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Gearbox and Drivetrain Models to Study Dynamic Effects of Modern Wind Turbines Irving P. Girsang, Student Member, IEEE, Jaspreet S. Dhupia, Member, IEEE, Eduard Muljadi, Fellow, IEEE, Mohit Singh, Member, IEEE, and Lucy Y. Pao, Fellow, IEEE
Abstract—Wind turbine drivetrains consist of components that directly convert kinetic energy from the wind to electrical energy. Therefore, guaranteeing robust and reliable drivetrain designs is important to prevent turbine downtime. Current drivetrain models often lack the ability to model both the impacts of electrical transients as well as wind turbulence and shear in one package. In this paper, the capability of the FAST wind turbine computer-aided-engineering tool, developed by the National Renewable Energy Laboratory, is enhanced through the integration of a dynamic model of the drivetrain. The dynamic drivetrain model is built using Simscape in the MATLAB/Simulink environment and incorporates detailed electrical generator models. This model can be used to evaluate internal drivetrain loads due to excitations from both the wind and generator. Index Terms—Gears, mechanical power transmission, resonance, variable-speed drives, vibration, wind energy.
Jeff JX
M N Nj Qaero Qem Qopp Rrot Vw
Effective inertia of the generator and the gearbox with respect to the low-speed side of the gearbox. Inertia of the drivetrain components, X ∈ {turbine rotor (rot), planet gears and the carrier (P C), carrier only (C), sun gear (S), generator (gen), planet gears (Pm ), m = 1, . . . , M , and parallel gear components (Gi ), i = 1, 2, 3, 4}. Number of planet gears. Overall drivetrain gear ratio. Gear ratio of each gear stage, j = 1, 2, 3, Nj ≥ 1. Wind aerodynamic torque. Generator electromagnetic torque. Rotor-opposing torque. Turbine rotor radius. Effective wind speed.
N OMENCLATURE αrot β λopt ωrot ceff fn keff kgear kmesh kY
rb
Turbine rotor angular acceleration. Gear helical angle. Optimum tip-speed ratio. Turbine rotor angular speed. Effective drivetrain torsional damping with respect to the low-speed side of the gearbox. Nonzero eigenfrequency of the two-mass model. Effective drivetrain torsional stiffness with respect to the low-speed side of the gearbox. Gear tooth stiffness. Constant gear meshing stiffness. Torsional stiffness of each drivetrain shaft, Y ∈ {lowspeed shaft (LSS), high-speed shaft (HSS), and lth intermediate shaft, l = 1, 2}. Gear base circle radius.
Manuscript received November 6, 2013; revised March 19, 2014; accepted April 14, 2014. Date of publication April 29, 2014; date of current version November 18, 2014. Paper 2013-IDC-868.R1, presented at the 2013 IEEE Energy Conversion Congress and Exposition, Denver, CO, USA, September 16–20, and approved for publication in the IEEE T RANSACTIONS ON I NDUS TRY A PPLICATIONS by the Industrial Drives Committee of the IEEE Industry Applications Society. I. P. Girsang and J. S. Dhupia are with Nanyang Technological University, Singapore 639798 (e-mail:
[email protected];
[email protected]). E. Muljadi and M. Singh are with the National Renewable Energy Laboratory, Golden, CO 80401 USA (e-mail:
[email protected]; mohit.
[email protected]). L. Y. Pao is with the University of Colorado Boulder, Boulder, CO 80309 USA (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2014.2321029
I. I NTRODUCTION
T
HE WIND energy industry has experienced substantial growth in recent decades, and there has been similar growth in the structural size of and output power from wind turbines. The operating conditions of wind turbines are largely determined by structural loadings such as wind turbulence and, in offshore wind turbines, sea wave excitations. Aeroelastic computer-aided engineering (CAE) tools such as FAST [1], Bladed [2], and HAWC2 [3] have been developed to model and simulate the dynamics of wind turbines in response to different wind fields and controllers. These tools simulate the most relevant environmental conditions and output time series of turbine operational load variations. Because the wind turbine drivetrain consists of components that directly convert rotational kinetic energy from the wind to electrical energy, ensuring the reliability of drivetrain designs is critical to preventing wind turbine downtime. Because of the steadily increasing size of wind turbines, larger forces and torques bring up the influence of the gearbox and other drivetrain flexibilities in the overall turbine dynamic response [4], [5], often leading to failure in the drivetrain components, particularly the gears [6]–[9]. Failure in drivetrain components is currently listed among the most problematic failures during the operational lifetime of a wind turbine. In particular, gearbox-related failures are responsible for more than 20% of the downtime of wind turbines. Although the expected lifetime of gearboxes is usually advertised as 20 years, in practice, gearboxes usually need to be replaced every 6 to 8 years [10], [11].
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TABLE I M ODEL PARAMETERS OF GRC W IND T URBINE
Further insights into wind turbine drivetrain dynamics will be helpful in understanding the global dynamic response of a wind turbine as well as in designing and preserving its internal drivetrain components. Thus far, however, in most of the aforementioned CAE tools, the drivetrain model is reduced to a few (mostly two) degrees of freedom, resulting in restricted detail in describing its complex dynamic behavior. Although researchers have developed dynamic models for wind turbine drivetrains with various levels of fidelity [12]–[21], these studies do not provide direct insights on the dynamic interactions between the drivetrain and other components of the entire wind turbine. Recent studies in [20] and [21] take a decoupled approach in which the global turbine response was first simulated using an aeroelastic CAE tool (i.e., HAWC2). After the simulation, the resulting loads and motion trajectories of the rotor as well as the nacelle were used as inputs to a high-fidelity model of the drivetrain to simulate its internal dynamic behavior. Thus, this approach fails to capture the influence of the drivetrain dynamics onto the overall turbine response. This paper aims to investigate the dynamic response of a wind turbine drivetrain by enhancing the capability of FAST through the integration of a dynamic model of the drivetrain. The drivetrain model is built using Simscape [22]. This tool extends the FAST capability in the MATLAB/Simulink environment, which can help in the drivetrain design as well as the verification of active control strategies to mitigate the drivetrain loads [23], [24]. This paper is organized as follows. Section II highlights the wind turbine properties modeled in this paper. Section III describes the different fidelity levels of the drivetrain model investigated in this paper. Possible resonant frequencies of the drivetrain are computed based on the eigenfrequency analysis in Section IV. The results are verified against eigenfrequencies published in the literature and obtained from experiments. Section V discusses the integration of the developed model into the FAST CAE tool. Finally, concluding remarks are given in Section VI. II. W IND T URBINE D ESCRIPTION The turbine modeled in this paper is based on the Gearbox Research Collaborative (GRC) turbine [25] at the National Renewable Energy Laboratory’s National Wind Technology Center. Table I summarizes the important properties of this turbine. The GRC wind turbine originally employed two fixed-speed wind turbine generators (WTGs). To model variable-speed operation, the WTG is modeled using a doubly fed induction generator (DFIG), shown in Fig. 1. Because the mechanical components of the drivetrain have much slower dynamics than
Fig. 1.
Schematic diagram of a DFIG. TABLE II PARAMETERS OF THE 750-kW DFIG
Fig. 2.
Modular drivetrain configuration of wind turbine.
the power electronics, an average model of the ac/dc/ac converter is used in this paper, in which the power electronic devices are replaced by controlled current sources. The induction generator model is based on a commercial wind turbine of the same rating available in the market. Table II summarizes the key parameters of the generator and the converter, which are used to build the variable-speed WTG model in the Simscape/ SimPowerSystems environment. For wind speeds below 12.5 m/s (the rated wind speed of this turbine), the output power of this WTG is controlled to track the maximum power coefficient (CP max ) while maintaining constant pitch angle at its optimum (−3.5◦ for this turbine). In variable-speed operation, the rotor speed ωrot is proportional to the wind speed Vw ωrot =
λopt Vw Rrot
where λopt is the desired optimum tip-speed ratio.
(1)
GIRSANG et al.: GEARBOX AND DRIVETRAIN MODELS TO STUDY DYNAMIC EFFECTS OF MODERN WIND TURBINES
Fig. 3.
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Five-mass model in SimDriveline to study dynamics of wind turbine drivetrain with fixed-speed induction generator.
two-mass model can be derived from the five-mass model as follows: Jeff = JP C +N12 JS +JG1 +N22 × JG2 +JG3 +N32 (JG4 +Jgen ) Fig. 4.
Two-mass model of wind turbine drivetrain.
(2)
1 1 1 1 1 = + 2 + + . keff kLSS N1 k 1 (N1 N2 )2 k2 (N1 N2 N3 )2 kHSS (3)
III. D RIVETRAIN M ODELING A. Five-Mass Model This paper focuses on a commonly used modular drivetrain configuration in operating turbines [12]. Fig. 2 shows the building blocks of the configuration. In this turbine, the multistage gearbox consists of a planetary (epicyclic) gear set at the lowspeed side followed by two parallel gear sets assembled using two intermediate shafts. Fig. 3 shows the five-mass model developed in the Simscape/ SimDriveline environment. A fixed-speed generator has an electrical torsional stiffness between the air gap magnetic field and the generator rotor. This stiffness behaves as a spring to the inertial reference frame of the drivetrain, which provides a restoring torque to the rest of the drivetrain. Such stiffness arises because of tight allowable speed variation in the fixed-speed turbine. Effects of this stiffness are prominent in the transient response of the generator (e.g., during start-up). Parameters for the five-mass model, including the electrical stiffness, are available in [24]. For a variable-speed generator, this restoring effect does not exist, and the drivetrain model shown in Fig. 3 will have a free boundary condition on the other side of the generator.
B. Two-Mass Model Fig. 4 illustrates the configuration of the two-mass model commonly used to model the drivetrain dynamics in wind turbine aeroelastic CAE tools, such as FAST [1]. Inputs into the model are the five parameters Jrot , keff , ceff , N , and Jeff /N 2 . The generator electrical torsional stiffness is generally not required in CAE tools because this stiffness is inherent to the generator model used for the analysis. Parameters of the
The effective drivetrain torsional damping ceff can be determined experimentally through several braking events [12]. The two-mass model cannot represent the different possible drivetrain configurations because the rest of the drivetrain is represented by one spring and one mass. Furthermore, as later presented in this paper, this model has limitations in providing insights on possible resonant excitations of the drivetrain as well as in analyzing the loads experienced by each of the drivetrain components. C. Pure Torsional Model of Gearbox In the two previously described drivetrain models, the meshing gear is modeled as an ideal static gain for mechanical power (i.e., torque and speed) transmission. In reality, the gear transmission error, which is defined as the difference between the actual and ideal angular positions of the rotating gear caused by the gear elastic deformation, contributes to the dynamics of the pair meshing gears. This phenomenon contributes to the definition of gear meshing stiffness. Several studies have been performed to investigate the dynamics of the gearbox using flexible multibody models built in various software packages [12]–[21]. These studies, however, focus on the internal dynamics of the gearbox, and the developed model packages are not readily compatible with available wind turbine aeroelastic CAE tools. In this paper, a purely torsional model of the gearbox with constant meshing stiffness is built in the Simscape/ SimDriveline environment. The model development and analysis on both planetary and parallel gear stages will be discussed in this section, followed by some remarks on the integration and simulation of this model with the aeroelastic CAE tool of interest (i.e., FAST) in Section V.
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Fig. 5. (a) Parallel gear stage, (b) dynamic model representation, and (c) model representation in Simscape/SimDriveline.
Fig. 7. Torsional model of planetary gear stage with M planet gears in Simscape/SimDriveline.
Fig. 6. Planetary gear set with three planet gears.
1) Parallel Gear Stage: Fig. 5(a) shows a parallel gear set, which is a torque reducer, commonly employed in wind turbine drivetrains. Fig. 5(b) represents its flexible equivalent, in which the meshing stiffness acts along the line of action of the meshing gears. This meshing stiffness kmesh , with respect to the input gear, can be represented as [15] kmesh = kgear (rb1 cos β)2
(4)
where the gear tooth stiffness kgear can be determined according to standards [26], [27]. 2) Planetary Gear Stage: Fig. 6 shows a planetary gear set with three planet gears, which is a similar configuration to the one installed in the GRC turbine. The rotational input is from the carrier of the planetary gear stage, which provides rotational motion through the planet gears, and finally to the sun gear. The ring gear is modeled to have flexible coupling with the fixed gear housing. Flexibility between the meshing planet and ring gears and between the meshing planet and sun gears can be modeled similar to that of a parallel gear set using (4), as shown in Fig. 5(b). Fig. 7 shows a purely torsional model of a planetary gear set built in the Simscape/SimDriveline environment. This model can be adapted for any M equispaced-planet gear set. IV. E IGENFREQUENCY A NALYSIS AND VALIDATIONS Eigenfrequencies of a system can be found either analytically or numerically. Equations of motion of a wind turbine drivetrain
are used to compute the eigenfrequencies in [18] and [24]. However, this approach becomes inconvenient as the order of the dynamic model increases. The developed drivetrain model in SimDriveline allows the usage of MATLAB/Simulink basic packages to numerically estimate the eigenfrequencies. The resulting eigenfrequencies were validated at both component level (i.e., the gearbox) and integrated drivetrain level. The eigenfrequencies of planetary gear sets were validated against those published in the literature, while those of the overall GRC drivetrain were validated against the results from field measurements. A. Eigenfrequencies of Purely Torsional Gearbox Model While some works have reported experimental measurements of gearbox eigenfrequencies [13], [28], it is difficult to justifiably replicate the results as the mechanical properties of the gearboxes are not publicly available. Thus, to validate the developed purely torsional gearbox, eigenfrequencies of the SimDriveline gear set models are compared with those reported in [15]. It is important to note that the gear parameters used in the component-level validation in this section is based on the ones originally used in [29], which are different from the ones implemented in the GRC drivetrain. Eigenfrequencies of this planetary gear set have been evaluated in other published works [15], [30]–[33]. In [15], the analysis was performed on the planetary gear sets with different numbers of planet gears. Estimating the eigenfrequencies using the SimDriveline models was done by first defining the excitation input and the output to be monitored. For analysis and verification, the input for the gearbox model was the torque to the carrier, while the output was the angular velocity of the sun gear as illustrated in Fig. 8. Based on the input–output configuration, MATLAB/ Simulink Control System Toolbox was used to compute the linear state-space representation of the model, the frequency
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Fig. 8.
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Input–output configuration on SimDriveline model for eigenfrequency analysis.
Fig. 9. FRF of three-planet planetary gear stage for the gearbox presented in [15]. TABLE III C OMPARISONS W ITH E IGENFREQUENCIES R EPORTED IN [15]
response function (FRF) of which has been used to indicate the eigenfrequencies. The implementation of this analysis is detailed in [34]. Fig. 9 shows the FRF of the planetary gear set that has three planet gears, where the sharp peaks correspond to the response amplifications at the gearbox eigenfrequencies. The comparisons for different numbers of planet gears show good agreement with the results presented in [15] and are summarized in Table III. B. Eigenfrequencies of Overall Drivetrain Model Ultimately, all necessary component models, including the purely torsional gearbox model discussed earlier, were integrated, and the parameters were set to build the overall GRC
drivetrain model. Eigenfrequency analysis for the drivetrain was performed with the torque to the turbine rotor as the input and the angular position of the generator as the output. The resulting eigenfrequencies are compared herein with the frequency components of several measured drivetrain transient responses [20]. The GRC turbine was equipped with a torque transducer to measure the operating drivetrain loads. Due to the limited sampling rate of 100 Hz, the measured response can only be used to validate the first drivetrain eigenfrequency. The first two transient responses shown in Fig. 10 are attributed to the generator. Hence, the analysis on the overall drivetrain model included the electrical torsional stiffness. Table IV summarizes the drivetrain eigenfrequencies both with and without the electrical torsional stiffness. Fig. 10(a) shows the torque measured on the low-speed shaft (i.e., the rotoropposing torque) during a generator start-up. The dotted box highlights the transient response oscillating at the drivetrain eigenfrequencies, which is revealed to be around 0.78 Hz. Fig. 10(b) shows another transient response when the drivetrain was upshifted to a higher speed generator. It reveals an eigenfrequency of 0.68 Hz. These two frequency readings are very close to the one calculated from the SimDriveline model, which is 0.84 Hz. The second mode of 4.62 Hz was not apparent in the field measurements due to two possible reasons. First, the energy stored in the second torsional mode is much smaller than that stored in the first one. Second, the second mode is attributed to the high-speed shaft. As discussed in the following section, excitations from the high-speed shaft get attenuated at the low-speed shaft side; thus, it may not appear as a dominant component in a measurement that contains noise. The experimental setup did not implement any torque measurements at the high-speed shaft. Fig. 11 shows a transient response, which is not attributed to the generator. In this event, a braking torque is applied mechanically through the disk brake to stop the turbine. The frequency decomposition of the transient rotor-opposing torque reveals a frequency of 1.76 Hz, which is close to an eigenfrequency of 1.83 Hz predicted from the SimDriveline model. These results illustrate the validity of the SimDriveline model to predict the eigenfrequencies of both an independent gearbox and an integrated wind turbine drivetrain. If the overall drivetrain is simplified to a two-mass model, the only nonzero eigenfrequency can be calculated using the parameters of (2) and (3) as 1 1 1 + keff . (5) fn = 2π Jrot Jeff
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Fig. 11. Transient rotor torque from field measurements during braking event.
inside the FAST CAE tool. For simplicity, the flexible modes of the other turbine components modeled inside FAST, such as those of the blades and tower, are not depicted in the schematic diagram in Fig. 12. In FAST, the two-mass drivetrain model is reduced to a single-mass model consisting of solely the rotor and the rigid shaft (as shown in the bottom part of Fig. 12). This is done by deactivating the flexibility of the drivetrain (simulating rigid transmission) and setting the gear ratio and the generator inertia to unity and zero, respectively. The rotor equation of motion can be expressed as Jrot αrot = Qaero − Qopp .
Fig. 10. Transient rotor torque from field measurements during generator transient events: (a) Start-up and (b) upshift. TABLE IV E IGENFREQUENCIES OF GRC D RIVETRAIN W ITH T ORSIONAL G EARBOX M ODEL
The resulting eigenfrequency using the two-mass model for the GRC drivetrain is 2.32 Hz, which is quite different from the first nonzero drivetrain eigenfrequency of 1.83 Hz predicted earlier. This discrepancy can create a significant difference in predicting the loads experienced by the drivetrain. V. M ODEL I NTEGRATION Fig. 12 illustrates the proposed strategy to integrate the described drivetrain models into the two-mass model inherent
(6)
FAST internally calculates the input aerodynamic torque Qaero from the defined wind profile but does not provide this torque as an output. However, as the rotor acceleration αrot is an available FAST output, the aerodynamic torque Qaero can be reconstructed using (6) to be one of the inputs to the external drivetrain model. In this process, the rotor inertia Jrot is assumed constant and replicated in the Simscape drivetrain model. The rotor inertia is connected to the flexible low-speed shaft, the purely torsional gearbox model, the high-speed shaft, and the generator inertia. The electrical machine and grid model will take the generator speed and provide the generator electromagnetic torque to the drivetrain. The rotor-opposing torque Qopp is required as an input to the FAST drivetrain model as well as to calculate the aerodynamic torque Qaero in (6). In SimDriveline, this rotor-opposing torque can be retrieved by utilizing the torque sensor element behind the built rotor body. In general, torque, velocity, and angularposition sensor elements can be placed flexibly within the Simscape drivetrain model to monitor the response of the drivetrain under various load conditions. In the remainder of this section, simulation results showing the effectiveness of the purely torsional gearbox model under different transient load cases are presented. Simulations using the FAST wind turbine CAE tool were conducted in the Simulink environment. In the simulations, all available wind turbine flexible modes in FAST—including that of the blades, tower, and drivetrain—were activated. Zero damping is
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Fig. 12. Proposed schematic of integrating the Simscape drivetrain model into the FAST aeroelastic CAE tool.
Fig. 13. Rotor speed response at wind speed of 7.25 m/s.
defined within the drivetrain model to highlight the transient response of the drivetrain. Aerodynamic damping computed within FAST is the only source of damping that stabilizes the overall drivetrain simulations. The results are compared with those using an undamped two-mass model of the drivetrain inherent in FAST.
Fig. 14. Transient response comparison of the rotor torque.
A. Transient Response Caused by Wind Excitation This simulation was performed under a constant wind speed of 7.25 m/s (below the rated wind speed), and the turbine speed was initialized to be 17.9 r/min. The start of simulation effectively imparts a large step input to the system that can excite all of the drivetrain modes, particularly during the transient period. Fig. 13 shows the turbine rotor speed using the integrated drivetrain model as well as the inherent FAST two-mass model. The rotor speed steadily increases to reach the optimal tip-speed ratio. Both models are in good agreement in the speed response of the turbine. Fig. 14 is the transient response comparison of the rotor torque of the two models. It reveals the excitation of the high eigenfrequency components coming from the highfidelity drivetrain/gearbox model. Fig. 15 highlights the distinction between the two models in predicting the steady-state load response of the drivetrain. It also shows that the integrated model is able to capture dynamic coupling from other parts of the turbine structures. The frequency of 0.4 Hz comes from the tower fore-aft mode, whereas
Fig. 15. Steady-state response comparison of the rotor torque.
the frequency of 0.9 Hz and its harmonics come from the blade passing frequency (3P). The response of the drivetrain model with the purely torsional gearbox is particularly high at two
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Fig. 16. Electromagnetic torque excitations resulting from a voltage drop on the grid.
times the blade passing frequency (i.e., 6P) of 1.8 Hz because it is very close to the estimated first eigenfrequency of 1.83 Hz. Thus, it predicts the amplification of load caused by resonance at the wind speed of 7.25 m/s. On the other hand, the twomass drivetrain model estimates an eigenfrequency of 2.32 Hz, which is at some distance from the harmonics of the blade pass frequency and hence predicts no resonance. B. Transient Response Resulting From Grid Excitation Another transient load can arise due to excitations from the grid events. One example of grid excitation is simulated in this section to predict loads on the gearbox. A voltage drop for 0.15 s, from 100% to 90% and back to 100% of the nominal root mean square voltage, is simulated after the turbine has reached steady state. As shown in Fig. 16, this voltage drop results in harmonic torque excitations onto the drivetrain with frequencies of 50.78 and 56.15 Hz. These frequencies are inherent to the generator characteristic. It is important to note that the frequency component of this torque excitation may cause resonances if the frequency matches any of the drivetrain eigenfrequencies. These resonances cannot be predicted using the standard twomass model because the two-mass model can predict only the lowest eigenfrequency of the drivetrain. Fig. 17 illustrates how this load gets transmitted to each stage of the multistage gearbox. The torque through each shaft, except the low-speed shaft, is shown in both time and frequency domains. The high-speed shaft experiences the largest proportion of high-frequency loads caused by grid excitations compared to other shafts. Therefore, this shaft and the gear set directly connected to it are most prone to failures from fatigue in the event of grid disturbances. Sudden increases in the generator electromagnetic torque excite the two lowest and most dominant modes of the drivetrain (i.e., 1.83 and 154 Hz). This torque also excites the system at its excitation frequencies of 50.78 and 56.15 Hz, but with less dominant effect than at the eigenfrequencies. The transmitted loads are reduced as the shaft gets further from the source of excitation, but the most
Fig. 17. Transmitted loads onto the gears because of grid excitation in (a) time and (b) frequency domains.
dominant drivetrain eigenfrequency of 1.83 Hz prevails during the transient regime. The developed high-fidelity drivetrain model can also be used in designing the drivetrain components to preserve or extend the life of the gearbox. In simulation analysis, this highspeed shaft stiffness was varied to 0.1 and 10 times of the nominal value to investigate its influence on the load transmitted to the gearbox. In practice, the generator and gearbox highspeed shaft are often connected through a mechanical coupler to provide for the misalignment of the shafts. However, this coupler reduces the effective stiffness between the generator and gearbox. Higher stiffness can be achieved by reducing the length of the high-speed shaft. The transmitted loads through the high-speed shaft to the gearbox were evaluated and shown in Fig. 18. A lower stiffness (i.e., using a coupler) appears to transmit more severe loads to the gearbox. This phenomenon is a result of reduction in the second drivetrain eigenfrequency due to the lower stiffness and vice versa, as shown in Fig. 18. The transmitted load gets amplified as the second eigenfrequency is brought down to 92.8 Hz, which is close to the second harmonics of the generator electromagnetic torque frequencies (i.e., resonance).
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R EFERENCES
Fig. 18. Transmitted loads onto the second parallel gear stage under various high-speed shaft stiffness values in (a) time and (b) frequency domains.
VI. C ONCLUSION In this paper, the capability of the FAST CAE tool is enhanced through the integration of a dynamic model of a drivetrain built using Simscape in the MATLAB/Simulink environment. As described in this paper, the implementation of the developed drivetrain model enables the CAE tool to be used in a number of ways. First, the model can be simulated under different wind and grid conditions to yield further insight into the drivetrain dynamics, particularly in terms of predicting possible resonant excitations. Second, the tool can be used to simulate and understand transient loads and their couplings across the drivetrain components. Third, the model can be used to design the various flexible components of the drivetrain such that transmitted loads onto the gearbox can be reduced.
ACKNOWLEDGMENT The authors would like to thank Dr. K. Nguyen and Dr. J. Jonkman for the fruitful discussions about integrating FAST with the external drivetrain model.
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Irving P. Girsang (S’12) received the B.Eng. degree in mechanical engineering from Nanyang Technological University (NTU), Singapore, in 2011. He is currently working toward the Ph.D. degree in the School of Mechanical and Aerospace Engineering and Energy Research Institute at NTU. His study is funded by the National Research Foundation (Clean Energy) Scholarship, administered by the Energy Innovation Programme Office Singapore. He was a Visiting Student Researcher at the National Wind Technology Center, Boulder, CO, USA, from May 2012 to July 2012. His research interest is in modeling and control for load mitigation of wind turbine drivetrain.
Jaspreet S. Dhupia (M’13) received the B.Tech. degree in mechanical engineering from the Indian Institute of Technology-Delhi, Delhi, India, in 2001 and the M.S. and the Ph.D. degrees in mechanical engineering from the University of Michigan, Ann Arbor, MI, USA, in 2004 and 2007, respectively. He has been an Assistant Professor at Nanyang Technological University, Singapore, since 2008, where he is leading a research group engaged in modeling, monitoring, and controls of electromechanical drivetrains. He is an author of more than 30 peer-reviewed articles. Prof. Dhupia has been a member of the American Society of Mechanical Engineers (ASME) since 2006. He served on the organizing committees for the IEEE/ASME International Conference on Advanced Intelligent Mechatronics in 2013 and the American Control Conference in 2014.
Eduard Muljadi (M’82–SM’94–F’10) received the Ph.D. degree in electrical engineering from the University of Wisconsin-Madison, Madison, WI, USA. He was with the California State University at Fresno, Fresno, CA, USA, from 1988 to 1992. In 1992, he joined the National Renewable Energy Laboratory, Golden, CO, USA. He is the holder of two patents on power conversion for renewable energy. His current research interests are in the fields of electric machines, power electronics, and power systems in general with an emphasis on renewable energy applications. Dr. Muljadi is a member of Eta Kappa Nu and Sigma Xi and an Editor of the IEEE T RANSACTIONS ON E NERGY C ONVERSION. He is involved in the activities of the IEEE Industry Application Society (IAS), IEEE Power Electronics Society, and IEEE Power and Energy Society (PES). He is currently a member of various committees of the IAS and a member of the Working Group on Renewable Technologies and the Task Force on Dynamic Performance of Wind Power Generation, PES.
Mohit Singh (M’11) received the M.S. and Ph.D. degrees in electrical engineering from The University of Texas at Austin, Austin, TX, USA, in 2007 and 2011, respectively. He is a Researcher with the National Renewable Energy Laboratory, Golden, CO, USA, working on the transmission and grid integration of renewable energy. His research is focused on the dynamic modeling of wind turbine generators (WTGs). His current interests include modeling and testing various applications of WTGs and other renewable energy resources. Dr. Singh is involved in the activities of the IEEE Power and Energy Society.
Lucy Y. Pao (M’91–SM’98–F’12) received the B.S., M.S., and the Ph.D. degrees in electrical engineering from Stanford University, Stanford, CA, USA, in 1987, 1988, and 1992, respectively. She is currently the Richard and Joy Dorf Professor in the Electrical, Computer, and Energy Engineering Department at the University of Colorado Boulder, Boulder, CO, USA. Her primary research focus is in the control systems area, with applications to flexible structures, atomic force microscopes, disk drives, tape systems, and wind turbines. Prof. Pao is a Fellow of the International Federation of Automatic Control and the Renewable and Sustainable Energy Institute. She was a member of the U.S. Defense Science Study Group from 2010 to 2011 and the General Chair for the 2013 American Control Conference. She is an IEEE Control Systems Society (CSS) Distinguished Lecturer and a recipient of the 2012 IEEE Control Systems Magazine Outstanding Paper Award. She has been a member of the IEEE CSS Board of Governors. She has recently given plenary lectures at the 2011 American Society of Mechanical Engineers (ASME) International Mechanical Engineering Congress and Exposition, the 2012 ASME Dynamic Systems and Control Conference, and the 2013 IEEE Conference on Decision and Control.
