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I ran 1000 simulations of 8760 data points of wind speed from what turned out to be a mixture distribution combining a normal and a Gamma distribution. This generated a total of 8,760,000 wind speeds. Each was delivered to an interpolating function generated from a digitized power curve of a 3MW nameplate capacity wind turbine. This resulted in 8,760,000 data points, each representing the average power delivered by the turbine for a hypothetical hour.

From there, finding the average power delivered was a simple process, and the result of this simulation was a mean power of 788 kW. This equates to a capacity factor of ~788*100/3000=26.3\%~. This is a surprisingly low number for the location and turbine chosen, given published figures at sites such as this that yield an implied capacity factor of 33.1%. Further, the model estimate has no allowance for planned and unplanned maintenance outages. And, of course, the 33.1% number is ostensibly from measured data, so, as Dr. Steve might say, "who ya gonna believe, me or your lyin' eyes?"

All that said, perhaps Dalhart isn't the ideal location, perhaps the wind gradient is steeper than the model I used, perhaps they've used more highly optimized equipment, perhaps the measured year had, for some reason, particularly strong (but not too strong) winds. I'm going to proceed with my analysis based on the model data.

So, the next step is to determine the storage required for the ability to deliver a given power at, say, 99.99% reliability. That is, the system should be able to supply the specified power for all but ~8760/10000=0.876~ hours/year. This is actually less than the SAIDI*SAIFI (system average interruption duration index, measured as the average duration of outages*system average interruption frequency index, measured as the average number of outages per customer per year) and so sounds quite reasonable if not overly conservative.

One assumption will be that, when the turbine is delivering more than the power under consideration and the storage facility is "topped off," we can send the power to the grid. Another will be that, for the level of power being considered, the storage system is capable of delivering power at that level. As I've discussed in previous posts, there are two primary characteristics of an energy storage installation: the quantity of energy that the system can store; and the rate at which it can deliver that energy.

Of note, approximately 4.0% of the time, the wind is below the cut in speed of the turbine and thus all energy delivered by the system must come from storage. The modeled wind exceeded the cut out speed of the turbine a negligibly small 0.0004% of the time. But there are no black swan events in the distribution (think tornadoes).

It took me a little time to decide on an effective way to proceed, but ultimately I decided to start with a guess of storage and loop through each increment (i.e., each hour's worth) of power (since the power is in kilowatts and the increments are hours, no conversion is necessary). If the storage plus the increment minus the steady use exceeded the maximum available storage, the excess was discarded and the maximum was kept for the next iteration. If the sum was less, that was kept for the next iteration. Upon completion, determine the number of iterations at which storage was zero or less, adjust maximum storage if and as necessary and try again. Using the mean power from all of the trials, no amount of storage sufficed, but reducing it to 725kW gave me what I wanted.

And finally, the result: If our 3MW turbine plus storage system is committed to delivering 725 kilowatts and we can provide 40MWh* of storage, there's effectively zero chance of not having the committed power available. Of course, the system can deliver greater power than that when the wind blows and/or when plenty of energy is stored but committing to greater power than 725kW or installing less storage than 40MWh means that there will be times when the system cannot deliver. Obviously, installing it in an integrated grid system can offset this, but the goal here was to determine what storage will enable what level of reliable base load power for a single turbine so the result is likely to be conservative. This is a virtue in the world of engineering. Below is a chart showing the first 100,000 increments with increment number on the x-axis and energy stored on the y-axis.

One widely discussed concept in energy generation is "capacity value," a very different concept (and number) than capacity factor. Basically, this number represents how much other generating capacity can be avoided with the installation of a generator and, for wind in particular, it is typically much lower than the capacity factor. Since there are times when no wind is blowing and demand does not abate, for an unaided turbine, sufficient generating capacity must be available to meet the demand, even though it may only be used sporadically. The goal of adding storage in this analysis is to bring the capacity value of the wind turbine close to the capacity factor.

As I noted in my previous post (on another topic), most utilities are not looking for days of storage (my analysis above determined that 48 hours of storage at 24.2% of the turbine's nameplate capacity would provide that power continuously and reliably), they're looking for a few hours. And, of course, the myriad complexities of transmission constraints, demand side variability, planned and unplanned generator outages, etc. have not been considered. Others have taken some of these into account using a similar methodology (i.e., Monte Carlo simulation). None that I've found, however, incorporate storage into the analysis. If I were a professor at a research institution or an NREL researcher or, perhaps, if I worked for a turbine manufacturer or a storage technology firm, I'd implement a much more sophisticated model incorporating the above factors as well as a wind farm as opposed to a single turbine.

Next in this series (which, as readers may have noted, may be interrupted by posts on other topics) will be an analysis of the economics of such a system, or at least the beginning of such an analysis. I anticipate that the cost will be prohibitive without pricing the externalities of fossil fuel generation (i.e., without implementing a carbon tax).

*In several trials, 35MW would have sufficed with no increments less than 0, but this run had a particularly calm stretch and, even with 40MW, had 0.0088% of the increments less than 0. However, this met the criteria of 99.99% reliability at 99.9912%.

## 1 comment:

Awesome article!

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