“Be kind, for everyone you meet is fighting a hard battle” - Often attributed to Plato but likely from Ian McLaren (pseudonym of Reverend John Watson)

## Sunday, September 13, 2015

### How much storage is needed, part 2

In my previous post, I started the process of attempting to estimate how much storage would be needed in order for wind in a favorable part of the US to be able to provide a stable source of base load power. I retrieved data on mean daily wind speed from Dalhart, TX and made an adjustment for wind speed at a hub height of 120 meters (the retrieved data was almost certainly for a 10 meter height).

If I plot a histogram of the daily mean wind speeds and from there determine a likely probability distribution, it's straightforward to estimate the probability that the mean wind speed for a day will exceed the cut-in speed of the Siemens SWT-3.0-108 turbine (3 meters/second as shown in the technical specifications) postulated in the previous post. I can also, if I wish, just use each daily mean wind speed, assume that that applies for 24 hours, map it onto the data sheet for the turbine, and sum that data for any particular period to come up with an estimate of generated energy over that period.

While that's a simple and straightforward exercise, it doesn't necessarily provide an excellent estimate. Turbines have cut-in speeds (below which no electricity is generated), cut-out speeds (above which turbine blades are feathered or otherwise protected from over stress and no electricity is generated), and a non-linear (and, for the matter of that, a non-cubic) response between those speeds. A typical curve relating wind speed to power generated for a 3 MW turbine is shown at right.

Further, power in wind is proportional to the cube of wind speed, so a variable wind averaging, say, 12 meters/second will deliver more power than a stable 12 meters/second wind. For example, suppose wind blows at a constant 6 meters/second for one 24 hour period then, for the next, it is still for 12 hours and and then blows at 12 meters/second for another 12 hours. There will be four times as much kinetic energy in the wind through a given swept area in the second case. Then, to further complicate matters and looking at the chart, the turbine reaches its maximum efficiency at about 12 meters/second and so the turbine would generate far less than four times the energy in the second case. I digitized the graph using the excellent WebPlotDigitizer and so I can calculate that, for this turbine, the first scenario would deliver 22.8 MWh while the second would deliver 36.1 MWh.

All of these factors play into what can be expected from a turbine and are captured in the "capacity factor" of an installed turbine. This is the ratio of the generated electricity over a period as a percentage of the electricity that the "nameplate capacity" of the turbine (here, 3 MW) would deliver.

What I'd REALLY like is a continuous stream of data but such data isn't available, Instead, I'll use a Monte Carlo simulation with pseudorandom numbers drawn from a distribution similar to the wind in Dalhart. I'll not be able to generate a continuous data stream, instead I'll simulate hourly data for a one year period (8760 samples).

So what does the distribution look like based on the data from Wolfram? To the left is a probability density histogram of the data extracted along with a smooth kernel distribution for the range of speeds reported. I confirmed that the null hypothesis that the wind speed data is distributed according to a Smooth Kernel Distribution is not rejected at the 5% level (P-Value=0.612) so this is what I'll be using.

Again, I don't want to try my readers' patience, so I'll stop here for this post. The next one will show the results of the simulation with some analysis of what I've found. Subsequently, I'll discuss a wind farm consisting of such turbines and what is needed for storage in order to assure that base load power and peaking power is available at some level yet to be determined.

But in the meantime, keep in mind that we're

Unknown said...

Very interesting... Somehow I'm suspicious that the storage will turn out to be possible and even a bit efficient overall. Wind is "free," but nothing else is. Second suspicion is that the initial investment will have to be impractically large, as we do not live in a country where we think any farther ahead than 1-1/2 election cycles.

What if we built great big fans to blow into the turbines?

Steve

Rob Ryan said...

Yes, our political system and our financial system discount the future to a completely irrational extent. The interstate system could never be built in times like this. And the capex for such an undertaking, measured in levelized cost of energy or simply dollars is huge. Add in the cost of getting the generated electricity to where people actually are, and it's possibly untenable. I just want to see what the energy aspect is, I
l'll follow up with the financial aspect at some future time. Such an analysis will, if I can do so, involve estimating the magnitude of the carbon tax necessary to make this an economically favorable investment.

As to your second suggestion, if we could do then we could tug on our boots to lift ourselves to the top of a tower,