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Wind power is an increasingly important alternative for obtaining energy supplies, both in large interconnected power systems and in smaller hybrid systems and even in backup systems. The temporal and spatial variability of the winds represent an obstacle to be overcome so that wind energy can be increasingly used. The capacity factor of wind farms shows how this variability impacts the operation of the plants and its value is of the order of 30% to 35%. The variability of the wind speed is influenced if the point of interest is on land or on sea, the shape of the surface, the proximity of water bodies, among other factors. The availability of wind is best described by the Weibull probability distribution, which has as one of its defining parameters one which is termed as shape parameter. This parameter is much higher as higher is the variability of the wind speed. This paper studies the subtle influence of Weibull shape parameter on the optimal combination of components in a wind diesel hybrid system, by means of computer simulations with the well known software Homer. The results indicate a relatively small influence (as expected) in the studied system, which appears particularly when the cost of diesel is higher and the availability of wind is lower.

The concern for reducing emissions of greenhouse gases has led the world to develop of new energy sources. Wind power is recognized as a reliable and affordable source of electricity and has become an important component of the energy systems in many countries [

The worldwide wind power capacity exceeded 280 GW in 2012, with an increase of 12% over the previous year. All wind turbines installed by the end of 2012 worldwide can provide 580 TWh a year, more than 3% of the global electricity demand [

In several countries where no left energy resources are available in significant amounts, the wind energy has been widely explored. In several systems, it can represent up to 30% of the energy available, including exploration of the potential overseas.

While a completely renewable energy matrix may be hard to achieve in several nations, hybrid systems are another matter altogether. Wind diesel hybrid systems can be a good solution for remote communities (isles or regions isolated by the harsh weather conditions), diminishing the dependence of fossil fuels and the necessity of paying high costs for the purchase of annual supplies of diesel fuels [

In the past, asynchronous electric machines seemed to be the best alternative for the conversion of wind energy. Over time, the technology of synchronous machines evolved considerably, enabling the provision of high quality electricity [

In recent years, there is also an intense development in the techniques available for locating turbines in an area where the wind potential is harnessed [

Brazil is experiencing a moment of intense excitement in the wind energy sector, with the auction of new areas for generation and free competition among stakeholders. In Brazil, the production of electricity from wind power exceeded 2700 GWh in 2011, which represented an increase of 24.3% over the previous year [

In Rio Grande do Sul, the southern state of Brazil, the estimated wind power potential onshore is 15.8 GW, 54.4 GW and 115.2 GW for areas with wind speed equal or greater than 7 m/s, at the heights of respectively 50 m, 75 m and 100 m. With an area of only 3.32% of the Brazilian territory, it has a wind potential equivalent to 15% of the estimated potential for Brazil for areas with speeds greater than 7 m/s or greater and heights of 50 m [

The temporal and spatial variability of the winds represent an obstacle to be overcome so that wind energy can be increasingly used. The capacity factor of wind farms shows how this variability impacts the operation of the plants and its value is of the order of 30% to 35%. An increase in the capacity factor can be obtained with the joint operation with reversible hydro power plants [

In order to determine the feasibility of a wind farm in a specific area, it is necessary to measure the wind speeds, recording the arithmetic mean every 10 minutes for the period of at least one year. With the collected data it is possible to construct a relative frequency distribution. Then, a probability density function (pdf) can be fitted for the data obtained [

The Weibull pdf is one of the main functions for modeling, being widely used worldwide. Nevertheless, this density function is not suited for all cases: a better fitting might be found with the Rayleigh, Burr, Gamma or Wakeby distributions, among an extensive list of other possibilities. It may be even possible, in a specific analysis, to use several distributions at the same time in order to obtain better results [

The main reason for the choice of the Weibull function for this work is its ability to fit a wide collection of wind data [

This article seeks to contribute showing results that reveal the influence of Weibull shape parameter on the performance of a wind diesel hybrid system in southern Brazil. The article specifically shows the influence of this parameter on the optimal combinations of the components of a wind diesel hybrid system designed to operate as a backup system. The conclusions were based on simulations with the software Homer.

The best way to characterize the wind potential wind at a given site is the description of the winds by a probability distribution. The Weibull probability distribution is the distribution that best describes the variability of wind speeds.

The probability density function for Weibull is given by equation (1). The parameter k is called the shape parameter and indicates the form of the probability distribution. In this equation, x must be greater than zero, λ is the scale parameter and k is the shape parameter.

In practical terms, higher values of the parameter k are related to the wind speed distributions with smaller variability.

A good tool that shows characteristics of the winds of Rio Grande do Sul (RS)^{1} is the Wind Atlas of RS, which

has detailed information about the wind regime in southern Brazil. The wind data maps are found in the resolution of 1 km × 1 km that were generated by measurements performed in 21 towers between 2000 and 2002. The information allowed preliminary feasibility studies and the identification of suitable sites for measurements aiming implantation of wind farms. Reference [

The estimated potential onshore is about 15.8 GW, 54.4 GW and 115.2 GW for areas with winds greater than or equal to 7.0 m/s, respectively at heights of 50 m, 75 m and 100 m. With an area of only 3:32% of the Brazilian territory, the state has potential of wind generation, at heights of 50 m and speeds from 7.0 m/s, equivalent to 15% of the estimated potential for Brazil. Technically, annual averages from about 6.0 m/s already constitute favorable conditions for the operation of wind farms.

Atlas of RS also brings a study of wind potential on water (offshore), which covers the three largest lakes in the state: Patos Lagoon^{2}, Mirim Lagoon^{3} and Mangueira Lagoon^{4}. These three lakes have a considerable wind potential: 18.52 GW, 19.51 GW and 19.74 GW, respectively, for winds from 7 m/s at the heights of 50 m, 75 m and 100 m.

At the height of 50 m [

Regarding the Weibull shape parameter [

These figures have not been reproduced here because it would be outside the scope of this article and it would not be possible to reproduce them with the necessary details.

The hybrid system considered in this study is a wind diesel system shown schematically in

The wind turbine is a type AOC 15/50, produced by Sea Forth Energy [

shown is the Weibull parameter to equal 2.1. Average speeds are typical of the northern part of the state. The series for the other values of k considered in the study were generated keeping the monthly average speeds.

Batteries 6FM55D model were adopted in the simulation [

In this paper, converter was used, including in a single component the functions of inverter and rectifier. The device can operate as rectifier and inverter with 100% of total capacity, with 85% performance as a rectifier and 90% as inverter. The lifetime is estimated at 15 years.

The two diesel generators are identical and have a capacity of 40 kW. The acquisition cost is US$ 40,000, with an hourly cost estimated at $ 1.50 for operation and maintenance. The lifetime is estimated at 25,000 hours with drive from 30% of rated load.

The software Homer [

The simulations were performed for an operation period of 25 years, with 12% annual interest and 6% internal rate of return. It was also established that the different generators could operate simultaneously and in parallel.

Five sets of simulations were performed, one for each value of the Weibull shape parameter. The values considered were 1.80, 2.10, 2.40, 2.70 and 3.00.

Simulations were performed for the following values for the optimization variables: 0, 1, 2, 3, 4 and 5 wind turbines; 0 kW and 40 kW for the second diesel generation set; 0, 24, 48, 72, 96 and 120 batteries; 0 kW, 25 kW, 50 kW, 75 kW and 100 kW for the converter.

Simulations were performed for the following values for the sensitivity inputs: 5 m/s, 6 m/s, 7 m/s, 8 m/s, 9 m/s and 10 m/s for the scaled annual average velocity of the wind; US$ 0.40, US$ 0.60, US$ 0.80, US$ 1.00, US$ 1.20 and US$ 1.40 per liter of diesel; 0.0%, 5.0% and 10.0% for maximum annual capacity shortage.

Then, five sets of 360 simulations, with 108 different values for the variables of sensitivity, were performed. The operation was completed after a total time of about 66 minutes for each set of simulations. The results are presented and discussed in the next section.

The effect of different values of k on the performance of the system of

The number of turbines included in the solutions is higher in the upper right corner, where there are higher average wind speed. In these solutions, there is less fuel consumption, even though the number of generators is the same as in other solutions. The largest number of turbines justifies the use of batteries, because storing energy will be cheaper than diesel consuming.

The effect of parameter k appears at the top of the line dividing the areas in blue and yellow. Smaller values

of k correspond to a higher number of solutions including wind turbines. The top of this line is located more to the extreme left of the space optimization, as can be seen in

Larger values of k correspond to less solutions including wind turbines, with the top of this dividing line moving to the right.

The area corresponding to solutions with batteries in these figures suffered growth with increasing k, occupying, with k equal to 3.00, almost double the original area, with k equal to 1.80. Probability distributions of wind speed with higher values of k have higher variability of speeds, with higher peaks availability offering energy to be accumulated in the batteries.

The changes in the cost of energy for the results shown in these figures appear respectively in

The same simulations for a maximum annual capacity shortage of 10% show interesting results.

This paper aims to study the influence of the Weibull shape parameter on the optimal combinations between components of a wind diesel hybrid system, also providing information on the performance of these systems.

The results show that the Weibull shape parameter directly influences the optimization space provided by Homer at points where the wind speed is smaller and the cost of diesel is increased.

The main influence of the Weibull shape parameter appears in systems that include batteries, increasing the number of solutions including batteries according to the shape parameter assumes larger values.

This work was developed as a part of research activities on renewable energy developed at the Instituto de Pes-

quisas Hidráulicas, Universidade Federal do Rio Grande do Sul. The authors acknowledge the support received by the institution. The last author acknowledges the financial support received from CNPq for his research work.

Mariana G. Benevit,Jones S. Silva,André G. Gewehr,Alexandre Beluco, (2016) Subtle Influence of the Weibull Shape Parameter on Homer Optimization Space of a Wind Diesel Hybrid Gen Set for Use in Southern Brazil. Journal of Power and Energy Engineering,04,38-48. doi: 10.4236/jpee.2016.48004