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Delegates are invited to meet and discuss with the poster presenters in this topic directly after the session 'How does the wind blow behind wind turbines and in wind farms?' taking place on Tuesday, 11 March 2014 at 16:30-18:00. The meet-the-authors will take place in the poster area.

Ove Undheim Kjeller Vindteknikk AS, Norway
Ove Undheim (1) F P Rolf-Erik Keck (2) Erik Berge (1) Linn Rognlien (3) Måns Håkansson (3)
(1) Kjeller Vindteknikk AS, Kjeller, Norway (2) University of Oslo, Oslo, Norway (3) Statkraft Development AS, Oslo, Norway

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Presenter's biography

Biographies are supplied directly by presenters at EWEA 2014 and are published here unedited

Ove Undheim holds a Ph.D in Computational fluid dynamics and turbulence modeling from The Norwegian University of Science and Technology (NTNU) in Trondheim. After finishing his Ph.D in 2005 he has been an employee at Kjeller Vindteknikk, the leading company in wind measurements and analyses in Norway. At Kjeller Vindteknikk he has been involved in most parts of the company portfolio, and he was the first branch manager at Kjeller Vindteknikk’s office in Stockholm. He has now a leading role for the analysis team at Kjeller Vindteknikk.


Time-dependent wind energy calculations


Present wind industry software (WindPRO, 2013, WAsP, 1993, Wind Farmer, 2013, and WindSIM, 2013) focus on resource assessment based on annual statistics of wind conditions. However, time-dependent processes not accounted for in the annual statistics, are also important and time-dependent modeling is expected to increase the accuracy of energy assessments. Furthermore, the knowledge from a time-dependent wind resource assessment can be utilized to optimize wind farm operation, maintenance and short-term energy forecasts. Multi-purpose time-dependent models can be beneficial for the wind industry. In this study a time-dependent approach and the importance of time-dependent calculations are therefore presented and analyzed.


The time-dependent wind farm model
Modelling approach
The time-dependent ambient conditions at the wind turbine locations are obtained from 10 min data recorded in a nearby meteorological mast. The observations are transformed to the turbine positions using a micro-scale model. In the test cases described below, the linear model WAsP has been utilized. The wind conditions of the analysed period at the meteorological mast are described by directional Weibull distributions for 36 sectors, and the wind speed frequency distribution for the sectors. The directional transfer ratios from WAsP between the meteorological mast and the turbines are used to estimate the ambient velocities at the turbine locations.
The N.O.Jensen model have been implemented and used for each consecutive time stamp (Katic, Højstrup and Jensen 1986). The wake decay constant is estimated based on the measured TI at the meteorological mast.
The simulation is carried out by starting with the undisturbed upwind turbines, and then looping trough all turbines along the direction of the wind. Using this methodology the wake adjusted velocities become available for each turbine in the wind farm.
Input data
The Smøla wind farm is owned and operated by Statkraft. The wind farm is located at the western coast of Norway (Figure 1), and it consists of 68 turbines built in two stages (Figure 1). The terrain is rather homogeneous, and the wind farm is located on an island and the offshore influence is quite strong. The period analysed in this study is from June 2007 to June 2008. The measured wind rose for this period is given in Figure 2. Dominating wind directions are south-southwest, southwest and west.

Figure 1 Left panel: The location of Smøla at the western coast of Norway. Right panel: Layout and numbering of the turbines of both Smøla 1 and 2.

Figure 2 The wind rose at Smøla.

Main body of abstract

Results from time-dependent calculations
Below we focus on time-dependent effects of density variation, turbine operation and turbulence and stability variation. The influences are analysed for different time scales.
Air density influence on seasonal variation
We have estimated the seasonal production differences caused by the air density. The velocities are density corrected according to IEC 61400-12-1 based on the air density calculated from measured temperature and pressure. The energy calculations based on time dependent air density is compared with the assumption of constant density throughout the year. The average temperature of the analysed year is 7.4ºC. The monthly production differences if a constant density is assumed are given in Figure 3. The underestimation in the winter months are about 1 % and the overestimation in the summer months are from 1-3 %. The annual difference in the overall mean value are however small in this case (0.04 % difference).

Figure 3: Monthly mean temperature together with the corresponding production bias caused by assuming constant density throughout the year.
Influence of turbine operation
The turbine operation has an influence on both the turbine itself, but also on neighboring turbines resulting from the wake. As the turbine wakes and operational status are all given in the time domain, the time dependent approach enables the possibility to evaluate operational losses in detail. In addition to the losses directly linked to the turbine down time, there is a loss caused by the startup time of the turbine. The most common reason to a turbine stop at Smøla is “pitch lubrication”. The stops are of 16–48 sec endurance, but the production losses caused by the shut down and the start up procedure are found to result in a production loss corresponding to 2-3 minutes operation. This is corrected for by adding a turbine start up time to each alarm code resulting in a turbine stop.
We have presented the influence of turbine operation in Figure 4. This is a period with wind speed of about 10 m/s from southwest. Turbine 38 has a considerable production loss within the period resulting from the turbine being out of operation. This results in a production gain of about 6 % for turbine 36 lying in the wake region of the non operating turbine 38 for wind direction of about 180º.

Figure 4 The production difference resulting from taking operational status of the turbines into account. Upper panel: Result for turbine 38, which is influenced with a production stop. Center panel: Result for turbine 36, which is influenced by the missing wake from turbine 38. Lower panel: Wind direction and velocity at the meteorological mast for the given period.
Influence of turbulence on wake losses
The power production depends on the turbulence reaching the turbine. This is valid both for the case when undisturbed flow reaches the turbine and for the case when the turbine is located in the wake of another turbine. Figure 5 shows the power as function of the estimated ambient wind speed at turbine 62. The ambient wind speed is calculated from the undisturbed meteorological mast applying modeled conversion ratios from WAsP. The velocity differences from the power curve, then becomes a measure of the velocity deficit caused by the wakes. The available data for each 0.5 m/s is grouped based on the turbulence intensity (TI). The group “TI lowest” contains the lowest turbulence intensities at all velocity intervals. The average TI of this group is 7.3 %. The corresponding average TI of “TI average” is 10.3 % and “TI highest” is 14.2 %. It is seen that the wake losses are larger for situations of low ambient turbulence than high ambient turbulence. The estimated wake losses are 27.3 % for “TI lowest”, 21.0 % for “TI average” and 16.3 % for “TI highest”. This effect is also resolved in the WAsP wake model when the wake decay constant is linked to the average turbulence intensity of each group. The corresponding wake losses from WAsP are 24.0 % for “TI lowest”, 17.5 % for “TI average” and 13.0 % “TI highest”.

Figure 5 The measured power at turbine 62 as function of the estimated non wake velocity at turbine 62 for different turbulence conditions.


Time dependent wind farm production is improved when the production is corrected for the air density variations throughout the year. The neglect of time-dependent density variations can give rise to errors of up to 3 % on a monthly basis. Still, only a minor influence on the annual production was seen in our case.
The operational status has in our study been linked directly to the energy production and wake simulations. This leads to improved accuracy of the production time series. The complete estimated production time series also become available for comparison with the measured power. Wind farm production analyses are not limited to episodes were all turbines are in operation for the wake estimates to be valid. This improves the production loss estimates caused by turbine down time, and can be linked to the operation and maintenance strategies.
The wake loss dependence on the ambient turbulence level is found to be of the order of 10 %. A major improvement in the wake loss calculations can therefore be obtained applying time-dependent calculations instead of annual statistics. The analysis even show that a rather simple wake model can successfully be applied to time dependent simulations by employing time dependent adjustments of the wake decay constant. The turbulence intensity is closely linked to atmospheric turbulence. If a relationship between turbulence intensity and stability is established, time-dependent wake losses as a function of stability can be calculated in the lack of turbulence measurements. The energy losses due to wakes have a strong time-dependency and errors in annual energy estimates by using simplified wind distributions and annual average turbulence intensities can easily amount to more than one percent of the total energy production.

Learning objectives
Several parameters important to the wind farm production are time dependent. The transfer from energy yield estimates based on annual statistics to time series is therefore important, both for a better understanding of the processes and for more accurate estimates. This also links the pre production analyses to production forecasting and operation and maintenance strategies.

Katic, I., J. Højstrup, and N. O. Jensen (1986). "A simple model for cluster efficiency." European Wind Energy Association Conference and Exhibition. Rome, Italy.
WAsP Manual (1993). Wind Analysis and Application Program (WAsP), 1993. Vol 2: Users Guide. Risø National Laboratory, Roskilde, Denmark, ISBN 87-550-178.
WindFarmer (2013).
WindPRO 2.6 (2008). User Guide. 1. Edition. EMD Internastional AS.
WindSIM (2013).