chapter 2 a review on wind power...

CHAPTER 2 – A REVIEW ON WIND POWER FORECASTING 23

CHAPTER 2

A REVIEW ON WIND POWER FORECASTING

Forecasting of wind power can be performed using several techniques.

Forecasting of the wind speed is a primary step involved in forecasting of wind power.

The wind speed forecast is used for predicting wind power using the manufacturer’s

power curve or any other wind turbine power curve model. Hence, in this chapter, a

review of existing wind speed forecasting models, wind turbine power curve models

and wind power forecasting models have been presented.

Part of the work reported in this chapter has been published as under:

1. Lydia. M., Suresh Kumar. S., Immanuel Selvakumar. A. and Edwin Prem Kumar. G.

(2014) “A Comprehensive Review on Wind Turbine Power Curve Modeling

Techniques”, Elsevier - Journal of Renewable and Sustainable Energy Reviews, 30,

452 - 460 (Impact Factor: 5.627) doi: 10.1016/j.rser.2013.10.030

2. Lydia. M. and Suresh Kumar. S. (2010) “Wind Farm Power Prediction : An

Overview” Fifth International Symposium on Computational Wind Energy, CWE2010,

23-27 May 2010, Chapel Hill, North Carolina, USA.

ftp://ftp.atdd.noaa.gov/pub/cwe2010/Files/Papers/291_edwin.pdf

3. Lydia. M. and Suresh Kumar. S. (2010) “A Comprehensive Overview on Wind Power

Forecasting” 9th

International Power and Energy Conference IPEC 2010, 27-29

October 2010, Suntec, Singapore, 268-273. DOI: 10.1109/IPECON.2010.5697118

http://dx.doi.org/10.1109/TSTE.2013.2247641

ftp://ftp.atdd.noaa.gov/pub/cwe2010/Files/Papers/291_edwin.pdf


2.1 REVIEW ON WIND SPEED FORECASTING TECHNIQUES

Forecasting of wind speed has become important in the recent days.

According to Abdel-Aal (2009), wind speed forecasts play a vital role for the operation

and maintenance of wind farms and for integration into power grids as well as in

shipping and aviation. Availability of accurate wind forecasts will definitely go a long

way in improving the security of power grid, increasing the stability of power system

operation and market economics and aid greatly in enhancing the penetration of wind

power (Abdel-Aal, 2009). This will definitely result in large scale reduction of

greenhouse gas emissions and the other pollutants emitted during the consumption of

the depleting conventional energy sources. Wind speed forecasting models aid in

effective management and safety of port areas too (Solari et al., 2012).

Wind speed forecasting models have been developed based on several

statistical and learning approaches.

2.1.1 Statistical Techniques

The wind speed probability distribution describes the likelihood that certain

values of wind speed will occur. The probability distributions are generally

characterized by probability density function (pdf) or a cumulative density function

(cdf)) (Manwell, 2009). The two commonly used probability distributions in wind data

analysis are the Rayleigh and Weibull distribution. Rayleigh distribution requires only

the knowledge of mean wind speed ( y ) and hence is the simplest velocity probability

distribution. The pdf and cdf of Rayleigh distribution is given below:

2

2 4exp

2 y

y

y

ypdf

-----(2.1)


2

4exp1

y

ycdf

-----(2.2)

The pdf and cdf of Weibull distribution is given in Equation (2.3) and Equation (2.4)

kk

c

y

c

y

c

kpdf exp

1

-----(2.3)

k

c

ycdf exp1 -----(2.4)

where k is the shape factor and c is the scale factor. Higher the value of k, lesser is the

observed wind speed variation. Olaofe and Folly (2013) carried out wind resource

assessment of their test site using Weibull’s and Rayleigh’s distribution.

The other statistical techniques used to forecast wind speed include Auto

Regressive Moving Average (ARMA), Empirical Mode Decomposition (EMD)

technique etc. Kavasseri and Seetharaman (2009) highlight the fact that accurate wind

speed forecasts are essential to schedule dispatchable generation and tariffs in the day-

ahead electricity market. They have developed fractional Auto Regressive Integrated

Moving Average (ARIMA) models to predict wind speed on 24h and 48h horizons.

The results suggested that this method was able to improve the forecasting accuracy by

an average of 42% compared to the persistence method. A linear prediction model for

wind speed forecasting has been developed based on current data and the previous one

/ and two years data corresponding to the same period (El-Fouly et al 2008). The wind

speeds predicted by this model showed significant improvement up to 54.4% for MAE

and 55.3% for RMSE.

A hybrid high-precision forecasting method based on EMD and time-series

analysis has been developed by Liu et al (2009). Li and Wang (2008) have developed

an EMD-ARMA model for short-term wind forecasting for wind farms. Erdem and

Shi (2011) predicted the tuple of wind speed and direction using ARMA based


approaches. Guo, Wu, Lu and Wang (2011) developed a new hybrid wind speed

forecasting method to forecast the daily average wind speed one year ahead. They

eliminated the seasonal effects from actual wind speed datasets using seasonal

exponential adjustment and used the back propagation neural network for prediction.

Gomes and Castro (2012) have developed forecasting models for wind speed and

power using ARMA and ANN (Artificial Neural Networks). They concluded that

ARMA models performed better than ANN but were slightly time consuming.

Wavelet transformation is a tool for time-frequency analysis. It decomposes

the highly non-linear wind speed time series into several approximate stationary time-

series (Lei and Ran 2008). A hybrid model based on wavelet-decomposition and

ARMA for short-term wind speed prediction of wind farm has been presented by Lei

and Ran (2008). Liu, Tian, Chen and Li (2010) proposed a hybrid statistical method to

predict wind speed and power. They developed a new short-term forecasting method

based on wavelets and classical time series analysis.

2.1.2 Soft-Computing Techniques

Barbounis and Theocharis (2007) employed local recurrent neural networks

for wind speed prediction using spatial correlation. The prediction performance was

improved by using online learning algorithms based on the recursive prediction error

approach. A hybrid model for short-term wind speed forecasting was developed using

Hyperbolic Tangent Unit (HTU)-based NN by Hervas-Martinez et al (2009). These

networks were trained using evolutionary algorithms and they outperformed the

conventional ANN like Multi-Layer Perceptron (MLP). Shuang et al (2007) developed

a wind speed forecasting model developed using ANN based on Tabu search

algorithm.


An ANN-based wind speed forecasting model has been developed by

Cadenas and Rivera (2009) and the performance of this model was tested with different

architectures and the simplest model with two layers, two input neurons and one output

neuron gave good results with MSE and MAE of 0.16% and 3.99% respectively. Wind

speed forecasting model was developed using three different NN types namely

adaptive linear element, back propagation and Radial Basis Function Network (RBFN)

by Li and Shi (2010). The performance of these models was evaluated using MAE,

MSE and MAPE. Tran et al (2009) developed a wind speed forecasting model based

on wavelet transform and cascade-correlation neural networks. Short-term wind speed

prediction model based on evolutionary support vector regression algorithms was

developed by Salcedo-Sanz et al (2011). A multiple architecture system for the

prediction of wind speed has been developed by Bouzgou and Benoudjit (2011).

Different regression algorithms like MLP, RBFN and Support Vector Machine (SVM)

has been used to build the model and three fusion strategies have been employed

namely simple, weighted and non-linear.

A short-term wind forecasting method based on Gaussian process, making

use of kernel machine technique and Bayesian estimation has been presented by Mori

and Kurata (2008). It reduced 27% and 12% of average error for MLP and RBFN

respectively. It also reduced the maximum error by 13% and 7.8% for MLP and RBFN

respectively. Abdel-Aal (2009) proposed the use of abductive networks based on the

group method of data handling, to model and forecast the mean hourly wind speed.

Monfared, Rastegar and Kojabadi (2009) developed a new technique for wind speed

forecasting based on fuzzy logic and artificial neural networks. Kusiak and Li (2010)

developed a data-driven approach for estimation of wind speed. They concluded that

for a given training and testing scenario, better prediction accuracy depended on higher

Pearson’s correlation coefficient.


Shi, Guo and Zheng (2012) have evaluated hybrid prediction techniques for

wind speed and power generation. The performance of two hybrid models, namely

ARIMA-ANN and ARIMA-SVM have been compared with the single ARIMA, ANN

and SVM forecasting models. It was observed that they don’t produce better

forecasting performance consistently for different forecasting time horizons. A

recurrent neural network based wind speed forecasting model has been developed by

Cao, Ewing and Thompson (2012).

Guo, Zhao, Lu and Wang (2012) developed a modified empirical mode

decomposition based ANN model for multi-step prediction of wind speed. Vaccaro,

Bontempi, Taieb and Villacci (2012) developed multiple-step ahead wind speed

prediction models based on adaptive local learning techniques. A spectral and a

multifractal analysis of time-series wind speed data were performed on 412 data each

of duration 350s, sampled at 20 Hz and its effect on wind energy production was

investigated (Calif and Schmitt, 2012). Time series wind speed data has a fractal

character and could be modelled using Weierstrass function fitted by genetic algorithm

(Barszcz et al., 2012). The main objective was to use it as a model of load of wind

turbine gears for simulation of different operational conditions for wind turbine

vibration modeling. Gan et al., (2012) developed a novel method of wind speed

prediction based on Mycielski algorithm. The wind speed values are converted to wind

states in order to apply this algorithm.

A combination forecasting model comprising of time series and back

propagation neural network prediction model for short-term wind speed prediction has

been developed (Nan et al., 2013). A wind speed forecasting bias correction method

based on empirical orthogonal function has also been proposed. Liu et al., (2013) have

developed three hybrid models for wind speed forecasting, based on the theories of

wavelet, wavelet packet, time- series analysis and artificial neural networks. The


performance of these models have been compared with some classical prediction

techniques including Adaptive Neuro-Fuzzy Inference System (ANFIS), wavelet

packet – RBF (Radial Basis Function) and persistence method. Jiang, Song and Kusiak

(2013) have developed a time-series forecasting model based on Bayesian theory and

structural break modeling. This Bayesian structural break model predicts wind speed

as a set of possible values, which could be used for wind turbine predictive control and

wind power scheduling.

2.2 REVIEW ON WIND TURBINE POWER CURVE MODELING

TECHNIQUES

A Wind Turbine Power Curve (WTPC) can go a long way in providing

accurate forecasting of wind power. The output power of a wind turbine significantly

varies with wind speed and hence every wind turbine has a very unique power

performance curve. A power curve aids in wind energy prediction without the technical

details of the components of the wind turbine generating system (Manwell et al. 2009).

The electrical power output as a function of the hub height wind speed is captured by

the power curve. Power curves for existing machines, derived using field tests, can be

obtained from the wind turbine manufacturers. The approximate shape of the power

curve for a given machine can also be estimated using the power characteristics of

rotor, generator, gearbox ratio and efficiencies of various components. The conversion

of power in the wind into actual power varies non-linearly because of the transfer

functions of available generators (Monteiro et al. 2009).

The data required for modeling a power curve is the wind speed and power

output recorded at periodic intervals over a long time. The historical data could either

be obtained from experimental wind farms or from the SCADA system. Once the

required data is available, the energy production of the wind turbine can be analyzed


using four different approaches namely, direct use of data averaged over a short time

interval, the method of bins, development of velocity and power curves from data and

statistical analysis using summary measures (Manwell et al. 2009).

2.2.1 IEC Power Curve

The International Standard IEC 61400-12-1 has been prepared by the

International Electrotechnical Commission (IEC) technical committee 88: Wind

turbines. The standard methodology for measuring the power performance

characteristics of a single wind turbine has been specified here. It is also applicable for

testing the performance of wind turbines of varied sizes and types. It can be used to

evaluate the performance of specific turbines at specific locations and also aid in

comparing the performance of different turbine models or settings (IEC 61400-12-1,

2005).

The power performance characteristics of wind turbines are ascertained by

the measured power curve and the estimated annual energy production. Simultaneous

measurements of wind speed and power output is made at a test site for sufficiently

long duration to create a significant database under varying atmospheric conditions.

The measured power curve is determined from this database. The annual energy

production is calculated, assuming 100% availability, by applying the measured power

curve to reference wind speed frequency distributions.

The measured power curve is determined by applying the “method of bins”,

for the normalized datasets using the following equations:

iN

j ji

i

i yN

y1 ,,n

1 -----(2.5)


iN

j ji

i

i PN

P1 ,,n

1 -----(2.6)

where yi is the normalized and averaged wind speed in bin i, yn,i,j is the normalized

wind speed of dataset j in bin i, Pi is the normalized and averaged power output in bin

i, Pn,i,j is the normalized power output of dataset j in bin i and Ni is the number of

10min data sets in bin i. The accuracy of WTPC models have improved by using the

profile information available using remote sensing instruments (Wagner and Courtney

2009). However, it has been stated by Trivellato et al. (2012), that the IEC-based

power curve gives the behavior of the wind turbine with the influence of site

turbulence. Though the current site data is rendered with reliable accuracy, the IEC

power curve contains the hidden effect of current site turbulence, in such a way that its

blind application to other sites is not very correct. The IEC procedure also ignores the

fast wind fluctuations through the 10 min averaging and the results in obtaining the

behavior of the machine independent of wind fluctuations. Hence the need for

modeling site-specific WTPC has gained great significance.

2.2.2 Power Curve Modeling Objectives

A WTPC modeled from the measured data in a particular site using better

modeling techniques will definitely overcome the drawbacks posed by the

manufacturer provided power curve and the IEC power curve. A power curve modeled

from the measured data deviates when some power outputs are negative implying wind

turbine is consuming energy due to low wind speed and some power outputs vary even

when the wind speed is constant. Hence it is necessary that a power curve is modeled

with minimum error. The objective for modeling a WTPC is four fold: wind energy

assessment and prediction, choice of wind turbines, monitoring and troubleshooting

and finally predictive control and optimization of wind turbine performance (Figure

2.1).


Fig. 2.1 WTPC Modeling Objectives

Wind Energy Assessment and Prediction

Wind resource assessment is the process by which wind farm developers

estimate the future energy production of a wind farm. Accurate assessments are crucial

to the successful development of wind farms. The meteorological potential of any

candidate site is equivalent to the available wind resource (Manwell et al. 2009). If the

wind speed data of the site is available, a WTPC can facilitate the estimation of wind

energy that can be produced over a period of time. Accurate WTPC models also help

in the planned expansion of wind farms (Norgaard and Holttinen, 2004). An analytical

method to estimate the output power variation in a wind farm has been devised using

dynamic power curves by Jin and Tian (2010).

Estimating and controlling the variability of wind farm power output aids in

providing stable wind power to the utility/grid and improves loss of load expectation


(LOLE). Olaofe and Folly (2013) have concluded that the analysis of the energy

outputs of the wind turbines based on the developed site power curves is more accurate

than the turbine power curves. The WTPC models can very well be used for wind

power forecasting at varying time horizons. Accurate forecasting of wind power in

intra-day and day-ahead electricity markets are the need of the day. The power curve of

a variable speed wind turbine has been modified using a new curve called the

controllers power curve to account for the wind dynamics and has resulted in more

accurate power prediction (Zamani et al. 2007).

Choice of Wind Turbines

WTPC models aid the wind farm developers to choose the generators of

their choice, which would provide optimum efficiency and improved performance.

The impact of WTPC on the cost of energy and optimal system configuration in a small

wind off-grid power system has been presented by Simic and Mikulicic (2007).

Judicious choice of a wind turbine generator that yields higher energy at higher

capacity factor can be done by using the normalized power curves proposed by

Jangamshetti and Rau (2001). These generalized curves, obtained from a new ranking

parameter known as Wind Turbine Performance Index, can be used at the planning and

development stages of wind power stations. The wind turbine capacity factor was

modeled using the site wind speed and turbine power curve parameters by Albadi and

El-Saadany (2009, 2010). An increase in energy yield up to 5% was obtained, when

the proposed model was used for optimum turbine-site matching.

Monitoring and Troubleshooting

A WTPC model can serve as a very effective performance monitoring tool

(Kusiak et al. 2009c). The model developed can be used as a reference for monitoring


the performance of wind turbines. An equivalent steady state model of a wind farm

under normal operating conditions has been realized using data-driven approach and

has been utilized for creation of quality control charts, with the aim of detecting

anomalous functioning conditions of the wind farms (Marvuglia and Messineo. 2012).

Monitoring the performance of a wind farm using three different operational curves has

been discussed by Kusiak and Verma (2013). The WTPC has been used to identify

various faults and its severity by Kusiak and Li (2011). The wind turbine power output

has been evaluated and deviations that may result in financial losses are calculated

using online monitoring of power curves (Schlechtingen 2013). The performance of

four different data mining approaches has been compared for this purpose.

Predictive Control and Optimization

Uluyol et al (2011), showed that the WTPC can be very useful for

performance assessment and for generation of robust indicators for component

diagnostics and prognostics. Higher reliability and lower maintenance costs can be

incurred by employing condition-based rather than hour-based monitoring. A copula

model of WTPC has been used for early identification and detection of incipient faults

such as blade degradation, yaw and pitch errors (Gill et al. 2012). The copula-power

curve condition monitoring correlates faults or anomalies to statistical signatures.

Kusiak and Li (2011) have shown that power curve models along with data mining

based model extraction could be used to predict specific faults with an accuracy of

60minutes before they occur.

Wind farm power curves are adversely affected by the changing

environmental and topographical conditions. Equivalent power curve models

incorporating the effect of array efficiency, high wind speed cut out, topographic

effect, spatial averaging, availability and electrical losses have been developed by


McLean (2008). The impact of wind speed reduction due to the wakes created by the

wind turbines upstream determines the array efficiency. The main factors affecting

array efficiency are wind farm layout, wind regime and the type of terrain. Offshore

wind farms are susceptible to a higher wake loss. The effect of topography is higher in

upland wind farms than the low land wind farms, because of the greater variation in

wind speed. This can be reduced by averaging the power from a range of power curves

at different wind speeds. An equivalent regional power curve is produced for each

wind farm by averaging, in order to reduce the variation of wind speeds experienced by

wind farms across a region. Availability and electrical efficiency of offshore sites are

generally lower than onshore sites.

The effects of the environmental parameters on wind turbine power

probability density function curve were studied by Jafarian et al (2008). These

parameters included the annual average wind speed, k-factor of Weibull distribution,

autocorrelation factor, diurnal pattern strength, altitude above sea level and variance of

monthly averaged wind speed in one year. It was found out that the altitude above sea

level (which determines the air density indirectly) and the k-factor of Weibull

distribution affected the wind turbine output power more than all the remaining

parameters.

Site-specific adjustments are required by wind turbine power curves in order

to address the effects of turbulence, complex terrain, wind shear, blade fouling and

icing, power curve measurement blockage effects and uncertainty in availability of

wind farms (Tindal et al. 2008). It was observed that for a site with 18% turbulence, a

1% reduction of energy took place. Hence for sites, where the predicted turbulence

levels and wake effects are more than 15%, a turbulence power curve adjustment factor

should be applied. For complex terrains, it was suggested that an up-flow power curve

adjustment factor be applied. To account for the uncertainty in power curve and wind


turbine availability, an allowance equivalent to 2% of the wind farm energy production

has also been suggested. As the output power of wind turbine varies as the cube of the

input wind speed, it is the variability in the wind speed that affects the power curve

most. If the annual mean wind speed varies by 10%, it was observed that the

corresponding variation in available wind energy was about 25% (Khalfallah and

Koliub 2007a).

The most important criteria to be addressed while formulating the various

techniques for WTPC modeling, is the model accuracy. Different performance

metrics have been used by various researchers. The most common metrics are AE, RE,

MAE, RMSE, sMAPE, NMAPE, coefficient of determination R2 etc.

2.2.3 Power Curve Modeling Techniques

A critical analysis of the various methods used of mathematical modeling of

wind turbines has been presented by Thapar et al. (2011). The two different kinds of

models developed by them are models based on fundamental equation of power

available in the wind and models based on the concept of power curve of the turbine.

It was concluded that models based on the equation of power were very cumbersome.

Models based on the power curve of the turbines gave fairly accurate results. The

different techniques available in literature for WTPC modeling have been classified

into parametric techniques and non-parametric techniques as shown in Figure 2.2.

Parametric Techniques

Parametric techniques are based on solving mathematical modeling

expressions. The actual wind turbine generator power output (Pa) can be expressed as

given below:


syy

ry

rP

ryy

cyyp

syy

cyy

ya

P )(

,0

)( -----(2.7)

where y is the wind speed, yc is the cut-in speed, yr is the rated speed and ys is the cut-

out speed, p(y) is the linear variable region between the cut-in speed and rated speed

and Pr is the rated power.

Fig. 2.2 WTPC Modeling Techniques

A) Linearized Segmented Model

This is the simplest parametric model where piecewise approximation of the

WTPC has been carried out using the equation of a straight line (Khalfallah and

Koliub, 2007).

Parametric Modeling Techniques

Linearized

Segmented Model

Polynomial Power Curve

Maximum Principle Method

Dynamical Power Curve

Probabilistic Model

Ideal Power Curve

4-Parameter Logistic Function

Non-Parametric Modeling Techniques

Copula Power Curve

Cubic Spline Interpolation

Neural Networks

Fuzzy Methods

Data Mining Algorithms


cmyP ------(2.8)

where P is the output power and y is the wind speed, m is the slope of the segment and

c is any constant (Figure 2.3). The data is fitted on to the linear segments using the

method of least squares, which estimates the coefficients by minimizing the summed

square of residuals. The residual of the ith

data point ri is defined as the difference

between the actual power output Pa(i) and the fitted response value Pe(i), and is

identified as the error associated with the data. The summed square of residuals (S) is

given by

N

i

ea

N

i

i iPiPrS1

2

1

2 ))()(( -----(2.9)

The least squares criterion assumes that the wind measures or forecasts are

error-free, which is never true in practice. This problem could be overcome by using

the Total Least Square (TLS) criterion, in which the contribution of the noise

components in both power and meteorological variables are accounted for in the model

parameter estimation (Pinson et al. 2008).

Fig. 2.3 Linearized Segmented Model

Power (kW)

Wind speed (m/s)

P4 = P5

P3

P2

P1 y1 y2 u3 y4 y5


B) Polynomial Power Curve

A WTPC has been modeled using polynomial expressions of varied orders

in different literatures (Jafarian and Ranjbar, 2010). Seven different models were used

to model the linear region of the wind turbine power curve by Akdag and Guler (2010)

and their energy output yields were calculated. A review of four commonly used

equations for representation of power curves of variable speed wind turbines namely

polynomial power curve, exponential power curve, cubic power curve and approximate

cubic power curve has been done by Carillo et al. (2013). All these four equations

have been used to model the linear region of the WTPC.

Quadratic Power Curve

Carillo et al. (2013) have used a second degree polynomial expression for

modeling the WTPC.

2

321)( ycyccup -----(2.10)

Where c1, c2 and c3 are constants determined from yc, ys and Pr. A WTPC based on the

method of least squares, using quadratic expressions for the linear region has been

presented by Thapar et al (2011). Three different quadratic expressions have been used

to approximate the linear region guaranteeing better accuracy.

s

c

yyyforcycyc

yyyforcycyc

yyyforcycyc

yp

23332

2

31

212322

2

21

11312

2

11

)( -----(2.11)

where c11, c12, c13, c21, c22, c23, c31, c32, c33 are coefficients of the quadratic equation and

y1 and y2 and wind speeds at heights h1 (m) and h2 (m) respectively.


Cubic Power Curve

A WTPC has been modeled using a cubic power expression by Carillo et al

(2013).

3

,2

1)( yACyp eqp -----(2.12)

where Cp,eq is a constant equivalent to the power coefficient. Model for WTPC based

on cubic law has also been used (Thapar et al. 2011). Since the fraction of the wind

power that gets converted to electrical power depends on several parameters like wind

speed, rotational speed of the turbine, angle of attack, pitch angle, mechanical and

electrical efficiencies, the accuracy decreases.

Approximate Cubic Power Curve

An approximate cubic power curve model has been derived by assigning

maximum value to the power coefficient (Cp,max) (Carillo et al. 2013).

3

max,2

1)( yACyp p -----(2.13)

Exponential Power Curve

The variable speed WTPC can be modeled using an exponential equation as

given below (Carillo et al. 2013):

)(2

1)( cp yyAKyp -----(2.14)

where Kp and are constants.


Ninth Degree Polynomial

The performance of polynomial models of fourth degree, seventh degree

and ninth degree has been compared using curve fitting toolbox of MATLAB (Raj

MSM et al, 2011). It was observed that the ninth degree polynomial given by Equation

(2.15) performed better than the other equations.

)(2

1)( cp yyAKyp -----(2.15)

where c1,…,c10 are constants. The shapes of the WTPC of different turbines with

varied design ratings are different. Hence, the major disadvantage of the polynomial

models is that there can never be a unique single set of generalized characteristic

equations that can be used for all types of turbines.

Model based on Weibull’s Parameters

A WTPC based on Weibull’s parameters has been used by Thapar et al

(2011) but the accuracy of modeling was very poor.

kbyayp )( -----(2.16)

where k

r

k

c

k

cr

yy

yPa

and

k

c

k

r

r

yy

Pb

It was observed that the model based on Weibull’s parameters lacked accuracy in the

range of cut-in to rated speed since Equation (2.16) did not accurately represent the

wind turbine power curve shape in that range (Thapar et al, 2011).

Among the polynomial based power curves, the quadratic power curve

showed the worst results due to its sensitivity to the data given by the manufacturer and

the approximate cubic power curve recorded a better performance (Carillo et al 2013).


However Raj et al (2011) observed that a polynomial of higher degree recorded better

performance.

C) Maximum Principle Method

The maximum principle method proposed by Rauh defines an empirical

power curve using a very simple method (Gottschall and Peinke 2008). 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{yj, Pk(j)}, where j is the

number of the speed bin and k(j) denotes the power bin with

i

jikik yyPPN )())(: and -----(2.17)

kjk NN )( -----(2.18)

where )(x is a Heaviside function defined by

else

widthbinparticularthewithxifx

0

221)( -----(2.19)

However, Gottschall and Peinke (2008) proved that 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.

D) Dynamical Power Curve

Determination of WTPC through a dynamical approach has been presented

using the Langevin Model by Gottschall and Peinke (2008). The main objective of this

method is to separate the dynamics of the wind turbine power output into two parts: a

deterministic and a stochastic part. The deterministic part corresponds to the actual

behavior of the wind turbine and the stochastic part corresponds to other external

factors such as the wind turbulence. The wind turbine power output is described as a


stochastic process that satisfies the Markovian property and hence can be separated

into a drift and a diffusion part.

)()()( tpyPtP stat -----(2.20)

where P(t) is the time series power data, Pstat is the stationary power value dependent

on the wind speed y and p(t) corresponds to short-time fluctuations around this value

caused by wind turbulence. The performance of the dynamical power curve was

compared with the IEC power curve and the maximum principle method according to

Rauh and was found to be much accurate.

The advantages of the dynamical power are that it could extract the

dynamical behaviour of any wind turbine with better accuracy and produce machine-

specific and site-independent results. Measurements taken for a short-time is enough

for this approach, where as the IEC power curve procedure requires long-term data and

also averages out all the dynamics (Milan 2008).

E) Probabilistic Model

A WTPC modeled using polynomial expressions is deterministic in nature,

since the relationship with the output power and the input wind speed is pronounced by

the modeling expressions. Jin and Tian (2010) proposed a probabilistic model for

WTPC as follows:

3)( yCyp p -----(2.21)

In this model, the wind turbine output power is a random number whose value is

determined by y, the wind speed and , the variation of the power output. 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.


F) Ideal Power Curve

The ideal power curve, as proposed by Trivellato et al (2012), describes the

intrinsic performance of the turbine, eliminating the hidden effect of the site

turbulence. The ideal power curve refers to ideal conditions such as steady and laminar

flow of wind, absence of yaw error and steady state power output. Assessment of wind

energy available in a test site and extension of power curve to sites with different

turbulence levels are the main applications of the ideal power curve. It is analytically

derived by a Taylor’s expansion and uses an accurate assumption of the ideal power

coefficient. The convergence of the Taylor’s expansion has been improved by

applying the Shanks’ transformation. This ideal power curve was successfully

compared with the IEC power curve. The calculation of annual energy estimated using

the ideal power curve was well within the inherent experimental error.

G) Four Parameter Logistic Function

The shape of the power curve is similar to the four parameter logistic

function and hence WTPC models have been developed based on this by Kusiak et al

(2009b, 2009c)

)11( yy nemeaP -----(2.22)

The vector parameters of the logistic function, a, m, n and determine its shape. The

parameters of the logistic function have been estimated using algorithms like least

squares, maximum likelihood and Evolutionary Programming (EP) (Kusiak et al

2009b).

Non-Parametric Techniques

Non-parametric techniques are used to solve the following equation:


)(yfP -----(2.23)

Several non-parametric methods have been used to find the relationship between the

input wind speed data and output power. A brief description of such techniques used

to model the WTPC has been given below:

A) Copula Power Curve Model

Copula is a distribution function in statistics and is used to describe the

dependence between random variables. A copula model of wind turbine performance

has been developed by Gill et al (2012) and Stephen et al (2011). This method

includes the measures of uncertainty while estimating the performance and also allows

comparison of inter-plant performance. A copula representation of a WTPC is

constructed by considering the power curve to be a bivariate joint distribution. To

make sure that the transformed variables have uniform distribution, accurate estimation

of wind speed and power marginals are essential. An estimated power curve copula is

shown as a non-parametric probability density estimate by Gill et al (2012). But this

approach can be made fully useful, only if a more advanced method of parametric

estimation of marginals and dependency is in place which may take the form of a

mixture density estimate of the marginals and cubic spline estimate of the copula. This

would aid in capturing and identifying changes in the operating regime also.

B) Cubic Spline Interpolation Technique

Interpolants and smoothing spline are the non-parametric fitting techniques

used to draw a simple, smooth curve through the data (Curve fitting Toolbox, 2002).

Interpolation is the process of estimating values that lie between two known data

points. The different kinds of interpolant methods include linear interpolation, nearest

neighbor interpolation, cubic-spline and Piece-wise Cubic Hermite Interpolation


(PCHIP). The WTPC model has been approximated using the cubic-spline interpolate

on technique by Thapar et al (2011). This method fits a different cubic polynomial

between each pair of data points. The method of least squares and cubic spline

interpolation performed extremely well for wind turbines with smooth power curve.

C) Neural Networks

An Artificial Neural Network (ANN) is an information-processing model

simulating the operation of the biological nervous system. It has a significant capacity

to derive meaning from complicated or imprecise data and finds application in

extraction of patterns and detection of trends that are too complex to be identified by

humans (Sivanandam and Deepa, 2010).

Under normal conditions, the equivalent steady state model of wind farm

has been realized using three different neural network models namely, Generalized

Mapping Regressor (GMR), a feed-forward Multi Layer Perceptron (MLP) and a

general regression neural network (GRNN) by Marvuglia and Messineo (2012). GMR

is a novel incremental self-organizing competitive network. NN models like radial

basis network and generalized regression network was used for estimation of annual

energy by Jafarian and Ranjbar (2010).

D) Fuzzy Methods

Fuzzy logic is basically a multi-valued logic which deals with approximate

reasoning. Fuzzy logic based on Takagi-Sugeno model was used to model the annual

wind energy produced by Jafarian and Ranjbar (2010). Modeling of WTPC using

fuzzy based methods includes fuzzy cluster center method, fuzzy c-means clustering

and subtractive clustering.


Fuzzy Cluster Center Method

Ustunas and Sahin proposed the application of fuzzy model based on cluster

center estimation to WTPC modeling (Ustuntas and Sahin, 2008). The wind turbine

power generation data are clustered and the cluster centers are determined using the

model algorithm. The more the number of clusters, higher is the accuracy of the

technique. The performance of the fuzzy cluster center method is better than the least

squares method.

Fuzzy C-Means Clustering

A WTPC model has been done using Fuzzy C-Means (FCM) clustering

algorithm by Raj et al (2011). Unlike K-means clustering, FCM eliminates the effect

of hard membership. It employs fuzzy measures as the basis for calculation of

membership matrix and identification of cluster centers, permitting data points to have

different degrees of membership to each of the clusters (Hammouda and Karray).

Fuzzy clustering and similarity theory have been applied by Suhua et al (2008) to

classify the measured wind speed data from different time. A fixed output value is

chosen to represent the wind turbine output power in that category.

Subtractive Clustering

Subtractive clustering algorithm has been used for modeling WTPC by Raj

et al (2011). This algorithm is very similar to mountain clustering, but the density

function is calculated only at every data point, instead of at every grid point

(Hammouda and Karray, 2000). The number of computations is reduced significantly,

since the data points themselves become cluster centers. According to Raj et al (2011),

the fuzzy cluster center method modeled the WTPC better than the other techniques.


E) Data Mining Algorithms

Data mining is all about solving problems and extracting valuable

information and patterns by analyzing data present in huge databases. The huge

volumes of data stored in the SCADA systems of wind farms present a priceless

opportunity for the application of data mining algorithms for wind turbine technology.

Non-parametric models of a WTPC have been obtained using five data mining

algorithms namely multi-layer Perceptron (MLP), random forest, M5P tree, boosting

algorithm and k-Nearest Neighbor (k-NN) by Kusiak et al (2009b). Among all these,

the k-NN algorithms performed better. The different parametric and non-parametric

methodologies employed by researchers for modeling of WTPC ultimately aim at

capturing the wind turbine performance accurately and thus use for energy prediction,

monitoring and predictive control of wind turbine operation.

2.3 REVIEW ON WIND POWER FORECASTING TECHNIQUES

The stochastic and random nature of wind makes it a necessity for novel

modeling approaches with improved performance. The wind industry needs accurate,

sophisticated models for forecasting of power and condition monitoring of wind farms.

These models involve large number of parameters and hence development of such

models is really a challenging task (Kusiak et al, 2009c). The techniques used for wind

power forecasting can be classified into three approaches: Physical approach,

Statistical approach and Learning approach. The different physical processes involved

in a wind farm namely, the wind conditions at the site, hub height of the turbines, wind

farm shading effects, turbine power curve, Model Output Statistics etc. are modeled in

the physical approach (Ernst et al, 2008). Figure 2.4 shows the main steps of the

physical approach based wind power forecasting.


Fig. 2.4. Physical Approach of Wind Power Forecasting

In statistical approach, the relationship between weather forecasts and

power production is described using explicit statistical analysis. This non-linear and

highly complex relationship is represented using suitable algorithms in the learning

approach. Evolutionary algorithms and other common soft- computing techniques

neural network, fuzzy logic etc. have also been combined to obtain more sophisticated

and improved models. An in-depth review of the current methods and advances in

wind power forecasting and prediction has been presented by Foley et al (2012). A

review on the developments of wind power prediction models to meet the offshore

requirements, performance of forecasting models and the importance of wind power

trading has been presented by Kariniotakis et al (2004).

Any advanced forecasting technique is implemented only if it outperforms

the conventional persistence model. The persistence model is a naive prediction

model, which assumes that the wind in the next time step will be the same as that

which occurred in the present time step (Monteiro et al 2009).

Wind Farm &

Terrain

Characteristics

PHYSICAL

MODEL

SCADA

Data NWP

(Atmospheric

Variables)

Wind

Generation

Forecast


2.3.1 Physical Approach

Numerical Weather Prediction (NWP) uses mathematical models to describe

physical processes. The physical approach consists of several submodels, which

contain the mathematical description of the physical processes relevant to the

translation. In this approach, the NWP forecasts are provided by the global model to

several nodes across a particular area (Monteiro et al 2009). The wind forecast at

certain grid point and model is translated using submodels, to power forecast at the

considered site and at a particular turbine height.

A power prediction model based on the forecasts from High Resolution

Limited Area Model (HIRLAM) of the Danish Meteorological Institute has been

developed for wind farms connected to electricity grid by Landberg (1999). An online

automatic prediction system for wind farm production output based on HIRLAM

model has been presented by Landberg (2001). The performance of the Eta model in

wind forecasting has been found out by Lazic et al (2010) using four common

measures of accuracy namely the mean difference, mean absolute difference, root mean

square difference and correlation coefficient. The possibility of integration of a short

term wind forecasting system with the grid in Romania has been explored using the

Weather Research and Forecasting (WRF) model and the Global Forecast System

(GFS) model (Dica et al 2009).

To avoid the forecasting errors of this approach, the power predictions are

post-processed using Model Output Statistics. The important disadvantage of this

approach is that it requires huge amount of high quality, online or offline measured

data.


2.3.2 Statistical Approach

The statistical approach involves the direct transformation of the input

variables into wind generation which takes place in the statistical block. Figure 2.5

shows the main steps of the statistical approach. The statistical block can combine

various inputs from the NWP model along with the data from the online SCADA data

for the estimation of wind power over a region. The statistical block can include one or

several linear or non-linear statistical models like Auto Regression (AR), Auto

Regressive Moving Average (ARMA) method, probability density function etc. With

these models, a direct estimation of regional wind power is possible from the input

parameters in a single step. A review of the statistical methods used for wind power

forecasting has been presented here.

Fig. 2.5 Statistical Approach of Wind Power Forecasting

Accurate wind power forecasts are increasingly important for integration of

wind energy to electricity grids. For a region with several distributed wind farms, a

STATISTICAL

MODEL

SCADA Data

NWP

(Atmospheric

Variables)

Wind

Generation

Forecast


method to make aggregated wind power predictions based on distances between

weather forecasting vectors has been presented by Lobo and Sanchez (2009). A wind

power forecasting method based on ARMA is developed by Rajagopalan and Santoso

(2009). The relationship between forecast accuracy and wind power variability has

also been studied. The feasibility of a comparatively low cost statistical model that

does not require any data beyond the historic power generation data, which might be

less accurate but of very high use for smaller wind farms have been explored by

Milligan et al (2003). The local variables of wind speed and direction has been

incorporated to statistically model the nonlinearities related to wind physics and other

complex dynamics and a benchmarking has been carried out between the regime-

switching and conditional parametric models (Gallego et al 2011). A hybrid statistical

method to predict wind speed and wind power, based on wavelets and classical time

series analysis has been presented by Liu et al (2010). The mean relative error of this

method is very small for multi-step forecasting and is robust in dealing with jumping

data.

Empirical Mode Decomposition (EMD) is a technique for analyzing non-

linear, non-stationary signal. It identifies the intrinsic oscillatory modes in a data

empirically by their characteristic time scales and then divides the data into Intrinsic

Mode Functions components. Short-term prediction of wind power using chaotic

theory and EMD has been presented by An et al (2012).

Systems with partially unknown information about its parameters and

characteristics are known as grey systems. A grey predictor model requires reduced

number of historical data, adapts itself to the dynamic behavior of the data and also

requires lesser processing time (El-Fouly et al 2007). These characteristics make it an

ideal choice for wind speed forecasting applications. A Grey predictor model for one-

step ahead average hourly wind speed forecasting and power prediction has been


developed by El-Fouly et al (2007). Guo (2009) developed a new Maximum Power

Point Tracking (MPPT) strategy based on grey wind speed prediction. This method

gives improved performance by reducing the search area and search time of the MPPT

process. A novel technique for wind speed forecasting and power prediction using

GM(1,1) model has been presented by El-Fouly et al (2006). Figure 2.6 shows the

different steps performed on the data using grey predictor model. AGO stands for

Accumulated Generating Operation and IAGO stands for Inverse Accumulated

Generating Operation. This technique showed an average accuracy of 11.2% better

than the persistent model for wind speed forecast and 12.2% for output power

prediction. An et al (2011) developed a wind farm power forecasting model based on

the combination of wavelet transform, chaotic time series and GM(1,1) method. The

actual wind turbine power output time series is pre-processed and decomposed using

wavelet transforms. The chaotic property of the data is identified and then future wind

farm power is predicted using GM(1,1) method.

Probabilistic forecasts provide the future probability of one or more events

(Juban et al 2007). The nature of the forecast variable can either be discrete or

continuous. A technique for producing the complete predictive probability density

function for wind power based on kernel density estimation methods have been

proposed by Juban et al (2007). Ensemble prediction systems give an assessment of

weather uncertainty using sophisticated estimate of the probability density function for

weather variables. The potential of weather ensemble predictions for wind power

forecasting has been explored by Taylor et al (2009).


Fig. 2.6 Grey Predictor Model GM (1,1) for Forecasting

Wind power prediction at a wind farm level is contaminated with two types

of uncertainty: one from the process of wind prediction and the other from the complex

wind farm structure and terrain characteristics. Hence adoption of entropy related

concepts for training mappers like neural networks for wind power prediction shows

significant improvement over the traditional approach of variance-based criterion.

Wind power forecasting using entropy-based criteria algorithms have been developed

by Bessa et al (2008a). Bessa et al (2008b) presents the significant improvements

obtained in wind power forecasting based on information entropy-related concepts.

Renyi’s entropy is combined with a Parzen windows estimation of the error probability

density function to form the basis of two criteria namely minimum entropy and

maximum correntropy, for both online and offline training of neural networks used for

wind power prediction (Bessa et al 2009).

Original data series )0(X

Develop the AGO data series )1(X

Calculate the GM(1,1) parameters

Predict the future point )1(X̂

Apply the IAGO to the predicted

values for the AGO data series

Predicted values for the original data

series )0(X̂


2.3.3 Learning Approach

Learning approach includes the application of soft-computing techniques

like Artificial Neural Networks (ANN), fuzzy logic, Adaptive Neuro-Fuzzy Inference

System (ANFIS) and other hybrid algorithms. Forecasting models based on learning

approach, try to learn the relationship between the forecast speed or power and the

input variables.

A neural network is a massively parallel distributed processor that learns the

input-output mapping of variables, without explicitly deriving the model equations.

Kariniotakis et al (1996) presents the development of a prediction model for wind

power output profile, based on recurrent high order NN. An algorithm to optimize the

performance of the architecture of the forecasting model has also been presented and

this model showed significant improvement in performance over the persistence model.

Forecasting of mean hourly wind speed data using time series analysis has been

presented by Steftos (2002). The task was accomplished using linear ARIMA models

and feed forward artificial neural networks. The models were tested on two different

datasets and the ANN model outperformed the ARIMA model. An NN-based

forecasting model was developed by More and Deo (2003) and it was proved that these

models gave more accurate forecasts than the conventional time-series ARIMA model.

ANN-based spatial correlation model has been developed by Alexiadis et al (1999) and

it has been proved that these models outperform the persistence model by reducing the

average errors by 20-40%. Li et al (2001) developed a four input NN, whose

performance is better than the traditional single input models.

A local recurrent NN model trained using Recursive Prediction Error (RPE)

algorithm for forecasting of wind speed and power has been developed by Barbounis et

al (2006a) and Barbounis et al (2006b). Spatial information from remote measurement


stations have been incorporated in the recurrent NN models by Barbounis and

Theocharis (2007). A feed-forward NN model with back propagation algorithm has

been developed for prediction of wind energy output by Mabel and Fernandez (2008).

The wind energy output is predicted using the average wind speed, relative humidity

and generation hours as the input to the NN (Figure 2.7). The fifth generation

mesoscale model (MM5) has been hybridized by incorporating ANN for short-term

wind speed prediction by Salcedo-Sanz et al (2009). The MM5 model is a physical

model that performs downscaling of the data from the global model in order to obtain

wind speed prediction in a smaller area.

Fig. 2.7. ANN Architecture for Wind Forecasting

A fuzzy expert system can incorporate fuzzy if-then rules and provide fine-

tuning of the membership functions according to the input-output patterns (Figure 2.8).

A Takagi, Sugeno and Kang (TSK) fuzzy model for wind speed prediction and power

generation in wind parks has been presented by Damousis and Dokopoulos (2001).

The fuzzy model is trained using Genetic Algorithms (GA) and provides better speed

forecasts from 30 minutes to 2 h ahead (Damousis et al 2004).

*Wind Speed

*Relative

Humidity

*Generation

Hours

Wind

Energy

Forecast

Input

Layer

Hidden

Layer

Output

Layer


Fig. 2.8 Fuzzy Expert System for Wind Forecasting

ANFIS, which is the integration of a NN with a fuzzy inference system,

exploits the advantages of both. A neuro-fuzzy system, is in fact, a neural network that

is functionally equivalent to a fuzzy inference model. A very short-term wind

prediction for power generation using ANFIS has been presented by Potter and

Negnevitsky (2006). An advanced statistical method for wind power forecasting

based on RBFN, fuzzy logic and self-organized map has been presented by Sideratos

and Hatziargyriou (2007).

Data mining refers to extracting of knowledge from large amounts of data.

It enables us to discover interesting patterns from databases and information

repositories. Data mining finds extensive application in predictive modeling.

Predictive models can be realized using algorithms like NN, Bayesian classification,

Support Vector Machine (SVM) and decision tree methods. Data mining models for

short-term power prediction has been developed by Kusiak et al (2009a) and Kusiak et

al (2009d). Data mining and evolutionary computation based models for prediction

and monitoring have been developed by Kusiak et al (2009c). Kusiak et al (2010d)

dealt with the optimization of wind turbine power using data mining and evolutionary

computation algorithms. Prediction of wind turbine parameters using virtual models

was developed by Kusiak and Li (2010c). The performance of these models was

Local & Remote

Measurements

Database

Fuzzy

Expert

System

User Defined

Forecast Horizon

Wind Energy

Forecast


dependent on the input parameters selected and the data mining algorithms used for

extracting the model. The power ramp rates of a wind farm have been predicted using

data mining by Zheng and Kusiak (2009).

A short-term wind power forecasting model based on the combination of

NN and wavelet transform has been discussed by Catalao et al (2011a). A short-term

wind power forecasting model combining wavelet transform, Particle Swarm

Optimization (PSO) and ANFIS has been developed by Catalao et al (2011b). This

approach offered better prediction accuracy and reduced time of computation. A

clustering approach for short-term prediction of power has been presented by Kusiak

and Li (2010a).

A comparison between two different ensemble models for short-term wind

power forecasting using common verification indices and diagrams has been developed

by Alessandrini et al. (2013). In deterministic approach, it was observed that a higher

resolution of the ensemble system led to better results when compared with high

resolution deterministic model. Kalman filtering techniques have been employed to

enhance the prediction accuracy of wind speed and wind energy forecast of Numerical

Weather Prediction (NWP) models (Cassola and Burlando, 2012). Wind power

prediction based on numerical and statistical models have been discussed by

Stathopoulos et al. (2013). They concluded that accurate power prediction is possible

if the local atmospheric conditions are estimated correctly. Sideratos and

Hatziargyriou (2012) developed models for wind power forecasting with a focus on

extreme power systems events. A novel adaptive learning method for online training

of Radial Basis Function Neural Networks (RBFNNs) was also presented. Wind

power forecasting model based on wavelet decomposition and chaotic time series has

been presented by An et al. (2011). Kusiak, Zheng and Song (2009) developed wind

farm power prediction models based data mining algorithms. A hybrid model for


short-term wind power prediction using empirical mode decomposition, chaotic theory

and grey theory was constructed by An et al (2010). Kusiak and Li (2010) developed a

short-term prediction model for power produced by wind turbines at low wind speeds

using clustering approach. Vaccaro et al. (2011) developed one-day- ahead wind power

forecasting models using data from multiple sources. It was proved that the

performance of this multi-model data fusion was better than the use of single-source

data. Catalao, Pousinho and Mendes (2011) proposed a hybrid method, combining

wavelet transform, PSO and an adaptive network based fuzzy inference system for

short-term prediction of wind power in Portugal.

Forecasting models developed based on learning approach and combination

of two or more approaches, give better and more accurate forecasts.

2.4 SUMMARY

Based on the exhaustive survey of literature on wind power forecasting,

three tasks have been carried out in this research work, namely the development of

Wind Speed Forecasting Models for different time horizons

Wind Turbine Power Curve Models

Wind Power Forecasting Models

An account of the various methodologies and models formulated in this regard has

been given in the subsequent chapters.

chapter 2 a review on wind power...

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