_{1}

In the present study, wind speed data of Jumla, Nepal have been statistically analyzed. For this purpose, the daily averaged wind speed data for 10 year period (2004-2014: 2012 excluded) provided by Department of Hydrology and Meteorology (DHM) was analyzed to estimate wind power density. Wind speed as high as 18 m/s was recorded at height of 10 m. Annual mean wind speed was ascertained to be decreasing from 7.35 m/s in 2004 to 5.13 m/s in 2014 as a consequence of Global Climate Change. This is a subject of concern looking at government’s plan to harness wind energy. Monthly wind speed plot shows that the fastest wind speed is generally in month of June (Monsoon Season) and slowest in December/January (Winter Season). Results presented Weibull distribution to fit measured probability distribution better than the Rayleigh distribution for whole years in High altitude region of Nepal. Average value of wind power density based on mean and root mean cube seed approaches were 131.31 W/m
^{2}/year and 184.93 W/m
^{2}/year respectively indicating that Jumla stands in class III. Weibull distribution shows a good approximation for estimation of power density with maximum error of 3.68% when root mean cube speed is taken as reference.

The world energy demand and consumption have increased seriously over last decades and most of this demand is met from fossil fuels. The use of fossil fuels and non-renewable form of energy has major impact on environment and our ecosystem through increasing pollution rate. In simple sense, energy and environment are major crisis of today. Many countries in the world are taking a step towards renewable form of energy to solve this challenge. Renewable energy sources like wind, solar, geothermal, hydro, biomass and ocean thermal energy have drawn attention from all over the world due to their almost inexhaustible and non-polluting characteristics. Wind energy being one of the important source for electricity production. It is vigorously pursued in many countries [

Like other kind of energy, wind energy is ultimately a solar resource. Wind systems are created mainly due to two main causes: 1) temperature differences between the equator and the poles (the earth’s latitudes), 2) the rotation of the earth. Dry air in the vicinity of 30˚N and 30˚S flows towards the equator where it replaces rising hot air [

As seen from the literature, much concentration has been given to Weibull function because it is found to give fit to the observed wind speed data both at the surface [

Weibull distribution is a two parameter function, namely, shape factor k (dimensionless) and scale parameter c (dimensional). It is used in describing the wind speed frequency distribution. Several methods have been proposed to estimate Weibull parameters. Graphic method, maximum likelihood method and moment methods are commonly used to estimate Weibull parameters. The purposes of estimation are: a) To retrospectively characterize past conditions; b) to predict future power generation at one location; c) to predict power generation within a grid of turbines; d) to calibrate meteorological data.

Nepal is landlocked country with diversity in its climate from Himalayan region to Terai (Plain Lands) within short range of distance. Nepal’s total energy consumption in the fiscal year of 2008/09 was 400.5 million GJ. Traditional sources such as fuel wood, crop residues, and animal dung shared 87.1% of total energy consumption with commercial sources like petroleum products, coal and electricity, and other renewable energy sources contributing only 12.2% and 0.7% of the total energy consumption, respectively [

Jumla is centre of Chandannath municipality in Jumla district and is located in Karnali zone of Nepal. The primary observation have shown that the region has wind potential. Since there was no similar study for this region, this study aimed to examine the wind energy potential of Jumla by finding Weibull and Rayleigh distribution parameters & determining the available power density. Besides applying mean wind speed, a root cube wind speed was applied to calculate the wind power and energy density. Since the wind power is proportional to cube of wind speed, it is a better representation of wind speed to be considered in calculations [

In real measurement, the wind speed tends to increase with height in most locations and depends mainly on atmospheric mixing and terrain roughness. Therefore, to calculate the total wind energy potential, the measured surface wind speed must be modified for an altitude different (40 m in this literature) from the normalized height (i.e. 10 m). For this reason the following equation was used: [

where, v_{mes} is the wind speed at normalized height (m/s), z_{mes} is the normalized height (m) and Z is the turbine height (m). The exponent m depends on factors as surface roughness and atmospheric stability. Numerically, it lies in the range of 0.05 - 0.5. Surface roughness (m) which is dependent on the terrain condition varies from 0.128 to 0.160 even in a very homogenous surface as flat or farm land. A typical value for surface roughness is 0.14 (for low roughness surface) and varies from less than 0.1 (for very flat land, water or ice surfaces) to more than 0.25 (for forest and woodlands). According to the literature, for neutral stable condition, m is approximately 0.143, which is commonly assumed to be constant in wind resource assessments. In this research, the surface roughness (m) is taken as 0.143 [

To investigate the feasibility of the wind energy resource at any site, the best method is to calculate the wind power density based on the measured data of the meteorological station. Another method is to calculate the wind power density using frequency distribution functions like Weibull distribution, Rayleigh distribution, chi- squared distribution, generalized normal, log normal-distribution, three parameter log-normal, gamma distribution, inverse Gaussian distribution, kappa, wakeby, normal two variable distributions, normal square root of wind speed distribution, as well as hybrid distribution [

As wind speed changes regularly, frequency distribution of wind speed based on time series data can be calculated. Exact probability density function describing the speed data is difficult to find. Weibull distribution is a two parameter function characterized by scale parameter c (m/s) and shape parameter k (dimensionless). When Probability of occurrence of certain velocity is given by [

The corresponding weibull cumulative density function (CDF) is given by

Rayleigh function is special case of Weibull function. When shape parameter k = 2, Weibull distribution becomes Rayleigh distribution.

Shape parameter k and scale parameter c can be calculated using many methods as shown by previous researches. Graphical method (GM), Method of moments (MOM), Standard deviation method (STDM), Maximum likelihood method (MLM), Power density method (PDM), Modified maximum likelihood method (MMLM), Equivalent energy method (EEM) are widely used. In literature about wind energy, these methods are compared several times however results and recommendations of the previous studies are different from each other. For this reason, according to the results of the studies, it might be concluded that suitability of the method may vary with the sample data size, sample data distribution, sample data format and goodness of fit tests [

where Г is the gamma function.

In order to check how accurately a theoretical probability density function fits with observation data, in this paper, four types of statistical errors are considered as judgement criterion. To evaluate the performance of considered distribution, the mean percentage error (MPE), mean absolute percentage error (MAPE), root mean square error (RMSE) parameter, and the chi-square test are performed [

where N is number of observations, y_{i}_{,m} is frequency of observation or i^{th} calculated value from measured data, x_{i}_{,w} is frequency of weibull or i^{th} calculated value from the weibull distribution and same set of formulas can be used when subscript w is replaced by r representing Rayleigh distribution.

Wind power density is measure of capacity of wind resources in specified site. Wind Power density can be measured based on many approaches [

Many researches have used mean velocity to calculate wind power density. Mean power can be calculated by:

Because the wind power is proportional to cube of velocity, root mean cube of wind speed gives better result and is defined as [

From Weibull distribution, power density can be calculated by:

From Rayleigh distribution, power density can be calculated by:

where P represents Wind Power Density (W/m^{2}) and ρ is density (kg/m^{3}) at studied region. A typical value used in all the literature consulted is average air density 1.225 kg/m^{3} corresponding to standard conditions (sea level, 15˚C) [

where g is the gravitational acceleration (9.81 m/s^{2}); T represents the average air temperature (K); T_{o} = 288 K (273 + 15); R is the gas constant (287 J/Kg/k) for air; and Г is vertical temperature gradient usually taken as 6.51 K/Km. Based on calculations, value of 1.231 was chosen as the air density.

However there is always an error in predicted value and measured value. Calculated wind power density by root mean cube speed or mean speed for the measured probability density distribution serves as reference power density (P_{m}). Power density predicted using Weibull and Rayleigh distribution (P_{W}) & (P_{R}) can be calculated using eqns. (15) & (16) respectively. Error in calculating the power density using distribution compared to measured value can be calculated as [

Knowing scale parameter (c) and shape parameter (k) of Weibull distribution function, average velocity can be predicted by Weibull and Rayleigh distribution [

Similarly, most probable wind speed (V_{mp}) and maximum energy carrying wind speed (V_{op}) also can be calculated using following formulas [

Wind direction is important parameter for selection of wind turbines. For this purpose, a wind rose plot is needed which shows dominant wind direction. Wind rose can be done from 4 point, 8 point, 16 point and 32 points. To some users, the 8-point rose is sufficient for their needs. To another user, yet for same purpose, a 16-point rose is absolutely necessary [

Wind speeds are different as months and seasons vary.

(May-October).

Year | Cold Season (November-April) | Warm Season (May-October) |
---|---|---|

2004 | 7.18 | 7.52 |

2005 | 6.14 | 6.89 |

2006 | 6.56 | 7.09 |

2007 | 6.59 | 6.26 |

2008 | 6.10 | 5.25 |

2009 | 5.34 | 6.46 |

2010 | 5.23 | 5.66 |

2011 | 5.07 | 5.06 |

2013 | 5.12 | 5.56 |

2014 | 4.29 | 5.95 |

Average | 5.76 | 6.17 |

available will be constant throughout.

The variation of wind speeds is often described using Weibull & Rayleigh density function. These are statistical tool which are widely accepted for evaluation of local wind probabilities and considered as a standard approach. Methods of Moments was used to calculate both weibull parameters. To calculate weibull parameters, yearly mean wind speed and standard deviation were calculate and shown in

Parameter | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2013 | 2014 | Whole Year |
---|---|---|---|---|---|---|---|---|---|---|---|

V_{m} (m/s) | 7.35 | 6.52 | 6.82 | 6.42 | 5.65 | 5.9 | 5.45 | 5.07 | 5.34 | 5.13 | 5.98 |

σ (m/s) | 2.13 | 2.5 | 2.07 | 2.01 | 1.85 | 2.26 | 1.8 | 1.76 | 1.85 | 1.81 | 2.15 |

k (-) | 3.84 | 2.83 | 3.65 | 3.54 | 3.36 | 2.83 | 3.32 | 3.14 | 3.16 | 3.09 | 3.03 |

c (m/s) | 8.13 | 7.32 | 7.56 | 7.13 | 6.29 | 6.63 | 6.07 | 5.66 | 5.97 | 5.73 | 6.69 |

_{mp} for weibull ranged from 5.01 to 7.52 m/s with an average of 5.86 m/s whereas for Rayleigh ranged from 4 to 5.75 m/s with an average of 4.73 m/s. Also, the highest value of V_{op} was at 2004. Weibull predicted it to be 9.07 m/s whereas Rayleigh predicted it as 11.5 m/s. Mean speed predicted by weibull was same as predicted main speed because same equation (6, 19) are used to calculate value of shape factor and mean speed. Rayleigh model predicted mean wind speed with maximum deviation of 0.37 m/s with 80% of difference not over 0.1 m/s. Root mean cube speed was calculated with an average value of 6.7 m/s. ^{2} is 0.03 for Weibull and 0.46 for Rayleigh. χ^{2} with lower value shows better goodness of fit. The MPE, MAPE & RMSE for Weibull distribution were 18%, 30% and 0.012 while these indices for Rayleigh distribution were 70%, 84% and 0.024 respectively. Literatures have found that the weibull model predict the actual value better than in comparison to the Rayleigh model which is supported by this study [

The power density calculated from measured probability density distributions and those obtained from models are presented in ^{2}/year. Extreme values of wind power calculate using root mean cube speed (for 2004 and 2011) were 306.36 and 109.29 W/m^{2}/year with an average of 184.93 W/m^{2}/year. The values of wind power which have been calculated by applying root mean cube speed approach were higher than that of arithmetic mean wind speed values. The wind power density calculated from root mean cube speed and predicted by weibull model are similar. Average wind power density predicted using Weibull and Rayleigh model are 183.28 and 244.82 W/m^{2}/year. ^{2}.

Errors in calculating the power density using Weibull and Rayleigh models are presented in

Year | Weibull | Rayleigh | V_{rmc } | ||||
---|---|---|---|---|---|---|---|

V_{mp } | V_{op } | V_{m } | V_{mp } | V_{op } | V_{m } | ||

2004 | 7.52 | 9.07 | 7.35 | 5.75 | 11.50 | 7.21 | 7.93 |

2005 | 6.28 | 8.85 | 6.52 | 5.18 | 10.36 | 6.49 | 7.48 |

2006 | 6.93 | 8.53 | 6.82 | 5.35 | 10.70 | 6.70 | 7.42 |

2007 | 6.50 | 8.09 | 6.42 | 5.04 | 10.09 | 6.32 | 7.00 |

2008 | 5.67 | 7.23 | 5.65 | 4.45 | 8.90 | 5.28 | 6.21 |

2009 | 5.68 | 8.00 | 5.90 | 4.69 | 9.37 | 5.88 | 6.67 |

2010 | 5.45 | 7.00 | 5.45 | 4.29 | 8.59 | 5.38 | 5.99 |

2011 | 5.01 | 6.62 | 5.07 | 4.00 | 8.01 | 5.02 | 5.62 |

2013 | 5.29 | 6.97 | 5.34 | 4.22 | 8.44 | 5.29 | 5.93 |

2014 | 5.05 | 6.74 | 5.13 | 4.05 | 8.11 | 5.08 | 5.70 |

Average | 5.86 | 7.90 | 5.98 | 4.73 | 9.46 | 5.93 | 6.70 |

Index | Weibull | Rayleigh |
---|---|---|

MPE | 18% | 70% |

MAPE | 30% | 84% |

RMSE | 0.012 | 0.024 |

χ^{2 } | 0.03 | 0.46 |

Year | Measured | Predicted | ||
---|---|---|---|---|

Mean Speed | Root Mean Cube Speed | Weibull | Rayleigh | |

2004 | 244.61 | 306.36 | 306.33 | 439.70 |

2005 | 170.91 | 257.93 | 248.43 | 321.50 |

2006 | 195.34 | 251.18 | 249.72 | 354.19 |

2007 | 163.02 | 211.09 | 211.04 | 297.01 |

2008 | 111.05 | 147.65 | 147.18 | 204.00 |

2009 | 126.72 | 182.52 | 183.91 | 238.31 |

2010 | 99.56 | 132.52 | 132.64 | 183.20 |

2011 | 80.06 | 109.29 | 109.64 | 148.53 |

2013 | 93.75 | 128.46 | 128.11 | 173.83 |

2014 | 82.94 | 114.25 | 114.62 | 154.26 |

Average | 131.31 | 184.93 | 183.28 | 244.82 |

challenge to forecasting power density with similar trend of decreasing speed and if similar trend is seen, it may be class 2 region some years later which is a subject of concern for investors. Similarly, road transportation puts a question mark for such projects is Himalayan region.

Reference | Mean Speed | Root Mean Cube Speed | ||
---|---|---|---|---|

Year | Weibull | Rayleigh | Weibull | Rayleigh |

2004 | 25.23 | 79.76 | −0.01 | 43.52 |

2005 | 45.36 | 88.11 | −3.68 | 24.65 |

2006 | 27.84 | 81.32 | −0.58 | 41.01 |

2007 | 29.46 | 82.19 | −0.02 | 40.70 |

2008 | 32.53 | 83.70 | −0.32 | 38.16 |

2009 | 45.13 | 88.06 | 0.76 | 30.57 |

2010 | 33.23 | 84.01 | 0.09 | 38.24 |

2011 | 36.95 | 85.52 | 0.32 | 35.90 |

2013 | 36.65 | 85.42 | −0.27 | 35.32 |

2014 | 38.20 | 85.99 | 0.32 | 35.02 |

Average | 39.58 | 86.44 | −0.89 | 32.39 |

In the present study we discussed analysis whose objective was to investigate the potential of wind energy resource in Jumla. For this purpose, wind speed data of Jumla station (DHM) were analyzed over a 10 year period from 2004 to 2014 (2012 excluded). The probability density distributions and power density were derived from time series data. Weibull and Rayleigh probability density function have been fitted to the measured probability distributions. The wind power density has been evaluated. The most important outcomes of the study can be summarized as follows:

1) Jumla is shown to be a marginal site (Class III) for wind energy generation as the region possesses moderate wind characteristics. This is shown by average monthly & yearly wind speed along with wind power density. Himalayan region is supposed to have higher power generation capability in Nepal. Jumla, as one of perceived potential site, being a class III region shows Nepal has modest probability of wind energy generation capability in large scale.

2) There is a decreasing trend in yearly & monthly wind speed in Jumla which is a subject of concern. Decrease of wind speed is more than in warm season. We emphasize global climate change for this effect. This will be a subject of concern for Government while they’re focusing on diverse source of energy after fuel crisis in Nepal and looking forward for wind energy development.

3) Warm season has higher mean wind speed compared to cold season and this will make sure, energy generation during warm and cold season don’t have much difference as density varies with temperature.

4) The Weibull distribution is fitting the measured probability distribution better than Rayleigh distribution and supports the studies done in other parts of the world.

These results fulfill our four reasons of estimation of weibull parameter mentioned in introduction section. Meteorological data was calibrated to characterize the past data which was used to predict power generation capability. The results obtained are satisfying. Meanwhile, further investigations are to be done based on a more detailed and systematic analysis of wind speed patterns. Similarly, wind rose is not shown because of non- availability of information on wind direction from the station. Future works shall be guided in that path.

Supports by Department of Mechanical Engineering, Pulchowk Campus, Institute of Engineering, Tribhuwan University is gratefully acknowledged and also the author would like to thank Department of Hydrology and Meteorology, Government of Nepal for providing wind data of Jumla station.

Ayush Parajuli, (2016) A Statistical Analysis of Wind Speed and Power Density Based on Weibull and Rayleigh Models of Jumla, Nepal. Energy and Power Engineering,08,271-282. doi: 10.4236/epe.2016.87026