reduction of the rotor blade root bending moment and ... · reduction of the rotor blade root...

Reduction of the rotor blade root bending moment

and increase of the rotational-speed strength of a 5

MW IPC wind turbine based on a stochastic

disturbance observer

Reduction of the rotor blade root bending moment and increase of the rotational-speed strength of a 5 MW IPC wind turbine based on a stochastic

disturbance observer > Taha Fouda > 29 Nov 2017

Chart 1

By : Taha Fouda

Supervised by:Prof. Siegfried Heier

Prof. Galal Salem

Introduction

𝑃 =1

2𝜌𝑅2𝑉3

Technology Roadmap Wind Energy, 2013 Edition, IEA, 2013



Chart 2

• Challenges

1. Higher Loads

2. Reduction in the natural frequencies

• Facing Challenges

Control System

• Observer-Based Disturbance Accommodation Control (DAC)

DAC theory addresses:-

1. The problems of dynamic modelling of uncertain disturbances.

2. Designing feedback/feedforward controllers

Introduction



Chart 3

DAC

Introduction

Disturbance model System model

Observer

FeedbackFeedforward

Combined model

Modelling

Observation

Control

Wind turbine estimated states

Disturbance estimated states



Chart 4

• A HAWT model consists of a rotor model, a drive train model, an electrical

generator model and a tower model.

• Nowadays, all described models can be implemented in various analytical

tools such as FAST, SymDyn and DUWECS (Linearization and simulation).

• The aero-elastic simulation tool FAST is used in this study for modelling of

National Renewable Energy Laboratory NREL 5 MW baseline turbine.

• FAST is developed by NREL for onshore & offshore / 3-bladed & 2-bladed wind

turbines

Modelling of wind turbine for controller design



Chart 5

Linearization

• Trim conditions

𝑉𝑚 = 18 𝑚/𝑠

Region III:

Constant speed=12,1 rpm

Rated power = 5 MW

𝜃𝑡𝑟𝑖𝑚 = 14.92°


𝑥1 1st tower fore-aft bending mode

𝑥2 Variable speed generator

𝑥3 1st flapwise bending-mode of blade 1



𝑥6 First time derivative of 1st tower fore-aft bending mode

𝑥7 First time derivative of Variable speed generator

𝑥8 First time derivative of 1st flapwise bending-mode of blade 1



• States 𝑥



Chart 6

Linearized wind turbine model


• 7

𝒚

generator speed

Blade 1 edgewise moment



Blade 1 flapwise moment



Tower side-to-side moment

Tower fore-aft moment

Tower torsional moment

𝒖

Blade 1 command pitch input



𝒛

Wind Disturbance



Chart 7

• Wind speed 𝑉 can be divided in two components

𝑉 = 𝑉𝑚 + 𝑣

Modelling of wind disturbance

DEWI DeutschesWindenergie Institut:, 2000



Chart 8

➢Turbulence

• The high frequency random variations of the flow.

• Stochastic process - Hard to be modelled in deterministic equations -Modell

just the characteristics via a Power Spectral Density (PSD).

• Dryden turbulence model will be used here.




Chart 9

• Dryden wind Turbulence model

• 𝐹𝑢𝑤 =𝑢 𝑠

𝑟 𝑠= 2𝜎𝑢

2𝑇𝑢 .1

1+𝑠𝑇𝑢

• ሶ𝑥𝐷𝑟𝑦 = മ𝐴𝐷𝑟𝑦𝑥𝐷𝑟𝑦 + മ𝐵𝐷𝑟𝑦𝑢

𝑧 = മ𝐶𝐷𝑟𝑦𝑥𝐷𝑟𝑦

മ𝐴𝐷𝑟𝑦= −𝑉

𝐿𝑢, മ𝐵𝐷𝑟𝑦 = 𝜎 2

𝑉

𝐿𝑢, മ𝐶𝐷𝑟𝑦 = 1

− 𝜎 : standard deviation of the flow variation, Turbulence intensity

- 𝐿𝑢 : Charactristic length ( is measured and modlled by Brockhaus11 )

• Extention for the 3 blades with different uncorelated white noise seeds




Chart 10

Rotation Sampling al Effect




Chart 11

• The turbine rotor samples

the eddy periodically with

each rotation until the eddy

passes the rotor.

• PSD shows the peaks at the

rotational frequency 𝑓1𝑏 and

at higher harmonics

(𝑓2𝑏 = 2𝑓1𝑏, 𝑓3𝑏 = 3𝑓1𝑏).

• This effect is represented by

the Inverted notch filter

response.

• Turbulence states are hard to measure

• According to the "internal model principle", the control quality or the potential

for disturbance rejection is increased; the more information there is available

on the character of the disturbance (turbulence).

• The ability of an observer to estimate non-measurable states from a set of

measurements using a model of the plant suggests the idea of extending the

model of the plant by a model of the disturbance.

• The discrete Kalman Filter will be used as an observer.

Observation



Chart 12

Combined model

Observation



Chart 13

The discrete Kalman Filter

Observation



Chart 14

• It is an optimal recursive data

processing algorithm that gives the

optimal estimates of the system

states for a linear system with

additive Gaussian white noise in the

process and the measurements.

• Kalman Filter estimates the states

and gives an error in the estimation

via the error covariance matrix 𝑃.

• It is optimal in the sense that it

minimizes the variance in the

estimated states.

മ𝑃𝑘 = 𝐸 𝑒𝑘 𝑒𝑘𝑇

The Discrete Kalman Filter algorithm

Observation



Chart 15

The Discrete Kalman Filter Tuning

• Via the determination of മ𝑄𝑣𝑎𝑟 and മ𝑅𝑣𝑎𝑟.

- മ𝑄𝑣𝑎𝑟: Process noise covariance matrix മ𝑄𝑣𝑎𝑟 = 𝐸 𝑤𝑘𝑤𝑖𝑇

- മ𝑅𝑣𝑎𝑟: Measurement noise covariance matrix മ𝑅𝑣𝑎𝑟 = 𝐸 𝑣𝑘𝑣𝑖𝑇

• Often just the main diagonal elements മ𝑄𝑣𝑎𝑟 and മ𝑅𝑣𝑎𝑟 are engaged.

• മ𝑅𝑣𝑎𝑟 is determined via sensors datasheet.

• മ𝑄𝑣𝑎𝑟 is determined via the average model uncertainties over the azimuth

angel.

Observation



Chart 16

Setting up design criteria

1. The standard deviation of the rotational speed

2. The standard deviation of the flap moment

Controller



Chart 17

Feedback Controller

• The Linear Quadratic Regulator (LQR) have been used as a full state feedback

controller for tuning the wind turbine plant.

• A linear time - invariant system is optimal if the following quadratic cost

function is minimized

𝐽 = 0∞(𝑥𝑇മ𝑄𝐿𝑄𝑅 𝑥 + 𝑢𝑇മ𝑅𝐿𝑄𝑅 𝑢)𝑑𝑡

It is minimized for the control law

𝑢 = −മ𝐾𝐿𝑄𝑅 𝑥

മ𝐾𝐿𝑄𝑅 = 𝑓(മ𝑄𝐿𝑄𝑅 , മ𝑅𝐿𝑄𝑅 )

Controller



Chart 18

Feedback Controller

• Design Parameters മ𝑄𝐿𝑄𝑅 & മ𝑅𝐿𝑄𝑅

• Rule of thump (Bryson‘s Rule)

𝑄𝑢 =1

𝑀𝑎𝑥(𝑥𝑢2)

𝑅 =1

𝑀𝑎𝑥(𝑢2)

𝑀𝑎𝑥 𝑥𝑢 simulation without no input

Intially 𝑅 𝐼 , then tuned by finding the maximum input in the simulation

Observation



Chart 19

Feedforward Controller

• മ𝐾∗ is the observer gain

മ𝐾∗ = മ𝐾𝑥 മ𝐾𝑥𝑑 𝑇

• The Controller gain

മ𝑅∗ = മ𝐾𝐿𝑄𝑅 മ𝑁

Controller



Chart 20

Feedforward Controller

ሶ𝑥

ሶ𝑥𝑑ሶ𝑒𝑥ሶ𝑒𝑥𝑑

=

മ𝐴 − മ𝐵മ𝐾𝐿𝑄𝑅000

മ𝐸 മ𝐶𝑑 − മ𝐵മ𝑁

മ𝐴𝑑00

മ𝐵മ𝐾𝐿𝑄𝑅0

മ𝐴 − മ𝐾𝑥മ𝐶

−മ𝐾𝑥𝑑മ𝐶

മ𝐵മ𝑁

0മ𝐸മ𝐶𝑑 − മ𝐾𝑥മ𝐹മ𝐶𝑑മ𝐴𝑑 − മ𝐾𝑥𝑑മ𝐹മ𝐶𝑑

𝑥𝑥𝑑𝑒𝑥𝑒𝑥𝑑

+

മ𝐵

000

𝑢𝑐𝑜𝑚

മ𝐸മ𝐶𝑑 − മ𝐵മ𝑁 = 0

മ𝑁 = മ𝐵−1മ𝐸മ𝐶𝑑

Controller



Chart 21

Stability

• Unstable system because of numerical problem with FAST caused by the

generator azimuth state after doing Multi-Blade Coordinate transformation(MBC).

• LQR tunes the wind turbine and the system becomes stable.

Results



Chart 22

MBCBlades

Tower

Generator

• Validation of the Linear Model

The linear system response is approximatly matched with the nonlinear

response.

• Validation of the Discrete Kalman Filter with the linear model

The Discrete Kalman Filter shows a good and fast estimation for the wind turbine

states and the disturbance states.

Results



Chart 23

The Controller Performance

Results

Uncontrolled

turbine

Feedforward

control

Feedforward/Feedbak

control

Generator speed 34,45 rpm 15,62 rpm 15,62 rpm

blade Flapwise

moment 6272,9 KNm 5442,65 KNm 240,63 KNm

Tower fore-aft

moment2503,39 KNm 647,23 KNm 633,66 KNm



Chart 24

Standard deviation of the rotational speed Comparison criteria

Comparative studies with a given "classical load

controller"



Chart 25

Modern Control Classical control

15 m/s 0,53 0,55

25 m/s 0,35 0,97

1. Observer based DAC is designed and implemented to reduce the rotor blade

root bending moment and increase the rotational-speed strength of a 5 MW

IPC wind turbine.

2. The ability of an observer to estimate non-measurable states from a set of

measurements using a model of the plant suggests the idea of extending the

model of the plant by a model of the disturbance.

3. The results show that the Discrete Kalman Filter has a good and fast

estimation for the linear systems with Gaussian noise.

4. The results show that the modern controller gives a better result than the

classical controller.

Conclousion



Chart 26

Thank you

???



Chart 27

reduction of the rotor blade root bending moment and ... · reduction of the rotor blade root...

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