be a value below GHH in
most regions. When HH was lower than GHH, both AEP and TIC were reduced, but COE was
reduced because the reduction in TIC was larger (Figure 10a). This was why the minimum COE was
derived at a height below GHH. This characteristic was more noticeable in S2 and S3 where the wind
speed was higher, by which lower OHHs were calculated in S2 and S3. In contrast, the differences in
the reduction rates of AEP and TIC decreased with higher OHH, and there was no significant
difference near GHH. This was the reason for the small change in COE at the S1 site, where OHH
was calculated to be 74 m. The increase rate of AEP at sites whose OHH was higher than GHH was
higher than the increase rate of TIC. This was why a lower COE was calculated at high OHH than
that of GHH. Most of these sites were low-wind speed (less than 5 m s
−1
mean wind speed) sites that
did not produce sufficient AEPs at a lower height below HH. Thus, OHH was calculated to be 80 m,
wherein an increase in AEP was larger than that of TIC.
Figure 10. Percentage change for AEP and total investment cost (TIC) with respect to (a) OHH and
(b) increment of RD.
In this study, RD was increased to compensate for AEP loss due to the reduction in HH, which
reduced COE further. This was because the increase in AEP due to the increase in RD was larger than
the increase in cost owing to the increase in RD, as shown in Figure 10b. The sites that needed AEP
loss compensation through the increase in RD were relatively high-wind speed sites, which was why
the power of the wind turbine proportional to the cubic area of wind speed was also large. The
reduced COE as a result of the AEP loss compensation was 13% compared to that of GHH, which
was larger than the reduction rate of OHH (7%) (Table 7).
The reduction in COE through the increase in RD was also consistent with the trend of the large
size of wind turbines [22]. Note, however, that the calculated OHHs in this study showed a different
trend. COE was minimized with lower OHH than GHH in high-wind speed sites but with higher
OHH in low-wind speed sites. In other words, the characteristic of OHH differed according to the
characteristics of the regional wind profile. Note that this study did not consider the limitation of the
wind turbine class according to strong winds and turbulence intensity.
Table 7. COE by 80 m, optimal hub height, and optimal hub height + rotor diameter.
Site COE with GHH
(€ MWh
−1
)
COE with OHH
(€ MWh
−1
)
COE with OHH + RD
(€ MWh
−1
)
S1 66.5 65.9 63.9
S2 26.1 24.7 22.9
S3 29.1 27.2 25.1
Energies 2019, 12, 2949 12 of 13
4. Conclusions
This study calculated AEP according to the changes in HH, using the time-series wind speed
profile data of the wind resource map in South Korea and proposed an algorithm to find the OHH
that minimized COE. In this study, not only was the AEP loss due to the lower OHH than GHH
compensated for by increasing RD, a measure to reduce COE was presented as well.
The main study results are summarized as follows:
(1) The inland plain site in South Korea exhibited minimum COE at a height of 74 m, which was
similar to GHH. Note, however, that regions with relatively high wind speed, such as onshore
or mountain sites, had OHHs of 63 m and 61 m or 17 m and 19 m lower, respectively, than that
of the inland site. The economic feasibility of wind farms is expected to improve by minimizing
COE in the future if OHH is selected according to the wind profile characteristics.
(2) Unlike the study results of Lee et al. [5], the OHH calculation algorithm in this study presented
a lower OHH than GHH in most sites except inland plain sites. OHH is determined according
to the regional wind profile characteristics and is characterized to be higher than GHH if the
wind resource is not sufficient in the lower layer of HH.
(3) This study also verified the reduction in COE when RD increased to compensate for the AEP
loss due to OHH. COE was reduced if RD increased in the entire area of South Korea. This was
because the increase in AEP was larger than the increase in TIC, owing to the increase in RD.
(4) This study was limited to onshore wind turbines. This was because the TIC of offshore wind
turbines varied much more than that of onshore wind turbines, and the relevant database was
not yet available. If the TIC database for offshore wind turbines is developed in the future, the
OHH that can minimize COE even offshore will be calculated. Based on the results in this study,
the offshore OHH is expected to be much lower than GHH.
Author Contributions: J.-T.L. designed and performed the simulations; H.-G.K. conceived a novel idea for the
research theme and supervised the investigation; J.-Y.K. and Y.-H.K. supported the wind resource data; and J.-
T.L. wrote the paper.
Funding: This research was conducted under the framework of the research and development program of Korea
Institute of Energy Research (B9-2414).
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
The following abbreviations are used in this manuscript:
AEP annual energy production
ASOS automated surface observing system
AWS automatic weather station
CAPEX capital expenditure
COE cost of energy
GHH general hub height
HH hub height
KMA Korea Meteorological Administration
LC labor cost
MC material cost
OHH optimal hub height
OPEX operation expenditure
RD rotor diameter
RDAPS regional data assimilation and prediction system
REWS rotor equivalent wind speed
RPM revolutions per minute
SBL surface boundary layer
TIC total investment cost
WRF weather research and forecasting
Energies 2019, 12, 2949 13 of 13
WT wind turbine
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