Blow-by-Blow PV System Efficiency: A Case Study for Storage
Original article: http://physics.ucsd.edu/do-the-math/2012/09/blow-by-blow-pv-system-efficiency/

Based on the graph, we might expect a whopping 15,000 cycles at 5% depth of discharge, dropping to 1000 cycles at about 55% depth. But notice that if we multiply the number of cycles by depth of discharge—effectively a total lifetime energy—the effect is far less dramatic. 15,000 times 0.05 is 750, while 1000 times 0.55 is 550. So only a 25% decrease in lifetime energy by driving eleven times harder.

I could double the size of my battery bank, doubling the up-front investment at the same time, and slightly more than doubling the time before I have to replace them. But if I plan on doing monthly maintenance (equalizing, cleaning, etc.), then I have twice the work! So I’m not terribly timid about hitting the batteries a little hard. 50% depth of discharge is not unusual for my system. Perhaps I’m being foolish and will wise up one of these years. For now, I look at the graph above and say: meh…

On the economic side, taking the advertised capacity for a lead-acid battery at face value, I can get a Trojan T-1275 for $235, and if treated gently it will provide an energy outlay of 750 full-cycle-equivalent discharges. Each full discharge has 12 V times 150 Ah, or 1.8 kWh. This works out to $0.17 per kWh. If I instead cycle at 50% and get 575 full-cycle equivalent outlay at a de-rated 1.5 kWh/cycle, the cost is about $0.28/kWh. Since my system uses the battery for half its energy needs, the effective cost of electricity for battery replacement alone is about $0.14/kWh, which is pretty close to the utility rate in San Diego.

At this point, I have sourced 1686 kWh from my four batteries in 30 months, or 422 kWh each. At a de-rated 1.5 kWh per battery, I have gone through 281 full-depth equivalent cycles. In about 915 days, this means my average cycle depth is 31% and I might expect 2000 such cycles (5.5 years; 620 full-depth equivalent cycles) at this level. So judging by this, I’m almost halfway done. Luckily for you, we’re much more than halfway done with this post. Here’s the wrap-up…

So is 62% Good or Bad? Waffle time…

The primary result is that I only get to use 62% of the energy delivered by my panels. The comparable number for a grid-tied system is something like 87–90% (inverter efficiency). My system suffers an additional 87% efficiency factor due to its full-tummy effect. This is close to the grid-tied inverter efficiency, so we can say that a panel in a small-scale off-grid system will likely deliver only something like 60–65% as much total energy as a grid-tied panel.

Doesn’t seem so good. On top of this, batteries are costly, as demonstrated before. So why would anybody go this route?

In remote locations, the cost of running utility power lines can be prohibitively expensive, quickly tipping the scales in favor of off-grid PV (the sunk investment in panels, etc. can be less than that in utility installation, in which case the cost of batteries offsets the steady utility bill). And I must say I enjoyed having power during the San Diego blackout of 2011. Moreover, I get pleasure out of having my own power generation capability. It’s part hobby, part independence, part practical. All cool.

My experiences have certainly impacted my views on large-scale solar ambitions. Like many, I am wowed by the incredible scale solar power offers: it’s a super-abundant resource. But grid-tied systems are deceiving. The grid acts like a giant, always-hungry battery by virtue of the fact that the stored energy in the form of coal and gas can be released at any time to balance power. This only works seamlessly when solar (and/or wind) input is a small fraction of the total. I often see numbers like 10–20% renewable penetration before big problems arise, but I have not studied this personally. The bottom line is that we’re discharging the Earth’s natural energy storage battery (the fossil fuels) and must replace storage with storage, if we want to continue our journey.

In any case, storage is costly—in energy, resources, and economically speaking. I pointed out in one of the first Do the Math posts the daunting scale for building a lead-acid battery big enough to satisfy the whole nation (not enough lead in the world, and a total budget-breaker even if lead were available).

My waffling here reflects the mixed bag nature of the problem. Storage is what it is: not great, but at least it can work, at a cost. The main lesson is that we shouldn’t be flippant about the degree to which storage difficulties limit our future energy ambitions. I see it every day in my imperfect personal PV microcosm.