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A Novel based Prolog Programming for Mean Wind Speed &

Weibull Distribution at Hiregudda, Karanataka, India

Mahesh K1*

., M V Vijaykumar 2., Gangadharaiah.Y.H

3

1*

Researcher Scholar JAIN University CSE dept and Faculty at

New Horizon College of Engineering Bangalore-560103, India.

2 Department of Computer Science Engineering, Dr AIT, India.

3 Department of Mathematics, New Horizon College of Engineering, India.

Abstract: The main objective of this paper is to estimate annual mean wind speeds at 10 m, 30 m

and 50 m. The annual mean wind speed is determined by PROLOG SWI platform using wind data

obtained from measurements for the 5 years period of 2006 to 2010 at Hiregudda, Bagalkot district

in Karnataka state, South India. The wind speed at heights of 10 m, 30 m and 50 m above ground

level were measured using 3- cup anemometers attached to booms on a 50 m lattice met tower. The

recording interval was 10 min. The results of mean wind speed data is the first step of prediction of

wind speed data of the site under consideration and a PROLOG program was designed and

developed to calculate the Annual mean wind speed data of the site. The statistical wind data set was

also analyzed using Weibull distributions in order to investigate the Weibull shape and scale

parameters.

Keywords: Prolog, Mean wind speed, Weibull Distribution, Weibull shape and Scale parameters.

1. Introduction

Wind data measurements over a period of five-years are required to obtain an

accurate assessment of the wind regime of an area. Over a period, the height of wind turbines

have seen phenomenal upward trend and thus it was also necessary to increase the height of wind

monitoring masts to the hub height. Presently 50 m tall tubular masts are used with instrumentation

at 10, 30 and 50 m AGL [1]. The data loggers from M/s NRG Systems, USA and M/S second wind

Inc, USA are used and theses units have multi-channel data logging capability along with facilities

for down loading data remotely. The averaging interval presently considered is 10 minutes, the

industry standard. Time series data are stored in removable memory cards collected manually form

the sites periodically. The respective State Nodal Agencies (SNAs) also have active role in the

implementation of the program. Fully automated data logger housed in shelter box with adequate

protection vandalism is used for data collection. Wind speed is measured using cup generator

anemometers and the rotational speed (frequency) of the cups is proportional to the wind speed. Wind

direction is referred to north in terms of degrees from north and the direction sensor consists of a

potentiometer giving proportional voltage signal. Data is sampled at a frequency of 0.5 Hz (2 seconds)

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and averaged over one hour or 10 minutes. The data logger is set to store the wind speed in the meter

per second and direction in degrees. The data presentation is mainly based on the analysis carried out

on hourly values of wind speed and directions [2]. Methodologies on wind farm design rely on these

data from the measuring station and careful analysis of wind flow, which takes into account the

topography and the roughness level of the surrounding land. Unless the data on wind speed,

direction, topographical features and roughness classes are accurate calculations may result in

significant errors in estimating the wind speed, which may lead to even greater errors in

energy estimation especially in complex terrains. In all of above cases, the first step is to estimate

the mean value of the wind speed that is expected on a site and afterwards, the wind energy that a

proposed wind farm would produce in an average year, is estimated. In this paper a model is

developed to estimate annual mean wind speed for a given period using PROLOG [3]. To develop

this model a sufficient set of unpublished wind data of the given site is taken into consideration.

There are several works that deal with the use of probability density functions to describe wind

speed frequency distribution [4].In general, the Weibull probability density function can be used to

estimate a site’s probability distribution of wind speed. The Weibull distribution technique is

widely accepted and used in the wind energy industry as the preferred method for describing wind

speed variations at a given site; some claim the Weibull distributions the best fit for describing

wind speed distribution [5].The Weibull probability density function is a two-parameter function

characterized by a dimensionless shape (k) parameter and scale (c) parameter (in unit of speed ).

These two parameters determine the wind speed for optimum performance of wind conversion

system as well as the speed range over which the device is likely to operate[6].In principle, this

opens up the need to estimate the model parameters, namely, k and c, from the measured data of

any location. This paper study also examines statistical wind data using Weibull distribution,

investigating various Weibull shape and scale parameters for the wind speed at heights of 10m,

30m, 50m for the site under consideration.

2. Prolog

PROLOG is a simple, yet powerful programming language, based on the principles of first

order predicate logic. The name of the language is an acronym for the French `PROgramma-tion en

LOGique'. About 1970, PROLOG was designed by A. Colmerauer and P. Roussel at the University

of Marseille, influenced by the ideas of R.A. Kowalski concerning programming in the Horn clause

subset of first order predicate logic. The name of PROLOG has since then been connected with a

new programming style, known as logic programming

Until the end of the seventies, the use of PROLOG was limited to the academic world. Only

after the development of ancient PROLOG interpreter and compiler by D.H.D. Warren and F.C.N.

Pereira at the University of Edinburgh, the language entered the world outside the research

institutes. The interest in the language has increased steadily. However, PROLOG is still mainly

used by researchers, even though it allows for the development of serious and extensive programs in

a fraction of the time needed to develop a C or Java program with similar functionality. The only

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explanation is that people like wasting their precious time. Nevertheless, there are a large number of

fields in which PROLOG has been applied successfully. The main applications of the language can

be found in the area of Artificial Intelligence; but PROLOG is being used in other areas in which

symbol manipulation is of prime importance as well. Some application areas are: Natural-language

processing, Complier construction, The development of experts systems, Work in the area of

computer algebra, The development of (parallel) computer architectures and Database systems [3].

PROLOG is particularly strong in solving problems characterized by requiring complex symbolic

computations. As conventional imperative programs for solving this type of problems tend to be

large and impenetrable, equivalent PROLOG programs are often much shorter and easier to grasp.

The language in principle enables a programmer to give a formal specification of a program; the

result is then almost directly suitable for execution on the computer. More-over, PROLOG supports

stepwise refinement in developing programs because of its modular nature. These characteristics

render PROLOG a suitable language for the development of prototype systems.

There are several dialects of PROLOG in use, such as for example, C-PROLOG, SWI-

PROLOG, Sicstus-PROLOG, LPA-PROLO,. C-PROLOG also called Edinburgh PROLOG was

taken as a basis for the ISO standard. However, there are a small number of dialects which change

the character of the language in a significant way, for example by the necessity of adding data-type

information to a program. A typical example is observed by the version of the PROLOG language

supported by Visual PROLOG. In recent versions of PROLOG, several features have been added to

the ISO standard. Modern PROLOG versions provide a module concept and extensive interfaces to

the operating system, as well as tools for the development of graphical user interfaces. In our

Program we have used SWI-PROLOG [3, 13].

3. Description of Data and Study Area A 50 m lattice met tower was installed near the Hiregudda at Biligi Taluk, Bagalkot District

of Karnataka State in Southern India [12]. The site coordinates are: latitude N 16° 19' 40'' and

longitude E 75° 33' 20''. The elevation of the site is 640m above mean sea level (AMSL). The met

tower was equipped with wind speed and direction sensors, a data logger, an ambient air

temperature sensor, and a lightening arrester for protecting the measuring equipment from a severe

thunder storm. Wind speeds and directions at 10 m, 30 m, and 50 m as well as ambient temperature

at 3 m above ground level (AGL) were measured between January 2006 to April 2010 with a 1 min

sampling interval and a 10 min recording interval. Wind speeds were measured using 3-cup

anemometers and wind directions were measured using standard wind vanes both of which were

attached to the end of booms mounted on the met tower. The instruments were connected to a NRG

data logger which was powered by a PV-battery system.

Table.1. Sample data of the site recorded by NRG data logger

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The resolution of wind speed measurements were 0.19 m/s and the resolution of wind direction

measurements were 1.4°. Measurement accuracy as specified by the instrument manufacturer was

±3% for wind speeds of 17-30 m/s. The measured wind speeds at 10 m, 30 m, and 50 m AGL were

analyzed using the Weibull distribution technique. Weibull parameters were investigated based on

the analytical method. A sample data obtained is has shown in the Table 1.

4. Programming in PROLOG and SWI PROLOG

Programming in Prolog is distinguished from programming in conventional languages in that

Prolog is a declarative language. Prolog programmers describe known facts and relationships within

the domain of the problem they wish to solve, together with a query defining the problem.

Programmers are freed from the task of prescribing the exact sequence of operations needed to solve

a problem as they must do in imperative languages. A more accurate description of the activity of

programming in Prolog is the development of logical specifications of the knowledge within a

particular domain that is necessary to solve a problem. Prolog allows for a declarative style of

programming and is essentially logic combined with control [15]. The logic part is the statement of

what the problem is that has to be solved. The control part is the statement of how it is to be solved.

Figure 1 indicates the relationship between Prolog and logic programming [13].

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algorithm = logic + control

what how

Horn resolution

clauses

PROLOG

PROLOG

Database interpreter

Figure 1: The relationship between PROLOG and logic programming.

The Prolog version that is used in the paper is the latest one of SWI-Prolog (5.6.52). SWI-

Prolog is a free software, been developed by Amsterdam University from 1990 to 2008, and despite

being free, it is very powerful and has been widely used for commercial and educational

applications. [14]

The reason for the selection of SWI-Prolog for our paper is basically two-fold. On the one

hand, SWI-Prolog has a convenient and easy-to-learn programming environment; the latter may

miss many of the accessories that other Prolog versions’ GUI environments have, but considering

our paper, which is rather straightforward, a simple one would suffice. On the other hand, SWI-

Prolog has a powerful Object-Oriented Programming extension. Since Object-Oriented

Programming is common sense for large-scale applications, several commercial or not versions of

Prolog, SWI-Prolog being among them, have been given such a scope by incorporating OOP

constructs, giving this way an efficient pseudo-OOP scope to its applications. Figure.2. Shows the

basic prolog flow chart used to estimate the mean annual or monthly wind speed of wind data of the

given site.

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Figure

2: Flow Chart

5. The Weibull wind speed probability density function

Wind power developers measure actual wind resources, in part, to determine the distribution

of wind speeds because of its considerable influence on wind potential. The Weibull wind speed

distribution is a mathematical idealization of the distribution of wind speed over time. The function

shows the probability of the wind speed being in a 1m/s interval centered on a particular speed (v),

taking into account both seasonal and annual variations for the years covered by the statistics. The

Weibull distribution function is given [7; 10] by:

1k k

k v vP v Exp

v c c

(1)

where p(v) is the frequency of occurrence of wind speed (v), c (in unit of m/s) is the scale factor

which is closely related the wind speed for the location, and k is the dimensionless shape factor

which describes the form and width of the distribution. The Weibull distribution is therefore

determined by the two parameters c and k. The cumulative Weibull distribution P(v) which gives the

probability of the wind speed exceeding the value v is expressed as:

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k

vP v Exp

c

(2)

Equation (2) above suggests that both k and c could be obtained from a regression analysis of P(v)

– v plot of the wind speed distribution data for a particular location.

However, meteorologists have characterized the distribution of wind speeds for many of the

World’s wind regimes in terms of the speed distribution patterns. For example, in temperate

climate (mid latitudes), a typical shape factor (k) of 2 offers a good approximation. For k = 2,

equation (1) or (2) is called the Raleigh wind speed distribution. Hence, the Raleigh distribution is

a special case of the Weibull function developed for estimation of wind potential in temperate

climate locations. Wind characteristics are essentially location specific and the performance of

wind power systems varies if actual wind conditions at the location differ from those standard

speed distributions.

On the other hand, the shape (k) factor has been suggested [11] to be obtainable using the mean

wind speed data (v) and standard deviation (σ) for the location as:

1.086

kv

(3)

While the scale factor has been given [13] as:

11

c

k

(4)

Where ( ) is the gamma function defined mathematically in general x-variable [5] as:

1

0

x nn e x dx

(5)

Analysis of equation (2) suggests that the wind speed probability density for v is higher if the

shape factor is high for that location. Hence, smaller values of k (k < 1) suggest that there is more

concentration of energy in the wind below the average speed (v) for the site, while higher values of k

(k > 1) could be interpreted that the wind speed in the site is dominated by values above the mean

speed [7]. This shows that knowledge of the exact value of k provides preliminary information on

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the wind speed regime for which wind turbines should be designed for any given location. On the

other hand the value of c for any location provides preliminary information on the characteristic

wind speed for the site for which a wind turbine should be designed. In this paper, we analytically,

find the empirical values of k and c for the windy site under consideration.

6. Results and Discussion

The annual mean wind speed was estimated by using PROLOG program from the measured

wind speeds at 10m, 30m, and 50m AGL at Hiregudda, Bagalkot district in Karnataka state, South

India. The design and developed PROLOG based Graphs are shown in Figures 4(a-e) respectively

and Weibull probability density functions were also calculated from the measured wind speeds at

10m, 30m and 50m AGL at the same site and are shown in Figures 5(a-e), respectively. It was found

that the annual Weibull shape parameter k, at 10-50 m AGL were in the range of 4.2 to 8.5 and

Weibull scale parameter c, were in the range of 4.0-6.2 m/s, thus corresponding to annual mean

wind speeds in the range of 3–5.6 m/s. A summary of annual Weibull shape and scale parameters

are given in Table 2. The annual mean wind values estimated from the available data for the overall

five years are presented in the Table 2. From the table it is seen that highest wind speeds 5.71m/s, at

the height of 50m in the year 2006, 4.96m/s at the height 30m in the year 2009 and 3.94m/s at height

10m in the year 2006. The variation of the described uses the Weibull two parameter density

functions. This is the statistical method accepted for the evaluation local wind probabilities and

considered as a standard approach.

Table 2: Annual Weibull shape parameter, scale parameter and mean speed obtained for

given site.

Years

K

c

Mean Speed

10 30 50 10 30 50 10 30 50

2006 5.046 8.054 8.1205 4.4128 2.2176 6.3952 3.94 1.98 5.71

2007 4.926 7.5644 8.22 4.2224 3.8976 6.16 3.77 3.48 5.50

2008 4.749 6.6333 7.994 4.1888 5.5104 6.1824 3.74 4.92 5.52

2009 4.666 6.969 8.4704 4.0365 5.5552 6.2608 3.60 4.96 5.59

2010 4.2428 6.8764 8.4518 3.1892 4.76 5.376 2.84 4.25 4.8

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Fig 4a. Annual mean wind speed for the year 2006

Fig 4b. Annual mean wind speed for the year 2007

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Fig 4c. Annual mean wind speed for the year 2008

Fig 4d. Annual mean wind speed for the year 2009

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0 2 4 6 80

0.2

0.4

0.6

0.8

Fig 4e. Annual mean wind speed for the year 2010

Fig 5a. Annual Weibull Distribution for year 2006

Wind speed in m/s

P(v)

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0 2 4 6 80

0.1

0.2

0.3

0.4

0.5

Fig 5b: Annual Weibull Distribution for year 2007

Fig 5c: Annual Weibull Distribution for year 2008

0 2 4 6 80

0.1

0.2

0.3

0.4

0.5

0.6

P(v)

P(v)

Wind speed in m/s

Wind speed in m/s

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Fig 5d. Annual Weibull Distribution for year 2009.

Fig 5e. Annual Weibull Distribution for year 2010

30

10

50

0 2 4 6 80

0.5

1.

1.5

0 2 4 6 80

0.1

0.2

0.3

0.4

0.5

0.6

P(v)

P(v)

Wind speed in m/s

Wind speed in m/s

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7. Conclusion

It is concluded that the designed and developed PROLOG program was successfully

implemented for plotting the annual mean wind speed data measured at different heights of 10m,

30m and 50m at Hiregudda at Biligi Taluk, Bagalkot District of Karnataka State in Southern India.

The Weibull shape parameters and scale parameters were estimated for the annual wind speed data

and tabulated and found that Weibull distribution using the graphical method was a useful technique

to conduct wind speed analysis from observed wind speed data at given site. From the observed

wind speed data during January 2006 to April 2010, the annual Weibull shape parameters, k, at 10-

50 m AGL were in the range of 4.2 to 8.5 and Weibull scale parameters, c, and were in the range of

4.0-6.2 m /s, thus corresponding to annual mean wind speeds in the range of 3–5.6 m /s. Finally,

analysis showed that strong and sufficient wind speed is available at the given site.

Acknowledgments

The authors gratefully acknowledge the Karnataka Renewable Energy Development Limited

(KREDL), a nodal agency by the ministry of non conventional energy resources Govt. of India for

providing the wind data resource assessment. The authors also acknowledge Jain University and

New Horizon College of Engineering for supporting in publishing of this research paper.

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