**Learning Goal: **I’m working on a statistics writing question and need guidance to help me learn.

** Your response should be submitted to this assignment as a Microsoft Word or Adobe PDF document. Late submissions will NOT be accepted. (The assignment looks like it is worth 0 points so that it doesn’t hurt anyone who chooses not to participate.)**

Our reading this week provides an example of the use of continuous distributions to model and understand an engineering challenge: wind speed distribution for a wind farm anywhere in the world. Differences in the modeling distributions, parameters, and limitations of several continuous distributions are discussed, including strengths and weaknesses relative to particular project settings.

Write and submit a summary of the article, with an ** emphasis on describing the statistical aspects **of the discussion rather than the actual wind farm application aspects. Make a point of what is happening in the discussion in terms of

**. Generalize your summary to what you want to be able to do on future projects that you might be involved in.**

*statistical capabilities and distinctions**To obtain the full extra credit, your submission should demonstrate that you can appreciate the power of the statistics described. Do not try to include the equations, and try to minimize any quotes you include. Your submission should reflect your thinking*.

The submission * MUST be YOUR original work*, and

*, giving credit to the words and idea’s you reference from the article. If you choose to do this extra credit assignment*

**MUST be cited correctly***. Your submission will be evaluated for originality by Turnitin. If you see that you submission was not original in it’s content, you should correct the submission and resubmit it. This is Extra Credit, and is not required.*

**“Do Not Plagiarize”****Assessing probabilistic modelling for wind speed from numerical weather prediction model and observation in the Arctic**

With the growing reliance on renewable energy resources in many regions of the world, studying the predictability of renewable energy is becoming progressively important

^{1}. As one of the cleanest renewable energy sources, wind energy has attracted growing attention worldwide

^{2}. In Norway, multiple wind energy projects have been developed for energy markets, and many more wind parks are in the design and planning stage. It is, therefore, essential to create a compelling and effective method for evaluating wind energy resources in the region. Accurately assessing local wind energy potential and resources is a crucial part of wind energy development and enhances investor confidence in financial feasibility and risk acceptability

^{3}. Wind resource potential varies considerably from one wind park site to another due to geographical and topographical differences. Therefore, an accurate assessment of a wind park’s wind energy potential is necessary when developing sustainable wind power projects

^{4}. A rigorous evaluation of the potential wind speed resources of a specific location directly affects the economic value, risk assessment, turbine selection, power generation estimation of the wind park, as well as the operation and management of wind power conversion systems

^{5}. In other words, proper attention to site selection is crucial for long-term sustainability gains in wind power investments, in addition to social priorities due to the recognized nuisance conflicts that have previously arisen in the context of wind power developments.

Since wind speed is variable, intermittent and uncertain, appropriate means should be used to describe its fluctuating nature

^{6}. The probability density function (PDF) and the related cumulative distribution function (CDF) are often used in wind resource assessments to quantify the theoretical wind energy potential of an area. Both of them intuitively reflect the statistical characteristics of wind speed. Wind is created by pressure differences between different regions, but terrain features like mountains, valleys, fjords and other surface irregularities create disturbances, meaning that wind speeds near the ground typically fluctuate significantly. The wind speed contributing to energy production in a wind turbine surrounded by complex terrain typically changes significantly; therefore, when the time scale is short, the statistical characteristics of the wind become uncertain and difficult to predict

^{7}. When the time scale is long, the probabilistic distribution of wind speed is relatively stable, and the long-term statistical characteristics of wind can be determined

^{8}. A common way of describing the wind energy at a site is to use its annual wind speed distribution. The PDF of wind speed is vital in valuing energy production for wind power and is an important evaluation index for estimating local wind resource potential.

## Methodology

### 1 . Wind energy

In wind engineering, the capacity factor (CF) is particularly useful when conducting a fast evaluation at the early design and planning stages of a wind park. Understanding the probability distribution of wind speed is essential to calculating the CF of wind parks.

where *f*(*v*) is the PDF of wind speed, which is the main target of this research *P*(*v*) reflects the turbine power curve used to describe the power fluctuations related to wind speed. *v*_{i}, *v*_{r}, *v*_{o}, and *P*_{r} represent the cut-in speed, the rated speed, the cut-off speed, and the rated power, respectively^{5,20}. The *g*(*v*) is a multiplier increasing from 0 to 1 within the interval, that depends on the wind turbine specification. A wind turbine reaches its maximum power output when the wind speed is in the interval between the rated and cut-off speed. Adequate knowledge of the wind speed interval corresponding to the wind turbine’s rated power is important for ensuring the efficient and economical operation of the turbine. Therefore, aside from the wind speed distribution modelling, we also paid special attention to wind speed in this rated power interval.

### 2 . Probability distribution

Tables 2 and 3 offer brief mathematical expressions of the seven ideal probability distributions used in the present study. These distributions are defined as follows.

- Gamma distribution is a two-parameter continuous probability distribution
- Generalized extreme value distribution (GEV) is a continuous probability distribution developed with extreme value theory
- Nakagami distribution is a generalized two parameters probability distribution model proposed by Nakagami Minoru
- It has received extensive attention, as it can model a broad range of fading channel conditions and describe many empirical data sets.
- Normal distribution, also called Gaussian distribution, is a continuous probability distribution for ideally describing a real-valued random variable
- Rayleigh distribution essentially describes the distribution of the mode of a stochastic two-dimensional vector when the two components of the vector are independent, have the same variance and are normally distributed with zero means
- T distribution is commonly used to estimate the mean of a small population that is normally distributed, where the standard deviation is unknown
- Weibull distribution is the theoretical basis for reliability analysis and life inspections and is widely used for describing the probability distribution of wind speed

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