Blow-by-Blow PV System Efficiency: A Case Study for Storage

A short while back, I described my standalone (off-grid) urban photovoltaic (PV) energy system. At the time, I promised a follow-up piece evaluating the realized efficiency of the system. What was I thinking? The resulting analysis is a lot of work! But it was good for me, and hopefully it will be useful to some of you lot as well. I’ll go ahead and give you the final answer: 62%. So you could peel away now and risk using this number out of context, or you could come with me into the rabbit hole…

System Recap

I started small, with two panels and a handful of parts. Intent on learning the ropes, I built two independent systems—one for each panel. I described the initial system(s) in a 2008 article in Physics Today. The system has since evolved to the point that I now have eight 130 W panels and four golf-cart batteries providing 60% of my home electricity needs. Primarily, the system powers our refrigerator, attic fan, television and associated entertainment components, two laptop computers, the cable modem and wireless hub, and a printer. Occasionally I’ll throw something else on the PV (in much the same way an Australian might casually throw some shrimp on the “barbie”). The current system is described in an earlier post.

I now have two-and-a-half years of stable operation/configuration, and I collect data as impulsively as a squirrel collects nuts. I use the Pentametric system to measure three currents and two voltages in the system, which lets me monitor energy use, battery health, etc. I collect the data in five minute intervals (accumulated, not sampled), and have nearly uninterrupted data spanning years. Are you ready for me to unload it on you?

What’s Being Measured?

Placement of measurements within the system: three currents and two voltages. In practice, currents are measured on the negative (neutral) lead.

Almost all of the analysis to follow comes from the Pentametric dataset. Currently I have the system configured to monitor:

  • VA: the battery bank voltage, across the 2×2 series/parallel arrangement of 12 V golf-cart batteries;
  • VB: a mid-point voltage on one of the two battery chains, of secondary value;
  • IC: the current supplied by the charge controller into the rest of the system;
  • ID: the net current into/out-of the battery bank;
  • IE: the net current through a single parallel chain of the battery bank.

VA times IC gives the power delivered by the charge controller. We’ll call this PMPPT, where MPPT stands for the maximum power-point tracker charge controller. VA times ID gives the net power going into or emerging from the battery, which we’ll call Pbatt. ID minus IE gives the current in the other (unmonitored) battery chain, for checking that one chain is not unequally splitting the workload. Once we account for any input current from the solar side, and the net current into the battery, the difference constitutes the total load. At night, when the solar current is zero, the story is simple: the battery must do all the work, so whatever current escapes is going to the load. In the daytime, the battery may or may not be receiving charge depending on whether the solar input exceeds load demand at that moment.

A Peek at the Data

So what kind of information can we get from the above data? The plot below represents a simplified version (leaving out the battery competition piece) of something I look at daily to check the system performance.

One day of PV generation in early May 2011. The red curve is the solar input, showing also a dotted line cosine function. The blue load curve is visually dominated by refrigerator cycles, showing also a large contribution from the attic fan in the afternoon. The black line is the battery, referenced to the scale on the right. Once the battery reaches is absorb-state voltage, the charge controller accepts a diminishing amount of solar input while holding the battery voltage steady. The green curve at bottom represents the battery state of charge, as computed by the Pentametric system.

Lots going on here. The red curve that starts out smooth and becomes jagged is the solar input (more exactly, the charge controller output, PMPPT). In a grid-tied system, without having to cater to a stuffed battery, the solar curve would resemble the dotted red curve in the absence of any clouds. The gap between the two red curves indicates the rejected solar resource: part of the cost of maintaining well-conditioned batteries.

The blue curve is the load. All the spikes are from the refrigerator, and the attic fan makes the big bulge mid-day. The attic fan begins demanding juice right about the time the battery is full and begins to refuse more food. This makes for a beautiful pairing: the attic fan only activates on sunny summer days, when the solar resource is abundant, and the batteries are mostly recharged by noon. The baseline is comprised of the constant load of modem/wireless, a 20 W TiVo (since eliminated), standby power of various devices, the inverter baseline power, and the power provided to PV system components (monitoring, communications, etc.). I can tell from the plot that no television activity took place that particular evening. Actually, we were in Seattle, so the house was pretty quiet.

The black curve is the battery voltage (right-hand scale). Every fridge cycle takes a small bite out of the voltage, until the battery reaches its “full” voltage, and transitions from “bulk” charging to “absorb state” charging. After some preset amount of absorb time (4 hours in my system), the battery is declared to be full, and put on a trickle diet called “float” stage. At this point, you can see the power supplied by solar (red) is barely higher than the load voltage (blue). It takes only about 10 W to maintain the float state. At about 5 PM, the solar input fell below the load demand (attic fan still on), and the battery voltage began to sag as it discharged—the system no longer rejecting incoming energy. When the attic fan shut off, the battery voltage recovered slightly before beginning its long nightly decline, scalloped by fridge bites.

Note also the declining amount of power needed to maintain absorb state, ultimately settling to a level a bit over 50 W. Each time the refrigerator comes on, more solar power is demanded, but always about 50 W more, so the battery sees the same net input. A clever load may be able to just match the difference between supply and demand. The attic fan approximates this function, but only crudely so.  I do have some control, in that I can flip a switch and put the attic fan back on utility.  In hot streaks, the attic fan can become a bit much for the PV system.

Finally, the green curve at bottom is the battery state of charge. It’s pegged at 100% for most of the afternoon, declining to about 70% by the end of the night. In warmer weather (in a non air-conditioned house), the refrigerator demands more power, so the battery sees more overnight drain. But in this sense, the supply and demand are somewhat matched. The refrigerator demands less energy in winter, when less solar energy is available.

Energy Produced

Before we talk efficiency, let’s just have a look at the energy haul over the last 30 months.  Presto—we have a graph:

Energy scorecard for my system these past years, in monthly kWh. Utility electricity is shown for comparison, and the “down time” is in percent. The battery contribution should be compared to the solar input curve, rather than to blue curve.  Alternating bars denote months, labeled across the bottom.

Obviously more solar energy is harnessed in the summer months. Various inefficiencies knock the energy down from the red curve to the blue curve by the time the energy is delivered indoors.  The black curve is how much energy came out of the battery, but before inefficiencies are tallied.  So it is best compared against the red curve (also pre-efficiency-cut) to get a sense for the role that batteries play throughout the year (more important in winter).  The worst system down-time was December 2010, when clouds kept the system shut down for 220 hours, or 29% of the time, at one point being down for five days straight.

The green dashed curve representing utility power has three noteworthy anomalies.  In the Fall of 2010, we had a housesitter, who used 190, 464, and 389 kWh in three months, blowing our typical 60 kWh out of the water.  Second, we were away during the Spring of 2011, this time producing an anomalously low utility footprint.  Finally, August 2012 featured a two day air-conditioning experiment featured in a recent Do the Math post.  Yeah, that’s going to leave a mark.  Look at the sacrifices I make for you folks!

System Efficiency

So how well does the system perform, after we account for all the nickel-and-dime tolls of inefficient components? To answer this, we need a model for the energy flow in the system.

We’ll start with the solar input. Sure, the PV panels convert about 16% of incident radiant energy into useful electrical power, and I lose something like 2% in the delivery wires. But let’s start our accounting where the wires meet the charge controller. We denote efficiencies by the Greek letter, eta (η). The power delivered by the MPPT charge controller is PMPPT = ηMPPTPsun, where Psun is the input solar power at the end of the delivery wire. So the MPPT (muppet) takes a little off the top.

The positive output terminal of the charge controller is common to the entire system: the battery, inverter, and any auxiliary devices are connected to this node. So power flows to the inverter, to the system components, and alternately to and from the battery from this point. The battery is not 100% efficient at storing energy, so more energy is put in than extracted, on balance. We can therefore imagine a net flow of power from the charge controller to all components.

What we care about at the end of the day is how much energy (or average power) is delivered to AC devices within the house. All of this must channel through the inverter (I use no DC appliances in my house).

The inverter takes some power in, and delivers less out. In practice, it looks like Pdeliv = ηinvPinv, where ηinv ≈ 0.885 for my system (measured numerous ways using Kill-A-Watt and Pentametric in tandem), and Pinv is the input power destined for delivery to an appliance. But that’s not the whole inverter story. The inverter takes an additional constant power draw, even to sit idle—another special “feature” of off-grid systems. For my inverter, this is a maddening 20 W! We’ll call this Pbase.

To round things out, we have net power going into the battery, Pbat (on a long time average, the battery is a net drain). And we have various devices, like the monitor, the display, the communication hub, the “Mate” display, and the terminal server for internet connectivity. These are DC devices that pull power directly from the DC system, bypassing the inverter. We’ll call power going to this amalgam Psys.

So are you ready? We end up with a power available for conversion at the inverter:

Pinv = PMPPT − Pbat − Psys − Pbase.

You with me? This just says that the charge controller is nice enough to provide energy to the system, but lots of hungry mouths just take and take, reducing the amount available for conversion to AC power. At least the battery regurgitates some of its intake when needed—but always keeping a little for itself.

So we can form an end-to-end expression by sticking in the efficiencies, ηMPPT and ηinv:

Pdeliv = (PsunηMPPT − Pbat − Psys − Pbase)ηinv.

Okay, so this is the master efficiency equation. Once we compute Pdeliv, we can compare this to Psun to get a total system efficiency: ηtot = Pdeliv/Psun.

Direct measurements from the Pentametric tell me PMPPT = ICVA and Pbatt = IDVA. I know that when the inverter determines that the batteries are low and switches to utility input, all that’s left loading the system is Psys, which I measure to be 9 W. I also know that when I unplug all devices from the AC delivery system, all that’s left is Psys + Pbase, from which I learn that Pbase = 20 W. In performing the computation, I must also be cognizant of when the inverter is on or off, so that Pbase is not always counted.

So we’re almost there. The last piece is ηMPPT, which I am not outfitted to measure directly (would need the Septametric, not yet marketed). Fortunately, the Outback company provides excellent data on their products, and they have a set of graphs for different configurations of their MX60 charge controller. For my setup, the curve they provide is reasonably fit by ηMPPT ≈ 0.991 − 13.5/PMPPT. This means that if I’m pulling 500 W through the charge controller, it’s expected to be 96.4% efficient, losing something like 18 W in the conversion.

Right. When we put it all together, my system over the last 30 months averages—you guessed it—ηtot = 62.2% efficient. Over this time, my system received an average of 4.3 kWh of input per day, and delivered an average 2.7 kWh into the house. Over the last 20 months (for which I have TED data), our average utility energy use is 1.8 kWh per day. That makes for a total daily electricity use of 4.5 kWh, 60% of which is from the PV system. The inverter was on 94% of the time, the other 6% spent rerouting utility power while waiting for the Sun’s return.

A Step Backward

Hold on. I have 8×130 W panels on the roof, for a total of 1040 W. According to the NREL database (see my exposition of this), San Diego should be getting about 5.7 kWh per day for each 1000 W of panel. I should be receiving 5.9 kWh per day, not 4.3 kWh. The implied mystery efficiency is around 75%.

Two things are happening here. The lesser evil is that my panels are not free of shading influences, especially in winter afternoons. But more important is that I have batteries. If the system is designed appropriately, batteries are periodically fully charged, and refuse some potential power. This is a practical inevitability with battery-based systems: if you want the batteries to properly charge, occasionally equalize, and thus live longer, you must be prepared to reject excess power sometimes.

Conveniently, some friends of mine have a ~2.6 kW grid-tied PV system (12×216 W panels) on a roof only a few miles (km) from my house. The system has excellent exposure, and an online database I can access. If I select sunny days when my batteries never reached absorb state (digging their way out of a deficit from days prior), and thus never rejected any incoming power, I can compare our systems and see that my friends reap about 2.65 times the energy that I do on these days. Armed with this conversion factor, I can now look at any and all days to learn how much energy I would expect to collect if my stupid batteries didn’t refuse extra juice. I find that on average my system accepts 87% of the energy that would nominally be available. Not terribly bad. On a monthly basis, the worst case is 72%. I’m not entirely accounting for my 25% shortfall of the NREL expectation, but I’ve closed the gap.

Above is a plot of the monthly system efficiency (the one that averages to 62%, weighted by energy, not by month), in black. Also plotted (in blue) is the fraction I capture relative to what I would expect from scaling my friends’ PV performance. The red dotted line is the combined effect. Incorporating this, I get a net performance compared to a grid-tied system of 55%.

One oddity of the plot above is a few months when my system appears to be getting nearly 100% of the available energy. This tends to happen in months plagued by a marine layer of clouds. The ragged clouds dissipate sooner the farther one lives from the ocean. My house is a bit farther from the ocean than my friends’ house, so I could easily believe that I’m receiving more direct sun on a number of these days, boosting my figures a bit. It is also true that the attic fan taxes the system in the summer, so I spend less time in absorb state rejecting power. I more efficiently grab solar energy, but at the expense of not fully satisfying the fussy batteries.

Component Efficiency

From before, we saw that my off-grid system converts 62% of the solar energy it accepts into energy we use in the house. Where does the other 38% go? We can reframe the problem into additive (subtractive) component contributions, fcomp, such that:

ηtot = (1 − fMPPT − finv − fbat − fsys − fbase).

We additionally stipulate that

(1 − fMPPT − finv) = ηMPPT×ηinv, [note: corrected from original]

and that the ratio (1 − fMPPT)/(1 − finv) is equal to ηMPPT/ηinv.

Doing this, I get that fMPPT = 0.048; finv = 0.112; fbat = 0.080; fsys = 0.044; and fbase = 0.093. In other words, out of the missing 38%, inverter inefficiency takes the largest, 11.2% bite. The DC components in the system take a 4.4% bite, and so on. They add to 38%. A plot shows trends over time.

In the winter, when the attic fan does not blow, and the refrigerator cycles less frequently, the inverter baseload becomes a more prominent fractional draw. Long winter nights and winter storms also mean that the batteries spend more time contributing power, and at a lower average state of charge. More of the system energy goes into charging batteries during this time of year, increasing their contribution to inefficiency.

A Look at the Batteries

It’s a lot for one post, I know. But the battery part probably doesn’t justify a post of its own, and we’ve come this far. So one more bit of exploration…

We can monitor how much current runs into and out of the batteries. The current times voltage is the power in or out. If we just count current, the relevant metric is current times time, or amp-hours (Ah). A battery is rated for how many amp-hours it can provide. For my system, I see a 92% charge efficiency, meaning if I put 100 Ah into the battery, I’ll get 92 Ah back. Energy efficiency is not quite this good, because the battery is at a higher voltage when putting charge in (look at battery charge curve in the first graph). Putting 1 Ah into a battery at 27 V will cost 27 Wh. But pulling that same 1 Ah back out at 24 V will only deliver 24 Wh of energy. So it goes. I get 83% energy efficiency on the average. Not terrible, all things considered.

Above is a month-by month plot of the charge efficiency (red) and the energy efficiency (blue). Looks like perhaps a bit of decline with time.

If your wits have not been overly dulled by this long post, you might have caught yourself wondering how I can tell you that the batteries are 83% energy efficient, yet earlier computed fbat = 0.080, or an 8% effect. Why not 17%? What am I hiding?

The key is that the batteries do not supply all the energy to the inverter/system. Generally speaking, this happens at night. And generally nights comprise half the time. Also relevant is when the big loads are demanded. Our use of an attic fan shifts load demand to the daytime, so much of the energy input from the sun goes to directly driving appliances while the batteries are being charged in parallel. It so happens that over the last 30 months, I compute that 50.2% of the total system load has been sourced from the battery. If we had no night-time loads, this number would drop, and if we had only night-time loads, it would approach 100%. It’s almost coincidental that I land so close to 50%. But 50% of the 17% energy deficit is pretty close to our 8% decomposition.

Battery Health

I can also look at battery health in one other way. The Pentametric knows my battery amp-hour rating (though I lied to it and said they were 125 Ah, not 150 Ah batteries). As it watches current flow in and out, it keeps track of the state of charge, accounting for a nominal charge efficiency. When it senses a successful absorb condition (high voltage, low current demand), it resets to 100%. In practice, this dead-reckoning comes out pretty close to the mark, so that the 100% recalibration is hardly needed.

But as the battery wears down, its capacity diminishes, so the same energy withdrawal will leave the system more depleted, showing a lower voltage. The manufacturer of my batteries (Trojan T-1275) provided a table of numbers for state of charge (%) and associated voltage at zero current draw. It’s that last bit that really catches. An active PV system never has the batteries disconnected and seeing zero current (especially not for the recommended few hours before the voltage settles to a reliable value). What to do?

Well, if we can develop a relationship between voltage, state of charge, and power output of the battery, we can “correct” to zero power, yes? Looking only at times when it’s dark (so the battery is only in discharge), we can try to fit the observed voltage with a simple function like V = V0 + a×SOC + b×P, where V0 is the (unknown) voltage of a dead battery at zero load, SOC is the state of charge (%), and P is the load (negative), in Watts; a and b are coefficients to be discovered. The ideal fully charged voltage at zero load becomes Vfull = V0 + 100a.

Above is an example fit for one “day” of data. Only nighttime points are used. The red fit line is not perfect, but does an okay job for such a simple, linear model. Note the defrost cycle just after midnight. For this example, we deduce the full-state voltage to be 25.51 V. The value a = 0.03095 means I drop 0.03 V for every percent reduction in SOC. We interpret b = 0.001 to mean that a 400 W load (like refrigerator defrost) will drop us 0.4 V.

Now what happens if we run this on a boatload of data, deriving individual fit parameters for each night? We get the following plot:

The thing that jumps out at me is the trend toward stability: the battery behaved a bit more erratically early on. The curves are tightening up of late, and pretty stable. But what do these parameters mean? I care most about the slope, representing parameter a in the fit. I care about it because I don’t want to see the battery lose voltage very fast. The SOC value is based on dead-reckoning of how much current has been drawn out. For a given withdrawal amount, the smaller the impact on voltage, the larger the effective capacity. So the fact that the slope is decreasing over time seems like great news!

The two measures are correlated by virtue of the fact that the “full-state” voltage is extrapolated to 100% SOC using—yup—the slope.

And one last trick. If I collect SOC values from the Pentametric and corresponding load-adjusted voltages based on the fits for each night, I can plot one against the other and make a best-fit line. The raw data are rather scattered, so I only plot the fit line for each of three years.

We see a similar pattern emerge here: the slope is softening (improving) over time. The manufacturer’s tabular values for this battery (the Trojan T-1275) are plotted as black points. Gee—the 2012 data comes the closest. Note that the SOC value is based on my de-rated battery capacity of 125 Ah: 83% of the advertised capacity. And it approximates the discharge curve pretty well from day one. I conclude that these batteries have never lived up to their 150 Ah promise. Batteries disappoint.

Do I think these batteries will continue to get better with age? Ha! Just this weekend I saw disappointing performance during equalization (required more current than I expected). And I haven’t seen absorb state settle down to sipping just 50 W for some time. My first set of batteries took a rapid nosedive after less than two years. This set appears to be doing better, but I’m not driving them quite as hard (safety in numbers: 4 is better than 2; new refrigerator is less jarring when it turns on and the defrost is half the power, so the batteries are not slammed as hard as a result).

Oh Battery: How Gently Must We Treat Thee?

Incidentally, it is well known that batteries will survive more cycles at lower depth of discharge. A useful graph from here shows this clearly:

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.

39 thoughts on “Blow-by-Blow PV System Efficiency: A Case Study for Storage

  1. Great piece. Do you have any data on avoided cost of electricity vs. the capital expenditure? I would be interested in an analysis of the economy of building my own solar array.

    Thanks for the engaging story.

    • Well, I sort-of touch on this at the end of the battery section. I compute that the cost of periodic battery replacement is in the same ballpark as the electricity cost avoided. To the extent this is true, I’ll tread water with the off-grid system, but will not recover the investment in panels, etc. If I were in a remote location, the capital expenditure would likely instantly offset the cost of routing utility electricity to the site—often even representing an instant savings. For urban settings, off-grid is not something you do to make money. But a grid-tied system can offset electricity cost short of ten years, after which it’s gravy.

  2. Wow. The cost of the batteries per delivered kWh is depressing. Are there alternatives? I could imagine running the fridge down to 32.1F in the sunlight, storing “cold” for use at night. And how does this compare to the cost of grid upgrades, if a substantial number of people go solar?

    My first experience with rejecting power came fiddling from with bike lights and a switching supply; I had a protective shunt that I thought was large enough for the switch to a hub alternator, but no, it was not. Be glad that solar panels are a voltage source, not a current source. It’s a constant concern — if the working load is ever disconnected, the voltage from the alternator shoots into the sky, at least double, perhaps triple the ratings on all the components attached to it.

    • There are alternatives to lead-acid batteries, but all more expensive. The only cheap batteries I can think of off the top of my head are fossil fuels (non-rechargeable on relevant timescales) and hydroelectric/pumped-storage (rechargeable, but small scale).

      • Thomas Edison’s alkaline battery costs about double lead-acid, but can last a lifetime… see http://ironedison.com/ for details. The discharge rate and acceptable discharge voltages require changing some settings on the charge controller and inverter, since the battery performs differently (can be discharged to 85% regularly, for example).

        • Given the critical impact of the batteries on this analysis, I’m very curious to know what the outcome of Tom’s experiment would have looked with NiFe batts.

          • That’s actually pretty easy to figure out.

            Tom’s batteries are good for about five years, which is typical. Edison batteries cost twice as much but last forever.

            So, for the first five years, Tom would pay double what he does today. After ten years, he’ll break even. Everything after that is profit.

            If you remember the Rule of 70, a five-year doubling period is equal to about a 16% annual interest rate, which is a screamin’ deal in any economy.

            Cheers,

            b&

      • More storage technologies are under active development which do not suffer from all the same constraints as electrochemical batteries. To date these are not targeted at the domestic scale.

        * Storage of solar heat past sunset for deferred solar thermal electric generation
        * Adiabatic compressed-air storage (separate storage of pressure and heat)
        * Reversible heat pump storage (storage of heat and cold in separate reservoirs)

        This last, I find very exciting. See http://www.isentropic.co.uk/news/46/66/UK-Government-backed-body-invests-in-Isentropic-s-revolutionary-low-cost-energy-storage-system .

  3. Great analysis and write-up.

    Now that you’ve analyzed your system, what changes do you plan to make, if any?

    • I was also curious about this, and I would be interested in an article on the effectiveness of this an similar measures such as:
      (less effective but sometimes sufficient) replacement for air conditioning by running a hose through a deep hole/under a pond/lake for house cooling.
      I don’t know exactly what an attic fan is (how big/effective), most houses here (Australia) have something called a whirlybird which is powered directly by the heat of the air in the roof/sunlight striking it with no electronic/complex mechanical parts. Is the attic fan much better than these?
      What about putting extra thermal mass (ice/rocks) in the fridge/freezer and having two thermostats?

  4. You are correct in your statement regarding a 10% to 20% renewable energy contribution to the grid; this level is basically determined by the amount of “spinning stock” or rapidly-available reserve generation available to the grid system operators who must match the supply to the instantaneous load. Today’s societal expectations for energy are intolerant of intermittent energy supply, so when a system nears it’s spinning stock reserve additional reserve generation must be built and ready to brought online, be it big hydro, idling gas turbines (not popular) or multi-megawatt fast-start NatGas / diesel reciprocating generators which can be brought from cold start to online in about 120 seconds. (See http://powergen.wordpress.com/2008/06/23/plains-end-power-plant-arvada-colorado/ for information about the reciprocal engine peaking plant used to offset renewable energy source intermittency in parts of Colorado). At grid scale levels, every megawatt of big wind or solar contribution still requires a megawatt of conventional reserve power to be present in order to balance supply and demand levels.

    • I think today’s expectations for electricity availability at any time of day regardless are an anomaly of human history. Those expectations could be altered fairly easily and quickly once high oil prices set in and people wake up to the fact that we are running out of energy. We’ve all been camping and can adapt to those kinds of constraints on a personal level — we’d just shift our personal energy use activities to times that have available electricity, otherwise pay outrageous prices for it.

      On the other hand, industrial users can’t really do this because many can’t just turn on and off at the drop of a hat. They need to stay running for weeks and months at a time. I think that’s the big challenge.

      Interesting about the natural gas genset power plant. I worked on one project which was a gigawatt NG combined cycle peaking plant that could turn on in only a few minutes. I was surprised when I heard how fast it could turn on. I also worked on a genset plant like the one you link to that used landfill gas. This gas could potentially be stored for use in a diurnal cycle. This could be available as a stored hydrocarbon source for peaking uses once fossil fuels decline but probably not on a scale big enough to provide relief (most of the material in landfills ultimately came from fossil fuels anyways, including biomass via fertilizers).

      A silver lining is that to provide a typical frugal family with desalinated water to fulfil their needs wouldn’t require much more than what a fridge uses, and since Tom’s modest PV setup is more than capable of powering his fridge, it would be fairly easy to desalinate water as well. Additionally, storing water is super easy so the diurnal variation isn’t even a consideration, it could be timed to only happen when the sun is shining.

      • “On the other hand, industrial users can’t really do this because many can’t just turn on and off at the drop of a hat. They need to stay running for weeks and months at a time. I think that’s the big challenge.”

        On a somewhat different scale, the same argument applies to the commercial sector, the other third of electricity demand in the US after residential and industrial. Needs there range from very reliable for portions of the day/week (eg, the insurance office with hundreds of 8-5 workers) to continuous (eg, the refrigeration at any place that prepares food). Accommodating erratic supplies of electricity would require major restructuring of the US economy.

      • “We’ve all been camping…”

        No – actually we all haven’t – there’s a failure in inductive reasoning here. Because I’ve been camping and would find it easy to alter my expectations certainly doesn’t mean that’s true for the general population. There are a considerable number of people who don’t camp (or who camp only where there are full electric hookups), and who in point of fact would not find it easy to alter their expectations, and who would instead demand that BAU continue – and at ‘reasonable’ prices no less – and who would vote into office whichever candidate promised to keep things that way. And that is, IMO, a much bigger challenge that the industrial user issue.

        It’s not a technology problem, one that simply requires a reconfiguration of the grid coupled with supply/demand economics – it’s a problem of societal inertia.

        Sociopolitical equations are not as easy to solve as physics equations, but we can’t just dismiss them if the goal is to come to an understanding of our situation. They’re first order.

      • “We’ve all been camping”

        Yeah, Oz is right to call you out on that. It’s a pretty privileged statement. And a subcultural one; only time I’ve been camping was on geology field trips in college. Childhood too poor, adulthood little interest.

        “we’d just shift our personal energy use activities to times that have available electricity”

        Like air conditioning? Or a fridge? Or a heat pump, if we moved away from fossil fuel home heating? No.

        • No, things like washing clothes, drying clothes, running the dishwasher, taking a hot shower, charging electric cars, leaving 10 lights on in the house, ignoring 24/7 phantom loads… …

          Luckily, switching to horizontal fridges would dramatically reduce refrigeration energy demand, and we could even have programmable thermostats that maintain the temperature at a higher level for a few hours when electricity is expensive. So let’s get on with that as a national program ASAP while we still have the energy left to build horizontal fridges! Or just throw a bunch of ice in (made when we have electricity) and turn it off for half the day.

          BTW, I actually camped in the bushes on the outskirts of the city and lived in my car for several weeks because I didn’t have a place to live, I’ve done it on and off my whole life, so camping is not a “privileged” activity. I do it all the time to save money. All you need is a sleeping bag. Or a car with foldable seats you can stretch out in the back of. Try it, assuming you don’t have back problems, it’s fun and will save you hotel costs.

          I stick to my original statement that extreme time-of-day price fluctuations for electricity would sway a very large portion of the population to very substantially alter when they use energy. Luckily, the air conditioning you mention would be needed mostly in the day when we’d have the power. It’s evening that would be the problem, when everyone’s cooking dinner and the sun is disappearing. And I guess some people would require AC to sleep at night but somehow people survived for centuries before AC.

          I agree with Oz’s comment that people will vote in the politician that promises to continue BAU with limitless energy available for cheap. That is today’s problem, however. In the near future, that won’t be a problem anymore because BAU will not continue and there won’t be any politician capable of continuing with BAU no matter how hard they try, and in this case we will see crazy prices for energy. Then people will be forced to change whether they want to or not, and I have a feeling that most would be able to do so much more than they believe they could (see first paragraph), once they rework their neuronal networks to change their mindsets, and stop bellyaching about it.

        • Heating can be solved with solar energy and changed house design (which people will start doing once energy gets expensive enough).
          Put enough heat capacity into a house, double glazed windows and good insulation in the walls and a roof that can let in the sunlight when you want it and you’ll have enough warmth for any climate.

          Fridges and heat pumps thankfully coincide their peak demand with when you’ll be getting energy. More efficient fridges are possible and it’s also quite possible to design a device that will stay cold for 24hr

    • Have a look at https://demanda.ree.es/demandaGeneracionAreasEng.html. This is the real time electrical generation and demand figures for Spain .As I write, about 26% of the load is supplied by wind and 15% by “other special regimes” which include solar, waste inceration, biomass, etc. A study of this graph over many months shows that the system can run quite comfortably with over 50% of the load being provided by wind. It also shows that its gas turbine peaker plants almost never run. It also shows that with 22 gigawatts of wind capacity spread over the whole country wind output over a day can change quite dramatically, but over the ten minute data points on the chart not so much – I guess you do have a weather service in the US which can adequately predict winds 24hrs in advance? Of course the charts also show that the system has the benefit of extremely flexible and despatchable hydro and pumped storage resources, addressing some of the points mentioned by Bill above. As always, potential renewable resources are dictated by local geographics, adoption by finance and politics.

      • Paul, the Spain energy markets are interesting, especially given their present economy, which is in to drain. It appears they’ve been exporting all or most of their solar and renewable energy to France for the past couple of years, having overbuilt their solar generation capability relative to their own nation’s load / demand. See: “The increased role of renewables facilities in Spain’s power generation mix has enabled the country to send up to 1,400 MW per hour to France, where record levels of demand are putting a strain on the system, data shows.” http://www.platts.com/RSSFeedDetailedNews/RSSFeed/ElectricPower/8903622 …. Spain is the largest operator of concentrating solar power (CSP) generation in the world, with 1.33GW nameplate installed as of 2012, so it looks like much of that energy is exported on sunny days – which makes it less of a problem to peak and match with Spain’s load.

        Since the world’s grids are AC, massive circuits that are precisely tuned to either 50 or 60Hz, and the frequency is a function of shaft RPM at the baseload plants, supply and demand have to be matched to keep the grid frequency within the tuning tolerance of the system, since the as-built impedance of the grid will not “deal” with much variation in V, A or F. If demand exceeds supply, the generator shaft speed “lugs” and the electricity “slows down” (as Dan Ingram famously said on WABC, as his synchronous turntables began playing music “in the Key of R” immediately prior to the 1965 New York blackout)! This is why all new grid feeder lines for wind and solar are proposed as high voltage DC, and in a next-generation grid, there would have to be vast amounts of new HVDC lines. The Edison / Westinghouse Wars, all over again :)

        • I don’t know what “has enabled the country to send up to 1,400 MW per hour to France” means. Bad units.

        • Bill, I have a somewhat different take on the things mentioned in your first paragraph above. Spain has been a net exported of electricity for some years (interestingly large exports to Morocco which are repaid by imports of LNG). This export output appears to be much more matched to the receipients needs than to the availability of renewables much of the time. I don´t see that Spain has “over built it´s solar capacity” in that we have never had to turn any solar production unit off because we have too much supply on the system. (Some wind generation has had to be turned off occasionally to my knowledge, not because the entire system couldn´t use the power, but because there have been local temporary transmission issues.)
          The solar concentrating power you mention is increasingly incorporating storage capabilities, this ability helps the CSPs meet the second daily peak in consumption which occurs in Spain around nine to ten o clock at night. If you look at many of the charts you will see that the output from “other special regime” which includes solar drops by about one gigawat somewhere around midnight. I believe but cannot confirm conclusively this occurs when the CSP storage systems are turned off. The most interesting facet of the system (which I have been closely following for years) is that the coal plants are becoming more flexible all the time, their apparent slew rates have been improving year on year. This year they are making a larger contribution than in the past couple of years due to dry weather; the hydro sector has had to cut back on it´s base load capabilities as a result, though not on the pumped storage and rapid response abilities which underpin the system. Coal production could be further cut if more CSP with storage was built.

  5. An alternative to just increase the electrical energy storage capacity and still “use” the solar energy already captured might be to go for a thermal energy storage. Depending on location and needs the excess energy could be stored as ice or hot water, compressed air or other similar.
    Timing energy demanding activities (washing, baking, vacuum cleaning etc.) to match the sun curve might also work for some.

  6. A point that I think often goes missing when contemplating the potential instability to the grid from a significant input from solar is that nobody’s suggesting we should start decommissioning the infrastructure we already have — infrastructure that’s already proven itself up to the job.

    Even though solar is intermittent, that doesn’t mean that it’s unpredictable. It’d be trivial to hook cloud cover observations and predictions into the code controlling the grid. The forecast for tomorrow shows a storm front moving into the region? Make sure the coal is in the hopper. Not a cloud on the horizon? Great time to do an overhaul on the diesel generators. Winter coming up? That’s your deadline for refueling the nuclear plant. A sudden afternoon thunderstorm system starts developing just out of town? Be ready to fire up the diesel generators. Late afternoon is here and the sun is starting to wane? Spin up the nuclear generators.

    There’s no need to let the perfect be the enemy of the good.

    Every watt generated by a solar panel is a watt that didn’t have to be generated by burning coal or petroleum or uranium. Sure, we’ll have to keep burning coal and petroleum and uranium for the long-term foreseeable future. The point is that, with solar, we not only don’t have to burn anywhere near as much, but our reserves last that much longer as well and we get that much more time to develop better storage methods.

    I’d also caution against confusing disaster planning with infrastructure planning. Sure, you can envision some sort of horrible nor’easter that cuts solar production to the entire Eastern Seaboard all at once for a week at a time. But there’s no more reason the infrastructure should be designed to keep chugging along as normal in that sort of scenario than we should expect our cities to withstand direct hits from once-in-a-century hurricanes. Power outages are already an expected problem in severe weather events that we know how to deal with; why is it the problems only become insurmountable or unacceptable for solar power?

    Lastly, batteries aren’t the only way of storing energy. It’s horribly inefficient, but we can already today make hydrocarbon fuels from solar energy and atmospheric CO2. But solar is abundant; with enough solar energy to spare (and the potential is certainly there), we could just as easily keep running our overnight and standby power plants on hydrocarbon fuels, but make those fuels on sunny days from the Sun and the air rather than dig them out of the ground.

    Cheers,

    b&

  7. I’m interested in how well your batteries current share – how hard is it to compute that? I’ve taken to testing AA cells when the appliances they power stop working – it’s surprising how high a fraction of the time it’s only one dead cell out of two or four, and the flashlight (or whatever) runs many more hours with just the one cell replaced.

  8. I’m from The Netherlands. My country’s ‘golden age’ was based on renewable energy sources, mostly wind-powered pumps, mills and ships.
    Energy was stored mostly as finished products like paper, paint, flour and sawn wood. Also as what you might call ‘negative pumped storage’ – natural reservoirs being pumped dry to create arable land.
    Electric power as an intermediate may alow solar panels, wind turbines and other power sources to be situated in energy-rich locations which aren’t most suitable for industrial and other consumers. But if large scale use of renewables has to depend on storing electric energy, then it will fail, as Tom’s analysis makes clear.
    In short, conversion into electric power can solve problems of distance, but not of time. Which means that a future industrial society can perhaps have plentyful energy for many applications; but it can’t be in the shape of a guaranteed amount of power at any time the consumer wants it. Instead, power will have to be used when it’s available.
    You might still have cold storage, but the device would look like an oldfashioned ice house rather than a fridge. You could still have an electrically powered hot bath, as a well-insulated boiler will keep its water hot for quite a while. Just make it big enough. But electric cooking would be more difficult. And that’s just one of many modern applications we’re very used too, yet won’t be economical in our post-modern world.

      • Damien,
        It’s quite true that the 17th century Netherlands also depended on sources of thermal energy, like wood. However, the wind was a large and very practical source of energy for a variety of industrial activities, and the key source of power for the Dutch East India Company, arguably the world’s first megacorporation (says Wikipedia).
        My point is that wind and sunlight can be the dominant power sources for an industrial society – but not when we try to store energy on a large scale. We’ll have to learn to think outside the box of megawatts available 24/7, at the flick of a switch.

        • I said “as well”, and the article notes the role of wind power. But the thermal power side, provided by wood and then peat and then coal, is big too. As I said, your golden age seems based on both wind (and cheap water transport) and peat.

          As for storage, we’ll see. We have more tools that we used to. The Dutch Golden Age didn’t even have tools for converting between thermal and kinetic energy; we have heat engines and heat pumps and electric heating and awesome chemistry and such.

          • Damien,
            I’m by no means trying to deny our thermal energy requirements, now and in the past. But wind power did things for the 17th century Netherlands that thermal energy couldn’t do at the time; steam power had yet to be invented.

            Certainly we now have more technology available. But so far, that has made little difference for the scalability of storage options. Either the raw materials just aren’t there, or/and the ERoEI takes too much of a beating in the various conversion processes, when the energy lost in the manufacturing and distribution of things like batteries is taken into account.

            The current and forseeable reality is that except in a few small scale applications, wind/solar power has to be used when available. Given the limited time we have left to shift our industrial society from fossil fuels to renewables, it would be wise to concentrate on using electric power as an intermediate to solve problems of distance rather than time.

            And in theory, that could make the storage problem disappear. A large scale HVDC network just might connect renewable sources and consumers in an area so large, that sufficient wind/solar power would nearly always be available from somewhere.

    • How out of the question is worldwide-scale HVDC (or superconducting including reasonable – or unreasonable – assumptions about technology improving?) transmission?

  9. Tom, here is a new source of energy you may not have even heard of (correct me if you’ve already mentioned it), and it may offer significant promise as a relatively cheap, clean, and renewable nation-sized rechargeable battery that uses existing technology and little in the way of rare exotic metals: reverse reverse osmosis (“osmotic power”).

    The Norweigans recently built a plant “producing” energy using osmotic flow from fresh water to salt. This is interesting in and of itself, although I think as a source of energy its ultimate magnitude will be limited in the future by scarce fresh water.

    However, if the efficiencies in the conversion processes of salt to fresh when we have excess solar power available, and then back to electricity via fresh to salt when we need power, are not too bad, then it may be worthy of consideration. Actually, the efficiencies of the two processes won’t ultimately be highly relevant because the two necessary ingredients – solar energy and sea water – are essentially unlimited. Even a 5% round trip efficiency might work if all we’re trying to do is add in capacity to even out supply with demand. What’s important is whether we could we get something like this up and running in time before the world collapses.

    I’m going to investigate the efficiencies and energy magnitudes we’re looking at, unless you beat me to it.

    http://www.statkraft.com/energy-sources/osmotic-power/

    http://www.ide-tech.com/articles/recovery-osmotic-power-swro-plants

    • I did a (literally) back of the envelope calculation for this. According to Wikipedia, the Norway plant produces 4 kW with 10 l/s fresh water flow. They say they can easily double this so let’s take it to 8 kW. This works out to 0.2 kWh/m3. Apparently 0.75 kWh/m3 is the thermodynamic limit. They also say they need 10 bars to do it and I will assume this pumping power requirement is taken account in the 0.2 kWh/m3 net power production.

      We can produce a cubic meter of fresh RO water for 3 kWh today. So the round trip efficiency is 0.2 / 3 = 7%.

      In your nation sized battery post you use 336 billion kWh needed for 7 days of power. I will me much more generous and say we only need it for 1 day since the grid will be spread out and it will never go to zero no matter what happens to the weather, and that we will have a decent nuclear base load, since if we are still able to hold society together long enough to contemplate building osmotic power plants then we will likely be able to build nuclear plants too. So I reduced it by factors of 7 and 2, or to 24 GkWh.

      At 0.2 kWh per m3, 24 GkWh = 120 Gm3 of fresh water, or a cube 5 km by 5 km. In other words, a typical lake.

      That’s the easy part, the hard part is building out the infrastructure capable of re-salinating that lake in 1 day. The world desalinates 60 million m3 a day, and 120 billion m3 is 2,000 times this. So to make an osmotic battery large enough for the US would require 2, 000 times more desalination capacity than we currently have in the whole world! Impossible? No. Easy? No. Likely? Not really. Feasible? If we really wanted to, maybe.

      This is an interesting situation because we are not limited by the energy carrier like in lead acid batteries etc., but by the scale of the infrastructure buildout necessary to do it, and our rapidly dwindling time horizon.

  10. Super analysis, and a lot of work. Your golf cart batteries are a low budget choice. I estimated battery storage costs for commercial use a bit higher, 21-23 cents/kWh in my new book, THORIUM: energy cheaper than coal, p 165.

    Storage technology, Capital cost recovery in cents/kWh
    Pumped hydro, 6
    Advanced lead acid 21
    Lithium ion 33
    Compressed air 2
    Flywheel 191
    Sodium sulfur 12
    Zinc bromine flow 7

  11. Thanks for the insightful post. Very engaging, and also very entertaining. Please do keep it up.

    In addition, could you please consider writing an article specifically on energy storage systems? I would love it if you could manage to use your math magic on other means of energy storage, such as the old timey/new fangled kinetic energy storage systems such as flywheel-based systems.

    Once again, keep up the good work. Kudos!

  12. Tom,

    Your “Don’t do this at home” disclaimer at the bottom of your “My Modest Solar Setup” post is incorrect. I suggest removing it or modifying it. The NEC does not prohibit DIY installations, never has, and no change was made to the 2011 version that affects this. Your local municipality or county may have a requirement that you use a state licensed contractor, but most have an alternative process or requirements for DIY home owners.

    Some states require a certification such as NABCEP to qualify for government incentives, but that does not prevent you from installing an off-grid system without incentives like you did, and California is not one of those states anyway. John Wiles may not currently be a licensed contractor in his home state but it is rubbish that he couldn’t be one if he wanted to, and I’m pretty sure he is NABCEP certified.

    I think DIYers should seek to understand code (as you did) and understand the risks that they take if they don’t follow it, including possible penalties if your local jurisdiction finds out about an installation that was done without a required permit. That’s about all that can be said that applies nationally. A disclaimer that said only that much would be more appropriate.

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