50th INDIAN GEOTECHNICAL CONFERENCE thigs/ldh/files/igc 2015 pune/THEME 8... · 50th INDIAN GEOTECHNICAL CONFERENCE 17 th–19 ... DYNAMICS OF ONSHORE WIND TURBINES WITH SOIL STRUCTURE

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50th INDIAN GEOTECHNICAL CONFERENCE 17th – 19th DECEMBER 2015, Pune, Maharashtra, India

Venue: College of Engineering (Estd. 1854), Pune, India

DYNAMICS OF ONSHORE WIND TURBINES WITH SOIL STRUCTURE INTERACTION

Breiffni Fitzgerald1 and Biswajit Basu2

EXTENDED ABSTRACT

The aim of this paper is to provide details on the development of structural dynamic models of wind turbines with soil structure interaction included. Findings are also presented on the dynamics of onshore wind turbines when soil structure interaction (SSI) included, this differs from many wind turbine vibration studies where the foundation is generally considered full fixed.

An Euler–Lagrangian wind turbine model based on energy formulation has been developed which considers the structural dynamics of the wind turbine system and the interaction between in-plane and out-of-plane vibrations of the blades and tower. The wind turbine is subjected to gravity loading and turbulent aerodynamic loading.

Three-dimensional models of wind turbine foundations have been designed and analysed in the finite element geotechnical code Plaxis, an illustration of one of these models is shown below in Fig. A. The rotation of the foundation is measured and used to calculate a rotational spring constant for use in the developed wind turbine models to describe the SSI between the wind turbine foundation and the underlying soil medium.

1Dr Breiffni Fitzgerald, School of Civil & Structural Engineering, Dublin Institute of Technology, Ireland [email protected] 2Prof. Biswajit Basu, Department of Civil, Structural & Environmental Engineering, Trinity College Dublin, Ireland [email protected]

Dr Breiffni Fitzgerald & Prof. Biswajit Basu

Figure A

This work has shown that SSI does not greatly affect the vibrations of the wind turbine blades. However, SSI can have a significant impact on the vibrations of the nacelle/tower by changing their frequency characteristics.

Keywords: Wind Turbine, Soil Structure Interaction, Structural Dynamics, Geotechnical

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DYNAMICS OF ONSHORE WIND TURBINES WITH SOIL STRUCTURE INTERACTION

Dr Breiffni Fitzgerald, School of Civil & Structural Engineering, DIT, Ireland, [email protected] Prof. Biswajit Basu, Dept. of Civil, Structural & Environmental Engineering, TCD, Ireland, [email protected] ABSTRACT: The aim of this paper is to provide details on the development of structural dynamic models of wind turbines with soil structure interaction included. Findings are also presented on the dynamics of onshore wind turbines when soil structure interaction (SSI) included, this differs from many wind turbine vibration studies where the foundation is generally considered full fixed. An Euler–Lagrangian wind turbine model based on energy formulation has been developed which considers the structural dynamics of the wind turbine system and the interaction between in-plane and out-of-plane vibrations of the blades and tower. The wind turbine is subjected to gravity loading and turbulent aerodynamic loading. Three-dimensional models of wind turbine foundations have been designed and analysed in the finite element geotechnical code Plaxis. The rotation of the foundation is measured and used to calculate a rotational spring constant for use in the developed wind turbine models to describe the SSI between the wind turbine foundation and the underlying soil medium. INTRODUCTION In most structural control studies wind turbines are analysed as structures with a fully fixed base. There have been many such studies in recent years [1-5]. In this simple model the soil-foundation system is not considered. This idealized model may lead to underestimation of the damping and could potentially lead to an overestimation of the stiffness and thus the structure's natural frequencies. It has been well known for decades that when a structural element is in contact with the ground the structural displacements and the ground displacements are not independent of each other. The process by which the response of the structure affects the response of the underlying soil and by which the response of the soil affects the response of the structure is known as soil-structure interaction (SSI). The effect of this on the response of the wind turbine is investigated in this work. Recent studies have also attempted to improve on this simplification [6-10]. In this paper a structural dynamic model of a wind turbine with SSI considered is developed. The effect of SSI on the response of a wind turbine’s blades and nacelle/tower is investigated. 3D models of wind turbine foundations have been

designed and analysed in the finite element geotechnical code Plaxis. The rotation of the foundation has been used to calculate a rotational spring constant for use in wind turbine models to describe the SSI between the wind turbine foundation and the underlying flexible soil medium. The multi degree of freedom (MDOF) model of a wind turbine has been developed using an Euler-Lagrangian approach leading to a time varying system with the possibility of negative damping. Time domain simulations are performed on the model using turbulent aerodynamic loading. WIND TURBINE MODEL The dynamic wind turbine model was formulated using the Lagrangian formulation expressed in Eq. 1 below. A schematic of the wind turbine model is shown in Fig. 1. !!"

!"!!!

− !"!!!

+ !"!!!

= 𝑄! (1) where T = kinetic energy of the system, V = potential energy of the system, q! = displacement


of the generalized degree of freedom (DOF) i and Q! = generalized loading for degree of freedom i.

Figure 1 Wind turbine model Each blade is modelled as a cantilever beam with uniformly distributed parameters as can be observed from the expressions for the kinetic and potential energies in Eq. 2 and Eq. 3. The in-plane and out-of-plane vibrations of the ith blade are modelled by two generalized DOFs, q!,!"(t) and q!,!"#(t). The coupled in-plane and out-of-plane mode shapes, ϕ!" x and ϕ!"# x , have been normalized at the tip so that q!,!"(t) represents the in-plane tip displacement and q!,!"#(t) represents the out-of-plane tip displacement. The structural twist of the blade is accounted for in the calculation of the in-plane and out-of-plane mode shapes. Therefore, these mode shapes each have both edgewise and flapwise components. The kinetic and potential energies of the model are derived including the motion of the nacelle/tower and are stated respectively in Eq. 2 and Eq. 3. These expressions are then substituted back into the Lagrangian formulation in equation (1) to allow the equations of motion to be determined.

𝑇 =12 𝜇 𝑥 𝑣!!𝑑𝑥

!

!

+12

!

!!!

𝑀!𝑞!,!"! +12 𝐼!,!"𝜃!,!"

!

+ !!𝑀!𝑞!,!"#! + !

!𝐼!,!"#𝜃!,!"#

! (2) 𝑉 =

12

𝐸𝐼!" 𝑥𝜕𝜃!,!"𝜕𝑥

!

+ 𝐸𝐼!"# 𝑥𝜕𝜃!,!"#𝜕𝑥

!

+2𝐸𝐼!"#$% 𝑥𝜕𝜃!,!"𝜕𝑥

𝜕𝜃!,!"#𝜕𝑥

+𝑁 𝑥𝜕𝑢!,!"𝜕𝑥

!

+ 𝑁 𝑥𝜕𝑢!,!"#𝜕𝑥

!

+𝐺 𝑥𝜕𝑢!,!"𝜕𝑥

!

+ 𝐺 𝑥𝜕𝑢!,!"#𝜕𝑥

!

𝑑𝑥!

!

!

!!!

+12𝐾!,!"𝑞!,!"

! +12𝐾!,!"𝜃!,!"

! +12𝐾!,!"#𝑞!,!"#

! + !!𝐾!,!"#𝜃!,!"#!

(3) where µμ(x) = mass of blade, L = length of the blade, v! = absolute velocity of the i!h blade, M! = mass of nacelle and I!,!" and I!,!"#are the in-plane and out-of-plane mass moments of inertia of the foundation respectively, these values are obtained from a finite element analysis of the turbine foundation. θ!,!" and θ!,!"# are the in-plane and out-of-plane foundation rotational degrees of freedom. The displacement of the tower in the rotor plane (side-to-side) is modelled by the degree of freedom, q!,!"(t) and the displacement of the tower out of the rotor plane (fore-aft) is modelled by the degree of freedom, q!,!"#(t). E is the modulus of elasticity of the blade. The parameters I!"(x), I!"#(x), and I!"#$%(x) are the second area moments of inertia and the second area products of inertia of a cross section of the blade respectively. The effect of the blade structural pre-twist is therefore accounted for in this model following Zhu [11]. The term K!,!" is the in-plane modal stiffness of the tower/nacelle and K!,!"# is the out-of-plane modal stiffness of the tower/nacelle. K!,!" and K!,!"# are the in-plane and out-of-plane rotational stiffness of the foundation respectively. The

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rotation of the blade leads to a centrifugal stiffening effect, N(x) denotes the centrifugal force that gives rise to this stiffening. The gravity force acting on the blade will also contribute to the stiffness of the blade. The term G(x) denotes the gravity force. In Eq. 3 θ!,!" =

!!!,!"!!

,θ!,!"# =!!!,!"#!!

, N(x) = Ω! µμ(ξ)ξdξ!! and G(x) =

− !!g cosψ! µμ(ξ)dξ!

! where ψ! is the azimuthal angle of the i!" blade. Substituting Eq. 2 and Eq. 3 back into Eq. 1 gives the equations of motion for the coupled wind turbine with foundation. The equations of motion are of the form described in Eq. 4.

M(t) q + C(t) q + K(t) q = Q +U! (4)

where M(t) , C(t) and K(t) are the time dependent mass, damping and stiffness matrices of the system respectively. q , q and q are the acceleration, velocity and displacement vectors and Q is the loading, including turbulent

aerodynamics loading and gravity loading. U! is the active control force vector which is defined later. Structural damping included in the system was assumed to be in the form of stiffness proportional damping. Wind Turbine Loading In order to have a realistic estimate of the aerodynamic loading to which the rotor is subjected, models based on the Blade Element Momentum (BEM) theory have been adopted according to a method developed by Hansen [12]. The rotor blade is discretized into smaller elements. Each element is located at a radial distance of r from the hub and has a chord length of c = c(r) and width dr. These elements are analysed in sections along their length and the forces are summed over all sections to get the total force on the rotor [4]. The rotor has a radius L and angular velocity Ω. For more detail about the

specifics of implementation of Hansen’s modified BEM method see [12]. A rotationally sampled turbulence model has been assumed in this paper. A rotating blade is subject to an atypical fluctuating wind velocity spectrum, known as a rotationally sampled spectrum [13]. The spectral energy distribution is altered due to the rotation of the blades. The variance shifts from the lower frequencies to peaks located at integer multiples of the rotational frequency [14]. The turbulent component of the wind velocity is quantified and included in the modified BEM method. This results in turbulent aerodynamic loading. The in-plane and out-of-plane loads are coupled for the model used in this paper. The loading effect of gravity has been considered. The gravity force causes a harmonic in-plane load on the blade.

Wind Turbine Foundation Model A 20x20x1m3 concrete foundation is designed and analysed in Plaxis [15]. The purpose of this analysis is to obtain rotational stiffness values, k!, for use in the wind turbine models derived. As the foundation is square and Mohr-Coulomb soil models are considered the foundation rotational stiffness values are the same for both in-plane (side-to-side) and out-of-plane (fore-aft) motion, i.e. k!,!" = k!,!"# = k! and I!,!" = I!,!"# = I! . The foundation is tested at an embedment depth of 2m. The depth of the soil layer is taken as 20m and the phreatic level as 2m below the ground surface. For the purposes of illustration a dense sand is considered in this paper, Table 1 outlines the properties of the soil.


Table 1 Soil properties

Mohr Coulomb soil parameters

Dense sand

ϒun 17 ϒsat 20 E 5000 ν 0.3 c 0.1 φ 35 ϕ 5 E’ (increment) 2000 c’(increment) 0 K0 0.5 rinter 0.65

The foundation is modelled in 3D. The 3D foundation considered is a square concrete foundation 20m2 and 1m deep. The concrete foundation itself is modelled by a linear isotropic plate of thickness 1m with Young's modulus value of 30x106kN/m2, a unit weight value of 24kN/m3 and Poisson's ratio value of 0.15. The mesh is set to Medium and the mesh around the plate is refined to a fineness factor of 0.25. The 3D model is shown in Fig. 2.

Figure 2 3D finite element model of foundation

The foundation is subject to a static gravity load and also a dynamic load due to the moment arising from the aerodynamic torque. This is applied to the foundation in Plaxis. The in-plane and out-of-plane rotations of the foundation, θ!,!" and θ!,!"#, are measured in Plaxis. From these values the

rotational stiffness, k!, can be calculated using Eq. 5.

k! =!!""#$%&

!!

(5) where M!""#$%& is the moment applied to the foundation (in-plane or out-of-plane) and θ! is the rotation of the foundation (in-plane or out-of-plane) measured by Plaxis. Numerical Simulations Numerical simulations have been performed to demonstrate the effects of SSI. The National Renewable Energy Laboratory (NREL) offshore 5-MW baseline wind turbine [16] has been used to develop and test the model. The proposed model has been implemented in MATLAB [17]. The blade considered is the LM61.5 P2 (manufactured by LM Wind Power, LM Wind Power Group, Kolding, Denmark), which is 61.5m long and has a total mass of 17,740 kg. The in-plane and out-of-plane mode shapes considered have been computed from blade structural data by using the Modes [18] finite element code. The wind turbine is assumed to be operating at its rated speed (12m/s) with a turbulence intensity of 20%. Fig.3 shows the blade loading in-plane and Fig. 4 shows the out-of-plane blade loading.

Figure 3 In-plane load on blade 1

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Figure 4 Out-of-plane load on blade 1 Fig. 5 shows the nacelle loading in-plane and Fig. 6 shows the out-of-plane nacelle loading.

Figure 5 In-plane loading on nacelle

Figure 6 Out-of-plane loading on nacelle The loading considered for the Plaxis analysis is the gravity load due to the turbine and the moment

due to aerodynamic torque. The gravity load is due to the weight of the turbine and is calculated thus: Blade mass: 3 x 17,740 kg Nacelle mass: 240,000 kg Tower mass: 347,460 kg Hub mass: 56,780 kg Total mass: 697,460 kg Total gravity load due to turbine: 6842 kN The moment, Mturbine, applied to the turbine depends on the turbulence intensity (20% in this example). In this example Mturbine = 10,300kNm. Applying this loading in Plaxis and using equation 5 yields the result that k! =5.15E10 Nm/rad. With the k! values obtained from the PLAXIS finite element analysis it is possible to run simulations to show the effect of SSI on the wind turbine system. We compare a wind turbine without SSI included to one with SSI included. Figure 7 shows that the blade vibration response is not affected by the inclusion of SSI.

Figure 7 Blade response with and without SSI However, if we examine out-of-plane response of


the tower/nacelle we see that the effects of SSI affect it; this is illustrated in Fig. 8.

Figure 8 Effect of SSI on nacelle/tower response The out-of-plane response of the nacelle/tower was changed due to interaction with the foundation. Figure 9 shows that the frequency of the nacelle/tower in the out-of-plane direction is lowered slightly due to the presence of the foundation. By comparing Figure a (SSI not included) to Figure b we can see that the dominant frequency has shifted from 1.948 rad/s to 1.791 rad/s due to the effect of SSI.

Figure 9 Nacelle frequency shift due to SSI

CONCLUSIONS This work has provided information on the development of a structural dynamic model of a wind turbine with soil structure interaction included. The paper also demonstrated the effects of SSI on the wind turbine dynamic system. It was shown that SSI does not greatly affect the blade vibrations. However, SSI can have a significant impact on the vibrations of the nacelle/tower by changing their frequency characteristics. REFERENCES

1. Fitzgerald, B., Basu, B., & Nielsen, S. R. (2013). Active tuned mass dampers for control of in-plane vibrations of wind turbine blades. Structural Control and Health Monitoring, 20(12), 1377-1396.

2. Fitzgerald, B., Arrigan, J., & Basu, B. (2010, July). Damage detection in wind turbine blades using time-frequency analysis of vibration signals. In Neural Networks (IJCNN), The 2010 International Joint Conference on (pp. 1-5). IEEE.

3. Fitzgerald, B., & Basu, B. (2014). Cable connected active tuned mass dampers for control of in-plane vibrations of wind turbine blades. Journal of Sound and Vibration, 333(23), 5980-6004.

4. Staino, A., Basu, B., & Nielsen, S. R. (2012). Actuator control of edgewise vibrations in wind turbine blades. Journal of Sound and Vibration, 331(6), 1233-1256.

5. Zhang, Z., Basu, B., & Nielsen, S. R. (2015). Tuned liquid column dampers for mitigation of edgewise vibrations in rotating wind turbine blades. Structural Control and Health Monitoring, 22(3), 500-517.

6. Harte, M., Basu, B. and Nielsen, S.R.K. (2012), Dynamic analysis of wind turbines including soil-structure interaction, Engineering Structures, 45 (2012) 509-518.

7. Harte, M., & Basu, B. (2013). Foundation impedance and tower transfer functions for offshore wind turbines. Proceedings of the Institution of Mechanical Engineers, Part

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K: Journal of Multi-body Dynamics, 1464419312473056.

8. Harte, M., & Basu, B. (2012). Soil-Foundation Models and Tower Transfer Functions for Offshore Wind Turbines. In 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 20th AIAA/ASME/AHS Adaptive Structures Conference 14th AIAA (p. 1417).

9. Ghosh, A., & Basu, B. (2005). Effect of soil interaction on the performance of liquid column dampers for seismic applications. Earthquake engineering & structural dynamics, 34(11), 1375-1389.

10. Fitzgerald, B., & Basu, B. (2013). Active tuned mass damper control of wind turbine nacelle/tower vibrations with damaged foundations. Key Engineering Materials, Vol. 569, pp. 660-667.

11. Zhu, TL. (2011) The vibrations of pre-twisted rotating Timoshenko beams by the rayleigh-ritz method. Computational Mechanics, 47:395.

12. Hansen, M. O. L. (2000), Aerodynamics of Wind Turbines. James & James (Science Publishers) Ltd.

13. Connell, J. (1982) The spectrum of wind speed fluctuations encountered by a rotating blade of a wind energy conversion system, Solar Energy, 29 (5) (1982) 363 – 375.

14. Murtagh, P.J., Ghosh, A.,Basu, B. and Broderick, B. M. (2008) Passive control of wind turbine vibrations including blade/tower interaction and rotationally sampled turbulence, Wind Energy, 11 (4) (2008) 305–317.

15. PLAXIS 3D 2012, Plaxis BV, Delft, the Netherlands

16. Jonkman, J.M., Butterfield, S., Musial, W., Scott, G. (2009) Definition of a 5-MWreference wind turbine for offshore system development. National Renewable Energy Laboratory, Technical Report,

NREL/TP-500-38060, Golden, Colorado; 2009.

17. MATLAB, version 7.9.0.2601 (R2009b), The MathWorks Inc., MA, USA

18. Buhl, M. (2005) Modes, NWTC Design Codes, May 2005, http://wind.nrel.gov/designcodes/preprocessors/modes/S

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50th INDIAN GEOTECHNICAL CONFERENCE thigs/ldh/files/igc 2015 pune/THEME 8... · 50th INDIAN GEOTECHNICAL CONFERENCE 17 th–19 ... DYNAMICS OF ONSHORE WIND TURBINES WITH SOIL STRUCTURE