Abstract

The existing nacelle testing methods require continuous improvements to satisfy the ever-increasing demands for testing modern wind turbines. One way to achieve this goal is to use advanced simulation techniques to undertake hybrid testing, in which experiments and simulations are combined to push the boundaries of nacelle testing even further. To do so requires the development of a virtual model of the test bench featuring the true test bench dynamics and functionalities. This contribution presents the development of a virtual model of the complete nontorque load application system of a nacelle test bench at Fraunhofer IWES. The model development methodology is explained and the impact of different levels of modeling depth of the hydraulic system model is investigated. It is concluded that modeling of friction and valve dynamics is necessary as they have significant influence on the generated loads. These findings can help in the development of virtual models of nacelle test benches and pave the way for performing hybrid testing for wind turbine nacelles.

1 Introduction

Modern wind turbine systems are designed to generate and supply electricity for an operational period of 20 years or more [1]. However, past years have shown a high rate of failures in both offshore and onshore wind turbine systems [2,3]. Such frequent failures cause long downtimes requiring costly repairs which dominate the overall operation and maintenance (O&M) costs [4,5]. This has raised the need for finding ways of developing more reliable wind turbine systems. One major way of developing reliable wind turbines is by extensive system level testing and experimental validation [6].

In recent years, nacelle test benches have become an attractive method for testing wind turbine drivetrains as compared to the conventional way of field testing. The most advanced nacelle test benches, like the Dynamic Nacelle Testing Laboratory (DyNaLab) at Fraunhofer IWES, incorporate sophisticated hardware-in-the-loop (HIL) schemes to enable the emulation of field-like loads on a nacelle in a controlled testing environment [7] (Fig. 1). They offer faster and reproducible test campaigns at a lower cost compared with field testing.

Fig. 1
DyNaLab test bench system
Fig. 1
DyNaLab test bench system
Close modal

However, wind turbine technologies are evolving rapidly and the operational capacities of wind turbines are breaking new records every year [8]. Consequently, the existing test benches must keep up with the growing demands of testing modern wind turbine nacelles. Upgrading the test bench operational capacity might be the obvious solution, but it is not necessarily the most feasible and realistic one. An alternative solution for complementing test bench capabilities is needed that is both economically feasible and applicable for all the existing test benches. This is where simulation techniques come into play. The advancements in simulation technology have allowed the development of complete virtual twins of the actual test setup and opened the doors for “hybrid testing” of wind turbine nacelles [9]. Combining the simulation results with the experimental measurements makes it possible to investigate the complex interactions between the device under test (DUT) and the test bench effectively. The virtual models of the RWTH Aachen University test benches [10,11] and the Clemson University test bench [12] have already demonstrated some of these advantages. These models have primarily been used for detailed analysis of the nacelle DUT. The ongoing VirtGondel research project [13] at Fraunhofer IWES aims to advance this technology further by using the virtual test bench model to augment the physical testing and provide a parallel virtual environment with load ranges beyond the test bench capacity. The virtual test bench model will also be utilized to further develop the existing methods for nacelle testing.

However, the development of such high-fidelity virtual models of a nacelle test bench for hybrid test application is challenging. The DyNaLab test bench features a hexapod system for the application of nontorque loads which comprises several servohydraulic actuators that are powered via a large hydraulic circuit. The selection of the required modeling fidelity that represents all the relevant system dynamics with optimal computation times for a system of such unique topology, size, and operational capacity is by no means trivial. Moreover, there is very limited information available in the literature for developing virtual models for a test bench of similar topology. The test bench model in Ref. [11] considers a simplified actuator dynamic model, whereas no details are given on the load application system model of the test bench in Ref. [10]. The test bench model in Ref. [12] considers a detailed model of the valve dynamics for studying the test bench control system and considers the cylinder pressure dynamics which are presented in Refs. [14,15]. However, the recommended modeling fidelity is still not evident from these works, as this was not the focus. This leaves the question of required modeling fidelity still open. For complete virtual testing, it is important to model all the relevant test bench dynamics that can influence the global system response. Therefore, a detailed study is needed to understand the important system characteristics and the required modeling fidelity.

This contribution presents the development of a virtual model of the complete nontorque load application system (LAS) of the DyNaLab test bench. Multibody simulation (MBS) is utilized for the modeling of the mechanical components of the LAS. The complete hydraulic system of the test bench is modeled using bond graph methods. Both system models are dynamically coupled via cosimulation in Simulink, which also features the LAS force control scheme using PI control. This allows implementation of the loads on the DUT in the same manner as on the actual bench. The model development methodology will be explained, and the influence of different levels of modeling depth of the system model investigated, and the model fidelity most relevant for capturing the system dynamics highlighted. The findings will aid the development of virtual models of similar test benches as the DyNaLab and shall open further doors for performing hybrid testing for wind turbine nacelles.

A detailed description of the test bench LAS is given in Sec. 2. The modeling methodology is explained in Sec. 3. The implemented cosimulation framework for the test bench LAS is described in Sec. 4. The case studies performed and discussion of the results are provided in Secs. 5 and 6. The paper ends with an outlook for future work in Sec. 7 and conclusion in Sec. 8.

2 DyNaLab Load Application System

The DyNaLab offers electrical and mechanical tests for a wind turbine nacelle of up to 10 MW power. With its direct drive and hexapod LAS, the test bench can apply loads on the nacelle DUT in six degrees-of-freedom (DOF) to emulate the wind loads. The LAS consists of a particular configuration of a 6DOF Stewart-Gough platform, which is driven by means of six servohydraulic cylinders. Figure 2 shows the force control scheme of the LAS. These cylinders are arranged in a hexagonal configuration. The LAS can apply up to 20 MNm bending moment and 2 MN thrust and shear forces.

Fig. 2
Inverse kinematics of the LAS
Fig. 2
Inverse kinematics of the LAS
Close modal

The internal control of the LAS transfers the desired loads at the load application point (LAP) to the individual cylinders. This transformation is governed according to an inverse kinematic approach that performs a mapping of desired LAP loads in the task space into the required amount of individual actuator loads in the joint space. Each actuator has a dedicated servovalve controller that receives the required actuator force set points to control the servovalve. Pressure sensors in each cylinder measure the generated cylinder forces which serve as the feedback signal to the actuator controller. In this manner, each actuator has a closed-loop in its respective joint space. This enables the application of nontorque loads in 5DOFs in a controlled fashion.

Each hydraulic actuator is connected to a comprehensive hydraulic circuit that ensures stable delivery of hydraulic fluid for the entire operating range of the test bench. Figure 3 shows a simplified representation of the test bench hydraulic circuit. A set of six motor powered displacement pumps supply pressurized fluid from the reservoir tank to the high pressure line. A series of accumulators are connected to the pressure lines for minimizing pressure ripples. The pressure line also consists of several relief valves for ensuring safe pressure limits. The return line delivers the low pressure through heat exchangers into the reservoir tank.

Fig. 3
Simplified representation of the DyNaLab hydraulic circuit (©IDOM)
Fig. 3
Simplified representation of the DyNaLab hydraulic circuit (©IDOM)
Close modal

3 System Modeling

3.1 Modeling of the Hydraulic Sub-Systems.

Elements of the hydraulic system of the test bench have been modeled using the bond graph method in 20-sim software [16]. The bond graph method is an energy-based modeling approach that provides a practical way of fully coupling multidomain systems with various power conversions. In the bond graph method, effort and flow variables, also known as power variables, are used to describe how the systems interact and exchange energy. This modeling approach categorizes each element of physical systems based on their ability for energy supply, storage, transformation, or dissipation. The kinetic and potential energy storage are represented by inertia (I) and capacitance (C) elements, respectively. Energy dissipation is represented by resistance (R) elements, while lossless energy transformation is depicted by transformer (TF) elements. These system components are interconnected with power bonds (denoted with a half arrow), representing the energy exchange. The sense of the half arrow gives the direction of the power. The causality of effort and flow variables is shown with a vertical stroke, which determines whether these variables are considered input or output in the respective bond graph elements. Elements under the same effort are associated with parallel junctions (0-junctions), whereas elements under the same flow are associated with series junctions (1-junctions).

The LAS is powered by a hydraulic system composed of several key subsystems such as the hydraulic supply unit, pipes, accumulators, and servocontrolled actuators. Modeling these subsystems using the bond graph approach gives the advantage of having complete control over the causal relationships between the component models. This helps in identifying and preventing algebraic loops in the system model. Furthermore, defining the coupling interface and the associated input and output variables between the hydraulic system model and the MBS model during cosimulation becomes straightforward as these variables are simply the power variables of the bond graph model at any interface. The constitutive equations for modeling these subsystems have been gathered from Ref. [17] and are described in Secs. 3.1.13.1.5.

3.1.1 Hydraulic Fluid Supply.

The test bench pump station supplies the hydraulic fluid to the circuit. This consists of a series of displacement pumps powered by an electric motor that drives the pumps to supply fluid to the manifold unit connected to the high-pressure line. Figure 4 shows the bond graph model of the fluid supply system and pressure relief valve. The motor is modeled as a modulated source of flow with rotation speed as the modulation signal. The main tank supplying the fluid is an effort source. The pump is modeled as a transformer element that converts motor power (speed and torque) into fluid power (pressure and flowrate) according to the following relation:
V˙=d2πω
(1)

where V˙ is the theoretical pump delivery as a function of pump displacement d and motor speed ω. The relief valve maintains the pressure in the system to a limit value. The relief valve opens fully when the line pressure exceeds the limit pressure and is fully closed when the line pressure is below the limit pressure. This is modeled as a modulated R element with line pressure as modulation signal.

Fig. 4
Bond graph model of hydraulic supply
Fig. 4
Bond graph model of hydraulic supply
Close modal

3.1.2 Fluid Pipe System.

The pipe model allows the consideration of fluid inertia, fluid compressibility, line resistance, and elasticity of the line material. Figure 5 shows the bond graph model of the pipe. The pipe and fluid capacitance is modeled as a C element of the following form:
C=AL(1β+5D4Et)
(2)
where A is the pipe area, L is the total pipe length, β represents the fluid bulk modulus, D is the pipe diameter, t is the pipe thickness, and E is the elastic modulus of the pipe material. The fluid inertia is lumped into a single I element that accounts for the total inertia of the fluid in the pipe and is defined as:
I=ρLA
(3)
where ρ is the fluid density. The line resistance is modeled as an R element with the following relation between pressure and flowrate for a laminar flow regime:
R=128LμπD4
(4)

where μ is the dynamic viscosity of the fluid.

Fig. 5
Bond graph model of hydraulic pipe
Fig. 5
Bond graph model of hydraulic pipe
Close modal

3.1.3 Accumulator.

Accumulators are storage elements that store flow part of the time for a delivery at sudden pressure drops. In this manner, they reduce ripples and pressure transients in the pressure line. The test bench accumulators are of bladder type with precharged gas. Such a device can be modeled as a flow storing C element. The constitutive relation of this element considering isentropic process is as follows:
P=[VoVoV˙dt]kPo
(5)

where k is the specific heat ratio for an isentropic process and Po and Vo are the nominal pressure and volume of the accumulator.

3.1.4 4/3 Proportional Valve.

The actuators are controlled by 4/3 proportional spool valves with individual PI controller. These are modeled as a circuit of modulated R elements with spool position as the modulation signal. Figure 6 shows the bond graph model of the spool valve. Each R element allows flow when active along with the appropriate pressure drop according to the equation:
V˙=V0xspoolPP0
(6)

where xspool is the spool displacement which is modeled by a second order transfer function characterized by the valve response frequency and damping.

Fig. 6
Bond graph model of the 4/3 proportional valve
Fig. 6
Bond graph model of the 4/3 proportional valve
Close modal

3.1.5 Hydraulic Actuator.

The actuators convert hydraulic power into mechanical power. Figure 7 shows the bond graph model of the hydraulic actuator. This is modeled by two transformer elements representing conversion from fluid power into mechanical power for each cylinder chamber
Pa=βV0a+AxpistonVa
(7)
Pb=βV0bAxpistonVb
(8)
Fig. 7
Bond graph model of the hydraulic actuator
Fig. 7
Bond graph model of the hydraulic actuator
Close modal
Each chamber volume is modeled by C element and the piston inertia is modeled with an I element. The actuator leakage reduces the effective flow rates and leads to power losses. The internal leakage between the two chambers and the external leakage through the piston rod can be modeled as an R element of the following constitutive relation:
V˙=πdδ312ρνlnP
(9)

where δ is the seal clearance and ln is the seal contact length. Two modulated effort sources are linked to the piston side. The first one applies the bumper force on the piston and the second one applies the forces from external loads on the piston.

The piston seal friction has also been considered. The steady-state friction model [18] and the LuGre model [19] are widely employed for modeling actuator friction. The steady-state friction model combines the Coulomb friction, viscous friction, and static friction and is described by the following equation:
Fr=Fc+(FsFc)e(ννs)n
(10)

where Fr is the friction force, Fc is the Coulomb friction force, and Fs is the static friction force. νs is the Stribeck velocity with n as the exponent that affects the slope of the Stribeck curve. The velocity between the sliding surface is defined by ν.

The LuGre model, which is a dynamic friction model, is governed by the following set of equations:
g(ν)=Fc+(FsFc)e(ννs)n
(11)
dzdt=νσ0zg(ν)ν
(12)
Fr=σ0z+σ1dzdt+σ2ν
(13)

where g(ν) is the Stribeck function that expresses the Coulomb friction and the Stribeck effect. σ0, σ1, and σ2 represent the average stiffness coefficient of bristles, the average damping coefficient of bristles, and the viscous friction coefficient, respectively. z represents the mean deflection of the elastic bristles. The first and second term of Eq. (13) represent the force of friction arising due to the elastic bending of the bristles while the third term represents the viscous friction. Both friction models defined by Eqs. (10) and (13) can be modeled as an R element in the bond graph model of the cylinder. However, in the presented work, the friction is modeled in the MBS system in the translational joints of each actuator. This results in two main advantages. First, the normal force is directly calculated in the MBS system. Second, the more robust HHT integrator of MSC Adams can be used to solve the differential equations.

3.2 Test Bench Hydraulic Circuit Model.

The actual hydraulic circuit of the test bench features several components that are there for safety and maintaining steady operation. By assuming that the entire system operates fault free and ignoring thermal effects, several components like filters, heat exchangers, check valves, and emergency drains can be ignored. Moreover, the goal of the virtual model is realistic simulation of the LAP loads. Therefore, only those aspects of the hydraulic circuit have been considered that are required for a realistic generation of the LAP forces under normal mode of operation. Figure 8 shows the selected abstraction of the test bench hydraulic circuit along with the equivalent bond graph model.

Fig. 8
Test bench hydraulic system schematic and equivalent bond graph model
Fig. 8
Test bench hydraulic system schematic and equivalent bond graph model
Close modal

The individual accumulators are lumped together as an equivalent model representing the combined volume of all the accumulators. The pipes are modeled as a lumped model as explained in Sec. 3.1.2. The fluid supply system assembly to which the hydraulic actuator components are connected closely resembles the actual test bench system. The hydraulic circuit model has defined interfaces that allow it to connect with external models that are located at the spool valve input signal, the piston force input and the piston velocity output.

3.3 Test Bench Multibody Simulation Model.

A high fidelity MBS model of the test bench has been developed that models all the components of the test bench drive system and LAS. Figure 9 shows the complete MBS model of the test bench and the calibration unit modeled using mscadams software [20]. The calibration unit is a steel reaction structure that serves as a DUT. The DUT structure with platform, flange adaptors, coupling, and motor rotor are modeled as flexible bodies. These bodies are created by modal reduction of their respective FE models using the component mode synthesis (CMS) method [21]. All components in the model are connected with each other and the ground using constraints according to their configuration in the actual system. Table 1 provides information on the MBS model fidelity. The choice of model fidelity for the test bench system and the DUT was mainly driven by the need to achieve the maximum accuracy possible without raising computational costs. More details on the test bench MBS model are provided in [22,23].

Fig. 9
The experimental setup with the calibration unit (left), virtual test bench in MBS (right)
Fig. 9
The experimental setup with the calibration unit (left), virtual test bench in MBS (right)
Close modal
Table 1

MBS model fidelity

ComponentsFidelity
MotorsRigid spring-mass system
Drive shaftFlexible body
Torque limiterFlexible body
Coupling flangesFlexible body
Coupling linksRigid body
BearingsBushing with 6 × 6 stiffness matrix
Interface flangeFlexible body
HexapodRigid body
ActuatorRigid body
Calibration unitFlexible body
PlatformFlexible body
ComponentsFidelity
MotorsRigid spring-mass system
Drive shaftFlexible body
Torque limiterFlexible body
Coupling flangesFlexible body
Coupling linksRigid body
BearingsBushing with 6 × 6 stiffness matrix
Interface flangeFlexible body
HexapodRigid body
ActuatorRigid body
Calibration unitFlexible body
PlatformFlexible body

4 Co-Simulation Framework

The high-fidelity test bench MBS model, the hydraulic system model, and the actuator controllers are coupled via cosimulation. This will allow emulation of the actual LAS of the DyNaLab test bench. Simulink serves as the cosimulation interface. The bond graph model of the hydraulic circuit developed in 20-sim is exported to Simulink as a functional mockup unit (FMU). The multibody simulation model of the test bench is imported as an Adams-Simulink block.

The hydraulic system model in 20-sim is fully coupled to the MBS model in Adams at the hydraulic actuator interface (as shown in Fig. 10). The 20-sim model receives the piston reaction force as input variables and delivers the piston velocities as output variables. The MBS model in Adams receives the piston velocities as input variables and applies them as constraints to the respective actuators. The resulting piston force reactions are delivered as output variables. Apart from these coupling variables, additional outputs are extracted from the MBS model and the 20-sim model for postprocessing of the results. These include the LAP forces, LAP displacements, piston displacements, and cylinder chamber pressures. Both the hydraulic model in 20-sim and MBS model in Adams communicate by passing the input and output variables back and forth with a communication interval that corresponds to the simulation step size. The hydraulic model in 20-sim uses the fourth order Runge–Kutta method for time integration with a step size of 60 μs. The Adams model uses the HHT integrator with a step size of 6 ms. Simulink provides the necessary rate transitions between the coupled models and performs the time integration using the 4th order Runge–Kutta method with a step size of 60 μs.

Fig. 10
Interfaces between the hydraulic actuator model, the controller, and the MBS model during cosimulation
Fig. 10
Interfaces between the hydraulic actuator model, the controller, and the MBS model during cosimulation
Close modal

Each individual hydraulic actuator model in 20-sim is controlled by a dedicated PI controller which is modeled in Simulink. The difference in the actuator set point force and the cylinder pressure calculated force is sent to the PI controller as an error signal. The PI controller attempts to reduce the error by controlling the spool positions. This way, the force is being controlled in the joint space that translates into the desired LAP forces in the task space according to the inverse kinematics of the hexapod system. This force control scheme is similar to the one implemented in the actual test bench.

5 Case Studies

Several case studies are performed with different model variations, which are listed in Table 2. In this way, the modeling features that are most relevant for force generation at the LAP can be identified. The base model represents an idealized hydraulic circuit that ignores the fluid inertial effects in the pressure line, the spool valve dynamics, and the frictional losses in the hydraulic cylinder and pipes. This is used as a reference, and all subsequent modeling details are added individually to the base model for comparison. Figure 11 shows the load profile considered for all the cases. The test load profile involves stepped loading in the beginning and sinusoidal load toward the end. This makes it possible to understand the system response for the static and dynamic load regimes. The tests are performed for three loading directions. These directions correspond to the thrust forces (Fx), the yaw forces (Fy), and the pitch forces (Fz) that are applied at the LAP. Though less realistic than actual field loads, such unidirectional load scenarios reveal key system characteristics that might otherwise be difficult to identify in the case of mixed load scenarios.

Fig. 11
Load profile for case studies
Fig. 11
Load profile for case studies
Close modal
Table 2

Model variations for case studies

VariationPipe modelCylinder frictionCylinder leakageValve dynamics
Base model××××
Case 1×××
Case 2×××
Case 3×××
Case 4×××
VariationPipe modelCylinder frictionCylinder leakageValve dynamics
Base model××××
Case 1×××
Case 2×××
Case 3×××
Case 4×××

Figure 12 shows the influence of modeling pipe in the hydraulic circuit. Three variations of pipe models have been used: the first variation considers the fluid inertia (green); the second variation considers the line friction (yellow); and the third variation combines the fluid inertial effects and line friction (red). The first two pipe model variations focus on the individual effects of fluid inertia and pipe friction, whereas the third model variation focuses on their combined effect on the system response. In all variations, the pipe capacitance has been modeled according to Eq. (2). It can be observed that, with the exception of the transition regions, the deviations are insignificant when compared to the base model.

Fig. 12
Case 1—influence of pipe system model. Hub forces (Fx), Hub forces (Fy), and Hub forces (Fz).
Fig. 12
Case 1—influence of pipe system model. Hub forces (Fx), Hub forces (Fy), and Hub forces (Fz).
Close modal

Figure 13 shows the influence of modeling the cylinder friction. Noticeable changes are observed for the static load case regions as the models with friction result in lower LAP force in axial direction when compared to the base model. For any given force set point for an actuator, the cylinder forces that are feedback to the PI controller are calculated from the pressure difference of the cylinder chambers in the joint space. The presence of friction raises this differential force. This results in cylinder forces reaching the set point values while the actual force applied at the piston end is less than the set point force (by a factor of the frictional force in the system). As a result, the PI controller assumes that the set point has been achieved by assessing the pressure differential force. This consequently leads to the difference in the generated LAP forces in the task space. The modeled friction has a maximum value of 0.5% of nominal actuator force, which has caused up to 12% deviations in the LAP forces. The deviations are greatest in the axial load case and are very minor for the remaining two directions. This is possibly due to larger movement of the pistons for the axial load case as compared to the pitch and yaw load cases. The friction models will return higher frictional forces for larger piston movements.

Fig. 13
Case 2—influence of cylinder friction. Hub forces (Fx), Hub forces (Fy), and Hub forces (Fz).
Fig. 13
Case 2—influence of cylinder friction. Hub forces (Fx), Hub forces (Fy), and Hub forces (Fz).
Close modal

Figure 14 shows the influence of modeling cylinder leakages. Deviations in the static load regions can be observed, as the model with the highest leakage rate tends to have a continuous drop in force levels. At any stationary force level, the leakage causes pressure drops that lead to a drop in the actuator forces. The PI controller continuously attempts to maintain the force levels and therefore, due to active controller actions, the resulting forces are noisier.

Fig. 14
Case 3—influence of cylinder leakage. Hub forces (Fx), Hub forces (Fy), and Hub forces (Fz).
Fig. 14
Case 3—influence of cylinder leakage. Hub forces (Fx), Hub forces (Fy), and Hub forces (Fz).
Close modal

Figure 15 compares the models with varying levels of valve dynamics. The results show significant deviations in the dynamic load regions and some noticeable noise in the transient regions of the step loads. The PI controller actions can possibly influence the valve response frequencies that can lead to deviations in the LAP forces. The results have shown that changes in valve response frequency of as much as 5% can cause up to 20% variations in dynamic LAP forces.

Fig. 15
Case 4—influence of valve dynamic. Hub forces (Fx), Hub forces (Fy), and Hub forces (Fz).
Fig. 15
Case 4—influence of valve dynamic. Hub forces (Fx), Hub forces (Fy), and Hub forces (Fz).
Close modal

From the presented results of the case studies, it is evident that certain elements of the hydraulic circuit have a more significant impact on the resulting LAP forces than the others. The cylinder friction and valve dynamics when modeled can significantly affect the model behavior. The cylinder leakage has shown minor changes in the constant force regions, whereas the modeling of the pipe has shown negligible changes in the results.

Furthermore, in almost all cases, the Fy and Fz hub forces showed more noise as compared to the Fx hub forces. One possible reason for this could be linked to the higher stiffness of the DUT structure in the Y and Z directions as compared to the X direction. This higher stiffness leads to higher-frequency pressure fluctuations in the hydraulic actuator model, which causes the actuator PI controller to react more aggressively, eventually leading to more noise in hub forces.

6 Model Validation

Based on the findings of the case studies, features such as cylinder friction and valve dynamics have been incorporated into the base model. A preliminary validation is performed for the virtual model by comparing the hub forces from simulations with experimental results for a sinusoidal load case. In the experimental setup (shown in Fig. 9), multiple load cells are installed between the DUT and the interface flange of the hexapod. This allows a direct measurement of forces at the load application point between the DUT and the hexapod unit during experiments. Figure 16 shows the comparison of hub forces simulated by the virtual model and those determined during experiments via the load cells. The virtual model can reproduce the dynamic axial forces with decent accuracy, having less than 4% deviation from the experimentally measured axial forces. However, the model appears to overestimate the generated Fy and Fz forces as compared to the experimental measurements of the corresponding loads. These deviations could be linked to several reasons, such as uncertainties in the model parameters of the hydraulic system, uncertainties in the MBS model, and uncertainties in the controller model. The actuator controller used in the virtual model is an abstraction of the actual controller on the test bench. Therefore, the modeled controller can have differences in dynamic behavior as compared to the actual controller on the test bench. Further investigations are needed to optimize the PI parameters that can make the controller more robust for all load directions.

Fig. 16
Validation of dynamic hub forces generated by the virtual test bench. model Hub force (Fx), Hub force (Fy), and Hub force (Fz).
Fig. 16
Validation of dynamic hub forces generated by the virtual test bench. model Hub force (Fx), Hub force (Fy), and Hub force (Fz).
Close modal

7 Future Work

Although several aspects were covered in the presented case studies, some modeling features that might require further investigation include, cylinder expansion, seal clearance variations, fluid viscosity variations, spool valve friction and hysteresis. In physical systems, the cylinders do expand at higher pressures leading to changes in the volume and seal clearance. This could influence the pressure dynamics and the leakage rates leading to fluctuations in actuator forces. The spool valves also have some level of friction and hysteresis effects that might have an influence on the actuator load response. The viscosity of fluids changes with variations in temperature. Changes in fluid viscosity can lead to changes in friction and leakages, which can influence the loads applied by the actuators.

In the presented work, only unidirectional load cases were considered to investigate the dynamic response of the LAS. Future work will involve further investigations using different types of mixed load cases that closely resemble the loads that are typically encountered by a wind turbine during field operation. Such investigations can help in estimating the capability of the test bench to reproduce field-relevant dynamic wind loads.

Furthermore, aspects concerning the behavior of the actuator PI controller require detailed investigations, which weren't the focus of this paper. However, it can have a strong influence on the generated hub forces, both in terms of response time and deviation from target setpoints. Further investigations are required to highlight the key aspects of developing actuator controller models that are both robust and resemble the behavior of the controllers on the actual test bench.

8 Conclusion

This contribution has provided insights into the modeling of the complete load application system of a multimegawatt wind turbine nacelle test bench. The important modeling aspects of a hydraulic circuit were revealed by a series of case studies with different modeling variations. The results showed that modeling of the actuator friction and valve dynamics has significant influence on the generated loads at the load application point. Introducing friction with stick-slip effects with a maximum value of 0.5% of the nominal actuator force can lead to up to 12% deviations in the LAP forces. Variations in valve dynamic response of as much as 5% can lead to up to 20% variations in dynamic LAP forces. Therefore, it is recommended to include these features in the system model. These findings can be relevant for modeling the load application systems of similar types of nacelle test bench systems.

Acknowledgment

The authors would like to thank the involved colleagues at Fraunhofer IWES for their contributions to the VirtGondel project. The funding of the VirtGondel project by the German Federal Ministry for Economic Affairs and Climate Action (BMWK) (No. 03EE2018) is kindly acknowledged.

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

Nomenclature

CMS =

component mode synthesis

DOF =

degree of freedom

DUT =

device under test

FMU =

functional mockup unit

HiL =

hardware-in-the-loop

LAS =

load application system

LAP =

load application point

MBS =

multibody simulation

O&M =

operation and maintenance

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