Influence of yaw control on flicker produced by wind turbines

Electrical Power and Energy Systems 153 (2023) 109376 Available online 20 July 2023 0142-0615/© 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/). Contents lists available at ScienceDirect International Journal of Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes Influence of yaw control on flicker produced by wind turbines Koldo Redondo a,∗, Jose Julio Gutierreza, Izaskun Azcarate b, Mikel Leturiondo a, Jose Antonio Urigüen b, Sofía Ruiz de Gauna a, Purificación Saiz a aCommunications Engineering Department, University of the Basque Country (UPV/EHU), Plaza Ingeniero Torres Quevedo 1, Bilbao, Spain bApplied Mathematics Department, University of the Basque Country (UPV/EHU), Plaza Ingeniero Torres Quevedo 1, Bilbao, Spain ARTICLE INFO Keywords: Wind turbine Yaw control Power quality Voltage fluctuations Flicker ABSTRACT IEC 61400-21-1 describes the procedure for measuring the flicker produced by a wind turbine. This is a complex procedure, as it involves the processing of voltage and current time series recorded in a grid connected wind turbine for its entire operating range. The standard assumes that the flicker produced by a wind turbine is related to wind variations and switching operations. The voltage and current signals recorded in a 2 MW Type III wind turbine located at a 32 MW wind power plant in Spain were used for the study. The work shows that most of the flicker produced by the wind turbine is due to the power consumption of the motor used by the yaw control system to orient the nacelle. These operations generate voltage changes whose amplitude is independent of the generated power. As the generated power increases, so does the number of yaw control operations and thus the flicker emitted. A simple analytical method is proposed to estimate the flicker produced by yaw control operations. The results confirm that incorporation of this strategy into the standard could considerably simplify the current flicker measurement procedure. 1. Introduction The harvesting of wind energy by wind turbines (WTs) is conditioned, among other aspects, by the yaw error. This is defined as the misalignment in horizontal plane between the wind direction and the WT rotor axis. The yaw error causes different undesired effects: the power captured decreases as the error increases [1,2]; it causes crosswind, which generates vibrations in the WT structure due to asymmetry loads [3]; and it modifies the direction of the wake and, therefore, the characteristics of the wind that reaches the other WTs of the wind power plant (WPP) [4,5]. Yaw control strategies are used to solve the effects outlined above. Some of them maximize power generation [2,6], using directly the wind direction obtained by conventional sensors to orient the WT as a function of the calculated yaw error [7–11]. These methods result in frequent yaw operations and WT performance with significant yaw errors [12]. Other methods predict the wind direction, and consequently the optimal nacelle orientation, based on Lidar sensors [13,14] or time series models [6,15]. There are strategies that operate without sensors, based on tracking of the maximum power point or the optimal rotor speed [16–19]. Other strategies aim to minimize the fatigue load experienced by the WT [20,21]. Finally, some strategies focus on the wake effect so that yaw control is applied to the whole WPP, to improve overall power generation [22,23], as in the case with extremum seeking control [24], as well as to minimize the overall fatigue loads [23]. ∗Corresponding author. E-mail address: [email protected] (K. Redondo). Yaw control actuators use one or more electrically driven gears to orient the nacelle in the set direction. Each nacelle orientation result in a sudden power consumption at motor startup. These power changes are injected into the grid generating voltage fluctuations, resulting in flicker emissions from the WPP. Flicker is defined as the impression of instability in visual sensation due to fluctuations in the brightness of light sources caused by fluctuations in their supply voltage [25]. IEC 61000-4-15 establishes the specifications for the implementation of the flickermeter [26]. This procedure defines a parameter that evaluates the annoyance produced by light fluctuations in a 10-min interval, called flicker severity, 𝑃𝑠𝑡 [27]. Fluctuations producing values of 𝑃𝑠𝑡 >1 are considered annoying. The international standard IEC 61400-21-1 [28] establishes the procedures for characterizing the flicker of WTs connected to the grid. The standard defines two scenarios: continuous operation, when fluctuations are due to the interaction between WT and changes in wind characteristics [29–33]; and switching operations, when rapid voltage changes are generated [34,35]. The implementation of the standardized procedure requires the compliance with an exhaustive test protocol that guarantees high measurement accuracy and the collection of large amount of electrical data over weeks to characterize the full operating power range [36–38]. https://doi.org/10.1016/j.ijepes.2023.109376 Received 10 March 2023; Received in revised form 26 May 2023; Accepted 11 July 2023 International Journal of Electrical Power and Energy Systems 153 (2023) 109376 2 K. Redondo et al. Fig. 1. Flicker coefficient measurement diagram according to the IEC 61400-21-1 [28]. The objective of this work was, on the one hand, to characterize the flicker produced by the motor startup of the yaw control system. On the other hand, since the IEC 61400-21-1 standard does not currently consider it, the work proposes a simple procedure to estimate the flicker due to yaw control, without the need to connect the WT to the grid. For the work, the three phase-to-neutral voltages and the three line currents were recorded during 35 days at a WPP in Spain. The manuscript is structured as follows: Section 2describes the flicker measurement procedures according to IEC 61400-21-1 that will be used to obtain results, as well as the characteristics of the WT studied and the database obtained. Section 3presents the results of the work: first, the effect that the power consumption due to the motor startup has on voltage and on instantaneous flicker perception; second, the influence of the yaw operations on the flicker severity both in continuous and in switching operations of the WT; third, a simply mathematical method to estimate the flicker produced by yaw operations based on the 𝑃𝑠𝑡 = 1 curve. Finally, Section 4summarizes the conclusions and main contributions of the work. 2. Materials and methods 2.1. Flicker measurement according to the IEC 61400-21-1 standard For both continuous and switching operations, the flicker coefficients, 𝑐(𝜓𝑘), are calculated according to Fig. 1. The time series of line current, 𝑖𝑚(𝑡), and phase-to-neutral voltage, 𝑢𝑚(𝑡), recorded at the WT terminals, are used as input signals. Block A implements the interaction between the WT and the grid, aiming at calculating the voltage 𝑢𝑓 𝑖𝑐 (𝑡), that contains those fluctuations produced exclusively by the WT. The standard specifies that 𝑢𝑓 𝑖𝑐 (𝑡)must be obtained for different grid impedance, determined by four phase angles 𝜓𝑘(30◦, 50◦, 70◦and 85◦) and the short-circuit apparent power of the grid, 𝑆𝑘,𝑓 𝑖𝑐 . Block B implements the IEC fllickermeter [26]. The procedure reproduces the response of the lamp-eye-brain system [39–41]. The incandescent lamp was taken as the reference since it was the most sensitive lighting technology to voltage fluctuations. The instantaneous flicker perception, 𝑃𝑖𝑛𝑠𝑡, is obtained as the output signal of the model. To calculate the annoyance produced by light fluctuations, a statistical and temporal integration of the 𝑃𝑖𝑛𝑠𝑡 values in 10-min is performed, obtaining the short-time flicker severity value 𝑃𝑠𝑡,𝑓 𝑖𝑐 . Block C obtains the flicker coefficient 𝑐(𝜓𝑘)by normalizing each value of 𝑃𝑠𝑡,𝑓𝑖𝑐 according to [28]: 𝑐(𝜓𝑘) = 𝑃𝑠𝑡,𝑓𝑖𝑐 ⋅𝑆𝐶𝑅 =𝑃𝑠𝑡,𝑓𝑖𝑐 ⋅ 𝑆𝑘,𝑓𝑖𝑐 𝑆𝑛 (1) where 𝑆𝑛is the rated apparent power of the WT. The standard suggests values for the short-circuit power ratio, 𝑆𝐶𝑅, between 20 and 50. During continuous operation, flicker coefficients for 10-min time series are classified into 11 power bins (0, 1, 2, up to 10), with the midpoint of these bins being 0%, 10%, 20%, up to 100% of the nominal power, 𝑃𝑛, respectively. Measurements are collected continuously with a minimum of 21 time series for each of the power bins, discarding the Table 1 Recorded WT characteristics. Parameter Description Value 𝑈𝑛Nominal voltage 690 V 𝐼𝑛Rated current 1500 A 𝑃𝑛Rated power 2 MW 𝑃 𝐹 Power factor range 0.98 CAP - 0.96 IND 𝑓0Main frequency 50 Hz 𝑣𝑖𝑛 Cut-in wind speed 4 m/s 𝑣𝑟𝑎𝑡𝑒𝑑 Rated wind speed 13 m/s 𝑣𝑜𝑢𝑡 Cut-out wind speed 25 m/s Table 2 Summary of WT measurements data base. Parameter Description Value 𝑁𝑇Total time series 4914 𝑁𝐶𝑂 Continuous operation 4380 𝑁𝑆𝑊 Switching operation 294 𝑁𝑁𝐺 Non-generation 240 𝑃𝑎𝑣𝑔 Average power 0.54(0.26–0.99) MW time series which contain switching operations or which correspond with non generation mode of the WT. Characterization of voltage fluctuations in switching operations is performed for a duration of 𝑇𝑝seconds, long enough to contain the entire switching operation avoiding the effects of the resulting continuous operation. This assessment is made by calculating the flicker step factor, 𝑘𝑓(𝜓𝑘), according to [28]: 𝑘𝑓(𝜓𝑘) = 1 130 ⋅𝑐(𝜓𝑘)⋅𝑇0.31 𝑝(2) and the voltage change factor, 𝑘𝑢(𝜓𝑘), according to [28]: 𝑘𝑢(𝜓𝑘) = √3⋅ 𝑈𝑓𝑖𝑐,𝑚𝑎𝑥 −𝑈𝑓𝑖𝑐,𝑚𝑖𝑛 𝑈𝑛 ⋅ 𝑆𝑘,𝑓𝑖𝑐 𝑆𝑛 (3) where 𝑈𝑛is the nominal voltage of the WT and 𝑈𝑓𝑖𝑐,𝑚𝑎𝑥 and 𝑈𝑓𝑖𝑐,𝑚𝑖𝑛 are the maximum and minimum rms values of the fictitious voltage 𝑢𝑓 𝑖𝑐 (𝑡). Calculation of both parameters must be carried out for at least 15 operations, obtaining the mean value as the final result. 2.2. Data collection Measurements from a 2 MW type III WT located at a 32 MW WPP in Spain were analyzed. WT characteristics are summarized in Table 1. It is a pitch regulated, upwind WT with active yaw control, three-blade rotor, and high-efficiency 4-pole doubly fed generator with wound rotor and slip rings. The yaw control system consists of four gears electrically operated by a 2.2 kW 6-pole asynchronous motor. It takes decisions based on the information received from the ultra-sonic anemometers mounted on top of the nacelle. The three phases-to-neutral voltages and the three line currents were recorded (at a sampling rate of 20 kHz) during 35 days, obtaining a total of 4914 10-min time series (see Table 2). The connection and shut-down events of the WT were identified, which allowed the time International Journal of Electrical Power and Energy Systems 153 (2023) 109376 3 K. Redondo et al. Fig. 2. Histogram of 10-min time series during continuous operation (blue), as a function of power intervals. The cases of switching operation (green) and non generation (red) have also been grouped separately. series to be classified into three groups: continuous operation (CO), switching (SW) and non-generation (NG). Almost 89% of them were continuous operations (𝑁𝐶𝑂 =4380), approximately 6% contained switching operations (𝑁𝑆𝑊 =294) and the remaining 5% corresponded to non-generation functioning mode (𝑁𝑁𝐺 =240). The average power 𝑃𝑎𝑣𝑔 of each time series was obtained, with a median value of 0.54 MW and interquartile range (IQR) of 0.26–0.99 MW. Fig. 2 shows the distribution of the time series related to functioning mode of WT. In continuous operation, power generation was close to 𝑃𝑛(bins 8–10) during 9% of the time, and it was below 50% of 𝑃𝑛during 75% of the time. The number of recorded time series met the requirements of IEC 61400-21-1. Fig. 2 shows that the entire WT operating range was recorded, with a minimum of 126 time series per bin. Moreover, 230 connections of WT were identified from the switching operation time series. 3. Results All the results described in this section were obtained for 𝜓𝑘= 85◦, close to the grid impedance reported by the WPP operator, and 𝑆𝐶𝑅 = 20. 3.1. Characterization of yaw control operations Each motor startup that orients the nacelle towards the set direction generates an energy consumption that produces voltage changes and, consequently, flicker. Fig. 3 illustrates the temporal evolution of the main magnitudes affected by a yaw operation. The motor startup (at 0.38 s) required an instantaneous current consumption of 115 A (7%), which reduced the generated power (a change of 110 kW was observed, which represented a reduction of 5.7%). The power consumption of the motor produced a sharp voltage drop (𝛥𝑉 =1.6 V) which corresponded to a relative voltage change amplitude of 𝑑𝑣 =𝛥𝑉 ∕𝑉= 0.4%. This produced a maximum instantaneous flicker perception value of 𝑃𝑖𝑛𝑠𝑡,𝑚𝑎𝑥 = 0.54. Voltage changes due to mentioned motor startups appeared regularly. For the total recorded time series more than 53,000 startups were identified according to IEC 61000-4-30 standard [42]. Fig. 4 presents the analysis of all the 10-min time series included in the study. The average amplitude of the voltage drops, 𝑑𝑣, did not depend on either the power or the WT functioning mode, with median (IQR) values of 0.379 (0.374–0.384)%. Number of yaw operations in 10-min, 𝑁, presented a high dispersion in all three WT modes. Only during continuous operation a dependence of 𝑁with power was observed. First, 𝑁remained constant (10 operations in 10-min) up to 1.5 MW, and then values increased from 1.5 MW upwards, exceeding 30 operations in 10-min at 𝑃𝑛. The magnitude of the voltage drop was mainly due to the characteristics of the motor used for the orientations of the nacelle. The relationship between 𝑁and power indicates that the activation rate of the actuators depended on the implemented control strategy. The consumption derived from motor startup had a negligible influence on the generated energy. Indeed, by simulating the behavior of a 10-min time series with an average power of 𝑃𝑎𝑣𝑔 = 2 MW and 𝑁= 30, each producing a power reduction of 110 kW and a voltage drop of 𝑑𝑣 = 0.37%, we obtained an energy loss of 𝐿𝑦= 92 Wh, representing 0.03% of the generated energy. However, from the flicker point of view, we obtained a flicker severity value of 𝑃𝑠𝑡 = 0.2, which, although still far from the threshold (𝑃𝑠𝑡 = 1), represented a relevant percentage of it. 3.2. Flicker measurement during continuous operation Panels (a), (b) and (c) of Fig. 5 show three cases of 10-min time series, classified into different power bins. The behavior explained in Section 3.1 was reproduced in a very similar way for each yaw operation. Abrupt increases in 𝑃𝑖𝑛𝑠𝑡 had similar values for the three time series (between 0.5 and 0.6), and well above the negligible values produced by the changing wind characteristics. Results for those cases are summarized in Table 3. The number of operations grew as the generated power increased. Energy losses were very low in all cases. The calculation of flicker coefficients due to yaw operations, 𝑐𝑦, were estimated mathematically considering the proportionality between the amplitude of the fluctuation and the flicker severity [43], as follows: 𝑐𝑦=𝑃𝑠𝑡,𝑦 ⋅𝑆𝐶𝑅 =𝑑𝑣 𝑑𝑣𝑟𝑒𝑓 (𝑁) ⋅𝑆𝐶𝑅 (4) where 𝑑𝑣 was the average of amplitudes 𝑑𝑣 (%) and the denominator 𝑑𝑣𝑟𝑒𝑓 (𝑁)(%) is the amplitude of 𝑁voltage drops in 10 min that produce 𝑃𝑠𝑡 = 1 according to [26]. For the three cases, 𝑐𝑦values of 2.74, 3.46 and 3.86 were obtained, respectively. Extracting from the 𝑃𝑖𝑛𝑠𝑡 signal the short time intervals containing the voltage drops produced by the motor startup, the flicker coefficients of each case were also calculated by IEC flickermeter. The obtained values had a deviation of less than 5% with respect to the values calculated using Eq. (4). The flicker coefficients exclusively due to wind variations, 𝑐𝑤, were also calculated by removing from 𝑃𝑖𝑛𝑠𝑡 the short intervals corresponding to the voltage drops produced by motor startup, with values 1.28, 1.28 and 1.39 for the three cases. International Journal of Electrical Power and Energy Systems 153 (2023) 109376 4 K. Redondo et al. Fig. 3. A segment of 2 s containing a yaw operation. From top to bottom: rms value of current (A); generated power (MW); rms value of voltage (V); and instantaneous flicker perception 𝑃𝑖𝑛𝑠𝑡. Fig. 4. Characterization of yaw control operations at each time series during CO (blue), SW (green) and NG (red). Top: the average amplitude of voltage drop in 10-min, 𝑑𝑣(%). Bottom: number of yaw control operations, 𝑁(in 10-min). Fig. 6 shows the results for the whole set of time series, it confirmed that the flicker due to the yaw operations, 𝑐𝑦, increased with the generated power due to the increase of 𝑁(Fig. 4), while the flicker due to wind variations, 𝑐𝑤, remained nearly constant for most of the power bins. Considering a quadratic law for the summation of different sources of flicker, described in IEC 61000-3-7 [44], 𝑐𝑦values were responsible for most of the flicker produced by the WT, above 80% of the total flicker at 𝑃𝑛. However, 𝑐𝑤values were considerably lower, representing less than 13% of the total flicker at 𝑃𝑛. Therefore, most of the flicker during continuous operation was due to yaw operations, and depended directly on 𝑁. Furthermore, it is possible to properly estimate the flicker produced by yaw operations International Journal of Electrical Power and Energy Systems 153 (2023) 109376 5 K. Redondo et al. Fig. 5. Three cases of 10-min time series of continuous WT operation: panel (a), (b) and (c) correspond with bin 5, 8 and 10, respectively. On each panel, the top plot is the delivered power, the middle plot is the rms values of voltage 𝑢𝑓 𝑖𝑐 (𝑡)and the bottom plot is the instantaneous flicker perception 𝑃𝑖𝑛𝑠𝑡(𝑡). Fig. 6. The median values of the flicker coefficients related to the power bins. The blue asterisks represent the flicker coefficient, 𝑐. The red circles represent the estimated flicker coefficient due to orientations of the nacelle, 𝑐𝑦. The green squares represent the flicker coefficient due to wind variations, 𝑐𝑤. Table 3 Results from cases in Fig. 5. Case (a) (b) (c) Power bin 5 8 10 𝑃𝑎𝑣𝑔 (MW) 0.91 1.57 1.93 𝐿𝑦(%) 0.02% 0.02% 0.03% 𝑐3.16 3.82 4.26 𝑑𝑣 (%) 0.38 0.38 0.37 𝑁(cpm) 0.9 2.0 3.0 𝑑𝑣𝑟𝑒𝑓 (𝑁)(%) 2.80 2.20 1.93 𝑐𝑦2.74 (75%) 3.46 (82%) 3.86 (82%) 𝑐𝑤1.28 (16%) 1.28 (11%) 1.39 (11%) by means of Eq. (4), i.e., using the curve 𝑃𝑠𝑡 = 1 and knowing 𝑁and 𝑑𝑣. 3.3. Flicker measurement in switching operations For flicker characterization in switching operations, an evaluation period of 𝑇𝑝= 5 s was used. Fig. 7 shows four cases of switching operations of the WT. The events associated to switching are marked with two vertical green dash lines. The first line indicates the release of the rotor brakes (at 0.83 s, 0.57 s, 1.27 s and 0.82 s for the panels (a),(b),(c) and (d), respectively), International Journal of Electrical Power and Energy Systems 153 (2023) 109376 6 K. Redondo et al. Fig. 7. Four switching operations with 𝑇𝑝= 5 s. (a) SW without motor startup. (b) SW with motor startup ahead. (c) SW with motor startup in middle. (d) SW followed by motor startup. On each panel, top plot represents the active power, middle plot represents 𝑢𝑓𝑖𝑐 (𝑡)rms voltage and bottom plot represents instantaneous flicker perception 𝑃𝑖𝑛𝑠𝑡. and the second corresponds to the generator connection, that is when the rotor reached the generator synchronism speed (at 2.41 s, 2.39 s, 2.90 s and 2.42 s for panels (a),(b),(c) and (d), respectively). These two events affected power, voltage and 𝑃𝑖𝑛𝑠𝑡 signals. But when the generator connection occurred, the instantaneous voltage drop resulted in a more significant rise of 𝑃𝑖𝑛𝑠𝑡. From that moment on, power generation started, producing a power surge, higher voltage oscillations and, therefore, higher 𝑃𝑖𝑛𝑠𝑡 values than before the generator connection. The events corresponding to the motor startup are marked with vertical red dash lines for the cases of panels (b), (c) and (d). Its effect on flicker was considerably more relevant than the impact of the switching operation. The excursion of 𝑃𝑖𝑛𝑠𝑡 was almost 10 times larger and, depending on the instant of the onset, even masked the effect of the switching operation. In panel (b) the motor startup occurred at 𝑡= 0.23 s, before releasing the rotor brakes. By 𝑡= 2.00 s the effect of yaw operation on 𝑃𝑖𝑛𝑠𝑡 vanished and its value was comparable to the effect of generator connection at 𝑡= 2.39 s. In panel (c) the motor startup occurred at 𝑡= 2.38 s, between the release of the rotor brakes and the generator connection. This connection produced a delay in the descent of 𝑃𝑖𝑛𝑠𝑡 at 𝑡= 2.90 s, but its effect was masked by the effect of the yaw operation. Finally, in panel (d) the motor startup occurred at 𝑡= 3.06 s, after generator connection at 𝑡= 2.42 s. The effect of yaw operation was superimposed on the effects from continuous operation, which was maintained after generator connection. The values of 𝑘𝑓and 𝑘𝑢obtained from Fig. 7 cases and the maximum values of 𝑃𝑖𝑛𝑠𝑡 in the interval 𝑇𝑝are listed in Table 4. Flicker Table 4 Flicker results for the switching operations from Fig. 7. Case 𝑃𝑖𝑛𝑠𝑡,𝑚𝑎𝑥 𝑘𝑓𝑘𝑢 (a) SW 0.05 0.03 0.05 (b) SW +yaw 0.66 0.09 0.11 (c) SW +yaw 0.57 0.09 0.10 (d) SW +yaw 0.62 0.09 0.08 during the switching operations without the influence of the yaw operation was clearly lower than flicker affected by it. For case (a), the value of 𝑃𝑖𝑛𝑠𝑡,𝑚𝑎𝑥 was more than 10 times lower than for cases (b), (c) and (d); the value of 𝑘𝑓was 3 times lower; and the value of 𝑘𝑢almost 2 times lower. Finally, Fig. 8 shows the flicker values of the whole set of switching operations, classified according to whether or not they were affected by a yaw operation. Of the total 230 switching operations, 96 were affected (42%). Median 𝑘𝑓for both classifications was 0.04 and 0.09 and median 𝑘𝑢was 0.05 and 0.10. The flicker emission due to a yaw operation turned out to be much more significant than the flicker emission due to a switching operation. In addition, almost half of the switching operations coincided with a yaw operation. This generated a mischaracterization of the effect on flicker due to the switching operation when the procedure of IEC 61400-21-1 standard [28] was employed. That is, the high values International Journal of Electrical Power and Energy Systems 153 (2023) 109376 7 K. Redondo et al. Fig. 8. Distributions of 𝑘𝑓(panel a) and 𝑘𝑢(panel b) for the whole set of the WT switching operations with or without coincident yaw operation. of 𝑘𝑢and 𝑘𝑓were caused by the presence of a yaw operation and not by the switching operation itself. 4. Discussion and conclusions According to the IEC 61400-21-1, the flicker produced by a WT must be evaluated during continuous operation and in switching operations. However, it does not specifically consider the flicker produced by yaw operations. The work analyzes the whole operating range, both in continuous operation and in switching operations, of a type III WT at a WPP in Spain, with the aim of studying the effect on the flicker produced by the consumptions derived from the startup of the motor used for yaw operations. Considering the yaw operation as an isolated event, its effect on flicker was three times more significant than the effect produced by the switching operation. During continuous operation, the yaw operations occur with high regularity, and the results showed that they should be considered as sources of voltage fluctuations. In this sense, the number of yaw operations and the measured flicker grew consistently with the generated power. Disaggregating the flicker exclusively due to yaw operations, it accounted for more than 80% of the total flicker. However, the contribution due to changing wind characteristics remained almost constant at levels below 15% of the total flicker. Currently, flicker reduction in wind power generation has been achieved through effective active and reactive power management [45, 46], increased use of complex control strategies [47,48] and the widespread use of variable speed WTs. For these reasons, most of the flicker corresponds to the consumption derived from yaw operations. Employing yaw control strategies that minimize the number of yaw operations [6] and the power consumption at motor startup appears to be the simplest ways to reduce the flicker produce by yaw operations. Recent studies propose the application of yaw control in the whole WPP, taking into account the wake effect [24]. Incorporating a reduction in the number of yaw operations into this approach would maximize power generation, minimize loads, as well as further minimize flicker emissions from the entire WPP. Since the voltage drops produced by motor startups are of constant amplitude, it is possible to use the 𝑃𝑠𝑡 = 1 curve to make an accurate mathematical estimate of flicker severity. Given the complexity of IEC 61400-21-1 and considering that most of the flicker is due to yaw operations, updating the standard using the proposed mathematical estimate would have significant advantages. First, it would be an assessment prior to connecting the WT to the grid. Secondly, since it would not be necessary to measure for weeks, the economic costs would be considerably reduced. Finally, it would simplify the procedure, reducing it to the analytical comparison of the yaw control system data with the 𝑃𝑠𝑡 = 1 curve. CRediT authorship contribution statement Koldo Redondo: Investigation, Visualization, Writing – original draft. Jose Julio Gutierrez: Conceptualization, Supervision, Funding acquisition. Izaskun Azcarate: Writing – review & editing, Formal analysis. Mikel Leturiondo: Data curation. Jose Antonio Urigüen: Writing – review & editing. Sofía Ruiz de Gauna: Writing – review & editing. Purificación Saiz: Formal analysis. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data availability Data will be made available on request. Acknowledgments This work was supported by the Basque Government (Basque Country, Spain) through the grant IT1590-22. References [1] Burton T, Jenkins N, Sharpe D, Bossanyi E. Wind energy handbook. Wiley. [2] Yang J, Fang L, Song D, Su M, Yang X, Huang L, Joo YH. Review of control strategy of large horizontal-axis wind turbines yaw system. Wind Energy 2021;24(2):97–115. http://dx.doi.org/10.1002/we.2564. [3] Manwell JF, McGowan J, Rogers A. Wind energy explained, theory, design and application. Wiley; 2009. 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