Unless you have a particular reason to worry about your connection to the grid, it's better to use demand management than batteries.
Let's take a Tesla S battery. It costs $30,000 [1]. It has a capacity of 85KWh, which lasts 265 miles. [2] The battery is down to 80% life after 100K miles [3], which is 377 cycles.
Say you fill up the battery at 5 cents/KWh and sell it at 20 cents/KWh. You've made $12.75. After 377 cycles, you've made almost $5000. You still have life in those batteries, but they are going to keep on getting worse, and the efficiency of energy in/energy out will start falling as well. Once you hit 40% they are probably useless. You might be able to run that $5000 two or three more times before you hit that.
You could only barely use the batteries to prolong their life. But you spent $30,000 on them! That's a lot of capital costs for something that isn't doing anything. And Li-Ions will gradually lose capacity even if you don't use them and store them in ideal conditions.
There are certainly efficiencies of switching from a car-bound battery to a stationary battery, although a lot of people posting on this page are talking about hooking up a car to do price arbitrage.
Well thought-out post, however, your math is singularly reliant on the 30,000$ price tag for the battery and although you did list the source, it's accuracy is in some doubt. First of all, you can pre-buy a replacement Tesla battery for 12,000$(source: found in your same link [1]), secondly, the information is old.
I don't think there is any doubt that the number has come down significant. I'm sure you are aware that Tesla is building out a huge battery plant, significantly increasing lithium batter production ability, this will absolutely bring batter prices down.
I would be extremely surprised if their own internal numbers show a pay-off time of longer than 3 to 5 years. It's not like Tesla doesn't have people who get into the numbers, as the numbers are the only thing that is going to sell.
I would expect the car is a much more harsh environment for the battery than my house. I'm not talking about vibration or temperature, though those matter, but electrical demand. A model S has a 310kW motor. Nothing in my house comes anywhere close to demanding 310kW. Of course the Tesla will rarely require the full 310kW, but its charge and recharge cycles are at the mercy of your driving.
You could smooth out the peaks in my home demand with probably just 10kW. Perhaps smooth out many of my neighbours peaks with 50kW. But my point is that there are no hard bounds that the battery needs to satisfy, unlike in a car when you have to supply the drive current or sink the brake current. You can tune a home battery's charge/discard cycles for maximum battery life rather than maximum performance. I don't have data for how much difference that would make to battery life, but I would guess it may be significant.
if the battery has capacity of 85 kWh and you're saying the motor consumes 310kW at max, then that would mean a model S only has a range (time) of 16 minutes?
Tesla estimates about 300 miles per charge at 60 MPH
(300/60 = 5 hours)
Every time you accelerate, you're drawing way more current from the battery than you do cruising at highway speed. So the average power draw is 17 kW/hr, but some of that happens in great bursts.
Using batteries seems like an insanely cost and environmentally-unfriendly way to engineer around billing practices of electrical utilities. I think we'd be much better off trying to get the numbers up for solar (installations, efficiency, lifespan, manufacturing) vs using vast quantities of highly toxic batteries powered from the grid from traditional power generation sources to game electrical utility billing for profit.
I really don't understand why this idea seems so popular with e.g. politicians.
Without weight constraints of a car, you can use larger fire-containment-cell sizes, significantly lowering manufacturing costs. Also, you are ignoring the value you can get back when you recycle the battery, which may be part of how Tesla is offing the $15,000 replacement.
I still don't know if the numbers would work out though.
I'm not sure that it is a safe assumption that this stationary battery will be based on lithium-ion cells. In the past, simple lead-acid batteries have far outperformed lithium-ion batteries in situations where weight and volume were not an issue.
I assume the primary issue now is cost, but if you can decouple the reaction -> electricity engine from the reactants to a greater degree, then it sounds attractive? I imagine increasing storage tankage is a much easier problem to solve than increasing energy density.
Wholesale LMPs are often more like $80/MWh at peak and -$60/MWh at nega-peak, but that still works out to 14¢/kWh, which is about the same difference you're calculating with.
Let's take a Tesla S battery. It costs $30,000 [1]. It has a capacity of 85KWh, which lasts 265 miles. [2] The battery is down to 80% life after 100K miles [3], which is 377 cycles.
Say you fill up the battery at 5 cents/KWh and sell it at 20 cents/KWh. You've made $12.75. After 377 cycles, you've made almost $5000. You still have life in those batteries, but they are going to keep on getting worse, and the efficiency of energy in/energy out will start falling as well. Once you hit 40% they are probably useless. You might be able to run that $5000 two or three more times before you hit that.
You could only barely use the batteries to prolong their life. But you spent $30,000 on them! That's a lot of capital costs for something that isn't doing anything. And Li-Ions will gradually lose capacity even if you don't use them and store them in ideal conditions.
There are certainly efficiencies of switching from a car-bound battery to a stationary battery, although a lot of people posting on this page are talking about hooking up a car to do price arbitrage.
[1] http://my.teslamotors.com/it_CH/forum/forums/battery-replace... and watch how hard it is for the guy to get an answer
[2] https://www.google.com/search?q=tesla+car+battery+capacity&o...
[3] http://www.plugincars.com/tesla-roadster-battery-life-study-... don't just read the headline