The math is fairly straightforward. I’ll be fairly optimistic in my assumptions; in many areas, solar will do better than this in practice.
The Model S uses 300 W-h/mi. We want to decide if the solar to power this is cheaper than an equivalent amount of gas. We might compare–conservatively–to a car that gets 30 mpg and where gas is $3/g. In that case, a mile costs $0.10 of gas.
Installed solar is perhaps $4 per peak watt. However, accounting for night time, and cloud cover, and seasonal effects, and so on, we might adjust that to $32/W average (that’s equivalent to 3 “good” hours of sunlight per day).
Multiplying this out, we get 300 W-h/mi * 32 /W = 9600 -h/mi. There are 8766 hours/yr, which gives us $1.10 y/mi.
$1.10 is a lot more than $0.10, but that’s just over the course of one year. We can already see that if the panels last decades, then solar is competitive. But a better way is to just figure out a reasonable interest and depreciation rate and multiply. 5% interest on a loan is perfectly doable as a home equity or similar. And the panels easily last 25 years, which makes for another 4% depreciation. $1.10 * 0.09 = $0.099, which is almost identical to the gas cost.
Of course, for just about every number I was wildly conservative. Cars the size and luxury level of a Model S get well under 30 mpg. Gas costs well over $3. In sunny areas, you’ll average well over 3 “good” hours of sun. Panels can be installed for <$4/W. And they will probably last more than 25 years. With the combined factors, the solar powered electric could easily be half the cost of the gas car.
If you’re on a budget and don’t have a family, you could consider something like the $4000 ELF instead, basically an enclosed bicycle with electric pedal assist and a rooftop solar panel. 20 mile range on the battery, charges in an hour at home or in 7 hours from its own panels.
Seems odd to compare an energy source to a vehicle. Shouldn’t there be two different comparisons: electric car vs gasoline car total cost of ownership over X years, and then personal solar array vs grid electricity over the same period of time?
If you don’t have EITHER an EV or a PV system, you’ll need to include both to compare with ICE cars.
If you already have an EV and are considering a PV system, you wouldn’t be comparing it to regular cars but to your local grid.
Heck, buy a Fisker “Karma”-that is, if the company is still in business. It has solar cells integrated into the roof. In a month’s operation, with sun very day, the cells will give you an extra 8 miles range. Considering the rooftop cells cost around $4000, a pretty poor ROI.
After current U.S federal and some state rebates, installed cost of a residential roof-top installation of 6 kW or so is more like $2.50/W or less (w/o battery storage, but with connection to the grid).
But solar panels do degrade, typically losing 0.5% to 1% of power per year, so 25 years is probably right or slightly optimistic (though replacing them won’t cost quite as much as installing the system to begin with as the mounts and wiring should be OK).
Not to hijack too bad, but I always thought the idea behind pushing electric for personal transportation (i.e. cars) wasn’t so much to reduce carbon emissions by directly eliminating tailpipe emissions, but rather to shift the emission points upstream to the electrical generation facilities, where you can realize a double-whammy per unit of energy used to move that car, namely due to economies of scale, you can run those plants far more efficiently than cars, and you have a lot fewer points to regulate and control emissions from. Doing stuff like electrostatic precipitators (to use a simple example) is much easier to manage and control at a powerplant than on everyone’s car.
In that sense, electric vehicles do make sense, but IMO, won’t take off until they can reliably go 300-400 miles on a charge at 70-90 mph with overnight recharging… There are enough people who drive relatively long distances for leisure, family visiting, etc… that drive those distances and speeds, and who won’t consider electric cars if they require a multi-hour stop in the middle to recharge.
This is true. However, the efficiencies gained by moving power generation to fixed facilities is offset by line losses and other inefficiencies in the electrical grid, and the distribution system itself is already loaded beyond capacity; requiring that it now deliver the energy demands for transportation as well would likely stress the system to the point of regular rolling brownouts. The standard idea is that excess energy demand would be generated by renewable sources such as solar and wind, but (at least in the United States) those sources represent only a tiny fraction of power generation and virtually all peak load in excess of nominal is provided by natural gas and coal fired plants.
“…can reliably go 300-400 miles on a charge at 70-90 mph…” is the bête noire avoided by electric car advocates; the reality is that there is no foreseeable battery technology that will provide anything like this capability at an economical price point. Lithium ion batteries like those used in the Tesla vehicles are already at their maximum economy of scale, i.e. making more of them won’t realize marginal reductions in cost. Lithium sulfur batteries are promoted as offering three times the energy capacity per mass but are still an immature technology, and based upon past trends of realized versus theorized performance the actual factor is likely to be less than two. Regardless, all electrochemical batteries suffer from the basic thermodynamic limitation that the reaction rate is proportional to the temperature of the battery, and this is proportional to the amount of energy that can be extracted out of the battery above a given potential and the amount of power it can provide. At cold ambient temperatures, the battery would either have to be massively oversized or heated from an external source in order to provide the same level of power as it would nominally provide in a warm climate. By contrast, internal combustion engines generate so much heat by the combustion process that the engine has to be designed to give it an outside and is often equipped with a separate system to carry heat away.
Well, I compared an energy source and a car to a different energy source and a car. It’s hard to compare either one in isolation since the systems are so different. Try to measure the energy produced by a solar system compared to the energy content of a gallon of gas, and you’ll get an answer that doesn’t actually tell you very much.
You’re right that you really want a full total cost of ownership calculation when making your buying decision, but aNewLeaf had a specific and false claim that I was disputing.
Grid is easy. The Model S uses 0.3 kW-h/mi. If your grid power is <$0.33/kW-h, then your cost is under $0.10/mi. In CA, the top electrical rates are over $0.33/kW-h, but that’s pretty rare and usually fixable with a different rate plan. In some places, electric rates are more like $0.05/kW-h, which makes the electric car quite a lot cheaper.
I was trying to avoid the complicating factor of subsidies, but yes.
The effective costs can go lower yet, depending on your rate plan. Basically, you sell daytime electricity back to the grid at a higher rate than you buy it back at night (to charge your car). It’s a rather nice advantage of solar power that it does its best when the grid is at peak load.
Right; there are a lot of factors here that are tough to tease apart. As you say, the non-panel parts should last essentially forever. The panels themselves will get cheaper over time. Under some conditions, it might make sense to replace the panels before their lifetime is over. If more efficient panels get cheap enough, they could pay for themselves by producing more power in the same area (i.e., using the same mounts).
The ideal solution for electric cars is to use a flow battery. It would recharge as fast as you could fill a tank of gas. But, I’m sure the power density is abysmal compared to lithium-ion and LiSu batteries.
When calculating the total cost of ownership, you have to consider the time value of your money. For example, if you invest $10,000 in solar power and it returns $10,000 in electricity over 25 years, you did not break even. You lost a substantial amount of money because if you took that $10,000 and instead of spending it on solar power you invested it at 5% per year, it would be worth $33,863.55 after 25 years. That’s how much you have to earn from your solar investment for it to be truly break-even. The same is true for any other energy source that requires a large up-front investment when compared to energy sources that you can buy as you need them.
You also can’t just take the kW/h rating of the battery and divide it by the kW/h rating of your battery, because there are significant charging losses. Batteries have an internal resistance, which means some of your electric energy is lost to heat. The same is true for the charger. As a rule of thumb, you can assume that you’ll need to put about 25% more energy into the system than you get back out, not including storage losses while your battery is sitting charged and unused.
My numbers were based on taking out a loan and accounting for depreciation, which is a mostly equivalent way of doing the calculation. With my original numbers, the panels pay for the base capital cost in the first 11 years and spend the remaining 14 years paying for the interest. We could quibble on the exact percentages, of course.
More like 10-15%. Vampire losses are a problem but are being worked on.
No, I don’t have a cite which says, “Lithium ion batteries have reached their maximal economy of scale.” What I do have is tracking the price of lithium ion batteries, which dropped by nearly half between 2009 and 2012 while production ramped up more than tenfold, and then has almost completely flattened out in late 2012 through the present, which is highly indicative of having reached minimum price per kWh. It should also be noted that the American Recovery and Reinvestment Act provided over US$2.4B in funds for battery technology of which a significant portion went to building facilities and research into processing methods for lithium ion batteries, and other monies provided to foreign interests such as LG for establishing manufacturing facilities abroad. In other words, developing the capability for manufacturing Li-ion batteries has been highly subsidized both domestically and internationally, and actual processing is automated to the point that there are likely not significant further improvements in reducing labor costs. In the last two years actual performance in terms of net energy density of Li-ion batteries has not improved appreciably, so achieving greater performance per production dollar is not in the cards, either.
Hasn’t improved appreciably or hasn’t improved? If we’re in a phase where we’re seeing 2% density improvements a year due to small refinements, then it just means the transition timescale might stretch out a decade or two. Of course, we might just hit a hard limit at some point, but I doubt anyone knows where that point is.
Do you have a link for the price of 18650 cells over time?
Well, ok but you’ll notice that 2012 was only last year. What does the long-term trend line look like for decreasing costs? I’d like to see your price tracking of Li-ion batteries if you don’t mind.
Technological innovation is not compound interest. You can’t just handwave a “2% density improvements a year” and prove that performance will be 15% better by 2020. Technology develops as innovation and basic physics allows, not at the whims and wishes of enthusiasts and moguls. Everyone who works with electrochemical batteries is well aware that even marginal improvements are challenging (and come mostly from changes in packaging and processing, not fundamental design or previously undiscovered efficiencies in the electrochemical reactions), and that order of magnitude performance improvements are simply not practicable.
I work with battery applications in my job, and for non-ordnance batteries Li-ion cells are the preferred choice because of their charging characteristics and stability. I do not have an online cite of either performance or cost trends; what I have are actual design and production details for current and proposed battery applications. That the cost history shows a large improvement and then almost completely flattens out in mid-2012 is highly indicative that near maximal performance per unit cost has been achieved (and then with significant government subsidy , and without some revolutionary innovation the only way of seeing further substantial reductions is either that raw materials become cheaper or the design and processing is somehow simplified. There are other electrolyte formulations which have the potential to offer greater energy density (such as the previously mentioned lithium sulfur or rechargable silver zinc) but are not yet practicable or cost competitive, and none are going to get within an order of magnitude of the energy mass density per power throughput of even low grade hydrocarbon fuels, thermodynamic reaction rate issues notwithstanding.
Enough technologies do work enough like compound interest that it can be a useful model at times. Moore’s Law is of course the quintessential example. Obviously it doesn’t always work that way.
Obviously I never suggested an order of magnitude improvement. Packaging and processing improvements sound exactly like the kind of thing which should show slow, continuous gains over time. No one is going to get a factor of 10, or even a factor of two, without a wholesale change in chemistry. But 10 or 20%? Seems reasonable to me. NiMH batteries lived in this realm for quite some time. They spent a decade or so ramping up from about 2000 mAh to 2800 (AA cells).
Any technology has low hanging fruit and not-so-low hanging fruit. You spend the first few years improving the stuff with the highest ROI. Then you spend a while longer fixing the stuff lower on the list.
They don’t need to. The Model S is already practical for a large number of people. Even another 10 or 20 percent would widen the net considerably. A factor of two and it’s pretty much game over for gasoline.