semi-active pendulum to control offshore wind turbine vibrations

Semi-Active Pendulum to Control Offshore

Wind Turbine Vibrations

Suzana M. Avila

Pedro V. B. Guimarães

University of Brasilia – Brazil

May 27th 2015

Presentation Topics

• Justification;

• Problems relating;

• Tuned mass damper;

• Goals;

• Problem description;

• Analysis and results;

• Final remarks.

Justification

• Wind farms located atthe seaboard, the socalled offshore windturbines, have someadvantages compared tothe onshore ones;

• Wind turbine towersgenerally are slender andflexible due to its highaltitude and can presentexcessive vibrations;

Structural Control

• An alternative widely studied in the last years to reduce excessive vibration is the structural control.

• It consists in the addition of external devicessuch as dampers or application of externalforces that change properties of stiffnessand/or damping.

Semi-active control

• Semi-active structuralcontrol do not add energy tothe structure and itsproperties can be varieddynamically.

• The semi-active systems aremore reliable and morerobust than active systems.

• These are controllablepassive devices since theydon’t apply any additionalforce to the structure.

Objective

• a semi-active tuned mass damper (TMD)pendulum is proposed to control excessivevibration of an offshore floating wind turbine.

• A bang bang control strategy was considered,TMD stiffness and damping values werecalculated trough optimal control theory.

Floating Offshore Wind Turbine

Hywind, Norway

Musial W, Butterfield S, Ram B. Energy from offshore wind. In: Offshore technology conference, Houston, Texas; 2006

Floating Offshore Wind Turbine

Structural Model

• The structure is modeled as an invertedpendulum discrete model.

• This model is presented as a preliminarymodel for structural control alternativesstudies, the results serve as a basis for realstructures design with a more carefulmodeling.

Wind force

Structural Model

Simplifying Assumptions

• Angular amplitude is kept within boundariesfor a linear behavior;

• A two dimension vibration system isconsidered;

• Wind loading is considered as a concentratedforce applied at the tower’s top;

• Wave loading and blade’s influence are disregarded;

Mathematical Formulation

𝑀1,1 𝑀1,2 𝑀1,3

𝑀2,1 𝑀2,2 𝑀2,3

𝑀3,1 𝑀3,2 𝑀3,3

𝜃 𝜃𝑑 𝑢

+

𝐶1,1 𝐶1,2 𝐶1,3𝐶2,1 𝐶2,2 𝐶2,3𝐶3,1 𝐶3,2 𝐶3,3

𝜃 𝜃𝑑 𝑢

+

𝐾1,1 𝐾1,2 𝐾1,3𝐾2,1 𝐾2,2 𝐾2,3𝐾3,1 𝐾3,2 𝐾3,3

𝜃𝜃𝑑𝑢

=𝐹 𝑡00

𝑴

𝜃 𝜃𝑑 𝑢

+C 𝜃 𝜃𝑑 𝑢

+ 𝑲𝜃𝜃𝑑𝑢

=𝐹 𝑡00

Equations of Motion

Mathematical Formulation

Space-State Equations

)()()()( tttt EfBuAzz

)(

)()(

t

tt

x

xz

CMKM

A11

0 I

DM

B1

0

HM

E1

0

Bang Bang Control

• The Bang Bang control, also called control ON / OFF control, is a feedback controller that suddenly changes between two limit values.

• This device compares the input with a target value, so that if the output exceeds the input, the actuator is switched off, otherwise, the actuator is now on.

• Low cost controller, further its simplicity and convenience.

Control Strategy

• The control strategy is to control structural response using bang bang control, varying pendulum TMD stiffness kd and damping cd, switching from one extreme set of values to the other.

• The optimal parameter values (kd and cd) are obtained based on linear optimal control algorithm (linear quadratic regulator – LQR)

Control Strategy

• First a LQR controller is designed assuming an activependulum TMD system and neglecting the actuatordynamics.

• The optimal actuator force u(t) is defined by the gain matrixG.

• The actuator force is not really applied at the TMD, this forceis applied through a semi-active damper.

Linear Optimal Control

• The linear optimal control problem consist in finding the control vector u(t) that minimizes the performance index J subject to state equations constraint.

• In structural control, the performance index is usually chosen as a quadratic function in z(t) and u(t), as follows

ft

t

dtttttJ

0

)()()()( RuuQzzTT

Numerical Results

Parametric Study

Rating 5 MWRotor, hub diameter 126, 3 m

Hub Height 90 mRotor mass 110,000 kgTower Mass 347,460 kg

Stewart, G.M., Lackner, M.A., 2011, “The effect of actuator dynamics on active structural control of offshore wind turbines”, Engineering Structures 33 (2011) 1807-1816

Offshore Wind Turbine Properties

𝑲𝒅 𝑪𝒅

OFF 5.9 x 106 N/m 4.4 x 105 Ns/m

ON(HSA) 5.9292 x 106 N/m 2.1654 x 106 Ns/m

ON(WNSA) 5.9112 x 106 N/m 1.1886 x 106 Ns/m

A time domain analysis was performed, four situations were considered for analysis:

1. structure without control

2. system with passive TMD (sTMD) considered as the semi-active turned OFF

3. system with semi-active ON, with optimum parameter for harmonic loading (HSA)

4. system with semi-active ON, with optimum parameter for white noise loading (WNSA).

Numerical Results

• Efficiency relation of the semi-active device in ON and OFF position (sTMD). This efficiency is measured by rms values

Numerical Results

𝐸𝐹𝐹 =𝜃𝑂𝐹𝐹 −𝜃𝑂𝑁

𝜃𝑂𝐹𝐹x 100 %

Numerical Results

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-60

-40

-20

0

20

40

60ON(HSA) VS OFF

% R

educ

tion

of O

N(H

SA

)

Wind Frequency

0.66 rad/s

0.74 rad/s

Numerical Results

0 50 100 150 200 250 300-4

-3

-2

-1

0

1

2

3

4

5x 10

-4

time (s)

(

rad)

Wind frequency = 0.66 rad/s

ON(HSA)

OFF

0 50 100 150 200 250 300-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5x 10

-4

time (s)

(

rad)

Wind frequency = 0.74 rad/s

ON(HSA)

OFF

Numerical Results

0 50 100 150 200 250 300-4

-3

-2

-1

0

1

2

3

4

5x 10

-4

time (s)

(

rad)

Wind frequency = 0.66 rad/s

Without Control

ON(HSA)

OFF

0 50 100 150 200 250 300

-2

-1

0

1

2

3

x 10-4

time (s)

(

rad)

Wind frequency = 0.74 rad/s

Without Control

ON(HSA)

OFF

Numerical Results

0 50 100 150 200 250 300-1.5

-1

-0.5

0

0.5

1

1.5

2x 10

-4 White noise wind force

Time (s)

(r

ad)

ON(HSA)

OFF

Numerical Results

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-20

-10

0

10

20

30

40

50ON(WNSA) VS OFF

% R

educ

tion

of O

N(W

NS

A)

Wind Frequency

0.66 rad/s

0.74 rad/s

Numerical Results

0 50 100 150 200 250 300-4

-3

-2

-1

0

1

2

3

4

5x 10

-4

time (s)

(

rad)

Wind frequency = 0.66 rad/s

ON(WNSA)

OFF

0 50 100 150 200 250 300-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5x 10

-4

time (s)

(

rad)

Wind frequency = 0.74 rad/s

ON(WNSA)

OFF

Numerical Results

0 50 100 150 200 250 300-1.5

-1

-0.5

0

0.5

1

1.5

2x 10

-4 White noise wind force

Time (s)

(r

ad)

ON(WNSA)

OFF

Bang Bang Simulation

0 50 100 150 200 250 300 350 400 450 5001

1.5

2

2.5

3

3.5

4

4.5

5

5.5x 10

4 Harmonic Wind Force

Time (s)

(

rad)

𝜔 = 0.66 𝑟𝑎𝑑/𝑠 𝜔 = 0.74 𝑟𝑎𝑑/𝑠 𝜔 = 1.5 𝑟𝑎𝑑/𝑠

Bang Bang Simulation

0 50 100 150 200 250 300 350 400 450 500-4

-3

-2

-1

0

1

2

3

4

5x 10

-4

Time (s)

(

rad)

Harmonic Wind Force

BangBang

OFF

ON

T

Bang Bang Simulation

0 50 100 150 200 250 300 350 400 450 500-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1x 10

5 White Noise Wind Force

Time (s)

(

rad)

Bang Bang Simulation

0 50 100 150 200 250 300 350 400 450 500-2

-1.5

-1

-0.5

0

0.5

1

1.5

2x 10

-4

Time (s)

(

rad)

White Noise Wind Force

BangBang

OFF

ON

Conclusions

• A bang bang (ON/OFF) control strategy was considered, semi-activeTMD stiffness and damping values were calculated trough optimalcontrol theory.

• Since the excitation is ignored in control algorithm, two loadingcases were considered: harmonic and white noise, leading to a setof two kd and cd parameters (HSA and WNSA).

• It was concluded that HSA parameters are the best choice forsetting the semi-active TMD ON position.

• Satisfactory results were found out compared to those of passiveTMD pendulum.

• Semi-active controller presents a good performance on reducingexcessive vibration amplitudes.

• Further studies would be necessary in order to test other controlstrategies to semi-active controller design.

Thank you!

• Contact:Suzana M. Avila – avilas@unb.brPedro V. B. Guimarães – pedrobarca@hotmail.com