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Adaptive Structural Control of Floating Wind Turbine with Application of MR Damper
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Energyonline Procedia 00 (2018) 000–000 Available onlineatat www.sciencedirect.com Available www.sciencedirect.com Energy Procedia 00 (2018) 000–000
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www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Energy (2019) 000–000 254–259 EnergyProcedia Procedia158 00 (2017) www.elsevier.com/locate/procedia
10th International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong Kong, 10th International Conference on Applied Energy China(ICAE2018), 22-25 August 2018, Hong Kong, China
Adaptive Structural Control of Floating Wind Turbine with The Structural 15th International Symposium on District Heating Cooling with Adaptive Control of Floating Wind and Turbine Application of MR Damper Application of MR Damper Assessing a,the feasibilitya of usinga the heat demand-outdoor Lei Wanga,*, Zhaohua Lianga, Ming Caia, Yang Zhangbb, Jinyue Yanbb Lei Wang *, Zhaohua , Ming Cai district , Yang Zhang Yan forecast temperature function forLiang a long-term heat, Jinyue demand College of Automation, Chongqing University, Chongqing 400044, China a
Automation, Chongqing University, 400044, China SE-100 44, Sweden School of ChemicalaCollege Science of and Engineering, KTH Royal Institute Chongqing of Technology, Stockholm a,b,c a a b c b School of Chemical Science and Engineering, KTH Royal Institute of Technology, Stockholm SE-100 44, Sweden b
I. Andrić a
*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Correc
IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b
Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Abstract c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France Abstract Floating wind turbine has become the most promising technology for deep-sea wind power generation. Therefore, some means to Floating wind turbineload has become the most technology fordeveloping. deep-sea wind power generation. Therefore, some control means to reduce the structural for stabilizing thepromising wind turbine has been In this paper, a semi-active structural is reduce the for stabilizing the wind hasmagnetorheological been developing. In(MR) this paper, a semi-active structural is realized bystructural replacingload the damper in passive TMDturbine with the damper. The damping force ofcontrol the MR Abstract realized by be replacing with (MR) damper. Theisdamping of includes the MR damper can changedthe bydamper alteringinthepassive voltageTMD applied to the it. Amagnetorheological simple and convenient control method designed,force which damper can be changed by altering the voltage applied to it.The A simple and convenient method is designed, includes adaptive control force design and retrogression controller. simulation results showcontrol that the semi-active controlwhich method has a District control heatingforce networks commonly addressed in the literature as results one of show the most effective solutions for decreasing adaptive designare and retrogression controller. The simulation that the semi-active control method hasthe a good damping effect, which mitigates much of the structural load with respect to the passive structural control. greenhouse emissions the building These systems investments which are returned through the heat good dampinggas effect, whichfrom mitigates much ofsector. the structural load withrequire respecthigh to the passive structural control. sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, Copyright © 2018 Elsevier Ltd. All rights reserved. © 2019 The Published by Elsevier Ltd. prolonging the investment return Copyright ©Authors. 2018 Elsevier Ltd. Allperiod. rights reserved. Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied This ismain an open access article under the CCthe BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) The scope of this paper is to assess feasibility using the heat demand – outdoor temperature Conference function for on heatApplied demand Selection and peer-review under responsibility of the of scientific committee of the 10th International Energy (ICAE2018). Peer-review under responsibility of thelocated scientific committee of ICAE2018 The as 10th Conference forecast. The district of Alvalade, in Lisbon (Portugal), was –used a International case study. The district on is Applied consistedEnergy. of 665 Energy (ICAE2018). buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district Keywords: floating wind turbine; magnetorheological damper; structural control renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were Keywords: floating wind turbine; magnetorheological damper; structural control compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications 1. Introduction error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation 1.(the Introduction scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). Wind is one of the increased flourishing energy sources in theupworld. wind aretofar The valuepower of slope coefficient on renewable average within the range of 3.8% to 8% Offshore per decade, that resources corresponds the Wind power is onethat of on the land, flourishing renewable energy sources in world. Offshore wind resources are far more abundant than especially where farthe away fromseason thethe coast. Floating turbines used to decrease in the number of heating hours of 22-139h during heating (depending on thewind combination ofare weather and more abundant thanconsidered). that on sea land, especially where away from the coast. Floating wind turbines used to capture wind energy in deep areas. Its structure is far more complex than theforonshore wind and are it represent renovation scenarios On the other hand, function intercept increased 7.8-12.7% perturbines decade (depending on the capture wind energy in deep sea areas. Its structure is to more complex than the onshore wind turbines and it represent the highest level of The wind power technology today. Compared to the the function onshore wind turbines, the floating one has extra coupled scenarios). values suggested could be used modify parameters for the scenarios considered, and the highest level of wind power technology today. Compared to the onshore wind turbines, the floating one has extra improve the accuracyitofisheat demand estimations. motions. Therefore, susceptible to wind and waves, and large structural load may be produced.
motions. Therefore, it is susceptible to wind and waves, and large structural load may be produced.
© 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Tel.: +86-136-2970-5707 . * E-mail Corresponding Tel.: +86-136-2970-5707 . address:author. [email protected] Keywords: Heat demand; Forecast; Climate change E-mail address: [email protected]
1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. 1876-6102 Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the 10th International Conference on Applied Energy (ICAE2018). Selection and peer-review under responsibility the scientific Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. 10.1016/j.egypro.2019.01.085
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Lei Wang et al. / Energy Procedia 158 (2019) 254–259 Author name / Energy Procedia 00 (2018) 000–000
255
At present, a lot of work has been done for the load mitigation control of wind turbines by many researchers. In the field of floating wind turbine, most current structural control methods are passive structure control. Lackner and Rotea [1] developed FAST-SC and used a passive tuned mass damper (TMD) in the nacelle of a barge type floating wind turbine. Stewart and Lackner [2] had established a linear model of mono-pile stationary wind turbine and three kinds of floating wind turbines with passive TMD. He et al. [3] established a linear model of barge type floating wind turbine with passive TMD in the nacelle. Colwell and Basu [4] studied the effect of TLCD on fatigue load in mono-pile wind turbine. Some researchers use active structural control. Hu and He [5] used a stroke-limited hybrid mass damper in nacelle of floating wind turbine. Stewart and Lackner [6] studied the influence of actuator dynamics and control-structure interaction on active structural control. Li and Gao [7] used the active structural control in the floating platform and designed a static output-feedback active structural controller with the generalized H∞ method. Semi-active structural control has many advantages over passive and active structural control. In this paper, a magnetorheological (MR) damper is used to replace the damper in TMD to realize a semi-active structural control. The TMD with magnetorheological damper (MR-TMD) has good performance, which can be placed in the nacelle of the floating wind turbine for structural control and achieve the purpose of load reduction. The remainder of this paper is as follows. In section 2, we establish the dynamic models of the floating wind turbine and the MR damper. The active control force and a retrogression controller are designed in section 3. Section 4 simulate the motion and load of the turbine tower and good results are obtained. We summarize the paper in section 5. 2. Dynamic model 2.1. Modeling of floating wind turbine
𝑚𝑚𝑡𝑡𝑚𝑚𝑑𝑑 𝑔𝑔
𝐹𝐹𝑚𝑚𝑟𝑟
The objective of this paper is to mitigate the fluctuation of the fore-aft pitch angle of the floating wind turbine. Fig. 1 shows the state of the floating wind turbine under the influence of wind and waves. The joint between the 𝑚𝑚𝑡𝑡 𝑔𝑔 tower bottom and the floating platform is regarded as the reference point. There are elastic moment and damping moment between the tower and the 𝑘𝑘𝑡𝑡 𝜃𝜃𝑡𝑡 𝑑𝑑𝑡𝑡 𝜃𝜃𝑡𝑡 platform. This indicates the state of the connection between them. 𝑘𝑘𝑝𝑝 𝜃𝜃𝑝𝑝 𝐼𝐼𝑡𝑡 𝜃𝜃𝑡𝑡 𝑑𝑑𝑝𝑝 𝜃𝜃𝑝𝑝 The dynamics of floating wind turbine is analyzed and the mathematic model is established by Lagrange’s dynamical equations to control the pitch 𝑚𝑚𝑝𝑝 𝑔𝑔 𝐼𝐼𝑝𝑝 𝜃𝜃𝑝𝑝 angle of the turbine tower [3]. According to the Lagrange’s dynamical equations, we can obtain the dynamic model of the floating wind turbine. Fig. 1. Dynamic model of floating wind turbine Because the wind turbine has a very small pitch angle under the influence of wind and waves, even in the extreme case, the pitch angle is not more than 10 degrees, the model can be linearized as
(1)
where represents mass; represents the rotational inertia relative to the joint; represents the spring coefficient; represents the damping coefficient; represents the angle to the vertical line; represents the distance from represent the floating platform, tower and TMD the vertical line of the TMD mass block. The subscripts , , respectively. represents the distance from the corresponding mass center to the bottom joint of the tower. In this model, a tuned mass damper model with a magnetorheological damper (MR-TMD) is applied. Then we can reduce the fore-aft pitch load of the tower by controlling the MR damper in TMD. This model is equivalent to the model in FAST-SC [2][3].
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Lei Wang et al. / Energy Procedia 158 (2019) 254–259 Author name / Energy Procedia 00 (2018) 000–000
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2.2. MR damper model The magnetorheological (MR) damper is a semi-active control device. The viscosity of the internal fluid can be effectively controlled by the voltage applied to it, thereby controlling the damping coefficient. In this paper, it is applied to a TMD in floating wind turbine. The magnetorheological damper has a hysteresis effect as a nonlinear friction device. Predecessors have done a lot of work in modeling its nonlinear behavior and various descriptions to its model have been given, for example, Bingham model, Bouc-Wen model, hyperbolic model, etc. One of the modeling methods is proposed by Sakai et al. [8] , which is modified on the basis of the Bouc-Wen model and combined with the LuGre friction model. The LuGre friction model was originally used to describe nonlinear frictional phenomena. Compared with the Bouc-Wen model, this damper model has simpler structure and the number of model parameters has been reduced. The following is an improved MR damper model: (2) 3. Adaptive control design In this part, a simple and convenient semi-active structural control method for floating wind turbine is designed with application of magnetorheological damper. First of all, we regard the damping force of the magnetorheological damper as an active force which is totally controllable, and design the desired active force with the specific state of the wind turbine using the adaptive control method. But we can't completely control the damping force in semiactive control, especially the direction of the force. Therefore, this paper designs a retrogression controller whose function is to turn the control which is obtained above into the control signal which can be realized by the magnetorheological damper. In the process, we need a inverse analysis system of the magnetorheological damper. The system can give the voltage according to the motion velocity and damping force of TMD mass block. 3.1. Design of controllable damping force According to the tower equation in the dynamic model of the wind turbine in (3), the following equation can be obtained. (3) where
.
Now we define the error of the pitch angle of the tower and the generalized error as and . where, is a constant. In practice, we consider the expected value of which is noted as
above to be equal to 0 or a small angle close to 0. Here, the convergence of can guarantee the convergence of and at the same time. Thus, and are convergent. In order to converge the generalized error , the following Lyapunov function is obtained
.
And the derivation of it is (4) It is obvious that the inequality , and is the maximum of . Thus, according to the Young’s inequality, we can get
is true, where
,
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Lei Wang et al. / Energy Procedia 158 (2019) 254–259 Author name / Energy Procedia 00 (2018) 000–000
257
(5) Now let’s induce the adaptive control law coefficient . Make (constant); is the estimation of , is the estimation error. In order to get the estimation error to zero, the following Lyapunov function is . The derivation is obtained (6) Combining the two Lyapunov functions, equation, we obtain
. Take the derivative of it, and plug in (5) and (6) into the
(7) The controller is designed as (8) . where the adaptive law coefficient is determined by The controller equation is substituted into equation (7) and the stability of the controller is proved as below.
where
and
proved. Thus , the controller can converge
. Lyapunov function satisfies the form of and
, so stability is
.
3.2. Inverse analysis system In this article, we need to get the control voltage by an inverse analysis system of the MR damper, which can calculate the voltage with the desired damping force designed above and the velocity of the mass in TMD. So the can meet with the desired damping force by controlling the voltage on the MR damper. real damping force In addition, because the internal state variable of the MR damper is unknown, we need an observer to estimate the value of it. The estimation for is noted as . (9) In this paper, we assume that the parameters in the magnetorheological damper are known and uses the parameters in table 1. In practice, the parameters of MR damper can be identified according to [13] and [14]. So
Lei Wang et al. / Energy Procedia 158 (2019) 254–259 Author name / Energy Procedia 00 (2018) 000–000
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5
(10)
where
is a small constant. The purpose of using
here is to avoid the situation that the divisor is 0.
3.3. Design of the retrogression controller is designed as an active control force, but we cannot fully control the In the previous part, the control force damping force in semi-active control. Sometimes the control force designed by the adaptive control method cannot be realized by the magnetorheological damper, only the magnitude of the damping force can be adjusted in a certain range. Therefore, this section reduces the control requirement to establish a retrogression controller to produce a control signal which can be realized by semi-active control. The retrogression controller is designed as follow. If
(
and
) or (
and
)
and ) or ( and ) If ( else represents the maximum of control voltage , denotes the voltage obtained by the inverse analysis where . means the damping force while the system with the relative velocity and the desired control force at the same velocity; is the damping force while the control voltage is 0 at the same control voltage is velocity. 4. Simulation Fig. 2 shows the pitching angle of the floating platform. It can be seen from the wind turbine model that the pitch angle of the platform directly affects the motion state of the entire wind turbine. In this paper, the control of the pitch angle of the tower is considered, and the pitch angle of the platform is regarded as the disturbance.
Fig. 2. Pitch angle of the platform
Fig. 4. Damping force of passive TMD and MR-TMD
Fig. 3. Passive TMD vs. MR-TMD
Fig. 5. Load comparison with MR-TMD and passive TMD
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Lei Wang et al. / Energy Procedia 158 (2019) 254–259 Author name / Energy Procedia 00 (2018) 000–000
259
Fig. 3 exhibits the comparison between the pitch angle of the floating wind turbine tower with passive TMD and semi-active MR-TMD in the nacelle. As we can see, the MR-TMD makes the curve smoother. And as time goes, the vibration of the angle in local curve decreases a lot. In Fig. 4, the damping force of passive TMD and MR-TMD is compared. The damping force of passive TMD is just between ± 6000N. It can be seen that the damping force of the magnetorheological damper increases significantly under voltage control. In Fig. 5, the load of the tower using a semi-active structural control with a MR-TMD and a passive structural control with a TMD are compared. We can see that in the semi-active control with a magnetorheological damper, the tower bending load is obviously smaller. The addition of the semi-active damping force reduces the vibration of the tower, and the angular acceleration of the tower is not as violent as the passive structural control. 5. Conclusion The semi-active structural control of floating wind turbine is studied in this paper. The magnetorheological damper is used in TMD replacing the normal damper. The obtained MR-TMD is placed in the nacelle of the floating wind turbine. The damping force can be controlled by the voltage applied to the magnetorheological damper. In order to achieve the purpose of vibration and load reduction, a simple semi-active control method is designed. We used adaptive control method to design an active control force and then designed the retrogression controller to convert it into a voltage signal that can be applied to the MR damper. The simulation results show that the MRTMD can reduce the bending load of the tower effectively. The future work can be load mitigation by applying MR-TMD to the floating platform of the floating wind turbine, which can also reduce the pitching load of the tower. We can consider of installing MR-TMD both in the nacelle and the floating platform, so that the structure vibration and load caused by wind and waves can be dealt with at the same time, and the effect of load reduction may be better. Acknowledgements This work presented herein was funded by Pilot Feasibility of Renewable Energy Integrated with Energy Storage in Buildings (FREE) and Integrating Renewable Energies and Storage Technologies into residential, office and industry buildings: towards near zero energy targets (iREST). References [1] [2] [3] [4] [5] [6] [7] [8]
Matthew A. Lackner, Mario A. Rotea. Passive structural control of offshore wind turbines. Wind Energ. 2011, 14, 373–388. Gordon Stewart, Matthew Lackner. Offshore wind turbine load reduction employing optimal passive tuned mass damping systems. IEEE transactions on control systems technology, 2013, 21(4), 1090-1104. Er-Ming He, Ya-Qi Hu, Yang Zhang. Optimization design of tuned mass damper for vibration suppression of a barge-type offshore floating wind turbine. Engineering for the Maritime Environment, 2017, 231(1), 302–315. Shane Colwell, Biswajit Basu. Tuned liquid column dampers in offshore wind turbines for structural control. Engineering Structures, 2009, 31, 358–368. Yaqi Hu, Erming He. Active structural control of a floating wind turbine with a stroke-limited hybrid mass damper. Journal of Sound and Vibration, 2017, 410, 447-472. Gordon M. Stewart, Matthew A. Lackner. The effect of actuator dynamics on active structural control of offshore wind turbines. Engineering Structures, 2011, 33, 1807–1816. Xianwei Li, Huijun Gao. Load mitigation for a floating wind turbine via generalized H∞ structural control. IEEE transactions on industrial electronics, 2016, 63(1), 332-342. Chiharu Sakai, Hiromitsu Ohmori, Akira Sano. Modeling of MR damper with hysteresis for adaptive vibration control. Proceedings of the 42nd IEEE Conference on Decision and Control, 2003, 3840-3845.
ScienceDirect ScienceDirect
Energyonline Procedia 00 (2018) 000–000 Available onlineatat www.sciencedirect.com Available www.sciencedirect.com Energy Procedia 00 (2018) 000–000
ScienceDirect ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Energy (2019) 000–000 254–259 EnergyProcedia Procedia158 00 (2017) www.elsevier.com/locate/procedia
10th International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong Kong, 10th International Conference on Applied Energy China(ICAE2018), 22-25 August 2018, Hong Kong, China
Adaptive Structural Control of Floating Wind Turbine with The Structural 15th International Symposium on District Heating Cooling with Adaptive Control of Floating Wind and Turbine Application of MR Damper Application of MR Damper Assessing a,the feasibilitya of usinga the heat demand-outdoor Lei Wanga,*, Zhaohua Lianga, Ming Caia, Yang Zhangbb, Jinyue Yanbb Lei Wang *, Zhaohua , Ming Cai district , Yang Zhang Yan forecast temperature function forLiang a long-term heat, Jinyue demand College of Automation, Chongqing University, Chongqing 400044, China a
Automation, Chongqing University, 400044, China SE-100 44, Sweden School of ChemicalaCollege Science of and Engineering, KTH Royal Institute Chongqing of Technology, Stockholm a,b,c a a b c b School of Chemical Science and Engineering, KTH Royal Institute of Technology, Stockholm SE-100 44, Sweden b
I. Andrić a
*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Correc
IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b
Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Abstract c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France Abstract Floating wind turbine has become the most promising technology for deep-sea wind power generation. Therefore, some means to Floating wind turbineload has become the most technology fordeveloping. deep-sea wind power generation. Therefore, some control means to reduce the structural for stabilizing thepromising wind turbine has been In this paper, a semi-active structural is reduce the for stabilizing the wind hasmagnetorheological been developing. In(MR) this paper, a semi-active structural is realized bystructural replacingload the damper in passive TMDturbine with the damper. The damping force ofcontrol the MR Abstract realized by be replacing with (MR) damper. Theisdamping of includes the MR damper can changedthe bydamper alteringinthepassive voltageTMD applied to the it. Amagnetorheological simple and convenient control method designed,force which damper can be changed by altering the voltage applied to it.The A simple and convenient method is designed, includes adaptive control force design and retrogression controller. simulation results showcontrol that the semi-active controlwhich method has a District control heatingforce networks commonly addressed in the literature as results one of show the most effective solutions for decreasing adaptive designare and retrogression controller. The simulation that the semi-active control method hasthe a good damping effect, which mitigates much of the structural load with respect to the passive structural control. greenhouse emissions the building These systems investments which are returned through the heat good dampinggas effect, whichfrom mitigates much ofsector. the structural load withrequire respecthigh to the passive structural control. sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, Copyright © 2018 Elsevier Ltd. All rights reserved. © 2019 The Published by Elsevier Ltd. prolonging the investment return Copyright ©Authors. 2018 Elsevier Ltd. Allperiod. rights reserved. Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied This ismain an open access article under the CCthe BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) The scope of this paper is to assess feasibility using the heat demand – outdoor temperature Conference function for on heatApplied demand Selection and peer-review under responsibility of the of scientific committee of the 10th International Energy (ICAE2018). Peer-review under responsibility of thelocated scientific committee of ICAE2018 The as 10th Conference forecast. The district of Alvalade, in Lisbon (Portugal), was –used a International case study. The district on is Applied consistedEnergy. of 665 Energy (ICAE2018). buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district Keywords: floating wind turbine; magnetorheological damper; structural control renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were Keywords: floating wind turbine; magnetorheological damper; structural control compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications 1. Introduction error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation 1.(the Introduction scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). Wind is one of the increased flourishing energy sources in theupworld. wind aretofar The valuepower of slope coefficient on renewable average within the range of 3.8% to 8% Offshore per decade, that resources corresponds the Wind power is onethat of on the land, flourishing renewable energy sources in world. Offshore wind resources are far more abundant than especially where farthe away fromseason thethe coast. Floating turbines used to decrease in the number of heating hours of 22-139h during heating (depending on thewind combination ofare weather and more abundant thanconsidered). that on sea land, especially where away from the coast. Floating wind turbines used to capture wind energy in deep areas. Its structure is far more complex than theforonshore wind and are it represent renovation scenarios On the other hand, function intercept increased 7.8-12.7% perturbines decade (depending on the capture wind energy in deep sea areas. Its structure is to more complex than the onshore wind turbines and it represent the highest level of The wind power technology today. Compared to the the function onshore wind turbines, the floating one has extra coupled scenarios). values suggested could be used modify parameters for the scenarios considered, and the highest level of wind power technology today. Compared to the onshore wind turbines, the floating one has extra improve the accuracyitofisheat demand estimations. motions. Therefore, susceptible to wind and waves, and large structural load may be produced.
motions. Therefore, it is susceptible to wind and waves, and large structural load may be produced.
© 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Tel.: +86-136-2970-5707 . * E-mail Corresponding Tel.: +86-136-2970-5707 . address:author. [email protected] Keywords: Heat demand; Forecast; Climate change E-mail address: [email protected]
1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. 1876-6102 Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the 10th International Conference on Applied Energy (ICAE2018). Selection and peer-review under responsibility the scientific Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. 10.1016/j.egypro.2019.01.085
2
Lei Wang et al. / Energy Procedia 158 (2019) 254–259 Author name / Energy Procedia 00 (2018) 000–000
255
At present, a lot of work has been done for the load mitigation control of wind turbines by many researchers. In the field of floating wind turbine, most current structural control methods are passive structure control. Lackner and Rotea [1] developed FAST-SC and used a passive tuned mass damper (TMD) in the nacelle of a barge type floating wind turbine. Stewart and Lackner [2] had established a linear model of mono-pile stationary wind turbine and three kinds of floating wind turbines with passive TMD. He et al. [3] established a linear model of barge type floating wind turbine with passive TMD in the nacelle. Colwell and Basu [4] studied the effect of TLCD on fatigue load in mono-pile wind turbine. Some researchers use active structural control. Hu and He [5] used a stroke-limited hybrid mass damper in nacelle of floating wind turbine. Stewart and Lackner [6] studied the influence of actuator dynamics and control-structure interaction on active structural control. Li and Gao [7] used the active structural control in the floating platform and designed a static output-feedback active structural controller with the generalized H∞ method. Semi-active structural control has many advantages over passive and active structural control. In this paper, a magnetorheological (MR) damper is used to replace the damper in TMD to realize a semi-active structural control. The TMD with magnetorheological damper (MR-TMD) has good performance, which can be placed in the nacelle of the floating wind turbine for structural control and achieve the purpose of load reduction. The remainder of this paper is as follows. In section 2, we establish the dynamic models of the floating wind turbine and the MR damper. The active control force and a retrogression controller are designed in section 3. Section 4 simulate the motion and load of the turbine tower and good results are obtained. We summarize the paper in section 5. 2. Dynamic model 2.1. Modeling of floating wind turbine
𝑚𝑚𝑡𝑡𝑚𝑚𝑑𝑑 𝑔𝑔
𝐹𝐹𝑚𝑚𝑟𝑟
The objective of this paper is to mitigate the fluctuation of the fore-aft pitch angle of the floating wind turbine. Fig. 1 shows the state of the floating wind turbine under the influence of wind and waves. The joint between the 𝑚𝑚𝑡𝑡 𝑔𝑔 tower bottom and the floating platform is regarded as the reference point. There are elastic moment and damping moment between the tower and the 𝑘𝑘𝑡𝑡 𝜃𝜃𝑡𝑡 𝑑𝑑𝑡𝑡 𝜃𝜃𝑡𝑡 platform. This indicates the state of the connection between them. 𝑘𝑘𝑝𝑝 𝜃𝜃𝑝𝑝 𝐼𝐼𝑡𝑡 𝜃𝜃𝑡𝑡 𝑑𝑑𝑝𝑝 𝜃𝜃𝑝𝑝 The dynamics of floating wind turbine is analyzed and the mathematic model is established by Lagrange’s dynamical equations to control the pitch 𝑚𝑚𝑝𝑝 𝑔𝑔 𝐼𝐼𝑝𝑝 𝜃𝜃𝑝𝑝 angle of the turbine tower [3]. According to the Lagrange’s dynamical equations, we can obtain the dynamic model of the floating wind turbine. Fig. 1. Dynamic model of floating wind turbine Because the wind turbine has a very small pitch angle under the influence of wind and waves, even in the extreme case, the pitch angle is not more than 10 degrees, the model can be linearized as
(1)
where represents mass; represents the rotational inertia relative to the joint; represents the spring coefficient; represents the damping coefficient; represents the angle to the vertical line; represents the distance from represent the floating platform, tower and TMD the vertical line of the TMD mass block. The subscripts , , respectively. represents the distance from the corresponding mass center to the bottom joint of the tower. In this model, a tuned mass damper model with a magnetorheological damper (MR-TMD) is applied. Then we can reduce the fore-aft pitch load of the tower by controlling the MR damper in TMD. This model is equivalent to the model in FAST-SC [2][3].
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2.2. MR damper model The magnetorheological (MR) damper is a semi-active control device. The viscosity of the internal fluid can be effectively controlled by the voltage applied to it, thereby controlling the damping coefficient. In this paper, it is applied to a TMD in floating wind turbine. The magnetorheological damper has a hysteresis effect as a nonlinear friction device. Predecessors have done a lot of work in modeling its nonlinear behavior and various descriptions to its model have been given, for example, Bingham model, Bouc-Wen model, hyperbolic model, etc. One of the modeling methods is proposed by Sakai et al. [8] , which is modified on the basis of the Bouc-Wen model and combined with the LuGre friction model. The LuGre friction model was originally used to describe nonlinear frictional phenomena. Compared with the Bouc-Wen model, this damper model has simpler structure and the number of model parameters has been reduced. The following is an improved MR damper model: (2) 3. Adaptive control design In this part, a simple and convenient semi-active structural control method for floating wind turbine is designed with application of magnetorheological damper. First of all, we regard the damping force of the magnetorheological damper as an active force which is totally controllable, and design the desired active force with the specific state of the wind turbine using the adaptive control method. But we can't completely control the damping force in semiactive control, especially the direction of the force. Therefore, this paper designs a retrogression controller whose function is to turn the control which is obtained above into the control signal which can be realized by the magnetorheological damper. In the process, we need a inverse analysis system of the magnetorheological damper. The system can give the voltage according to the motion velocity and damping force of TMD mass block. 3.1. Design of controllable damping force According to the tower equation in the dynamic model of the wind turbine in (3), the following equation can be obtained. (3) where
.
Now we define the error of the pitch angle of the tower and the generalized error as and . where, is a constant. In practice, we consider the expected value of which is noted as
above to be equal to 0 or a small angle close to 0. Here, the convergence of can guarantee the convergence of and at the same time. Thus, and are convergent. In order to converge the generalized error , the following Lyapunov function is obtained
.
And the derivation of it is (4) It is obvious that the inequality , and is the maximum of . Thus, according to the Young’s inequality, we can get
is true, where
,
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Lei Wang et al. / Energy Procedia 158 (2019) 254–259 Author name / Energy Procedia 00 (2018) 000–000
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(5) Now let’s induce the adaptive control law coefficient . Make (constant); is the estimation of , is the estimation error. In order to get the estimation error to zero, the following Lyapunov function is . The derivation is obtained (6) Combining the two Lyapunov functions, equation, we obtain
. Take the derivative of it, and plug in (5) and (6) into the
(7) The controller is designed as (8) . where the adaptive law coefficient is determined by The controller equation is substituted into equation (7) and the stability of the controller is proved as below.
where
and
proved. Thus , the controller can converge
. Lyapunov function satisfies the form of and
, so stability is
.
3.2. Inverse analysis system In this article, we need to get the control voltage by an inverse analysis system of the MR damper, which can calculate the voltage with the desired damping force designed above and the velocity of the mass in TMD. So the can meet with the desired damping force by controlling the voltage on the MR damper. real damping force In addition, because the internal state variable of the MR damper is unknown, we need an observer to estimate the value of it. The estimation for is noted as . (9) In this paper, we assume that the parameters in the magnetorheological damper are known and uses the parameters in table 1. In practice, the parameters of MR damper can be identified according to [13] and [14]. So
Lei Wang et al. / Energy Procedia 158 (2019) 254–259 Author name / Energy Procedia 00 (2018) 000–000
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(10)
where
is a small constant. The purpose of using
here is to avoid the situation that the divisor is 0.
3.3. Design of the retrogression controller is designed as an active control force, but we cannot fully control the In the previous part, the control force damping force in semi-active control. Sometimes the control force designed by the adaptive control method cannot be realized by the magnetorheological damper, only the magnitude of the damping force can be adjusted in a certain range. Therefore, this section reduces the control requirement to establish a retrogression controller to produce a control signal which can be realized by semi-active control. The retrogression controller is designed as follow. If
(
and
) or (
and
)
and ) or ( and ) If ( else represents the maximum of control voltage , denotes the voltage obtained by the inverse analysis where . means the damping force while the system with the relative velocity and the desired control force at the same velocity; is the damping force while the control voltage is 0 at the same control voltage is velocity. 4. Simulation Fig. 2 shows the pitching angle of the floating platform. It can be seen from the wind turbine model that the pitch angle of the platform directly affects the motion state of the entire wind turbine. In this paper, the control of the pitch angle of the tower is considered, and the pitch angle of the platform is regarded as the disturbance.
Fig. 2. Pitch angle of the platform
Fig. 4. Damping force of passive TMD and MR-TMD
Fig. 3. Passive TMD vs. MR-TMD
Fig. 5. Load comparison with MR-TMD and passive TMD
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Lei Wang et al. / Energy Procedia 158 (2019) 254–259 Author name / Energy Procedia 00 (2018) 000–000
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Fig. 3 exhibits the comparison between the pitch angle of the floating wind turbine tower with passive TMD and semi-active MR-TMD in the nacelle. As we can see, the MR-TMD makes the curve smoother. And as time goes, the vibration of the angle in local curve decreases a lot. In Fig. 4, the damping force of passive TMD and MR-TMD is compared. The damping force of passive TMD is just between ± 6000N. It can be seen that the damping force of the magnetorheological damper increases significantly under voltage control. In Fig. 5, the load of the tower using a semi-active structural control with a MR-TMD and a passive structural control with a TMD are compared. We can see that in the semi-active control with a magnetorheological damper, the tower bending load is obviously smaller. The addition of the semi-active damping force reduces the vibration of the tower, and the angular acceleration of the tower is not as violent as the passive structural control. 5. Conclusion The semi-active structural control of floating wind turbine is studied in this paper. The magnetorheological damper is used in TMD replacing the normal damper. The obtained MR-TMD is placed in the nacelle of the floating wind turbine. The damping force can be controlled by the voltage applied to the magnetorheological damper. In order to achieve the purpose of vibration and load reduction, a simple semi-active control method is designed. We used adaptive control method to design an active control force and then designed the retrogression controller to convert it into a voltage signal that can be applied to the MR damper. The simulation results show that the MRTMD can reduce the bending load of the tower effectively. The future work can be load mitigation by applying MR-TMD to the floating platform of the floating wind turbine, which can also reduce the pitching load of the tower. We can consider of installing MR-TMD both in the nacelle and the floating platform, so that the structure vibration and load caused by wind and waves can be dealt with at the same time, and the effect of load reduction may be better. Acknowledgements This work presented herein was funded by Pilot Feasibility of Renewable Energy Integrated with Energy Storage in Buildings (FREE) and Integrating Renewable Energies and Storage Technologies into residential, office and industry buildings: towards near zero energy targets (iREST). References [1] [2] [3] [4] [5] [6] [7] [8]
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