Submitted by Euan Mearns via OilPrice.com [4],
In How Much Battery Storage Does a Solar PV System Need? [5] I assumed that the rooftop PV system would generate just enough power to fill annual domestic demand and that the surplus power generated in summer would be stored for re-use in the winter in Tesla batteries. The result was an across-the board generation cost of around $35/kWh. Clearly the Tesla battery storage option isn’t economically viable, or at least not under the scenario I chose.
As Phil Chapman and others pointed out in comments, however, this is not the only way a domestic solar PV system can generate enough year-round power to allow a household to go off-grid. Another is to overdesign the system so that it’s large enough to fill demand in winter when solar output is at a minimum and simply curtail the excess power generated in summer. How does this “no storage” option pan out?
To evaluate the no-storage case I use the same four scenarios as for the battery storage case (Equator, 20, 40 and 60 degrees north latitude) and add another (50 degrees north latitude) to provide more detail. The following assumptions are the same as before:
Household consumption is 5,000 kWh/year.
Household demand is constant through the year at 13.7 kWh/day, or 0.57 kWh/hour.
One assumption is clarified:
The impacts of short-term changes in cloud cover are ignored.
What this means is that I haven’t allowed for an unusually cloudy or unusually sunny week or month. Latitudinal variations in cloudiness are, however, allowed for in the load factors used to estimate generation (15% at the Equator, 17% at 20 degrees N, 16% at 40 degrees N, 12% at 50 degrees N and 10% at 60 degrees N) which are derived from metered panel output data.
One assumption is changed. PV panels are now pointed in the direction that provides maximum winter generation, not maximum year-round generation. To do this panels at 60N must be angled at 83 degrees south relative to the horizontal instead of 49 degrees, panels at 40N at 63 degrees instead of 35 degrees, panels at 20N at 43 degrees instead of 18 degrees and panels on the Equator at 23 degrees instead of zero degrees. The impact is to increase winter solar generation (by 21% at latitude 60N) and decrease annual solar generation (by 14% at 60N) everywhere except on the Equator, where the quirks of orbital geometry generate the opposite effect.
And while I refer to it as the no-storage case there will inevitably be times when the rooftop solar system won’t generate enough energy to meet household demand, meaning that some backup storage will be needed. To supply it I add one 10kWh Tesla battery storage unit, which would be capable of filling demand for at least one powerless winter night, and just in case I also add a 3kW backup gasoline generator. (Fossil fuel backup for a “100% renewables” installation is acceptable. The island of Eigg [6] in Scotland backs up its hydro, wind and solar with diesel generators and the island of El Hierro [7] in the Canaries backs up its wind/pumped hydro system with a 10MW oil-fired plant, and nobody complains).
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Now to the results. We will again discuss the scenarios in sequence. The solar module output data used to construct them are from PVeducation [8].
Rooftop solar system on the Equator:
Figure 1 shows annual generation from a rooftop solar system on the Equator that is large enough to meet demand at the time of minimum solar generation, which with the panels angled 23 degrees south (or north) relative to the horizontal occurs at mid-year. System specifics are:
Installed capacity: 5.4 kW
Load factor based on consumption: 10.6%
Annual generation: 6,518 kWh
Annual consumption: 5,000 kWh
Curtailed: 1,518 kWh (23%)
Figure 1: Demand, consumption and curtailment, rooftop solar system on the Equator with panels at 23 degrees to the horizontal
As noted earlier, however, this option is actually less efficient than adjusting system capacity to meet minimum demand with the panels pointing vertically upwards (Figure 2). Specifics of this case are:
Installed capacity: 4.0 kW
Load factor based on consumption: 14.1%
Annual generation: 5,263 kWh
Annual consumption: 5,000 kWh
Curtailed: 263 kWh (5%)
This option meets demand with a smaller PV system (4.0 versus 5.4kW) and cuts the amount of surplus generation that has to be curtailed from 23% to 5%. This is, therefore, the option we will go with.
Figure 2: Demand, consumption and curtailment, rooftop solar system on the Equator with panels at zero degrees to the horizontal
Rooftop solar system at latitude 20 north:
Figure 3 shows the data for this case. The 43 degrees south panel inclination generates a double-peaked generation curve with minima at the end of the year and at mid-year. System capacity increases by only 0.1kW relative to the Equator and curtailment is still low at 10%. System specifics are:
Installed capacity: 4.1 kW
Load factor based on consumption: 13.9%
Annual generation: 5,556 kWh
Annual consumption: 5,000 kWh
Curtailed: 556 kWh (10%)
Figure 3: Demand, consumption and curtailment, rooftop solar system at latitude 20 degrees north
Rooftop solar system at latitude 40 north:
Figure 4 shows the data for this case. At this latitude, system capacity has to be increased to 6 kW to meet winter demand and curtailment becomes significant at 33% of total annual generation. System specifics are:
Installed capacity: 6.0 kW
Load factor based on consumption: 9.6%
Annual generation: 7,429 kWh
Annual consumption: 5,000 kWh
Curtailed: 2,429 kWh (33%)
Figure 4: Demand, consumption and curtailment, rooftop solar system at latitude 40 degrees north
Rooftop solar system at latitude 50 north:
Figure 5 shows the data for this case. At this latitude system capacity more than triples relative to the Equator, more than half of the power generated has to be curtailed and the load factor decreases to less than 5%. System specifics are:
Installed capacity: 12.6 kW
Load factor based on consumption: 4.5%
Annual generation: 11,516 kWh
Annual consumption: 5,000 kWh
Curtailed: 6,516 kWh (57%)
Figure 5: Demand, consumption and curtailment, rooftop solar system at latitude 50 degrees north
Rooftop solar system at latitude 60 north:
Figure 6 shows the data for this case. At latitude 60N the winter sun is so weak that 87kW of installed capacity is needed to meet demand, the load factor falls to less than 1% and over 90% of annual generation is curtailed. The fact that 87kW of PV panels occupies an area of over 400 square meters and won’t fit on most rooftops doesn’t help either. System specifics are:
Installed capacity: 87.0 kW
Load factor based on consumption: 0.7%
Annual generation: 65,570 kWh
Annual consumption: 5,000 kWh
Curtailed: 60,570 kWh (92%)
Figure 6: Demand, consumption and curtailment, rooftop solar system at latitude 60 degrees north
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Economics
I estimated capital costs and cash production costs ($US) for the above cases based on the following assumed installation costs, which although subject to uncertainty should at least be in the ball park:
PV panels: $4,000/kW installed.
10kW Tesla battery storage unit: $5,000 installed
3kW Honda generator: $3,000 installed
I estimated generation costs simply by dividing the capital cost by 100,000 kWh, which is the usable power the system will generate assuming a 20-year life. This is of course a very crude way of doing it but it’s the way homeowners with rooftop systems usually look at economics. (My neighbor, whose $9,000 system cuts his electricity bill by $1,000/year, claims an 11% return on investment.) The results are summarized in the Table below:
And Figure 7 plots cash costs against latitude:
Figure 7: Cash generation cost versus latitude, rooftop solar systems
I draw the following conclusions from these results:
1. The no-storage rooftop solar option is vastly more economic than the battery storage option discussed in the previous post.
2. Households in some parts of the tropics can already install rooftop solar systems that will allow them to go off-grid without suffering an economic penalty. The $0.24/kWh cash costs for rooftop solar in tropical latitudes are comparable to what residential users now pay for grid electricity in a number of countries.
3. Latitude places limits on where a rooftop solar system will allow a household to go off grid. The farther north (or south) of the Equator we go the more inefficient the system becomes, until at latitudes of much over 40 degrees the economics become marginal at best and at latitudes much over 50 degrees they become prohibitive (sorry, Scotland).
4. Latitude will constrain the growth of off-grid residential rooftop solar because most of the residential rooftop market is at higher latitudes in the Northern Hemisphere.
But going off-grid with rooftop solar might still be economically-viable if you happen to live in the tropics, right?
Well, not exactly. There’s a hitch.
My solar system:
I do happen to live in the tropics – at latitude 20N in Mexico to be exact – and two years ago I installed 2.25kW of PV panels on my roof at a cost of about $7,000. Since then the panels have operated at a load factor of slightly better than 20%, generating ~4,000 kWh/year. They have cut my consumption of grid electricity from about 4,800kWh/year to about 800kWh/year and reduced my monthly electricity bill from over $100/month to about $5/month (electricity in Mexico is heavily subsidized for low-consumption users). So on a cash basis my panels will pay for themselves in six or seven years.
And by installing a battery and buying a backup generator I could go completely off-grid. Why don’t I do it?
Because it would cost me thousands of dollars more and save me less than $100 a year. It’s far cheaper for me to buy a few kilowatts from the Comisión Federal de Electricidad when I need them than to install storage of my own.
And there’s the hitch. A rooftop solar system may make overall sense if the cost of grid electricity is high enough, but batteries and backup generators still aren’t remotely competitive with grid electricity when it comes to load-following.
