a study on the combined wave spectrum model...

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Combined 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

]

U10 [m/s]

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0 5 10 15 20

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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m2]

f [Hz]

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

[m]

U10 [m/s]

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T1/3

[m]

U10 [m/s]