model analysis on wind energy technology

7/28/2019 Model Analysis on Wind Energy Technology

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MODEL ANALYSIS ON WIND ENERGY TECHNOLOGY

Increasing negative effects of fossil fuel combustion on the environment in addition to its

limited stock have forced many countries to explore and change to environmentally friendlyalternatives that are renewable to sustain the increasing energy demand. Changing to renewable

sources and the implementation of effective conservation measures would ensure sustainability.

Alternatives to conventional energy sources, especially the renewable ones, are becoming

increasingly attractive because of the limited fossil fuel reserves and the adverse effects

associated with their use. The renewable energy resources include solar, wind, wave, geothermal

and bio-energy. If these resources are well established, it can provide complete security of

energy supply.

Currently, the wind energy is one of the fastest developing renewable energy source technologies

across the globe. Wind energy is an alternative clean energy source compared to fossil fuel,which pollute the lower layer of the atmosphere. It has the advantage of being suitable to be used

locally in rural and remote areas. The increasing demand for energy supply coupled with limited

energy resources creates an urgency to find new solutions for this energy shortage.

Nowadays, wind analysis gives remarkable information to researchers involved in renewable

energy studies. The use of wind energy can significantly reduce the combustion of fossil fuel and

the consequent emission of carbon dioxide. Supplementing our energy base with clean and

renewable sources of energy has become imperative due to the present days' energy crisis and

growing environmental consciousness. Knowledge of the statistical properties of the wind speed

is essential for predicting the energy output of a wind energy conversion system. Because of thehigh variability in space and time of wind energy, it is important to verify that the analyzing

method used for the measuring wind data will yield the estimated energy collected that is close to

the actual energy collected. In recent years many efforts have been made to construct an

adequate model for the wind speed frequency distribution

ANOVA

Analysis of variance is a statistical technique used to compare more than two population means

by isolating the sources of variability. A One-Way Analysis of Variance is a way to test the

equality of three or more means at one time by using variances.

Assumptions

The populations from which the samples were obtained must be normally or

approximately normally distributed.

The samples must be independent.

The variances of the populations must be equal.


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Hypotheses

The null hypothesis will be that all population means are equal, the alternative hypothesis is that

at least one mean is different.

In the following, lower case letters apply to the individual samples and capital letters apply to theentire set collectively. That is, n is one of many sample sizes, but N is the total sample size.

Grand Mean

The grand mean of a set of samples is the total of all the data values divided by the total sample

size. This requires that you have all of the sample data available to you, which is usually thecase, but not always. It turns out that all that is necessary to find perform a one-way analysis of

variance are the number of samples, the sample means, the sample variances, and the sample

sizes.

Another way to find the grand mean is to find the weighted average of the sample means. Theweight applied is the sample size.

Total Variation

The total variation (not variance) is comprised the sum of the squares of the differences of each

mean with the grand mean.

There is the between group variation and the within group variation. The whole idea behind theanalysis of variance is to compare the ratio of between group variance to within group variance.

If the variance caused by the interaction between the samples is much larger when compared to

the variance that appears within each group, then it is because the means aren't the same.

Between Group Variation

The variation due to the interaction between the samples is denoted SS(B) for Sum of SquaresBetween groups. If the sample means are close to each other (and therefore the Grand Mean) this

will be small. There are k samples involved with one data value for each sample (the sample

mean), so there are k-1 degrees of freedom.

The variance due to the interaction between the samples is denoted MS(B) for Mean Square

Between groups. This is the between group variation divided by its degrees of freedom.

Within Group Variation

The variation due to differences within individual samples, denoted SS(W) for Sum of Squares

Within groups. Each sample is considered independently, no interaction between samples isinvolved. The degrees of freedom is equal to the sum of the individual degrees of freedom for

each sample. Since each sample has degrees of freedom equal to one less than their sample sizes,


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and there are k samples, the total degrees of freedom is k less than the total sample size: df = N -

k.

The variance due to the differences within individual samples is denoted MS(W) for MeanSquare Within groups. This is the within group variation divided by its degrees of freedom. It is

the weighted average of the variances (weighted with the degrees of freedom).

F test statistic

Recall that a F variable is the ratio of two independent chi-square variables divided by their

respective degrees of freedom. Also recall that the F test statistic is the ratio of two samplevariances, well, it turns out that's exactly what we have here. The F test statistic is found by

dividing the between group variance by the within group variance. The degrees of freedom for

the numerator are the degrees of freedom for the between group (k-1) and the degrees of freedomfor the denominator are the degrees of freedom for the within group (N-k).

Wind velocity

(m/s) Power co-eff

1 0.38

1.2 0.39

1.25 0.41

1.33 0.42

1.4 0.43

1.5 0.44

1.6 0.45

1.7 0.46

1.8 0.48

1.9 0.48

2 0.5

2.2 0.55

2.4 0.57

3 0.57

3.14 0.58


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Anova: Single Factor

SUMMARY

Groups Count Sum AverageVariance

Wind velocity (m/s) 15 27.42 1.828

0.40123

1

Power co-eff 15 7.11 0.4740.004497

ANOVA

Source of Variation SS df MS F

P-

value F crit

Between Groups

13.7498

7 1

13.7498

7

67.7786

6

5.84E-

09

4.19597

2

Within Groups 5.6802 280.202864

Total19.43007 29

CONCLUSION:

model analysis on wind energy technology

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