Short Course on Wind Turbine Modeling and Control - Part II: Control - C.L. Bottasso Politecnico di Milano Milano, Italy Korea Institute of Machinery and Materials

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Short Course on Wind Turbine Modeling and
Control- Part II Control -C.L.
BottassoPolitecnico di MilanoMilano,
ItalyKorea Institute of Machinery and
MaterialsKangwon National UniversityOctober
18-19, 2007
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Control System Architecture
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Control System Architecture
Wind farm supervisor
Sensors Positions, speeds, accelerations,
stresses, strains, temperature, electrical
fluid characteristics, etc.
Actuators Actuator control system
Wind turbine

• Supervisor
• Choice of operating condition
• Start up
• Power production
• Emergency shut-down

Observers Wind, tower blades
Active control system Control strategy
Communication and reporting
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Supervisory Control System

• Main 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,
  teetering angle, rotor tilt, )
• Fluid properties and levels
• Electrical systems (voltages, grid
  characteristics, )
• Icing conditions, humidity, lighting,

• Main tasks
• Operational managing and monitoring
• Diagnostics, safety
• Communication, reporting and data logging
• Operational states
• Idling
• Start Up
• Normal power production
• Normal shut down
• Emergency shut down

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Supervisory Control System
Representative operational state monitoring logic
V gt V cut-in
RPM gt Wcut-in
Idling
Power production
Start up

• Failures
• Overspeed high rotor accel.
• Vibrations

Emergency shut down
V gt V cut-off
Normal shut down
V lt V cut-in
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Control Strategies
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Control Strategies

• Basic wind turbine control strategies and power
  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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Control Strategies
Power coefficient Tip speed ratio (TSR)
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Control Strategies
Constant rotor speed
Direct grid connection Generator provides
whatever torque required to operate at or near
given angular speed
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Control Strategies
Constant TSR

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

Constant TSR strategy
Constant rotor speed strategy
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Control Strategies
Power-wind speed curve
Constant TSR strategy (cubic)
Constant rotor speed strategy
Power deficit for constant speed wrt constant TSR
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Control Strategies

• Constant rotor speed strategy 2 vs. strategy 1
• Higher cut in speed
• Lower wind speed to reach rated power
• Smaller power deficit

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Control Strategies
Annual energy yield
Weibull distribution

• Constant rotor speed strategy 2 vs. strategy 1
• Smaller power deficit wrt to constant TSR, but
  at improbable wind speeds
• Higher energy yield

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Control Strategies
Control above rated speed
Constant power constant rotor speed curve
(cubic)
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Control Strategies
Below rated speed torque control
Above rated speed pitch control
Variable-speed pitch/torque regulated wind
turbine
Often, smoothing for milder transition between
regions
No torque to promote rotor acceleration
Region 2 - below rated speed constant TSR
strategy
Region 3 - above rated speed constant power
strategy
Region 1
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Control Strategies
Below rated speed torque control
Above rated speed torque-stall control
Variable-speed passive-stall/torque regulated
wind turbine
Stall region, high dispersion
Below rated speed constant TSR strategy
Above rated speed (roughly) constant power
strategy
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Control Strategies
Rotor disk
Constant-speed passive-regulation wind turbine
Below rated speed constant rotor speed strategy
Above rated speed (roughly) constant power
strategy
Below rated speed constant rotor speed strategy
Above rated speed yaw or tilt rotor to reduce
effective wind
Stall region, high dispersion
Yaw/tilt out-of-the-wind regulation
Stall regulation
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Control Strategies

• Further 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 control strategies 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 Control

• Orient the rotor in line with the wind field to
  increase power
• Note some small wind turbine will also yaw out
  of the wind to reduce loads in high winds
• Passive or free yaw, used in small wind
  turbines
• Active yaw
• If V lt V cut in no action
• If V gt V cut in
• Compute yaw error averaging over window
  (typically tens of sec.s) to reduce duty cycle
• Region 2 realign if yaw error gt yaw threshold2
  (typically 15 deg)
• Region 3 realign if yaw error gt yaw threshold3
  (typically 8 deg)
• Realign at low yaw rate to reduce gyroscopic
  loads
• If yaw error lt small threshold (typically a
  fraction of a deg), engage yaw brake to eliminate
  backlash between drive pinion and bull gear

Downwind rotor
Tail fin
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Reduced Models
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Reduced Models for Model-Based Controllers
Non-linear collective-only reduced model

• Equations
• Drive-train shaft dynamics
• Elastic tower fore-aft motion
• Blade pitch actuator dynamics
• Electrical generator dynamics
• States
• Inputs

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Reduced Models for Model-Based Controllers

• Equations of motion
• Tip speed ratio
• Wind (mean wind turbulence)

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Reduced Models for Model-Based Controllers

• Rotor force and moment coefficients
• 
  computed off-line with CpLambda
  aero-servo-elastic model, averaging periodic
  response over one rotor rev
• Stored in look-up tables

? Dependence of and
on mean wind accounts for deformability
of tower and blades under high winds
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Reduced Models for Model-Based Controllers
Blade
Example individual-pitch model
Nacelle inertia
Torque actuator
Equivalent shaft stiffness
Yaw actuator

• States
• 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)
• Inputs

Pitch actuator
Generator
Tower
Equivalent flap hinge and spring

• Rigid body
• Beam
• Revolute joint
• Actuator
• Boundary condition

Equivalent tower stiffnesses
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Reduced Models for Model-Based Controllers

• Model 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
  using Automatic Differentiation tools like
  ADOL-C, ADIC, etc.)
• Numerical, by finite differences

Linearization trim points
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Observers
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Tower State Observer

• Kalman modal-based tower observer
• Accelerations
• Curvatures
• Unknown modal amplitudes
• Modal bases
• Process measurement noise
• ? Remarks
• 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

Accelerometer
Strain gage
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Tower State Observer

• State space form
• with
• Optimal Kalman state estimate
• Filter gain matrix
• Propagated states and outputs based on
  accelerometric reading
• Curvature reading

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Tower State Observer
Tower tip velocity estimation
Filter warm-up
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Tower State Observer

• Kalman modal-based tower and blade state
  observer
• Compute or measure modal bases for blades and
  tower
• Integrate tower kinematic equations from
  accelerations
• Correct with tower strain gage curvature
  readings
• Integrate blade kinematic equations from blade
  and tower accelerations
• Correct with blade strain gage curvature readings

Accelerometers
Strain gages
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Wind Observer

• 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 reconstruct wind blowing on rotor
  from reliable measurements (pitch setting, rotor
  speed, etc.)

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Wind Observer

• Extended Kalman wind 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

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Wind Observer
Hub wind estimation
? Turbulent wind ( m/sec)
? EOG1-13 case
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Wind Observer
Simple mean hub wind reconstruction from torque
balance equation More in general The rotor
system is a sensor which responds to temporal as
well as spatial wind variations Model-based
interpretation of response can be used for
reconstructing vertical and horizontal wind shear
for improved rotor control Example introduce
spatial assumed modes and wind states
Rotor disk
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Simulation Environment
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Control Laws Virtual Testing Environment
Wind generator
Process noise
Linux real-time environment
Measurement noise
Virtual plant
Sensor models
CpLambda aero-servo-elastic model
Controller
Kalman filtering Wind tower/blade state
estimation

• Supervisor
• Choice of operating condition
• Start up
• Power production
• Normal shut-down
• Emergency shut-down

• Feedback controller
• PID
• MIMO LQR
• RAPC
• Adaptive reduced model

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Control Laws
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Control Laws Three Case Studies

• Case 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

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Control Laws Optimal PID

• Optimal wind-scheduled PID
• Tabulated electrical torque ?
• Optimization of gains
• based on aeroelastic analyses in CpLambda

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Control Laws Optimal PID

• Gain 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

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Control Laws Optimal PID

• PID gain optimization procedure (continued)
• For each mean wind
• ? Regard cost as sole function of unknown gains
• ? Minimize cost (using Noesis Optimus)
• Evaluate cost with CpLambda aero-servo-elastic
  model
• Global optimization (GA)
• Local refinement (Response Surface gradient
  based minimization)

CpLambda Aeroelastic response in turbulent wind
for given gains

• Optimizer
• Global local algorithms
• Functional approximators

(possible constraints)
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Control Laws MIMO NonLinear-Wind LQR

• Wind-scheduled MIMO LQR
• ? Reduced model in compact form
• where
• ? Wind parameterized linear model
• where
• Remarks
• Model linearized about current mean wind
  estimate
• Non-linear dependence on instantaneous turbulent
  wind
• Wind not treated as linear disturbance (as
  commonly done)

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Control Laws MIMO NonLinear-Wind LQR
Wind-scheduled MIMO LQR (continued) ?
Regulation cost where ? MIMO formulation
tracking quantities for
reg. 2 3
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Control Laws MIMO NonLinear-Wind LQR
Wind-scheduled MIMO LQR (continued) ? Closed
loop controller with Kalman estimated states
and wind
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Control Laws NonLinear Adaptive Ctrl.

• Design controller which
• Can handle non-linearities of plant
• Is adaptive
• - 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 constraints (e.g. max loads in blades
  or tower)
• Can be implemented in real-time (no iterative
  scheme, fixed number of operations per
  activation)
• ? Non-linear model-adaptive predictive control

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Control Laws NonLinear Adaptive Ctrl.
Non-linear Model Predictive Control (NMPC) Find
the control action which minimizes an index of
performance, by predicting the future behavior of
the plant using a non-linear reduced model. -
Reduced model - Initial conditions - Output
definition Cost with desired goal
outputs and controls. Stability results
Findeisen et al. 2003, Grimm et al. 2005.
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Control Laws NonLinear Adaptive Ctrl.
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Control Laws NonLinear Adaptive Ctrl.
Predictive model-adaptive control
Prediction window
Prediction window
Tracking cost
Tracking cost
Prediction window
Tracking cost
Goal response
Prediction error
Prediction error
Steering window
Steering window
Prediction error
Plant response
Steering window
Predictive solutions
1. Tracking problem
3. Reduced model update
2. Steering problem

• Reduced model adaption
• 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.)

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RAPC Motivation

• For any given problem wealth of knowledge and
  legacy methods which perform reasonably well
• Quest for better performance/improved
  capabilities undesirable and wasteful to neglect
  valuable existing knowledge
• Reference Augmented Predictive Control (RAPC)
  exploit available legacy methods, embedding them
  in a non-linear model predictive adaptive control
  framework
• Specifically
• Model augment reduced models to account for
  unresolved or unmodeled physics
• Control design a non-linear controller
  augmenting linear ones (MIMO Nonlinear-Wind LQR)
  which are known to provide a minimum level of
  performance about certain linearized operating
  conditions

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RAPC Motivation

• Approach
• Choose a reference model / reference control law
• Augment the reference using an adaptive
  parametric function
• Adjust the function parameters to ensure good
  approximation of the actual system / optimal
  control law (parameter identification)
• Reasons for using a reference model / control
• Reasonable predictions / controls even before
  any learning has taken place (otherwise would
  need extensive pre-training)
• Easier and faster adaption the defect is
  typically a small quantity, if the reference
  solution is well chosen

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RAPC Reduced Model Identification
The principle of reference model augmentation
Same wind, same inputs
Same wind, same inputs
Neural Network
Trained on-line to minimize mismatch
Augmented reduced model
Plant
Reduced model
Dissimilaroutputs
Similar outputs
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RAPC Reduced Model Identification

• Neural augmented reference model
• reference (problem dependent) analytical model,
• Remark reference model will not, in general,
  ensure adequate predictions, i.e.
• when system
  states/controls,
• 
  model states/controls.
• Augmented reference model
• where is the unknown reference model defect
  that ensures
• when i.e.
• Hence, if we knew , we would have perfect
  prediction capabilities.

Reference reduced model
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RAPC Reduced Model Identification
Approximate with single-hidden-layer neural
networks where and functional
reconstruction error
matrices of synaptic weights and biases
sigmoid
activation functions
network input. The reduced model parameters
are identified on-line using an Extended Kalman
Filter.
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RAPC Reduced Model Identification
Tower-tip velocity for multibody, reference, and
neural-augmented reference with same prescribed
inputs
Fast adaption
Red reference model
Black CpLambda multibody model
Blue reference model neural network
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RAPC Reduced Model Identification
Defect and remaining reconstruction error
after adaption
Red defect
Blue remaining reconstruction error
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RAPC Neural Control
The principle of neural-augmented reference
control

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RAPC Neural Control
Prediction problem Enforcing optimality, we
get

• Model equations

• State initial conditions

• Adjoint equations

• Co-state final conditions

• Transversality conditions

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RAPC Neural Control
It can be shown that minimizing control is
(Bottasso et al. 2007)

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RAPC Neural Control

• Reference augmented form
• where is the unknown control
  defect.
• Remark if one knew , the optimal
  control would be available without having to
  solve the open-loop optimal control problem.
• Idea
• Approximate using an adaptive
  parametric element
• Identify on-line, i.e. find
  the parameters which minimize the
  reconstruction error .

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RAPC Neural Control

• Iterative procedure to solve the problem in
  real-time
• Integrate reduced model equations forward in
  time over the prediction window, using and
  the latest available parameters (state
  prediction)
• Integrate adjoint equations backward in time
  (co-state prediction)
• Correct control law parameters , e.g. using
  steepest descent

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RAPC Neural Control
Remark the parameter correction step seeks to
enforce the transversality condition Once this
is satisfied, the control is optimal, since the
state and co-state equations and the boundary
conditions are satisfied.
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RAPC Neural Control
Future
Past
Future
Past
Target
Tracking cost
Prediction error
State
Control
Optimal control
Prediction horizon
Steering window

• Predict control action

• Predict state forward

• Repeat

• Predict co-state backwards

• Update estimate of control action, based on
  transversality violation

• Advance plant

• Update model, based on prediction error

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RAPC Neural Control

• Drop dependence on time history of goal
  quantities
• Approximate temporal dependence using shape
  functions
• Associate each nodal value with the output of a
  single-hidden-layer feed-forward neural network,
  one for each component
• where
• Output
• Input
• Control parameters

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RAPC Neural Control

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RAPC

• RAPC can handle constraints on inputs and outputs
  (not covered in this paper)
• Present results
• Reference model collective-only,
• Reference controller MIMO Nonlinear-Wind LQR
• Work in progress
• Reference model with individual blade pitch,
  flap dynamics
• Reference controller periodic MIMO
  Nonlinear-Wind LQR
• Constraints on inputs and outputs

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Results
Two consecutive EOG1-13 in nominal conditions
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Results

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

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Results

• Observations
• Significant advantage of model-based (especially
  non-linear and adaptive) 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 less pronounced
• - It appears difficult to very significantly
  outperform a well tuned simple controller (PID)

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Cyclic Pitch Control
Case study a simple LQR approach to cyclic pitch
control Consider individual-pitch model where
rotor azimuth all other states Model
linearization Remark azimuth dependent
coefficient matrices
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Cyclic Pitch Control

• Possible approaches
• Full state feedback
• a) Integrate Riccati eq. until periodic solution
  to obtain optimal periodic feedback gain matrix
• b) Solve steady Riccati eq. for several
  then 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 complex than Riccati eq., approach a)
  complicated

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Cyclic Pitch Control

• Full state feedback collective pitch vs.
  individual pitch LQR
• Steady wind, wind shear, tower shadow, rotor
  up-tilt
• Observations
• Very similar behavior for a) and b) strategies,
  c) slightly worst
• Significant peak-to-peak reduction for cyclic
  control, at the cost of increased duty cycle

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Hardware Implementation
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Control System Hardware
Decentralized PC/PLC based architecture
Slip-ring or wireless bridge
Decentralized control module
Ethernet
Pitch regulator
Remote visualization
CAN-Bus, RS485
Realtime fiber optic network (FAST-Bus, Profibus,
Ethernet)

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

Control panel
Main controller
Ethernet
Wireless, ADSL
Remote visualization
www access
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Control System Hardware
Connection to PoliMi PC/104 control research
platform
Analog I/O
Communication with other devices, controller units
Digital I/O
Profibus
Programmable PC module, communication with
external terminal
www.bachmann.info

• Data acquisition from sensors
• Command to servos, pitch and yaw

? Vibration sensor
Tower and blade accelerometer ?
On-board cup anemometer ?
Rotor speed encoder ?
temperature, pressure, yaw, pitch,
? Generator and inverter
Tower and blade strain gauges ?
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PoliMi Control Research Platform
PLC-based decentralized control module cabinet
Hardware for supporting research and field
testing on advanced control laws, state and wind
estimators, integrated diagnostics

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

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

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PoliMi Control Research Platform
Versalogic Cheetah PC104 SBC with Intel Pentium M
1.6 GHz and Extreme Graphics 2 Video (-40 to
60C), 2 configurable serial ports, 1 Ethernet
interface, 2 usb ports
Data acquisition module 16-bit A/D
Internal communication PC/104 bus
HE104 High Efficiency Power Supply 50 Watt,
5V_at_10A, 12V_at_2A, -40 to 85C
Hard disk 44 pin (replaceable with a solid state
disk)
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PoliMi Control Research Platform
To servos Pitch, yaw, torque setpoints
From sensors Anemometer, inverter, pitch
regulator, yaw
? Collect data, interface with servos, compute
yaw control

• Torque
• Rotor speed
• Azimuth
• Blade pitch angle
• Wind

Serial communication RS485 _at_1Hz

• Pitch control
• Torque control

• Complete compatibility with and minimum impact
  on existing on-board system
• Substantial computing power
• On-board system can give control to and regain
  control from research platform at any time

Analog inputs Tower accelerations and strain
gauges
? Controller and observer algorithms, interface
with on-board industrial controller
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References
Wind Turbines Part 1 Design Requirements, IEC
61400-1, 2005 Manwell J.F., McGowan J.G., and
Rogers A.L., Wind Energy Explained Theory,
Design and Application, 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, 2001 Stol 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
Model Predictive Control An Overview, European
Journal of Control, 9190206, 2003 Fausett L.,
Fundamentals of Neural Networks, Prentice-Hall,
New York, 1994