Investigation on the impact of electrical faults on the loads and exposures of wind turbine gears

For the design of a wind turbine, it is necessary that the design process takes into account the stresses of real operation to a high degree of detail so that targeted dimensioning can be carried out. Depending on its design, the drivetrain of a wind turbine includes a gearbox that connects the rotor to the generator. During operation of a wind turbine, transient load conditions can occur due to loopback from the power grid and faults in the frequency converter. The influence of the resulting stress and possible damage to the gears used in the gearbox is unclear in the design phase. While the stresses on the gears can often be simulated with a high degree of accuracy for constant operating conditions and can thus be integrated into the drivetrain design, this is not the state of the art for dynamic load conditions. The objective of this report is a method for considering dynamic loading events in the design of the cylindrical gear stage used in wind turbine gearboxes using a coupled multi-body simulation and a finite element based tooth contact analysis. Afterwards the method is used to quantify the stress on the tooth flank and tooth root due to special electrical events such as short circuits between the frequency converter and generator or power grid faults for various converter designs. The simulation analyses show that different converter concepts have different effects on the resulting gear load during electrical faults, but are not significantly decisive for the accumulated damage due to elastic material behavior between generator and gear.


Introduction and motivation
The importance of wind energy in the energy supply of the future will increase in coming years while costs for wind turbines (WT) steadily decline [1]. Operational costs of WT can be reduced by an increase in the reliability. In order to improve the WT reliability (neither over nore under-dimensioning), all load scenarios during the lifetime, e.g. electrical faults, need to be considered in the design process.
Different studies show that the grid transmission lines of wind turbines have a significant failure rate of faults per 100 km per year [2,3], and according to the survey of SHENG the annual failure rate of the electrical system e.g. for standard variable-speed wind turbines amounts to approximately fr = 1.1 events per year [4]. Dependent on the WT concept, grid faults can lead to dynamic generator torque excitations with amplitudes significantly higher than the rated torque [5]. Due to the high levels of wind power penetration on the continent, grid code requirements in different European countries increasingly demand that wind farms, taking into account the relevant consequences of grid faults, withstand grid disturbances [6,7].
Faults in the power electronics [8], e.g. the converter, can also induce significant torque excitations [9,10]. To quantify the loads due to grid faults, fault ride through (FRT) tests can be performed in the field or on test benches. Furthermore, validated multi-body simulation (MBS) models can be used to simulate the loads resulting from grid faults and short circuit converter faults that often cannot be tested on the test bench due to the high risk of component damage. With the help of the validated simulation models, the stress due to these special events on many drive train components can be evaluated efficiently without the need of costly measurement devices. A simulation chain for determining the risk of dynamic driven stresses and exposures to a cylindrical gear stage of a WT's gearbox during transient electrical faults is not state of the art.

Objective and approach
Resulting from the deficit mentioned, the objective is a method to evaluate the stresses and exposures to a gear stage during highly dynamic load cases as they appear during power grid faults and frequency converter faults. To quantify the risk of damage to the investigated gear stage, the induced kinematics, elastic deflections and drive train loads have to be analyzed and compared to established damage criterions. For the determination of these, a multibody simulation (MBS) model with two different grid connection concepts is used that is coupled to a validated finiteelement-based tooth contact analysis (FE-based TCA).
First, the MBS model is parametrized with the characteristics of the mechanical and electrical components. Furthermore, the control system of the nacelle and the load cases are set up. Second, the load cases are calculated in the MBS whereby the time-dependent courses of torques, forces, deformations and speeds are saved. The critical gear stage due to the overloads is identified. Afterwards, the load and deflection data is used as an input to the FE-based TCA that calculates established load values such as the flank pressure   Fig. 2. Therefore, grid faults directly affect the magnetic field in the stator and result in dynamic load scenarios [5]. A fault ride through scenario corresponding to the current European grid codes is investigated for this concept. The WT has to stay connected to the grid during the fault without shutting off [11].
In the full size converter concept (FSC), the WT is completely decoupled from the grid due to a frequency converter with direct current intermediate circle. Thus, grid faults do not affect this concept significantly. For the FSC WT a power converter fault is investigated. The fault leads to a three-phase short circuit between the generator and the converter, e.g. as result of a permanent conducting state due to a damage in the machine side converter phase module. Detailed descriptions of both the effect of the grid fault for the DFIG WT as well as the converter fault for the FSC WT can be found in a previous publication [12].

Modelling transient loads on gears of a wind turbine gearbox
Quasi-static load conditions in gearboxes and in special in gears can be modelled with a high degree of accuracy regarding the flank pressure, tooth root stresses, noise excitation and efficiency due to FE-based TCA methods. However, these approaches are depending on input values from the surrounding total system such as torques, speeds and deflections due to loads or manufacturing errors. In contrast to a FE-based simulation approach for the tooth contact, an MBS model is able to determine transient load conditions for each component of the investigated drive train by the possibility of modelling the control systems and electrical components applying a time integration. Therefore, the idea of coupling results out of an MBS to a FE-based TCA is combines the benefit of modelling transient situation as well as exact load effects.

Multi-body simulation of a wind turbine nacelle
The MBS model of the research nacelle drive train is connected to analytical models for the control, the generator, the power electronics and the power grid via co-simula-  [13,14]. The MBS model also includes components of the test bench such as the drive, which applies the rotor torque, the coupling elements between drive and nacelle as well as the non-torque load unit which applies the forces and bending moments that act on the nacelle hub, ref. to Fig. 3. The test bench model has been validated in extensive test procedures according to IEC 61400 and a converter fault in idling mode [13,14]. The gearbox of the research nacelle (ref. to Fig. 4) has one planetary stage on the rotor side followed by two helical gear stages with a resulting gear ratio of itotal = 62.775. The gear pairs are modelled using SIMPACK's gear pair force element FE225 including backlash and ideal stiff gear bodies. The bearing characteristics are implemented based on manufacturer data via force elements using one-dimensional profiles for radial and axial direction including nonlinearity and clearance [14]. The housing of the gearbox is modelled to be linear elastic determining its stiffness via a conventional finite-elements analysis that was carried out before. The focus in this paper is on the local exposure of the High Speed Gear Stage (HSS). This gear stage is in focus because the electromagnetic generator torque excitation has the highest influence on the HSS due to the direct coupling of the generator to the HSS pinion shaft. Furthermore, the components on the HSS have the highest failure rate within the gearbox of a WT [15].
The rotor torque of the WT, which is applied via the motor model, sets a rotor torque via a speed control loop until the fault is triggered. As the fault is triggered the rotor torque is simplified in this paper via linear approximation in order to independently investigate the influence of the electrical faults. For the grid fault effect duration of t 100 ms of the grid fault for the DFIG WT, the rotor torque is kept constant. This is in line with the real WT behavior, which typically cannot control the WT blade and therefore the rotor torque in this short timeframe. For the short circuit fault between generator and converter in the SCIG WT a complete shutdown of the WT is assumed so that the controller will pitch out the rotor quickly. Thus, the WT will stall and after around t 300 ms no more rotor torque is applied. The generator torque is applied to the drive train by the electrical substitute model of the generator. The non-torque loads resulting from the wind are disregarded in this paper to focus on the exposures due to electrical faults and to prevent cross influences. The level of abstraction of the modeling was chosen with the intention of representing the real test rig application, so that a comparison of the simulations with measurements can be performed in future work. The aim was to obtain a real deformation behavior and a correct system response to dynamic input variables by a high degree of modeling of all stiffnesses and mass inertias. A reduction of the system to, for example, only one cylindrical gear stage (e.g. HSS), which is common for the investigation of quasi-stationary operating points, is not expedient at this point, since the elasticity of further components between the HSS and the rotor, which forms the largest mass inertia and influences the dynamic stress, would be completely neglected.
For both the DFIG and FSC concepts, the same generator with slight adaptations is used. The parameters of the generator are implemented according to manufacturer's data (ref. to Table 1). The analytic generator model represents the fundamental waves of the electromagnetic force generation. This modelling depth was determined to be sufficient for the investigation of damage relevant loads within the drive train of the WT [13].
The grid model is a parameter model only representing its inductances [13]. Both the PSC and the FSC are modelled according to state-of-the-art guidelines [16]. The MBS model of the research nacelle on the CWD test bench (ref. to Fig. 4) has been set up and validated during a national project at the CWD [9,10,13,14,17].
In addition to former validations, the displacement behavior of the HSS gear stage as a function of the load torque has been investigated on the CWD test rig. For this purpose, the distance changes were measured and evaluated at four positions of the HSS pinion and at three positions of the HSS gear using inductive distance measurement technology. In Fig. 5 center, the measurement results of the sensors are plotted vs. the generator torque. A torque run- Adaption to Generator Adaption to Rotor Gearbox Input up was considered as the test scenario, in which only the rotor's own weight was additionally applied as a non-torque load. In order to infer the resultant skew and tilt of the gear stage from the measured distance values, the bending behavior was predicted analytically for the HSS pinion shaft, as shown on the right of Fig. 5.
The knowledge about the mounting position of the sensors and the ideal bending behavior of the HSS pinion shaft were then used to compare the displacement behavior of the real gearbox on the test rig with the data on angular axis displacement of the HSS from the MBS. In particular, angular axis misalignments in the form of skew and tilt are especially relevant to the load distribution in the gear mesh, as these can cause unfavorable contact on the face borders of the meshing gears. In contrast, a center distance deviation is less relevant for an involute cylindrical gear stage, since this type of gear reacts robustly to this sort of deviation [18].  In contrast to the sensors for the axle position of the HSS gear, which measure the change in the axis angle on the face of the wheel body, this type of sensor attachment could not be made for the HSS pinion. For this reason, a method was developed to convert the measured distance values on the pinion shaft into the axis angles, which is explained in Fig. 6 on the left. When validating the displacement behavior by means of test rig measurements, it must be pointed out that only the load-related component can be considered. Due to a missing reference system in the determination of distance variations in combination with load-free occurring bearing clearances, this is unavoidable.
The rotating HSS pinion shaft exhibits runout deviations at the measuring points due to the manufacturing process, so that the measured values fluctuate per revolution regardless of the load condition. Due to this, implausible outliers are initially removed from the measuring points and replaced by interpolated values. Due to the high sampling rate, this is possible without any information loss. For reasons of data Since the distance sensors of the HSS pinion shaft are measuring distance values on another position of the shaft than the position of the gear is, as in an ideal case, a conversion must be done. The bending lines in Fig. 5 show that otherwise an incorrectly signed inclination of the bending lines is calculated and would be used as the axis misalignment. A multidimensional bending line model is used to calculate the resulting axis skew and tilt for the measured distance values.
To compare the load-induced displacement, a torque runup was performed on the test rig, whose measured load data (speeds, torques) were used as input variables of the MBS to determine the tilt angles beta and gamma. Due to the high degree of dynamics and the system inertia, the torque in the MBS is not assigned to one single angular displacement. There is good agreement of tendency between the MBS and the test rig for the angle gamma, although the load-dependent course of this angle is more pronounced on the test rig. The behavior of the angle beta on the test rig is similarly indifferent to that determined by the MBS. In principle, the real structure appears to be more displaced than the MBS model, which may be due to insufficiently accurate representation of the skewness behavior in the model, for example. However, the load-dependent displacement of the gear stage can be assumed to be valid in good agreement. This approach was already used successfully in previous researches [19]. The FE-based tooth contact analysis uses a surface contact approach in which the contact line position is precalculated load-free. A spring model substituting the contacting tooth flanks is then solved for each rolling position. This obtains results for the forces at each node of the FE grid, which are converted into tooth root stress and HERTZIAN pressure over the flank surface.

Finite element based tooth contact analysis and local damage accumulation
As an input of the TCA, the time variable position of the gear axes as well as the transmitted forces of the gear stage are used. The time related results of the MBS are transferred into discrete angular steps, which include exactly one gear mesh at the HSS each. For every angular step in the range where the power grid fault occurs, one calculation within the tooth contact analysis is carried out. Within the calculation, the time-individual load and gear alignment is taken into account. As a result, the course of tooth flank pressures and tooth root stresses during the power grid fault and a short circuit and can be derived.
Beside the calculation of the load of the gear, the focus is to quantify the damage risk due to the transient event. For this purpose, a posterior method is used in which the tooth flank is divided into discrete partial flank surfaces. Each tooth flank and root is divided into nb = 40 elements in the width direction and np = 14 elements in the height direction (ns = 560 elements in total per flank and root). For the tooth flank fatigue (pitting) and the tooth root fatigue, WOEHLER lines are applied for an induction hardened quenched and tempered steel according to data from SCHLECHT (as per DIN 3990 Parts 2, 3 and 5) [20]. That follows an exemplary used material. Subsequently, a determination of the damage equivalence factor S is carried out according to ISO 6336 part 6 for each of the ns = 560 flank surface and root elements. According to the damage accumulation hypothesis according to PALMGREEN-MINER, failure is to be expected for S = 1. The number of load cases is defined according to the recommendation of ISO 6336 part 6. The time course of torque and displacement from the MBS is analyzed. The simulated nS = 10,000 time steps are sorted into the specified number of nL = 64 load bins and provided with a time fraction according to their frequency occurring in the load case. Subsequently, the determined load cases are calculated in the TCA and their individual damage is calculated in relation to local position according to the mathematical description of the WOEHLER line. In this way, it is possible to evaluate in a dedicated manner which tooth area is exposed to the highest stresses and tends to be at the highest risk of fracture [21,22].
The gear geometry is mapped in the TCA according to its nominal design. In addition to the macro geometry, this also includes micro-geometric corrections of the profile and flanks. Figure 8 shows the essential gear data. The microcorrections applied during the grinding process were defined in a previous project with regard to stress and excitation behavior and are shown in three dimensions as a deviation from an ideal involute geometry [23].

Effects of electrical transient events on the load of gears in wind energy gearboxes
Two electrically-induced transient load events are investigated with respect to the dynamic load magnitude and damage risk of the HSS gears. The first event is a voltage drop of the power grid, which can be caused by the start-up of external high loads. The second event considered is a shortcircuit of the generator windings, which can be caused by internal insulation faults.

Power grid fault
The three phase line to line voltages (UU-V, UV-W, UW-U) for the investigated powergrid fault for the WT with DFIG concept are reduced at measuring time t = 10 s. The voltages decrease linearly to 5% of the nominal value over a period of t = 3 ms. This voltage level is kept for t = 97 ms. Then the fault is cleared and the voltages increase to the nominal value again linearly over t = 3 ms. As a result the generator torque shortly exceeds the rated torque by a factor of around two before it rapidly decreases to zero, ref. to Fig. 9.
The mechanical HSS torque oscillates shortly after the fault is triggered, presumably due to an excited rotational natural frequency. Compared to its nominal value the HSS torque increases by around 19% in maximum. At t = 10.1 s the voltage surges to its nominal value again. As a result the generator torque increases rapidly. It shortly exceeds the rated torque by a factor of around 2.5 before it declines to the rated value again. As a result the speed of rotation of the HSS decreases significantly and the mechanical HSS torque increases with a sharp peak. The control also detects the restored normal grid operation and starts increasing the drive torque as well. Subsequently, the HSS torque undershoots and overshoots the nominal operating value, whereby the oscillation amplitude decreases due to damping effects. At t = 11.5 s the WT got back to normal operating mode [12]. Figure 10 shows the results of the FE-based TCA with respect to the flank and root load of the HSS pinion for the transient course of the power grid fault. The load case was divided into nS = 10,000 time increments, whereby each time step was characterized individually acc. to the variables for torque and gear displacement determined from the MBS. The flank pressure is shown in the center of Fig. 10, with the distribution of the maximum values achieved depending on their position on the tooth flank. The maximum flank pressure of pH,max = 1,330 MPa is found to be slightly decentral on the flank, due to the micro geometric corrections and displacements of the shafts and housing. Compared to the nominal value of the flank pressure, that existed before the grid fault was triggered, the maximum flank pressure that occurs during the grid fault, exceeds the nominal value by about 7%. The microgeometry applied to the tooth flanks of the HSS compensates for system deformations at high torques in such a way that the highest pressures are almost centered on the tooth flank despite load-induced deformation. The plot includes all influences of the real tooth contact such as the ideal microgeometry (target specification in the design) and misalignments from the MBS.
In contrast, Fig. 10   to the torque increase during this load case, the percentage increase of the tooth flank and tooth root load is less significant. This is because, in addition to the force load, other factors also have an influence on the pressure and stress in the TCA. Increasing load leads to an enlargement of the contact zone of the two tooth flanks, so that more contact points are considered in the FE mesh. Accordingly, the relationship between a torque increase and an increase in flank pressure and root stress is not necessarily proportional.

DFIG
In order to determine the stress on the HSS due to the transient power grid fault, the load spectrum corresponding to the time history of the torque for the load case under investigation is first created. To reduce the overall simulation time and in accordance with the normative standard, all nS = 10,000 time steps are divided into nL = 64 load case bins, ref. to Fig. 11 center. It can be noted that the nominal load point with TGen = 26 kNm (load bin N°37) is the most frequent with a relative frequency of occurrence of about F = 5.9%.
From the discretized load cases, an individual damage is calculated on the basis of their amplitude and frequency of occurrence according to their position in the WOEHLER line and the criterion acc. to PALMGREEN-MINER [24]. Based on the material model used here (induction-hardened quenched and tempered steel), it can be seen in Fig. 11, bot-tom right, that the stress at the nominal load point results in the highest individual damage due to its frequency and that the maximum load amplitudes have a minor effect in the evaluated time period. In principle, therefore, the result as to the extent to which a transient special case influences the service life of the gearing depends on the material utilization at the nominal operating point.
In addition, the summed damage of the HSS pinion tooth flank is formed taking into account the location of the stresses. For this purpose, the damage sums are calculated and displayed individually for the divided surface elements in the width and height direction from the frequency of the resulting pressures. The plot shows the accumulated total damage of all teeth in mesh. The distribution of the damage among the individual teeth would require that the rolling position at the onset of the power grid fault is known exactly, since the distribution of the stress among the individual teeth depends on it. In the direct comparison between the max. flank pressure from Fig. 10 to Fig. 11 top right, it is evident that the same flank element does not experience both the highest pressure and accumulated damage. This is due to the frequency of the stress, which is decisive in addition to the amplitude. The reciprocal maximum value of the accumulated damage of the load case under consideration indicates the maximum service life of the gear. For the case of a power grid fault always occurring at the same rolling position, a failure of the flank would occur after approximately NL = (2.5 10 -5 ) -1 single power grid faults.

Short circuit of generator
Another load case considered is a short circuit between the phase windings of the generator. The FSC configuration is modelled in the MBS. This fault replicates the effects of increase immediately after the initiation of the short circuit that induces the highest loads, but the subsequent oscillation amplitude one period later that produces the greatest loads on flank and in root.
For the FSC configuration with the load case of the shortcircuit, the load spectrum was derived in the same way as for the DFIG for the considered time period of t = 9.95 to t= 10.3s, ref. to Fig. 14 below. Compared to the collective for the DFIG power grid fault from Fig. 11, it can be seen that torques above the rated load occur with much lower frequency and instead the torques below the rated load dominate the collective almost uniformly. With regard to the individual damage curves of the tooth flank of the pinion and gear, it can be seen that the curves have the  Fig. 14 center. However, the stresses of this flank element differ by a factor of about 50,000, so that the power grid fault is to be classified as more critical in the period under consideration, with the main share being generated by the nominal load. If only the overload due to the special events should be evaluated, only the share exclusively their exposures E in the load spectrum (occurrence frequency of bins) must be considered. These are E = 0.3207 for the DFIG power grid fault and E = 0.1011 for the FSC short circuit with respect to the total stress during the load cases considered.

Summary
The objective of the paper is the development of a method to evaluate the stresses and exposures to a gear stage during highly dynamic load cases resulting from transient electrical faults. A simulation chain determining the risk of dynamic driven stresses from transient events resulting in transient load exposures to a cylindrical gear stage of a WT's gearbox is not state of the art.
An established damage criterion is applied on tooth root and flank loads to quantify the risk of damage to gear stage of a WT. The time-dependent loads resulting from two different power grid connection concepts (DFIG and FSC) of the WT are coupled with a validated FE-based TCA. The effects of the grid fault for a DFIG WT as well as the short circuit for the FSC WT are investigated regarding the gear load and the damage.
For the power grid fault of DFIG and the short circuit of FSC, very similar maximum loads are achieved for maximum flank pressure and load on the tooth root of the HSS pinion. The maximum flank pressure and tooth root stress exceed the nominal value by about 7% and 11% respectively. It can be seen that it is not the direct load increase immediately after the initiation of the short circuit, that induces the highest loads, but the subsequent oscillation amplitude one period later that produces the greatest loads on flank and in root.
For the investigated WT, no significant damage accumulation was detected for one single occurrence of the load case. However, this statement cannot be applied to all types of gearboxes in wind turbines, since the elastic transfer path between the generator and the gearing as well as the rotational natural frequencies of the system play a decisive role. The frequency and magnitude of the failures can vary significantly which could have an influence on the results [1][2][3]. Although the accumulated damage of the investigated load cases is small compared to the loading at nominal operation, even a small overload could lead to a crack due to material inhomogeneities in the microstructure, so that crack growth can subsequently occur at lower loads which, in principle, should be in the range of duration fatigue strength. As a result, damage to the HSS cannot be completely ruled out by the load cases presented. Furthermore, the overloads can result in other damage, such as smearing of the rolling bearing elements or heat scuffing, which must be considered in detail.

Outlook
The developed method to simulate transient load scenarios using a load bin classification shows to be versatile, enabling a wide variety of time-dependent load cases to be evaluated regarding the load and exposures of gears, being useful not only for electrical failures in WTs. Also for the study of even more complex cases in which transient overloads may occur, as in situations of cross influence between WT in large wind farms for example, the method is able to figure out the resulting danger of damage to the gearbox [26]. Furthermore, the simulation chain could be expanded with a dedicated weakest link model of the material structure in order to determine the damage risk for inhomogeneous structures. For the validation of the simulated results, the performance of test bench investigations is aimed to obtain a validation of the findings with regard to the dynamic overloads occurring in special electrical fault cases.