The premise is a super efficient battery and inverter. You still charge up the batteries from a power source, but you can get power off-peak at a discount rate and save it, or use solar and save it. This is a nobel cause, but you still need to fill the batteries from a source. Batteries have loss, and if you look at the proposal from a purely power perspective, you have a loss due to the cost of conversion; however, you could have a net-gain monetarily if you can purchase power cheaper and reuse it.
The kicker is that I find power to be inexpensive in the USA, when compared to what I paid in Japan (unless you are in Hawai'i). The questions I see are:
1) At what point does it make sense to purchase an expensive battery pack?
2) How large does it have to be to be useful?
To start, here's a summary of energy density in Mega-Joules per Kilogram.
and then you can assume Telsa is using what they know: 20130187591, 20130181511.
In my figure, one needs to remember that energy storage is not conversion! This means that there are losses to different degrees depending on the power source. In the Telsa patents, you have a fast and a slow responding battery and a controller that makes the battery usage general purpose because you use different batteries for sustained load or instantaneous load, which makes sense for both a car or a house. In the case of batteries, you store energy that is saved/recovered as DC power, and then you take a 15% conversion loss to AC for houses.
How much power does the average American home use? 10000kWh per year. To make the math easy, let's day that it's 900kWh per month, so 30kWh per day. Let's say that you only want to save a single hour of power, that's 1kWh.
Ignoring losses of the conversion, the 12v truck battery gives you about 1kWh. If you wanted to save a day's work of power, you'd need 30 of these. So, what Telsa is actually offering is an attempt to scale down power for space. Lithium-Ion batteries being 7x better than lead acid for energy density, that would still be the displacement of about 4 lead acid batteries. The question is if Tesla can get the cost down for the batteries, and the conversion efficiency up. In 30 battery case, that would be $3k in batteries. Tesla would have to hit price point much lower than that; however, would it still be worth it. The cost of power varies greatly; however, let's say that you save 5cents per kWh by charging off peak, and store 5kWh per day at a discount. This results in 25 cents of savings per day. That's $USD 91.25 per year in savings, if your new found cheap power doesn't make you use more of it. (Higher efficiency cars seem to make us use more gas, for example [Knittel, Christopher R. 2011. "Automobiles on Steroids: Product Attribute Trade-Offs and Technological Progress in the Automobile Sector." American Economic Review, 101(7): 3368-99.])
Bottom line, assuming that the lifecycle of the batteries do not exist, and converters are 100% efficient, and you save five cents per kilowatt hour, you'll need the device to come to market at $91.25 if you want to recoup the device cost in a year.
