Wind power prediction Techniques

1. Wind Turbine Energy
Project Guide: Prof. Rajesh Wadhwani
Project members:
Lovely Mandal
Akash Rai
Amit Chaudhary
Dhiresh Das

2.  Study of effects of various factors which influence the
performance of the wind turbines and to predict wind
turbine energy at a given wind speed by generating
wind turbine energy vs. wind speed graph using the
training data available from wind turbine fields, using
machine learning techniques.
Objective

3.  A well-designed and optimum energy system will be cost
effective, reliable and in addition, would improve the
quality of life of its consumers.
 Wind turbine power curve shows the relationship between
the wind turbine power and hub-height wind speed. It
captures the wind turbine performance.
 It plays an important role in condition monitoring and
control of wind turbines.
 Accurate models of power curve serve as an important
tool in wind power forecasting and aid in wind farm
expansion.
Why we study about it?

4.  The basic power stages of a wind energy conversion
system are shown in Fig:
Basics of wind energy conversion
system

5. Powers equations
• Instantaneous wind power
available in a cross sectional
area A perpendicular to a wind
stream moving at a speed of n
(m/s) having air density r is
expressed as
 This wind power is converted
into mechanical power Pm by
the wind turbine, which is
given by
• This mechanical power is then
supplied to the mechanical
transmission system (gear,
etc.) the output of which, i.e.
Pt is fed to electrical
generator as input.
 The generator output is then
given as

6. There are three main factors that determine the power
output of a wind turbine:
1. wind speed distribution of selected site where wind
turbine is installed.
2. the tower height
3. power output curve of chosen wind turbine (determined
by the aerodynamic power efficiency Cp, mechanical
transmission efficiency hm and generator efficiency hg).
 The following slides gives a brief explanation of above points.
Factors influencing the power
output of the wind turbine

7.  It has been found from long term study of wind speed
variation at many locations around the world, that the
Weibull probability distribution function f (n), describes
the wind speed distribution, most suitably.
 The wind speed n is distributed as Weibull distribution, if
its probability density function is
 Depending upon the wind profile of the selected site, value
of Weibull’s Shape parameter (k) and Weibull’s Scale
parameter (c) changes.
Wind speed distribution of selected
site

8. The impact of tower height and roughness of
the terrain on the performance of WECS
 The most common of these
expressions to express
relationship between wind
speed and height is
 amount of output energy
generated by a wind turbine, is
dependent on the height at
which wind turbine is located
and on the roughness of the
terrain.

9. Power Curve
Wind turbine power curve shows the relation between wind turbine power
and wind speed at hub height. It captures the performance of the turbine.
The basic three important wind
speeds identified where wind turbine
power curve of various turbines
shows similar characteristic are :
 Theoretically the relation
between power and wind
speed is given as:
P = 0.5 ρ π R2 Cp u3
 All other parameters are
constant except Cp (power
coefficient denoting
percentage of power
captured) and u3 (wind speed).
Rated speed
Cut-in speed
Cut-out speed

10. IEC Power curve
it is a standard methodology to measure power performance characteristic
of wind turbine, given by International Electrical commission technical
committee-88.
 It is generated by collecting data
(simultaneous measurements of
wind speed and power output)
for sufficiently long duration
under varying atmospheric
conditions and creating a
database.
 The power curve is determined
by applying the method of bins
for normalised datasets.
Drawbacks
 The power curve determined by
this method has hidden effects
of current site turbulence.
 It ignores the fast wind
fluctuations by averaging the
wind speeds over duration of 10
min, hence this results in
behaviour of machine
independent wind fluctuations.

11. WTPC Modelling
It does statistical analysis of data and performance metrics validates the
modelling procedures.
Requirements
 1. Modelling data: historical data or
data collected over a long duration
from a supervised wind farm are
analysed using the following
methods: averaged over short time
intervals, by using method of bins,
power curve and statistical analysis.
 2. Factors affecting power curves:
changing environmental and
topological conditions. The effects
of topological conditions can be
reduced by averaging power from a
range of power curves at different
wind speeds.
 3. Modelling accuracy: achieved by
reducing errors such as, absolute
error, relative errors etc
Methodology:
Mathematical modelling of wind
turbines can be based either of
one way:
 1. Fundamental equation of
power available in the wind.
(Cumbersome approach)
 2. Concept of power curve of
the turbine. (Gives fairly
accurate results)

12.  The models can be classified into two categories:
 Models based on fundamental equations of power
available in the wind.
 Models based on the concept of power curve of wind
turbine.
Models for predicting behaviour of
wind turbine

13. Models based on fundamental equations of
power available in the wind.
• Ashok presented that wind
power output can be calculated
by
 Nelson et al. evaluated
average hourly wind speed
data and converted it to wind
turbine power and stated that
• where, Effad is assumed as 95%.
• For wind speeds between rated
speed and the furling speed of the
wind turbine, the power output
will be equal to the rated power
of the turbine.
• For wind speeds less than the cut-
in speed or greater than the
furling speed of the turbine,
power output from the turbine
would be zero.

14. Models based on fundamental equations
of power available in the wind.
• Kolhe et al. stated that power
output of WECS is given by
 Habib et al. proposed that maximum
attainable power from a wind
energy conversion system assuming
mechanical electrical conversion
efficiency of 100% is given by
• El-Shatter et al. have calculated the
power captured by the wind turbine as
 Variation in values of ht, hg and Cp
with wind speed and design of wind
turbine.
 Variation in value of air density with
changing weather conditions.
 Variation in the value of Pe for various
wind speed ranges.
 Due to interdependence of the
parameters(wind speed, the
rotational speed of turbine,
 turbine blade parameters (angle of
attack, pitch angle etc.),) and their
variation with change in wind
speed,due to such factor accourate
results are not generated.
Limitations

15. Models based on a presumed shape
of power curve.
1.Model based on linear
power curve:
 Yang et al.and Abouzaher et al.
assumed that output power of the
wind turbine increases linearly with
the wind speed from cut-in to rated
wind speed and then it remains
constant from rated to furling
speed. Accordingly, following
characteristic equations have been
proposed for modelling the wind
turbine:
Limitations
 This method, though very
simple, does not give accurate
results in the range of cut-in to
rated speed, as power curve of a
wind turbine is seldom linear.

16. Models based on a presumed shape
of power curve.
2.Model based on cubic law
 Deshmukh et al.and Chedid et
al. have presented that output
power density (in W/m2) from a
wind turbine generator can be
calculated as given
Limitations
 Variations in parameter.

17. Models based on a presumed shape
of power curve
3. Model based on cubic spline
interpolation technique.
 the output power of wind turbine is
calculated through interpolation of
values of data provided by the
manufacturer, by using cubic spline
interpolation.
 For wind turbines having smooth
power curve the models based on,
method of least squares and cubic
spline interpolation both replicate the
performance of actual turbine almost
exactly.
 For wind turbines having non-smooth
(not that smooth) power curve model
based on the method of least squares
replicates the performance of actual
wind turbine almost exactly.

18. There are various methods for mathematical modeling of wind
turbines graphs.
Given below is an classification based on the same:
WTPC modelling can be
further classified as: (i)
Parametric techniques (ii)
Non-parametric techniques.

19. Based on solving mathematical
equations for power at
different wind speeds: cut-in
(uc), rated speed (ur) and cut-
out (us).
Following slides contains some
parametric techniques .
Parametric techniques

20. 1. Linearized segmented model
 piecewise approximation of the
WTPC using straight line
segment equations. Data is
fitted using least square
methods, the equation for which
error value is the least, is taken
as the best suited curve
equation.

P = mu + c
Limitations
 the approach is not practical,
as it assumes the wind
measures as error free.
 This can be overcome by total
least square criterion which
keeps contribution of noise
components and
meteorological variables in
account.

21. 2. Polynomial power curve
 used to model linear region of
WTPC. Polynomial equations of
different degrees can be used,
such as quadratic, cubic,
approximate cubic power etc.
 Cubic power curve
 Approximate cubic power
curve, where Cpeq is replaced
by Cpmax.
Limitations
 There can never be a unique set of
generalised characteristic that can
be used for all types of turbines, as
their shapes vary with every
different turbine. It lacks accuracy
between cut-in and rated speed.
Quadratic equation shows worst
results due to sensitivity of the data
given by manufacturers, compared
to it cubic curves gives better
results.

22. 3. Maximum principle method
 The power curve is defined by
the location, where, in a given
wind speed bin, the maximal
density of points Pi is found i.e.
the power curve is given by the
points {uj,Pk(j)}, where j is the
number of the speed bin and
k(j) denotes the power bin.
Limitations
 Rauh's method of maximum
principle overestimated the
points in the region of
transition to the rated power
in the WTPC and the accuracy
of the method was also not
good.

23. 4. Dynamic power curve
 It is defined by Rauh’s
empirical power curve which
separates the dynamics of the
wind turbine power into two
parts: (I) deterministic part –
actual behaviour of wind
turbine (II) stochastic part-
corresponds to the external
factors such as wind
turbulence. This part can be
further classified in in drift and
diffusion part.
Advantages
 it is very much accurate. It
could extract dynamic
behaviour of the wind and can
produce machine independent
and site specific results.
Measurement taken over a
short time duration is enough.

24. 5. Probabilistic model:
 This model characterizes the
dynamics of wind energy
production and estimates the
uncertainty in wind power
when the wind turbine
generators operate in the
region between cut-in and
rated wind speed. The wind
turbine power is assumed to
follow the normal distribution
with a varying mean and
constant standard deviation.
 The wind turbine output
power is a random number
whose value is determined by
u, the wind speed and ε, the
variation of the power output.

25. 6. Ideal power curve
 The main application of the ideal power curve is assessment of
wind energy available in a test site extension of power curve to
sites of different turbulence levels. It deals with conditions such as
steady and laminar flow of wind, absence of yaw error and steady
state power output.

26. 7. Four parameter logistic function
 here the parameters as
estimated using lease square
method, maximum likelihood
method and logistic
programming method. The
parameters are obtained using
genetic algorithms (GA),
particle swarm optimization
(PSO) and differential
evolution (DE).
Advantages
 shows more accuracy than
many non-parameterized
techniques.

27. 8. Five parameter logistic function
 the expression and parameter
are solved using GA, EP, PSO
and DE. Advantage
 compared to all parametric and
non-parametric models, this
shows the best results.

28.  It is solved by using the assumption i.e.
P= f(u).
Following are some are some of the non-parameterised
models:
Non-parametric techniques
it is used to find a relationship between wind speed and power generated.

29.  It is a distribution function which describes the
relation between two variables. It includes the
measurement of uncertainty while estimating the
performance and also allows the comparison
between inter-plant performances.
1. Copula power curve model

30. 2. Cubic spline interpolation
technique
 the process of estimating
values that lie between two
known data points. The
different kinds of interpolant
methods include linear
interpolation, nearest
neighbour interpolation, cubic-
spline and Piece-wise Cubic
Hermite Interpolation (PCHIP).
This method fits a different
cubic polynomial between
each pair of data points.
 Advantage
perform extremely well for
wind turbines with smooth
power curve

31. 3. Neural network
• it is an information-processing
model simulating the operation
of the biological nervous
system.
• The equivalent steady state
model of wind farm has been
built using three different
neural network models namely:
(I) generalized mapping
regressor (GMR) - novel
incremental self-organizing
competitive network, (II) a feed
forward multi-layer perceptron
(MLP) - used for estimation of
annual energy and a general
regression neural network
(GRNN) - radial basis network.
Advantages
 Using a separate neural network for
each turbine. This scheme can
greatly reduce the size and
complexity of the neural network
 The operation of a wind farm usually
requires some of the wind turbines
to be off-line. The scheme of a
neural network for each turbine will
not be influenced by the cases that
some turbines are off-line.
 Third, this approach scales better for
large wind farms.

32. Neural Network Model
 The trained NN can be used to estimate the
wind turbine power generation directly based
on wind velocity and direction information.
 Even though the traditional method uses
coefficients reflecting actual wind speed
relationships among the turbines and reference
anemometers, there is still a large difference
between the measured and estimated wind
power. This occurs because it does not reflect
the dynamic performance of a wind turbine
under changing wind conditions and many
other factors. The superior neural network
results are due to its ability to learn such
factors..
 characteristics of wind power generation are
first evaluated in order to establish the relative
importance for the neural network. A four input
neural network is developed and its
performance is shown to be superior to the
single parameter traditional model approach.

33. 4. Fuzzy methods
it is a multi-valued logic deals with approximate reasoning. It consists of
following methods.
 (i) Fuzzy cluster centre method: data
are clustered and the number of
cluster centres is determined using
the modelling algorithm. The more
the number of clusters, higher is the
accuracy of the technique. Its
performance is better than least
square method.
 (ii) Fuzzy c-mean clustering:
eliminates the effect of hard
membership. Uses membership
matrix and identifies cluster centres,
allowing data points to have
different degrees of membership for
different clusters.
 (iii)Subtractive clustering:
density function is calculated
for every data point instead of
every grid point, reducing
number of calculations.
 Advantage: gives best model
of WTPC.

34. References
 “Critical analysis of methods for
mathematical modelling of wind turbines”,
Vinay Thapar, Gayatri agnihotri, vinod
krishna Sethi, 10 march 2011, Elsevier
 “A comprehensive review on wind turbine
power curve modeling techniques”, M.
Lydia, S. Suresh Kumar, A. Immanuel
Selvakumar, G. Edwin Prem Kumar, 21
October 2013, Elsevier
 “Using Neural Networks to Estimate Wind
Turbine Power Generation”, Shuhui Li,
Member, IEEE, Donald C. Wunsch, Senior
Member, IEEE, Edgar A. O’Hair, and Michael
G. Giesselmann, Senior Member, IEEE, IEEE
TRANSACTIONS ON ENERGY CONVERSION,
VOL. 16, NO. 3, SEPTEMBER 2001