Computing the real impact of wind turbine power curve upgrades : a SCADA-based multivariate linear method and a vortex generator test case

Computing the real impact of wind turbine power curve upgrades: a SCADA-based multivariate linear method and a vortex generator test case Davide Astolfi 1,‡*, Francesco Castellani 1,‡, Mario Luca Fravolini1,‡, Silvia Cascianelli1,‡, Ludovico Terzi 2,‡ 1 University of Perugia Department of Engineering, Via G. Duranti 93 06125 Perugia (Italy); davide.astolfi@unipg.it; francesco.castellani@unipg.it; mario.fravolini@unipg.it; silvia.cascianelli@unipg.it 2 Renvico srl, Via San Gregorio 34, Milano 20124, Italy; ludovico.terzi@renvico.it * Correspondence: davide.astolfi@unipg.it; Tel.: +39 075 585 3709 ‡ These authors contributed equally to this work.


Introduction
The upgrade of operating wind turbines has been spreading in the wind energy industry, in order to improve the efficiency of the conversion of wind kinetic energy.This kind of interventions has material and labor cost and producible energy is lost during the installation.Therefore, the priority of wind farm owners dealing with wind turbine upgrades is to estimate realistically the profitability.
Furthermore, the adoption of upgrades might exacerbate stressing mechanical conditions to which wind turbines are subjected.For example, a typical control system upgrade arising this kind of issues is the extension of the wind turbine operation above the cut-out wind speed [1,2].For this reason, the analysis of wind turbine upgrades through operational data is attracting an increasing attention in the wind energy scientific literature. is inquiring how the relationship between wind speed and power output changes: the International Electrotechnical Commission (IEC) [3] has established widely accepted standards for analyzing the power curve.Basically, the power output of the wind turbine is averaged on wind speed intervals (commonly of 0.5 or 1 m/s); the dependency on ambient factors is addressed by normalizing the wind speed to standard air density conditions (at sea level and 15 • C).Typically, data describing the wind turbine operating under the wake of a nearby one [4][5][6][7][8] are filtered away.
The power curve analysis is simple and intuitive, but has some drawbacks for the study of wind turbine upgrades.One drawback is that data describing the wind turbines operating under the wake of a nearby one are filtered away.The rationale for this choice is that the power curve is commonly used for detecting within what extent the performances under optimal conditions, i.e., the absence of wakes, resemble the expected theoretical ones.However, in the case of wind turbine upgrades the focus should rather be in the actual performances (and therefore in the production improvement) in the real operating conditions, that include wakes, icing, wind shear induced by the terrain [9][10][11][12] and so on.This drawback can be circumvented by disregarding within a certain extent the IEC guidelines and, for example, deciding not to filter away data associated to wind turbines operating under wake.
However, there is a further drawback that cannot be circumvented when it manifests: it might happen that the wind turbine upgrade affects the measuring chain of the Supervisory Control And Data Acquisition (SCADA) system.In such case, the power curve analysis cannot be performed because of the unavailability or the insufficient quality of the necessary measurements.
Therefore, the general strategy for quantifying the effects of an upgrade is comparing the post-upgrade production against a reliable simulation of the pre-upgrade production in the same conditions.The model for simulating the power output of the upgraded wind turbine can be the power curve when possible, or it can be a more complicated model if necessary, as in the test case of the present work.The study of this kind of problems and the formulation of adequate data-driven models addressing the occurring criticality is quite recent and there are substantially three relevant studies on this topic: [13], [14] and [15].In [13], a kernel plus method is proposed for computing wind turbine performance upgrades.In general, kernel regression is a non-parametric method: the available measurements are employed for simulating an output after being weighted with a kernel function (typically Gaussian).In [13], a modified version of the kernel is proposed (hence, named kernel plus) for addressing dataset dimensionality and bias issues: it has a hybrid structure that includes multiplicative kernel functions in an additive model.This method is employed for studying pitch angle control optimization and aerodynamic retrofitting (vortex generators installation on the blades [16]).In [14], an academia-industry joint study is presented and the test cases are two onshore wind farms that have been upgraded through the installation of vortex generators.The approach is twofold: on one hand, SCADA data with 10 minutes of sampling time are employed; on the other hand, high-frequency power data are employed.The estimates of production improvement are shown to be similar.The adopted methods are the kernel plus (as in [13]) and a power-power approach, based on observing how the difference between the power of the upgraded wind turbine and the power of a reference wind turbine changes after the upgrade.
This study, as well as [15], also is a partnership between academia and industry: the involved company is Renvico 1 , owning and managing 335 MW of wind turbines in Italy and France.In [15], three cases of upgrades on the wind turbines owned by Renvico are studied: (1) the pitch angle optimization near the cut-in, (2) the installation of vortex generators and passive flow control devices, (3) the extension of the power curve for high wind intensity through a soft cut-out strategy.It is argued that a data-driven study of the impact of wind turbine power curve upgrades in complex environments can lead to estimates that are non-negligibly different from what can be obtained basing on the hypothesis of ideal operating conditions as flat terrain, absence of wake interactions and so on.The complexity of one of the test cases in [15] has inspired a systematic investigation of wind turbine power curve upgrades: this is one of the motivations of the present work and of its philosophy, focused on the formulation of the method as well as the computation of the upgrade impact.
The test case of the present work is a multi-megawatt wind turbine from a wind farm sited in a very complex terrain [11,17,18] that has been upgraded through the installation of vortex generators [16,19,20] and passive flow control devices [21], increasing the lift and therefore the energy production of the turbine.This has been a pilot test and the decision of adopting the retrofitting on the whole wind farm has been based on the quantification of the benefits by means of this study.One key point of this study is that the measurements from the nacelle anemometer of the retrofitted wind turbine are unreliable.This implies that the power curve analysis is impossible and, moreover, the wind speed of the upgraded wind turbine cannot be used to model its power output.For this reason, the wind turbines nearby the upgraded one must be used as reference for the wind conditions.Furthermore, the complexity of the terrain makes it difficult to reliably use the power-power approach of [14], because the power difference between two wind turbines fluctuates severely.Therefore, a more complex and robust procedure must be formulated.
On these grounds, an appropriate multivariate linear model has been identified by means of stepwise regression.Since the stability and the quality of the results were required features, particular care has been devoted to the validation of the model.
Therefore, the outcome of this work is not only the computation of the production improvement (2% of the annual energy production is the estimated order of magnitude), but also the procedure for selecting the appropriate inputs and validating the model.The method is generalizable to the study of whatever kind of wind turbine upgrades.Moreover, having tested it for the study of an upgrade in complex terrain on a data set having the severe issue of the unreliability of nacelle anemometry, it is demonstrated its robustness and versatility.
The structure of the paper is the following.In Section 2, the test case and the data sets are described.Section 3 is devoted to the description of the method.The results are collected in Section 4.
In Section 5 conclusions are drawn and further directions are indicated.

The test case and the data set
The wind farm under investigation has recently attracted a certain attention in the scientific literature, because it is an interesting test case for the study of wind flow, wake-terrain interactions and wind turbine performances in complex terrain [11,17,18].In Figure 1, the layout of the wind farm is sketched.From the contour lines, it is possible to appreciate the complexity of the terrain.The upgraded wind turbine object of this study is denoted as T7 (colored in red in Figure 1).The wind turbines in the farm are multi-megawatt, the rotor diameter with blades is 93 meter and the hub height is 80 meters above ground level.The cut-in is 4 m/s and the cut-out is 25 m/s and the nominal wind speed is 13-14 m/s.The rotor rotational speed goes from 6 to 16 rpm.The gearbox is 3-stage, the generator is asynchronous having synchronous speed of 1500 rpm and the main brake is aerodynamic through pitch angle adjustment.For this study, the SCADA collected data have been exploited and organized in two datasets as follows:

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• The first dataset is denoted as D bef and contains the data collected from 01/01/2016 to 01/07/2017.It is a period during which the standard blade configuration was adopted.
• The second dataset is denoted as D aft and contains the data collected from 01/09/2017 to 01/05/2018.It is a period during which T7 has been operating with the improved blade configuration.
The SCADA data are recorded with 10 minutes of sampling time through a microprocessor controller and are WPS-transmitted via modem.

The method
Before discussing the method, it is interesting to motivate why a power curve analysis cannot be performed for a qualitative assessment of the production improvement.In Figure 2, the power coefficient C p as estimated from the SCADA data during the D aft data set is reported as a function of the wind speed for the upgraded turbine T7 and for another sample wind turbine from the wind farm, T2.Note that T2 has been selected as reference, but whatever wind turbine (except, of course, T7) could have been chosen for a qualitative comparison.The power coefficient is defined as: where P is the measured power output, ρ is the air density on site, A is the blade swept area and v ∞ is the undisturbed wind speed as reconstructed from the nacelle wind speed through the nacelle transfer function.From Figure 2, it can be noticed that the measurements for T7 are implausible, because well above the Betz limit.The possible explanation for this fact is that the nacelle transfer function has not been updated by the manufacturer after the upgrade of T7.The same conclusion can be drawn also by another point of view: assume that the wind speed measurements at T7 during D aft are plausible.Therefore, an order of magnitude estimation of the production improvement can be simply computed by comparing the produced power against the theoretical power, according to the pre-upgrade power curve provided by the wind turbine manufacturer.Doing this, it is obtained that the improvement is of the order of 10% of the annual energy production.This is of course implausible, because vortex generators and passive flow control devices are known to provide an improvement of the order of few percents.The conclusion is that the wind speed measurements at T7 are unreliable after the installation of the upgrade.
On the grounds of the above discussion, it is necessary to adopt the wind turbines nearby T7 as references for assessing the energy improvement.In the following, an argument is reported why a power-power approach (similar to the one in [14]) can't be considered robust enough for the present test case sited in a very complex terrain.
The idea is studying how the difference between the power of the upgraded wind turbine (T7) and a reference wind turbine (T6 is selected because it is the nearest) changes after the upgrade of T7.
Therefore, the difference of the powers of T7 and T6 is computed on the data sets D bef and D aft , once they are opportunely filtered.The requests for the filter are that the T7 and T6 are producing power and that T7 catches free wind: therefore, the nacelle position corresponding to the sectors free from wakes (on the grounds of IEC guidelines [3]) are selected.The results are collected in Figure 3: the x-axis is the power of the reference wind turbine (T6) and the y-axis is the power difference between T7 and T6.Data are averaged in T6 power intervals having amplitude of the 10% of the rated power.
In Figure 3, for the post upgrade data set, also the standard deviation of the data inside each interval is reported.It clearly arise that the average behavior of the power difference is compatible with the conclusion that there has been a power improvement for T7, but the data sets before and after the upgrade are perfectly compatible between one standard deviation of the data inside each T6 power interval.On these grounds, the power-power method has been considered not solid enough for this test case and this is definitely reasonable, because the terrain is very complex.Therefore, it has been decided to formulate a more robust model, at the possible cost of increasing its complexity.This has been done in a completely general way.

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The output of the model, denoted as y, is the power output of T7.The possible input data at disposal, from each of the remainder 16 wind turbines in the farm, are: • nacelle wind speed, • power output, • individual blade pitch angles, • rotor revolutions per minute, • high speed rotor temperature.
The data are filtered on the condition of power output production from all the wind turbines in the farm (using the appropriate counter of grid production, available in the SCADA data set) and of power production of T7 below the rated, because at rated power the upgrade has no visible effect.
In the following, the procedure is reported for selecting the inputs appropriately.Note that, the measurements of the output y are assembled in a column vector y and the values of the inputs x are assembled in a matrix x.A stepwise regression is performed: it is a systematic method for adding and removing terms from a multilinear model, based on their statistical significance in a regression task.
The algorithm begins with an initial model and then compares the explanatory power of incrementally larger and smaller models, where 'larger' and 'smaller' refers to the number of used regression terms.
The candidate models are obtained via the stepwise regression algorithm based on the value of the p remove parameter.This is an exit tolerance for the probability of rejecting the hypothesis of a zero coefficient for a given input in the model.
In this work, to obtain a robust input selection strategy and consequently a reliable estimate of the power output of the turbine under investigation, the value of the p remove parameter has been chosen after an extensive study.The tested values of p remove are 10 −γ with γ = 1, . . ., 15.For each value of p remove , the input selection and estimation pipeline is subjected J times to k-fold cross-validation [22].
In particular, the data set D bef is divided J times randomly in two subsets: (k-1)/k of the data are used for training the model and the remaining 1/k are used for for validation.k has been set to 10 for this study, because the objective is validating the model for very short folds, in order to test its robustness.
J has been set to 300 to increase the significance of the study.
For each of the j = 1, . . ., J runs of the cross-validation, for a given value of p remove , the most significant inputs are selected and the estimation model is obtained as follows.matrix x train j,γ , constructed with the inputs using the measurements selected for the training, is normalized and its pseudo-inverse is used to compute the weight matrix as and the estimated output on the validation data set is computed as For each of the J runs, the mean absolute error is computed as follows: Subsequently, it is possible to average the δj,γ over j and obtain the average mean absolute error for a given γ: It arises that δγ is of the same order of magnitude ( 100 kW) for each value of p remove : the improvement in choosing p remove = 10 −1 instead of p remove = 10 −15 is averagely only 3 kW in δγ , at the cost of employing many more regressors (13 against 3) and having a less stable model (the number of possible regressor configurations is much higher).
For whatever choice of p remove ≤ 10 −10 , instead, one obtains that the selected inputs are the same (except for a small number of outliers explaining the values in the third row of Table 1) and they are: • the power output of T6, • the power output of T9, • the rotor revolutions per minute of T8.
Therefore, the decision is modeling the power output of T7 as a function of the three above inputs.
Besides the statistical significance of the method adopted for identifying the appropriate inputs for modeling the power of T7, support to the decision comes from the fact that it is definitely plausible.In fact, the wind turbines selected for the inputs are the nearest to T7 and one input per nearby wind turbine is selected, therefore there is no redundant information.Furthermore, it is reasonable that in such a complex terrain the power output or the rotor revolutions are more stable than the wind speed (because the wind turbine acts like a filter) and are preferable to model the power of T7.
In the following Section 4, it is shown how to use this model to obtain an estimate of the energy improvement since the adoption of the T7 upgrade.

The results
The data sets at disposal are employed as follows: • D aft (also named D2 for simplifying the notation in the following) is used in its entirety to quantify the performance improvement.
The approach is based on the analysis, for the data sets D1 and D2, of the residuals R between the measurement y and the estimation ŷ as a function of the inputs x (power of T6, power of T9, rotor revolutions per minute of T8, as indicated in Section 3).In other words, the interest is in how the residuals vary after the upgrade with respect to before.Therefore, consider Equation 5 with i = 1, 2. R(x i ) = y(x i ) − ŷ(x i ). ( For i = 1, 2, one computes Since ∆ i is constructed with the relative discrepancies of power data each having the same sampling time (10 minutes), the quantity provides a percentage estimate also of the energy improvement.
The above procedure has been repeated several times, with several random choices of D0 and D1 for training and validating the model, until the standard deviation of the estimates of ∆ has reached a plateau.In Table 2, statistics are reported for the discrepancy between estimation and measurement for the different choices of the D0 and D1 data sets: average residual between measurement and estimation (δ ave ), average mean absolute error ( δave ), average standard deviation of the residuals (σ δ ).From Tables 2, it arises that the average discrepancy between estimation and measurement is negligible on the D1 data set after having trained the model with the data sets D0; the measurements instead are averagely 50 kW higher in the post upgrade data set D2 with respect to the estimate provided by the model trained with pre-upgrade data.This is a clear indication of the fact that the wind turbine upgrade produces a non-negligible power improvement.
Further, a Student's t-test can be performed to detect the difference in the residuals R(x 1 ) and R(x 2 ).The t statistic is computed as In Equation 8, N 1 and N 2 are the number of measurements respectively in D1 and D2, R2 and R1 are the average residuals between measurement and model respectively in D1 and D2 and σ R is given by where S 1 and S 2 are the standard deviations of the residuals in data sets D1 and D2.For each of the model runs, the value of the t statistic is computed to be less than 10 −14 : this means that the probability that the data sets are compatible with the hypothesis that there has not been an improvement in the production of T7 is practically zero.The improvement is appreciable also from Figure 4: it is a plot of R(x 1 ) and R(x 2 ) on a sample model run.The data are averaged in power production intervals, whose amplitude is 10% of the rated.
This plot allows to appreciate how the residuals between measurements and estimations vary after the upgrade: the difference between measurement and estimation increases in the post-upgrade period, especially approaching rated power.5), for data sets D1 and D2 and for a sample run of the model.
The described procedure, being based on repeated random choices of D0 and D1, allows to have not only an average estimation of the energy improvement, but also a standard deviation (and therefore reasonable lower and upper limits for the energy improvement).The average energy improvement is ∆ = 3.9%.In other words, since the upgrade has been installed, T7 has produced below rated power the 3.9% more than it would have done without aerodynamic improvement.The standard deviation is σ ∆ = 0.2%: therefore, reasonable upper and lower limits of the energy improvement are ∆ + = 4.1% and ∆ − = 3.7%.This corresponds to an estimation of the improvement of annual energy production (AEP) of the order of ∆ AEP = 2.0 ± 0.1%.

Conclusions and further directions
In this work, a test case of wind turbine upgrade (installation of vortex generators and passive flow control devices) has been studied using SCADA data.This work has been organized as a collaboration between academia and industry and it is hopeful that the outcomes stimulate further cooperation.The objective has been a realistic computation of the production improvement since the adoption of the upgrade.
This kind of problems is non-trivial in general, because wind turbines are subjected to non-stationary operation conditions and therefore the most appropriate approach is comparing the post-upgrade production against a simulation of the pre-upgrade production under the same conditions.
In particular, the selected test case was challenging for two reasons: the first is that the data set at disposal has a severe limitation.In particular, the nacelle anemometer of the upgraded wind turbine is unreliable in the post-upgrade period.Therefore, the wind turbines nearby the upgraded one must be employed as reference of the external conditions.The second peculiarity of the test case is that the wind farm is sited in a very complex terrain and therefore it is difficult to select the appropriate inputs for modeling the power of the upgraded wind turbine.This has stimulated the formulation of a general method for studying wind turbine upgrades, based on stepwise regression for selecting the  This test demonstrates the versatility and the good estimation capabilities of the proposed approach, which make it suitable to be deployed in operative contexts.

Figure 1 .
Figure 1.The layout of the wind farm.

PreprintsFigure 2 .
Figure 2. The power coefficient C p , as computed from the SCADA data, vs. nacelle wind speed: T7 and a sample wind turbine (T2), D aft data set.

Figure 3 .
Figure 3.The power difference between T7 and T6, before and after the upgrade.

Figure 4 .
Figure 4.The average difference R between measurements and simulation (Equation5), for data sets D1 and D2 and for a sample run of the model.

Figure A1 .
Figure A1.The average difference R between measurements and simulation (Equation5), for data sets D1 and D2 and for a sample run of the model.T4 test case.

Figure
FigureA1is, similarly to Figure4, a plot of R(x 1 ) and R(x 2 ) on a sample model run, once the data are averaged in power intervals of 10% of the rated.The difference with respect to Figure4is evident: in FigureA1, the average residuals R(x 1 ) and R(x 2 ) as a function of the power are almost identical the ones with respect to the others.

J Table 1 .
Results of the model validation

Table 2 .
Statistical behavior of the residuals between measurement and estimation, for the different random choices of the D0 and D1 data set.