Uploaded by PSUwind on 07.08.2012

Transcript:

Now I'm going to show how to match a Weibull distribution

to your wind data. This is just one method of doing it,

they are a lot of different approaches. We're looking at

the histogram that was created before, which

we're going to try overlay a Weibull distribution to this and match it.

So if we go back to the original data, we need to have some idea of what the wind power density was

of this site. So we're going

calculate that for each time step,

1/2 times rho, times velocity in m/s cubed.

We're going to do that for every time step, and copy it down.

Take the average of those values,

you see it's 115.3 W/m squared. So that's power per unit area

of the swept rotor. Now if we go back to our data

in our plot, we're going to create now a column

with the Weibull distribution. I'm going to use the built in Weibull function in Excel

weibull.dist

It's asking for the velocity, which is going to be our bin

value. And then alpha is the shape factor,

which I'll talk about in a second.

And then the beta is the lambda, which is our

scale factor. Then it's asking if this is a cumulative function or not,

and we don't want the cumulative function, so we're going to say false. And now I'm going to

fix those shape and scale factors

so that they don't change as I copy this down.

Raising the dollar signs. So I copy

this down and this creates the Weibull curve I've already gutted automatically.

Automatically plotting over here, so you can see it overlaid.

I wanted to point out that the average velocity

of the this data set had to be 4 and 1/2 m/s, and in order to calculate

the lambda, which is a function of the average velocity is also a function of the

scale factors. And we don't necessarily now that, so we're guessing 2,

which is the Rayleigh distribution as a starting point. But that's really

the number that we need match here. So in order to match it I'm going to again calculate the

the wind power density

1/2 times rho

times again the bin velocity cubed

and then we also need multiply this by

the Weibull distribution or the percentage of time which it spends

at each of the bins. And then

we're going to sum this column, instead of average it because it's already a weighted

average. And we get 106.59 W/m squared. And just for comparison purposes

I'm going to bring the value from the other page over, it's

115.3 W/m squared.

So you can just adjust k here,

and you can fiddle with it until they match. That's one way of doing it, or you can use the solver function.

And with the solver function we're going to set the objective cell,

to be this number, which we want to match this number.

The value that we're going to match is this 115.3, and we're going to do

it by changing the k value. So it will run through all the iterations.

It's found a solution, and lets say we want keep that, and it comes out to

1.85 for the shape factor. You can see that the plots

don't perfectly overlay one another, that's because the original data may not have been the

perfect Weibull distribution, but you do have them matched to have similar

power density which is important in terms of wind resource assessment.

to your wind data. This is just one method of doing it,

they are a lot of different approaches. We're looking at

the histogram that was created before, which

we're going to try overlay a Weibull distribution to this and match it.

So if we go back to the original data, we need to have some idea of what the wind power density was

of this site. So we're going

calculate that for each time step,

1/2 times rho, times velocity in m/s cubed.

We're going to do that for every time step, and copy it down.

Take the average of those values,

you see it's 115.3 W/m squared. So that's power per unit area

of the swept rotor. Now if we go back to our data

in our plot, we're going to create now a column

with the Weibull distribution. I'm going to use the built in Weibull function in Excel

weibull.dist

It's asking for the velocity, which is going to be our bin

value. And then alpha is the shape factor,

which I'll talk about in a second.

And then the beta is the lambda, which is our

scale factor. Then it's asking if this is a cumulative function or not,

and we don't want the cumulative function, so we're going to say false. And now I'm going to

fix those shape and scale factors

so that they don't change as I copy this down.

Raising the dollar signs. So I copy

this down and this creates the Weibull curve I've already gutted automatically.

Automatically plotting over here, so you can see it overlaid.

I wanted to point out that the average velocity

of the this data set had to be 4 and 1/2 m/s, and in order to calculate

the lambda, which is a function of the average velocity is also a function of the

scale factors. And we don't necessarily now that, so we're guessing 2,

which is the Rayleigh distribution as a starting point. But that's really

the number that we need match here. So in order to match it I'm going to again calculate the

the wind power density

1/2 times rho

times again the bin velocity cubed

and then we also need multiply this by

the Weibull distribution or the percentage of time which it spends

at each of the bins. And then

we're going to sum this column, instead of average it because it's already a weighted

average. And we get 106.59 W/m squared. And just for comparison purposes

I'm going to bring the value from the other page over, it's

115.3 W/m squared.

So you can just adjust k here,

and you can fiddle with it until they match. That's one way of doing it, or you can use the solver function.

And with the solver function we're going to set the objective cell,

to be this number, which we want to match this number.

The value that we're going to match is this 115.3, and we're going to do

it by changing the k value. So it will run through all the iterations.

It's found a solution, and lets say we want keep that, and it comes out to

1.85 for the shape factor. You can see that the plots

don't perfectly overlay one another, that's because the original data may not have been the

perfect Weibull distribution, but you do have them matched to have similar

power density which is important in terms of wind resource assessment.