Saturday, May 2, 2015

On Tesla's PowerWall

When you're a hammer, everything around you is a nail.

Tesla's in the energy storage business. That much is clear. Until now, they're couched it in the form of electric vehicles, but let's face it - there's very little to the drivetrain of an electric car. That's partially because electric propulsion is very nearly ideal for transportation - maximal torque at 0 RPM, a wide torque curve (so no need for multiple gear ratios), the ability to turn both directions without gearing, regenerative braking... It's a far simpler thing than the internal combustion engine we've been using for over 100 years. But only recently has the energy storage problem for EVs been taken on, much less solved. Tesla has been a big factor perhaps not in coming up with the solution, but normalizing it, at the very least.

But let's look at the PowerWall - which lays bare the real business Tesla is in. The PowerWall has exactly two use cases that make any sense:

  1. Off-grid solar energy storage.
  2. Time-of-use energy billing arbitrage.
#1 is a tiny market. Most solar panel installations are grid-tied, which means that they use the grid as an energy storage reservoir. In actual fact, the grid can't store energy at all - at least not presently - but the tiny amount of solar production is easily dwarfed by peak usage demand. But if everyone put enough solar panels up to fully supply their energy needs, then the utility procurement curve would be vastly different, to say the least. But back to off-grid systems, the idea of battery backup for solar is not at all new. What is new is a company of Tesla's stature jumping in with a product useful in that space. And that's because, again, that market is virtually nonexistent.

#2 is the more interesting play. In fact, it's completely orthogonal to solar. It's also completely new. Only since the advent of smart meters has time-of-use electricity metering been possible. Like all arbitrage systems, it relies on the basic law of good economics - buy low, sell high. You charge the battery when your ToU rates are low, and then run that power back into the grid during the daytime when rates are high. With such a system in place, it's entirely feasible that your net electric bill might actually be zero, or even negative (in actual fact, I'm pretty sure it will take electric utilities a few milliseconds before they disallow that).

But putting one of these in every garage is a terrible idea. Far better would be to put the equivalent of 100 or 1000 of these in every substation. That done, the load leveling would make the utility's energy procurement costs plummet (since peak-fill energy is far, far more expensive both in cost and carbon than baseline). Tesla says they're working on that too. But if so, then this entire PowerWall exercise is merely a marketing stunt and Tesla may only expect to sell a handful of them (at least, the residential size version).

Still, for those with ToU billing, playing the arbitrage game may be a winning strategy in the short term. The cost for 10 kW-hr is slated to be $3500, but you still need an inverter. A SunnyBoy of appropriate size is around $2000 or so. With installation, I could see such a system being a total of $7500. If such a system could conservatively save $100 a month in ToU energy costs, the payback period would be just under 6 years. Not bad. And not a single solar panel installed.

Monday, April 13, 2015

The Blacklist: Statistics and The King Family

On a recent episode of the blacklist, the central plot device was centered around a bizarre family whose scion waged repeated battles to the death to secure their inheritance. These battles were in the form of auctions for illegal goods. Whichever brother secured for the family the fewer proceeds would be required to play one round of Russian Roulette.

The problem with this becomes immediately apparent with only a small amount of thought about the statistics involved.

It's clear from the episode that the game is the "classic" variant - the cylinder is spun each time. Clearly if it weren't, there would be a fatality within 6 rounds (although it's possible the revolver in the episode was not a six-shooter, they're by far the most common, so we'll assume here that the gun has six positions and that the referee loaded only one bullet).

But when you spin the cylinder, you randomize its position, meaning that the gun has no memory of past events at all (in truth, the gun is not designed for random selection, but we can assume that the spin is performed with enough variability to offer some imprecision, and thus, unpredictability). That means that the odds of being shot in any one round are 1 in 6 - 16.6%

Fairly unlikely? Sure. But play often enough, and those odds start catching up rapidly. To make the picture easier, let's turn it around. The odds of surviving are 5 in 6 every round. At the start, there is a 100% chance of survival if you do nothing at all. 5 out of 6 times, you pull the trigger, you survive - 83.3% of the time. Spin the cylinder and do it again, and now your odds are 83.3% of 83.3%. That works out to 70%. After four rounds, your odds are 50-50. After ten, your odds of survival are now one in six.

So for the episode to ring true, either the King Family held vastly fewer auctions than is implied, or the family started out with far more progeny to whittle through, or they were extraordinarily fortunate.

In the end, Red Reddington picks up the revolver and shoots King Sr. with it - the random selection this time coming up trumps. Red laughs at the irony, shouting "what are the odds?" Pretty good, it turns out.