WIND FARM PERFORMANCE MONITORING WITH ADVANCED WAKE MODELS 1 3 1 4 2 N. Mittelmeier , S. Amelsberg , T. Blodau , A. Brand , S. Drueke , 2 1 2 M. KΓΌhn , K. Neumann , G. Steinfeld 1) REpower Systems SE, Γberseering 10, 22297 Hamburg, Germany E-mail:
[email protected], Tel: +49 40 55555 090 3489 2) ForWind, University of Oldenburg, Germany 3) RWE Innogy, Germany 4) ECN, Netherlands
Summary Wind farm underperformance can lead to significant losses in revenues. Based on knowledge of the environmental conditions the aim of the presented method is to predict the power output of a wind farm in real time. Deviations between the calculated and the measured power output are an indication for underperformance. To calculate the expected wind farm power output, different wake models were tested and benchmarked against measurements at the offshore wind farm Alpha Ventus. Look-up tables are used to speed up computational expensive models. A sensitivity analysis for different model settings at certain environmental conditions has been worked out. To estimate the confidence of detected underperformance a detailed discussion of uncertainties is given. Finally a demonstration of the methodβs ability to detect degradation is given.
1. Introduction Efficient detection of underperformance or curtailments of wind turbines maximises asset value. Incorrect parameter settings, damage to the blade, pitch malfunctions or yaw errors all lead to underperformance. Five percent lower power performance has the same yield impact as 438 hours of downtime per year at mean wind speed. Seeing this risk, there is a rising demand from wind farm owners to constantly monitor the performance of their investment.
2. Method To detect underperformance at a wind turbine, it is necessary to know the optimum power output under the prevailing condition. This method uses measurements from a met mast to determine the environmental conditions and calculates the power output ππ predicted with a wake model and compares this value with the turbine measured power ππ . Wake models are used to pre-calculate the power output ππ,π,π for each wind turbine for each bin with wind speed π and wind direction π and save it in a two dimensional matrix. The predicted power output ππ is derived from the matrix with linear interpolation knowing the measured wind speed and wind direction. This enables to consider the
results even of very advanced and computationally expensive models in real time. Commonly used power measurements are averages of 10 minutes. Due to the fact that there is a high scatter on power measurements for the same wind speed and wind direction bin, averaging π quantities of 10 minutes time samples is necessary until the power value converges to a satisfactory degree. To lower the uncertainties from the measurement chain, normalisation is introduced. Therefore the power of the wind turbine under observation πππ is correlated to the power of a reference wind turbine ππππ . This leads to the equations (1) and (2). π=
π
πππππ 1 οΏ½ π πππππ π=1
π
π=1
π
π
πππππ 1 π= οΏ½ π πππππ
(1)
(2)
where ππππ and ππππ are the measured and predicted power of the observed turbine. πππππ and πππππ are the measured and predicted power of the reference turbine.
The level of performance can be described with equation (3): π (3) π = 100 β οΏ½1 β οΏ½ π where π describes the deviation of the measured correlation and the model predicted correlation in percent. If π is larger than the uncertainty, underperformance has been detected. A detailed discussion on uncertainties is given in Section 5.
3. Wake Model Benchmark To choose a suitable wake model, seven different software tools for power predictions have been compared to measurements at the wind farm Alpha Ventus which is located at around 45 km north of the German island Borkum. It consists of twelve turbines of the 5 MW class. Here only the northern six turbines AV1 to AV6 of type REpower 5M with a rotor diameter of 126m and a hub height of 92m are considered. (Fig. 1)
[267.5Β° β 272.5Β°] to 270Β°. (For AWM a single 270Β° result was used.) Wind speed is normalized by the wind speed at rated power. Power is normalized by the power of the reference turbine. The models were supposed to calculate for a Hellman shear exponent πΌ = 0.1 and a mean turbulence intensity of ππΌ = 5%. The SCADA data was filtered for the conditions 3.5% < TI β€ 6.5% and -0.2< πΌ β€ 0.8.
Fig. 2 Power of AV5 normalized with AV1
Fig. 3 shows the same evaluation as Fig. 2 but for the wind turbine AV6 which operates under double wake conditions. The SCADA results are displayed with an error bar of Β±π standard deviation and the number of values in each bin.
Fig. 1: North part of Alpha Ventus wind farm
Table 1 shows the list of wake models under investigation. Table 1: Wake models of the benchmark
Abbr. SCADA FA FJ FF AWM Fuga WPJ WEV
Description Measurement [267.5 β 272.5] FLaP Ainslie FLaP N.O. Jensen FarmFlow Ansys Windmodeller Fuga 2.5 WindPRO 2.8 N.O.Jensen Windfarmer Eddy Viscosity
In Fig. 2 the normalised power of wind turbine AV5 from the directional sector [267.5Β° β 272.5Β°] is compared to the predicted power of the models which calculated at a resolution 1Β° and averaged
Fig. 3: Power of AV6 normalized with AV1
Fig. 2 and Fig. 3 clearly indicate that the very simplified Jensen Model (FJ, WPJ) with a wake decay parameter of 0.04 has the slope too high. In some cases this leads to under- in other cases to over prediction of rel. power. For a total wind farm prediction these errors might cancel out, but the model seems to be less suitable for performance monitoring. The Ainslie and Fuga models (FA, WEV, Fuga) are much closer to the SCADA than the Jensen model but Ansys Windmodeller and FarmFlow are closest. These two models contain the most detailed physics and therefore are very computational expensive.
With pre-calculated results stored as matrices these models are applicable for the purpose of real time monitoring. A full description of the wake model benchmark is provided in [1]. In the following demonstration the FarmFlow model has been used.
4. Model Sensitivity and Calibration DΓΆrenkΓ€mper et al. [2] have shown the influence of marine boundary layer characteristics on power curves. With increasing turbulence intensity TI, the wake effects are reduced. The model is able to reflect this effect (Fig. 4 and Fig. 5.) The graphs in Fig. 4 show the normalized power of AV5 at 8 m/s wind speed at different turbulence intensities. The wake of AV4 is visible at 270Β° and the wake of AV 1 at 315Β°.
sensitivity of this behaviour must be reflected at the estimation of uncertainties (Section 5). With a perfect model, ideal turbine operation and an averaging period π β β, the performance deviation π would be zero. As the real world is different, we need to introduce a calibration factor. With a well selected training set of measured SCADA data, the model bias can be estimated and taken into account. The graph in Fig. 6 shows π with increasing π. After approx. 450 averaging quantities the variance of the prediction arrives at a satisfying low level. Fig. 6 also displays how the correction factor shifts the corrected prediction towards zero.
Fig. 6: Calibration factor for the wake model
The determined correction factor is applied during the monitoring period. Fig. 4: FarmFlow results with different settings for turbulence intensity at 8 m/s
Fig. 5 compares the normalized power curve of AV5 at 270Β° Β±2.5Β° for the turbulence intensity bin 3.5% < TI β€ 6.5% to the model calculations tuned for TI equal to 5%, 8% and 11%.
5. Uncertainty Treatment It is essential to understand the uncertainties of the method to judge the confidence in underperformance detection. Any false alarm can cause unnecessary trouble shooting. The important measurands of the method are the measured power and the predicted power for each wind turbine under observation and for reference (ππππ , πππππ , ππππ , πππππ ). For each of these power values, a combined uncertainty [3] can be derived with Equation (4). πΎ
π’π (π) = οΏ½(ππ β π’π )2 π=1
Fig. 5: Normalized FarmFlow power curves with different settings for turbulence intensity for 270°±2.5°.
The wake model has similar behaviour as the findings from measurements in [2]. The
(4)
where ππ is the sensitivity factor and π’π the uncertainty of the k-th component of the measurement chain. Due to the fact, that we look at each measurand under different environmental conditions the statistical type A uncertainties are not applicable.
Therefore only type B uncertainties of the measurement chain are considered. Table 2 shows the uncertainty components of the predicted power ππ . Table 2: Uncertainties of the predicted power k 1 2
3
4
5 6
7
8 9 10
Uncertainty Component Anemometer calibration Anemometer Operational characteristics Anemometer Mounting effects Wind speed data acquisition Wind vane calibration Wind vane mounting effects Wind vane data acquisition Temperature sensor Pressure sensor wake model env. condition modelling (TI)
Sensitivity ck,i,j ππ π,π β ππ πβ1,π οΏ½ οΏ½ πππ β ππβ1,π ππ π,π β ππ πβ1,π οΏ½ οΏ½ πππ β ππβ1,π ππ π,π β ππ πβ1,π οΏ½ οΏ½ πππ β ππβ1,π ππ π,π β ππ πβ1,π οΏ½ οΏ½ πππ β ππβ1,π ππ π,π β ππ πβ1,π οΏ½ οΏ½ πππ β ππβ1,π ππ π,π β ππ πβ1,π οΏ½ οΏ½ πππ β ππβ1,π ππ π,π β ππ πβ1,π οΏ½ οΏ½ πππ β ππβ1,π
ππ π,π 288.15 πΎ ππ π,π 1013 βππ ππππΌπ‘,π,π β ππππΌ π‘β1,π,π οΏ½ οΏ½ ππΌπ‘,π,π β ππΌπ‘β1,π,π
Uncertainty uk,i,j 0.05 [m/s] 0.043 + 0.0043 Β· V[m/s] 0.015 V[m/s]
0.03 [m/s]
1.5Β° 3Β°
0.5Β°
2.1 [K] 3.0 [hPa] 0.5 [%]
Table 2 provides the sensitivity factors, with ππ π,π being the power value in the matrix referring to the wind speed bin π and the wind direction bin π. ππ,π being the wind speed and ππ,π being the wind direction of the element. ππππΌ is the power matrix calculated for a specific turbulence intensity. Table 3 shows the uncertainty components of the measured power ππ .
therefore yields an inacceptable rate for underperformance detection. The wind speed measurement has the largest effect on the uncertainties. To lower this impact, the monitoring method is based on normalised measurements and normalised predictions. A wind speed error at the met mast has a much lower impact on the ratio of the power of two turbines than on their absolute power performance. π’(π) = π’ οΏ½
ππππ οΏ½= πππππ 2
πππππ π’π οΏ½ππππ οΏ½ π’π οΏ½πππππ οΏ½ = β οΏ½οΏ½ οΏ½ +οΏ½ οΏ½ ππππ ππππ πππππ
2
(5)
Equation (5) explains how to calculate the uncertainty of a summation in quadrature for division [4]. The equation is equivalent for π’(π) and is applied on each 10 min sample. With the two uncertainties π’(π) and π’(π) being independent the standard propagation of errors for π can be simplified according to [5] to the following equation: π’2 (π) = οΏ½
ππ 2 2 ππ 2 οΏ½ π’ (π) + οΏ½ οΏ½ π’2 (π) ππ ππ
(6)
which leads to an uncertainty in π of: π’(π) =
100 π 2 οΏ½π’2 (π) + οΏ½ οΏ½ π’2 (π) π π
(7)
The uncertainty derived by (7) can be displayed as a bandwidth which leads to the following graph in Fig. 7:
Table 3: Uncertainties of the measured power k 1 2 3 4
Uncertainty Component Current transformer Voltage transformer Power transducer Power data acquisition
Sensitivity ck,i,j 1
Uncertainty uk,i,j 0.0043 P [kW]
1
0.003 P [kW]
1
0.003 Prated [kW] 0.001 Prated [kW]
1
It is seen in power curve verifications, that the uncertainty of the measurement chain that includes a met mast and all its devices usually is about 5%. In our case, the wake model will add further uncertainties which would lead to even higher values and
Fig. 7: Uncertainty band width of the calibrated model
Fig. 7 indicates a quite low level of uncertainty below 5.5%. The confidence level is one standard deviation, which is considered to be acceptable for underperformance detection.
6. Demonstration In section 3 to 5, a monitoring model was chosen, celebrated and the uncertainty in the method was estimated. Next the capability of the method to detect underperformance will be demonstrated. For now, we will concentrate on the three wind turbines in a row with wind from 264Β° to 285Β°. AV4: free flow, AV5: single wake, AV6: double wake. Fig. 8 illustrates the layout of Alpha Ventus and FINO 1 met mast and highlights the turbines of this demonstration case.
Measurements from above rated wind speed are removed to concentrate on the part of the power curve where underperformance is more difficult to detect. Working with relative predictions the prediction error in percent rises with lower power production at low wind speeds. Therefore the model is supposed to treat only measurements above 5 m/s. At first we try to estimate the required number of power samples π for the most simple case. AV4 is operating at free flow conditions and therefore the performance of the wake model does not have any influence.
Fig. 8: Wind turbines in the demonstration
The SCADA data from Alpha Ventus has been contaminated with errors that the model is supposed to detect. Two kind of errors are forced into the data. The first manipulation simulates a degradation of 7% for which the original data set that has been used to calibrate the model is multiplied by 0.93. The second test case is a simple power curve curtailment at 60% rated power.
Fig. 9: Scatterplot with normalized power vs. normalized wind speed for the three turbines with the two error test cases
Normalized power data, for different manipulations at each turbine are given in Fig. 9. The green coloured points indicate correct turbine performance. The blue dots describe the degradation and the red dots are the data with the curtailment.
Fig. 10: Degradation at AV4 (free flow)
In Fig. 10 to Fig. 15 the green graph displays the performance deviation π for increasing number of samples π for the turbine without manipulated performance. The blue centreline is the data with the degradation and it is surrounded by the uncertainty band of the method. The red centreline refers to the data with a curtailment. It can be seen, that the uncertainty band increases with the wake influence.
Fig. 11: Curtailment at AV4 (free flow)
Fig. 12: Degradation at AV5 (single wake)
For the purpose of this demonstration π = 65h β 6 = 390 quantities has been chosen. Now we are monitoring the wind farm Alpha Ventus with AV5 as βblack sheepβ. The original data of AV5 is multiplied by 0.93 to simulate a degradation of 7%. The monitoring sector is 265Β° to 290Β° to demonstrate a detection under wake conditions. For every possible turbine combination, ππππ πππ£ππ , πππππππππ has to be derived with (3). With six turbines in the wind farm this leads to 36 levels of performance values. To get a quick farm overview the wind farm performance monitoring matrix is introduced.
Fig. 13: Curtailment at AV5 (single wake)
Fig. 14: Degradation at AV6 (double wake)
Fig. 16: Wind farm performance monitoring matrix
Fig. 15: Curtailment at AV6 (double wake)
To determine the required observation quantities π the green graph has to be outside of the uncertainty band of the data with underperformance. Assuming all quantities of the 10 minute average values being chronologically connected, Table 4 provides the duration T for detection of underperformance in hours. It makes clear that a detection of underperformance in a wake situation with higher uncertainty band needs a longer period of observation. Table 4: Observation period T in [h] T [h] Not in wake Single waked Double waked
Degraded 4.5 63 65
Curtailed 23 65 65
Fig. 16 is a graphical representation of the correlation results. The diagonal values are 0. The values off the diagonal are absolute values squared. I.e. the matrix element AV5/AV1 highlights the result for ππ΄π5,π΄π1 . Higher values are represented by darker shades of grey. It is striking that all fields with an involvement of AV5 have an increased discoloration, thus the wind farm performance monitoring matrix is useful to detect the βblack sheepβ in the farm, i.e. AV5.
7. Conclusion A method for wind farm performance monitoring with advanced wake models was introduced. The uncertainties in measurements could be reduced by normalization and referencing correlations. A suitable wake model was determined, calibrated and used in a demonstration
case. Here the method was capable of detecting a degradation of 7% with the confidence of one standard deviation.
Acknowledgement The presented work is partly funded by the Commission of the European Communities, Research Directorate-General within the scope of the project βClusterDesignβ (Project No. 283145 (FP7 Energy)).
References [1]
G. Steinfeld, N. Mittelmeier, S. DrΓΌke, A. Brand, T. Hait, and S. Amelsberg, βReport on the results of benchmarks for wake models,β FP7 ClusterDesign, 2013.
[2]
M. DΓΆrenkΓ€mper, J. Tambke, G. Steinfeld, D. Heinemann, and M. KΓΌhn, βInfluence of marine boundary layer characteristics on power curves of multi megawatt offshore wind turbines,β in DEWEK, 2012, pp. 1β4.
[3]
JCGM, βEvaluation of measurement data β Guide to the expression of uncertainty in measurement,β JCGM 1002008, vol. 1, no. September, p. 134, 2008.
[4]
S. Bell, βA Beginnerβ s Guide to Uncertainty of Measurements,β Meas. Good Pract. Guid., vol. 11, no. 2, p. 41, 2001.
[5]
H. Ku, βNotes on the use of propagation of error formulas,β J. Res. Natl. Bur. Stand. (1934)., vol. 70C, no. 4, pp. 263β273, 1966.
