There has been lots of buzz over announcements from Tesla that they will sell a battery for home electricity storage manufactured in the "gigafactory" they are building to make electric car batteries. It is suggested that 1/3 of the capacity of the factory might go to grid storage batteries.

This is very interesting because, at present, battery grid storage is not generally economical. The problem is the cost of the batteries. While batteries can be as much as 90% efficient, they wear out the more you use and recharge them. Batteries vary a lot in how many cycles they will deliver, and this varies according to how you use the battery (ie. do you drain it all the way, or use only the middle of the range, etc.) If your battery will deliver 1,000 cycles using 60% of its range (from 20% to 80%) and costs $400/kwh, then you will get 600kwh over the lifetime of a kwh unit, or 66 cents per kwh (presuming no residual value.) That's not an economical cost for energy anywhere, except perhaps off-grid. (You also lose a cent or two from losses in the system.) If you can get down to 9 cents/kwh, plus 1 cent for losses, you get parity with the typical grid. However, this is modified by some important caveats:

• If you have a grid with very different prices during the day, you can charge your batteries at the night price and use them during the daytime peak. You might pay 7 cents at night and avoid 21 cent prices in the day, so a battery cost of 14 cents/kwh is break-even.
• You get a backup power system for times when the grid is off. How valuable that is varies on who you are. For many it's worth several hundred dollars. (But not too many as you can get a generator as backup and most people don't.)
• Because battery prices are dropping fast, a battery pack today will lose value quickly, even before it physically degrades. And yes, in spite of what you might imagine in terms of "who cares, as long as it's working," that matters.

The magic number that is not well understood about batteries is the lifetime watt-hours in the battery per dollar. Lots of analysis will tell you things about the instantaneous capacity in kwh, notably important numbers like energy density (in kwh/kg or kwh/litre) and cost (in dollars/kwh) but for grid storage, the energy density is almost entirely unimportant, the cost for single cycle capacity is much less important and the lifetime watt-hours is the one you want to know. For any battery there will be an "optimal" duty cycle which maximizes the lifetime wh. (For example, taking it down to 20% and then back up to 80% is a popular duty cycle.)

The lifetime watt hour number is:

Number of cycles before replacement * watt-hours in optimum cycle

The $/lifetime-wh is:

(Battery cost + interest on cost over lifetime - battery recycle value) / lifetime-wh

(You must also consider these numbers around the system, because in addition to a battery pack, you need chargers, inverters and grid-tie equipment, though they may last longer than a battery pack.)

I find it odd that this very important number is not widely discussed or published. One reason is that it's not as important for electric cars and consumer electronic goods.

Electric car batteries

In electric cars, it's difficult because you have to run the car to match the driver's demands. Some days the driver only goes 10 miles and barely discharges before plugging in. Other days they want to run the car all the way down to almost empty. Because of this each battery will respond differently. Taxis, especially Robotaxis, can do their driving to match an optimum cycle, and this number is important for them.

A lot of factors affect your choice of electric car battery. For a car, you want everything, and in fact must just do trade-offs.

• Cost per kwh of capacity -- this is your range, and electric car buyers care a great deal about that
• Low weight (high energy density) is essential, extra weight decreases performance and range
• Modest size is important, you don't want to fill your cargo space with batteries
• Ability to use the full capacity from time to time without damaging the battery's life much is important, or you don't really have the range you paid for and you carry its weight for nothing.
• High discharge is important for acceleration
• Fast charge is important as DC fast-charging stations arise. It must be easy to make the cells take charge and not burst.
• Ability to work in all temperatures is a must. Many batteries lose a lot of capacity in the cold.
• Safety if hit by a truck is a factor, or even safety just sitting there.
• Long lifetime, and lifetime-wh affect when you must replace the battery or junk the car

Weight is really important in the electric car because as you add weight, you reduce the efficiency and performance of the car. Double the battery and you don't double the range because you added that weight, and you also make the car slower. After a while, it becomes much less useful to add range, and the heavier your battery is, the sooner that comes.

That's why Tesla makes lithium ion battery based cars. These batteries are light, but more expensive than the heavier batteries. Today they cost around $500/kwh of capacity (all-in) but that cost is forecast to drop, perhaps to $200/kwh by 2020. That initial pack in the Tesla costs $40,000, but they will sell you a replacement for 8 years down the road for just $12,000 because, in part, they plan to pay a lot less in 8 years. No surprise Tesla is building a factory. With their own factory, they can accelerate the price drop and reap all the benefits for themselves.

I should note I have often seen it proposed that a great use for used electric car batteries is grid storage. Why? An 85kwh battery pack that used to deliver 240 miles of range becomes much less attractive when it only goes 120 miles. It is less than half as attractive because it still weighs the same. It's like a 42kwh pack but much worse. However, in grid storage the weight is unimportant, and all that matters is the remaining lifetime, which might still be decent -- and the electric car owner will sell it to you for cheap.

What's odd here is that Tesla is talking about making new batteries for home/grid storage.

Lion as grid storage?

Their factory is expected to be a Lithium Ion factory. But that's not usually a good choice for grid storage. Lithium-ion is the optimal battery for weight, but weight is not a factor at all for house batteries. In fact, today, no battery is really cheap enough to be economical for home grid storage. Their plan suggests one of two things:

1. They plan to make other types of battery in the factory, and these different batteries will be cost effective, or
2. They expect to produce a new generation of Lithium-Ion battery that's both cheap enough and has a high enough lifetime watt-hour number to be economical. That means one that handles many more cycles than current batteries tend to provide.

Both are very interesting. I am eager to hear what they really have. One factor I've heard reports of involves the "value of recycled battery" number in my formula above. The reports suggest that battery packs may still have lots of useful life in other applications once their capacity has gotten too low due to heavy use, and this can boost that residual price, and thus reduce the $/lifetime-wh.

I noted above that depreciation is a real issue. Some people think that once they install a system and pay for it, it doesn't matter how much it depreciates. It matters in a couple of ways. First of all, if batteries in the market are getting cheaper fast, that automatically drops the residual value of your battery after it wears out. If you did your calculation presuming a 50% value, and new batteries only cost 40% of what you paid, your used batteries are going to be worth a lot less.

Secondly, as the batteries depreciate, the resale value drops. Many people sell their homes. But even if they don't, you face the "what if I had just paid for grid power and waited to get the battery?" calculation. If the day you buy, batteries are 15 cents/lifetime-kwh and grid is 10 cents, but in 2 years the batteries are 7 cents/lifetime-kwh, your right move would have been to take the money you were going to spend on the batteries and invest it, buy grid power and then get more batteries for the same money 2 years later. Unlike computers, where you need a computer today even though you know it will cost half the price in 2 years, with power you have an option today of just using the grid and saving money, to get your more bang for your buck (total) when the price has stabilized.

On top of this, the real "price per kwh" I calculate above is not a fixed number, but a sliding cost based on the depreciation of the battery and the time value of money. Since a grid storage battery pack should last many years, the time value of money is a factor, and the early kwh probably cost more than the later ones with most depreciation curves.

But no, not for off-grid solar and wind

Many people have reacted to this announcement by declaring it to be good news for solar and other renewables. It is, but not in the way some have thought. I've seen writers talking about people with solar panels disconnecting from the power grid thanks to these cheap battery packs. People who live off the grid use battery packs, but at a cost that is immense compared to what on-grid people pay.

You would never want to disconnect from the grid because you have batteries and solar. You don't control when solar panels make electricity. That depends on the weather. Most operators of off-grid battery packs try to keep them close to full, so that they can survive a period of cloudy or rainy days on what they have. But when batteries are full (or even in the upper end of their range like 80%) they can't take much more power. When they are full, you just throw away the power, because you have nowhere to put it. It's next to impossible to design a system that constantly keeps the batteries low enough to always store all the extra solar or wind power that comes.

When you are connected to the grid, any power you can't use or store gets fed back to the grid to serve other people. As a result less coal is burnt at the coal plant, and everybody wins. (Except the coal mine.) If other people on the grid have batteries (but no solar panels) your extra power can go into their batteries if it's cheap.

Cheap grid storage is great for solar and wind, but only if done in a grid. It doesn't have to be a huge grid, but it needs to be enough that we don't throw away the renewable power because we have no load or spare storage to put it into. Solar power happens to come during the day when demand is high, so usually you can use it right away. Wind blows randomly, but often at night, where people will buy it at a low price to store it.