A Nonlinear Variable
Speed Tracking Control
for Wind Turbine Systems
In Celebration of the Life,
Mathematics and Memories
of Chris Byrnes
Wei Lin
Dept. of Electrical Engineering and Computer Science
Case Western Reserve University, Cleveland, Ohio
Joint work with Dr. Z. Lu at Emerson Network Power
Introduction

Components of a typical wind turbine
The wind encounters the rotor
on the horizontal-axis turbine,
causing it to spin.
The low-speed shaft transfers
energy to the gear box, which
steps up in speed and spins
the high speed shaft. The high
speed shaft causes the
generator to spin, hence
generating electricity.
The yaw system is used to
turn the nacelle so that the
rotor faces into the wind.
(Figure courtesy of the U.S. Department of Energy)
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Outline
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Introduction
Wind Speed Estimation
Wind Turbine Modeling
Nonlinear Control Design
Simulation Study
Summary
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Introduction

Output power of a typical wind turbine operating in different wind
speed regions, denoted by 1, 2, 3.
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Turbine Control
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Supervisory Control: Start and shut-down the turbine

Yaw Control: Turn the turbine to face the wind

Pitch and Generator Control: Capture the maximum
power without exceeding safe rotor speed and stress
and convert the wind power into electricity.

Grid-side Inverter Control: Synchronize with and send
the energy to the power grid.
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Wind Turbine Control System
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Turbine Control in Region 2
Control objective:
To control generator torque (and hence, the rotor speed)
to achieve the maximum Cp at all wind speed.

From the graph, it is easy to see
that we can keep the pitch angle
fixed (at about -1 degree) and
control the tip speed ratio (λ) to
about 8.5.
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Turbine Control in Region 2

Wind power that can be captured by a practical wind turbine


Cp curve has a unique maximum at
With fixed pitch angle, we want to keep the tip speed ratio at its
optimal point
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The rotor speed must track the reference signal
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Wind Speed Estimation
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Stochastic approach
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Rotor effect wind speed estimation
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Wind Speed Estimation
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Step 1: Estimation of Wind Turbine Mechanical Power
Wind power (Pm) can be calculated from the power extracted to
generator (Pe) and the mechanical power loss (Ploss)
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Wind Speed Estimation
It can be approximated by the discrete time format
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Wind Speed Estimation

Step 2: Wind Speed Calculation
Newton-Raphson
iterative method
The wind speed estimation
Rotor speed reference signal
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Wind Turbine Modeling

If the rotor speed can track the reference signal, then the
tip speed ratio can be maintained at the optimal point. As
a result, we have the following relationship
where
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Wind Turbine Modeling
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Two Mass Drive Train
Let
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Wind Turbine Modeling
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If a perfectly rigid low speed shaft is assumed, then the
two-mass drive-train model reduces to a one-mass
drive-train model.
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Nonlinear Control Design
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Nonlinear Tracking Control Formulation
Deign the control input Te to forceω to track the reference
signalω*.

Challenge: Neither in normal form nor in lower triangular
form
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Nonlinear Control Design

Introduce a change of coordinates
where
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Nonlinear Control Design
Challenges still exists:
  Still neither in normal form nor in lower triangular form
  Although it is nonminimum-phase, more than one state
variables are involved in the zero dynamics.
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
Solution: Partial Feedback Design
Instead of achieving asymptotic tracking for all states,
onlyξ1 (→ω*) achieve asymptotic tracking and keep other
states bounded.
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Nonlinear Control Design
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Theorem 1 (State Feedback)
Consider an equivalent wind turbine system (17)-(20), for a
given twice differentiable reference speed signalω*, there
exists a state feedback controller
such that the rotor speed ξ1 can globally track the desired speed
ω* asymptotically.
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Nonlinear Control Design
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Proof of Theorem 1
Step1: Change of coordinates
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Nonlinear Control Design
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Proof of Theorem 1 (cont’d)
Step2: Lyapunov design for e1 and e2
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z is guaranteed to be bounded since (e1, e2)→0 andδ(·) is bounded.
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Nonlinear Control Design
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Output feedback design motivation:
Torsional angleθk (z ) is difficult to measure.

Theorem 2 (Output Feedback)
Consider an equivalent wind turbine system (17)-(20), for a
given twice differentiable reference speed signalω*, there
exists a output feedback controller
such that the rotor speed ξ1 can globally track the desired
speed ω* asymptotically.
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Nonlinear Control Design
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Proof of Theorem 2
Step1: Reduced order observer design
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Nonlinear Control Design
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Proof of Theorem 2 (cont’d)
Step2: Feedback controller design
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Nonlinear Control Design
  Proof
of Theorem 2 (cont’d)
Step3: Closed-loop stability analysis
z is guaranteed to be bounded because of (e1, e2)→0, asymptotic
stability of the observer and boundedδ(·).
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Simulation Study
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Reference speed signal
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Simulation Study
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Simulation Results
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Nonlinear Control Design
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Theorem 3 (One-Mass Drive-Train Model)
Consider a reduced wind turbine system model
for a given twice differentiable reference speed signalω*, there
exists a feedback controller
such that the rotor speedω can asymptotically track the desired
speedω*.
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Nonlinear Control Design
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Proof of Theorem 3
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Summary
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Wind turbine control problem in Region 2
Rotor effect wind speed estimation
Two-mass drive-train modeling
Nonlinear tracking control for maximum power capture
based on two-mass drive-train model
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Acknowledgement

This work was supported in part by the Robert Herbold
Faculty Fellow Award and the funding from Alstom
Power Inc.
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