Transient response modelling for wind turbines based on synthetic wind speeds. DEL Presentation. Thomas Woolmington 28th February 2014

Transcription

1 Transient response modelling for wind turbines based on synthetic wind speeds. DEL Presentation Thomas Woolmington 28th February 2014

2 Overview Introduction to Wind Energy Data Acquisition and Statistical Summarisation The Generation of Power Curves Current Power Prediction Techniques. Artificial Wind Speeds System Response Modeling Acknowledgements

3 Overview Introduction to Wind Energy Data Acquisition and Statistical Summarisation The Generation of Power Curves Current Power Prediction Techniques. Artificial Wind Speeds System Response Modeling Acknowledgements

4 Introduction to Wind Energy Kinetic wind energy is harnessed by converting to mechanical energy via the turbine rotor and then into electrical energy through the generator: Wind Energy if fundamentally derived from an extension of kinetic energy formula! P = C. p ρ. A. u 2 3 where the mechanical output power (P) is a function of the performance coefficient of the turbine C p, the density of air (ρ), the area swept by the turbine projected in the direction of the wind (A) and wind-speed (u).

5 Introduction to Wind Energy It is worth considering that Cp is limited by Betz limit of 59.3% efficiency however an important fact that is often missed is that this is strictly speaking only applicable in laminar kinetic mass flow systems. (N.B. Turbulence and Pressure drop are not considered!) As wholly laminar environments are rarely present in real world scenarios it is evident that further investigation is required when trying to bound the likely coefficient of performance in a turbulent environment.

6 Introduction to Wind Energy

7 Introduction to Wind Energy VAWT Functions in wind from any direction Functions in Turbulent or gusty Wind 12/03/hawt-and-vawt.jpg HAWT Can only accept wind from a single direction 12/03/hawt-and-vawt.jpg

8 Introduction to Wind Energy Numerous Field studies have shown that for similar size VAWT and HAWT turbine installations in similar environments that the VAWT outperform compared to their HAWT counterpart. Question: Why does the prescribed standard and or general research acceptancein this area not have different power prediction calculations based on VAWT and HAWT classification?

9 Overview Introduction to Wind Energy Data Acquisition and Statistical Summarisation The Generation of Power Curves Current Power Prediction Techniques. Artificial Wind Speeds System Response Modeling Acknowledgements

10 Data Acquisition and Statistical Summarisation DUBLex (Dublin, Urban Boundary Layer Experiment) UCD, DIT and NUI Maynooth. High resolution data for multiple purposes e.g. CO 2 monitoring / temp / moisture / wind speed Has multiple applications air quality / litter dumping / temp. hot spots / urban wind generation. A mast installation is on top of DIT Kevin Street for approximately 1 year also Marrowbone Lane URB1 St Pius SUB2

11 Data Acquisition and Statistical Summarisation Longitudinal (Cosine corrected) wind speed in a 10 minute sample. (Red arrows) Met Mast 6000 wind (speed/direction) observations or one window of 10 minutes Meteorological equipment measures 3D 10Hz wind data Then converted to conform with IEC Mean Wind Direction (over duration of observatrion window) w Individual wind vector u Longtitudinal wind velocity vector v Lateral wind velocity vector Vertical wind velocity vector However should we be using polar wind speeds (black arrows) for VAWTs w u v Cosine Corrected Wind Vector Mean of all cosine corrected wind speeds along the mean (window) direction line (Interpreted from IEC, 2006)

12 Data Acquisition and Statistical Summarisation From this industrial standard 10 minute bins are drawn based on longitudinal values of mean TI and a proposed new metric T Df This metric essentially measures how noisy a signal is. T Df = unbounded Fractal Dimension by Fourier means Analysis

13 Data Acquisition and Statistical Summarisation 1 Df = 1.00 Black Noise Df = 1.50 Brown Noise Df = 2.00 Pink Noise Df = 2.50 White Noise 0.5 Analysis

14 Df =1 is effectively 0% turbulence by the T Df metric Data Acquisition and Statistical Summarisation However the current TI metric would classify this sample as having 31% turbulence The current TI metric does not allow for trends within the wind speed sample N.B.the T Df metric does not cater for the spread of the erratic signal Therefore there is a need for both metrics when describing a wind speed signal

15 Overview Introduction to Wind Energy Data Acquisition and Statistical Summarisation The Generation of Power Curves Current Power Prediction Techniques. Artificial Wind Speeds System Response Modeling Acknowledgements

16 The Generation of Power Curves The ability to predict the power from a micro wind turbine has long been a source of controversy within industry. Inaccuracies in excess of 30% have been recorded but rarely quoted due to commercial sensitivity. Common issues that have been quoted have been the lack of accurate data / poor site assessment / overestimated manufacturers data. Also there is an ever increasing argument as to the inaccuracy of power curves so much so that IEC (2006) has specified strict criteria as to how and what needs to be measured. However this involves the use of regressive averaging which has an unknown statistical error for each turbine tested

17 The Generation of Power Curves 6 5kW demo model Power Curve 5 Power output t kw This particular study was for a 5kW turbine in a rural environment. Why is there such a spread for the power per wind speed division? Wind Speed m/s

18 The Generation of Power Curves 5kW demo model Power Curve 6 5 Power output t kw Note this power curve is only representative for this particular environment i.e. Typically tested in a low turbulence environment Wind Speed m/s

19 Overview Introduction to Wind Energy Data Acquisition and Statistical Summarisation The Generation of Power Curves Current Power Prediction Techniques. Artificial Wind Speeds System Response Modeling Acknowledgements

20 Current Power Prediction Methods 10 minute wind speed distributions can be fitted into Weibull distributions even in turbulent environments! High Turbulence (Urban/suburban) Med Turbulence (Suburban/Rural) Low Turbulence (Rural/Off-shore) Low ū Logarithmic PDF Logarithmic / Rayleigh PDF Rayleigh PDF Medium ū Logarithmic / Rayleigh PDF Rayleigh PDF Rayleigh / Gaussian PDF High ū Rayleigh PDF Rayleigh / Gaussian PDF Gaussian PDF The shape and/or scale of the distribution will change due to the turbulence measured in the sample. This gives a different spread of wind speeds and therefore adjusts the power curve based on turbulence. Probability Sample Weibull Distributions sh=0.5 sc=1 sh=1.0 sc=1 Exponential sh=1.5 sc=1 sh=2.0 sc=1 Reyleigh sh=2.5 sc=1 sh=3.0 sc=1 sh=3.5 sc=1 sh=4.0 sc=1 sh=4.5 sc=1 sh=5.0 sc=1 Gaussian

21 Current Power Prediction Methods Dynamic modelling based on best fit Gaussian histogram model for each 10 minute window Av erage Turbine Pwr. Power [kw] TI=10% TI=15% TI=20% TI=25% TI=30% TI=35% TI=40% TI=45% TI=50% TI=55% TI=60% TI=65% TI=70% TI=75% Wind Speed [m/s]

22 Current Power Prediction Methods Dynamic modelling based on best fit Weibull histogram model for each 10 minute window Power [kw] Wind Speed [m/s] Av erage Turbine Pwr. TI=10% TI=15% TI=20% TI=25% TI=30% TI=35% TI=40% TI=45% TI=50% TI=55% TI=60% TI=65% TI=70% TI=75%

23 The Generation of Power Curves Previous works have investigated the statistical accuracy of both of the above processes. Both the Weibull and the Albers (Gaussian) approximations have high mathematical accuracies. >95% of all values lie within 0.05 of Prated of the turbine even when using narrow wind speed bins (0.5m/s). Major Assumption! This model relies on an instantaneous response model! Mechanical inertia, Blade response, Generator pick up, inverter pick up is not considered in a frequency based power prediction model! A time series model needs to be developed in order to consider the above!

24 Overview Introduction to Wind Energy Data Acquisition and Statistical Summarisation The Generation of Power Curves Current Power Prediction Techniques. Artificial Wind Speeds System Response Modeling Acknowledgements

25 Artificial Wind Speeds Generation of Artificial wind speed signals based on TI, T Df and mean speed If we consider a 10 minute bin of 10Hz data summarised to mean, TI and T Df Question: What can we do with it? It is pointless in proposing a new metric (T Df ) unless it has some practical application So lets consider mixing Gaussian statistics with non Gaussian statistics!

26 Artificial Wind Speeds Consider a series of 600 random numbers (n x ) between 0-1 subjected to the following convolution ( ) in the frequency domain. Where: T Df (Turbulent Fourier Dimension)=(5-q)/2 Frequency domain equivalent with i indexing filter For this example lets take a T Df of 1.8, a TI of 0.45 (45%), and a u mean of 7.5 m/s

27 Artificial Wind Speeds Generating a fractal curve of known T Df gives the following graph. u m/s 10 TDf = mean fractal curve Fractal noise is scale invariant and as such has the same fractal properties at any scale Note the amplitude is not defined! 2 If we zoom in the concept becomes clearer! time in seconds

28 Artificial Wind Speeds Zooming in shows the fractal self symmetry within the curve. However this is not scaled and as such is of no use on its own. If we normalise to unit Standard deviation (divide by standard deviation) uniform scaling is maintained giving; u m/s TDf = mean fractal curve time in seconds

29 Artificial Wind Speeds Now that the curve is normalised around zero a known spread can be applied. u m/s 10 TDf = 1.80 normalised 0 mean fractal curve Standard dev is = mean x TI 8 6 So multiply across to give the next slide time in seconds

30 Artificial Wind Speeds Now that the curve has a spread indicative of the standard u m/s 10 TDf = 1.80 TI = 0.45 TI spread fractal curve deviation it is now time to add in an 8 average time in seconds

31 Artificial Wind Speeds This artificial wind speed has the same statistical properties as an original recording of T Df, TI and u mean. u m/s 10 8 Fractal curve with TDf = 1.80, TI = 0.45, Umean = 7.5 Early comparisons have shown this model to have a 97% statistical accuracy compared to a frequency bin equivalent However this is not over the full data set time in seconds

32 Overview Introduction to Wind Energy Data Acquisition and Statistical Summarisation The Generation of Power Curves Current Power Prediction Techniques. Artificial Wind Speeds System Response Modeling Acknowledgements

33 System Response Modelling If we consider the seriality of wind speeds as consecutive first order transients based on how quick will the system be able to respond to a change in wind speed. If we assume that these transients have a natural growth / decay curve as influencing the input response function (wind speed). In simple terms how quickly can the system respond to a change in input parameter? Adapted Heaviside step function De-convolution theory normally could be used as a means of acquiring an input response function however in this instance the base point (u start ) is constantly changing. This new model can then be benchmarked etc.

34 System Response Modelling If we consider the first 25 points of the previous artificial time series. u m/s Artificial Time Series Note strictly speaking this should only be displayed as points as they are specific datums at a known time time in seconds

35 System Response Modelling Also strictly speaking we do not know what happens between each of these points. u m/s Artificial Time Series at datum points This can be used then as an input argument What time constant whether growth or decay is suitable? time in seconds

36 System Response Modelling Where: U res = u per unit time U start = initial u at start of transient window u = change in u over transient window As τ increases e.g. larger turbines have greater inertia u m/s τ =1 simulation of system response Time Series Modelling Incorporating System Inertia Wind Speed Recordings System Responce time in seconds

37 System Response Modelling Where: U res = u per unit time U start = initial u at start of transient window u = change in u over transient window As τ increases e.g. larger turbines have greater inertia u m/s τ =5 simulation of system response Time Series Modelling Incorporating System Inertia Wind Speed Recordings System Responce time in seconds

38 System Response Modelling Where: U res = u per unit time U start = initial u at start of transient window u = change in u over transient window As τ increases e.g. larger turbines have greater inertia u m/s τ =25 simulation of system response Time Series Modelling Incorporating System Inertia Wind Speed Recordings System Responce time in seconds

39 System Response Modelling Statistical accuracy of the system response model.

40 Overview Introduction to Wind Energy Data Acquisition and Statistical Summarisation The Generation of Power Curves Current Power Prediction Techniques. Artificial Wind Speeds System Response Modeling Acknowledgements

41 Acknowledgements The author(s) would like to acknowledge Dr. Rowan Fealy, of the National University of Ireland, Maynooth (NUIM) and Dr. Gerald Mills, University College Dublin, (UCD) for providing the wind data employed in this analysis and also Axel Albers, for helpful comments at the early stages of the research.

42 Thank you