The Roof Pitch

Abstract: This one is long enough for an abstract so here goes:
An estimate of the available US residential roof surface area is made and the fraction of current net generation that can be replaced with solar power is as much as 46% using this area. Policy issues that could hamper full attainment are discussed. A new fast Norwegian model for electrifying transportation which also provides 0.5 days stationary storage of total generation is considered and found likely to move rooftop solar from its policy limited maximum fraction of 22% towards 46%. Utilities are advised to avoid long term purchase contracts for new nuclear power.

All the trees behind my house were cut down during nesting season with machines straight out of The Lorax. The machine would grip the trunk and, with a high pitched whine, the machine would sever the tree from the ground in about 4 seconds, then back off carrying the tree upright and drop the tree somewhat indiscriminately out off the way. Last fall I put together a new metal shed (with much cursing for the last bits of roof that were hard to get to). It turns out that the old wooden shed was on property that is to be developed in front of the house and it was so old it could not be moved. Doesn't leak though. Nothing has been happening though since the trees were all cut down out back. It could be that houses won't sell for what the developers thought they might so they are holding off.

I don't quite know why we are building so many houses. There aren't that many more of us. Maybe it is the divorce rate. We need two houses per family.

Trees are what grow over most of my neighbor's homes. I picked mine to have sun and a south facing roof. I used to live under a ginourmous sweetgum tree and it's shade cooled that house in the summer, but a good bit of insulation in this house seems to work better. But, with trees being slaughtered using those strange contrivances which, I'm sure, violate Dr. Suess' intellectual property rights, I'm not going to suggest that my neighbor's homes be included in these calculations. We'll estimate assuming all roofs get sun, but there is no suggestion that those that don't should. And, with things slowing down in the building trades, we'll use numbers from a couple of years ago which might compensate for some shady roofs.

What are we doing? We're going to calculate how much sunlight can be turned into electricity just using home roofs. The thing is, FedEx, Google, GM, Coke, Walmart, Kohls, Target, BJs, Cosco, Staples and other businesses are all turning sunlight into electricity using their roofs so they can save money. But, their buildings use so much energy that only about 30% of what they use can be covered this way. But, a house can cover what it needs pretty easily because we tend to like a little less activity at home. Keeping the doors open for shopper past midnight to sell a book about a boy wizard would not allow us much rest. So, can houses make up the difference so that businesses can run on 100% real energy too?

These calculations came about because Robert Rapier had been looking at biodiesel and finding that it would be quite hard to cover transportation with what could be produced. Robert is a contributor to The Oil Drum which we've scolded before. His conclusion was that the future is solar. The main reason is land use. If we use rooted plants to get real energy, they don't put all their efforts into just converting sunlight into stored energy. They are more interested in their social life, hobnobbing with bees, sharing delicious seed holders for dispersal and generally sharing news through their roots. So, as we've seen, only a little bit of real energy is available for harvest compared to all that was used. Robert decided that if we want to have food, we can't also grow fuel at the level that we use it. Now the standard example came up that a square of land in Nevada about 80 miles on a side running a solar thermal plant at 20% efficiency can produce all the energy we use. This is an easy calculation: Nevada has regions that get 9 kWh per square meter of sunlight per day on average over a year, or 375 Watts per square meter of average power. At 20% efficiency you get 75 of those. So we just divide the 1.2 TW of energy we use that we calculated earlier by 75 W per square meter to get the number of square meters we need. Divided again by a million gives 16000 square kilometers. The square root of this, 126 km, gives the length of the edge of the square which is about 80 miles.

Now, many people objected that this was impractical even though it was just an example of how little land is actually needed compared to what we farm. So, we set to calculating what could be done with roofs since this is surface area that is already being used. We need an estimate of the size of a typical roof, how many roofs there are and what the typical available sunlight is. This is a rough estimate (remember the trees) so we won't do anything fancy like match houses in states with the solar resource in that state.

Let's begin. For a home size we'll take 1700 sq ft from 2002, for the number of houses we'll take 124,500,000 occupied and vacant from 2005 and for the available power we'll take 5 kWh/m^2/day from the middle of the country. We're going to adjust the home size which comes out to be 158 m^2 down to 100 m^2 because some houses have more than one story. We'll only use half the roof (50 m^2) assuming that this is the south facing side, or if we cover east and west facing surfaces we only get to use half at one time. Then we'll take a system efficiency of 17%. Each roof then produces 1.8 kW as average power (5 kWh/m^2/24 hours* 50 m^2 *0.17). All roofs produce 0.22 TW. In 2005 average net generation in the US was 0.46 TW (4.055e12 Wh/365 days/24 hours). So the roofs can provide 46% of the electricity the nation uses. But the residential sector uses 37% of the whole generation. The roofs can thus provide extra power for the businesses but they can't cover the whole thing, only about half of what businesses can't do for themselves. Hydro and wind provide about 9% of generation so we are looking for another 100% -(30% of 35% = 10% commercial solar)-(46% residential solar) = 35% to cover the rest of the commercial and also the industrial sectors. Wind power can certainly do this while, as we saw in the case of the Nevada example, solar farms on non-agricultural land can also work.

Just like the businesses that are converting as much of their power use as they can to save money, homes can do the same thing and it turns out we can get a majority of our electricity using just roofs. All of this works essentially under net metering and 41 states have such laws. But many allow the utilities to confiscate the excess power produced within a year of generation. So, unoccupied homes should not be counted in this circumstance. Also, their are few incentives for landlords to save their tenants money so we might want to consider only owner occupied homes. With these limitations, we only get 60% of the residential sector or 22% of the total. These restrictions would seem to be more important than shading from trees. There is some transfer between the rented, owned and vacant buildings so we'll likely get to close to the whole residential sector eventually, and, for the vacant homes, with the utilities confiscating over production, there should be little reason to maintain artificial caps on net metering capacity since they'll see a very healthy overall 11% profit if the owners of the vacant properties don't put in server farms or some other means of using the power generated at the property. We should note that this is actually a huge profit because distributed generation means that expensive upgrades to much of the distribution system can be delayed or avoided all together. In fact, it may well be that utilities can maximize profits by paying a fraction of retail for generation above use rather than nothing. In that case, as the cost for panels comes down, their may be an incentive to use all of the roof.

But, there is a much more important thing coming that will increase the fraction of roof area that is used. The ghost energy depleting industries that we want to displace like to use talking points that emphasize how little real energy we a using right now. They'll sometimes acknowledge the 30% growth per year in renewables, but then pick a date about 15 years before that growth shuts them down to say that the amount of generation will still be small. Then they say that we need more coal, oil, gas and uranium to meet projected demand, hiding the fact that new capacity there will be very expensive because it won't ever be used for its design lifetime. They also ignore the fact that the dollar cost of real energy is plummeting while the dollar cost of ghost energy is only going up. The effect this has of the growth rate can only be positive, especially since renewable energy fabrication is so nimble compared to power plant construction. So, a 150% annual growth rate may not be out of the question. A number of individual companies are planning 100% annual growth just to keep their market share high, a number than investors look at closely. Planning for 100% annual growth takes some doing, but it is much less cumbersome than gaining approval for a new nuclear plant, especially in today's security environment.

The thing that is coming is actually a new business model for transportation that will increase the amount of power people use at home while decreasing the amount of gasoline they use. Companies that manufacture hybrid vehicles are saying that they expect the cost to manufacture these will be the same as for their other lines in a few years. The reason for this is that though the systems are a little more complex, the cost of retooling per unit goes down as the share of production goes up. These vehicles can be modified to have electric only operation with a range of about 40 miles by adding more batteries. But, the batteries are expensive even though the cost of running the vehicles is much less expensive. Batteries, like solar panels degrade in performance over time but for different reasons. For solar panels it is high energy particles which degrade performance while for batteries it is use which degrades performance. The behavior of solar panels has interesting implications for the estimation of the quantity Energy Returned Over Energy Invested (EROEI) because this becomes quite dependent on what level of performance you are willing to accept. If you cut off at a 20% degradation in 25 years, with a 2 year payback time, you get a value of 12.5 trending towards 25 with recycling (because you don't have to purify the silicon again). But, if you accept a 60% degradation you get a value of 33 trending towards 66, the highest for any energy source. You might be willing to accept a 60% degradation if you are replacing the lost performance with less expensive more efficient panels as needed so long as you still have roof space. With batteries for transportation, you really have to set a lower acceptance criterion for performance degradation because the car won't get so far with degraded batteries. Battery degradation also depends on the manner of use. Transportation is a tough environment while managed power storage is a benign environment because an individual battery can be treated gently.

The new business model for transportation takes advantage of this behavior of batteries. Noticing that at least 75% of a battery's useful life will be outside of a vehicle, a company in Norway is planning on leasing about a quarter of the of a battery's life for transportation then selling the remaining battery life to utilities for the power storage we need. Stationary storage does not need nearly the performance levels required by transportation. Now, transportation is about 28% of our total energy use with most of that in trips under 40 miles. By passing batteries on to utilities, the transportation sector will be providing storage for about half of our total energy use. You might think it would be 84%, but using batteries is much more efficeint than gasoline engines so the transportation sector energy use will shrink by about 2 thirds. The business model greatly reduces the cost apportioned to transportation for batteries, making electricity as a transportation fuel very attractive, while at the same time saving utilities money on their most expensive generation costs by allowing storage to cover peak demand. This makes mostly electric transportation the least expensive, especially since people will add capacity to their roofs at lower costs when this mechanism comes in over the fleet replacement timescale. The effect of this is to increase residential use of electricity by about 30%, and similarly increase the contribution of the residential sector to distributed generation. But, the businesses that are adopting solar power now, won't get this energy because it will be displacing gasoline use instead. Notice, though, that the increase in electricity demand this implies is met with real energy even under current net metering policies (excluding overall caps).

In consideration of this, to maximize profits, investor owned utilities should be pursuing a policy of divesting themselves of ghost energy generating capacity, avoiding like the plague very long term ghost energy purchase agreements, especially for any new inflexible nuclear generating capacity, and encouraging rooftop solar as much as they possibly can while working out clever ways to profit from the approximately half day of energy storage they can anticipate coming in from the transportation sector. In short, they should adopt a supermarket or warehouse business model, where they profit by the continual exchange of real energy that their distribution networks can provide. And that is the pitch for rooftop solar.