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

Transcription

1 Chart 1 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 By : Taha Fouda Supervised by: Prof. Siegfried Heier Prof. Galal Salem

2 Chart 2 Introduction P = 1 2 ρr2 V 3 Technology Roadmap Wind Energy, 2013 Edition, IEA, 2013

3 Chart 3 Introduction 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

4 Chart 4 Introduction Modelling DAC Disturbance model System model Combined model Observer Observation Disturbance estimated states Wind turbine estimated states Feedforward Feedback Control

5 Chart 5 Modelling of wind turbine for controller design 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

6 Chart 6 Modelling of wind turbine for controller design Linearization Trim conditions V m = 18 m/s Region III: Constant speed=12,1 rpm Rated power = 5 MW θ trim = States x x 1 x 2 1 st tower fore-aft bending mode Variable speed generator x 3 1 st flapwise bending-mode of blade 1 x 4 1 st flapwise bending-mode of blade 2 x 5 1 st flapwise bending-mode of blade 3 x 6 x 7 First time derivative of 1st tower fore-aft bending mode First time derivative of Variable speed generator x 8 First time derivative of 1 st flapwise bending-mode of blade 1 x 9 First time derivative of 1 st flapwise bending-mode of blade 2 x 10 First time derivative of 1 st flapwise bending-mode of blade 3

7 Chart 7 Modelling of wind turbine for controller design Linearized wind turbine model u Blade 1 command pitch input Blade 2 command pitch input Blade 3 command pitch input z Wind Disturbance y generator speed Blade 1 edgewise moment Blade 2 edgewise moment Blade 3 edgewise moment Blade 1 flapwise moment Blade 1 flapwise moment Blade 1 flapwise moment Tower side-to-side moment Tower fore-aft moment Tower torsional moment 7

8 Chart 8 Modelling of wind disturbance Wind speed V can be divided in two components V = V m + v DEWI DeutschesWindenergie Institut:, 2000

9 Chart 9 Modelling of wind disturbance 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.

10 Chart 10 Modelling of wind disturbance Dryden wind Turbulence model F uw = u s r s = 2σ u 2 T u. 1 1+sT u xሶ Dry = മA Dry x Dry + മB Dry u z = മC Dry x Dry മA Dry = V L u, മB Dry = σ 2 V L u, മC Dry = 1 σ : standard deviation of the flow variation, Turbulence intensity - L u : Charactristic length ( is measured and modlled by Brockhaus11 ) Extention for the 3 blades with different uncorelated white noise seeds

11 Chart 11 Modelling of wind disturbance Rotation Sampling al Effect The turbine rotor samples the eddy periodically with each rotation until the eddy passes the rotor. PSD shows the peaks at the rotational frequency f 1b and at higher harmonics (f 2b = 2f 1b, f 3b = 3f 1b ). This effect is represented by the Inverted notch filter response.

12 Chart 12 Observation 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.

13 Chart 13 Observation Combined model

14 Chart 14 Observation The discrete Kalman Filter 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. മP k = E e k e k T

15 Chart 15 Observation The Discrete Kalman Filter algorithm

16 Chart 16 Observation The Discrete Kalman Filter Tuning Via the determination of മQ var and മR var. - മQ var : Process noise covariance matrix മQ var = E w k w i T - മR var : Measurement noise covariance matrix മR var = E v k v i T Often just the main diagonal elements മQ var and മR var are engaged. മR var is determined via sensors datasheet. മQ var is determined via the average model uncertainties over the azimuth angel.

17 Chart 17 Controller Setting up design criteria 1. The standard deviation of the rotational speed 2. The standard deviation of the flap moment

18 Chart 18 Controller 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 (x T മ Q LQR x + u T മR LQR u)dt It is minimized for the control law u = മK LQR x മK LQR = f(മq LQR, മR LQR )

19 Chart 19 Observation Feedback Controller Design Parameters മQ LQR & മR LQR Rule of thump (Bryson s Rule) Q u = 1 Max(x u 2 ) R = 1 Max(u 2 ) Max x u Intially R simulation without no input I, then tuned by finding the maximum input in the simulation

20 Chart 20 Controller Feedforward Controller മK is the observer gain മK = മK x മK T xd The Controller gain മR = മK LQR മN

21 ሶ ሶ ሶ Chart 21 Controller Feedforward Controller xሶ x d e x e xd = മA മBമK LQR മE മC d മBമN മA d 0 0 മBമK LQR 0 മA മK x മC മK xd മC മBമN 0 മEമC d മK x മFമC d മA d മK xd മFമC d x x d e x e xd + മB u com മEമC d മBമN = 0 മN = മB 1 മEമC d

22 Chart 22 Results Stability Unstable system because of numerical problem with FAST caused by the generator azimuth state after doing Multi-Blade Coordinate transformation(mbc). Blades Tower MBC Generator LQR tunes the wind turbine and the system becomes stable.

23 Chart 23 Results 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.

24 Chart 24 Results The Controller Performance 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 moment 2503,39 KNm 647,23 KNm 633,66 KNm

25 Chart 25 Comparative studies with a given "classical load controller" Standard deviation of the rotational speed Comparison criteria Modern Control Classical control 15 m/s 0,53 0,55 25 m/s 0,35 0,97

26 Chart 26 Conclousion 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.

27 Chart 27 Thank you???