Mitigation of transient torque reversals in indirect drive wind turbine drivetrains

Bearing failure in wind turbine gearboxes is one of the significant sources of down-time. While it is well-known that bearing failures cause the largest downtime, the failure cause(s) is often elusive. The bearings are designed to satisfy their rolling contact fatigue (RCF) life. However, they often undergo sudden and rapid failure within a few years of operation. It is well-known that these premature failures are attributed to surface damages such as white surface flaking (WSF), white etching cracks (WECs) and axial cracks. In that regard, transient torque reversals (TTRs) in the drivetrain have emerged as one of the primary triggers of surface damage, as explained in this paper. The risk associated with TTRs motivates the need to mitigate TTRs arising in the drive-train due to various transient events. This paper investigates three TTR mitigation methods. First, two existing devices, namely, the torsional tuned mass damper and the asymmetric torque limiter, are studied to demonstrate their TTR mitigation capabilities. Then, a novel idea of open-loop high-speed shaft mechanical brake control is proposed. The results presented here show that while the torsional tuned mass damper and the asymmetric torque limiter can improve the torsional vibration characteristics of the drivetrain, they cannot mitigate TTRs in terms of eliminating the bearing slip risk associated with TTRs. However, the novel approach proposed here can mitigate TTRs both in terms of improving the torque characteristic in the high-speed shaft and reducing the risk of bearing slip by actuating the high-speed shaft brake at the onset of the transient event. Furthermore, the control method is capable of mitigating TTRs with the mechanical limitations of a pneumatic actuator in terms of bandwidth and initial dead time applied to it. This novel approach allows the wind turbines to protect the gearbox bearings from TTRs using the existing hardware on the turbine.

the onshore wind market reached 72.5 GW, 18% lower than the previous year due to a slowdown in China and the United States due to COVID-19; however, is still the second-best year in its history. The wind energy market is expected to pick up again postpandemic. A total of 21.1 GW offshore wind was commissioned in 2021 making it the best-ever year for offshore wind. This is three times more than the previous year. New offshore installations represented 22.5% of all new installations in 2021, helping bring the world's total offshore capacity to 57 GW, which is 7% of global installations. The CAGR (Compound Annual Growth Rate) for onshore wind in the next 5 years is 6.1%, with average annual installations of 93.3 GW. In total, 466 GW is likely to be built in 2022-2026. The CAGR for offshore wind in the next 5 years is 8.3%. 1 This expected growth in the wind energy market is also supported by Fortune Business Insights 2 report that the global wind turbine gearbox market is expected to grow from $19.33 billion in 2021 to $32.55 billion by 2028 at a CAGR of 7.7% in the forecast period, 2021-2028. Thus, indirect drive (geared) wind turbines will play a major role in the future wind energy market. Kaa et al 3 also present a similar outlook as they have reported that both the gearbox (indirect drive) wind turbine and the direct drive wind turbine have their merits, and in markets, such as wind energy, the two designs can co-exist. There does not seem to be a clear winner.
To achieve the projected cumulative growth in wind energy, it is necessary to improve their lifetime by developing more robust and resilient wind turbines. One major challenge is reducing downtime occurring from the failure of different parts of the turbine, where gearbox failures typically result in the longest turbine downtime. 4,5 Although the failure rates of the gearboxes are low compared with the electric and control systems, the mechanical components account for more than 75% of the total downtime. 5 It is also important to note that drivetrain module repair costs are typically more expensive than the electrical/control components due to crane costs. The main contributors to gearbox failures are bearings ≈ 70% followed by gears ≈ 26%, and other failures constitute the remaining ≈ 4%. 6 Forty-eight percent of all failures are attributed to highspeed shaft bearings, followed by 13% to the intermediate shaft bearings and 7% to the planetary bearings. 6 All other component failures (gears and others) account for the remaining 32%. Therefore, it is clear that bearing failures contribute greatly to wind turbine gearboxes' unpredictable and premature failure. Surface damages on high-speed shaft bearings, planetary bearings and intermediate speed shaft bearings mainly limit the service life. 7 Bearings are designed to satisfy a minimum rolling contact fatigue (RFC) life. However, failures within a few years of operation are observed because smearing/scuffing, white etching cracks (WECs) and axial cracking failure modes differ from the classical RCF failure mode.
Two prevalent surface failure modes in multimegawatt wind turbine gearbox bearings are as smearing/scuffing 8 and white structure flaking (WSF). 9 Slip is often considered as being essential to the formation of white etching areas (WEAs) 9 and smearing damage. 8 Slip can independently lead to either smearing/scuffing damage and WSF or severely promote WEA formation. 10 Once an event initiates subsurface WEA formations, normal rolling action of the bearing can initiate cracks at the junction of the inclusion-like areas. 11 The crack inevitably propagates to the surface and becomes a WEC, which grows axially across the raceway and causes premature bearing failures. 11 The drivers and mechanisms of the onset of smearing/scuffing or white etching surface formation are still highly contested. Evans 9 presents an extensive review of operational modes, drivers and mechanics that lead to three types of WECs and axial cracks: (a) hydrogen-induced, (b) electro-thermal stress-induced and (c) mechanical stress-induced. Some of the drivers identified by researchers are hydrogen embrittlement, sliding kinematics, water contamination, low Hertzian contact pressure, electrical potential, lubricant additives and tensile hoop stress. 9,12 However, the slip and impact loading during transient torque reversals (TTRs) is suggested to be a leading candidate in causing stress-induced subsurface WEA damage as illustrated in Sharpley. 11 In an indirect drive doubly fed induction generator (DFIG) wind turbine, the phenomenon of TTRs typically involves rapid reversals and multiple zero-crossings in the shaft torque Figure 1A. The multiple zero-crossings in shaft torque are accompanied by rapid reversals of the bearing loaded zone. This phenomenon is termed bearing load reversals (BLRs) where the bearing radial loading angle rapidly changes its sign by ≈ 180 ∘ , as shown in Figure 1B. To elaborate on the subsequent events, Figure 2 shows the formation of surface damage from TTRs. However, it must be noted that Figure 2 shows the sequence of events that arise from TTRs and does not include all drivers that lead to slip/skid and eventually to surface damage in multimegawatt wind turbine bearings.
The risk of damage associated with TTRs described above demonstrates the need to identify operational modes that lead to TTRs and consequently mitigate the damaging effect of TTRs to protect the bearings from surface damage. In a previous investigation, the authors identified that grid faults like symmetric voltage dips and emergency shutdowns lead to TTRs. Similar observations were also made by Röder et al 13,14 as they found an increased risk of smearing during grid and converter faults. To mitigate the risk associated with TTRs, three different approaches have been investigated here and their performance evaluated for symmetrical voltage dip and emergency shutdown events in a DFIG wind turbine.
Among the three approaches, first, a torsional tuned mass damper (TMD) and an asymmetric torque limiter are investigated separately. Next, a novel active control of the high-speed shaft mechanical brake in an open-loop architecture has been proposed.
An important task in this process is to develop a metric that can quantify the risk associated with TTRs. Röder et al 14 used frictional power intensity (FPI) to estimate a smearing criterion indicating the risk of smearing. However, sophisticated simulation models or instrumentation is required to track indicators such as a rise in inlet temperature or a rise in FPI. In the absence of such models or instrumentation, Eatherton et al 15 used metrics such as the maximum amplitude of oscillations and maximum negative torque excursion in the high-speed shaft to quantify the damaging effect of TTRs. However, these torque measurements do not account for the BLRs described in Figure 1. Therefore, a metric is required that can account for BLRs during TTR to accurately quantify the risk associated with TTRs. To this end, a quantity termed as slip-risk duration is proposed to be used here. The slip-risk duration represents the time duration spent by the bearings in a high slip-risk situation. The metric is formulated by defining thresholds, exceeding which signifies an increased risk of slip. Based on the reviewed literature, the two important thresholds are identified as follows: (a) a critical radial bearing load, below which it can be considered that the bearings are lightly loaded, and (b) a critical inner-raceway speed, above which the shaft is rotating fast. Ideally, to formulate these thresholds, the bearing at hand must be tested using the appropriate choice of lubricant and temperature. In the lack of such experimental results, these thresholds are determined from the literature 8,16,17 and have been assumed as follows: 1. Low radial bearing forces ≤ 1%C (dynamic load rating) accompanied by the sporadic and rapid reversal of radial load direction.
2. Simultaneously, the inner-raceway speed must be higher than 2.6 m/s. F I G U R E 2 Formation of surface damage from transient torque reversals (Note: This diagram only shows the sequence of events that arise from transient torque reversals (TTRs) and does not include all drivers that lead to slip/skid and subsequently to surface damage in multimegawatt wind turbine bearings.). WEA, white etching area; WEC, white etching crack; WSF, white structure flaking.
The time spent by the bearings beyond these thresholds is quantified as the risk of slip/smear associated with the different transient events.
The proposed metric above is based on the assumption that the amount of bearing preload is small. With substantial preload, the chosen loading threshold of 1%C should be revised. This metric, along with torque measurements like the amplitude of the maximum oscillations and maximum negative torque excursion, is used to evaluate the performance of the mitigation methods investigated and proposed in this paper.
The topic of vibration mitigation in wind turbine drivetrains has been sparsely addressed in the literature. In one of the earliest studies, Fateh et al 18 presented a nonlinear technique based on the sliding mode control theory to mitigate torsional vibrations in grid-connected DFIG-based wind turbines. The author derived a compensation torque to be superimposed onto a desired torque formulated based on a maximum power tracking algorithm. The proposed controller was able to reduce torsional vibrations in the drivetrain. Lee et al 19  and a swing rod attached to the output end of the former. However, these studies do not consider the effect of TTRs in terms of BLRs. Therefore, no conclusion can be drawn on their effect on BLRs and the induced slip risk. In this paper, we proposed a novel approach that can mitigate TTRs both in terms of improving the torque characteristic in the high-speed shaft and reducing the risk of bearing slip. This paper is structured as follows: first, the model used for the numerical investigation is detailed in Section 2. Next, Section 3 describes the three TTR mitigation methods investigated here. In Section 4, first, the results of the torsional TMD and the asymmetric torque controller are presented. Then the results of the proposed open-loop control strategy for the high-speed shaft brake are presented. Section 4 is concluded with of comparison of the three mitigation methods. The paper ends with recommendations to mitigate TTRs in multimegawatt DFIG wind turbine drivetrains during grid faults and emergency shutdowns.

| GENERIC MODEL OF A MW ONSHORE WIND TURBINE
A generic 2 MW wind turbine model is developed inspired by the behaviour/power production of a Vestas V90 machine. The state-of-the-art aeroelastic simulation tool OpenFAST 21 is used for aeroelastic simulations of the wind turbine in this paper. The generic 2 MW wind turbine model is developed by downscaling the NREL 5 MW reference wind turbine 22 guided by Vestas V90-2.0 23 power curve and the available SCADA data. The generic turbine has a cut-in wind speed of 3.5 m/s, reaches its maximum power at 13 m/s and automatically shuts down if the hubheight wind speed is higher than 25 m/s. The drivetrain of the turbine consists of a three-stage gearbox composed of one planetary stage and two parallel stages and a DFIG. During an emergency shutdown, aerodynamic braking only is used to bring the turbine to a standstill. The 2 MW wind turbine specifications used in this paper are summarized in Table A1. The generator power versus wind speed and generator torque versus generator speed characteristics are shown in Figure 3. It must be noted that the generic 2 MW wind turbine model used here is not aimed to be an exact representation of a Vestas V90 wind turbine but serves as a baseline 2 MW wind turbine model that mimics the performance of a Vestas V90-2.0 23 turbine. The coupled numerical model used in this paper comprises a multibody dynamic model of the wind turbine drivetrain developed in SIMPACK, a dynamic model of the DFIG and the associated control systems developed in Simulink ® . Furthermore, these two models are coupled with the wind turbine simulator OpenFAST to offer a high-fidelity numerical model of the coupled electromechanical system. The models are briefed in the following.

| Multibody drivetrain model in SIMPACK
A model of the drivetrain has been developed using the multibody system simulation software SIMPACK. 24 The four-point drivetrain has a threestage gearbox with one planetary stage and two helical stages. The main shaft is supported by two spherical bearings, and the high-speed shaft (HSS) is supported by three bearings as shown in Figure 4. The main bearings are connected directly to the bedplate, whereas all other bearings are connected to the gearbox housing. The downwind end of the high-speed shaft is connected directly to the generator. The structural members of the drivetrain are modelled as rigid bodies. All gears are modelled using the primitive 25: Gear Wheel from the SIMPACK library using the data presented in Table A2. The SIMPACK Force Element 225: Gear Pair is used for a detailed description of all tooth contact between two meshing gear wheels with involute geometry. The 225: Gear Pair element allows multiple tooth meshing, whereby all the individual tooth pairing contacts along the line of action are calculated. The resulting overall transfer forces and torques are calculated by adding the individual forces at each contacting tooth. The 225: Gear Pair element is capable of estimating the time-varying meshing forces between two gear wheels. The shaft(s) flexibility is modelled using the SIMPACK Force Element 43: Bushing Cmp in SIMPACK. In this study, the torsional stiffness of the shafts is used. The bearings are modelled using Force Element 88: Rolling Bearing in SIMPACK with the data presented in Table A3.

| 2MW DFIG
This subsection provides a brief description of the grid-connected DFIG and the associated rotor side and grid side control. The generator is modelled using the Asynchronous Machine SI Units block in Simulink ® . The generator parameters are provided in Table A4. The stator is connected directly to the grid (the transformer is ignored), and the rotor is connected through the back-to-back AC/DC/AC converter. The grid is modelled using a Three-Phase Programmable Voltage Source Simulink ® block, and the mechanical speed Ω m of the shaft is obtained from the SIMPACK model and is assumed to be equal to the high-speed shaft velocity at the generator end. A majority of the blocks used to develop the grid-connected DFIG model are provided by the Simscape™ Electrical™ Specialized Power Systems library. The powergui is an environment block that contains the equivalent Simulink ® circuit that represents the state-space equations of the models in the Simscape Electrical Specialized Power Systems library. 2.2.1 | Vector control of DFIG using an AC/DC/AC converter The rotor side converter (RSC) and the grid side converter (GSC) controllers are modelled in the dq reference frame where the d-axis is aligned with the stator flux space vector. Due to this orientation, at the RSC, direct rotor current control is analogous to stator reactive power control, and quadrature rotor current control is analogous to stator active power control or electromagnetic torque control. At the GSC, direct grid current control is analogous to DC bus voltage control, and quadrature grid current control is analogous to grid reactive current control.

Control of RSC
The rotor side controller has a cascading structure with two control loops. The outer loop controls the stator's active and reactive power, and the inner loop controls the rotor's direct and quadrature currents. As noted previous, the dq-frame separates the two outputs, and hence, the torque/ active power can be controlled independently using the q rotor current and the reactive power can be controlled independently by the d rotor current. In this paper, active and reactive power references are not used, thus eliminating the outer loops. Instead, during normal operation, i dr (direct rotor current) is set to zero, minimizing reactive current, and indirect speed control method is used to set the reference electromagnetic torque based on the mechanical rotor speed. The reference and the measured rotor currents are then fed to two independent PI (proportionalintegral) controllers to determine the reference rotor voltage. Finally, the reference rotor voltage is sent to the PWM Generator (2-Level) Simulink ® block to generate switching signals for a two-level voltage source converter (VSC) modelled in Simulink ® using an Universal Bridge block. The control architecture is shown in Figure 5B.

Control of GSC
The GSC controller is designed to control power flow through the rotor to the grid and the DC bus voltage of the back-to-back converter. The GSC controller also has a cascading structure similar to the RSC controller. Again, the dq-frame separates the control of the DC bus voltage and reactive power delivered to the grid. The DC bus voltage and the reactive power delivered at the grid can be controlled independently using the direct and quadrature grid currents, respectively. The DC bus voltage controller, typically a PI controller, is used to determine the reference grid direct current. The reactive power delivered at the grid can be set to zero, therefore rendering the reference quadrature grid current zero. However, the reactive grid power can be set to a reference value based on grid code requirements. The obtained reference signals and measured signals of the grid direct and quadrature currents are sent to two independent PI controllers to obtain the reference filter voltage. Similar to the RSC, the reference voltage signal is sent to a PWM Generator (2-Level) Simulink ® block to generate switching commands for a two-level VSC. The control architecture is shown in Figure 5C.

| Performance during severe grid voltage dips
When a grid voltage dip is seen directly by the stator, the rotor voltage should simultaneously and significantly increase to prevent high rotor currents. However, due to the dimensioning of the converter, it can only provide the rotor with voltages of approximately one third of the stator voltage. Due to the slow evolution of stator flux and the rotor voltage limitation, the DFIG is unable to maintain rotor currents below the safe limits without losing control. 25 Crowbar protection is activated to accelerate flux evolution while simultaneously recovering converter control as quickly as possible to solve these problems imposed by the voltage dips.
As demanded by grid codes, to provide low voltage ride through (LVRT) capabilities, the wind turbine must remain connected during the voltage dip while providing reactive power through the stator. The step undertaken during a severe voltage dip in this paper is as follows: 1. Initially, the DFIG operates at a speed determined by inflow wind speed.
2. When the voltage dip occurs, it is detected by a rise in rotor current. However, this detection takes a few milliseconds (typically 0.5-5 ms), and the system cannot guarantee control during this period.
3. On detecting the voltage dip, the crowbar is activated to demagnetize the machine. While the crowbar is open, the converter is inhibited to protect it from overcurrent. The crowbar activation duration depends on the machine's design and is a compromise between safety and fulfilment of grid codes. Typically, the crowbar is activated for 50-200 ms. 26 In this paper, the crowbar is activated for 100 ms.
4. Once the flux has decayed, the crowbar is deactivated, and control is restored to the rotor converter. For the remaining duration of the fault, the entire rotor current is used to provide reactive power by setting d-current to the rated rotor current. 5. Once the voltage is recovered, normal operation is resumed.

| Coupling the drivetrain and generator models with OpenFAST
As described in the previous sections, the wind turbine is modelled in the open-source software OpenFAST, 27 the drivetrain is modelled in SIMPACK, 24 and the grid-connected DFIG is modelled in Simulink ® . Therefore, the three models must be externally coupled. In this paper, the three models are coupled in Simulink ® . OpenFAST offers an interface to Simulink ® implemented as a Level-2 S-Function called FAST S-Function. The interface is written in C, and it calls a DLL of OpenFAST routines, which are written in FORTRAN. On the other hand, SIMPACK provides a co-simulation interface between SIMPACK and MATLAB ® Simulink ® called SIMAT. Using SIMAT, the two co-simulation partners exchange their results with a given time step using the TCP/IP protocol. This allows the user to take direct advantage of the complex mechanical systems modelled in SIMPACK and the control systems designed in Simulink ® . The coupling mechanism adopted in this paper is motivated by the results presented in Girsang et al. 28 In this mechanism, the drivetrain torsional model in OpenFAST is turned off, and the gearbox ratio is set to 1. The resulting opposing torque is measured at the low-speed shaft and used in place of the opposing generator torque. The SIMPACK model, at the rotor end, accepts the three-dimensional rotor torques/moments and transverse forces. The force transfer is depicted graphically in Figure 5A. As mentioned in the previous section, the 2 MW DFIG model is developed in Simulink ® and solved in discrete time using the powergui environment block. Zeroth-order hold is used in Simulink ® to connect the continuous and discrete-time systems. The coupled system in Simulink ® and the associated control systems are shown in Figure 5.

| MITIGATION OF TTRS
This section summarizes the three TTR mitigation methods investigated in this paper. In the first two subsections, the TMD and the asymmetric torque limiter are described. Next, a novel open-loop control strategy for the high-speed shaft mechanical break is presented.

| TMD
A TMD is installed in front of the generator and behind the high-speed shaft coupling of the wind turbine drivetrain as this presents the most convenient location on the generator side of the drivetrain. To design the torsional TMD, a simplified 2-degrees of freedom (DOF) model instead of the SIMPACK multibody model presented in Section 2.1 is used. Further, the generator and the torsional TMD are represented on the main shaft using the effective inertia and stiffness given in Equation A3. The schematic of the 2-DOF model coupled with the TMD is presented in Figure 6 resulting in a 3-DOF system where the degrees of freedom are q ¼ ½q rot , q gen , q d represented on the main shaft of the drivetrain. All high-speed shaft parameters on the main shaft of the drivetrain are represented with the superscript eff .
For a chosen effective rotation inertia of the drivetrain, J eff TMD (or mass ratio of the TMD μ) the optimal effective stiffness k eff TMD (or tuning ratio β) and damping ratio ζ d are estimated using the classical Den Hartog formula 29 as follows.
The applicability of Den Hartog's formula in Equation (1) is described in Appendix A. The relationship between the inertia J TMD and the spring stiffness k TMD of the TMD on the high-speed shaft can also be obtained from Equation (A3). Typically, the TMD is tuned to the dominant eigenfrequency of the primary structure. The wind turbine drivetrain sketched in Figure 6 if modelled with a free-free boundary condition has an eigenfrequency given by Equation (A3). However, the drivetrain does not operate under a precise free-free boundary condition. Therefore, the dominant eigenfrequency is identified from numerical simulation as 1.53 Hz and is used to tune the TMD.

| Asymmetric torque limiter
The asymmetric torque limiter allows torque in one direction (locked clutch) while allowing free relative motion in the opposite direction (free clutch). With the asymmetric torque limiter connected between the high-speed shaft coupling and the generator shaft, the HSS coupling and the generator shaft can rotate in two directions. But the transmission of torque to the HSS coupling is limited only to one direction. This paper has used the SIMPACK force element FE 19 One-Way Clutch Cmp to model such an ideal asymmetric torque limiter. This force element is used to transmit torque in one direction (locked clutch) while allowing free relative motion in the opposite direction (free clutch). For example, an input shaft can rotate in two directions, but the transmission of torque to the output shaft is possible only in one direction. The transmission of torque is realized in only one direction of relative velocity between the input and the output shaft, depending on how the user sets the direction. The transmission starts or ends each time the direction of the relative velocity changes. In this paper, the FE 19 One-Way Clutch Cmp is locked when the joint velocity state is positive and unlocked (free) when the joint velocity state is negative. When the clutch is locked, it acts as a linear spring and damper to transmit the torque. Algorithmically, it can be expressed as follows: F I G U R E 6 Schematic diagram of the drivetrain coupled with a torsional tuned mass damper (TMD).
if q c > δ then where q c is the relative rotation of the joint, k c is the rotational stiffness and c c is the rotational damping coefficient of the locked clutch. δ is the tolerance (a small negative quantity) and τ is the torque transmitted by the one-way clutch. To represent a locked clutch, the stiffness and damping must be chosen sufficiently high so as to not alter the drivetrain's natural frequencies. Parallelly, care must be taken to avoid numerical issues arising from very high stiffness. In this paper, the stiffness k c ¼ 200 Â k HSS and damping c c ¼ 200 Â c HSS are assumed.

| High-speed shaft brake
The fundamental reason for load-induced TTRs is the sudden change or absence of the generator torque at the generator end of the drivetrain.
Therefore, it can be intuitively hypothesized that the fluctuations in the generator end of the drivetrain can be controlled actuation of the highspeed shaft brake which is mounted directly on the high-speed shaft. Based on this idea, an open-loop control strategy for the high-speed shaft brake is proposed in this paper with the aim to mitigate TTRs. The actuator of the friction disk brakes is modelled by a first-order system [30][31][32] HðsÞ where ω 0 is the bandwidth of the actuator. Literature 33 also suggests an actuator bandwidth of ω 0 ¼ 72 rad/s for brake with a torque rating similar to the one assumed in this paper. In this paper, first, an actuator bandwidth of 72 rad/s is assumed. Then, the effect of slower actuators on the performance of the disc brake is investigated by decreasing the bandwidth in Section 4.3.3.
Furthermore, the high-speed shaft brake torque capacity must be sufficiently large to deliver the torque required to mitigate the TTRs.
According to DNVGL-ST-0437 34 and IEC 61400-1, 35 the most unfavourable load (maximum or minimum) for the mechanical brake can be obtained from DLC (Design Load Case) 8.1. The design torque for the high-speed shaft brake is obtained as where γ f ¼ 1:5 is the partial safety factor for loads, γ m ¼ 1:2 is the partial safety factor for materials and γ n ¼ 1:3 and partial safety factor for consequences of failure. T l is the aerodynamic moment obtained from the most unfavourable conditions corresponding to DLC 8.1. For the generic 2 MW wind turbine, the worst-case aerodynamic moment on the HSS is obtained as T l ¼ 4:5 kNm. Hence, the design braking torque is obtained as 10.5 kNm. The design braking torque is close to the rated generator torque of the turbine and is sufficient to mitigate TTRs as shown in the following sections. Furthermore, it can be noted that industrial disk brakes easily deliver these torque ratings. 36,37

| RESULTS
In this subsection, the results are presented to demonstrate the capabilities of the three mitigation approaches described above. The section is

| Simulation results for the TMD
The TMD is installed as described in Section 3.1 and tuned to the fundamental frequency of the drivetrain. The fundamental frequency of the drivetrain is obtained from numerical simulations. The inertia of the TMD is assumed to be 10% of the inertia of the generator rotor. The optimum linear stiffness and damping are estimated as per Equation (1).
The results are presented in Figure 7. In Figure 7, a 90% symmetric voltage dip is simulated at 10 s using the parameters presented in Table 1. It can be observed in Figure 7 that the torsional vibration characteristic of the drivetrain is improved by the installation of the TMD. The oscillations in the high-speed shaft torque and the radial bearing force initiated by the grid fault are mitigated to an appreciable extent by the TMD. However, it can be observed in Figure 7D that the BLRs are not mitigated by the TMD. Therefore, it can be concluded that the TMD improves the torsional characteristics of the drivetrain; however, it fails to mitigate the BLRs and the associated risk of slip including surface damage.
T A B L E 1 Symmetrical voltage drop events.

| Simulation results for the asymmetric torque limiter
In this subsection, the performance of an asymmetric torque limiter is demonstrated. As described in Section 3.2, the results are presented in Figure 8, and it can be observed that the asymmetric torque limiter prevents the high-speed shaft torque from reversing its sign. In doing so, the asymmetric torque limiter improves the radial bearing loading characteristics in Figure 8C, but it is unable to prevent BLRs as shown in Figure 8D.
Therefore, similar to the TMD, it can be concluded that while the asymmetric torque limiter can improve the torsional characteristics of the drivetrain, it fails to mitigate the BLRs and the associated risk of slip including surface damage.

| Simulation results for the high-speed shaft brake actuation
The novel proposal of active high-speed shaft brake actuation to mitigate TTRs is demonstrated in this subsection. The fundamental idea is to deploy the pre-existing mechanical brake during a transient event for a short duration to prevent TTRs. To demonstrate the capabilities of this method, both load cases are considered in the following including the symmetric voltage dip and emergency shutdown events.
F I G U R E 8 (A-D) High-speed shaft bearing A response at a wind speed of 12m/s-with and without asymmetric torque limiter. HSS, highspeed shaft.

| Symmetric voltage dip
The open-loop control for the mechanical brake has three fundamental parameters: (a) the brake torque magnitude, (b) the brake duration and (c) the bandwidth of the torque actuator. In this subsection, first, the effect of the brake torque magnitude and the brake duration is investigated.
Using the slip-risk duration metric introduced in Section 1, the risk of damage associated with an event can be quantified. Graphically, the slip-risk duration can be represented as the summation of the shaded areas in Figure 9. Note the difference in the time scale in Figure 9A,B. It can be observed that the slip-risk duration during a grid fault event at low wind speeds is much higher than the same event at a higher wind speed, and the transient response of the bearing is very different. It can also be noted that in these two events, the mechanical HSS brake is unable to mitigate the TTRs.
Next, the effect of the brake torque magnitude and the brake duration on the slip-risk duration is evaluated through a sensitivity analysis and is presented in Figure 10. Figure 10 shows the contour plots of the slip-risk duration. In the contour plot, the third parameter is held at the baseline value shown in the title of the plot. The important results obtained from the sensitivity study are enumerated in the following.
First, some high-level commentary is made as follows: 1. The slip-risk duration generally reduces with increasing wind speeds/rotor torque, brake torque magnitude and braking duration. We consider that for a slip-risk duration below 50 ms, the slip risk is mitigated for all practical purposes.
2. Considering the entire domain of operation, the results show that the slip risk can be eliminated by applying the HSS brake with a magnitude of 40%-50% of the rated generator torque for a duration of > 1 s.
Next, some finer observations are made as follows: 1. In Figure 10, the first contour plot shows the contours of the slip-risk duration with respect to HSS torque and brake torque (in terms of percentage of rated generated torque). Generally, the slip-risk duration decreases with increasing HSS torque and brake torque. However, a valley can be observed that shows that the slip-risk duration is lower at the braking torque of 30% compared with 15% or 45%. These three points are marked on the plot with diamond markers. To elaborate on these three cases, the time histories of these events are plotted in Figure 11. It can be observed that the dynamic characteristics of the radial bearing load at a brake torque of 30% are better compared with 15% or 45%. Figure 10, the third plot shows a valley where the slip-risk duration is lower at a brake duration of 0.55 s compared with 0.25 s or 0.85 s.

In
These three points are marked on the plot with diamond markers. To elaborate on these three cases, the time histories of these events are plotted in Figure 12. Here again, the dynamic characteristics of the bearing load at a brake duration of 0.55 s are better compared with 0.25 s or 0.85 s.
These observations elucidate two important ideas: 1. The brake torque magnitude and brake duration are strongly coupled to the fault in terms of the voltage dip level, the recovery speed, the duration of the fault and so on. Therefore, for each event, there exists an 'optimum' that can mitigate the TTRs with minimum effort.
F I G U R E 9 (A, B) Shaded area showing the slip-risk duration for different wind speeds for a brake torque of 45% and a brake duration of 250 ms (note the difference in x-axis scale in the two figures). HSS, high-speed shaft.
2. This 'optimum' brake torque and brake duration is dependent on the fault characteristics, and each fault type requires separate consideration.
One way of approaching this problem is with closed-loop control architecture. But, in this paper, for the purposes of proof-of-concept and ease of construction, an open-loop controller is adopted. In the open-loop control architecture, the brake torque magnitude and brake duration are selected to mitigate all cases of grid faults.
The results show that drivetrain (bearing) dynamics and the associated slip-risk duration are heavily coupled to the transience created by braking parameters. The analyses show that the slip risk is significantly reduced if the right parameters (in terms of brake torque magnitude and brake duration) are selected to land in the valleys of the contour plots. However, not only is finding these parameters difficult but they are also extremely sensitive to the dynamics of the drivetrain and the wind turbine. Therefore, the more intuitive and conservative design suggests selecting the braking parameters such as the slip-risk duration is eliminated for all operating conditions. Figure 10 shows that slip risk can be eliminated by applying the HSS brake with a magnitude of 40%-50% of the rated generator torque for a duration of > 1 s.
It can be observed here that the required brake duration is closely connected to the duration of the fault. Grid codes suggest that the turbine should resume operation when the fault is recovered to 90% of the prefault level. With that in regard, further investigation has been carried out, and it was found that the TTRs can be mitigated by ceasing the braking action when the fault is recovered to 90% of the prefault event (results omitted for brevity). Therefore, it is recommended in this paper, that for symmetric voltage dips, the mechanical brake be deployed when the rotor crowbar is activated using the same trigger. The braking magnitude must be 50% of the rated generator torque. The braking is stopped when the fault is recovered to 90% of the prefault level when the turbine is required to resume normal operation.

| Emergency shutdown
In this subsection, the mechanical HSS brake is used to mitigate TTRs during emergency shutdown events. During emergency shutdown events, the brake is deployed at the same time when the emergency shutdown is initiated and the braking is stopped when the high-speed shaft speed is lower than 50 rpm. The magnitude of the braking torque is determined by a sensitivity analysis. Figure 13 shows that a braking torque of 80% of the rated generator torque is required to mitigate TTRs at a wind speed of 26 m/s. It can also be noted here that it was found that a braking torque of 60% was required at a wind speed of 12 m/s to mitigate the slip risk. Therefore, for a conservative design, a braking torque magnitude of 80% of the rated generator torque is recommended in this paper for all emergency shutdown events. It can be noted here that 80% of the rated generator torque amounts to 9.6 kNm which is lower than the design braking torque of the mechanical brake estimated in Section 3.3.

| High-speed shaft brake actuator bandwidth and dead time
The performance of the high-speed shaft mechanical brake depends on the actuator dynamics. The pneumatic actuator of the mechanical brake can be approximately modelled by a first-order system as described in Section 3.3. In a first-order system, the bandwidth and the dead time dictate the response of the actuator to the control demand.
The effect of the actuator bandwidth and the dead time on the performance of the mechanical brake are investigated and demonstrated in Figures 14 and 15, respectively. Figure 14 shows that the actuator offers significant mitigation capabilities with bandwidths as low as 18 rad/s which is significantly lower than the generally accepted actuator bandwidths for brake of similar torque rating. 33 The performance starts to deteriorate significantly at lower bandwidths of 9 rad/s and below. Figure 15 shows that the performance of the brake deteriorates significantly when the initial dead time is greater than or equal to 250 ms.
However, up to 100 ms the brake offers excellent TTRs mitigation capabilities.

| Comparison of TTR mitigation strategies
In this subsection, the mitigation strategies investigated in this paper are compared. For qualitative comparison purposes, the mechanical damper obtained from this study are compared against Figures 4 and 5 in Eatherton et al. 15 To compare the different devices, three parameters are chosen as follows: • Peak-to-peak HSS torque-the maximum peak-to-peak amplitude after the emergency shutdown has been initiated.
• Maximum negative HSS torque excursion-maximum negative torque recorded in the high-speed shaft after the emergency shutdown has been initiated.
F I G U R E 1 6 (A, B) Comparison of mitigation methods-emergency shutdown. HSS, high-speed shaft; TMD, tuned mass damper.
T A B L E 2 Ratio of controlled response to the uncontrolled/baseline response-emergency shutdown. F I G U R E 1 7 Comparison of mitigation methods-symmetrical voltage dip. HSS, high-speed shaft.
• Slip-risk duration-the metric proposed in this paper that estimates the time spent by the bearings in high slip risk. This metric cannot/has not been evaluated for the RTD proposed in Eatherton et al. 15 The results are compared against the uncontrolled case and graphically presented in Figure 16 and quantitatively (in terms of the ratio to the uncontrolled case) in Table 2. The results show that while the TMD and the asymmetric torque limiter are capable of reducing peak-to-peak HSS torque amplitude and the negative HSS torque excursion, they are unable to reduce the slip-risk duration. In fact, the asymmetric torque limiter seems to increase the slip-risk duration thus deteriorating the bearing loading characteristics. The RTD proposed by Eatherton et al 15 reduces the peak-to-peak oscillation amplitude and the maximum negative torque excursion. However, its effect on the slip-risk duration cannot be determined. Finally, the proposed brake control strategy is capable of fully mitigating the slip-risk duration while simultaneously reducing the peak-topeak oscillation amplitude and the maximum negative torque excursion.
To conclude, a similar comparison is carried out for the symmetrical voltage drop event in Figure 17. The results (in terms of the ratio to the uncontrolled case) are provided in Table 3. In this case, the RTD proposed in Eatherton et al 15 is eliminated from the comparison as the model is not available. Again, it can be observed that the TMD and the asymmetric torque limited can improve the HSS torque characteristics in terms of peak-to-peak amplitude and maximum negative excursion, but they are unable to mitigate the slip risk. On the other hand, the proposed brake control is capable of mitigating the slip risk in addition to the peak-to-peak amplitude and the maximum negative incursion.

| CONCLUSIONS
This paper investigated three methods of mitigating TTRs in an indirect drive DFIG wind turbine drivetrain. In this regard, first, two existing devices in the industry, namely, the TMD and the asymmetric torque limiter, were investigated. To investigate the performance of these methods, a high-fidelity model is developed by coupling together a wind turbine model in OpenFAST, a drivetrain model in SIMPACK and a grid-connected DIFG model in Simulink. The developed model allows the investigation of the coupled electromechanical dynamics of the wind turbine. Within the framework of the developed numerical models, it was shown that while these devices are capable of improving the torsional characteristics of the drivetrain in terms of peak-to-peak amplitude and maximum negative torque excursion in the high-speed shaft, they are unable to mitigate the slip risk associated to the transient events of symmetric voltage dips and emergency shutdowns investigated in this paper. To successfully mitigate the slip risk associated with TTRs, a novel approach of using the pre-existing high-speed shaft mechanical brake in an open-loop architecture has been proposed. The results presented in this paper show that the proposed brake control is capable of mitigating the slip risk associated with TTRs in the drivetrain. The paper has also shown that the mechanical brake is capable of mitigating the slip risk with the mechanical limitations in terms of torque rating, actuator bandwidth and initial dead time in place. For the two transient events considered in this paper, the following recommendations are offered: • Symmetric voltage drops: The mechanical brake is deployed together with the electrical crowbar that protects the rotor against overcurrent using the same electronic trigger. The brake is deployed to achieve a torque of 50% of the rated generator torque. It is turned off when the voltage recovers to 90% of its prefault level.
• Emergency shutdown events: The mechanical brake is deployed when the emergency shutdown is initiated using the same trigger. The brake is deployed to achieve a torque of 80% of the rated generator torque. It is turned off when the generator speed is below 50 rpm.
The authors want to highlight that further research is required to identify other types of events (grid, converter and generator faults) that may lead to TTRs and increase the risk of slip-induced surface damage in gearbox bearings.
List of symbols used in this paper is as follows:

APP E NDIX A: DERIVATION OF A SIMPLIFIED DRIVETRAIN MODEL COUPLED WITH A TORSIONAL TMD
For the drivetrain in Figure 6, it is assumed that the rotor is rotating at a constant speed Ω and the generator rotation can be obtained as q rot ¼ Ωt where q r is the relative rotation between the rotor and the generator due to the elasticity of the shaft. This assumption reduces the degrees of freedom from q ¼ ½q rot , q gen , q d to q ¼ ½q r , q d . The equations of motion of this resulting 2-DOF system can be derived using the Euler-Lagrangian formalism as where J eff The equations of motion are then normalized by J eff gen , and the Rayleigh damping term is added to the equations of motion.