Control of an offshore wind turbine modeled as discrete system

Control of an offshore wind turbine modeled as discrete system

Pedro Varella Barca Guimarães Suzana Moreira Avila

UNIVERSIDADE DE BRASÍLIA - BRAZIL

EO L UnB-UFG

Guide

• Introduction

• Objectives

• Inverted Pendulum Model • Motion’s Equation

• Transfer Function

• Numerical Analysis

• Proportional Control • Block Diagram (Closed-Loop)

• Graphic Result

• Block Diagram (Open-Loop)

• Conclusions

Introduction

Introduction

Offshore wind park at Cumbria Onshore wind park at Britain

Introduction

Guide

• Introduction

• Objectives





• Graphic Result


• Conclusions

Objectives

• Analise offshore wind turbine’s linear dinamic behavior and stability, modeled as an inverted pendulum;

• Look for a critical situation for its torcional spring to apply a proportional control.

Guide

• Introduction

• Objectives





• Graphic Result


• Conclusions

Inverted Pendulum Model

Motion’s Equation

(𝑀 +𝑚𝑏 +𝑚𝑐) (𝑚𝑏 + 2.𝑀). 𝑎

(𝑚𝑏 + 2.𝑀). 𝑎 𝐼 + (𝑚𝑏 + 2.𝑀). 𝑎2𝑢 𝜃

+ 𝑐 00 0

𝑢 𝜃

+ 0 00 𝐾𝑚 − 𝑚𝑏 + 2.𝑀 . 𝑔. 𝑎

𝑢𝜃

=𝐹

2. 𝑎. 𝐹


Transfer Function

• A = (mb + 2.M).a².(mc - M) + (M + mb + mc).I

• B = (I + (mb + 2.M).a²).c

• C = (M + mb + mc).(Km – (mb + 2M).a.g)

• D = (Km – (mb+2M).a.g).c

𝐺 = 𝑠 𝑚𝑏 +𝑚𝑐 . 𝑎 + 2. 𝑐. 𝑎

𝑠3. 𝐴 + 𝑠2. 𝐵 + 𝑠. 𝐶 + 𝐷


Numerical Analysis

Km values Poles

Km = 8,2763.1014 -0,0000 + 840,21i -0,0000 - 840,21i

-0,0000

Km = 8,2763.108 -0.0014 + 0.6997i -0.0014 - 0.6997i

-0.0034

Km = 8,2763.107 0.3805 -0.3832 -0.0034

Guide

• Introduction

• Objectives





• Graphic Result


• Conclusions

Proportional Control

Block Diagram (Closed-Loop)


Graphic Result


Block Diagram (Open-Loop)


Transfer Function

• A = (mb + 2.M).a².(mc - M) + (M + mb + mc).I

• B = (I + (mb + 2.M).a²).c

• C = (M + mb + mc).(Km – (mb + 2M).a.g) + (mb+mc).(mc + mb + M)

• D = (Km – (mb+2M).a.g).c + 2.c.a.(mc + mb + M)

Poles:

• -0,0000 + 0,1656i;

• -0,0000 - 0,1656i;

• -0,0061.

𝐺 = 𝑠 𝑚𝑏 +𝑚𝑐 . 𝑎 + 2. 𝑐. 𝑎

𝑠3. 𝐴 + 𝑠2. 𝐵 + 𝑠. 𝐶 + 𝐷

Guide

• Introduction

• Objectives





• Graphic Result


• Conclusions

Conclusions

• The inverted pendulum is a system originally unstable and with a non-linear behavior;

• It was possible to identify a critical situation to apply the proportional control;

• The proportional control was effective for this problem:

• Stabilized the system;

• Kept it within the regime of small displacements.

References

• Ogata, K., Modern Control System, 4ª Edição, Prentice-Hall, New Jersey, 2002

• Pao L.Y. and Johnson K.E., A tutorial on the dynamics and control of wind turbines and wind farms Proceedings of the American Control Conference, St Louis, EUA, 2009

• A. C. Drummond, K. C. Oliveira, A. Bauchspiess, Estudo do Controle de Pêndulo Inverso sobre Carro utilizando Rede Neural de Base Radial, IV Congresso Brasileiro de Redes Neurais, 1999.

• Gordon M. Stewart, Matthew A. Lackner, The effect of actuator dynamics on active structural control of offshore wind turbine, 2011

Thank you!

• Contact:

Pedro Varella - [email protected]

Suzana Avila - [email protected]

Control of an offshore wind turbine modeled as discrete system

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