CLBottasso Short Course PartII Wind Turbine Control

8/6/2019 CLBottasso Short Course PartII Wind Turbine Control

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Short Course on Wind Turbine

Modeling and Control- Part II: Control -

C.L. BottassoPolitecnico di Milano

Milano, Italy

Korea Institute of Machinery and Materials

&Kangwon National UniversityOctober 18-19, 2007

Short Course on Wind Turbine

Modeling and Control- Part II: Control -

C.L. BottassoPolitecnico di Milano

Milano, Italy

Korea Institute of Machinery and Materials

&Kangwon National UniversityOctober 18-19, 2007


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Control System Architectureontrol System Architecture


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POLITECNICO di MILANO DIA

Control System Architectureontrol System Architecture

Windindturbineurbine

SensorsPositions, speeds,accelerations, stresses,strains, temperature,electrical & fluidcharacteristics, etc.

SensorsPositions, speeds,accelerations, stresses,strains, temperature,electrical & fluidcharacteristics, etc.

SupervisorChoice of operating condition: Start up Power production Emergency shut-down

SupervisorChoice of operating condition:

Start up Power production Emergency shut-down Active control

systemControl strategy

Active controlsystemControl strategy

ObserversWind, tower & blades

ObserversWind, tower & blades

Wind farmsupervisorWind farmsupervisor

Communication and reportingommunication and reporting

ActuatorsActuator controlsystem

ActuatorsActuator controlsystem


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Supervisory Control Systemupervisory Control System

Main tasksain tasks : Operational managing and monitoring Diagnostics, safety

Communication, reporting and data logging

Operational statesperational states : Idling Start Up Normal power production Normal shut down

Emergency shut down

Main input dataain input data : Wind speed Rotor speed

Blade pitch Electrical power Temperatures in critical area Accelerations

but also Stresses, strains (blades, tower) Position, speed (yaw, blade, actuators, teeteringangle, rotor tilt, )

Fluid properties and levels Electrical systems (voltages, grid characteristics, ) Icing conditions, humidity, lighting,


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Supervisory Control Systemupervisory Control System

Idlingdling Power

production

Power

productiontart uptart up

Normal shut downormal shut down

Emergency

shut down

Emergencyshut down

V > V cut-inV > V cut-in RPM > cut-in

RPM > cut-in

V > V cut-offV > V cut-off

V < V cut-inV < V cut-in

Failures Overspeed & high rotor accel.

Vibrations

Failures Overspeed & high rotor accel.

Vibrations

Representative operational state monitoring logic:


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Control Strategiesontrol Strategies


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Basicasic wind turbine control strategies and power curvesower curves : Constant TSR strategy Constant rotor speed strategy Below and above rated speed control Variable speed pitch-torque regulated wind turbine Stall and yaw/tilt control



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C P

Power coefficient:

Tip speed ratio (TSR):

C P =P

1/ 2AV 3

= RV

C P = C P ( , ,Re,M )

C P

= const.


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C P


Constant rotor speedonstant rotor speed : = const. =

V = R

V

C

P

V = R/

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C P

max

= const.

Direct grid connection:Generator provides whatever torque requiredto operate at or near given angular speed

V aero cut in =

R/ max < V cut in


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Constant TSRonstant TSR : = const. = = V

R

P =12

AV 3C P

=

V

Constant rotorspeed strategy

Constant TSR strategy

= const. =

V

V r ( const. )

Indirect grid connection: Through power electronic converter Allows for rapid control of generator torque

V, C P ( const. ) C P ( const. )


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V

P

P r

= Constant TSR strategy (cubic)

= Constant rotor speed strategy

= const.

Powerower -wind speed curveind speed curve :

V aero cut in ( const. ) V aero cut in ( const. )

Power deficit for constantspeed wrt constant TSR

V r ( const. )

V r ( const. )


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P

P P

V V

V

1 2

=

= =

=

1

= 2

Constant rotor speed strategy 2 vs.onstant rotor speed strategy 2 vs.strategy 1trategy 1 : Higher cut in speed

Lower wind speed to reach rated power Smaller power deficit


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P P

V V

= =

= 1

= 2

Annual energy yield: E = Y Z V

out

V inP (V )f w dV

f w f w

Weibull distribution

E

V

= 2

= 1Constant rotor speed strategy 2vs. strategy 1:

Smaller power deficit wrt toconstant TSR, but at improbablewind speeds Higher energy yield


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Control above rated speedontrol above rated speed :

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V > V r

C P

C P

Constant power constant rotor speed curve(cubic)

C P = C

P

3

P = P r = 12AV 3C P ( , ) = const.

= = const.

T =P = const.

= R

V


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V


P

V r

P r

=

V r

V V r

V V r

= V /RRegion 2 - below ratedspeed: constant TSRstrategy

Region 3 - above ratedspeed: constant powerstrategy

Below rated speed:torque control

Above rated speed:pitch control

Variableariable -speed pitch/torquepeed pitch/torqueregulated wind turbineegulated wind turbine :

T = 1 / 2ARV 2C P

/ T T = P r /

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C P

V cut outV cut in

Regio

1

No torque to promoterotor acceleration

V

Often, smoothing for mildertransition between regions


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V


P

V r

P r =

Below rated speed:constant TSR strategy

Above rated speed:(roughly) constantpower strategy

Variableariable -speed passivepeed passive -stall/torquetall/torqueregulated wind turbineegulated wind turbine :

Stall region, highdispersion

V r

V V r

V V r

= V /R

Below rated speed:torque control

Above rated speed:torque-stall control

T T = P r /

V


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V


P

V r

P r =

Below rated speed:

constant rotorspeed strategy

Above rated speed:

(roughly) constantpower strategy

Constant-speed passive-regulation wind turbine:

=

Stall region, highdispersion

V

P

V r

P r =

Below rated speed:

constant rotorspeed strategy

Above rated speed:

yaw or tilt rotor toreduce effective wind

=

Stall regulation Yaw/tilt out-of-the-wind

regulation

V

V cos

Rotor disk


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Further wind turbine control goalsurther wind turbine control goals : Fatigue damage reduction in turbulent wind Gust load alleviation Disturbance rejection Resonance avoidance

Actuator duty cycle reduction Periodic disturbance reduction (gravity, wind shear, tower shadow, )

Usually, these goals should be achieved together with the basic controlasic controlstrategiestrategies deriving from the power curves, i.e. Region 2: maximize energy capture Region 3: limit output power to rated value



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Yaw Controlaw ControlOrient the rotor in line with the windn line with the wind field to increase powerNote: some small wind turbine will also yaw out of the wind to reduce loads in high winds

Passiveassive or free yaw, used in small wind turbines:

Activective yaw:- If V < V cut in = no action- If V > V cut in :

- Compute yaw error averaging over window (typically tens of sec.s) to reduce duty cycle- Region 2 = realign if yaw error > yaw threshold 2 (typically ~15 deg)- Region 3 = realign if yaw error > yaw threshold 3 (typically ~8 deg)- Realign at low yaw rate to reduce gyroscopic loads- If yaw error < small threshold (typically a fraction of a deg), engage yaw brake to eliminatebacklash between drive pinion and bull gear

Downwind rotorail fin


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Reduced Modelseduced Models

R d d M d l f M d l B dReduced Models for Model Based


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Reduced Models for Model-BasedControllers


Equationsquations : Drive-train shaft dynamics Elastic tower fore-aft motion Blade pitch actuator dynamics Electrical generator dynamics

Statestates :

Inputsnputs :

T el eT el c T l

J G

J R

c

e

T a

F a

M T , C T , K T

Non-linear collective-only reduced model:

c , T el c

d

d, d, , e , e , T el e

Reduced Models for Model BasedReduced Models for Model Based


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Equations of motionquations of motion :

Tip speed ratio: Wind: (mean wind + turbulence)

(J R + J G ) + T l ( ) + T el e T a ( , e , V w d, V m ) = 0M T d + C T d + K T d F a ( , e , V w d, V m ) = 0

e + 2 e + 2( e c) = 0

T el e + 1 (T el e T el c ) = 0

= R/ (V w d)

V w = V m + V t



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Rotor force and moment coefficientsotor force and moment coefficients :

computed off-line with CpLambdapLambda aero-servo-elastic model, averaging periodic response over one rotor rev

Stored in look-up tables

T a =12

R3C P e ( , e , V m )

(V w d)2

F a =12 R2C F e ( , e , V m )(V w d)2

V m Dependence of and

on mean windaccounts for deformabilityeformability of towerand blades under high winds:

C P e ( , e , V m )C F e ( , e , V m )

C F e ( , e , V m ), C P e ( , e , V m )



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Rigid body Beam Revolute joint Actuator Boundary condition

Blade

Generator

Nacelle inertia

Yaw

actuatorPitchactuator

Torqueactuator

Tower

Equivalenttowerstiffnesses

Equiv

en

sh

s

fne

Equivalent flap hingeand spring

Statestates : 3 flap angles (or blade modal amplitudes) Rotor azimuth Shaft torsion

3 tower angles (fore-aft, side-side, torsion)(or tower modal amplitudes)

Yaw angle

(and their rates)

Inputsnputs :

Examplexample : individual-pitch modelT el c

c1 c2

c3

c1 , c2 , c3 , T el c



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Model linearizationodel linearization : needed for implementation of controllers(e.g. LQR) and model-based observers (e.g. Kalman filter)

Possible approaches: Analytical Automated (e.g. Maple, or directly from software usingAutomatic Differentiation tools like ADOL-C, ADIC, etc.) Numerical, by finite differences

P T

V V V VLinearization trim points

x = f (x , u , p) x = A (x , u , p ) x + B (x , u , p ) u u = u u x = x x

x u p


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Observersbservers


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Tower State Observerower State Observer

q = vv = ( T ) 1 T (a + n w )

Accelerometer

Strain gage

c = 00 q n v

q

n w , n v

Kalmanalman modalodal -based tower observerased tower observer :

Accelerations:

Curvatures: Unknown modal amplitudes: Modal bases: Process & measurement noise:

Remarksemarks : Fore-aft and side-side identification Multiple modal ampl. (sensor number and position for observability) Formulation applicable also to identification of flap-lag blade states


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State space form:

with

Optimal Kalman state estimate:

Filter gain matrix Propagated states and outputs based on accelerometric reading: Curvature reading:

x = Ax + Bu + W n wy = Cx + Du + V n v

x k = x

k + K k (y k y

k )

x = ( q T , v T )T u = a y = c

A = 0 I 0 0 B = 0 C = 00 0 D = 0 W =

0

V = I K k

x k , y

k

y k

b


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Filter warm-up

Tower tip velocity estimation:

S Ob


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Accelerometers

Strain gages

Kalmanalman modalodal -based tower and bladeased tower and bladestate observertate observer :

Compute or measure modal bases for

blades and tower

Integrate tower kinematic equationsfrom accelerations Correct with tower strain gage curvaturereadings Integrate blade kinematic equations

from blade and tower accelerations Correct with blade strain gage curvaturereadings

i d Obi d Ob


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Anemometer: Cup, but also laser, ultrasonic, etc. Measurements highly inaccurate because of

Rotor wake Wake turbulence Nacelle disturbance

Sufficient accuracy for supervision tasks and yaw alignment Not sufficient for sophisticated control law implementation

Need ways to reconstructeconstruct wind blowing on rotor from reliableeliablemeasurementseasurements (pitch setting, rotor speed, etc.)

Wind Observerind Observer

Wi d Obi d Ob


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Extendedxtended Kalmanalman wind observerind observer :

Wind equation: Output measurement torque-balance equation:

Non-linear state-space form:

with

Extended Kalman estimate

with measured output to enforce torque-balance equation

Mean wind reconstructed with moving average on 10 sec window

V w = nw

y = ( J R + J G ) + T l ( ) + T el e T a ( , e , V w d, V m ) + nv

x = f (x, u , n w )y = h(x, u , n v )x = V w

u= (

,

,

e ,

d, V m )T

xk = x

k + K k (yk y

k )

yk = 0

V m

Wi d Obi d Ob


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Hub wind estimation:

Turbulent wind ( m/sec)V m = 15

EOG1-13 case

Wi d Obind Obser er


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Simple mean hub wind reconstruction from torque balance equation

More in general:The rotor system is a sensorensor which responds to temporalemporal as well asspatialpatial wind variations

Model-based interpretation of response can be used for reconstructingvertical and horizontal wind shear for improved rotor control

Example: introduce spatial assumed modes and wind states

V (t, ) = V 0 (t) + V s (t)sin + V c(t)cos

Rotor disk


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Simulation Environmentimulation Environment

Control Laws: Virtual TestingControl Laws: Virtual Testing


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gEnvironmentEnvironment

Virtual plantirtual plant

Sensorensormodelsodels

CpLambdaCpLambda

aero-servo-elastic model

Windgenerator Processnoise

SupervisorupervisorChoice of operating condition:

Start up Power production Normal shut-down Emergency shut-down

Controller

Feedback controllereedback controller PID MIMO LQR RAPC Adaptive reduced model

Linux real-time environment

Kalmanalman filteringilteringWind & tower/blade state estimation

Measurementnoise


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Control Lawsontrol Laws

Control Laws: Three Case Studiesontrol Laws: Three Case Studies


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Case studiesase studies : PID: gain optimization and wind scheduling LQR: handling region 2-3 transition and wind scheduling Adaptive non-linear predictive control A simple LQR approach to cyclic pitch control

Control Laws: Three Case Studiesontrol Laws: Three Case Studies

Control Laws: Optimal PIDontrol Laws: Optimal PID


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Optimal windptimal wind -scheduled PIDcheduled PID :

Tabulated electrical torque

Optimization of gains

based on aeroelastic analyses inCpLambda

c = K p(V m )( ) + K i (V m )

Z t

t

T i

( )d + K d (V m )

T el c = T el c ( )

K p(V m ), K i (V m ), K d (V m )



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Gain optimization procedureain optimization procedure :

For each mean wind in region 3, define cost function

Equivalent fatigue loads for tower and blades

based on rain-flow analysis ( ASTM E 1049-85 ):

Tunable weighting factors:

V m

M eq T

, M eq Bi

J (V m ) = M eq T + M eq Bi =(1 , 3) +Z 600 sec0 w 2e + wd d2 + w ( )2 + wP (P P )2dt

w , wd , w , wP

M eq =

Xi

M mf,i N i /N tot

!1/m



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PID gain optimization procedureID gain optimization procedure (continued):

For each mean wind :

Regard cost as sole function of unknown gains

Minimize cost (using Noesis Optimus): Evaluate cost with CpLambdapLambda aero-servo-elastic model Global optimization (GA) Local refinement (Response Surface + gradient based minimization)

V m

J (V m ) = J (K p(V m ), K i (V m ), K d (V m ))

Optimizerptimizer Global & local algorithms Functional approximators

CpLambdapLambdaAeroelasticresponse inturbulent windfor given gains

K p (V m ) , K i (V m ) , K d (V m )

J (V m )(possible constraints)

Control Laws: MIMO NonLinear-Wind LQRontrol Laws: MIMO NonLinear-Wind LQR


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Control Laws: MIMO NonLinear Wind LQRontrol Laws: MIMO NonLinear Wind LQR

Windind -scheduled MIMO LQRcheduled MIMO LQR : Reduced model in compact form:

where Wind parameterized linear model:

where

Remarksemarks : Model linearized about current mean wind estimate Non-linear dependence on instantaneous turbulent wind Wind not treated as linear disturbance (as commonly done)

x = f (x , u , V w , V m )

x = ( d,

d, , e ,

e , T el e )T

u = ( c , T el c )T

x = A (V w , V m ) x + B (V w , V m ) u

x = x x (V m ) u = u u (V m )

V mV w



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Windind -scheduled MIMO LQRcheduled MIMO LQR (continued):

Regulation cost:

where

MIMO formulation: tracking quantities for reg. 2 & 3:

J =12

Z

0

x T Q x + u T R u

dt

x (V m ), u (V m )

x = x x (V m ), u = u u (V m )



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Windind -scheduled MIMO LQRcheduled MIMO LQR (continued):

Closed loop controller:

with Kalman estimated states and wind

u = K (V w , V m )(x x (V m ))

Control Laws: NonLinear Adaptive Ctrl.ontrol Laws: NonLinear Adaptive Ctrl.


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Design controller which: Can handle nonon -linearitiesinearities of plant Is adaptivedaptive :

- Can adjust to off-design conditions (e.g. ice accretion,specifics of installation, hot-cold air variations, etc.)

- Can correct for unmodeled or unresolved physics and

modeling errors Can handle constraintsonstraints (e.g. max loads in blades or tower) Can be implemented in realeal -timeime (no iterative scheme, fixednumber of operations per activation)

Nonon -linear modelinear model -adaptive predictive controldaptive predictive control



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Control Laws: NonLinear Adaptive Ctrl.pNonon -linear Model Predictive Controlinear Model Predictive Control (NMPC):

Find the control action which minimizes an index of performance,by predicting the future behavior of the plant using a nonon -linearinearreduced modeleduced model .

- Reduced model:

- Initial conditions:- Output definition:

Cost:

with desired goal outputs and controls.

Stability resultstability results : Findeisen et al. 2003, Grimm et al. 2005.

L(y , u ) = ( y y

)T

Q (y y

) + ( u u

)T

R (u u

)

minu ,x ,y

J = Z t 0 + T p

t 0L(y , u ) d t

s.t.: f (x , x , u ) = 0 t [t0 , t 0 + T p]

x (t0) = x 0y = g (x ) t [t0 , t 0 + T p]

()



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FuturePast

Steering window

Prediction window

Prediction errorState tracking error

Control tracking error

t0

t0 t0 + T p

t0 + T s

Computed control u (t)Goal control u (t)

: p .p

Goal response x (t)Predicted response x (t)

Plant response

ex (t)

x 0



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pp

1. Tracking problem

Plant response

3. Reduced model update

Predictive solutions

2. Steering problem

Prediction window

Steering window

Tracking cost

Prediction error

Prediction window

Tracking cost

Steering windowPrediction error

Tracking costPrediction window

Steering window

Prediction error

Goal

response

Predictive modelredictive model -adaptive controldaptive control :

Reduced modeleduced model adaptiondaption : Predict plant response with minimum error (same outputs when same inputs) Self-adaptive (learning) model adjusts to varying operating conditions (ice, air density, terrain, etc.)

Past Futureast Futureast Future

Past Future

Past Future

RAPC: MotivationAPC: Motivation


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For any given problem: wealth of knowledgenowledge and legacyegacy methodswhich perform reasonably well Quest for better performance/improved capabilities: undesirablendesirable

and wastefulasteful to neglect valuable existing knowledgeReference Augmented Predictive Controleference Augmented Predictive Control (RAPCAPC): exploit availablelegacy methods, embedding them in a non-linear model predictiveadaptive control framework

Specifically: Modelodel : augment reduced models to account for unresolved orunmodeled physics Controlontrol : design a non-linear controller augmenting linear ones(MIMO Nonlinear-Wind LQR) which are known to provide a minimumlevel of performance about certain linearized operating conditions

RAPC: MotivationAPC: Motivation


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Approach:pproach: Choose a reference model / reference control laweference model / reference control law Augment the reference using an adaptivedaptive parametric functionarametric function Adjustdjust the function parameters to ensure good approximation ofood approximation ofthe actual system / optimal control lawhe actual system / optimal control law (parameter identification)

Reasons for using a reference model / controleasons for using a reference model / control: Reasonable predictions / controls even before any learningven before any learning hastaken place (otherwise would need extensive pre-training) Easier and faster adaption: the defect is typically a small quantitymall quantity ,if the reference solution is well chosen

RAPC: Reduced Model IdentificationAPC: Reduced Model Identification


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Plantlant

u , V w u , V w

Reduced modeleduced modelAugmentedugmentedreduced modeleduced model

+ Neural NetworkNeural Network

Dissimilaroutputs

Same wind,same inputs u , V w

Same wind,same inputs

Similaroutputs

Trained on-lineto minimizemismatch

x

ex x

ex

The principle of reference model augmentationeference model augmentation :



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Neural augmented reference modeleural augmented reference model:reference (problem dependent) analytical model,

Remarkemark : reference model will notot , in general, ensure adequatedequatepredictions, i.e.

when = system states/controls,

= model states/controls.Augmented reference model:ugmented reference model:

where is the unknownnknown reference model defectefect that ensureswhen i.e.:

Hence, if we knewf we knew , we would have perfect predictionerfect prediction capabilities.

d

d

eu = u ,

ex 6= x

x , uex ,

eu

ex = x

f ref (x , x , u ) = 0

f ref (x , x , u ) = d (x , u )

eu = u

T el eT el eT el cT el c T lT l

J GJ G

J RJ R

c c

e e

T aT a

F aF a

M T , C T , K T M T , C T , K T

dd

Referencereduced model

f ref (

ex ,

ex ,

eu ) d (

ex ,

eu ) = 0



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Approximate withsingleingle

-hiddenidden

-layer neural networksayer neural networks :

where

and

= functional reconstruction error;

= matrices of synaptic weights and biases;= sigmoid activation functions;

= network input.

The reduced model parameterseduced model parameters

are identified on-line using an Extendedxtended Kalmanalman Filterilter .

d

( ) = ( (1), . . . , (N n ))T

W m , V m , a m , bm

i = ( x T , u T )T

pm = ( . . . , W m ik , V m ik , a m i , bm i , . . . )T

d (x , u ) = d p(x , u , pm ) +

d p(x , u , pm ) = W mT

(V mT

i + a m ) + bm



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Tower-tip velocity for multibody, reference, and neural-augmentedreference with same prescribed inputs:

Black: CpLambdamultibody model

Red: reference model

Blue: reference model+neural network

Fastast adaptiondaption



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Defect and remaining reconstruction error after adaption:di i

Red: defect

Blue: remainingreconstruction error

RAPC: Neural ControlAPC: Neural Control


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FuturePast

Prediction window

x 0

t0

t0

t0

+ T p

Goal response x

(t)

Goal control u (t)

x (t), t < t 0

u (t), t < t 0

The principle of neuraleural -augmented reference controlugmented reference control :

Optimal solution u NMPC (t)

Optimal solution x (u NMPC (t))

Sub-optimal solution u ref (t)

Sub-optimal solution x (u ref (t))

Augmented sol. x (u ref (t) + NN )

Augmented sol. u ref (t) + NN



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Prediction problemrediction problem :

Enforcing optimalitynforcing optimality , we get:

minu ,x ,y

J = Z t 0 + T p

t 0L(y , u ) d t

s.t.: f (x , x , u ) = 0 t [t0 , t 0 + T p]

x (t0) = x 0y = g (x ) t [t0 , t0 + T p]

f (x , x , u , pm ) = 0 , t [t0 , t 0 + T p],x (t0) = x 0 ,

d( f T

,x )

dt + f T ,x + y T ,x L ,y = 0 , t [t0 , t 0 + T p], (t0 + T p) = 0 ,

L ,u + f T ,u = 0 , t [t0 , t 0 + T p].

Model equations:

Adjoint equations:

Transversality conditions:

State initial conditions:

Co-state final conditions:



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FuturePast

Prediction window

x 0

t0

t0

t0

+ T p

Goal response x (t)

Goal control u (t)

u (t)

Optimal control u (t)

x (t), t < t 0

u (t), t < t 0

(, , , )

It can be shown that minimizing controlinimizing control is(Bottasso et al. 2007)

u (t) =

x 0 , y

(t), u (t), t



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Reference augmented form:eference augmented form:

where is the unknown control defect.

Remarkemark : if one knew , the optimal control would be availablewithout having to solve the open-loop optimal control problem.

Ideadea :- Approximatepproximate using an adaptive parametric element:

- Identifydentify on-line, i.e. find the parameterswhich minimize the reconstruction error .

pc

u (t) = u ref (t) + x 0 , y (t), u (t), t (, , , ) (, , , )

(, , , )

x 0 , y

(t), u (t), t

= p

x 0 , y

(t), u (t), t, p c

+ c

p(, , , )



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Iterative procedureterative procedure to solve the problem in real-time: Integrate reduced model equations forwardorward in time over theprediction window, using and the latest available parameters(state prediction):state prediction):

Integrate adjoint equations backwardackward in time (coco -state prediction):tate prediction):

Correctorrect control law parameters , e.g. using steepest descent: pc

u ref p c

p c = J ,p c p newc = p oldc J ,p c

d( f T , x )

dt+ ( f ,x + u T ,x f ,u )

T + y T ,x L ,y + uT ,x L ,u = 0 t [t0 , t 0 + T p]

(t0 + T p) = 0

f (x , x , u , pm ) = 0 t [t0 , t0 + T p]x (t0) = x 0



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Remarkemark : the parameter correction step

seeks to enforce the transversalityransversality conditionondition

Once this is satisfied, the control is optimalptimal , since the state and co-state equations and the boundary conditions are satisfiedatisfied .

pc = J ,p c

Z t 0 + T p

t0

T ,p c (L ,u + f T ,u ) d t = 0



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Tr ac k i n g c o s t

Fu tu re Targe t

Predictredict state forward

Predictredict co-state backwards

Predictredict control action

p c = J ,p c

Updatepdate estimate of control action, based on transversality violation Advancedvance plant Updatepdate model, based on prediction error

Past

Op t i m a l c o n t r o l

Pr e d i c t i o n e r r o r

Repeatepeat

Futu rePast

Pred ic t ion hor i zonSteer i ng w indow

S t a t e

Con t ro l

x (t)

(t)

u (t)



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- Drop dependence on time history of goal quantities:

- Approximate temporal dependence using shape functions:

- Associate each nodal value with the output of a singleingle -hiddenidden -layerayerfeed-forward neural networkeural network , one for each component:

where

Output:

Input:

Control parameters:

px 0 , y (t), u (t), t, pc px 0 , y (t0), u (t0), t, pc px

0 , y

(t0), u

(t0), , pc

(1 ) pkx 0 , y (t0), u (t0 ), pc+ pk +1 x 0 , y (t0), u (t0), p co c = W T c (V

T c i c + a c) + bc

o c = ( T p0, T p

1, . . . , T p

M

1)T

i c = x T 0 , x T

(t0), u T

(t0)T

pc = ( . . . , W c ij , . . . , V c ij , . . . , a c i , . . . , bc i , . . . )T



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FuturePast

Prediction window

x 0

t0

t0 t0 + T p

x (t), t < t 0

u (t), t < t 0

u (t0)

x (t0)NN pk

x (t)

u (t)

RAPCAPC


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RAPC can handle constraints on inputs and outputs (not covered inthis paper)

Present resultsresent results : Reference model: collective-only, Reference controller: MIMO Nonlinear-Wind LQR

Work in progressork in progress : Reference model with individual blade pitch, flap dynamics

Reference controller: periodic MIMO Nonlinear-Wind LQR Constraints on inputs and outputs

x = ( d, d, , e , e , T el e )T

Resultsesults


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Two consecutive EOG 1-13 in nominal conditions:

ResultsesultsNormalized total regulation error in 600 sec turbulent wind


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Normalized total regulation error in 600 sec turbulent wind Cold air & ice accretion (degraded airfoil performance):

Resultsesults


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Observationsbservations : Significant advantage of model-based (especially non-linear andadaptive) controllers in

- Turbulent off-design conditions- Strong gusts

It appears that adaptive element is able to correct deficiencies of

reference reduced model, even in the presence of large errors In nominal conditions, and for the collective pitch case:

- Differences in turbulent response of PID, LQR and RAPC are lesspronounced

- It appears difficult to very significantly outperform a well tunedsimple controller (PID)

Cyclic Pitch Controlyclic Pitch Control


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Case studyase study : a simple LQR approach to cyclic pitch controlConsider individual-pitch model

where

= rotor azimuth

= all other states

Model linearization:

Remarkemark : azimuth dependent coefficient matrices

x = ( , x T )T

x

x = f (x , u , p) = f ( , x , u , p)

x = A ( , x , u , p ) x + B ( , x , u , p ) u



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Possible approachesossible approaches : Full state feedback:

a) Integrate Riccati eq. until periodic solution to obtain

optimal periodic feedback gain matrixb) Solve steady Riccati eq. for severalthen interpolate resulting gain matrices

c) Average periodic coefficient matrices over one revolution

solve steady Riccati eq. to get averaged gain matrix Output feedback: a), b) or c), but governing eq. more complexthan Riccati eq., approach a) complicated

K ( , x

, p

) i , 0 i 2

K ( i , x , p )

bA (x , p ) = (1 / 2 )Z

2

0A ( , x , p ) d

bB (x , p ) = (1 / 2 )

Z 2

0

B ( , x , p ) d

cK (x , p )

Full state feedback collective pitch vs. individual pitch LQR



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p p Q

Steady wind, wind shear, tower shadow, rotor up-tilt

Observationsbservations : Very similar behavior for a) and b) strategies, c) slightly worst Significant peak-to-peak reduction for cyclic control, at the cost ofincreased duty cycle


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P

O L I

P

O L I

d i

d i M I M I t

e c n i c

o

t e c n i c

o

l a n o

l a n o

Hardware Implementationardware Implementation

Control System Hardwareontrol System HardwareDecentralized PC/PLC based architecture


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Main controller

Remote visualization www access

Decentralizedcontrol module

Pitch regulator

Ethernet Wireless,ADSL

Realtime fiber optic network(FAST-Bus, Profibus, Ethernet)

CAN-Bus, RS485

Ethernet

Remote visualization

Decentralized PC/PLC based architecture

Control panel

Slip-ring orwireless bridge

RIO = Reconfigurable I/O PLC = Programmable Logic Controller PROFIBUS = Process Field Bus CAN BUS = Controller Area Network RS485 = Serial communication


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PoliMi Control Research PlatformoliMi Control Research PlatformPLC-based decentralizedcontrol module cabinet


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Leitwind 1.2 MW Wind Turbine Hub height 65m Rotor radius 38m

control module cabinet

PC/104 architecture, Pentium M 1.6 GHz Linux real-time operative system

Hardwareardware for supporting researchesearch and fieldieldtestingesting on advanced control laws, state andwind estimators, integrated diagnostics

V l i Ch t h PC104 SBC ith I t l

PoliMi Control Research PlatformoliMi Control Research Platform


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Data acquisition module 16-bit A/D

Versalogic Cheetah PC104 SBC with IntelPentium M 1.6 GHz and Extreme Graphics 2Video (-40 to +60C), 2 configurable serialports, 1 Ethernet interface, 2 usb ports

HE104 High Efficiency PowerSupply 50 Watt, +5V@10A,+12V@2A, -40 to +85C

Hard disk 44 pin (replaceablewith a solid state disk)

Internal communicationPC/104 bus

To servos:From sensors:

PoliMi Control Research PlatformoliMi Control Research Platform


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Torque Rotor speed Azimuth Blade pitch angle Wind

Serial communication RS485 @1Hz

Pitch control Torque control

Pitch, yaw, torquesetpoints

Anemometer, inverter,pitch regulator, yaw

Analog inputs:

Tower accelerations andstrain gauges

Collect data, interface withservos, compute yaw control

Controller and observer algorithms,interface with on-board industrialcontroller

Complete compatibility with andminimum impact on existing on-boardsystem Substantial computing power On-board system can give control toand regain control from researchplatform at any time

Referenceseferences


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Wind Turbines Part 1: Design Requirements, IEC 61400-1, 2005

Manwell J.F., McGowan J.G., and Rogers A.L., Wind Energy Exp lained: Theory, Design andApplication , John Wiley & Sons, New York, NY, 2002

Burton T., Sharpe D., Jenkins N., and Bossanyi E., Wind Energy Handbook , John Wiley & Sons, New

York, NY, 2001Stol K.A., and Fingersh L.J., Wind Turbine Field Testing of State-Space Control Designs, NREL/SR-500-35061, 2003

Findeisen R., Imland L., Allgower F., and Foss B., State and Output Feedback Nonlinear ModelPredictive Control: An Overview, European Journal of Control , 9:190206, 2003

Fausett L., Fundamentals of Neural Networks , Prentice-Hall, New York, 1994

CLBottasso Short Course PartII Wind Turbine Control

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Transcript of CLBottasso Short Course PartII Wind Turbine Control