A study on the combined wave spectrum model...
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1. Ishihara, T., A. Yamaguchi and S. Taki: The challenge to the world first floating wind farm, Grand Renewable Energy 2014, 2014.
2. Tanemoto, J. and T. Ishihara: A study on the joint probability distribution of wind and wave. The 15th World Wind Energy Conference, Tokyo, 4p., 2016.
Wind and wave measurements obtained at Fukushima offshore floating wind turbine demonstration site are used. These are measured on floating substation.
Wave spectrum model is one of the important parameters for the load calculation of offshore wind turbines and its support structures. At the site facing open ocean such as Pacific Ocean, a double peaked spectrum is observed when wind wave and swell is mixed. In this study, a combined wave spectrum model for wind wave and swell is proposed and validated by using measurement data obtained at Fukushima offshore floating wind turbine demonstration site[1].
In this study, a combined wave spectrum model of wind wave and swell is proposed. By using proposed spectrum model, double peaked spectrum can be produced. Proposed spectra are validated through a case study and one year's of bin average spectrum obtained from measurements, and shows better agreement than those obtained by JONSWAP model.
A study on the combined wave spectrum model of wind wave and swell
Jun TANEMOTO1, Takeshi Ishihara2 and Atsushi YAMAGUCHI2 1Wind Energy Institute of Tokyo Inc., 2The University of Tokyo
PO.054
1. Introduction 3. Combined Wave Spectrum Model 4. Result
2. Measurement
5. Conclusions
References
The combined spectrum is modeled as linear combination of wind wave and swell, both of which are assumed to follow JONSWAP spectrum.
Combined Wave Spectrum Model
Latitude / Longitude N 37°18’ 39” / E 141°14’ 24”
Distance from coast 20km
Water depth 120m
Component Equipment Note
Wind speed Doppler
lider
Wind speeds at 10m above
sea level is estimated by
using wind speed measured
at 20m and 40m for each 20
minutes assuming power
law.
Wave height /
Wave period
Wave
meter
Zero up-cross H1/3 and T1/3
are used.
Wave
spectrum
Wave
meter
Frequency: 0.0078~0.1Hz
(every 0.0078Hz) Acknowledgement
This research is carried out as a part of a project of Fukushima floating offshore wind farm demonstration project which is Funded by the Ministry of Economy, Trade and Industry, Japan. The authors wish to express their deepest gratitude to the concerned parties for their assistance during this study.
Location of the Project
Wave
Meter
Doppler
Lidar 22.95m
18m
Appearance of Floating Substation
Summary of Measured Component Used in This Study
Floating substation
20km
Floating wind turbine
fSfSfS SWC
fSC
For the calculation of combined spectrum, wave heights and periods of both wind wave and swell components are needed. However, these components are not directly measured. In this study, following formulas are used to identify them.
Wind Wave and Swell Components
Combined Wave Spectrum
: Combined wave spectrum
fSW : Wind wave component (by JONSWAP model)
fSW : Swell component (by JONSWAP model)
f : Frequency
An example of combined spectrum model
Models of Mean Wave Height and Period for Wind Wave and Swell as Functions of Wind speeds[2]
• Wind Speed
• Wave Height
• Wave Period
Proposed
Model
Wave Spectrum
Measurement
Validation
Measurement
(for Input) Wave spectrum
model
Measurement
(for Validation)
Input
These measurements are used as follows:
Simple Flow Chart of This Study
Wind wave Swell
H1/3
T1/3
10
10
,3/1
,3/1
,3/1
U
UtH
C
W
H
H
mes
10
10
,3/1
,3/1
,3/1
U
UtH
C
S
H
H
mes
10
10
,3/1
,3/1
,3/1
U
UtT
C
W
T
T
mes
10
10
,3/1
,3/1
,3/1
U
UtT
C
S
T
T
mes
Formulas for the Identification of wave parameters
where subscript mes denotes time series of measurement. are the model wave height and period as a function of wind speed, proposed by Tanemoto and Ishihara[2], as shown in following figures:
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μH
1/3
[m
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U10 [m/s]
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μT
1/3
[s]
U10 [m/s]
Measured mean values for each wind speed bin
Wind wave model (μH1/3,W and μT1/3,W)
Swell model (μH1/3,S and μT1/3,S)
Combined model (μH1/3,C and μT1/3,C)
Proposed model is compared with a measurement. An double peak spectrum can be predicted by using proposed model.
Case Study
Average Spectrum for Wind Speed Bin
Wave Height Wave Period
Measurement
Wind speed
(at 10m)
10.3m/s
H1/3 2.04m
T1/3 6.50s
Wind
Wave Swell
H1/3 1.46m 1.57m
T1/3 4.78s 9.30s
Identification
Input Parameters and Predicted Spectrum on an Event
Wind speed bin averaged spectrums are compared. Proposed model shows better agreement with measurements for lower frequency part of the spectrum.
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Measurement
JONSWAP
Combined model
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Wind Speed: 7-8m/s Wind Speed: 12-13m/s
Wind Speed: 2-3m/s Average Spectrums for Each Wind Speed Bin.
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H1/3
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U10 [m/s]
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[m]
U10 [m/s]