“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 20, 2015

### How much storage is needed, part 3

 Image credit: www.theyogakids.com
Previously, I imported the daily mean wind speed recorded at Dalhart, TX (at the airport, I assume) for the period beginning January 1, 2000 through the most recent day recorded in Wolfram's curated weather data. I adjusted the wind speeds using a relatively standard model to estimate the wind speed at a turbine hub height of 120 meters from the (presumably) data at 10 meters. I also have digitized the data for a 3 MW nameplate capacity wind turbine. Further, I've used Mathematica's Interpolation capability to provide a "plug and play" function whose input is a wind speed and whose output is power from the turbine.

The plan from here is to do a Monte Carlo simulation from the smooth kernel distribution that's the best fit to the wind data. I'll use 8,760 points per simulation (the number of hours in a non-leap year) and use the speeds and the turbine data to determine power available over that hour.

Now, there are quite a few "yeahbutz" here, among them:

• I've not done an analysis of any periodicity in the wind data, at some point that will need to be done via a Fast Fourier Transform from the time domain into the frequency domain to determine whether adjustments are necessary.
• Wind speed is a continuous variable, assuming a constant speed for each hour will lead to inaccuracies.
• There will never be 120 meter hub height towers with 108 meter diameter rotors at an airport. As a pilot, I certainly support this! Thus, any real wind turbine will be at some other location.
• The Hellman exponent in the estimation of wind at hub height was chosen rather arbitrarily. Actual wind data at that height would provide a much better estimation.
Nevertheless, this calculation should provide a baseline estimate for the order of magnitude of storage necessary for a single turbine to deliver some amount of base load power.

 From Czisch & Ernst 2001
And it's likely that the estimate will be conservative, given that the most likely scenario is a wind farm rather than a single turbine and that several wind farms with reasonably wide geographic separation are most likely to be feeding energy to the grid. And many studies have shown that the correlation of power produced by groups of wind farms decreases with increasing geographic separation at all time scales (see chart at right, h/t to Dr. Steve Carson). To be clear, low correlation is a good thing when considering base load power because we desire that, when turbine/wind farm A suffers a low wind speed, turbine/wind farm B takes up some of the slack and vice versa.

Next, it's time to state the specific goals of the simulation:
• Determine the average power (and thus the capacity factor) of the turbine.
• For a series of specified base load capacities, determine the storage necessary to provide this power through the periods when the turbine is not providing that power.
• Determine minimum reliability (i.e., how many hours can be tolerated per year during which the turbine/storage cannot deliver the base load capacity. This will either need to be tolerated or supplemented with some other, typically natural gas fired, power plant).
OK, enough preamble, next will come the actual results of the simulation and conclusions, with suggestions for where to go from here, both with respect to the model and with respect to some speculation on what it means for the combination of renewables and storage as they penetrate the grid at greater levels.